Advances in Colloid and Interface Science, 34 (1991) 477-535 Elsevier Science Publishers B.V., Amsterdam
477
Adsorption of Ions, Polyelectrolytes and Proteins M.A. Cohen Stuart, G. J. Fleer, J. Lyklema, W. Norde, and J.M.H.M. Scheutjens Department of Physical and Colloid Chemistry Dreijenplein
6
6703 HB Wageningen The Ne~erl~ds 1 IIltroduction ........................................................
.478
2 Electrosorption of ions and small molecules: chemical and electrical fntwractions.......................................................... 479 488 3 Lattice theory of electroso~tion ..................................... a) l&tiCe Variant Of the Gauy-ChapmanStem model ................ b) Volume filing and chemical interactions .......................... c ) Theoretical results ................................................ 4 Polyelectrolyte adsorption model .................................... a) Conformations b) Theoretical
.................................................... resufts................................................50
Strom2 nolvelectrolvtes ........................................... Weak Dolvelectrolvtes ............................................ 5 Polyelcctrolyte adsorption experiments .............................. a) Introductory b) Adsorption
remarks.............................................50 of strong ~iye~trolgtes
of weak polyelectrolgtes ............................... d) Metastablestates..................................................51 e) Adsorption of polyampholytes ..................................... 6 Protein adsorption ................................................... remarks .............................................
b) Adsorbed amount ................................................. c ) Co-adsorption of small tons ...................................... d) Energy and entropy of protein adsorption ........................ ...................................................... A&nowledgement ............................................................. References.
0001~8666/91/$20.65
0
1991-
492 492 499 499 1 501 504 508 8
............................ .509
c) Adsorption
a) Intr~~to~
.488
Elsevier Science Publishers B.V.
515 8 519 521 521 523 .527 -528 531 531
478
1 Introduction According interactions (i)
to
present-day
insights,
there
are
four
types
of
that play a role in colloid science:
Van der Waals
forces,
that are always
attractive
for particles
of the
same nature (ii)
Electrostatic
and attractive (iii)
Solvent
(iv)
Osmotic
interactions,
for opposite structure-based
adsorption,
and
are operative
entropic
been
polymer
interactions
are
may
known
elements
development
and larger polymers
two decades
experiments.
because
configurational considerable and
and electrostatic progress
relatively
effects
simple
and
adsorption
polyelectrolytes,
the state of the art. In describing
systematic
state
are strongly
we shall review
monograph
theory
has by a
that the
of Verwey
and
of
more
can
adsorption. already
Overbeekz).
be
the
complex
is far from complete.
polyelectrolyte
description
interrelated.
has been made in the area of ions, small
of
first
can have a
supported
we may
of
is much more complicated
and proteins
ion
the
the situation
polyampholytes
a
amounts
and is now
understanding
in small
small amounts
are involved,
At present,
the
of interactions
are understood. macromolecules
Although
which
of which
state. The existence
colloids
over the past
For charged
molecules
(i) and (ii)
and Overbeekz).
for more than a century:
destabilize
of appropriate
essential
macromolecular
and Verwey
a new
effect. As far as uncharged
developed
number
to
in which only factors
and Landaul)
is still in its inceptive
of type (iv) is already stabilizing
related
or repulsive.
theory for systems
Derjaguin
structure
understanding added
interactions
is now almost fifty years old and known as the DLVO-theory,
its founders
Solvent
for the same charge sign
short range forces
that may be attractive
The basic stability after
that are repulsive
signs
theoretical
molecules
In the present the electrostatic
many found
By treating
elements in
the
these
way, we hope to pay a tribute to these authors.
like paper, effects
recur
of
admirable effects
in a
479
Given the variation
of phenomena
in polyelectrolyte
and protein
adsorption, it is mandatory to systemize the treatment and we shall do so by adopting the following hierarchy: (1) The structure
of “simple” double layers and the adsorption
of low
molecular weight molecules and ions. In order to avoid unrealistically high ion concentrations
close to a highly charged surface, the well-
known concept of a (single) Stern-layer, exclusion
accounting
for the volume
between surface and ions besides specific adsorption,
is
very useful (section 2). (2) A self-consistent
field model of “simple” double layers which also
takes into account the mutual volume exclusion between the ions (and solvent). To that end, the multilayer Stem-model
introduced by
Bdhmer et al.31will be discussed (section 3). (3) Extension
of
this
incorporating
the
model
to
polyelectrolyte
configurational
properties
adsorption of
flexible
by chain
molecules (section 4). (4) Experimental verification of the theory for (strong and weak) simple polyelectrolytes experimental
(section
5).
In this
data on polyampholytes
section
also
some
recent
(for which the theory, so far,
has not yet been applied) will be given. (5) Adsorption
of proteins, for which the internal coherence (structural
stability) plays an important role. An a priory theory for these systems is not yet available, experimental
hence the approach
is essentially
based
on
evidence (section 6).
2 Electrosorption of ions and small molecules: chemical and electrical interactions The
distinction
between
electrical
and
chemical
contributions
pervades the entire domain of colloid and interface science. In its most elementary including
form,
it is reflected
charge-determining
in the adsorption (or
of simple
potential-determining)
ions
ions, and
counterions. Several features of colloid stability, the distinction between interaction
at constant potential
and at constant charge being one of
them, cannot be understood without properly recognizing
the chemical
and electrical contributions to the Gibbs energy of double layer formation.
480
Resolving
this
issue
was
one
theory. Also for our purpose At the
outset
“chemical”. suffices hence,
of the main
this distinction
it is necessary
to define
Since we will deal mainly
to identify
potentials
achievements deserves
of the DLVO
due attention.
the terms
“electrical”
with mean field approximations,
of mean force with average
potentials
it and,
use
(1)
I& = pi + viev for the relation the
and
between
chemical
potential
the electrochemical ).ti, and
potential
the
w. In eq. (1). vi is the
elementary
charge.
pi and w depend
potential
valency
In an inhomogeneous on the position
fii of component
(macroscopic
or
mean)
of component
system
z, but
i,
electric
i, and
e the
(such as a double
layer)
iii is constant
throughout
the
system. Equation
(1) implies
an element
of definition
to the Gibbs energy of an ionic species is by definition
chemical.
if the chemical
contribution
bonding,
hydrophobic
Henceforth,
form
adsorption symbol
by virtue
Au: while is that
tenets
realizing
Au:
specific hydrogen
. ..) is nonzero.
of the
terms may be included point
we shall call any adsorption
in colloid
chemical
that
science
attraction
of charge-determining
Au:
for by vrev
(such as Van der Waals interaction,
effects,
It is one of the basic layers
in that any contribution
i that is not accounted
ions
that electrical or (Gibbs)
to a surface.
non-configurational
double
energy
We
use
(or local)
of the
entropy
in it, thus making it a Gibbs energy. The important
does
not contain
the
configurational
entropy
of the
adsorptive. The charge-determining electrical
field
reflected (i)
in a number
chemical (ii)
is just
surface
Addition
continue
potential
v(O),
equal
to the
This
is
against
the
immediately
including
ions
and solution.
at the surface
adsorption. to
adsorb,
thereby
till this potential
difference
The driving
in the
gradually
has risen
chemical
so far
potential
force for the adsorption
is the
part Au; of this difference.
Indifferent
screen
their
of observations,
the surface
viev(O)
between
ions accumulate from
Charge-determining
increasing that
resulting
the
electrolytes
electrostatic
of such
(of which repulsion
electrolytes
allows
no ions adsorb between
specifically:
charge-determining
the adsorption
of the latter
Auy20) ions. ions to
481
proceed
further.
In other words,
surface
charge density
at given surface
potential
o(0) due to charge-determining
w(O), the
ions becomes
higher. There
is no distinction
ions and specifically
of principle
adsorbing
between
charge-determining
ions. Only if it is known from model
considerations that a certain ion type has a special affinity for the surface (e.g., Ag+ for silver halides, and H+ for oxides) does it make sense to identify them as “surface ions”. For protons on oxides Au: is of the order of
12-20
kT at room
whereas
temperature4).
Au: for
the
strongly
specifically binding Cdz+- ion is lo-16 kT51, which is not much lower. On the other hand, for weakly specifically adsorbing ions, like alkali ions on AgI, Au; is only a few kT-unit&I. It is now only one step towards small organic molecules. They may be charged or uncharged. For charged surfactants on hydrophobic surfaces, each CH2-group contributes an amount of order kT to Au;, whereas the electrical term for vi = 1 is about kT for each 25 mV of potential at the location where the charged group finds itself in the adsorbed state. The electrical and chemical contributions other,
depending
on the
indifferent
electrolyte
favourable
and adverse
screened. For long polyelectrolytes,
charge
may counteract signs.
Studying
may be diagnostic
organic
electrostatic molecules,
the picture
such
also contribute
polymers
to the adsorption
influence
because
as uncharged more
the driving force for the adsorption
both are and
because,
conformational
behaviour.
of
between
polymers
complicated
addition to chemical and electrical interactions, effects
the
in discriminating
contributions,
becomes
or reinforce each
in
entropy
For uncharged
is always of a chemical
nature. It is worth noting that a rather low chemical adsorption energy per segment (often a value well below 1 kT suffices) may lead to a strong binding of the chain as a whole. This is why linear uncharged polymers tend to adsorb tenaciously
on a variety of surfaces.
uncharged, electrolyte that is indifferent little effect on this adsorption the polymer).
However,
If the surface is
with respect to the surface has
(except when salt affects the solvency of
especially
for highly
charged
surfaces,
the
counterions neutralizing the surface charge compete for space and upon addition
of electrolyte
the adsorption
of polymer may decrease.
further discussion we refer to sections 4 and 5.
For a
482 Polyelectrolytes
have,
apart
from the chemical
contribution,
an
electrostatic part in their Gibbs energy of adsorption. With an uncharged surface,
this
electrostatic
polyelectrolyte.
effect
opposes
the
accumulation
of the
In the case of charged surfaces, there is an additional
electrostatic component in the adsorption energy, which may be positive or negative,
depending
screen all electrostatic
on the charge interactions,
signs.
Indifferent
electrolytes
both the intermolecular
repulsion
and the segment-surface interaction, so that they have at least two - often - effects.
antagonistic
These
situations
are more fully dealt with in
sections 4 and 5. In order to interpret more quantitatively the structure of the double layer and the effect of small molecules, the Gouy-Chapman picture 7. 81is usually inadequate, for at least two reasons: it considers the ions as point charges without volume (giving unrealistically high ion concentrations in regions
of high
adsorption. reasonably
A
and
potentials), simple
extension
it does
not
account
proposed
by
Sterns)
for
specific
works
in a number of cases, despite its relative simplicity.
quite In this
model, a chemical contribution is assigned to the adsorption energy of an ion and the volume exclusion between adsorbed ions and the surface is incorporated. Below we briefly treat this Stern-theory. A further extension to the more general
case where
also the mutual
overlap
of ions is
accounted for in a self-consistent way will be given in section 3. The basic premise of the Stern-model and ion volume
are considered
important
is that specific interactions only in the solution
layer
adjacent to the surface. The reasoning is that chemical interactions are short-ranged distance
and that usually the ion concentrations
from
the surface.
The potential
parallel
are low at some to the surface
is
considered to be smeared out, which is typical for a mean-field model. We denote the potential in the middle of this first layer, usually called the inner Helmholtz-layer.
as ~(1). Beyond the Stern-layer,
the outer Helmholtz-plane, Poisson-Boltzmann
that is, beyond
the double layer is assumed
to obey the
equation, i.e., its composition is formulated in terms
of the Gouy-Chapman theory. The
adsorption
isotherm
of a neutral
species
approximation, be written as a Langmuir equation:
i can, as a first
483
where $I = &(l) is the volume fraction of component i in the Stern-layer and $p is the bulk solution
volume
fraction.
If desired,
$i may be
identified with the fraction of the surface occupied by i. We prefer to use volume fractions in order to maintain consistency with the more general multilayer Stern-model to be discussed in section 3. Equation
(2) can conveniently
be derived
for a two-component
solution (solvent and one solute) using a lattice theorylo). It accounts for volume exclusion in the Stern-layer through the factor 1 - oi, but not for that in the solution: in order to achieve that, ‘pt should be replaced by @/(l - $).
Moreover, it is not generally valid for a system of more than
two components
(e.g., several types of ions and one or more neutral
solutes) because all these components occupy volume. For big monomers the statistics could be modified by letting more than one site match with one monomer, leading to a more complicated equation. In the Langmuir-picture,
Au; contains the adsorption energy and any
local entropy of adsorption: obviously the configurational entropy of the adsorbate is included in the term +I/( 1 - $1). If there is lateral interaction, an
additional
coordination parameter Moreover,
contribution number
Z&w@I could be added,
in the surface
that is positive
layer
for repulsion
where
Z, is the
and w a pair interaction
and negative
for charged species an electrostatic
for attraction.
term vieyr(1) enters. In
this way,
which
is a special
equationllv
form
of the Frumkin-Fowler-Guggenheim
(FFG)
12). Note that this equation does not explicitly account for
dipole orientation effects. Unlike eq. (2). which is explicit, equation (3) is an implicit equation in $1: not only does oi occur in the exponent but v( 1) is also a function of $1, and a suitable relation between the two has to be established. The FFG equation recurs as a special case in the multilayer Stern-model, see eq. (17) of section 3. The adsorption
energy AU: is then written as -x&T
where xS is a dimensionless adsorption energy parameter, and instead of w the conventional Flory-Huggins parameter x, which is a measure of the solute-solvent interaction, occurs. Moreover, the volume fraction oi in the lateral interaction term is replaced by the difference between a contact
484
fraction
in the surface layer and in the bulk solution.
The complete
solution in the multilayer Stern-model involves such an FFG-equation for each lattice layer in the system and not just for the ilrst layer. For all layers except the first, the adsorption energy term Au; is usually zero. For further details we refer to section 3. We shall now give a few experimental
examples
of low molecular
weight electrosorption. The purposes are to illustrate some of the trends discussed above, and to establish a bridge towards the following sections. Most examples given below are for AgI as the sorbent which, because of its hydrophobic surface and controllable surface charge and potential, is an excellent model system.
Figure 1. Surface charge on dispersed AgI as a function of pAg, in the presence of different concentrations of n-butanol13). Indifferent electrolyte 10-l M XN03. Temperature 25°C.
Figure 1 illustrates the influence of n-butanol on the electrical double layer on AgIlsl. The surface charge o(O) due to Ag+ or I- ions is plotted as a function of pAg I -log[Ag+l,
which quantity is directly related to the
surface potential y(O): if pAg increases by one unit, ~(01 becomes more negative electrolyte
by an amount concentration
of 58 mV (at ZOOC). In this experiment,
the
is high and kept constant, so that the diffuse
part of the double layer is compressed
and the Stern-layer,
where the
butanol is adsorbed, gives the dominating contribution. The picture shows that uncharged adsorbates can also screen the surface charge, though this is a more subtle process than with electrolytes. Butanol has basically two effects:
485 (i)
the lowering
of the dielectric
partial displacement
constant
in the Stern-layer
and the
of the counterions reduce the capacity 0(0)/w(O) of
this layer, which shows up as a smaller slope of the o(O)-pAg curve, and (ii) the replacement
of oriented water dipoles adjacent
to the surface
causes a shift in the point of zero charge (pzc), i.e., the pAg-value where o(0) = 0. If the curves were plotted as o(0) - w(O), the curves would all intersect each other at the pzc. If plotted against pAg, as in fig. 1, the curves are shifted along the horizontal axis and a common intersection point (tip) is found at a pAg above the pzc. In this tip the replacement of water in the Stern-layer by butanol has no consequence for the surface charge. The amount
of adsorbed
butanol
(rb) is too small to be detected
analytically, let alone the minor change of rb with pAg. However, it follows straightforwardly from the Gibbs adsorption equation that rb as a function of o(O) or, for that matter,
as a function
of pAg, passes
through
a
maximum at the tip. It is interesting to note that a very similar behaviour was found for n-butanol on mercuryl4). The model hydrophobic
interpretation
considers
the adsorption
bonding139 1s). Hence, on a butanol-covered
as driven by AgI-surface the
hydroxyl groups point towards the solution. A supporting observation is that
due
to
counter(cat)ions increases
this
butanol
adsorption
the
lyotropic
sequence
for
reverses. On bare hydrophobic AgI the specific binding
in the order Li+ < K+ < Rb+.
whereas
on butanol-covered
hydrophilized AgI it is the other way aroundIs).
PAg
Figure 2. Surface charge on dlspersed AgI as a function of pAg. in the presence of tetrabutyl ammonium (TBA+) nitratel6). Indifferent electrolyte O.lM KNOs. temperature 22oc.
486
Common
intersection
since been found including
for a variety
charged
ammonium function
ones.
(TBA+)
ammonium
points such as those observed
ions.
of other low molecular
Figure
nitratela).
Similar
As for n-butanol,
of o(0) or pAg passes
ions it was possible because
adsorbing surface
cations.
The
is positive,
point,
stronger
competition
positive
direction.
decreases
with increasing
sight
between
is rather
region,
I- and TBA+
for polyampholytes
and
increasing specifically
at low pAg, Au&.
where
adsorption
surface of the
be explained
sites.
experience
cation
by the
In addition,
where
attraction
the
To the right
sometimes
between
which
dipole less
adsorbate
TBA+ on
competition orientation
5 and 6, similar examples
proteins,
as a
methods.
with
o(O). Also this phenomenon,
for surface
if the electrostatic
ions
TBA+ ions, and o(0) shifts in the
may
effects may play a role. In sections found
adsorbs
the
negative
unexpected,
tetraalkyl
of these
by the
contribution
of the voluminous
for other
negative
the I- ions on the crowded
In this
tetrabutyl
at the tip. For some
of I- is facilitated
that TBA+
have
adsorptives,
for
by direct analytical more
points to a chemical
of the intersection
first
fact
apply
a maximum
becomes
adsorption
weight
example
adsorption
to verify this maximum
the
an
curves
the
through
To the left of the tip. o(0) [TBA+]
2 gives
for butanol
will be given adsorption
and
is
surface
is
increased. Koopall7)
has demonstrated
also be obtained When
the
adsorbed
carrier in trains
layer
electrophoretic electrolyte,
electrolyte
Having return
by train
this
to the statement
distinguish
between
established
the
is
that
above
on the segment chemical
of the
the data
and
with
electrostatic
diagnostic
species
we
of the tool
Figures
l9). They have in common cationic
the
distribution.
the influence
contributions.
of
of carrier
of small molecules
additional
and chemical
segments
the coverage
this information
that studying
a useful
of such trendsls.
adsorption
only
in low concentrations
useful information
electrostatic
and 4 are illustrations coverage
Combining
obtained
made
concentration
low
high,
on AgI.
By comparing
both play a role in the electrosorption
electrolyte
alcohol
he was able to determine
segments.
way
is
by this method.
layer thickness,
in
for polyvinyl
concentration
monomers,
then provided
interactions
particularly
are detected
with those of simple the first
that curves like those in figs. 1 and 2 can
for polymers,
decreases
to 3
that at with
487
Figure 3. Influence of the indifferent electrolyte concentration on the adsorption of tetrabutyl ammonium (TESA+) ions on AgIl*). The pAg was fixed at 11.5. temperature 22OC.
r
Figure 4. Influence of the indifferent electrolyte concentration on the adsorption of dodecylpyridinium chloride (DPC) on kaoIinitel** 19). The pH was fixed at 7. temperature 2ooc.
increasing salt concentration: then there is again a common intersection point, above which the salt effect is the other way around. Below the tip, the competition
between the cation of the electrolyte
and the organic
cation (ion exchange) leads to a smaller adsorption of the latter. At the tip, the electrophoretic mobility of the covered particles is zero: here the particles with their adsorbates are uncharged
(isoelectric). Beyond this
point, the screening by the salt makes the accumulation
of the organic
ions easier. The fact that the adsorption continues to increase beyond the tip points to a chemical driving force. Such an adsorption causes charge accumulation,
which
would
inhibit
further
adsorption
unless
these
488
charges higher
are screened. electrolyte
In
the
This screening
next
chapter
we
predicted
by rhe multilayer
3 Lattice
theory
Very model
Bohmer
were assigned just
volume
polymeric
were
avoided
(Debye-Htickel next
a of the segments
to vary with the distance could be modelled,
is not
types of
a mean field and ions
more consistent The theory only
u-eat
leaving
to assign
of Bijhmer
in those
the
approximation) surface.
case
model
where
and only electrical
to show sow- chemical
low
cases
where
by
the ionic success
However,
to all the components these demands.
molecular
aspects
weight
till section
each lattice
interactions
interactions
E
In this way weak is determined
layer
filling
in
In this
ions
is behaving
play a role. Then
and the volume
it
and
4. We separate
into two parts. First we deal with the lattice version
Gouy-Chaprnan-Stern
the
permittivity
new trends.
a volume
oi
or by
bater221,
have had considerable
et al.31 satisfies
the polyelectrolyte
relation
The fact that small ions have
data and predicting
the system.
as point
a linear
from the surface.
drawback
the
Very high counterion
to the
equilibrium.
a serious
is deffnitely
Stern-layer
lattice
(several
through
of .which the charge
experimental
the discussion
also
account
and the dielectric
in interpreting
we
into
by using
of a Stern-layer
are low, and these models
section,
species)
theory73).
concentrations
moiecuies,
takes
of this mode120. 211, polyelectrolytes
a local association-dissociation no volume
are
a multicomponent
which
and the potential
of ionination
polye!ectrolytes
trends
of all the components
molecules,
near the surface
the charge
were allowed
similar
a fixed charge and the small ions were considered
the incorporation degree
that
like in the Gouy-Chapman
concentrations between
find
et al31 presented
In earlier versions
charges,
shall
adsorption
and excluded
small ions, uncharged approach.
of
Stern-model.
polyelectrolyte
interactions
in the presence
of electrosorption
recently,
for
is more effective
concentrations.
of the like a
we proceed
constraint
are
incorporated. a) Lattice
variant of the Gouy-Chapman-Stem
The molecules one could
assign
are assumed solvent
model
to be arranged
molecules
on a lattice.
(H201, small
In principle,
ions (e.g., OH-. H30+,
489
Na+, Cl-, etc.),
and small uncharged
solutes
one lattice
site each.
However, since ions in aqueous solution are strongly hydrated, one could also take lattice cells with a volume equal to that of an (average) hydrated ion and assume an equal volume for clusters of water molecules. As water is a highly structured
solvent, it is not an unrealistic
assumption
to
consider the water molecules to be clustered. Lattice cells of this size are also considered to occupy one polyelectrolyte segment (section 4).
Figure 5.
(a) Lattice with a solution of solvent (open circles), ions, and uncharged solutes (black circles) in a sobent, next to a charged surface. lb) Potential profile v(z) and field strength profile E(z) in an electrical double layer according to the multilayer Stem-model. The field strength changes at each charged plane (z = 0. 1, . ..) due to the plane charge density C(Z). and at each boundary between the layers (z = l/2. l/3. . ..) due to a change in the dielectric permittivlty ELz).The potential drops linearly in each half-layer because there is no space charge.
Like in the Gouy-Chapman theory 7.8). the potential is only a function of the distance from the surface: lateral fluctuations
are neglected
by
adopting a mean-field approach. The charge of the ions and segments is assumed
to be located
on planes in the middle of each lattice layer
parallel to the surface, thus forming an assembly of Stern-layers
(see
figure 5). The layers are numbered from z = 0 (the surface) to z = M (in the bulk solution). The interplane separation e equals the diameter of a segment or ion. In between the midplanes there is no charge so that the electric
displacement
permittivity
D(z),
which
is the product
E(Z) and the electric field strength
of the
dielectric
E(z). is constant. The
490
quantity
E(Z) is the
permittivity
relative
dielectric
Q, of free space. According
constant
in layer
to standard
z times
D(z) = &(z)E(z) = ia z’=O
(4)
The field strength
E(z) changes
I, 2, . ..). because
of the presence
boundaries
(z=i,g,
discontinuously
E(Z) is taken
the various denoted
of charges.
...) there are changes
in each layer leads to another imation,
the
electrostatics:
components.
because
dielectric
to be a linear
at the mid-planes However,
a different
permittivity
combination
(z = 0,
also at the layer composition
E. As a first approx-
of the permittivities
If in layer z the volume fraction
of component
of i is
by o‘(z), we have (5)
e(z) = &4$(Z)
i where
Ei is the permittivity
extends
over solvent,
densities equals
v&z)e,
charge
uncharged
are functions
component
of the pure solutes
of the volume
component
The charge
charge
of each unit i
and ai(z) the degree of ionization
i in layer z, and e is the elementary
density
summation
and all ions. The plane
fractions.
where vi is the valency
i. The
charge.
Then
of
the plane
o(z) is given by:
o(z) = Cviai(z)eoi(z)
/ a,
(6)
i Here,
as is the surface
the surface zero
volume
area of a lattice
charge density fraction
site. Equation
is that
for i = S, where
S is the solid
$3(z) = 1 for z I 0 and @s(z) = 0 for z 2 1. Generally, species,
VI = -1 for negative
ones. The degree equilibrium polyacid).
which
(where constant surface
also for
adsorbent:
vi = 0 for uncharged
and vi = +l
can be unity (e.g., for H30+, concentration.
for positive OH-, and salt
For example,
of a weak acid residue A (or a segment
can be represented
the
of a weak
by the reaction
H+A-
W = H20
and
H = H30+),
Kd = (a~/(1 - aA)lIHI/(Wl. the
(or segments)
of the local counterion
dissociation
HA+W$
ions
of ionization
ions) or a function
(6) applies
o(O) by putting z = 0. In this case the only non-
ratio
(H)/(W)
should
is determined
by
In the concentration be replaced
by the
the
dissociation
gradient ratio
near the
of contact
491
fractions
(I$H(Z))/($W(Z)).
The contact fraction
(@i(z)) is the average
volume fraction of component i around a site in layer z. To this average, three layers (z - 1, z. and z + 1) contribute. Hence, (@l(z)) is given by (@i(Z)) = Q$,(z - l)+ Q$i(z) + h.#z + 1)
(7)
where ho is the fraction nearest neighbours within layer z. and X1 that with each of the layers z - 1 and z + 1. For example, in a hexagonal lattice b = 2x1 = 6/12, and in a cubic lattice Xo = 4x1 = 4/6. Obviously, Xo + 2X1= 1. For the local degree of dissociation we arrive at
ol*wl = 1+K~‘(oH(z))/(ow(Z)) Note
that
&
concentration.
is
a dimensionless
(8) quantity
The normally used dissociation
moles/P, corresponds
to K = Q( lOsa,dN&-1
rather
than
a molar
constant K. which is in . The conversion
factor is
the molar concentration of pure solvent. It is straightforward
to compute the electrical
potential
from the
field strength. The potential on each plane at z = 1, 2, 3, . .. is related to that on the previous plane by ~(z+l)=+{E(z)+E(z++)}
(9)
where I is the lattice layer thickness. We assume that all molecules obey Boltzmann statistics. Accordingly, the concentration proportional
of ions, solvent molecules, and other monomers are -u*(z)/kT , where ul(z) is the energy
to a Boltzmann factor e
(with respect to the bulk solution) of species i in layer z. In the bulk solution, up = u,(m) s 0. If the interactions nature,
ui(z) is simply the electrostatic
are only of an electrostatic
energy u:‘(z)
of monomer
i in
layer z:
uf(z) =vp,bdeW)
(10)
As before, the volume fraction of component denoted
as $.
The
volume
components is then obviously
fraction
i in the bulk solution is
distribution
of the monomeric
492
(11) If there
are
components solved u,(z)
only
present,
numerically. gives
equation
immediately
potential
In order
iteratively
until equation
uncharged total
density is
Nevertheless, accounted
and
for
magnitude are
present,
equations
simple
and
condition
positive,
hence
ui(z)
example
is not and
ui(z)
w(O)
equation
are
adjusted
finite
(12),
equation
lateral
below,
of
the
monomers
is
However, packing obeyed.
of molecules
layers
restricts
is easily
is the
high concentrations
factor of positive ions
not
and monovalent
concentrations
for all
than the original
(and association)
thickness
of negative
it follows
equation. no
sophisticated
so that unrealistically
in the
is zero
are inhomogeneously
restricted:
more
since dissociation
that
molecules
eq.
is already
the
above,
with the Gouy-Chapman
molecules
error
neutrality
energies
potential with
(10) is obeyed for all i and z.
(10) and (11). The weighting
exp(ev(z)/kT)
charge
(4) and (9) lead to the potential
the potential
If only uncharged
the
(7)
and plane
be consistent
of the potential
ions do not occur.
using equations
o(0) or surface
incorporated model
to
should
the model
Gouy-Chapman
can be
according
the permittivity
Only the charged
of
distributions
charge
in full agreement
constraint
fraction
equations
this,
polymeric
set which
the surface
in the
molecules.
distributed, the
that,
a closed
no
distribution
to achieve
It is clear
form
can then be calculated
Finally,
provided
This
4-11
and
an initial guess for the set of potentials
(5) and (6) provide
distributions.
is given.
interactions
the volume
(11). Any dissociation
on each plane, (10).
equations
For example,
and (8). Equations density
electrostatic
of
salt ions
obtained
from
ions in layer z is
is exp(-ev(z)/kT).
From
the
that half of the ions in the bulk solution (11)
leads
to
the
well-known
is
relation
%aIt (z) = &3Ii cosh(ev(z) / kT]. The volume fraction of uncharged molecules is 1 - okIt in any layer z. The total volume fraction in layer z is then 1 + o~gIt(cosh{e~(z)/kT) (according b)
- 11, which
to the Debye-Htickel
Volume filling
approaches
unity
approximation)
only
at low otaIt
or
at low v(z).
and chemicaI interactions
The next step is the complete of the ions and molecules.
incorporation
We require
of the hard core volume
that each lattice
layer is just
fully
493
occupied.
In terms of volume fractions the packing constraint
can be
expressed as: &(z)=l i
(12)
for all z. This boundary condition is imposed by a lateral pressure which affects the potential energy of all monomers in a given layer in the same way.
More specifically,
Boltzmann
statistics
are maintained
but the
potential energy ul(z) is incremented by a term u’(z), which is positive or negative since the local pressure can be higher or lower than in the bulk solution. The effect of such a term is that the Boltzmann multiplied
by a factor exp(-u’(z)/kT)
which normalizes
factors are
the sum of the
volume fractions to unity and at the same time induces a redistribution of the molecules
because
of the accompanying
change
potential profile. Note that no extra independent
in the electric
parameter is needed:
equation (12) fully determines the value of u’(z). Like the self-consistency of ion distribution the
profile
and electric potential, all molecule distributions
of u’(z)
become
self-consistent.
In the
example
exp(u’(z)/kT] would have the value 1 + Q!&(cosh(e~(z)/kT)
and
above,
- 11 for any z,
but the potential profile v(z) would be different from the simplified case u’(z) = 0. Obviously, electrical
the potential
contribution,
energies
may contain,
also other interactions.
apart
from
the
Let us first consider a
binary mixture of solvent 1 and uncharged solute 2, where the molecules are attracted by the surface so that their energy levels in the first layer are lower than in the bulk solution by amounts uf and uz, respectively. In this case u:‘(z)=0
for any z. If there are no other contact interactions
than try, ui(z) = 0 for all layers except the first. This implies @i(z) = @ for z 2 2, according to eq. (11). For z = 1 we have in this simple case l+(l) = u’(1) + UQ From
eq.
(13)
(11)
($2 / I$) exp(-Au; / kT) difference
between
we
can
where
a solute
now
eliminate
Au; = uz - ut and a solvent
is the
u’( 1):
$,(l)/@,(l) =
adsorption
If we define
a
dimensionless adsorption energy parameter xS as x, = - Au; / kT (which
is
positive if the solute adsorbs preferentially with eq. (12):
molecule.
energy
from the solvent), we have
For
dilute
solutions
Langmuir
(I$; -C-C1). this
equation,
It is straightforward l+(z) = u’(z) + The adsorption interactions For
the
model
energy contribution
can be used.
is identical
the
simple
is usually zero for z t 2, but long range
The electrical
contact energy
term is given
interactions, up
to XIJand to the contact
i. This contact
are defined
with
energy of a molecule
Generally,
+ ...
up
any
fraction
by eq. (10).
suitable
through
of a solute
i in the layer z with other molecules
molecule
to
other interactions.
One way is to express
The contact
proportional levels
be included. neighbour
parameter@). segment)
to incorporate
u?(z) + u;‘(z)+ q(z)
could
nearest
result
see eq. (2) in section 2.
solution
Flory-Huggins
molecule
x-
(or polymer
(or segments)
of type j is
(@I(z)) of molecules
j around
fraction
is formulated
in eq. (7). Since the energy
respect
to the bulk
solution,
i with all other components
the total
contact
j is given by
u~t(zl=kT~Xlj[(~j(z))-O~} 1 If the solvent expressing u:(z)
is monomeric,
it in the
and up(z),
solvent
underlining
Since the solvent
it is always profile
@l(z)
possible and
to eliminate
the
potential
that u’(z) is not an independent
is uncharged,
u’(z) by energies
variable.
u1e1 = 0 . For the ratio @i(z)/@1 (z) we find
from eqs. (11) and (15):
(17)
where equation
Au:(z)
= u:(z)
applies
simultaneous the volume
as before,
for any component
equations constraint
It is instructive the special
- u:(z)
and
Aup
= uft(z) - $(z).
i and any layer z. The whole
may be solved
numerically,
taking
This set of
into account
(12). to compare
eq. (17) with the FFG-equation
case of a two-component
system
(e.g., solvent
(3). For
and one type of
495
salt) where the adsorption is restricted to a monolayer, eq. (17) reduces to nearly the same form as eq. (3). Note, however, that the volume of the co-ions is neglected in the FFG-picture. Hence, if @I( 1) = 1 - o2( 1). where component
2 is the counter-ion. and @ = 1, the factors containing the
volume fractions are the same in eqs. (3) and (17). The term Au: in eq. (3) is identified term u:‘(l)
as the difference between u; and u:. The electrostatic
is the same in both models. For the contact term At$(l)
may write,
using
(@l(l))
XIX + 2~{(@2(1)) - $},
+ (@2(l))
we
= 1 - hl and eq. (16). A$(l)/kT=
where x = ~12 This contribution
closely resembles
the lateral interaction term in the FFG-equation: the constant hlx may be incorporated
in Auf,
and w may be replaced by 2x/Z, where Z is the
lattice coordination number. Since Z, = hoZ, the term &w& in eq. (3) can be written as 2koxoi. The full model gives, for small @,
essentially the
same result because in that case (@2(l)) = I&z(l). The illustrations given above show that the multilayer Stern-model is easily adapted to different types of interactions, which may be long range as well as short range. Before proceeding to the application of the model to polyelectrolyte shown
in section
adsorption (section 4), we compare some of the trends 2 (figures
l-4)
with the predictions
of the model
calculations. c)
Theoretical results
d(nr’
Figure 6. Comparison between the multilayer Stern-model and the GouyChapman model. Potential decay in the electrical double layer, for three concentrations of monovalent ions and ~(0) = 100 mV. The full curves were computed from the Poisson-Boltzmann equation, the various symbols correspond to computations with the multi-layer Stemmodel, using various lattice spacings C. All x and xS parameters are zero and E = 60 E, for all components.
In fig. 6 we show the potential profiles v(z) for a charged wall in the presence of indifferent electrolyte at three different salt concentrations cs, for an intermediate surface potential of 100 mV. The distance d in fig. 6 equals zl. The curves in fig. 6 were calculated using the Gouy-Chapman theory7.s)
based on the Poisson-Boltzmann
equation,
the points were
obtained from the multilayer model using different values for I. It is seen
496
that
for the given
surface
potential
(100 mV) the results
virtually
coincide, which means that volume exclusion plays almost no role. For higher pronounced,
surface
potentials
and the multilayer
the accumulation
of ions is more
model leads to a slower decay of v(z)
close to the surface and, consequently, a lower surface charge than the single Stern-layer
model. Further away from the surface (a few lattice
layers) the profile becomes exponential, with a decay length equal to the Debye-length. just like in the Gouy-Chapman
picture. These trends are
fully consistent with Monte Carlo simulations by Camey and Torrie24).
Figure 7. Potential decay in the electrical double layer in the absence (dotted curve) and presence [full curve) of a specifically adsorbing monomer A, according to the multilayer Stern-mode13). Parameters: - I+I(O)= 400 mV. c, = 0.1 M. x$” =lO, other xS and all x parameters zero, L = 0.6 nm, components, hexagonal
d (nm)
The effect of a neutral monomeric adsorbate on v(z) at 0.1 M salt is illustrated in fig. 7. The adsorbate is assumed to adsorb strongly (xs = 10). Notwithstanding displacing
the high surface potential
counterions
(400 mV) it is capable
from layer 1 so that the potential
of
decays more
slowly in layers 1 and 2 than it does in the absence of the adsorbate. Beyond layer 2 the potential decay is exponential again, with the same decay
length
(1 nm for
10-l M salt) as in the absence
of specific
adsorption. In fig. 8 we present the surface charge-surface
potential
relation
(‘titration curve’) for a similar case: a charged surface in the presence of 0.1
M indifferent
electrolyte
and
a neutral
specifically
adsorbing
adsorbate. It is seen that at given ~(0) the adsorbate reduces the amount of charge, simply because of the fact that it reduces the screening by counterions
close to the surface. Since o(O) is plotted as a function of
w(O). the two curves intersect at the p.z.c. When comparing this result with the data given in fig. 1 we note that the shape of the curves is somewhat
different. This is because the ions in this example have no
chemical
affinity
with
the
surface.
Assigning
them
a
non-zero
Au,” (and/or Au_“) would produce a shift in the pzc and would make the
497
curves asymmetric (unless Au: = Au_“), see fig. 9 below. Related to this is the question of the partial polarization the layer of water adjacent to the solid
phase,
Adsorption
which
contributes
to the
establishment
of the
of molecules in the first layer changes this polarization
pzc. but
this feature has not yet been included in the model.
m
100
-100 mV
J, (0)
-1.0, 05
Figure 8. Theoretical titration curves 40) - 1+40)In the absence and presence of a specifically adsorbing monomer A. The surface charge is given as the dimensionless quantity a&0)/e, the number of elementaly charges per lattice site. Parameters: X* = 3, ux = 2 where x = SOlvent or iOk). &A = 2h,. L = 0.31 nm. other parameters as in fig. 7.
I
I
.
,
U(O) e
-0.6
-0.6
-0.4
-0.2
0.0 0
- 200
-400
-600
-800 mv
tiC0)
Our next adsorbing
example
cation
(fig.
9) illustrates
on the charge
potential
Figure 9. Theoretical titration curves o(O) - ~(0) in the absence and presence of a specifically adsorbing catton A:. Parameters: x:=5, ! = 0.31 nni, other parameters as in fig. 7.
the effects relation,
of a strongly again
at 0.1 M
indifferent electrolyte. In this case the cation was modeled as As, i.e., as a trimer with a charge of +1/s for each segment. The segmental adsorption energy xf
was chosen to be 5, so that this cation, with a rather diffuse
charge and a total adsorption energy of -15 kT, somewhat resembles the TBA+
ion in figs.
2 and 3. The
conformational
properties,
treated
according to section 4b, are different but in this case the electrostatic effects dominate. Four titration curves o(O) - ~(0) are shown, for bulk solution volume fractions (I: of 0. 10-7. 10-6, and 10-S M. respectively.
It is clear that
498
now there is a shift in the p.z.c. towards
the positive
side and a common
intersection
v(O). Below
this tip the organic
cation
point
at a strongly
promotes
increases
co-adsorption
-o(O),
qualitatively
beyond
along
is again
affinity
for the surface.
considerably
as found
the same
curves
of negative
charge-determining
the tip the reverse
the same
explained
negative
related
applies.
All these
in the experiment
lines.
The
different
ions
and
trends
are
(fig. 2) and
shape
can be
of the o(O) - ~(0)
to the fact that the small ions have no chemical Even a small Au: or Au_” would high electrolyte
at this relatively
affect
the results
concentration.
Figure 10.
Theoretical adsorption isotherms of a monomeric cation A+ on a surface with surface potential ~(0) = -100 mV. at three concen-
trations of indifferent electrolyte. The adsorbed amount 13: is given in monolayers. Parameters: xt =15, EA = 5 ~0.C= 0.31 nm. other parameters as in fig. 7.
Our last example When A+ adsorbs between
of this section
onto a negative
adsorbate
and surface,
is again for a monomeric
surface,
but a repulsive
adsorbate
molecules.
Indifferent
may have
a reducing
or an enhancing
seen
in our
isotherms
final
of
logarithmically around
(at
for
competition
with
(including
to be screened the theoretical 4 is striking. to
monomeric
mV
salt
monolayers. so that
point
the
Above
that is
electrolyte
are
The
That
our
coverage,
reduced
plotted
semi-
to
at
repulsion
of A+: below
due
is
intersect
lateral
the
electrostatic point,
the
so that there is nothing
has no effect.
whereas
This
adsorption
In the intersection
that these figures picture
and therefore
curves
in fig. 10 with the experimental adsorptives,
neighbouring
10) where
adsorption
counterions.
It may be added units.
(fig.
potential)
enhances
both
cation A+. interaction
on the adsorption.
A+) is just isoelectric,
and indifferent
oligomeric
section
adsorption
adsorbed
screens
effect
surface
one between
concentrations.
salt
indifferent
curves
electrolyte
of this
-100
three
important
intersection
apply
A+
r = 0.12
becomes
surface
example
there is an attractive
The similarity
ones in figs. 3 and
(and also figs.
figures
nevertheless
of
1 and 2)
8 and
10 are
applies
so well
for is
499
explained
by the fact that in practice the electrostatic
effects, notably
those in the first layer, dominate. Having description
established
that the multilayer
of the electrosorption
turn our attention
Stern-model
gives a fair
of ions and small molecules, we now
to the extension
of this model
to polyelectrolyte
adsorption. 4 Polyelectrolyte adsorption model a) Conformations As compared previous
to the monomer
section,
a theory
electrosorption for
model discussed
in the
adsorption
again
polyelectrolyte
is
considerably more complicated because the conformational entropy of the flexible
chains has to be accounted
for. Earlier models had to make
drastic assumptions in order to cope with the complex interplay of long range electrostatics,
short range chemical interactions
and conforma-
tional effects. The first model is due to Hesselink25.26) and is an extension of an early polymer adsorption model of Hoeve27). The latter is based upon an assumed However,
exponential
Hesselink
assumption
form
calculated
of the segment the electrostatic
that the charge in the adsorbed
density
distribution.
free energy under the layer is homogeneously
distributed. As a result, very dilute and extremely thick adsorption layers were
predicted.
In more
recent
models,
which
have
been
briefly
discussed in the introduction of section 3, the segment density profile is not
predetermined
and
very
thin
layers
are
obtained
if the
salt
can deaf with polymers
without
the
properties
are
concentration is not too high. The multilayer introduction
Stern-model
of extra parameters.
The configurational
treated along the lines of the Scheutjens-Fleer
theoryzs-so) where all the
possible conformations are taken into account by assigning each segment of a chain a weighting factor e-urWKT that depends on the local environment
according
to eq. (15).
For polyelectrolytes,
contains an electrostatic contribution, given by eq. (10).
ui(z)
again
500
Figure 11. Schematic illustration of a lattice with a solution next to a solid adsorbent. The solution sites are filled with solvent (open circles). small ions, and three polyelectrolyte chains (of five segments each) in specified conformations c. d and e. Conformations c and d are adsorbed and have r”(l) = 3 and @(I) = 2 seg-ments. respectively. in the first layer. Conformation e is free (nonadsorbed). with f(4) = 1 and 175) = 4.
Here we do not treat publications39
28-30).
is a modification
the
model
in
detail
and
refer
to
earlier
Th e principles can be illustrated with fig. 11, which
of fig. 5a. In this figure three chain molecules
are
indicated in specified conformations (labeled c, d and e). Each conformation
may have a different energy, depending on the
position (layer number) of the segments. The energy of a chain is the sum of the energies ui(z) of its segments, taking into account their spatial distribution. (hence,
If ri is the number of segments of a chain of component i
x-i-1 is the number
conformation
of bonds),
the Boltzmann
factor Gy of a
c is then the product of the x-i Boltzmann
factors of the
segments, multiplied by a product of ri-1 bond weighting factors ho or 11. By summation over all possible conformations, the volume fraction profile of the polyelectrolyte component i has r:(z)
is obtained.
If conformation
c of (polymeric)
segments in layer z, the volume fraction profile
becomes:
(18) This equation also applies to monomers (ri = 1): in this case r:(z)
= 1 if
the monomer is in layer z, GF is just the simple Boltzmann factor e-u*(zl/KT, and the summation over c involves only one term, so that eq. (18) reduces to eq. (11). For chain molecules more complicated.
the expression
For example, the conformation
for Gf is
labeled c in fig. 11.
501
having
five segments
(rl = 5). two “parallel”
bonds,
and two “perpen-
dicular” bonds, has an energy u: = 3u,(l) + 2u,(2). In this case rF( 1) = 3, r:(2) = 2, and Gf = A$: exp(-ur / kT). Similarly, for conformations d and e in fig. 11 we have the Boltzmann factors Gy = hoh: exp(-up / kT) and GF = h&exp(-u:
/kT), where uf =2u,(l)+u,(2)+~,(3)+~,(4)
and u: = u,(4)+
4ui (5), respectively. The summation in eq. (18) is most easily performed using a matrix formalism. We refer to refs. 3 and 28-30 for more details of the theory and the numerical theoretical
procedures.
In the next six figures we give some
results obtained with the multilayer
Stem-model.
In a few
cases the data were obtained with an earlier version of the mode12o-22)but under such conditions that the difference, if any, is very small. b) Theoretical
results
Strong nolvelectrolvtes
1
In figures strong
10
5
z
15
20
Figure 12. Semilogarithmic segment density profiles of a strong polyelectrolyte adsorbing on an uncharged surface, at various salt concentrations3g). For comparison, the profile for an uncharged polymer is also given. Parameters: $b = 104. r = 2000, f = 0.71 IXIL~~= 2. x = 0.5. E = 80 q, for all components. hexagonal latice.
12 and 13 we show some results for the adsorption
polyelectrolytes.
Fig.
12 gives
semilogarithmic
of
concentration
profiles near an uncharged surface, at various salt concentrations cs and at a constant
polyelectrolyte
bulk solution volume
fraction
of 10-a. The
figure was computed with the model of Evers et al.22) but the results of the multilayer Stem-model
are virtually the same: only at the higher salt
502
concentrations
some minor
differences
occur. The most conspicuous
feature of fig. 12 is the minimum at low ionic strength, which originates from the high potential generated by the adsorbed molecuies,
repelling
other chains, that are consequently depleted. Under these conditions. the adsorbed
amount
conformations,
is low and the adsorbed
chains
adopt
very
flat
with only a few short loops and hardly any tails. As a
result, the chain length dependence is also very weak. With increasing cs the adsorbed amount (and the chain length dependence) increases and the minimum in the profile becomes shallower. ~though
the minimum at
low cs in fig. 12 is rather pronounced on the logarithmic scale used for o(z), it could probably not be detected experimentally, because of the low absolute values of the concentrations involved.
1.5 1
1.0
CS
2.0 M
Figure 13. The adsorbed amount e”p [in equivalent monolayers) of a strong polyelectrolyte (v = -1) as a function of the salt concentration c, at three surface charge densities ~(0)~). The abscissa axis scale is linear in 4,. Parameters: r = 500. ~~=t~,L=O.6nm,~~=1,~=0.5 for polymer-solvent or polymer-ion interaction. other xs and x parameters zero. Ed = 20~~. E = 80&, for the other components.
In fig. 13 we present adsorbed amounts as a function of indifferent salt concentration, for three different values of the (fixed] surface charge. The abscissa scale in this figure is linear in u’cs. The polymer is assumed to have a weak chemical (specific) interaction with the surface and the surface charge is taken opposite to that of the polymer. Small ions have only electrostatic interactions with the surface, At low ionic strength, the adsorption is nearly proportional to the surface charge. If the surface is uncharged, the adsorption is almost zero. and when the surface charge is increased, the amount of adsorbed polymer adjusts itself such that the surface charge is slightly overcompensated.
The extent of overcompen-
sation depends on xs. At high ionic strength the adsorption increases by nearly the same amount for all surface charge levels, the slope being slightly higher for lower surface charge. This implies that the adsorbed amount changes by only a small factor when the surface charge is high, but shows a dramatic relative increase when the surface is near to neutral.
503
Of course, the enhancement of adsorption by salt is due to the screening of lateral electrostatic repulsions in the polymer layer. We note that electrostatic
interactions
between
colloidal
particles
(with bare, smooth walls) are usually already entirely screened at salt concentrations
of about 0.1 M, whereas with adsorbed ‘polyelectrolytes
screening effects still play a role up to 2M. In colloid stability only longrange interactions are important, and since in 0.1 M salt the Debye length K-1 is only becomes
1 nm the electrostatic
repulsion
between
small with respect to the long-range
However,
the
conformation
(and
colloids
then
Van der Waals forces.
adsorption)
of polyelectrolytes
is
determined by interactions between charges in close proximity, and salt affects these interactions even if ~-1 is considerably below 1 nm. This is also the reason why a strong polyelectrolyte
does not reach the same
adsorption properties as the corresponding uncharged polymer would do, not even at very high ionic strength,
although
with increasing
cs its
behaviour tends towards that of the uncharged polymer. Since in most problems
of screening
due to electrolyte
the basic
length scale is the Debye length ~-1, which varies as ~2.~. it might be anticipated that the adsorbed amount of the polyelectrolyte also increases linearly
with
accordingly.
c or, for that matter, Indeed
the curves
with dc,.
Fig.
are (approximately)
13 was linear
plotted
in dc, for
higher salt concentrations, but at low cs the dependence is not so simple. In that range the charge compensation
between surface and adsorbed
polyelectrolyte dominates, and 0: depends more weakly on k,. One uncharged
might
compare
polymers.
polyelectrolyte
In the latter
adsorption
with
case two parameters
that
govern
of the
adsorption behaviour: xs for the segment-surface interaction and x for the segment-segment
interaction
in the solvent.
One could
visualize
a
polyelectrolyte as an uncharged polymer with an overall xs-parameter that contains
a chemical
part (xs as defined before) plus an electrostatic
contribution that depends on surface charge and ionic strength. If surface and polyelectrolyte
are oppositely
charged.
this electrostatic
part is
positive, favouring the adsorption. It decreases with increasing cs. In this case, salt opposes the adsorption of the polyelectrolyte. Similarly,
one
could
imagine
an
effective
X-parameter.
Its
electrostatic part is always negative because of the mutual electrostatic repulsion between the segments, and it also decreases with increasing cs. Hence, the electrostatic part of x tends to decrease the adsorbed amount.
504
At low cS the overall
x is low
polyelectrolytes
show
the same
trends
low adsorbed
amounts,
flat conformations
solvents:
dependence.
With
electrolytes
o(O), see fig. negative,
adsorption
interesting
situation
adsorption
energy
electrical
energy
adsorption
the adsorbed
energy
below.
14,
of
of a segment, vev(1).
Rewriting
Hiickel
approximation
o(o)cr =
e
This equation from
the surface
poly-
chemical
xS + hl~,
An
to
the
by a repulsive
out at xsc. the minimum
the conformational
this in terms of the surface
more
decreases.
contribution
is balanced
comes
to compensate
linear in
charge
transition:
entropy
loss
xsc = xS + hrx -
charge by using the Debye-
one obtains:
(x,+$x-x,)
(19)
can be used to estimate
the critical
good
and
is approximately
of the chain, we have an adsorption/desorption vev(1).
in (extremely)
and weak chain length
polyelectrolyte
the
If that balance
needed
adsorbing
x increases
By making
when
so that
polymers. amount
a negative
arises
negative),
as polymers
more like uncharged above,
13 and fig.
the
often
c S the effective
increasing
behave
As discussed
(and
surface
charge
the chemical
o(O)“’
where
contribution
xS + Xix
the polyelectrolyte
is just
fully desorbed. Of
course,
such
a
balance
between
chemical
interactions
could also occur with small molecules,
will
to a sharp
it lead
interaction effect.
transition.
for the many
It is
sensitive
this
probes
monomers
cooperativity of
This
the
which
makes
interactions
that
electrical
but only for polymers
is because
in a chain
and
the
leads that
each
same
polymers of
segment
to a cooperative their
are
very
monomers
experiences. Weak
nolvelectrolvtes It is possible
by including now
becomes
degree
to extend
a degree
following
relation
polyelectrolyte
of dissociation
va(z)e~(z),
of dissociation
eq. (19) to the case of weak a(z) into the electrical
as in eq. (10). Rewriting
ab in the bulk solution,
for the critical
just desorbs:
surface
a(z)
polyelectrolytes energy,
which
in terms
of the
Evers et al.22) derived
charge
~$0)~~ where
the
the weak
505
(xs+~lmc)
O(“)cr =Kcab+(l-ab)
(20)
(X,+h,X-&)
la5*
Numerical
results
for the adsorption
of a weak
polyelectrolyte
(pK = 4) as a function of o(O) obtained by Evers et al.221 are shown in fig. 14. The adsorption is indeed linear in o(O), with a slope that decreases if the polyelectrolyte molecules,
charge becomes less. For sufficiently charged macro-
there is a clear adsorption/desorption
transition
at o(O)Cr
which shifts towards more negative values as the negative polymer charge decreases. It is found that o(0)Cr as it comes out of the numerical results is well described by eq. (20).
a uncharged 0.5 -
1
2
3
4
5
6
PH
7
I3
Figure 15. Degree of dissociation a( 1) on the surface and ab in solution for a weak polyacid. as a function of pH3). The quantity all) was computed for three surface charge densities o(O). Parameters: c, = 0.1 M. pK = 5, other parameters as in fig. 13.
That the distinction between a(l) and oh is not meaningless is borne out by fig. 15 where a(11 is plotted as a function of pH for three values of surface
charge
density
a(O). For comparison,
ab is also shown. At
506
pH > 4.5, dissociation to the high density significantly expulsion adjusts a(l)
at the surface of segments.
enhance
the
is less than in the bulk solution,
However,
dissociation
of H+ from the surface
region.
itself such as to effectively
a strongly at low
due
The local degree
neutralize
surface
to the
can
strong
of dissociation
the surface charge:
at low pH
is higher than ab, the more so as o(O) increases.
2
4
Figure 16. Adsorbed amount of a weak polyacid as a function of pH for three fixed surface charges3). Parameters as in fig. 15.
8
6 PH
The amount has
effect
of the
is shown
positive
charge. of the
polymer
and
adsorption
chemical small
Three
we
surface
neutral. affinity
the
same
its adsorption adsorbing
amount
with
have
trends At
carries
to three different
as in fig. surface
increasing
charged 13: a low
charge
pH < 2 the
segments
competition
effects
driven by the
have to compete
Therefore surface
attraction
were
segments
already
between
a is
with
we now see a charge:
to find
discussed
as the towards
a place
to
in section
2.
the salt ions and the surface
this effect.
on positively
part of fig. 16 is at intermediate charged
below the pK of the dissociating as
for polymer
and
polymer
goes up, more and more small ions are attracted it harder
i.e. it
a constant
a strongly
is now entirely
charged.
adsorbed
is again weak,
surface
to the
Therefore,
is highly
on the
corresponding
proportional
the surface
enhance
understood
density
pH > 6, we
conformation.
The most interesting adsorption
At
to see
We may add that specific will further
are shown,
xs. However,
making
Similar
The
polymer
in adsorbed charge
charge
charge.
charge.
is nearly
flat
the surface, adsorb.
curves
expect
which
ions when
decrease
(negative)
surface
corresponding essentially
polyelectrolyte
in fig. 16. Here the polyelectrolyte
a pH-dependent
values
be
positive
pH,
due
follows.
As
surfaces
has a maximum
group of the polymer. the
chain
acquires
pH. Here the at a pH slightly
This maximum some
charge,
can the
507
attraction
to the surface is no longer purely chemical.
An additional
electrostatic contribution builds up, so that the adsorption is enhanced. Moreover, the polyelectrolyte
can now compete more efficiently with the
small ions in neutralizing the surface charge. Soon, however, the lateral repulsion
between
charges
on the chain reverses
the trend and the
adsorption decreases strongly until the charge on the polymer reaches it maximum value.
2
3
4
5
6
7
8
as in fig. parameters
15.
PH
If the pH is increased from 4 to 6. major structural changes occur as one would expect: strong reductions in size and mass of tails and loops and a concomitant increase in train fraction with increasing pH (fig. 17). The trends displayed in fig. 17 are easily understood from the discussion given above:
flat adsorbed
conformation
at low pH where the polymer is only weakly charged. The
chains at high pH and a more extended
transition occurs around or just below the pK, and coincides more or less with the maximum in fig. 16.
508
5 Polyelectrolyte adsorption experiments a)
Introductory In this
section
electrolytes
with
comparison have
remarks
particular,
this
means
will
largely
polymers
like
electrolytes predicts
that
every
exclude
we
will
monomer results
true
section.
systems
which
on
with
with
it should
properties,
versa.
an ionizable
simple,
strongly
referring obvious
group.
with
branched either
be emphasized
In
flexible
oligomers,
and with copolymers,
It is not always
essentially
or vice
concentrate carries
poly-
For this
unit
DNA,
Finally,
equilibrium
free energy.
for adsorbed
of the model
obtained
(double-stranded)
(proteins).
select
as those
like polyethyleneimine
or biological lowest
where
data
in the preceding
we must
characteristics
homopolymers
experimental
discussed
to be meaningful
the same
This
we compare
the theory
stiff poly-
synthetic
that the theory
to the
(stable)
that real systems
state
of
can reach
this state and, if they do, how rapidly this occurs. We might even suspect that
a polyelectrolyte
metastable
has
a good
chance
to be strongly
trapped
in a
state by many strong ionic bonds. We will return to this point
at the end of this section.
In fact, with proteins
(section
6) this feature
is
even more salient. The
adsorption
described
by
experimental
of simple,
no
more
parameters.
number
of techniques.
internal
degrees
addressed. accepted when
The
and
of long
contributions
when range
that
The normal The
masses however, the
of multiple
structure
conditions
is usually mass
as
are readily have
question
already
measured
so large leads
of by a
a number
of structure
anchoring
well
a function
must
of be
to the generally-
which leaves room for a lot of variation
(and polymer
the repulsion
between
(as in polyelectrolytes),
primary
structure)
monomer
units
a flat
structure
from loops and tails is most favourable,
of zero net monomer/monomer formation
molecules adsorbed
Adsorbed
possibility
experimental
For example,
the
Polymers,
of freedom
‘loop-train-tail’
small
than
interaction
with
whereas
(polymer
change.
is very strong minor
in the case
in a O-solvent)
the
of long loops and tails is much more likely. averaged
spatial
to the interface
shape
scatteringsz)
of
this
distribution
is usually
profile
has
of monomer
called been
units
the segment studied
and. for some cases, by neutron33)
by
(or segments)
density means
proillesr). of
neutron
or X-ray reflection34).
An
509
alternative is to study the thickness of the adsorbed layer, operationally defined
in terms of a particular
optical
techniques
escence3611, hydrodynamic sedimentation and pores, (surface
experiment.
(reflectometry 351, total
We mention internal
the use of
reflection
techniques 311 (determination
fluor-
of diffusion or
coefficients of colloidal particles, flow through capillaries electrokinetics),
force
balance,
and
‘disjoining
osmotic
pressure
pressure’
techniques311
of concentrated
colloidal
dispersions). It may be added that when people speak of the “average thickness” of an adsorbed polymer layer, they are referring to a quantity that is not unique in the sense that different types of experiment produce different “thicknesses”. In particular by hydrodynamic and electrokinetic techniques a “hydrodynamic thickness” is measured, determined by extended loops
and
tails.
“ellipsometric
This
thickness
thickness”
which
is usually reacts
much
on the
higher
index
than
the
of refraction
difference between polymer and solution and hence essentially reflects the inner parts of the adsorbates. b) Adsorption
of strong polyelectrolytes
1.0 h...
0.15 74 0.5
0
1
kg/ml M
v,
NoCl
2
3
4
780
:.. Sta.*
kg/
mol
5
dhm)
Figure 18. Segment densityprofilesfor poIystyrenesulphonateof two diiIerentmolecular weightson positively ifuUcurves)and negativeIy(dottedcurves)chargedpolystyrenelatex as obtainedby smalIangleneutronscattering37). A suitable model polyelectrolyte
is polystyrene
sulphonate
(PSS). It
contains strong negative sulphonate groups. It can be prepared from anionically defined Segment
polymerized narrow density
styrene
fractions profiles
negative polystyrene
and is commercially
over a large
range
for PSS adsorbed
available
of molecular
both on positive
in wellweights. and on
latex particles were measured by means of small
510
angle neutron is confined
scatterings71. These profiles show that most of the polymer
in a thin layer, even at moderate
trends shown in this figure are consistent computations,
ionic strength (fig. 18). The
with those predicted by model
see fig. 12. At the salt concentrations
used in the experi-
ment, the minima in the theoretical profiles are insignificant
or absent.
Figure 19. Adsorbed amount of polystyrene sulphonate of three different molecular weights as a function of the square root of the concentration NaCI. The adsorbent is po~yo~ethylene3s~ [full curves) or silica at pH 23g) (dashed curve).
When PSS is adsorbed the lateral interactions Such
systems
on (almost) uncharged
were studied
by Papenhuyzen
crystals of polyowethylene who
adsorbed
uncharged.
PSS on silica
Both authors
et al.381 who used single
at pH 2, where
amounts
concentration
(fig. 19). curves for
this
find that the adsorption
the adsorbed
curve
the effects of
(POM) as the substrate, and by Marra et al.39)
manner with ionic strength, the extent depending
theoretical
surfaces,
in the polymer layer show up in their purest form.
oxide
is virtually
increases
in a regular
on molecular
weight. If
I- are plotted against the square root of the salt are obtained
o(0) = 0 in fig.
is negligible
whereas
that are very similar to the
13. In the
at high
absence
electrolyte,
f
experimental
error, linearly with &,. The slope of the linear parts at high
es increases
with increasing
molecular
weight:
longer loops and tails (when the electrostatic Papenhuyzen
cs it increases,
of added
long chains
interactions
et al.381 have shown that the molecular
is well predicted
by the model. For a further discussion
within can form
are screened).
weight dependence of this aspect we
refer to figures 24 and 25, below. The very fact that adsorption must be due to a non-zero
does occur on these uncharged
chemical
adsorption
surfaces
energy (xs). The resuhs
obtained
with SiO2 (pH 2) and POM are very similar, from which we
deduce that xs is nearly the same for both substrates.
I0 mm-’ r c
0.5 -L--
/’
P
.A
/exp-
.@--
_-‘)A
0.5
AI
_A’
t 1
-rM
them ,A .--
,
I
1F3
mm*
I
10
10-l M
c*
Figure 20. Comparison between experimental adsorbed amount I? (in mg mW2) for polylysine on negatively charged Agl and theoretical amount 9; (in equivalent monolayers), as a function of the salt concentration2** *O). The polylysine (307 amino acid residues) was adsorbed from NaBr-solutions at pH = 6 and pAg = 11. The parameters used in the model are: r = 300, Qi = 10T4, up = 0.71, o(0) = 0.2 e/a, with a, = 0.3 nm , B= 4.85,~=0.6,e=8Oc, iraIl cubic lattice components, Go = 4/6).
Another interesting model polyelectrolyte is polylysine (PL), which is a polybase that can also be obtained in relatively well-defined with a narrow molecular
weight distribution.
The intrinsic
fractions pK of the
primary amine group (- 10.8) is such that the molecule is fully positively charged up to pH-values of about 8. The L-stereoisomer
(poly-L-lysine)
can develop a helical secondary structure but only at pH 2 10.5. Helices are not found with the racemic random poly-Dllysine. homopolyaminoacids.
polylysine
becomes
The
very
small,
becomes
adsorption
insoluble
of PL onto
Just like most when
the charge
silver-iodide
(AgI)
crystals20.401and onto silica and glass 411has been carefully studied by Van der Schee et al.201and Bonekamp et al. 4o+*ll, respectively. Both poly-L and poly-Dllysine relevant enhanced
were used but significant differences were not found in the
pH range
(2 8). As with the neutral
by the addition
surfaces,
of salt in the case of Agl
adsorption
is
(fig. 20). For
comparison, theoretical curves computed by Van der Schee et al. are also shown in fig. 20, with a log~i~mic
scale for es; the agreement is semi-
quantitative. In the case of silica, however, there is only a minor salt effect with a weak maximum around 10-l-10-2 M, rather than a
monotonous
increase (fig. 21). This is probably due to specific adsorption of (sodium) counterions on the silica, which compete for surface sites with the iysine residues, We then have two opposing tendencies: (if increased screening of lateral
interactions,
leading
to enhanced
adsorption:
(ii) increased
screening of attractive polymer surface interactions, leading to a weaker
512
binding that
the
polymer
of polymer.
Since
outcome
depends
the latter on the
and the substrate.
I
0.0 -
is a specific
chemical
In order to model
one would have to assign a chemical
1
effect
adsorption
I
natures
one, we expect of the
these results
salt,
the
theoretically,
energy to the small ion.
I’
mg m-2
A-&
lA
7.51 c.3
/
0.6 -
Ol.-
O---L
/
0
\
0
clz-
o----c
0
10-3
I.0 10-2
10-lM 0
c. Figure 21. Effect of the NaCl concentration on the adsorption of polylysine (307 amino acid resfdues) on silica [Aerosil 0x50). at three different pH values41).
(0)
Figure 22. Adsorption of polylysine (190 amino acid residues) on silica (Aerosol 0x50) from 0.01 M NaBr. as a function of the surface charge4f).
Figure 23. Adsorption of pofyacryhc acid (M = 2000 kg/mol) on hematite as a function of the surface charge, in the presence of 1 mM NaC104. The data were computed22) from the ex ertments of Gebhardt and Fuerstenau42 P The surface charge of hematite has been measured by potentiometrtc titration in the absence of polyacrylic acid.
The effects respectively. substrate
of the surface
charge
that can carry an appreciable
the polymer.
can be seen from figs. 22 and 23,
The data in fig. 22 are for polylysine Charge
force for adsorption.
compensation
charge
adsorbed
of opposite
is thus an additional,
onto silica,
a
sign to that of strong
driving
This is borne out by the results, which show that the
513
adsorbed amount at relatively low ionic strength (lea-lo-2 entirely electrostatically
M) is nearly
determined. Similar conclusions were drawn by
Evers et al.22) from data provided by Gebhardt and Fuerstenat@i,
for
polyacrylic acid adsorbed on hematite (fig. 23). The curves of figs. 22 and 23 display the linear behaviour predicted by the model calculations
(fig.
14) and show that the agreement between theory and experiment is quite satisfactory. The extrapolation of the linear section of fig. 22 to I = 0 gives a positive value for the critical surface charge density o(0)Cr, compare eq. (19). This points to a non-zero chemical component
to the adsorption
energy. A similar conclusion applies to fig. 23, where the charge signs are opposite.
r
6050-
Figure 24. Adsorption of polystyrene sulphonate on polyoqnnethylene crystals, as a function of molecular weight. at three NaCl concentrations38). M (kg/mole)
The effect of molecular weight M on the adsorption of PSS on POM and on silica, respectively,
is shown in figs. 24 and 25. At low ionic
strength the adsorbed molecules adopt very flat conformations and there is nearly no molecular weight dependence. As the ionic strength goes up, the slope of the F versus
log M curve increases
as well. This is in
agreement with the discussion given in section 3 (after fig. 13) about the influence
of salt on the overall (effective)
concluded
that the negative electrostatic
the solvent molecular
poorer with increasing
weight dependence
X-parameter.
contribution
There
it was
effectively makes
cs. For uncharged
polymers,
the
of P increases with increasing x. In poor
solvents F continues to increase with M as the chains become longer, but in good solvents F(M) reaches a plateau at high M. For PSS, we do not find such a plateau. Apparently, water is a rather poor solvent for PSS
514
when
the
charge
on
the
polymer
is strongly
screened
by
a high
salt
concentration.
M f kglmole)
Figure 25. Molecular weight dependence for the adsorption of polystyrene sulphonate on activated Cab-0-Sil. at pH 2 and various concentrations of NaCl (a) and MgCl,(b)3g). In the taken,
original
an attempt
weight dependence
paper@. was
39) from which
figures
24
made to compare quantitatively
of r with theoretical
computations.
and
25 were
the molecular These authors
used an early version of the polyelectrolyte adsorption theory, based upon an extension
of the Roe-theory431 instead
Scheutjens-Fleer
of the more sophisticated
mode12s-30). They concluded that the agreement was
satisfactory,
but that their model predicts too weak a molecular weight
dependence
at high M. This is probably due to an artefact in the Roe-
theory, where tails are neglected. It is very likely that a better agreement between theory and experiment would be obtained if the conformational statistics
are better accounted
for, e.g., by using the Seheutjens-Fleer model. So far, such a full analysis has not been made.
515
/ k
60~x10‘5monomole
6Oc
50
40
30
/g
/
0’
.P’O 4%
/
A0
_l-n
0
31
Figure 26. Adsorption isotherms of polystyrene sulphonate on polyoxymethylene crystals from 2.18 M NaCl. for three different molecular wetghts381. 200
100
Qk
may be concluded
It
experimental
trends
neutral
substrates
to what
adsorbing more
indicated effects
is
availabless).
macromolecules interpenetrate. have
rounded
could
adsorb
in mutually
shape. The mean-field
those
theory,
are these
for well-fractionated
(by chain some
explanation degradation)
evidence
is that ‘blobs’
the
adsorbed
which
to adsorption
of monomers,
than
for such
inhomogeneous:
repelling
that this leads with
on the
of sulphonation)
strongly
the
However,
isotherms
One possible
suggestion44)
expect
in common
degree
of the supplier:
laterally
is
One might more
than is common substrates.
Another
layer
adsorption
by the mean-field
(as to the
by the specifications
theory.
of PSS adsorption
are less homodisperse
heterogeneous
polyelectrolyte
which
is predicted
that in general
by recent
feature
in fig. 26, where
on well-defined
is that the PSS samples
examples
described
are much more ‘rounded’
polymers and/or
the above
One unexplained
is shown
In contrast
isotherms
from
are excellently
there is one exception. given.
3@l PPm
the do not
isotherms
i.e.,
a more
theory is of course unable to take this into
account. c) Adsorption
of weak polyelectrolytes
One
known
of the best
acid (PAA). It is a simple
model
polyacid,
weak
polyelectrolytes
with an intrinsic
is polyacrylic
dissociation
constant
516
K of pK = 4.6. Therefore, and almost side
chains,
so that
precipitation) candidate
at low charge charge.
(--NR:)
independent, polymer
densities
such
between
which
groups
surface
a suitable
on the effects
carried
to have
so that
show up most clearly.
(or even
It is therefore
concentrates
zero
of
out by Blaakmeer
(PS) lances with fully dissociating
in order charge,
virtually
no hydrophobic
as hypercoiling
are absent.
study
used polystyrene
surface
positive
charge
effects
Such a study was recently
These authors
positive
is variable
pH range. Also it contains
complicating
for a fundamental
the polymer et alas).
its dissociation
100% in a suitable
a constant,
the effects
We denote
i.e..
pH
of a variable
this positively
charged
latex as PS+.
- O.Wl
[KNOJ
M
zoappm IPW
In
section
adsorbing
on
intersect might
a negative the same
indeed
near to the plateau adsorption
model
affect
As
taken
the surface
to happen
adsorption
isotherms
at different
ionic
plus adsorbate
two adsorption
of the isotherm
which
a consequence,
isotherms
adsorbed
which
show a similar amount.
equilibrium
concentration.
The
that in the saturated
polydisperse
nature of the PAA used.
point
it is situated
difference
We
for PAA on PS+
but only by a very
experimentally
intersection
However,
strengths,
on a positive
by indifferent
is indeed
A+
point. This point is very
implies
screening
for
is isoelectric.
with poly A- adsorbing
seem to have an intersection
I only slightly,
calculations
(relative)
that
layer the surface charge is overcompensated,
amount.
should
saw
surface,
In fig. 27 we present
latex which
small
10) we
at the point where
expect
surface.
3 (fig.
(+160 mC/m2) at pH = 4.045).
at about
electrolyte found.
the same
at a much
is probably
The
related
lower to the
517
Above
we found
polyelectrolyte polyelectrolytes can
adjust
effectively complex
that
adsorption (figs.
their
the salt
dependence
13, 19 and 20). The reason
degree
of dissociation
the surface charge is nearly
concentration
is only weak, and much smaller
neutral.
such
for weak
than for strong
is that the weak groups as to compensate
more
(fig. 15). As a result, the substrate-adsorbate In the overall
balance
of all the interactions,
salt then has only a minor effect.
Jo
0
2
4
6
8
Figure 28. Comparison of the experimental adsorbed amount r (In mg/m*. left-hand scale) for a weak polyacid with the theoretical 0: (in equivalent monolayers. right-hand scale). as a function of PHIL). The experimental points are for polyacrylic acid (71 kg/mol) onto a cationic latex with ~(01 = 160 mC/m2 at an equilibrium concentration of 100 ppm in lo- 1 M KNOX. The full curve was computed with the model of Bdhmer et a1..3) using $I; = 104. pK = 4.25, o(O) = 160 mC/m2, cs = 0.1 M. L =0.6nm. r=500, x:=2, andX=0,5forthe polymer-solvent and polymerion interaction. The other xS and X-parameters are zero, and E = 80 ~0 except Ed which is 20 ~0.
10
w
The central fig.
28, where
function
and most striking the
adsorbed
of pH, at constant
there is a clear maximum
of Blaakmeer’s
result
amount
of PAA
ionic strength
onto
work is given in
PS+ is plotted
(10-l M KNOa).
It is seen that
at a pH below pK. Such a maximum
had been
predicted
four years earlier by Evers et al.22) and later by Bijhmer
see
16. A
fig.
maximum is given
qualitative
in fig. 28, where
Stem-model.
The agreement
the experimental one. Nevertheless, observation positively
explanation
was given in the discussion the curve
occurrence
was calculated
is about
Blaakmeer’s
of this interesting
system both polymer
the
study provides
TiO246) the effect
although
one pH-unit
pattern.
below
a
comparison
the multilayer the position
of
the theoretical
the first well-documented
In studies
was never
with
et al.3).
of such
of fig. 16. A quantitative
is quite satisfactory,
maximum
charged
for
as a
of PAA adsorption
discovered
and surface have a pH dependent
since
charge.
on
in that
518
d) Metastable
states
It has been noted more than once polyelectrolytes
do not necessarily
surrounding adsorbed
solution.
amount
For
changes
in surface
PL/AgI
system.
polyelectrolytes strong
macromolecules conditions finally
More
study
increasing
of
and not by chain
attachment
polymer/surface
is more
adsorbed
at pH
relaxation
processes
extremely
slow;
for
this
consistent et also)
3 onto
is
determined with
the
data.
for the adsorption
a carboxylic
in adsorbed
PS latex
polyelectrolyte
in the case studied
surface.
it was
by
the
provided found
by a
that
but decreased
would
predict
the
by
with
the
‘frozen’
conditions
Studies
the very
that the
determined
during
of adsorption
of polyvinyl-4-pyridine provide layers
they found
The
than by those
of molecules by
between
dictated was
entirely
A picture
that
by the
be sufficiently
rather
on coverage,
contacts
than
on the
viewpoint
Theory
rather observed
formed
conformations
in the that the
followed
might
processes
weight.
length.
positions
by Pefferkom
bonds
surface
et a1.49). where
molecular
and
reversibly
ionic
did not depend
coverage
kinetics
that
charged
have
evidence
number
conformations
route taken,
they first touch the surface
by Denoyel
of adsorption
with
not entirely
relaxation
then
to changes
Also Van der Schee4s)
seem
inhibit
would
imposed.
calorimetric much
would
under which
enthalpy
were
with adsorbed
et a1.47) found
on the experimental
and an oppositely
to efficiently
reversibly
Meadows
conditions.
charge
It
respond
example,
depends
on the final experimental
that systems
47. 48)
evidence
do occur,
a relaxation
that
but are
time
of 37
hours. We may conclude experimental should
results
be aware
from this that it is always with
equilibrium
theories,
of the fact that relaxation
very useful but when
to compare
doing
times may be widely
so one different
from one case to the next and that experimental
time scales
be chosen
in the first part of this
section found
accordingly.
illustrate
that it is perfectly
in experiment
very well.
The examples and those
discussed possible
obtained
to do so since
with equilibrium
may have to the trends
theories
agree
519
e) Adsorption
of polyampholytes
So far we have dealt exclusively with simple polyelectrolytes
which
carry only one kind of charged group. Restricting ourselves to this kind of system helped us understand the role of electrostatic interactions in the adsorption
of such macromolecules.
Proteins constitute a group of with at least two new complicating factors: (i)
charged macromolecules
they have important intramolecular attractions which give the molecule a certain
degree
of rigidity,
(ii) they carry both positive
charges, i.e., they are polyampholytes. between
simple polyelectrolytes
and negative
In an attempt to reduce the gap
and proteins we discuss here another
interesting
study carried out by Blaakmeer
ampholytic
polyaminoacids
were adsorbed
et a1.511, where onto PS latices.
synthetic both with
positive (PS+) and negative (PS-) surface groups.
r 0.4
-
.n’”
.2-w R \
0.2 -
a; ‘9
0
2
4
6
8
m
10
Figure 29. The adsorbed amount of the oligomer (Lys-Glu-GlyI4 onto negatively charged latex (-25 mC/m2) as a function of the pH. at an equilibrium concentration of 200 ppm51). The ionic strength (KC1 + HCl or KC1 + NaOH) was 0.1 M.
As polyampholytes, copolymers of glutamic acid and lysine were used. One polymer was a random copolymer of 60% glutamic acid and 40% lysine, with a molecular weight of about 20 kg/mol. The other adsorptive was a specially synthesized tetramer of L-lysyl-L-glutamyl-glycine, homodisperse
i.e., a
oligomer with twelve amino acid residues, of which four
carried a carboxylic
and four an amino group. This oligomer
(with an
isoionic point at 8.4) is soluble in water at any pH between 1 and 12, but the random copolymer appeared to be insoluble between pH 4.1 and 5.7, i.e., around its isoelectric point (iep) which is at pH = 4.9. If electrostatic effects would play the dominant
role one might expect
adsorption behaviour for the polyampholyte.
the following
At the negative side of the
i.e.p. adsorption onto PS+ would be preferred, whereas the reverse would
520
occur on PS-. However, both
sides
adsorbed
since the absolute
of the iep, lateral amount
becomes
less
adsorbed
amount
on each
repulsion side, just
at a pH where
it is highly
polymer
and surface
range
where
about
the same for the negatively
they attract
should
dictate
as P for
Hence
decrease
of the
polyelectrolyte a maximum
in the pH range
repel each other, and a minor decrease would
be more
a lowering
a weak
charged.
at or near the iep, a strong
where
pattern
value of the charge goes up on would
be the pattern
expected.
and positively
or less symmetrical
If xs would
charged
with
in the
segments,
respect
be that
to reversal
of
the surface charge. The adsorption
of the oligomer
onto PS- follows
(fig. 29) and the data for the random pH 9.7, respectively, to anticipate maxima
complex.
against
proteins
usually
to the iep of the protein
In this case, the explanation molecule
trend
at low pH and at
that for flexible
at a pH corresponding
of the protein
the expected
taken
with it (fig. 30). It is interesting
6 by mentioning
are also found
resilience
1 6 -
are also consistent
section
plus adsorbent
copolymer
involves
conformational
the internal
changes,
mg mm2 /
P!?
I-
Figure 30. The adsorbed amount of a Lys-Glu polypeptide onto negatively (-25 mC/m2) and positively (+90 mC/m2) charged latex as a function of the pH. at an equilibrium concentration of 200 ppm in 0.1 M KC151). The polypeptide (20 kg/mole) was a random copolymer of 40 mol % glutamic acid and 60 mole % lysine. It is insoluble in water around pH 5.
I I
&
\ \
q
w 08-
ps+ . T_A-
I ,I
I
a
\ \-*
.
.,.,..A
:
AA. 4
0
a
12
w
However, is lower even
at pH 7 the adsorbed
on PS+,
regions.
and -NRg difference
despite
Clearly,
adsorption. between
amount
of the polyampholyte
than on PS-, and at pH > 11 the adsorption the negative
As a possible
-SO,
and -NH;
explanation
is found effect
electric
charge
stronger
is considered
the ionic
Evidence
experimentsdl).
to be chemical
pH-
drives
than that between
size of the latter cation.
in conductometric
that
on PS+ or absent
in these
field which
we suggest
is perhaps
due to the larger
nonelectrostatic
polyampholyte
it is not only the overall
is small
the
bond -COO-
for such a
Of course
this
in our terminology,
521
corresponding
to a different xs. Another contributing
factor might be a
strong competition by the OH--anion for surface sites, especially at high pH. The matter is, however, not yet completely understood: certain asymmetry
in solution
properties
point also plays a role. Such assymmetry
with respect
perhaps a
to the isoionic
does indeed show up in the
viscosity of the copolymer solution. The study discussed above is only a first, but promising, step towards a better
understanding
polyampholytes.
of the interfacial
behaviour
The gap between simple polyampholytes
of
(synthetic)
and proteins is
still very great and statistical theories have so far not been invoked to interpret protein adsorption. The main reason is the difficulty of handling the multitude of specific internal interactions, some of them persisting in off-equilibrium
states. We shall therefore discuss proteins at interfaces
mainly from an experimental point of view. 6 Protein adsorption a) Introductory Proteins
remarks
are copolymers
containing
some twenty different
amino acid
monomers. The amino acids are linked to each other in a polypeptide chain, as illustrated in fig. 31. Two of the three bonds in the peptide unit are free to rotate, whereas the C-N bond is fixed because of its partial double bond character. The side groups R, R’, . .. are positioned in the trans configuration, so that rotation around the bonds in the main chain is minimally
hindered.
Furthermore, negatively
The side groups
vary greatly
some of the side groups charged,
so
that
the
in hydrophobicity.
are positively
protein
and others are
molecule
is
a
complex
polyampholyte. As compared
to synthetic
polyelectrolytes,
globular
aqueous environment adopt a compact three-dimensional
proteins
in
structure. This
structure is determined by various types of interaction occurring inside the protein aqueous
molecule,
environment.
but also between
the protein
The main structure-determining
molecule
and its
factors are: (i)
dehydration of hydrophobic side groups, which favours the formation of a compact structure, and (ii) the tendency to maximize the conformational
522
Figure 31. Structure of a peptideunit in a polypeptide chain. Rotation is possible around two of the three bonds, the middle C-N bond is fixed in the trans configuration. of the
entropy internal other
structures minor,
globular The
Gibbs
per
including
amino
acid
residue reasons
of the external
conditions,
In
investigating
metastable
structures,
considered.
All told,
the synthetic
of the
native
this
protein in many
ways
structure
the
that
proteins
discussed
are more
surfaces. sight
of proteins from the
from
of the different
data
aqueous
sides,
determined
by: (il changes
the protein
molecule,
the sorbent
surface,
seem between
sections,
which
protein
proteins
be
than and so
ions),
molecules.
a variety the
techniques.
of solid
relative
at
generally is mainly
surface
and
the protein
and
of charged
and (iii) structure
was
Although
it is now
between
of the
problem
and interfaces
a redistribution The
studies
of the adsorbent
interactions
involves
weight
onto system
conflicting,
in the hydration
(ii) Coulomb
low molecular
adsorbing
of the
using various
sometimes
that the interaction
(including
always
complicated
in the previous
solution
complexity
established
in the
of freezing
behaviour.
In view
approached first
purely
being one of
must
Over the past fifteen years there have been numerous adsorption
for
1 kT
by alteration
possibility state,
the
of a few
less than
of an adsorbent stable
native stable.
(taking
in the range
is so low
adsorption,
off the absolutely
the
marginally
can be easily changed
the introduction
of
and some
that
with much
amount
formation
These,
reason
is typically
conformations
polyelectrolytes
is their adsorption
the
This corresponds
and
thermodynamic them.
are
as the reference)
of protein.
the
thermodynamically
of stabilization
structure per gram
is usually
counteracts and P-sheets.
a-helices
contributions
structure
energy
which
molecule,
opposing
protein
unfolded Joules
protein
groups
rearrangements
importance
of these
523
contributions obviously depends on the nature of the system and in some systems
specific
attraction
may occur. Special
attention
deserve
the
structural alterations because this is a typical protein feature. Their Gibbs energy change ApsG (where the subscript ps stands for protein structure) is positive, because otherwise the molecule would spontaneously
pass
from its native state to another one. However, the rise in entropy (TAP&S) due to the enhanced randomization
to a large extent compensates
the
unfavourable ApsH due to structure breakdown, hence ApsG may be small and can then easily be surmounted by factors (i) or (ii). The occurrence of such conformational
changes
adsorption
of structurally
behaviour
allows
us to differentiate “soft” molecules
“rigid” ones (ApsG large). In comparison
between
(ApsG small) and
with polyampholytes
feature is that for soft proteins part of the three-dimensional can break
down, which
gives rise to an increase
the
the new structure
in conformational
entropy: rigid molecules rather behave like bulky monomers. Below some general features of protein adsorption will be discussed, after
which
the
various
observations
will
be
integrated
into
a
thermodynamic analysis. b) Adsorbed amount As for most polymers, protein adsorption isotherms more often than not show a high affinity character, i.e., the initial part of the isotherm coincides with the f-axis,
after which a (pseudo-)plateau
is reached.
However, protein adsorption isotherms having a finite initial slope are not rarities. When the adsorption isotherm is not of the high affinity type, the corresponding character.
desorption
isotherm
With polydisperse
usually
polymers
does show a high affinity
such irreversibility
has been
explained by the adsorption preference of the larger moleculessal. Upon increasing
the polymer
concentration
in solution,
the high molecular
weight fraction in the adsorbed layer becomes gradually enriched. If, after establishment molecules
of equilibrium,
the system
is diluted,
remain at the surface until concentrations
reached which are below the limit of detectability.
the adsorbed in solution
are
With proteins that
tend to aggregate in solution preferential adsorption of such aggregates over monomers has been founds3, s4. 55). which can explain the hysteresis. However, also in homodisperse protein systems real hysteresis has been observedss. 57). It implies that the adsorbing protein molecule differs from
524
the
desorbing
desorbed before
one;
protein
more
molecule
adsorption.
other
sources,
This
to
creation
of entropy58).
content%
is more
increase
for instance
system
induce
the findings
specifically,
by acid,
Thus
the
positive
of Gibbs
than
base
that
the
protein
be supplied added
by
to the
hysteresis
of hysteresis
implies
is in line with
secondary
a larger conformational
will return to this point in subsection
of the
of the
must
have a decreased
5% 60,611 and, consequently,
energy
or electrolyte,
the occurrence
proteins
Gibbs
energy
Furthermore,
desorption.
that desorbed
that
structure
entropy. We
d.
Figure 32. of the therms
Plateau values
adsorption isoas a function of
pH, for human serum albumin from 0.05 M
electrolyte solution on various surfaces: positive and negative polystyrene latex (PS), neutral polvoxymethylene cry&is (POM). negative silica (SiOz) and positive hematite (a-Fez@) 68. 85).
l-
0
n
I
”
4
I
I
I
I
I
5
6
7
6
9 PH
As
a rule,
plateaus. value
protein
For many proteins
at the isoelectric
32 such
adsorption
Tmax(pH)
isotherms
curves
for serum
It must
area of the adsorbent
be realized
electrostatic
material
in
the
repulsion both
hydrophobicity,
with
protein
between such
the specific uncertainty
collected
charged ample
to
their
of the
On the other
spontaneously
with
protein,
hand, the
evidence
that
than
molecules.
to
All
charge
curves
rather
the structural
(PS) the
than
are very
density
are strongly
and
affected
by protein-sorbent
alterations
native
lateral
Tmax(pH)
As the adsorbents surface
dissolved
polystyrene
point is due to structural rather
adsorbed
a maximum.
respect
are
regarding
molecule the
In fig.
surfaces
leads to a proportional
it is clear that the r ma(pH)
characteristics
interactions. place
on various
on negatively
al.67. 6s) ha ve
in fig. 32 show
different, by the
albumin
in l-ma, at either side of the isoelectric
rearrangements curves
et
attain a maximum
complex62-66).
that the uncertainty
in the value for rmax. For albumin Norde
Imz.
these plateau values,
surface
decrease
well-established
point of the protein-sorbent
shown.
surfaces,
develop
protein,
do not take hence
the
525
adsorbate is necessary to induce them. The fact that albumin also adsorbs at the hydrophilic su,rfaces of hematite (a-FeaOs) under
conditions
of electrostatic
repulsion,
and silica ($02).
implies
that very
even little
interaction between albumin and surface suffices to realize this structural change, after which the Gibbs energy of the adsorbed protein is so much lowered that high affinity binding ensues. As this dominant structural change is a protein property, the influence of the nature of the surface is suppressed. 1.5 mg I+ c
r mclr
0.5
PH
33. Plateau values of the adsorption isotherms as a function of pH. for ribonuclease from 0.01 M electrolyte on various surfaces 6g* 70]. For the abbreviattons of the adsorbents see fig. 32. Figure
Another category of proteins shows a different Pmax(pH) patternsas 70). This is illustrated
in fig. 33 for the adsorption
of ribonuclease
different surfaces. At the hydrophobic PS surface Pma(pH) independent
of the charge on the protein molecule
at
is essentially
and of the charge
contrast between the protein and the surface. The plateau values account for a complete monolayer of native molecules. This suggests that no or only minor structural changes in the adsorbing ribonuclease
molecules
occur. The behaviour is in agreement with the relatively strong internal coherence ribonuclease uncharged
of
the does
ribonuclease not adsorb
polyoxymethylene
molecule.
For
the
same
on the less hydrophobic, (POM)
surface,
and
also
reason,
essentially not
on the
hydrophilic surface of a-FezOs. unless it is electrostatically attracted. The relative importance of the contributions
of hydration changes,
Coulomb interaction, and structural rearrangements
for protein adsorp-
526
tion has been systematically studied experimentally by Arai and Norde71). They used a series of proteins that are similar in size and shape, i.e., lysozyme
(LSZ), ribonuclease
(RNase), myoglobin
(MGB), and a-lactal-
bumin (aLA). Unfolding induced by heat721 and by denaturing agents731 reveal that the structural order
LSZ, RNase,
summarized
stability of these
MGB, aLA.
Plateau
in fig. 34. The charge
proteins decreases in the
values
of the isotherms
of the proteins
are
is qualitatively
indicated by plus and minus signs. PS+;
5-_+32mV
PS -; c=-69mV
2 - mg m-2
rmar
r mar;
aLA1 l-
t&B? LsZ++RNase+
aFetOs+;
55+20mv
aFe20, - ; c_-_-47mv
I
Figure 34. Adsorption of lysozyme (LSZ). ribonuclease (RNase), myoglobin (MGB) and alactalbumin (c&A) on hydrophobic polystyrene (PSI and hydrophilic hematitie (a-FezO3) surfaces71). The electrolyte concentration was 0.05 M. An indication of the surface charge is given through the c-potential of the bare surface, and of the protein charge by + and signs.
At the hydrophobic PS surfaces all proteins adsorb. As a trend, the electrostatic interaction between the sorbent and the protein is reflected in Pmax. However, both on positive and negative PS, aLA adsorbs more strongly
than would
be expected
on the basis
of the electrostatic
interaction. This observation is in line with the relatively “soft” nature of this protein. At the hydrophilic a-Fez03
surfaces the adsorption of LSZ
and RNase is dominated by electrostatic interaction but again aLA behaves differently, for the same reason.
527
All of this fits into the picture that proteins that have a high structure stability
behave
as “hard” particles.
Their adsorption
is governed
by
electrostatic interaction and (partial) dehydration of the sorbent and the protein. Proteins having a low structure stability (“soft” proteins) possess an additional driving force for adsorption which is related to structural rearrangements. Consequently, soft proteins may adsorb spontaneously on a hydrophilic surface even under electrostatically unfavourable conditions. In competition from a mixture containing all four proteins, the least stable
aLA
tends
to
adsorb
preferentially74).
It follows
that the
contribution from structural rearrangements is an important factor in the competition,
resulting
in preferential
adsorption
of the “soft” proteins
over the “hard” ones. c) Co-adsorption of small ions
r/r_
Even
though
adsorbing
protein
Figure 35. The change of the electrokinetic charge upon adsorption of human plasma albumin onto hematite, as a function of the relative adsorption76). The charge effect results from the transfer of low molecular weight ions between the solution and the adsorbed layer. The electrolyte concentration was 0.01 M.
molecules
may
change
their
structure, they usually form a compact adsorbed layerso). Any ensuing adverse
build-up
of electrostatic
repulsion
can be avoided
by the
incorporation of small ions from solutions7* 75). The ion transfer between the solution and the adsorbed layer can be experimentally comparing
the electrokinetic
estimated by
charge density oek of the protein-covered
sorbent on the one hand and those of the bare sorbent and the dissolved protein
molecules
on the other 67. 70). Figure 35, taken from work by
Koutsoukos et a1.76),shows Aado&, the change of o& upon adsorption, as a function of the relative adsorption T/Fma for human serum albumin on negatively charged a-Fe203. The dependence of Aado& on pH points to an increasing uptake of positive ions with increasing negative charge on the protein and the sorbent surface. Furthermore, the linear relation between
and PiPmax [for Pifmax > 0.3) indicates
Aado&
adsorbed
protein
incorporated
molecule
is accompanied
that each additionally
by the same amount
of
charge.
Since the co-adsorption of ions reduces the charge antagonism, it is electrostatically
favourable. However, the chemical effect of transferring
low molecular weight ions from the aqueous solution into the non-aqueous protein
layer is unfavourable
and, hence, opposes the overall protein
adsorption process. Indeed, maximum affinity for protein adsorption has been found under circumstances
where the charge of the protein itself
just matches the charge on the sorbent surface75). d) Energy and entropy of protein a~sorp~n The
affinity
of the protein
adsorption
process
is, at constant
temperature T and pressure p, determined by the change in the Gibbs energy G AadG = AadH - TA,,S
(2 1)
or, if written per molecule of protein Aadg = Aadh - TA,os where H is the enthalpy and S the entropy and g, h and s stand for the same
quantities
per
thermodynamically spontaneously
molecule,
For
adsorption
to be
if the energy of activation is low. In the literature many
examples are encountered of extremely
respectively.
possible, AadG should be negative. The process occurs where protein adsorption is treated in terms
simple models. For instance,
various
authors77-s@
have
analyzed the isotherms as if obeying Langmuir premises, i.e., they assume, either or not tacitly. that the adsorption is reversible, site-bound, and that lateral interaction
and internal structural changes can be disregarded.
Obviously,
all of this is at variance
conclusion
derived from such interpretations,
of values to A,dG,
must be considered
with reality.
Consequently,
any
including the assignment
with suspicion.
For the same
reasons and for lack of definition of the notion “isosteric”, applying the Clausius-Clapeyron
equation
in order to analyze the influence
of the
temperature on the adsorbed amount is questionable. Yet, whatever the adsorption mechanism, Le Chatelier’s principle remains valid: the positive value for X/X
for the adsorption
of serum albumin on PS surfaces,
529
measured
at constant
protein
concentration
therms,
implies
an endothermic
sorbent
systems
AadH was determined
71. 76).
process,
It was found that this quantity
adsorption
is driven by entropy
In their thermodynamic and ribonuclease unravelled
determined
(which involves ments
sorbent
conditions
high
above,
groups
and rearrangeIn some
that TAadS should also be positive
and that,
the
TAP&S is one contribution
from hydrophobic
of charged
contribution),
force.
changes
enthalpy
subprocesses:
in hydration).
as to be the sole driving
derives
of serumalbumin
adsorption
redistribution
(including
at least under the given conditions, stated
overall
and a chemical
structure
AadH > 0, implying
67.
that the
Norde and Lyklemasl)
from the most important
surface,
an electrical
in the protein
confirming
of the adsorption
charged PS surfaces,
calorimetrically
of the
protein-
by microcalorimetry5s.
increase.
AadH in terms of its contributions dehydration
Aa,jH > 0. For various
directly
is often positive,
analysis
on negatively
the
in the initial parts of the iso-
process
One other
dehydration
is entropically
to T&S,
driven. As
but it can never be so important
of the surfaces,
entropic
term
but there are more
contributions. The
Gibbs
substance
energy
may
model substance) Gibbs
involved
be estimated between
energy
of dehydration For instance,
PS surface the estimatessl) AdhH = -1.4 25W).
Taking
becomes
firmly
more
are A&G
effect -TAdhS = -15.4 an adsorbed Such
at hydrophobic
of hydration
of a
substance
(or a
phase. Obviously,
negative
with
increasing
at 25OC of hydrophobic
mJ m-2 and a small enthalpy
amount
the
= -16.8 mJ m-2, which results from a
mJ m-2 (1 mJ m-2 corresponds
molecule.
of that
for the dehydration
with a molar mass of 50 kg/mol, protein
the state
partitioning
water and a non-aqueous
hydrophobicity. large entropy
in changing from
to about
0.25
of 1.5 mg m-2 for a protein this would
a large
value
surfaces,
even
yield
explains under
-T&hS
why
=
change
kT nm-2 at molecule
-226
kT per
all proteins
unfavourable
adsorb
electrostatic
conditions. The Gibbs energy change groups
contains
an electric
and Agch. respectively. accumulation
of net charge
electrical
depend double
from the redistribution
and a chemical
As ion incorporation
does not attain large values. and A&,
resulting
in the protein Its value
on the composition
(medium) compensates sorbent
of charged
contribution,
AgeI
for unfavourable
contact
region,
Agel
and sign, as well as those for Ahe and the dielectric
layers before and after adsorption.
constants
respectively.
of the
530
The ated
chemical
from
aqueous
model
studies
media.
positive
For
on the transfer
most
spontaneous
the chemical protein
development
contribution An
adsorbed
do not unfold indicates
that
than
potential
way
to non-
quantity
is
solution.
the
of a loose
constant
observation
structure,
effect
avoid
is the formation
The general
chemical
opposes
to
for water and small ions. In
layer the dielectric
the exposure
this
to ion incorporation
into such a loose the
aqueous
ions
alternative
layer, that is freely permeable
to that of the bulk
unfavourable
weight
can be estim-
negative values for both Aheh and Aseh
adsorption.
such a highly hydrated proteins
of ions from
molecular
of a high electrostatic
loopy adsorbed
layer,
low
as a result of compensating
82, 831, so that
close
Ag ch of ion incorporation
contribution
that globular
but form a compact
of ion
of hydrophobic
is relatively
incorporation parts
is less
of the protein
to
water as would occur upon unfolding. Adsorption
involves
a change
this, in turn, may induce the protein, molecule, they
which
are still
stabilized
shielded is
from
secondary
intramolecular
if
structures
of the protein to a reduction for the protein
spectrometry human and
Norde
molecule.
of secondary
SiO2.
method, adsorption, desorption
The which
structural desorbed
reduction
with possible
component.
from the a-helix
that
state corresponds structure.
structural
structure,
i.e.
the subscript
surfaces
ps
dichroism content
of
of a-Fe203
to the desorption
change
up to a certain
a reduction
data811 indeed
on circular
to be insensitive
the
groups
A loss of
conformational
in the a-helix
from the hydrophilic
restructuring
to a random
cause
protein
Based
expanded
side
sheets.
of calorimetric
a reduction
step. The helix breakdown
50% in the adsorbed
and pleated
ApsG < 0). As before,
appeared
suggests
acid
is
the sum of
a more
amino
(and tertiary)
of the
solution
whereas
may therefore
Analysis
parts of
of structural
in
which leads to an increased
et al.851 inferred
serum albumin
type
favours
between
as helices
ApsH > 0 and APsS > 0 (yielding stands
This
interaction
and
in such a way that
structure
interactions
interaction
structures,
Hydrophobic
surface
compact
interaction
of the protein
are in the interior
with water.
the
hydrophobic
hydrophobic
of such secondary
to the sorbent
determining
Hydrophobic
supports
rearrangements. environment
contact
probable
structure
structure.
points
exposed
by intramolecular
the other
entropy
structural
in an aqueous
may become
rearrangement
in the environment
occurs
extent
from 65% in the native
upon
during protein
the to
to ca. 90 amino acids transferred Based
on the assumption
of four
531
possible conformations
per peptide unit in the random structures41 and
one in the helix, the resulting increase in conformational
entropy, A+,
amounts to k ln4 per amino acid, or, for the entire protein molecule, 90 k ln4 = 125 k, so that TApss = +125 kT per protein molecule. Calorimetry under the same conditions gave Aadh values of +80 kT and +55 kT for serum albumin adsorption enthalpies
on a-Fe203
is driven
and SiO2. respectively.
by an entropy
increase.
It follows that the
These
positive
are sums of positive and negative contributions.
overall
When this
algebraic sum is less than Apsh, the entropy rise TApss may be enough to overcome Aadh, as in this example. The fact that Aadh c Apsh implies that the entropy rise due to structural rearrangements is not the sole driving force. However, it may be concluded that an increase in conformational entropy
plays an important
role in the adsorption
of the soft serum
albumin molecule on a hydrophilic surface with the same charge sign. Overviewing
all the features
involved
in protein
adsorption,
it is
obvious that basically the same configurational, chemical and electrostatic features occur as with polyelectrolytes or monomeric adsorptives. In principle, therefore,
the theoretical
picture
to proteins.
However,
can be extended
developed
for polyelectrolytes
in practice
this challenging
prospect is still far in the future because of the great number of specific interactions
in proteins,
a complication
that is most dramatically
re-
flected in the positive adsorption entropy, which is found in some cases. This positive contribution
is at least partially
attributable
to intrinsic
structural alterations. Acknowledgement The assistance of Marcel Biihmer in obtaining results with the multilayer Stern-model is gratefully acknowledged. References 1.
B.V. Dejaguin
and L.D. Landau, Acta Physicochim. U.R.S.S. 14 (1941)
633. 2.
E.J.W. Verwey
and J.Th.G.
Overbeek,
Theory
of the Stability
Lyophobic Colloids, Elsevier, (Amsterdam, New York) 1948.
of
532
3.
M.R. Bohmer, O.A. Evers, and J.M.H.M. Scheutjens, Macromolecules
4.
L.G.J. Fokkink, A. de Keizer, and J. LykIema, J. CoIIoid Interface Sci.
23 (1990) 2288. 127 (1989) 116. 5.
L.G.J. Fokkink, A. de Keizer, and J. LykIema, J. Colloid Interface Sci.
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J. Lyklema, Discuss. Faraday Sot. 42 (1966) 81.
135 (1990)
118.
7.
G. Gouy, J. Phys. (4) 9 (1910). 457; Ann. Phys. (9) 7 (1917) 129.
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9.
0. Stem, 2. Elektrochem. 30 (1924) 508.
10. T. Hill, Introduction to Statistical Thermodynamics,
Addison-Wesley,
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Statistical
Thermodynamics,
Cambridge Univ. Press, Cambridge (U.K.) (1939) 426. 13. B.H. Bijsterbosch and J. Lyklema, J. Colloid Interface Sci. 20 (1965) 665. 14. E. Blomgren, J. O’M. Bockris, and C. Jesch, J. Phys. Chem. 65 (1961) 2000. 15. B. Vincent, B.H. Bijsterbosch, and J. LykIema, J. Colloid Interface Sci. 37 (1971) 171. 16. A. de Keizer and J. LykIema, J. CoIIoid Sci. 75 (1980) 171. 17. L.K. KoopaI and J. Lyklema, Faraday Discuss. Chem. Sot. 59 (1975) 230. 18. A. de Keizer, M.R. BGhmer, T. Mehrian, and L.K. KoopaI. Colloids Surfaces 51 (1990). 339. 19. T. Mehrian, A. de Keizer and J. Lyklema, paper presented at the 8th Int. Symp. on Surfactants in Solution, Gainesville, Fl. USA (1990). 20. H.A. van der Schee and J. Lyklema, J. Phys. Chem. 88 (1984) 6661. 21. J. Papenhuyzen,
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Principles
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Ithaca, N.Y., (1953). 24. S.L. Cameyand G.M. Tonie. Adv. Chem. Phys. 56 141 (1984). 25. F.Th. HesseIink. J. Electroanal. Chem. 37 (1972) 317 . 26. F.Th. Hesselink. J. Colloid Interface Sci. 60 (1977) 448 .
533
27. C.A.J. Hoeve, J. Chem. Phys. 44 (1966) 1505: J. Polym. Sci. C30 (1968) 361. 28. J.M.H.M. Scheutjens and G.J. Fleer, J. Phys. Chem. 83 (1979) 1619. 29. J.M.H.M. Scheutjens and G.J. Fleer, J. Phys. Chem. 84 (1980) 178. 30. J.M.H.M. Scheutjens and G.J. Fleer, Macromolecules
18 (1985) 1882.
31. M.A. Cohen Stuart, T. Cosgrove, and B. Vincent, Adv. Colloid Interface Sci. 24 (1986) 143. 32. T.Cosgrove, T.L. Crowley, B. Vincent, K.G. Barnett, and Th.F. Tadros, Faraday Discuss. Chem. Sot. 16 (1982) 101. 33. F.D. Blum, B.R. Sinka, and F.C. Schwab,
Macromolecules 23 (1990)
3592. 34. M.J. Grundy, R.M. Richardson, S.J. Roses, J. Penfold and R.C. Ward, Thin Solid Films 159 (1988) 43. 35. P. Schaaf, P. Dejardin, and A. Schmitt, Langmuir 3 (1987) 1131. 36. I. Caucheteux. H. Hex-vet. R. Jerome, and F. Rondelez, J. Chem. Sot. Faraday Trans. 86 (1990) 1369. 37. T. Cosgrove, T.M. Obey, and B. Vincent. J. Colloid Interface Sci. II 1 (1986) 409. 38. J. Papenhuyzen, G.J. Fleer and B.H. Bijsterbosch, J. Colloid Interface Sci. 104 (1985) 530. 39. J. Marra.
H.A. van der Schee,
G.J. Fleer,
and J. Lyklema,
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Adsorption from Solution, R. Ottewill, C.H. Rochester and A.L. Smith, eds., Acad. Press, (1983) p. 245. 40. B.C. Bonekamp, H.A. van der Schee and J. LykIema. Croat. Chem. Acta 56 (1983) 695. 41. B.C. Bonekamp and J. Lyklema, J. Colloid Interface Sci. 113
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67; B.C. Bonekamp. Ph.D. Thesis, Wageningen Agricultural University, The Netherlands
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42. J.E. Gebhart and D.W. Fuerstenau. Colloids Surfaces 7 (1983) 221. 43. R.J. Roe, J. Chem. Phys. 60 (1974) 4192. 44. M.A. Cohen Stuart, J. Phys. France 49 (1988) 1001. 45. J. Blaakmeer, Macromolecules
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M.A. Cohen Stuart
and G.J. Fleer,
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46. A. Foissy. A. El Attar, and J.M. Lamarche, J. Colloid Interface Sci. 96 (1983) 275. 47. J. Meadows, P.A. Williams, M.J. Garvey, R.A. Harrop, and G.O. Phillips, Colloids Surfaces 32 (1988) 275.
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48. H.A. van der Schee, Thesis, Wageningen Agricultural University, The Netherlands 49.
(1984).
R. Denoyel, G. Dinand, F. Lafuma, and R. Audebert, J. Colloid Interface Sci. (1990), in press.
50. E. Pefferkorn
and H. Elaissari, J. Colloid Interface Sci. (1990). in
press. 51. J. Blaakmeer, M.A. Cohen Stuart, and G.J. Fleer, J. Colloid Interface Sci. (1990). in press. 52. M.A. Cohen Stuart, G.J. Fleer, and J.M.H.M. Scheutjens, J. Pol. Sci., Pol Phys. Ed. 18 (1980) 559. 53. R.L.J. Zsom, J. Colloid Interface Sci. 111 (1986) 434. 54. H.G.W. Lensen, D. Bargeman,
P. Bergveld,
C.A. Smolders,
and J.
Feyen, J. Colloid Interface Sci. 99 (1984) 1. 55. E. Brynda, M. Houska, and F. Lednicky, J. Colloid Interface Sci. 113 (1986)
164.
56. W. Norde, F. MacRitchie, Interface Sci. 112
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57. H.P. Jennissen, Makromol. Chem. Macromol. Symp. 17 (1988) 111. 58. H.P. Jennissen,
in Surface and Interfacial
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Polymers, Vol. 2, J.D. Andrade, ed., Plenum Press, New York, (1985) 295. 59. B.M.C. Chan and J.L. Brash, J. Colloid Interface Sci. 84 (1981) 263. 60. M.E. Soderquist and A.G. Walton, J. Colloid Interface Sci. 75 (1980) 386. 61. H. Sato, T. Tomiyama,
H. Morimoto, and A. Nakajima,. ACS Symp.
Series 343 (1987) 76. 62. P.G. Koutsoukos,
C.A. Mumme-Young,
W. Norde and J. Lyklema,
Colloids and Surfaces 5 (1982) 93. 63. P. Bagchi and S.M. Bimbaum, J. Colloid Interface Sci. 83 (1981) 460. 64. H. Shirahama, K. Takeda, and T. Suzawa, J. Colloid Interface Sci. 109 (1986) 552. 65. A.V. Elgersma,
R.L.J. Zsom. W. Norde. and J. Lyklema, J. Colloid
Interface Sci. (1990). in press. 66. A.V. Elgersma,
R.L.J. Zsom, W. Norde, and J. Lyklema,
Colloids
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69. W. Norde, in Surfactants
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Bothorel, eds., Plenum Press, New York, 1986, p. 1027. 70. W. Norde, Colloids and Surfaces 10 (1984) 24. 7 1. T. Arai and W. Norde, Colloids Surfaces 51 (1990) 1. 72. P.L. Privalov, Adv. Protein Chem. 33 (1979) 167. 73. F. Ahmad and C.C. Birgelow, J. Biol. Chem. 257 (1982) 12935. 74. T. Arai and W. Norde, Colloids Surfaces 51 (1990) 17. 75. J.G.W.M. Fraaije, Ph.D. Thesis, Wageningen Agricultural University, The Netherlands
(1987).
76. P.G. Koutsoukos, W. Norde, and J. Lyklema, J. Colloid Interface Sci. 95 (1983) 385. 77. J.L. Brash and Q.M. Samak, J. Colloid Interface Sci. 65 (1978) 495. 78. A. Schmitt, R. Varoqui, S. Uniyal, and J.L. Brash, J. Colloid Interface Sci. 92 (1983) 25. 79. J.D. Aptel, J. C. Voegel, and A. Schmitt, Colloids Surfaces 29 (1988) 359. 80. B.R. Young, W.G. Pitt, and S.L. Cooper, J. Colloid Interface Sci. 124 (1988) 28. 81. W. Norde and J. Lyklema, J. Colloid Interface Sci. 71 (1979) 350. 82. M.H. Abraham, J. Chem. Sot. Faraday Trans. I 69 (1973) 1375. 83. M.H. Abraham, Nasehzadeh,
E.Ah-Sing,
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Creighton.
“Proteins,
Structures
and Molecular
1983, Ch. 5. 85. W. Norde and J. Lyklema, Colloids Surfaces 38 (1989) 1.
Properties”,
477
Adsorption of Ions, Polyelectrolytes and Proteins M.A. Cohen Stuart, G. J. Fleer, J. Lyklema, W. Norde, and J.M.H.M. Scheutjens Department of Physical and Colloid Chemistry Dreijenplein
6
6703 HB Wageningen The Ne~erl~ds 1 IIltroduction ........................................................
.478
2 Electrosorption of ions and small molecules: chemical and electrical fntwractions.......................................................... 479 488 3 Lattice theory of electroso~tion ..................................... a) l&tiCe Variant Of the Gauy-ChapmanStem model ................ b) Volume filing and chemical interactions .......................... c ) Theoretical results ................................................ 4 Polyelectrolyte adsorption model .................................... a) Conformations b) Theoretical
.................................................... resufts................................................50
Strom2 nolvelectrolvtes ........................................... Weak Dolvelectrolvtes ............................................ 5 Polyelcctrolyte adsorption experiments .............................. a) Introductory b) Adsorption
remarks.............................................50 of strong ~iye~trolgtes
of weak polyelectrolgtes ............................... d) Metastablestates..................................................51 e) Adsorption of polyampholytes ..................................... 6 Protein adsorption ................................................... remarks .............................................
b) Adsorbed amount ................................................. c ) Co-adsorption of small tons ...................................... d) Energy and entropy of protein adsorption ........................ ...................................................... A&nowledgement ............................................................. References.
0001~8666/91/$20.65
0
1991-
492 492 499 499 1 501 504 508 8
............................ .509
c) Adsorption
a) Intr~~to~
.488
Elsevier Science Publishers B.V.
515 8 519 521 521 523 .527 -528 531 531
478
1 Introduction According interactions (i)
to
present-day
insights,
there
are
four
types
of
that play a role in colloid science:
Van der Waals
forces,
that are always
attractive
for particles
of the
same nature (ii)
Electrostatic
and attractive (iii)
Solvent
(iv)
Osmotic
interactions,
for opposite structure-based
adsorption,
and
are operative
entropic
been
polymer
interactions
are
may
known
elements
development
and larger polymers
two decades
experiments.
because
configurational considerable and
and electrostatic progress
relatively
effects
simple
and
adsorption
polyelectrolytes,
the state of the art. In describing
systematic
state
are strongly
we shall review
monograph
theory
has by a
that the
of Verwey
and
of
more
can
adsorption. already
Overbeekz).
be
the
complex
is far from complete.
polyelectrolyte
description
interrelated.
has been made in the area of ions, small
of
first
can have a
supported
we may
of
is much more complicated
and proteins
ion
the
the situation
polyampholytes
a
amounts
and is now
understanding
in small
small amounts
are involved,
At present,
the
of interactions
are understood. macromolecules
Although
which
of which
state. The existence
colloids
over the past
For charged
molecules
(i) and (ii)
and Overbeekz).
for more than a century:
destabilize
of appropriate
essential
macromolecular
and Verwey
a new
effect. As far as uncharged
developed
number
to
in which only factors
and Landaul)
is still in its inceptive
of type (iv) is already stabilizing
related
or repulsive.
theory for systems
Derjaguin
structure
understanding added
interactions
is now almost fifty years old and known as the DLVO-theory,
its founders
Solvent
for the same charge sign
short range forces
that may be attractive
The basic stability after
that are repulsive
signs
theoretical
molecules
In the present the electrostatic
many found
By treating
elements in
the
these
way, we hope to pay a tribute to these authors.
like paper, effects
recur
of
admirable effects
in a
479
Given the variation
of phenomena
in polyelectrolyte
and protein
adsorption, it is mandatory to systemize the treatment and we shall do so by adopting the following hierarchy: (1) The structure
of “simple” double layers and the adsorption
of low
molecular weight molecules and ions. In order to avoid unrealistically high ion concentrations
close to a highly charged surface, the well-
known concept of a (single) Stern-layer, exclusion
accounting
for the volume
between surface and ions besides specific adsorption,
is
very useful (section 2). (2) A self-consistent
field model of “simple” double layers which also
takes into account the mutual volume exclusion between the ions (and solvent). To that end, the multilayer Stem-model
introduced by
Bdhmer et al.31will be discussed (section 3). (3) Extension
of
this
incorporating
the
model
to
polyelectrolyte
configurational
properties
adsorption of
flexible
by chain
molecules (section 4). (4) Experimental verification of the theory for (strong and weak) simple polyelectrolytes experimental
(section
5).
In this
data on polyampholytes
section
also
some
recent
(for which the theory, so far,
has not yet been applied) will be given. (5) Adsorption
of proteins, for which the internal coherence (structural
stability) plays an important role. An a priory theory for these systems is not yet available, experimental
hence the approach
is essentially
based
on
evidence (section 6).
2 Electrosorption of ions and small molecules: chemical and electrical interactions The
distinction
between
electrical
and
chemical
contributions
pervades the entire domain of colloid and interface science. In its most elementary including
form,
it is reflected
charge-determining
in the adsorption (or
of simple
potential-determining)
ions
ions, and
counterions. Several features of colloid stability, the distinction between interaction
at constant potential
and at constant charge being one of
them, cannot be understood without properly recognizing
the chemical
and electrical contributions to the Gibbs energy of double layer formation.
480
Resolving
this
issue
was
one
theory. Also for our purpose At the
outset
“chemical”. suffices hence,
of the main
this distinction
it is necessary
to define
Since we will deal mainly
to identify
potentials
achievements deserves
of the DLVO
due attention.
the terms
“electrical”
with mean field approximations,
of mean force with average
potentials
it and,
use
(1)
I& = pi + viev for the relation the
and
between
chemical
potential
the electrochemical ).ti, and
potential
the
w. In eq. (1). vi is the
elementary
charge.
pi and w depend
potential
valency
In an inhomogeneous on the position
fii of component
(macroscopic
or
mean)
of component
system
z, but
i,
electric
i, and
e the
(such as a double
layer)
iii is constant
throughout
the
system. Equation
(1) implies
an element
of definition
to the Gibbs energy of an ionic species is by definition
chemical.
if the chemical
contribution
bonding,
hydrophobic
Henceforth,
form
adsorption symbol
by virtue
Au: while is that
tenets
realizing
Au:
specific hydrogen
. ..) is nonzero.
of the
terms may be included point
we shall call any adsorption
in colloid
chemical
that
science
attraction
of charge-determining
Au:
for by vrev
(such as Van der Waals interaction,
effects,
It is one of the basic layers
in that any contribution
i that is not accounted
ions
that electrical or (Gibbs)
to a surface.
non-configurational
double
energy
We
use
(or local)
of the
entropy
in it, thus making it a Gibbs energy. The important
does
not contain
the
configurational
entropy
of the
adsorptive. The charge-determining electrical
field
reflected (i)
in a number
chemical (ii)
is just
surface
Addition
continue
potential
v(O),
equal
to the
This
is
against
the
immediately
including
ions
and solution.
at the surface
adsorption. to
adsorb,
thereby
till this potential
difference
The driving
in the
gradually
has risen
chemical
so far
potential
force for the adsorption
is the
part Au; of this difference.
Indifferent
screen
their
of observations,
the surface
viev(O)
between
ions accumulate from
Charge-determining
increasing that
resulting
the
electrolytes
electrostatic
of such
(of which repulsion
electrolytes
allows
no ions adsorb between
specifically:
charge-determining
the adsorption
of the latter
Auy20) ions. ions to
481
proceed
further.
In other words,
surface
charge density
at given surface
potential
o(0) due to charge-determining
w(O), the
ions becomes
higher. There
is no distinction
ions and specifically
of principle
adsorbing
between
charge-determining
ions. Only if it is known from model
considerations that a certain ion type has a special affinity for the surface (e.g., Ag+ for silver halides, and H+ for oxides) does it make sense to identify them as “surface ions”. For protons on oxides Au: is of the order of
12-20
kT at room
whereas
temperature4).
Au: for
the
strongly
specifically binding Cdz+- ion is lo-16 kT51, which is not much lower. On the other hand, for weakly specifically adsorbing ions, like alkali ions on AgI, Au; is only a few kT-unit&I. It is now only one step towards small organic molecules. They may be charged or uncharged. For charged surfactants on hydrophobic surfaces, each CH2-group contributes an amount of order kT to Au;, whereas the electrical term for vi = 1 is about kT for each 25 mV of potential at the location where the charged group finds itself in the adsorbed state. The electrical and chemical contributions other,
depending
on the
indifferent
electrolyte
favourable
and adverse
screened. For long polyelectrolytes,
charge
may counteract signs.
Studying
may be diagnostic
organic
electrostatic molecules,
the picture
such
also contribute
polymers
to the adsorption
influence
because
as uncharged more
the driving force for the adsorption
both are and
because,
conformational
behaviour.
of
between
polymers
complicated
addition to chemical and electrical interactions, effects
the
in discriminating
contributions,
becomes
or reinforce each
in
entropy
For uncharged
is always of a chemical
nature. It is worth noting that a rather low chemical adsorption energy per segment (often a value well below 1 kT suffices) may lead to a strong binding of the chain as a whole. This is why linear uncharged polymers tend to adsorb tenaciously
on a variety of surfaces.
uncharged, electrolyte that is indifferent little effect on this adsorption the polymer).
However,
If the surface is
with respect to the surface has
(except when salt affects the solvency of
especially
for highly
charged
surfaces,
the
counterions neutralizing the surface charge compete for space and upon addition
of electrolyte
the adsorption
of polymer may decrease.
further discussion we refer to sections 4 and 5.
For a
482 Polyelectrolytes
have,
apart
from the chemical
contribution,
an
electrostatic part in their Gibbs energy of adsorption. With an uncharged surface,
this
electrostatic
polyelectrolyte.
effect
opposes
the
accumulation
of the
In the case of charged surfaces, there is an additional
electrostatic component in the adsorption energy, which may be positive or negative,
depending
screen all electrostatic
on the charge interactions,
signs.
Indifferent
electrolytes
both the intermolecular
repulsion
and the segment-surface interaction, so that they have at least two - often - effects.
antagonistic
These
situations
are more fully dealt with in
sections 4 and 5. In order to interpret more quantitatively the structure of the double layer and the effect of small molecules, the Gouy-Chapman picture 7. 81is usually inadequate, for at least two reasons: it considers the ions as point charges without volume (giving unrealistically high ion concentrations in regions
of high
adsorption. reasonably
A
and
potentials), simple
extension
it does
not
account
proposed
by
Sterns)
for
specific
works
in a number of cases, despite its relative simplicity.
quite In this
model, a chemical contribution is assigned to the adsorption energy of an ion and the volume exclusion between adsorbed ions and the surface is incorporated. Below we briefly treat this Stern-theory. A further extension to the more general
case where
also the mutual
overlap
of ions is
accounted for in a self-consistent way will be given in section 3. The basic premise of the Stern-model and ion volume
are considered
important
is that specific interactions only in the solution
layer
adjacent to the surface. The reasoning is that chemical interactions are short-ranged distance
and that usually the ion concentrations
from
the surface.
The potential
parallel
are low at some to the surface
is
considered to be smeared out, which is typical for a mean-field model. We denote the potential in the middle of this first layer, usually called the inner Helmholtz-layer.
as ~(1). Beyond the Stern-layer,
the outer Helmholtz-plane, Poisson-Boltzmann
that is, beyond
the double layer is assumed
to obey the
equation, i.e., its composition is formulated in terms
of the Gouy-Chapman theory. The
adsorption
isotherm
of a neutral
species
approximation, be written as a Langmuir equation:
i can, as a first
483
where $I = &(l) is the volume fraction of component i in the Stern-layer and $p is the bulk solution
volume
fraction.
If desired,
$i may be
identified with the fraction of the surface occupied by i. We prefer to use volume fractions in order to maintain consistency with the more general multilayer Stern-model to be discussed in section 3. Equation
(2) can conveniently
be derived
for a two-component
solution (solvent and one solute) using a lattice theorylo). It accounts for volume exclusion in the Stern-layer through the factor 1 - oi, but not for that in the solution: in order to achieve that, ‘pt should be replaced by @/(l - $).
Moreover, it is not generally valid for a system of more than
two components
(e.g., several types of ions and one or more neutral
solutes) because all these components occupy volume. For big monomers the statistics could be modified by letting more than one site match with one monomer, leading to a more complicated equation. In the Langmuir-picture,
Au; contains the adsorption energy and any
local entropy of adsorption: obviously the configurational entropy of the adsorbate is included in the term +I/( 1 - $1). If there is lateral interaction, an
additional
coordination parameter Moreover,
contribution number
Z&w@I could be added,
in the surface
that is positive
layer
for repulsion
where
Z, is the
and w a pair interaction
and negative
for charged species an electrostatic
for attraction.
term vieyr(1) enters. In
this way,
which
is a special
equationllv
form
of the Frumkin-Fowler-Guggenheim
(FFG)
12). Note that this equation does not explicitly account for
dipole orientation effects. Unlike eq. (2). which is explicit, equation (3) is an implicit equation in $1: not only does oi occur in the exponent but v( 1) is also a function of $1, and a suitable relation between the two has to be established. The FFG equation recurs as a special case in the multilayer Stern-model, see eq. (17) of section 3. The adsorption
energy AU: is then written as -x&T
where xS is a dimensionless adsorption energy parameter, and instead of w the conventional Flory-Huggins parameter x, which is a measure of the solute-solvent interaction, occurs. Moreover, the volume fraction oi in the lateral interaction term is replaced by the difference between a contact
484
fraction
in the surface layer and in the bulk solution.
The complete
solution in the multilayer Stern-model involves such an FFG-equation for each lattice layer in the system and not just for the ilrst layer. For all layers except the first, the adsorption energy term Au; is usually zero. For further details we refer to section 3. We shall now give a few experimental
examples
of low molecular
weight electrosorption. The purposes are to illustrate some of the trends discussed above, and to establish a bridge towards the following sections. Most examples given below are for AgI as the sorbent which, because of its hydrophobic surface and controllable surface charge and potential, is an excellent model system.
Figure 1. Surface charge on dispersed AgI as a function of pAg, in the presence of different concentrations of n-butanol13). Indifferent electrolyte 10-l M XN03. Temperature 25°C.
Figure 1 illustrates the influence of n-butanol on the electrical double layer on AgIlsl. The surface charge o(O) due to Ag+ or I- ions is plotted as a function of pAg I -log[Ag+l,
which quantity is directly related to the
surface potential y(O): if pAg increases by one unit, ~(01 becomes more negative electrolyte
by an amount concentration
of 58 mV (at ZOOC). In this experiment,
the
is high and kept constant, so that the diffuse
part of the double layer is compressed
and the Stern-layer,
where the
butanol is adsorbed, gives the dominating contribution. The picture shows that uncharged adsorbates can also screen the surface charge, though this is a more subtle process than with electrolytes. Butanol has basically two effects:
485 (i)
the lowering
of the dielectric
partial displacement
constant
in the Stern-layer
and the
of the counterions reduce the capacity 0(0)/w(O) of
this layer, which shows up as a smaller slope of the o(O)-pAg curve, and (ii) the replacement
of oriented water dipoles adjacent
to the surface
causes a shift in the point of zero charge (pzc), i.e., the pAg-value where o(0) = 0. If the curves were plotted as o(0) - w(O), the curves would all intersect each other at the pzc. If plotted against pAg, as in fig. 1, the curves are shifted along the horizontal axis and a common intersection point (tip) is found at a pAg above the pzc. In this tip the replacement of water in the Stern-layer by butanol has no consequence for the surface charge. The amount
of adsorbed
butanol
(rb) is too small to be detected
analytically, let alone the minor change of rb with pAg. However, it follows straightforwardly from the Gibbs adsorption equation that rb as a function of o(O) or, for that matter,
as a function
of pAg, passes
through
a
maximum at the tip. It is interesting to note that a very similar behaviour was found for n-butanol on mercuryl4). The model hydrophobic
interpretation
considers
the adsorption
bonding139 1s). Hence, on a butanol-covered
as driven by AgI-surface the
hydroxyl groups point towards the solution. A supporting observation is that
due
to
counter(cat)ions increases
this
butanol
adsorption
the
lyotropic
sequence
for
reverses. On bare hydrophobic AgI the specific binding
in the order Li+ < K+ < Rb+.
whereas
on butanol-covered
hydrophilized AgI it is the other way aroundIs).
PAg
Figure 2. Surface charge on dlspersed AgI as a function of pAg. in the presence of tetrabutyl ammonium (TBA+) nitratel6). Indifferent electrolyte O.lM KNOs. temperature 22oc.
486
Common
intersection
since been found including
for a variety
charged
ammonium function
ones.
(TBA+)
ammonium
points such as those observed
ions.
of other low molecular
Figure
nitratela).
Similar
As for n-butanol,
of o(0) or pAg passes
ions it was possible because
adsorbing surface
cations.
The
is positive,
point,
stronger
competition
positive
direction.
decreases
with increasing
sight
between
is rather
region,
I- and TBA+
for polyampholytes
and
increasing specifically
at low pAg, Au&.
where
adsorption
surface of the
be explained
sites.
experience
cation
by the
In addition,
where
attraction
the
To the right
sometimes
between
which
dipole less
adsorbate
TBA+ on
competition orientation
5 and 6, similar examples
proteins,
as a
methods.
with
o(O). Also this phenomenon,
for surface
if the electrostatic
ions
TBA+ ions, and o(0) shifts in the
may
effects may play a role. In sections found
adsorbs
the
negative
unexpected,
tetraalkyl
of these
by the
contribution
of the voluminous
for other
negative
the I- ions on the crowded
In this
tetrabutyl
at the tip. For some
of I- is facilitated
that TBA+
have
adsorptives,
for
by direct analytical more
points to a chemical
of the intersection
first
fact
apply
a maximum
becomes
adsorption
weight
example
adsorption
to verify this maximum
the
an
curves
the
through
To the left of the tip. o(0) [TBA+]
2 gives
for butanol
will be given adsorption
and
is
surface
is
increased. Koopall7)
has demonstrated
also be obtained When
the
adsorbed
carrier in trains
layer
electrophoretic electrolyte,
electrolyte
Having return
by train
this
to the statement
distinguish
between
established
the
is
that
above
on the segment chemical
of the
the data
and
with
electrostatic
diagnostic
species
we
of the tool
Figures
l9). They have in common cationic
the
distribution.
the influence
contributions.
of
of carrier
of small molecules
additional
and chemical
segments
the coverage
this information
that studying
a useful
of such trendsls.
adsorption
only
in low concentrations
useful information
electrostatic
and 4 are illustrations coverage
Combining
obtained
made
concentration
low
high,
on AgI.
By comparing
both play a role in the electrosorption
electrolyte
alcohol
he was able to determine
segments.
way
is
by this method.
layer thickness,
in
for polyvinyl
concentration
monomers,
then provided
interactions
particularly
are detected
with those of simple the first
that curves like those in figs. 1 and 2 can
for polymers,
decreases
to 3
that at with
487
Figure 3. Influence of the indifferent electrolyte concentration on the adsorption of tetrabutyl ammonium (TESA+) ions on AgIl*). The pAg was fixed at 11.5. temperature 22OC.
r
Figure 4. Influence of the indifferent electrolyte concentration on the adsorption of dodecylpyridinium chloride (DPC) on kaoIinitel** 19). The pH was fixed at 7. temperature 2ooc.
increasing salt concentration: then there is again a common intersection point, above which the salt effect is the other way around. Below the tip, the competition
between the cation of the electrolyte
and the organic
cation (ion exchange) leads to a smaller adsorption of the latter. At the tip, the electrophoretic mobility of the covered particles is zero: here the particles with their adsorbates are uncharged
(isoelectric). Beyond this
point, the screening by the salt makes the accumulation
of the organic
ions easier. The fact that the adsorption continues to increase beyond the tip points to a chemical driving force. Such an adsorption causes charge accumulation,
which
would
inhibit
further
adsorption
unless
these
488
charges higher
are screened. electrolyte
In
the
This screening
next
chapter
we
predicted
by rhe multilayer
3 Lattice
theory
Very model
Bohmer
were assigned just
volume
polymeric
were
avoided
(Debye-Htickel next
a of the segments
to vary with the distance could be modelled,
is not
types of
a mean field and ions
more consistent The theory only
u-eat
leaving
to assign
of Bijhmer
in those
the
approximation) surface.
case
model
where
and only electrical
to show sow- chemical
low
cases
where
by
the ionic success
However,
to all the components these demands.
molecular
aspects
weight
till section
each lattice
interactions
interactions
E
In this way weak is determined
layer
filling
in
In this
ions
is behaving
play a role. Then
and the volume
it
and
4. We separate
into two parts. First we deal with the lattice version
Gouy-Chaprnan-Stern
the
permittivity
new trends.
a volume
oi
or by
bater221,
have had considerable
et al.31 satisfies
the polyelectrolyte
relation
The fact that small ions have
data and predicting
the system.
as point
a linear
from the surface.
drawback
the
Very high counterion
to the
equilibrium.
a serious
is deffnitely
Stern-layer
lattice
(several
through
of .which the charge
experimental
the discussion
also
account
and the dielectric
in interpreting
we
into
by using
of a Stern-layer
are low, and these models
section,
species)
theory73).
concentrations
moiecuies,
takes
of this mode120. 211, polyelectrolytes
a local association-dissociation no volume
are
a multicomponent
which
and the potential
of ionination
polye!ectrolytes
trends
of all the components
molecules,
near the surface
the charge
were allowed
similar
a fixed charge and the small ions were considered
the incorporation degree
that
like in the Gouy-Chapman
concentrations between
find
et al31 presented
In earlier versions
charges,
shall
adsorption
and excluded
small ions, uncharged approach.
of
Stern-model.
polyelectrolyte
interactions
in the presence
of electrosorption
recently,
for
is more effective
concentrations.
of the like a
we proceed
constraint
are
incorporated. a) Lattice
variant of the Gouy-Chapman-Stem
The molecules one could
assign
are assumed solvent
model
to be arranged
molecules
on a lattice.
(H201, small
In principle,
ions (e.g., OH-. H30+,
489
Na+, Cl-, etc.),
and small uncharged
solutes
one lattice
site each.
However, since ions in aqueous solution are strongly hydrated, one could also take lattice cells with a volume equal to that of an (average) hydrated ion and assume an equal volume for clusters of water molecules. As water is a highly structured
solvent, it is not an unrealistic
assumption
to
consider the water molecules to be clustered. Lattice cells of this size are also considered to occupy one polyelectrolyte segment (section 4).
Figure 5.
(a) Lattice with a solution of solvent (open circles), ions, and uncharged solutes (black circles) in a sobent, next to a charged surface. lb) Potential profile v(z) and field strength profile E(z) in an electrical double layer according to the multilayer Stem-model. The field strength changes at each charged plane (z = 0. 1, . ..) due to the plane charge density C(Z). and at each boundary between the layers (z = l/2. l/3. . ..) due to a change in the dielectric permittivlty ELz).The potential drops linearly in each half-layer because there is no space charge.
Like in the Gouy-Chapman theory 7.8). the potential is only a function of the distance from the surface: lateral fluctuations
are neglected
by
adopting a mean-field approach. The charge of the ions and segments is assumed
to be located
on planes in the middle of each lattice layer
parallel to the surface, thus forming an assembly of Stern-layers
(see
figure 5). The layers are numbered from z = 0 (the surface) to z = M (in the bulk solution). The interplane separation e equals the diameter of a segment or ion. In between the midplanes there is no charge so that the electric
displacement
permittivity
D(z),
which
is the product
E(Z) and the electric field strength
of the
dielectric
E(z). is constant. The
490
quantity
E(Z) is the
permittivity
relative
dielectric
Q, of free space. According
constant
in layer
to standard
z times
D(z) = &(z)E(z) = ia z’=O
(4)
The field strength
E(z) changes
I, 2, . ..). because
of the presence
boundaries
(z=i,g,
discontinuously
E(Z) is taken
the various denoted
of charges.
...) there are changes
in each layer leads to another imation,
the
electrostatics:
components.
because
dielectric
to be a linear
at the mid-planes However,
a different
permittivity
combination
(z = 0,
also at the layer composition
E. As a first approx-
of the permittivities
If in layer z the volume fraction
of component
of i is
by o‘(z), we have (5)
e(z) = &4$(Z)
i where
Ei is the permittivity
extends
over solvent,
densities equals
v&z)e,
charge
uncharged
are functions
component
of the pure solutes
of the volume
component
The charge
charge
of each unit i
and ai(z) the degree of ionization
i in layer z, and e is the elementary
density
summation
and all ions. The plane
fractions.
where vi is the valency
i. The
charge.
Then
of
the plane
o(z) is given by:
o(z) = Cviai(z)eoi(z)
/ a,
(6)
i Here,
as is the surface
the surface zero
volume
area of a lattice
charge density fraction
site. Equation
is that
for i = S, where
S is the solid
$3(z) = 1 for z I 0 and @s(z) = 0 for z 2 1. Generally, species,
VI = -1 for negative
ones. The degree equilibrium polyacid).
which
(where constant surface
also for
adsorbent:
vi = 0 for uncharged
and vi = +l
can be unity (e.g., for H30+, concentration.
for positive OH-, and salt
For example,
of a weak acid residue A (or a segment
can be represented
the
of a weak
by the reaction
H+A-
W = H20
and
H = H30+),
Kd = (a~/(1 - aA)lIHI/(Wl. the
(or segments)
of the local counterion
dissociation
HA+W$
ions
of ionization
ions) or a function
(6) applies
o(O) by putting z = 0. In this case the only non-
ratio
(H)/(W)
should
is determined
by
In the concentration be replaced
by the
the
dissociation
gradient ratio
near the
of contact
491
fractions
(I$H(Z))/($W(Z)).
The contact fraction
(@i(z)) is the average
volume fraction of component i around a site in layer z. To this average, three layers (z - 1, z. and z + 1) contribute. Hence, (@l(z)) is given by (@i(Z)) = Q$,(z - l)+ Q$i(z) + h.#z + 1)
(7)
where ho is the fraction nearest neighbours within layer z. and X1 that with each of the layers z - 1 and z + 1. For example, in a hexagonal lattice b = 2x1 = 6/12, and in a cubic lattice Xo = 4x1 = 4/6. Obviously, Xo + 2X1= 1. For the local degree of dissociation we arrive at
ol*wl = 1+K~‘(oH(z))/(ow(Z)) Note
that
&
concentration.
is
a dimensionless
(8) quantity
The normally used dissociation
moles/P, corresponds
to K = Q( lOsa,dN&-1
rather
than
a molar
constant K. which is in . The conversion
factor is
the molar concentration of pure solvent. It is straightforward
to compute the electrical
potential
from the
field strength. The potential on each plane at z = 1, 2, 3, . .. is related to that on the previous plane by ~(z+l)=+{E(z)+E(z++)}
(9)
where I is the lattice layer thickness. We assume that all molecules obey Boltzmann statistics. Accordingly, the concentration proportional
of ions, solvent molecules, and other monomers are -u*(z)/kT , where ul(z) is the energy
to a Boltzmann factor e
(with respect to the bulk solution) of species i in layer z. In the bulk solution, up = u,(m) s 0. If the interactions nature,
ui(z) is simply the electrostatic
are only of an electrostatic
energy u:‘(z)
of monomer
i in
layer z:
uf(z) =vp,bdeW)
(10)
As before, the volume fraction of component denoted
as $.
The
volume
components is then obviously
fraction
i in the bulk solution is
distribution
of the monomeric
492
(11) If there
are
components solved u,(z)
only
present,
numerically. gives
equation
immediately
potential
In order
iteratively
until equation
uncharged total
density is
Nevertheless, accounted
and
for
magnitude are
present,
equations
simple
and
condition
positive,
hence
ui(z)
example
is not and
ui(z)
w(O)
equation
are
adjusted
finite
(12),
equation
lateral
below,
of
the
monomers
is
However, packing obeyed.
of molecules
layers
restricts
is easily
is the
high concentrations
factor of positive ions
not
and monovalent
concentrations
for all
than the original
(and association)
thickness
of negative
it follows
equation. no
sophisticated
so that unrealistically
in the
is zero
are inhomogeneously
restricted:
more
since dissociation
that
molecules
eq.
is already
the
above,
with the Gouy-Chapman
molecules
error
neutrality
energies
potential with
(10) is obeyed for all i and z.
(10) and (11). The weighting
exp(ev(z)/kT)
charge
(4) and (9) lead to the potential
the potential
If only uncharged
the
(7)
and plane
be consistent
of the potential
ions do not occur.
using equations
o(0) or surface
incorporated model
to
should
the model
Gouy-Chapman
can be
according
the permittivity
Only the charged
of
distributions
charge
in full agreement
constraint
fraction
equations
this,
polymeric
set which
the surface
in the
molecules.
distributed, the
that,
a closed
no
distribution
to achieve
It is clear
form
can then be calculated
Finally,
provided
This
4-11
and
an initial guess for the set of potentials
(5) and (6) provide
distributions.
is given.
interactions
the volume
(11). Any dissociation
on each plane, (10).
equations
For example,
and (8). Equations density
electrostatic
of
salt ions
obtained
from
ions in layer z is
is exp(-ev(z)/kT).
From
the
that half of the ions in the bulk solution (11)
leads
to
the
well-known
is
relation
%aIt (z) = &3Ii cosh(ev(z) / kT]. The volume fraction of uncharged molecules is 1 - okIt in any layer z. The total volume fraction in layer z is then 1 + o~gIt(cosh{e~(z)/kT) (according b)
- 11, which
to the Debye-Htickel
Volume filling
approaches
unity
approximation)
only
at low otaIt
or
at low v(z).
and chemicaI interactions
The next step is the complete of the ions and molecules.
incorporation
We require
of the hard core volume
that each lattice
layer is just
fully
493
occupied.
In terms of volume fractions the packing constraint
can be
expressed as: &(z)=l i
(12)
for all z. This boundary condition is imposed by a lateral pressure which affects the potential energy of all monomers in a given layer in the same way.
More specifically,
Boltzmann
statistics
are maintained
but the
potential energy ul(z) is incremented by a term u’(z), which is positive or negative since the local pressure can be higher or lower than in the bulk solution. The effect of such a term is that the Boltzmann multiplied
by a factor exp(-u’(z)/kT)
which normalizes
factors are
the sum of the
volume fractions to unity and at the same time induces a redistribution of the molecules
because
of the accompanying
change
potential profile. Note that no extra independent
in the electric
parameter is needed:
equation (12) fully determines the value of u’(z). Like the self-consistency of ion distribution the
profile
and electric potential, all molecule distributions
of u’(z)
become
self-consistent.
In the
example
exp(u’(z)/kT] would have the value 1 + Q!&(cosh(e~(z)/kT)
and
above,
- 11 for any z,
but the potential profile v(z) would be different from the simplified case u’(z) = 0. Obviously, electrical
the potential
contribution,
energies
may contain,
also other interactions.
apart
from
the
Let us first consider a
binary mixture of solvent 1 and uncharged solute 2, where the molecules are attracted by the surface so that their energy levels in the first layer are lower than in the bulk solution by amounts uf and uz, respectively. In this case u:‘(z)=0
for any z. If there are no other contact interactions
than try, ui(z) = 0 for all layers except the first. This implies @i(z) = @ for z 2 2, according to eq. (11). For z = 1 we have in this simple case l+(l) = u’(1) + UQ From
eq.
(13)
(11)
($2 / I$) exp(-Au; / kT) difference
between
we
can
where
a solute
now
eliminate
Au; = uz - ut and a solvent
is the
u’( 1):
$,(l)/@,(l) =
adsorption
If we define
a
dimensionless adsorption energy parameter xS as x, = - Au; / kT (which
is
positive if the solute adsorbs preferentially with eq. (12):
molecule.
energy
from the solvent), we have
For
dilute
solutions
Langmuir
(I$; -C-C1). this
equation,
It is straightforward l+(z) = u’(z) + The adsorption interactions For
the
model
energy contribution
can be used.
is identical
the
simple
is usually zero for z t 2, but long range
The electrical
contact energy
term is given
interactions, up
to XIJand to the contact
i. This contact
are defined
with
energy of a molecule
Generally,
+ ...
up
any
fraction
by eq. (10).
suitable
through
of a solute
i in the layer z with other molecules
molecule
to
other interactions.
One way is to express
The contact
proportional levels
be included. neighbour
parameter@). segment)
to incorporate
u?(z) + u;‘(z)+ q(z)
could
nearest
result
see eq. (2) in section 2.
solution
Flory-Huggins
molecule
x-
(or polymer
(or segments)
of type j is
(@I(z)) of molecules
j around
fraction
is formulated
in eq. (7). Since the energy
respect
to the bulk
solution,
i with all other components
the total
contact
j is given by
u~t(zl=kT~Xlj[(~j(z))-O~} 1 If the solvent expressing u:(z)
is monomeric,
it in the
and up(z),
solvent
underlining
Since the solvent
it is always profile
@l(z)
possible and
to eliminate
the
potential
that u’(z) is not an independent
is uncharged,
u’(z) by energies
variable.
u1e1 = 0 . For the ratio @i(z)/@1 (z) we find
from eqs. (11) and (15):
(17)
where equation
Au:(z)
= u:(z)
applies
simultaneous the volume
as before,
for any component
equations constraint
It is instructive the special
- u:(z)
and
Aup
= uft(z) - $(z).
i and any layer z. The whole
may be solved
numerically,
taking
This set of
into account
(12). to compare
eq. (17) with the FFG-equation
case of a two-component
system
(e.g., solvent
(3). For
and one type of
495
salt) where the adsorption is restricted to a monolayer, eq. (17) reduces to nearly the same form as eq. (3). Note, however, that the volume of the co-ions is neglected in the FFG-picture. Hence, if @I( 1) = 1 - o2( 1). where component
2 is the counter-ion. and @ = 1, the factors containing the
volume fractions are the same in eqs. (3) and (17). The term Au: in eq. (3) is identified term u:‘(l)
as the difference between u; and u:. The electrostatic
is the same in both models. For the contact term At$(l)
may write,
using
(@l(l))
XIX + 2~{(@2(1)) - $},
+ (@2(l))
we
= 1 - hl and eq. (16). A$(l)/kT=
where x = ~12 This contribution
closely resembles
the lateral interaction term in the FFG-equation: the constant hlx may be incorporated
in Auf,
and w may be replaced by 2x/Z, where Z is the
lattice coordination number. Since Z, = hoZ, the term &w& in eq. (3) can be written as 2koxoi. The full model gives, for small @,
essentially the
same result because in that case (@2(l)) = I&z(l). The illustrations given above show that the multilayer Stern-model is easily adapted to different types of interactions, which may be long range as well as short range. Before proceeding to the application of the model to polyelectrolyte shown
in section
adsorption (section 4), we compare some of the trends 2 (figures
l-4)
with the predictions
of the model
calculations. c)
Theoretical results
d(nr’
Figure 6. Comparison between the multilayer Stern-model and the GouyChapman model. Potential decay in the electrical double layer, for three concentrations of monovalent ions and ~(0) = 100 mV. The full curves were computed from the Poisson-Boltzmann equation, the various symbols correspond to computations with the multi-layer Stemmodel, using various lattice spacings C. All x and xS parameters are zero and E = 60 E, for all components.
In fig. 6 we show the potential profiles v(z) for a charged wall in the presence of indifferent electrolyte at three different salt concentrations cs, for an intermediate surface potential of 100 mV. The distance d in fig. 6 equals zl. The curves in fig. 6 were calculated using the Gouy-Chapman theory7.s)
based on the Poisson-Boltzmann
equation,
the points were
obtained from the multilayer model using different values for I. It is seen
496
that
for the given
surface
potential
(100 mV) the results
virtually
coincide, which means that volume exclusion plays almost no role. For higher pronounced,
surface
potentials
and the multilayer
the accumulation
of ions is more
model leads to a slower decay of v(z)
close to the surface and, consequently, a lower surface charge than the single Stern-layer
model. Further away from the surface (a few lattice
layers) the profile becomes exponential, with a decay length equal to the Debye-length. just like in the Gouy-Chapman
picture. These trends are
fully consistent with Monte Carlo simulations by Camey and Torrie24).
Figure 7. Potential decay in the electrical double layer in the absence (dotted curve) and presence [full curve) of a specifically adsorbing monomer A, according to the multilayer Stern-mode13). Parameters: - I+I(O)= 400 mV. c, = 0.1 M. x$” =lO, other xS and all x parameters zero, L = 0.6 nm, components, hexagonal
d (nm)
The effect of a neutral monomeric adsorbate on v(z) at 0.1 M salt is illustrated in fig. 7. The adsorbate is assumed to adsorb strongly (xs = 10). Notwithstanding displacing
the high surface potential
counterions
(400 mV) it is capable
from layer 1 so that the potential
of
decays more
slowly in layers 1 and 2 than it does in the absence of the adsorbate. Beyond layer 2 the potential decay is exponential again, with the same decay
length
(1 nm for
10-l M salt) as in the absence
of specific
adsorption. In fig. 8 we present the surface charge-surface
potential
relation
(‘titration curve’) for a similar case: a charged surface in the presence of 0.1
M indifferent
electrolyte
and
a neutral
specifically
adsorbing
adsorbate. It is seen that at given ~(0) the adsorbate reduces the amount of charge, simply because of the fact that it reduces the screening by counterions
close to the surface. Since o(O) is plotted as a function of
w(O). the two curves intersect at the p.z.c. When comparing this result with the data given in fig. 1 we note that the shape of the curves is somewhat
different. This is because the ions in this example have no
chemical
affinity
with
the
surface.
Assigning
them
a
non-zero
Au,” (and/or Au_“) would produce a shift in the pzc and would make the
497
curves asymmetric (unless Au: = Au_“), see fig. 9 below. Related to this is the question of the partial polarization the layer of water adjacent to the solid
phase,
Adsorption
which
contributes
to the
establishment
of the
of molecules in the first layer changes this polarization
pzc. but
this feature has not yet been included in the model.
m
100
-100 mV
J, (0)
-1.0, 05
Figure 8. Theoretical titration curves 40) - 1+40)In the absence and presence of a specifically adsorbing monomer A. The surface charge is given as the dimensionless quantity a&0)/e, the number of elementaly charges per lattice site. Parameters: X* = 3, ux = 2 where x = SOlvent or iOk). &A = 2h,. L = 0.31 nm. other parameters as in fig. 7.
I
I
.
,
U(O) e
-0.6
-0.6
-0.4
-0.2
0.0 0
- 200
-400
-600
-800 mv
tiC0)
Our next adsorbing
example
cation
(fig.
9) illustrates
on the charge
potential
Figure 9. Theoretical titration curves o(O) - ~(0) in the absence and presence of a specifically adsorbing catton A:. Parameters: x:=5, ! = 0.31 nni, other parameters as in fig. 7.
the effects relation,
of a strongly again
at 0.1 M
indifferent electrolyte. In this case the cation was modeled as As, i.e., as a trimer with a charge of +1/s for each segment. The segmental adsorption energy xf
was chosen to be 5, so that this cation, with a rather diffuse
charge and a total adsorption energy of -15 kT, somewhat resembles the TBA+
ion in figs.
2 and 3. The
conformational
properties,
treated
according to section 4b, are different but in this case the electrostatic effects dominate. Four titration curves o(O) - ~(0) are shown, for bulk solution volume fractions (I: of 0. 10-7. 10-6, and 10-S M. respectively.
It is clear that
498
now there is a shift in the p.z.c. towards
the positive
side and a common
intersection
v(O). Below
this tip the organic
cation
point
at a strongly
promotes
increases
co-adsorption
-o(O),
qualitatively
beyond
along
is again
affinity
for the surface.
considerably
as found
the same
curves
of negative
charge-determining
the tip the reverse
the same
explained
negative
related
applies.
All these
in the experiment
lines.
The
different
ions
and
trends
are
(fig. 2) and
shape
can be
of the o(O) - ~(0)
to the fact that the small ions have no chemical Even a small Au: or Au_” would high electrolyte
at this relatively
affect
the results
concentration.
Figure 10.
Theoretical adsorption isotherms of a monomeric cation A+ on a surface with surface potential ~(0) = -100 mV. at three concen-
trations of indifferent electrolyte. The adsorbed amount 13: is given in monolayers. Parameters: xt =15, EA = 5 ~0.C= 0.31 nm. other parameters as in fig. 7.
Our last example When A+ adsorbs between
of this section
onto a negative
adsorbate
and surface,
is again for a monomeric
surface,
but a repulsive
adsorbate
molecules.
Indifferent
may have
a reducing
or an enhancing
seen
in our
isotherms
final
of
logarithmically around
(at
for
competition
with
(including
to be screened the theoretical 4 is striking. to
monomeric
mV
salt
monolayers. so that
point
the
Above
that is
electrolyte
are
The
That
our
coverage,
reduced
plotted
semi-
to
at
repulsion
of A+: below
due
is
intersect
lateral
the
electrostatic point,
the
so that there is nothing
has no effect.
whereas
This
adsorption
In the intersection
that these figures picture
and therefore
curves
in fig. 10 with the experimental adsorptives,
neighbouring
10) where
adsorption
counterions.
It may be added units.
(fig.
potential)
enhances
both
cation A+. interaction
on the adsorption.
A+) is just isoelectric,
and indifferent
oligomeric
section
adsorption
adsorbed
screens
effect
surface
one between
concentrations.
salt
indifferent
curves
electrolyte
of this
-100
three
important
intersection
apply
A+
r = 0.12
becomes
surface
example
there is an attractive
The similarity
ones in figs. 3 and
(and also figs.
figures
nevertheless
of
1 and 2)
8 and
10 are
applies
so well
for is
499
explained
by the fact that in practice the electrostatic
effects, notably
those in the first layer, dominate. Having description
established
that the multilayer
of the electrosorption
turn our attention
Stern-model
gives a fair
of ions and small molecules, we now
to the extension
of this model
to polyelectrolyte
adsorption. 4 Polyelectrolyte adsorption model a) Conformations As compared previous
to the monomer
section,
a theory
electrosorption for
model discussed
in the
adsorption
again
polyelectrolyte
is
considerably more complicated because the conformational entropy of the flexible
chains has to be accounted
for. Earlier models had to make
drastic assumptions in order to cope with the complex interplay of long range electrostatics,
short range chemical interactions
and conforma-
tional effects. The first model is due to Hesselink25.26) and is an extension of an early polymer adsorption model of Hoeve27). The latter is based upon an assumed However,
exponential
Hesselink
assumption
form
calculated
of the segment the electrostatic
that the charge in the adsorbed
density
distribution.
free energy under the layer is homogeneously
distributed. As a result, very dilute and extremely thick adsorption layers were
predicted.
In more
recent
models,
which
have
been
briefly
discussed in the introduction of section 3, the segment density profile is not
predetermined
and
very
thin
layers
are
obtained
if the
salt
can deaf with polymers
without
the
properties
are
concentration is not too high. The multilayer introduction
Stern-model
of extra parameters.
The configurational
treated along the lines of the Scheutjens-Fleer
theoryzs-so) where all the
possible conformations are taken into account by assigning each segment of a chain a weighting factor e-urWKT that depends on the local environment
according
to eq. (15).
For polyelectrolytes,
contains an electrostatic contribution, given by eq. (10).
ui(z)
again
500
Figure 11. Schematic illustration of a lattice with a solution next to a solid adsorbent. The solution sites are filled with solvent (open circles). small ions, and three polyelectrolyte chains (of five segments each) in specified conformations c. d and e. Conformations c and d are adsorbed and have r”(l) = 3 and @(I) = 2 seg-ments. respectively. in the first layer. Conformation e is free (nonadsorbed). with f(4) = 1 and 175) = 4.
Here we do not treat publications39
28-30).
is a modification
the
model
in
detail
and
refer
to
earlier
Th e principles can be illustrated with fig. 11, which
of fig. 5a. In this figure three chain molecules
are
indicated in specified conformations (labeled c, d and e). Each conformation
may have a different energy, depending on the
position (layer number) of the segments. The energy of a chain is the sum of the energies ui(z) of its segments, taking into account their spatial distribution. (hence,
If ri is the number of segments of a chain of component i
x-i-1 is the number
conformation
of bonds),
the Boltzmann
factor Gy of a
c is then the product of the x-i Boltzmann
factors of the
segments, multiplied by a product of ri-1 bond weighting factors ho or 11. By summation over all possible conformations, the volume fraction profile of the polyelectrolyte component i has r:(z)
is obtained.
If conformation
c of (polymeric)
segments in layer z, the volume fraction profile
becomes:
(18) This equation also applies to monomers (ri = 1): in this case r:(z)
= 1 if
the monomer is in layer z, GF is just the simple Boltzmann factor e-u*(zl/KT, and the summation over c involves only one term, so that eq. (18) reduces to eq. (11). For chain molecules more complicated.
the expression
For example, the conformation
for Gf is
labeled c in fig. 11.
501
having
five segments
(rl = 5). two “parallel”
bonds,
and two “perpen-
dicular” bonds, has an energy u: = 3u,(l) + 2u,(2). In this case rF( 1) = 3, r:(2) = 2, and Gf = A$: exp(-ur / kT). Similarly, for conformations d and e in fig. 11 we have the Boltzmann factors Gy = hoh: exp(-up / kT) and GF = h&exp(-u:
/kT), where uf =2u,(l)+u,(2)+~,(3)+~,(4)
and u: = u,(4)+
4ui (5), respectively. The summation in eq. (18) is most easily performed using a matrix formalism. We refer to refs. 3 and 28-30 for more details of the theory and the numerical theoretical
procedures.
In the next six figures we give some
results obtained with the multilayer
Stem-model.
In a few
cases the data were obtained with an earlier version of the mode12o-22)but under such conditions that the difference, if any, is very small. b) Theoretical
results
Strong nolvelectrolvtes
1
In figures strong
10
5
z
15
20
Figure 12. Semilogarithmic segment density profiles of a strong polyelectrolyte adsorbing on an uncharged surface, at various salt concentrations3g). For comparison, the profile for an uncharged polymer is also given. Parameters: $b = 104. r = 2000, f = 0.71 IXIL~~= 2. x = 0.5. E = 80 q, for all components. hexagonal latice.
12 and 13 we show some results for the adsorption
polyelectrolytes.
Fig.
12 gives
semilogarithmic
of
concentration
profiles near an uncharged surface, at various salt concentrations cs and at a constant
polyelectrolyte
bulk solution volume
fraction
of 10-a. The
figure was computed with the model of Evers et al.22) but the results of the multilayer Stem-model
are virtually the same: only at the higher salt
502
concentrations
some minor
differences
occur. The most conspicuous
feature of fig. 12 is the minimum at low ionic strength, which originates from the high potential generated by the adsorbed molecuies,
repelling
other chains, that are consequently depleted. Under these conditions. the adsorbed
amount
conformations,
is low and the adsorbed
chains
adopt
very
flat
with only a few short loops and hardly any tails. As a
result, the chain length dependence is also very weak. With increasing cs the adsorbed amount (and the chain length dependence) increases and the minimum in the profile becomes shallower. ~though
the minimum at
low cs in fig. 12 is rather pronounced on the logarithmic scale used for o(z), it could probably not be detected experimentally, because of the low absolute values of the concentrations involved.
1.5 1
1.0
CS
2.0 M
Figure 13. The adsorbed amount e”p [in equivalent monolayers) of a strong polyelectrolyte (v = -1) as a function of the salt concentration c, at three surface charge densities ~(0)~). The abscissa axis scale is linear in 4,. Parameters: r = 500. ~~=t~,L=O.6nm,~~=1,~=0.5 for polymer-solvent or polymer-ion interaction. other xs and x parameters zero. Ed = 20~~. E = 80&, for the other components.
In fig. 13 we present adsorbed amounts as a function of indifferent salt concentration, for three different values of the (fixed] surface charge. The abscissa scale in this figure is linear in u’cs. The polymer is assumed to have a weak chemical (specific) interaction with the surface and the surface charge is taken opposite to that of the polymer. Small ions have only electrostatic interactions with the surface, At low ionic strength, the adsorption is nearly proportional to the surface charge. If the surface is uncharged, the adsorption is almost zero. and when the surface charge is increased, the amount of adsorbed polymer adjusts itself such that the surface charge is slightly overcompensated.
The extent of overcompen-
sation depends on xs. At high ionic strength the adsorption increases by nearly the same amount for all surface charge levels, the slope being slightly higher for lower surface charge. This implies that the adsorbed amount changes by only a small factor when the surface charge is high, but shows a dramatic relative increase when the surface is near to neutral.
503
Of course, the enhancement of adsorption by salt is due to the screening of lateral electrostatic repulsions in the polymer layer. We note that electrostatic
interactions
between
colloidal
particles
(with bare, smooth walls) are usually already entirely screened at salt concentrations
of about 0.1 M, whereas with adsorbed ‘polyelectrolytes
screening effects still play a role up to 2M. In colloid stability only longrange interactions are important, and since in 0.1 M salt the Debye length K-1 is only becomes
1 nm the electrostatic
repulsion
between
small with respect to the long-range
However,
the
conformation
(and
colloids
then
Van der Waals forces.
adsorption)
of polyelectrolytes
is
determined by interactions between charges in close proximity, and salt affects these interactions even if ~-1 is considerably below 1 nm. This is also the reason why a strong polyelectrolyte
does not reach the same
adsorption properties as the corresponding uncharged polymer would do, not even at very high ionic strength,
although
with increasing
cs its
behaviour tends towards that of the uncharged polymer. Since in most problems
of screening
due to electrolyte
the basic
length scale is the Debye length ~-1, which varies as ~2.~. it might be anticipated that the adsorbed amount of the polyelectrolyte also increases linearly
with
accordingly.
c or, for that matter, Indeed
the curves
with dc,.
Fig.
are (approximately)
13 was linear
plotted
in dc, for
higher salt concentrations, but at low cs the dependence is not so simple. In that range the charge compensation
between surface and adsorbed
polyelectrolyte dominates, and 0: depends more weakly on k,. One uncharged
might
compare
polymers.
polyelectrolyte
In the latter
adsorption
with
case two parameters
that
govern
of the
adsorption behaviour: xs for the segment-surface interaction and x for the segment-segment
interaction
in the solvent.
One could
visualize
a
polyelectrolyte as an uncharged polymer with an overall xs-parameter that contains
a chemical
part (xs as defined before) plus an electrostatic
contribution that depends on surface charge and ionic strength. If surface and polyelectrolyte
are oppositely
charged.
this electrostatic
part is
positive, favouring the adsorption. It decreases with increasing cs. In this case, salt opposes the adsorption of the polyelectrolyte. Similarly,
one
could
imagine
an
effective
X-parameter.
Its
electrostatic part is always negative because of the mutual electrostatic repulsion between the segments, and it also decreases with increasing cs. Hence, the electrostatic part of x tends to decrease the adsorbed amount.
504
At low cS the overall
x is low
polyelectrolytes
show
the same
trends
low adsorbed
amounts,
flat conformations
solvents:
dependence.
With
electrolytes
o(O), see fig. negative,
adsorption
interesting
situation
adsorption
energy
electrical
energy
adsorption
the adsorbed
energy
below.
14,
of
of a segment, vev(1).
Rewriting
Hiickel
approximation
o(o)cr =
e
This equation from
the surface
poly-
chemical
xS + hl~,
An
to
the
by a repulsive
out at xsc. the minimum
the conformational
this in terms of the surface
more
decreases.
contribution
is balanced
comes
to compensate
linear in
charge
transition:
entropy
loss
xsc = xS + hrx -
charge by using the Debye-
one obtains:
(x,+$x-x,)
(19)
can be used to estimate
the critical
good
and
is approximately
of the chain, we have an adsorption/desorption vev(1).
in (extremely)
and weak chain length
polyelectrolyte
the
If that balance
needed
adsorbing
x increases
By making
when
so that
polymers. amount
a negative
arises
negative),
as polymers
more like uncharged above,
13 and fig.
the
often
c S the effective
increasing
behave
As discussed
(and
surface
charge
the chemical
o(O)“’
where
contribution
xS + Xix
the polyelectrolyte
is just
fully desorbed. Of
course,
such
a
balance
between
chemical
interactions
could also occur with small molecules,
will
to a sharp
it lead
interaction effect.
transition.
for the many
It is
sensitive
this
probes
monomers
cooperativity of
This
the
which
makes
interactions
that
electrical
but only for polymers
is because
in a chain
and
the
leads that
each
same
polymers of
segment
to a cooperative their
are
very
monomers
experiences. Weak
nolvelectrolvtes It is possible
by including now
becomes
degree
to extend
a degree
following
relation
polyelectrolyte
of dissociation
va(z)e~(z),
of dissociation
eq. (19) to the case of weak a(z) into the electrical
as in eq. (10). Rewriting
ab in the bulk solution,
for the critical
just desorbs:
surface
a(z)
polyelectrolytes energy,
which
in terms
of the
Evers et al.22) derived
charge
~$0)~~ where
the
the weak
505
(xs+~lmc)
O(“)cr =Kcab+(l-ab)
(20)
(X,+h,X-&)
la5*
Numerical
results
for the adsorption
of a weak
polyelectrolyte
(pK = 4) as a function of o(O) obtained by Evers et al.221 are shown in fig. 14. The adsorption is indeed linear in o(O), with a slope that decreases if the polyelectrolyte molecules,
charge becomes less. For sufficiently charged macro-
there is a clear adsorption/desorption
transition
at o(O)Cr
which shifts towards more negative values as the negative polymer charge decreases. It is found that o(0)Cr as it comes out of the numerical results is well described by eq. (20).
a uncharged 0.5 -
1
2
3
4
5
6
PH
7
I3
Figure 15. Degree of dissociation a( 1) on the surface and ab in solution for a weak polyacid. as a function of pH3). The quantity all) was computed for three surface charge densities o(O). Parameters: c, = 0.1 M. pK = 5, other parameters as in fig. 13.
That the distinction between a(l) and oh is not meaningless is borne out by fig. 15 where a(11 is plotted as a function of pH for three values of surface
charge
density
a(O). For comparison,
ab is also shown. At
506
pH > 4.5, dissociation to the high density significantly expulsion adjusts a(l)
at the surface of segments.
enhance
the
is less than in the bulk solution,
However,
dissociation
of H+ from the surface
region.
itself such as to effectively
a strongly at low
due
The local degree
neutralize
surface
to the
can
strong
of dissociation
the surface charge:
at low pH
is higher than ab, the more so as o(O) increases.
2
4
Figure 16. Adsorbed amount of a weak polyacid as a function of pH for three fixed surface charges3). Parameters as in fig. 15.
8
6 PH
The amount has
effect
of the
is shown
positive
charge. of the
polymer
and
adsorption
chemical small
Three
we
surface
neutral. affinity
the
same
its adsorption adsorbing
amount
with
have
trends At
carries
to three different
as in fig. surface
increasing
charged 13: a low
charge
pH < 2 the
segments
competition
effects
driven by the
have to compete
Therefore surface
attraction
were
segments
already
between
a is
with
we now see a charge:
to find
discussed
as the towards
a place
to
in section
2.
the salt ions and the surface
this effect.
on positively
part of fig. 16 is at intermediate charged
below the pK of the dissociating as
for polymer
and
polymer
goes up, more and more small ions are attracted it harder
i.e. it
a constant
a strongly
is now entirely
charged.
adsorbed
is again weak,
surface
to the
Therefore,
is highly
on the
corresponding
proportional
the surface
enhance
understood
density
pH > 6, we
conformation.
The most interesting adsorption
At
to see
We may add that specific will further
are shown,
xs. However,
making
Similar
The
polymer
in adsorbed charge
charge
charge.
charge.
is nearly
flat
the surface, adsorb.
curves
expect
which
ions when
decrease
(negative)
surface
corresponding essentially
polyelectrolyte
in fig. 16. Here the polyelectrolyte
a pH-dependent
values
be
positive
pH,
due
follows.
As
surfaces
has a maximum
group of the polymer. the
chain
acquires
pH. Here the at a pH slightly
This maximum some
charge,
can the
507
attraction
to the surface is no longer purely chemical.
An additional
electrostatic contribution builds up, so that the adsorption is enhanced. Moreover, the polyelectrolyte
can now compete more efficiently with the
small ions in neutralizing the surface charge. Soon, however, the lateral repulsion
between
charges
on the chain reverses
the trend and the
adsorption decreases strongly until the charge on the polymer reaches it maximum value.
2
3
4
5
6
7
8
as in fig. parameters
15.
PH
If the pH is increased from 4 to 6. major structural changes occur as one would expect: strong reductions in size and mass of tails and loops and a concomitant increase in train fraction with increasing pH (fig. 17). The trends displayed in fig. 17 are easily understood from the discussion given above:
flat adsorbed
conformation
at low pH where the polymer is only weakly charged. The
chains at high pH and a more extended
transition occurs around or just below the pK, and coincides more or less with the maximum in fig. 16.
508
5 Polyelectrolyte adsorption experiments a)
Introductory In this
section
electrolytes
with
comparison have
remarks
particular,
this
means
will
largely
polymers
like
electrolytes predicts
that
every
exclude
we
will
monomer results
true
section.
systems
which
on
with
with
it should
properties,
versa.
an ionizable
simple,
strongly
referring obvious
group.
with
branched either
be emphasized
In
flexible
oligomers,
and with copolymers,
It is not always
essentially
or vice
concentrate carries
poly-
For this
unit
DNA,
Finally,
equilibrium
free energy.
for adsorbed
of the model
obtained
(double-stranded)
(proteins).
select
as those
like polyethyleneimine
or biological lowest
where
data
in the preceding
we must
characteristics
homopolymers
experimental
discussed
to be meaningful
the same
This
we compare
the theory
stiff poly-
synthetic
that the theory
to the
(stable)
that real systems
state
of
can reach
this state and, if they do, how rapidly this occurs. We might even suspect that
a polyelectrolyte
metastable
has
a good
chance
to be strongly
trapped
in a
state by many strong ionic bonds. We will return to this point
at the end of this section.
In fact, with proteins
(section
6) this feature
is
even more salient. The
adsorption
described
by
experimental
of simple,
no
more
parameters.
number
of techniques.
internal
degrees
addressed. accepted when
The
and
of long
contributions
when range
that
The normal The
masses however, the
of multiple
structure
conditions
is usually mass
as
are readily have
question
already
measured
so large leads
of by a
a number
of structure
anchoring
well
a function
must
of be
to the generally-
which leaves room for a lot of variation
(and polymer
the repulsion
between
(as in polyelectrolytes),
primary
structure)
monomer
units
a flat
structure
from loops and tails is most favourable,
of zero net monomer/monomer formation
molecules adsorbed
Adsorbed
possibility
experimental
For example,
the
Polymers,
of freedom
‘loop-train-tail’
small
than
interaction
with
whereas
(polymer
change.
is very strong minor
in the case
in a O-solvent)
the
of long loops and tails is much more likely. averaged
spatial
to the interface
shape
scatteringsz)
of
this
distribution
is usually
profile
has
of monomer
called been
units
the segment studied
and. for some cases, by neutron33)
by
(or segments)
density means
proillesr). of
neutron
or X-ray reflection34).
An
509
alternative is to study the thickness of the adsorbed layer, operationally defined
in terms of a particular
optical
techniques
escence3611, hydrodynamic sedimentation and pores, (surface
experiment.
(reflectometry 351, total
We mention internal
the use of
reflection
techniques 311 (determination
fluor-
of diffusion or
coefficients of colloidal particles, flow through capillaries electrokinetics),
force
balance,
and
‘disjoining
osmotic
pressure
pressure’
techniques311
of concentrated
colloidal
dispersions). It may be added that when people speak of the “average thickness” of an adsorbed polymer layer, they are referring to a quantity that is not unique in the sense that different types of experiment produce different “thicknesses”. In particular by hydrodynamic and electrokinetic techniques a “hydrodynamic thickness” is measured, determined by extended loops
and
tails.
“ellipsometric
This
thickness
thickness”
which
is usually reacts
much
on the
higher
index
than
the
of refraction
difference between polymer and solution and hence essentially reflects the inner parts of the adsorbates. b) Adsorption
of strong polyelectrolytes
1.0 h...
0.15 74 0.5
0
1
kg/ml M
v,
NoCl
2
3
4
780
:.. Sta.*
kg/
mol
5
dhm)
Figure 18. Segment densityprofilesfor poIystyrenesulphonateof two diiIerentmolecular weightson positively ifuUcurves)and negativeIy(dottedcurves)chargedpolystyrenelatex as obtainedby smalIangleneutronscattering37). A suitable model polyelectrolyte
is polystyrene
sulphonate
(PSS). It
contains strong negative sulphonate groups. It can be prepared from anionically defined Segment
polymerized narrow density
styrene
fractions profiles
negative polystyrene
and is commercially
over a large
range
for PSS adsorbed
available
of molecular
both on positive
in wellweights. and on
latex particles were measured by means of small
510
angle neutron is confined
scatterings71. These profiles show that most of the polymer
in a thin layer, even at moderate
trends shown in this figure are consistent computations,
ionic strength (fig. 18). The
with those predicted by model
see fig. 12. At the salt concentrations
used in the experi-
ment, the minima in the theoretical profiles are insignificant
or absent.
Figure 19. Adsorbed amount of polystyrene sulphonate of three different molecular weights as a function of the square root of the concentration NaCI. The adsorbent is po~yo~ethylene3s~ [full curves) or silica at pH 23g) (dashed curve).
When PSS is adsorbed the lateral interactions Such
systems
on (almost) uncharged
were studied
by Papenhuyzen
crystals of polyowethylene who
adsorbed
uncharged.
PSS on silica
Both authors
et al.381 who used single
at pH 2, where
amounts
concentration
(fig. 19). curves for
this
find that the adsorption
the adsorbed
curve
the effects of
(POM) as the substrate, and by Marra et al.39)
manner with ionic strength, the extent depending
theoretical
surfaces,
in the polymer layer show up in their purest form.
oxide
is virtually
increases
in a regular
on molecular
weight. If
I- are plotted against the square root of the salt are obtained
o(0) = 0 in fig.
is negligible
whereas
that are very similar to the
13. In the
at high
absence
electrolyte,
f
experimental
error, linearly with &,. The slope of the linear parts at high
es increases
with increasing
molecular
weight:
longer loops and tails (when the electrostatic Papenhuyzen
cs it increases,
of added
long chains
interactions
et al.381 have shown that the molecular
is well predicted
by the model. For a further discussion
within can form
are screened).
weight dependence of this aspect we
refer to figures 24 and 25, below. The very fact that adsorption must be due to a non-zero
does occur on these uncharged
chemical
adsorption
surfaces
energy (xs). The resuhs
obtained
with SiO2 (pH 2) and POM are very similar, from which we
deduce that xs is nearly the same for both substrates.
I0 mm-’ r c
0.5 -L--
/’
P
.A
/exp-
.@--
_-‘)A
0.5
AI
_A’
t 1
-rM
them ,A .--
,
I
1F3
mm*
I
10
10-l M
c*
Figure 20. Comparison between experimental adsorbed amount I? (in mg mW2) for polylysine on negatively charged Agl and theoretical amount 9; (in equivalent monolayers), as a function of the salt concentration2** *O). The polylysine (307 amino acid residues) was adsorbed from NaBr-solutions at pH = 6 and pAg = 11. The parameters used in the model are: r = 300, Qi = 10T4, up = 0.71, o(0) = 0.2 e/a, with a, = 0.3 nm , B= 4.85,~=0.6,e=8Oc, iraIl cubic lattice components, Go = 4/6).
Another interesting model polyelectrolyte is polylysine (PL), which is a polybase that can also be obtained in relatively well-defined with a narrow molecular
weight distribution.
The intrinsic
fractions pK of the
primary amine group (- 10.8) is such that the molecule is fully positively charged up to pH-values of about 8. The L-stereoisomer
(poly-L-lysine)
can develop a helical secondary structure but only at pH 2 10.5. Helices are not found with the racemic random poly-Dllysine. homopolyaminoacids.
polylysine
becomes
The
very
small,
becomes
adsorption
insoluble
of PL onto
Just like most when
the charge
silver-iodide
(AgI)
crystals20.401and onto silica and glass 411has been carefully studied by Van der Schee et al.201and Bonekamp et al. 4o+*ll, respectively. Both poly-L and poly-Dllysine relevant enhanced
were used but significant differences were not found in the
pH range
(2 8). As with the neutral
by the addition
surfaces,
of salt in the case of Agl
adsorption
is
(fig. 20). For
comparison, theoretical curves computed by Van der Schee et al. are also shown in fig. 20, with a log~i~mic
scale for es; the agreement is semi-
quantitative. In the case of silica, however, there is only a minor salt effect with a weak maximum around 10-l-10-2 M, rather than a
monotonous
increase (fig. 21). This is probably due to specific adsorption of (sodium) counterions on the silica, which compete for surface sites with the iysine residues, We then have two opposing tendencies: (if increased screening of lateral
interactions,
leading
to enhanced
adsorption:
(ii) increased
screening of attractive polymer surface interactions, leading to a weaker
512
binding that
the
polymer
of polymer.
Since
outcome
depends
the latter on the
and the substrate.
I
0.0 -
is a specific
chemical
In order to model
one would have to assign a chemical
1
effect
adsorption
I
natures
one, we expect of the
these results
salt,
the
theoretically,
energy to the small ion.
I’
mg m-2
A-&
lA
7.51 c.3
/
0.6 -
Ol.-
O---L
/
0
\
0
clz-
o----c
0
10-3
I.0 10-2
10-lM 0
c. Figure 21. Effect of the NaCl concentration on the adsorption of polylysine (307 amino acid resfdues) on silica [Aerosil 0x50). at three different pH values41).
(0)
Figure 22. Adsorption of polylysine (190 amino acid residues) on silica (Aerosol 0x50) from 0.01 M NaBr. as a function of the surface charge4f).
Figure 23. Adsorption of pofyacryhc acid (M = 2000 kg/mol) on hematite as a function of the surface charge, in the presence of 1 mM NaC104. The data were computed22) from the ex ertments of Gebhardt and Fuerstenau42 P The surface charge of hematite has been measured by potentiometrtc titration in the absence of polyacrylic acid.
The effects respectively. substrate
of the surface
charge
that can carry an appreciable
the polymer.
can be seen from figs. 22 and 23,
The data in fig. 22 are for polylysine Charge
force for adsorption.
compensation
charge
adsorbed
of opposite
is thus an additional,
onto silica,
a
sign to that of strong
driving
This is borne out by the results, which show that the
513
adsorbed amount at relatively low ionic strength (lea-lo-2 entirely electrostatically
M) is nearly
determined. Similar conclusions were drawn by
Evers et al.22) from data provided by Gebhardt and Fuerstenat@i,
for
polyacrylic acid adsorbed on hematite (fig. 23). The curves of figs. 22 and 23 display the linear behaviour predicted by the model calculations
(fig.
14) and show that the agreement between theory and experiment is quite satisfactory. The extrapolation of the linear section of fig. 22 to I = 0 gives a positive value for the critical surface charge density o(0)Cr, compare eq. (19). This points to a non-zero chemical component
to the adsorption
energy. A similar conclusion applies to fig. 23, where the charge signs are opposite.
r
6050-
Figure 24. Adsorption of polystyrene sulphonate on polyoqnnethylene crystals, as a function of molecular weight. at three NaCl concentrations38). M (kg/mole)
The effect of molecular weight M on the adsorption of PSS on POM and on silica, respectively,
is shown in figs. 24 and 25. At low ionic
strength the adsorbed molecules adopt very flat conformations and there is nearly no molecular weight dependence. As the ionic strength goes up, the slope of the F versus
log M curve increases
as well. This is in
agreement with the discussion given in section 3 (after fig. 13) about the influence
of salt on the overall (effective)
concluded
that the negative electrostatic
the solvent molecular
poorer with increasing
weight dependence
X-parameter.
contribution
There
it was
effectively makes
cs. For uncharged
polymers,
the
of P increases with increasing x. In poor
solvents F continues to increase with M as the chains become longer, but in good solvents F(M) reaches a plateau at high M. For PSS, we do not find such a plateau. Apparently, water is a rather poor solvent for PSS
514
when
the
charge
on
the
polymer
is strongly
screened
by
a high
salt
concentration.
M f kglmole)
Figure 25. Molecular weight dependence for the adsorption of polystyrene sulphonate on activated Cab-0-Sil. at pH 2 and various concentrations of NaCl (a) and MgCl,(b)3g). In the taken,
original
an attempt
weight dependence
paper@. was
39) from which
figures
24
made to compare quantitatively
of r with theoretical
computations.
and
25 were
the molecular These authors
used an early version of the polyelectrolyte adsorption theory, based upon an extension
of the Roe-theory431 instead
Scheutjens-Fleer
of the more sophisticated
mode12s-30). They concluded that the agreement was
satisfactory,
but that their model predicts too weak a molecular weight
dependence
at high M. This is probably due to an artefact in the Roe-
theory, where tails are neglected. It is very likely that a better agreement between theory and experiment would be obtained if the conformational statistics
are better accounted
for, e.g., by using the Seheutjens-Fleer model. So far, such a full analysis has not been made.
515
/ k
60~x10‘5monomole
6Oc
50
40
30
/g
/
0’
.P’O 4%
/
A0
_l-n
0
31
Figure 26. Adsorption isotherms of polystyrene sulphonate on polyoxymethylene crystals from 2.18 M NaCl. for three different molecular wetghts381. 200
100
Qk
may be concluded
It
experimental
trends
neutral
substrates
to what
adsorbing more
indicated effects
is
availabless).
macromolecules interpenetrate. have
rounded
could
adsorb
in mutually
shape. The mean-field
those
theory,
are these
for well-fractionated
(by chain some
explanation degradation)
evidence
is that ‘blobs’
the
adsorbed
which
to adsorption
of monomers,
than
for such
inhomogeneous:
repelling
that this leads with
on the
of sulphonation)
strongly
the
However,
isotherms
One possible
suggestion44)
expect
in common
degree
of the supplier:
laterally
is
One might more
than is common substrates.
Another
layer
adsorption
by the mean-field
(as to the
by the specifications
theory.
of PSS adsorption
are less homodisperse
heterogeneous
polyelectrolyte
which
is predicted
that in general
by recent
feature
in fig. 26, where
on well-defined
is that the PSS samples
examples
described
are much more ‘rounded’
polymers and/or
the above
One unexplained
is shown
In contrast
isotherms
from
are excellently
there is one exception. given.
3@l PPm
the do not
isotherms
i.e.,
a more
theory is of course unable to take this into
account. c) Adsorption
of weak polyelectrolytes
One
known
of the best
acid (PAA). It is a simple
model
polyacid,
weak
polyelectrolytes
with an intrinsic
is polyacrylic
dissociation
constant
516
K of pK = 4.6. Therefore, and almost side
chains,
so that
precipitation) candidate
at low charge charge.
(--NR:)
independent, polymer
densities
such
between
which
groups
surface
a suitable
on the effects
carried
to have
so that
show up most clearly.
(or even
It is therefore
concentrates
zero
of
out by Blaakmeer
(PS) lances with fully dissociating
in order charge,
virtually
no hydrophobic
as hypercoiling
are absent.
study
used polystyrene
surface
positive
charge
effects
Such a study was recently
These authors
positive
is variable
pH range. Also it contains
complicating
for a fundamental
the polymer et alas).
its dissociation
100% in a suitable
a constant,
the effects
We denote
i.e..
pH
of a variable
this positively
charged
latex as PS+.
- O.Wl
[KNOJ
M
zoappm IPW
In
section
adsorbing
on
intersect might
a negative the same
indeed
near to the plateau adsorption
model
affect
As
taken
the surface
to happen
adsorption
isotherms
at different
ionic
plus adsorbate
two adsorption
of the isotherm
which
a consequence,
isotherms
adsorbed
which
show a similar amount.
equilibrium
concentration.
The
that in the saturated
polydisperse
nature of the PAA used.
point
it is situated
difference
We
for PAA on PS+
but only by a very
experimentally
intersection
However,
strengths,
on a positive
by indifferent
is indeed
A+
point. This point is very
implies
screening
for
is isoelectric.
with poly A- adsorbing
seem to have an intersection
I only slightly,
calculations
(relative)
that
layer the surface charge is overcompensated,
amount.
should
saw
surface,
In fig. 27 we present
latex which
small
10) we
at the point where
expect
surface.
3 (fig.
(+160 mC/m2) at pH = 4.045).
at about
electrolyte found.
the same
at a much
is probably
The
related
lower to the
517
Above
we found
polyelectrolyte polyelectrolytes can
adjust
effectively complex
that
adsorption (figs.
their
the salt
dependence
13, 19 and 20). The reason
degree
of dissociation
the surface charge is nearly
concentration
is only weak, and much smaller
neutral.
such
for weak
than for strong
is that the weak groups as to compensate
more
(fig. 15). As a result, the substrate-adsorbate In the overall
balance
of all the interactions,
salt then has only a minor effect.
Jo
0
2
4
6
8
Figure 28. Comparison of the experimental adsorbed amount r (In mg/m*. left-hand scale) for a weak polyacid with the theoretical 0: (in equivalent monolayers. right-hand scale). as a function of PHIL). The experimental points are for polyacrylic acid (71 kg/mol) onto a cationic latex with ~(01 = 160 mC/m2 at an equilibrium concentration of 100 ppm in lo- 1 M KNOX. The full curve was computed with the model of Bdhmer et a1..3) using $I; = 104. pK = 4.25, o(O) = 160 mC/m2, cs = 0.1 M. L =0.6nm. r=500, x:=2, andX=0,5forthe polymer-solvent and polymerion interaction. The other xS and X-parameters are zero, and E = 80 ~0 except Ed which is 20 ~0.
10
w
The central fig.
28, where
function
and most striking the
adsorbed
of pH, at constant
there is a clear maximum
of Blaakmeer’s
result
amount
of PAA
ionic strength
onto
work is given in
PS+ is plotted
(10-l M KNOa).
It is seen that
at a pH below pK. Such a maximum
had been
predicted
four years earlier by Evers et al.22) and later by Bijhmer
see
16. A
fig.
maximum is given
qualitative
in fig. 28, where
Stem-model.
The agreement
the experimental one. Nevertheless, observation positively
explanation
was given in the discussion the curve
occurrence
was calculated
is about
Blaakmeer’s
of this interesting
system both polymer
the
study provides
TiO246) the effect
although
one pH-unit
pattern.
below
a
comparison
the multilayer the position
of
the theoretical
the first well-documented
In studies
was never
with
et al.3).
of such
of fig. 16. A quantitative
is quite satisfactory,
maximum
charged
for
as a
of PAA adsorption
discovered
and surface have a pH dependent
since
charge.
on
in that
518
d) Metastable
states
It has been noted more than once polyelectrolytes
do not necessarily
surrounding adsorbed
solution.
amount
For
changes
in surface
PL/AgI
system.
polyelectrolytes strong
macromolecules conditions finally
More
study
increasing
of
and not by chain
attachment
polymer/surface
is more
adsorbed
at pH
relaxation
processes
extremely
slow;
for
this
consistent et also)
3 onto
is
determined with
the
data.
for the adsorption
a carboxylic
in adsorbed
PS latex
polyelectrolyte
in the case studied
surface.
it was
by
the
provided found
by a
that
but decreased
would
predict
the
by
with
the
‘frozen’
conditions
Studies
the very
that the
determined
during
of adsorption
of polyvinyl-4-pyridine provide layers
they found
The
than by those
of molecules by
between
dictated was
entirely
A picture
that
by the
be sufficiently
rather
on coverage,
contacts
than
on the
viewpoint
Theory
rather observed
formed
conformations
in the that the
followed
might
processes
weight.
length.
positions
by Pefferkom
bonds
surface
et a1.49). where
molecular
and
reversibly
ionic
did not depend
coverage
kinetics
that
charged
have
evidence
number
conformations
route taken,
they first touch the surface
by Denoyel
of adsorption
with
not entirely
relaxation
then
to changes
Also Van der Schee4s)
seem
inhibit
would
imposed.
calorimetric much
would
under which
enthalpy
were
with adsorbed
et a1.47) found
on the experimental
and an oppositely
to efficiently
reversibly
Meadows
conditions.
charge
It
respond
example,
depends
on the final experimental
that systems
47. 48)
evidence
do occur,
a relaxation
that
but are
time
of 37
hours. We may conclude experimental should
results
be aware
from this that it is always with
equilibrium
theories,
of the fact that relaxation
very useful but when
to compare
doing
times may be widely
so one different
from one case to the next and that experimental
time scales
be chosen
in the first part of this
section found
accordingly.
illustrate
that it is perfectly
in experiment
very well.
The examples and those
discussed possible
obtained
to do so since
with equilibrium
may have to the trends
theories
agree
519
e) Adsorption
of polyampholytes
So far we have dealt exclusively with simple polyelectrolytes
which
carry only one kind of charged group. Restricting ourselves to this kind of system helped us understand the role of electrostatic interactions in the adsorption
of such macromolecules.
Proteins constitute a group of with at least two new complicating factors: (i)
charged macromolecules
they have important intramolecular attractions which give the molecule a certain
degree
of rigidity,
(ii) they carry both positive
charges, i.e., they are polyampholytes. between
simple polyelectrolytes
and negative
In an attempt to reduce the gap
and proteins we discuss here another
interesting
study carried out by Blaakmeer
ampholytic
polyaminoacids
were adsorbed
et a1.511, where onto PS latices.
synthetic both with
positive (PS+) and negative (PS-) surface groups.
r 0.4
-
.n’”
.2-w R \
0.2 -
a; ‘9
0
2
4
6
8
m
10
Figure 29. The adsorbed amount of the oligomer (Lys-Glu-GlyI4 onto negatively charged latex (-25 mC/m2) as a function of the pH. at an equilibrium concentration of 200 ppm51). The ionic strength (KC1 + HCl or KC1 + NaOH) was 0.1 M.
As polyampholytes, copolymers of glutamic acid and lysine were used. One polymer was a random copolymer of 60% glutamic acid and 40% lysine, with a molecular weight of about 20 kg/mol. The other adsorptive was a specially synthesized tetramer of L-lysyl-L-glutamyl-glycine, homodisperse
i.e., a
oligomer with twelve amino acid residues, of which four
carried a carboxylic
and four an amino group. This oligomer
(with an
isoionic point at 8.4) is soluble in water at any pH between 1 and 12, but the random copolymer appeared to be insoluble between pH 4.1 and 5.7, i.e., around its isoelectric point (iep) which is at pH = 4.9. If electrostatic effects would play the dominant
role one might expect
adsorption behaviour for the polyampholyte.
the following
At the negative side of the
i.e.p. adsorption onto PS+ would be preferred, whereas the reverse would
520
occur on PS-. However, both
sides
adsorbed
since the absolute
of the iep, lateral amount
becomes
less
adsorbed
amount
on each
repulsion side, just
at a pH where
it is highly
polymer
and surface
range
where
about
the same for the negatively
they attract
should
dictate
as P for
Hence
decrease
of the
polyelectrolyte a maximum
in the pH range
repel each other, and a minor decrease would
be more
a lowering
a weak
charged.
at or near the iep, a strong
where
pattern
value of the charge goes up on would
be the pattern
expected.
and positively
or less symmetrical
If xs would
charged
with
in the
segments,
respect
be that
to reversal
of
the surface charge. The adsorption
of the oligomer
onto PS- follows
(fig. 29) and the data for the random pH 9.7, respectively, to anticipate maxima
complex.
against
proteins
usually
to the iep of the protein
In this case, the explanation molecule
trend
at low pH and at
that for flexible
at a pH corresponding
of the protein
the expected
taken
with it (fig. 30). It is interesting
6 by mentioning
are also found
resilience
1 6 -
are also consistent
section
plus adsorbent
copolymer
involves
conformational
the internal
changes,
mg mm2 /
P!?
I-
Figure 30. The adsorbed amount of a Lys-Glu polypeptide onto negatively (-25 mC/m2) and positively (+90 mC/m2) charged latex as a function of the pH. at an equilibrium concentration of 200 ppm in 0.1 M KC151). The polypeptide (20 kg/mole) was a random copolymer of 40 mol % glutamic acid and 60 mole % lysine. It is insoluble in water around pH 5.
I I
&
\ \
q
w 08-
ps+ . T_A-
I ,I
I
a
\ \-*
.
.,.,..A
:
AA. 4
0
a
12
w
However, is lower even
at pH 7 the adsorbed
on PS+,
regions.
and -NRg difference
despite
Clearly,
adsorption. between
amount
of the polyampholyte
than on PS-, and at pH > 11 the adsorption the negative
As a possible
-SO,
and -NH;
explanation
is found effect
electric
charge
stronger
is considered
the ionic
Evidence
experimentsdl).
to be chemical
pH-
drives
than that between
size of the latter cation.
in conductometric
that
on PS+ or absent
in these
field which
we suggest
is perhaps
due to the larger
nonelectrostatic
polyampholyte
it is not only the overall
is small
the
bond -COO-
for such a
Of course
this
in our terminology,
521
corresponding
to a different xs. Another contributing
factor might be a
strong competition by the OH--anion for surface sites, especially at high pH. The matter is, however, not yet completely understood: certain asymmetry
in solution
properties
point also plays a role. Such assymmetry
with respect
perhaps a
to the isoionic
does indeed show up in the
viscosity of the copolymer solution. The study discussed above is only a first, but promising, step towards a better
understanding
polyampholytes.
of the interfacial
behaviour
The gap between simple polyampholytes
of
(synthetic)
and proteins is
still very great and statistical theories have so far not been invoked to interpret protein adsorption. The main reason is the difficulty of handling the multitude of specific internal interactions, some of them persisting in off-equilibrium
states. We shall therefore discuss proteins at interfaces
mainly from an experimental point of view. 6 Protein adsorption a) Introductory Proteins
remarks
are copolymers
containing
some twenty different
amino acid
monomers. The amino acids are linked to each other in a polypeptide chain, as illustrated in fig. 31. Two of the three bonds in the peptide unit are free to rotate, whereas the C-N bond is fixed because of its partial double bond character. The side groups R, R’, . .. are positioned in the trans configuration, so that rotation around the bonds in the main chain is minimally
hindered.
Furthermore, negatively
The side groups
vary greatly
some of the side groups charged,
so
that
the
in hydrophobicity.
are positively
protein
and others are
molecule
is
a
complex
polyampholyte. As compared
to synthetic
polyelectrolytes,
globular
aqueous environment adopt a compact three-dimensional
proteins
in
structure. This
structure is determined by various types of interaction occurring inside the protein aqueous
molecule,
environment.
but also between
the protein
The main structure-determining
molecule
and its
factors are: (i)
dehydration of hydrophobic side groups, which favours the formation of a compact structure, and (ii) the tendency to maximize the conformational
522
Figure 31. Structure of a peptideunit in a polypeptide chain. Rotation is possible around two of the three bonds, the middle C-N bond is fixed in the trans configuration. of the
entropy internal other
structures minor,
globular The
Gibbs
per
including
amino
acid
residue reasons
of the external
conditions,
In
investigating
metastable
structures,
considered.
All told,
the synthetic
of the
native
this
protein in many
ways
structure
the
that
proteins
discussed
are more
surfaces. sight
of proteins from the
from
of the different
data
aqueous
sides,
determined
by: (il changes
the protein
molecule,
the sorbent
surface,
seem between
sections,
which
protein
proteins
be
than and so
ions),
molecules.
a variety the
techniques.
of solid
relative
at
generally is mainly
surface
and
the protein
and
of charged
and (iii) structure
was
Although
it is now
between
of the
problem
and interfaces
a redistribution The
studies
of the adsorbent
interactions
involves
weight
onto system
conflicting,
in the hydration
(ii) Coulomb
low molecular
adsorbing
of the
using various
sometimes
that the interaction
(including
always
complicated
in the previous
solution
complexity
established
in the
of freezing
behaviour.
In view
approached first
purely
being one of
must
Over the past fifteen years there have been numerous adsorption
for
1 kT
by alteration
possibility state,
the
of a few
less than
of an adsorbent stable
native stable.
(taking
in the range
is so low
adsorption,
off the absolutely
the
marginally
can be easily changed
the introduction
of
and some
that
with much
amount
formation
These,
reason
is typically
conformations
polyelectrolytes
is their adsorption
the
This corresponds
and
thermodynamic them.
are
as the reference)
of protein.
the
thermodynamically
of stabilization
structure per gram
is usually
counteracts and P-sheets.
a-helices
contributions
structure
energy
which
molecule,
opposing
protein
unfolded Joules
protein
groups
rearrangements
importance
of these
523
contributions obviously depends on the nature of the system and in some systems
specific
attraction
may occur. Special
attention
deserve
the
structural alterations because this is a typical protein feature. Their Gibbs energy change ApsG (where the subscript ps stands for protein structure) is positive, because otherwise the molecule would spontaneously
pass
from its native state to another one. However, the rise in entropy (TAP&S) due to the enhanced randomization
to a large extent compensates
the
unfavourable ApsH due to structure breakdown, hence ApsG may be small and can then easily be surmounted by factors (i) or (ii). The occurrence of such conformational
changes
adsorption
of structurally
behaviour
allows
us to differentiate “soft” molecules
“rigid” ones (ApsG large). In comparison
between
(ApsG small) and
with polyampholytes
feature is that for soft proteins part of the three-dimensional can break
down, which
gives rise to an increase
the
the new structure
in conformational
entropy: rigid molecules rather behave like bulky monomers. Below some general features of protein adsorption will be discussed, after
which
the
various
observations
will
be
integrated
into
a
thermodynamic analysis. b) Adsorbed amount As for most polymers, protein adsorption isotherms more often than not show a high affinity character, i.e., the initial part of the isotherm coincides with the f-axis,
after which a (pseudo-)plateau
is reached.
However, protein adsorption isotherms having a finite initial slope are not rarities. When the adsorption isotherm is not of the high affinity type, the corresponding character.
desorption
isotherm
With polydisperse
usually
polymers
does show a high affinity
such irreversibility
has been
explained by the adsorption preference of the larger moleculessal. Upon increasing
the polymer
concentration
in solution,
the high molecular
weight fraction in the adsorbed layer becomes gradually enriched. If, after establishment molecules
of equilibrium,
the system
is diluted,
remain at the surface until concentrations
reached which are below the limit of detectability.
the adsorbed in solution
are
With proteins that
tend to aggregate in solution preferential adsorption of such aggregates over monomers has been founds3, s4. 55). which can explain the hysteresis. However, also in homodisperse protein systems real hysteresis has been observedss. 57). It implies that the adsorbing protein molecule differs from
524
the
desorbing
desorbed before
one;
protein
more
molecule
adsorption.
other
sources,
This
to
creation
of entropy58).
content%
is more
increase
for instance
system
induce
the findings
specifically,
by acid,
Thus
the
positive
of Gibbs
than
base
that
the
protein
be supplied added
by
to the
hysteresis
of hysteresis
implies
is in line with
secondary
a larger conformational
will return to this point in subsection
of the
of the
must
have a decreased
5% 60,611 and, consequently,
energy
or electrolyte,
the occurrence
proteins
Gibbs
energy
Furthermore,
desorption.
that desorbed
that
structure
entropy. We
d.
Figure 32. of the therms
Plateau values
adsorption isoas a function of
pH, for human serum albumin from 0.05 M
electrolyte solution on various surfaces: positive and negative polystyrene latex (PS), neutral polvoxymethylene cry&is (POM). negative silica (SiOz) and positive hematite (a-Fez@) 68. 85).
l-
0
n
I
”
4
I
I
I
I
I
5
6
7
6
9 PH
As
a rule,
plateaus. value
protein
For many proteins
at the isoelectric
32 such
adsorption
Tmax(pH)
isotherms
curves
for serum
It must
area of the adsorbent
be realized
electrostatic
material
in
the
repulsion both
hydrophobicity,
with
protein
between such
the specific uncertainty
collected
charged ample
to
their
of the
On the other
spontaneously
with
protein,
hand, the
evidence
that
than
molecules.
to
All
charge
curves
rather
the structural
(PS) the
than
are very
density
are strongly
and
affected
by protein-sorbent
alterations
native
lateral
Tmax(pH)
As the adsorbents surface
dissolved
polystyrene
point is due to structural rather
adsorbed
a maximum.
respect
are
regarding
molecule the
In fig.
surfaces
leads to a proportional
it is clear that the r ma(pH)
characteristics
interactions. place
on various
on negatively
al.67. 6s) ha ve
in fig. 32 show
different, by the
albumin
in l-ma, at either side of the isoelectric
rearrangements curves
et
attain a maximum
complex62-66).
that the uncertainty
in the value for rmax. For albumin Norde
Imz.
these plateau values,
surface
decrease
well-established
point of the protein-sorbent
shown.
surfaces,
develop
protein,
do not take hence
the
525
adsorbate is necessary to induce them. The fact that albumin also adsorbs at the hydrophilic su,rfaces of hematite (a-FeaOs) under
conditions
of electrostatic
repulsion,
and silica ($02).
implies
that very
even little
interaction between albumin and surface suffices to realize this structural change, after which the Gibbs energy of the adsorbed protein is so much lowered that high affinity binding ensues. As this dominant structural change is a protein property, the influence of the nature of the surface is suppressed. 1.5 mg I+ c
r mclr
0.5
PH
33. Plateau values of the adsorption isotherms as a function of pH. for ribonuclease from 0.01 M electrolyte on various surfaces 6g* 70]. For the abbreviattons of the adsorbents see fig. 32. Figure
Another category of proteins shows a different Pmax(pH) patternsas 70). This is illustrated
in fig. 33 for the adsorption
of ribonuclease
different surfaces. At the hydrophobic PS surface Pma(pH) independent
of the charge on the protein molecule
at
is essentially
and of the charge
contrast between the protein and the surface. The plateau values account for a complete monolayer of native molecules. This suggests that no or only minor structural changes in the adsorbing ribonuclease
molecules
occur. The behaviour is in agreement with the relatively strong internal coherence ribonuclease uncharged
of
the does
ribonuclease not adsorb
polyoxymethylene
molecule.
For
the
same
on the less hydrophobic, (POM)
surface,
and
also
reason,
essentially not
on the
hydrophilic surface of a-FezOs. unless it is electrostatically attracted. The relative importance of the contributions
of hydration changes,
Coulomb interaction, and structural rearrangements
for protein adsorp-
526
tion has been systematically studied experimentally by Arai and Norde71). They used a series of proteins that are similar in size and shape, i.e., lysozyme
(LSZ), ribonuclease
(RNase), myoglobin
(MGB), and a-lactal-
bumin (aLA). Unfolding induced by heat721 and by denaturing agents731 reveal that the structural order
LSZ, RNase,
summarized
stability of these
MGB, aLA.
Plateau
in fig. 34. The charge
proteins decreases in the
values
of the isotherms
of the proteins
are
is qualitatively
indicated by plus and minus signs. PS+;
5-_+32mV
PS -; c=-69mV
2 - mg m-2
rmar
r mar;
aLA1 l-
t&B? LsZ++RNase+
aFetOs+;
55+20mv
aFe20, - ; c_-_-47mv
I
Figure 34. Adsorption of lysozyme (LSZ). ribonuclease (RNase), myoglobin (MGB) and alactalbumin (c&A) on hydrophobic polystyrene (PSI and hydrophilic hematitie (a-FezO3) surfaces71). The electrolyte concentration was 0.05 M. An indication of the surface charge is given through the c-potential of the bare surface, and of the protein charge by + and signs.
At the hydrophobic PS surfaces all proteins adsorb. As a trend, the electrostatic interaction between the sorbent and the protein is reflected in Pmax. However, both on positive and negative PS, aLA adsorbs more strongly
than would
be expected
on the basis
of the electrostatic
interaction. This observation is in line with the relatively “soft” nature of this protein. At the hydrophilic a-Fez03
surfaces the adsorption of LSZ
and RNase is dominated by electrostatic interaction but again aLA behaves differently, for the same reason.
527
All of this fits into the picture that proteins that have a high structure stability
behave
as “hard” particles.
Their adsorption
is governed
by
electrostatic interaction and (partial) dehydration of the sorbent and the protein. Proteins having a low structure stability (“soft” proteins) possess an additional driving force for adsorption which is related to structural rearrangements. Consequently, soft proteins may adsorb spontaneously on a hydrophilic surface even under electrostatically unfavourable conditions. In competition from a mixture containing all four proteins, the least stable
aLA
tends
to
adsorb
preferentially74).
It follows
that the
contribution from structural rearrangements is an important factor in the competition,
resulting
in preferential
adsorption
of the “soft” proteins
over the “hard” ones. c) Co-adsorption of small ions
r/r_
Even
though
adsorbing
protein
Figure 35. The change of the electrokinetic charge upon adsorption of human plasma albumin onto hematite, as a function of the relative adsorption76). The charge effect results from the transfer of low molecular weight ions between the solution and the adsorbed layer. The electrolyte concentration was 0.01 M.
molecules
may
change
their
structure, they usually form a compact adsorbed layerso). Any ensuing adverse
build-up
of electrostatic
repulsion
can be avoided
by the
incorporation of small ions from solutions7* 75). The ion transfer between the solution and the adsorbed layer can be experimentally comparing
the electrokinetic
estimated by
charge density oek of the protein-covered
sorbent on the one hand and those of the bare sorbent and the dissolved protein
molecules
on the other 67. 70). Figure 35, taken from work by
Koutsoukos et a1.76),shows Aado&, the change of o& upon adsorption, as a function of the relative adsorption T/Fma for human serum albumin on negatively charged a-Fe203. The dependence of Aado& on pH points to an increasing uptake of positive ions with increasing negative charge on the protein and the sorbent surface. Furthermore, the linear relation between
and PiPmax [for Pifmax > 0.3) indicates
Aado&
adsorbed
protein
incorporated
molecule
is accompanied
that each additionally
by the same amount
of
charge.
Since the co-adsorption of ions reduces the charge antagonism, it is electrostatically
favourable. However, the chemical effect of transferring
low molecular weight ions from the aqueous solution into the non-aqueous protein
layer is unfavourable
and, hence, opposes the overall protein
adsorption process. Indeed, maximum affinity for protein adsorption has been found under circumstances
where the charge of the protein itself
just matches the charge on the sorbent surface75). d) Energy and entropy of protein a~sorp~n The
affinity
of the protein
adsorption
process
is, at constant
temperature T and pressure p, determined by the change in the Gibbs energy G AadG = AadH - TA,,S
(2 1)
or, if written per molecule of protein Aadg = Aadh - TA,os where H is the enthalpy and S the entropy and g, h and s stand for the same
quantities
per
thermodynamically spontaneously
molecule,
For
adsorption
to be
if the energy of activation is low. In the literature many
examples are encountered of extremely
respectively.
possible, AadG should be negative. The process occurs where protein adsorption is treated in terms
simple models. For instance,
various
authors77-s@
have
analyzed the isotherms as if obeying Langmuir premises, i.e., they assume, either or not tacitly. that the adsorption is reversible, site-bound, and that lateral interaction
and internal structural changes can be disregarded.
Obviously,
all of this is at variance
conclusion
derived from such interpretations,
of values to A,dG,
must be considered
with reality.
Consequently,
any
including the assignment
with suspicion.
For the same
reasons and for lack of definition of the notion “isosteric”, applying the Clausius-Clapeyron
equation
in order to analyze the influence
of the
temperature on the adsorbed amount is questionable. Yet, whatever the adsorption mechanism, Le Chatelier’s principle remains valid: the positive value for X/X
for the adsorption
of serum albumin on PS surfaces,
529
measured
at constant
protein
concentration
therms,
implies
an endothermic
sorbent
systems
AadH was determined
71. 76).
process,
It was found that this quantity
adsorption
is driven by entropy
In their thermodynamic and ribonuclease unravelled
determined
(which involves ments
sorbent
conditions
high
above,
groups
and rearrangeIn some
that TAadS should also be positive
and that,
the
TAP&S is one contribution
from hydrophobic
of charged
contribution),
force.
changes
enthalpy
subprocesses:
in hydration).
as to be the sole driving
derives
of serumalbumin
adsorption
redistribution
(including
at least under the given conditions, stated
overall
and a chemical
structure
AadH > 0, implying
67.
that the
Norde and Lyklemasl)
from the most important
surface,
an electrical
in the protein
confirming
of the adsorption
charged PS surfaces,
calorimetrically
of the
protein-
by microcalorimetry5s.
increase.
AadH in terms of its contributions dehydration
Aa,jH > 0. For various
directly
is often positive,
analysis
on negatively
the
in the initial parts of the iso-
process
One other
dehydration
is entropically
to T&S,
driven. As
but it can never be so important
of the surfaces,
entropic
term
but there are more
contributions. The
Gibbs
substance
energy
may
model substance) Gibbs
involved
be estimated between
energy
of dehydration For instance,
PS surface the estimatessl) AdhH = -1.4 25W).
Taking
becomes
firmly
more
are A&G
effect -TAdhS = -15.4 an adsorbed Such
at hydrophobic
of hydration
of a
substance
(or a
phase. Obviously,
negative
with
increasing
at 25OC of hydrophobic
mJ m-2 and a small enthalpy
amount
the
= -16.8 mJ m-2, which results from a
mJ m-2 (1 mJ m-2 corresponds
molecule.
of that
for the dehydration
with a molar mass of 50 kg/mol, protein
the state
partitioning
water and a non-aqueous
hydrophobicity. large entropy
in changing from
to about
0.25
of 1.5 mg m-2 for a protein this would
a large
value
surfaces,
even
yield
explains under
-T&hS
why
=
change
kT nm-2 at molecule
-226
kT per
all proteins
unfavourable
adsorb
electrostatic
conditions. The Gibbs energy change groups
contains
an electric
and Agch. respectively. accumulation
of net charge
electrical
depend double
from the redistribution
and a chemical
As ion incorporation
does not attain large values. and A&,
resulting
in the protein Its value
on the composition
(medium) compensates sorbent
of charged
contribution,
AgeI
for unfavourable
contact
region,
Agel
and sign, as well as those for Ahe and the dielectric
layers before and after adsorption.
constants
respectively.
of the
530
The ated
chemical
from
aqueous
model
studies
media.
positive
For
on the transfer
most
spontaneous
the chemical protein
development
contribution An
adsorbed
do not unfold indicates
that
than
potential
way
to non-
quantity
is
solution.
the
of a loose
constant
observation
structure,
effect
avoid
is the formation
The general
chemical
opposes
to
for water and small ions. In
layer the dielectric
the exposure
this
to ion incorporation
into such a loose the
aqueous
ions
alternative
layer, that is freely permeable
to that of the bulk
unfavourable
weight
can be estim-
negative values for both Aheh and Aseh
adsorption.
such a highly hydrated proteins
of ions from
molecular
of a high electrostatic
loopy adsorbed
layer,
low
as a result of compensating
82, 831, so that
close
Ag ch of ion incorporation
contribution
that globular
but form a compact
of ion
of hydrophobic
is relatively
incorporation parts
is less
of the protein
to
water as would occur upon unfolding. Adsorption
involves
a change
this, in turn, may induce the protein, molecule, they
which
are still
stabilized
shielded is
from
secondary
intramolecular
if
structures
of the protein to a reduction for the protein
spectrometry human and
Norde
molecule.
of secondary
SiO2.
method, adsorption, desorption
The which
structural desorbed
reduction
with possible
component.
from the a-helix
that
state corresponds structure.
structural
structure,
i.e.
the subscript
surfaces
ps
dichroism content
of
of a-Fe203
to the desorption
change
up to a certain
a reduction
data811 indeed
on circular
to be insensitive
the
groups
A loss of
conformational
in the a-helix
from the hydrophilic
restructuring
to a random
cause
protein
Based
expanded
side
sheets.
of calorimetric
a reduction
step. The helix breakdown
50% in the adsorbed
and pleated
ApsG < 0). As before,
appeared
suggests
acid
is
the sum of
a more
amino
(and tertiary)
of the
solution
whereas
may therefore
Analysis
parts of
of structural
in
which leads to an increased
et al.851 inferred
serum albumin
type
favours
between
as helices
ApsH > 0 and APsS > 0 (yielding stands
This
interaction
and
in such a way that
structure
interactions
interaction
structures,
Hydrophobic
surface
compact
interaction
of the protein
are in the interior
with water.
the
hydrophobic
hydrophobic
of such secondary
to the sorbent
determining
Hydrophobic
supports
rearrangements. environment
contact
probable
structure
structure.
points
exposed
by intramolecular
the other
entropy
structural
in an aqueous
may become
rearrangement
in the environment
occurs
extent
from 65% in the native
upon
during protein
the to
to ca. 90 amino acids transferred Based
on the assumption
of four
531
possible conformations
per peptide unit in the random structures41 and
one in the helix, the resulting increase in conformational
entropy, A+,
amounts to k ln4 per amino acid, or, for the entire protein molecule, 90 k ln4 = 125 k, so that TApss = +125 kT per protein molecule. Calorimetry under the same conditions gave Aadh values of +80 kT and +55 kT for serum albumin adsorption enthalpies
on a-Fe203
is driven
and SiO2. respectively.
by an entropy
increase.
It follows that the
These
positive
are sums of positive and negative contributions.
overall
When this
algebraic sum is less than Apsh, the entropy rise TApss may be enough to overcome Aadh, as in this example. The fact that Aadh c Apsh implies that the entropy rise due to structural rearrangements is not the sole driving force. However, it may be concluded that an increase in conformational entropy
plays an important
role in the adsorption
of the soft serum
albumin molecule on a hydrophilic surface with the same charge sign. Overviewing
all the features
involved
in protein
adsorption,
it is
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the theoretical
picture
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developed
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in proteins,
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that is most dramatically
re-
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