Journal of Chromatography A, 1332 (2014) 35–45

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Journal of Chromatography A journal homepage: www.elsevier.com/locate/chroma

Mass transfer mechanism in chiral reversed phase liquid chromatography Fabrice Gritti, Georges Guiochon ∗ Department of Chemistry, University of Tennessee, Knoxville, TN 37996-1600, USA

a r t i c l e

i n f o

Article history: Received 25 October 2013 Received in revised form 12 January 2014 Accepted 14 January 2014 Available online 31 January 2014 Keywords: Chiral separation Mass transfer resistance Adsorption–desorption steps trans-Stilbene Tri-tert-butylbenzene Lux 5 ␮m Cellulose-1

a b s t r a c t The mechanism of mass transfer in chiral chromatography was investigated using an experimental protocol already applied in RPLC and HILIC chromatography. The different contributions to the reduced height equivalent to a theoretical plate (HETP) include the longitudinal diffusion HETP term, the solid–liquid mass transfer resistance HETP term, the short-range eddy dispersion HETP term, and the long-range eddy dispersion HETP term. Their accurate measurement permits the determination of the adsorption rate constant kads of trans-stilbene enantiomers on a column packed with Lux 5 ␮m Cellulose-1 particles. The experimental results demonstrate that the number of adsorption–desorption steps per unit time of chiral compounds on polysaccharide-based chiral stationary phases is four orders of magnitude smaller than that of achiral compounds. © 2014 Elsevier B.V. All rights reserved.

1. Introduction Polysaccharide-based chiral stationary phases (CSP) are the class of phases that is most widely used for the analysis of biochemicals and pharmaceutical compounds by HPLC [1–4]. Besides their broad range of applications in NPLC, these phases can be used in RPLC, with aqueous mixtures of either methanol or acetonitrile as mobile phases [5,6]. Their numerous applications to the separation of racemic mixtures were reviewed by Tachibana [7]. The most successful polysaccharide-based CSPs are derived from cellulose tris(3,5-dimethyl-phenylcarbamate), which has a wide chiral recognition ability, a good chemical stability, a good loadability, and is highly repeatable [8]. In addition to their selectivity, the efficiency of columns packed with these polysaccharide-based CSPs plays a major role in the successful separation of important pairs of enantiomers in chiral RP-HPLC for which the selectivity factor is insufficient [6]. The efficiencies reported for polysaccharide-based CSPs [9] are generally smaller than those measured for either RPLC silica-C18 [10,11] or HILIC [12–15]. This fact holds true for low molecular weight compounds eluted with similar mobile phases which have the similar viscosity and diffusion coefficients. In both the RPLC and HILIC retention modes, the mass transfer resistance around and above

∗ Corresponding author. Tel.: +1 8659740733; fax: +1 865 974 2667. E-mail addresses: [email protected], [email protected] (G. Guiochon). 0021-9673/$ – see front matter © 2014 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.chroma.2014.01.040

the optimum velocity is essentially controlled by the eddy diffusion term that originates from velocity biases taking place over long-range distances, like the column diameter [11]. In practice, the HETP of columns packed with sub-3 ␮m particles remains nearly constant at high mobile phase velocities for small molecules [12], so the rate constants of adsorption on all sites in both RPLC and HILIC are assumed to be very large. In contrast, the apparent C term of the van Deemter plots measured in chiral chromatography is relatively large compared to those measured in RPLC or HILIC. The question remains of whether such a steep C-behavior is due to a slow diffusivity of analytes across the CSP particles or to a small number of adsorption–desorption events (e.g., to a small value of the adsorption rate constant) on both non-selective and selective sites [16]. Recent calculation of the macroscale transport and the HETP in the bulk region of column beds demonstrated the crucial role of the microscopic characteristics of the adsorption–desorption kinetics on chromatographic performance [17]. For a retention factor of 1.0 and a reduced velocity of 60, an increase of the reduced plate height by 1.0 unit is expected if the average residence time in the stationary phase increases from 0.02 to 200 ␮s (e.g., with a decreasing frequency of adsorption–desorption steps from about 5 × 107 s−1 to only 5 × 103 s−1 ) [17]. The first goal of this work was to understand the mechanism of mass transfer in chiral RP-HPLC, using an experimental protocol reported earlier [18]. A method based on extrapolation was previously used [19]. A cellulose-based CSP, a mobile phase made of methanol and water, a neutral racemic compound, and a reference achiral compound were selected for the purpose of

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List of symbols Roman letters A() reduced eddy diffusion plate height B reduced longitudinal diffusion coefficient with reference to the interstitial linear velocity sample concentration at the discrete elution time ti Ci (mol/m3 ) cp sample concentration in the internal mesoporous volume (mol/m3 ) cs sample concentration in the stationary phase (mol/m3 ) Ca reduced solid–liquid mass transfer resistance coefficient due to a slow adsorption–desorption process Cp reduced solid–liquid mass transfer resistance coefficient due to the finite rate of diffusion across the particle D dimensionless constant defined in Eq. (14) Dn Dean number Dp effective sample diffusivity across the particle (m2 /s) Deff effective diffusion coefficient of the packed bed (m2 /s) dp average particle diameter (m) bulk molecular diffusion coefficient (m2 /s) Dm F(m ) Hindrance diffusion factor Fv flow rate (m3 /s) Fv,PP flow rate applied during the peak parking method (m3 /s) reduced plate height h hTC reduced long-range eddy dispersion plate height hTC,comp compensation reduced long-range eddy dispersion plate height from the Luna to the Lux column H plate height (m) molecular flux through the particle (mol/m2 /s) j k retention factor zone retention factor k1 kp particle retention factor adsorption rate constant (s−1 ) kads Kc Kozeny–Carman constant k0 specific permeability (m2 ) Ka equilibrium Henry’s constant for the sample distribution between the solid phase in the particle and the liquid eluent phase N column efficiency L column length (m) total pressure drop (Pa) Ptot Pex system pressure drop in absence of the chromatographic column (Pa) rc column inner radius (m) radius of the coiled capillary tube (m) Rcoil rtube capillary tube inner radius (m) Sc Schmidt number first discretized elution time (s) t1 tN last discretized elution time (s) tleft elution time (adsorption) at 10% of the peak height (s) elution time (desorption) at 10% of the peak height tright (s) ti discretized elution time (s) parking time (s) tp tR retention time at the peak apex (s) tp increment of the peak parking time (s)

u ucenter uS V0

interstitial linear velocity (m/s) linear velocity in the center of the capillary tube (m/s) superficial linear velocity (m/s) column hold-up volume (m3 )

Greek letters ˇ parameter in Torquato’s model of effective diffusion in packed beds defined by Eq. (7) ˇ1 positive root of the quadratic Eq. (26) ˇ2 negative root of the quadratic Eq. (26) 2 PP increment of the peak variance measure in the peak parking method (s2 ) e external column porosity p particle porosity t total column porosity p intra-particle obstruction factor obstruction factor caused by randomly packed none porous particles to the diffusion in the external bulk mobile phase  eluent viscosity (Pa s) first moment (s) 1 1,PP first moment recorded during the PP experiments for a zero parking time (s) 1,PP.ex extra-column first moment in the PP conditions (s) second central moment (s2 )  2  reduced interstitial linear velocity ratio of the effective diffusivity of the sample in the

porous region of the particle to its bulk diffusion coefficient ω1 diffusion eddy dispersion coefficient related to trans-channel velocity bias flow eddy dispersion coefficient related to trans1 channel velocity bias ω2 diffusion eddy dispersion coefficient related to short-range inter-channel velocity bias in columns packed with non-porous particles 2 flow eddy dispersion coefficient related to shortrange inter-channel trans-column velocity bias in columns packed with non-porous particles eluent density (kg/m3 ) v2,ex extra-column volume variance (m6 ) v2,tube total volume variance (m6 )

2 adjustable parameter in Torquato’s model of effective diffusion Eq. (6)

applying the method. The experimental protocol used had already been tested and validated in both RPLC [10] and HILIC [14,15]. The total reduced HETP h was measured from the moments of peaks recorded in a wide range of flow rates [20,21]. The diffusion coefficients Dm of the analytes in the bulk phase were measured by the capillary method [22,23]. The reduced longitudinal diffusion coefficient B was directly measured by the peak parking method [24–26]. The mass transfer resistance coefficient Cp due to a finite diffusion rate across spherical and fully porous particles was obtained by combining the results of the peak parking method and a validated model of effective diffusion along packed beds [27–29]. The short-range eddy dispersion HETP term was obtained from statistical analysis of packed beds [30]. The long-range eddy dispersion HETP was measured under RPLC conditions for a column of the same dimension and packed with particles of the same size as the chiral column used in this work [31]. The second goal of this work was to use the results of this experimental deconvolution

F. Gritti, G. Guiochon / J. Chromatogr. A 1332 (2014) 35–45

of the total reduced plate height to find how slow was the adsorption–desorption process, how small was the number of adsorption–desorption steps during a long average residence time in the stationary phase, and how much this affected the overall column efficiency of a column packed with a polysaccharide-based CSPs operated under reversed-phase conditions. 2. Theory 2.1. Definitions The total, external, and internal porosities of a column are t , e , and p , respectively. The diffusion coefficient of an analyte in the bulk mobile phase is Dm , the apparent analyte diffusivity through the fully porous particles is Dp = Dm , being the dimensionless ratio of the sample diffusivity through the particles to its bulk diffusion coefficient. The coefficient is a lumped coefficient, provided by the peak parking experiments. It includes the contributions of the solid adsorbent surface and of the pore volume to the total sample diffusivity through the whole particle volume (Dp ). The reference concentration gradient (dC/dx) used for the definition of Dp (j = − Dp dCdx) is measured in the bulk phase. In RPLC, can be both smaller (for weakly retained compounds) and larger (for retained compounds) than unity [10]. In HILIC, it is always smaller than unity [14]. The effective diffusion coefficient along a heterogeneous packed bed (made of the particles and the external eluent) is Deff . The zone retention factor k1 is given by [32]: k1 =

1 − e

e



p + (1 − p )Ka



(1)

where Ka is the Henry constant or ratio of the equilibrium concentrations in the stationary phase (Cs ) and in the bulk phase (Cm ). k1 refers to the ratio of the analyte elution time to the time that it spends in the interstitial column volume (e rc2 ). The conventional retention factor, k , is the ratio of the same elution time to the time spent in the accessible pore volume (t rc2 ). The relationship between k1 and k is: (1 + k1 )e = (1 + k )t

(2)

=

udp Dm

(3)

where u in the average interstitial linear velocity along the column given by: u=

Fv

e rc2

(4)

where Fv is the volumetric flow rate and rc is the inner column radius. 2.2. Reduced HETP equation The overall reduced plate height h is the sum of the longitudinal diffusion term B/, the total eddy diffusion term A(), the trans-particle mass transfer resistance term due to the finite diffusivity of the analyte through the particles Cp  and its (slow) adsorption–desorption kinetics Ca . It is written: h=

B + A() + Cp  + Ca  

2.2.1. The longitudinal diffusion term The longitudinal diffusion term is derived from the effective diffusion coefficient of the analyte in a heterogeneously packed bed [34,35]. It includes the contributions of the diffusion processes taking place in the external and the internal eluent volumes, on the adsorbent surface and in the volume of the stationary phase. A physically relevant model of effective diffusion in a system consisting of packed spheres immersed in a homogeneous medium is the Torquato model [27] that describes the effective diffusion of packed spheres immersed in a homogeneous medium and distributed randomly. It is written [34,35]: Deff =

1 e (1 + k1 )



1 + 2(1 − e )ˇ − 2e 2 ˇ2 1 − (1 − e )ˇ − 2e 2 ˇ2



Dm

(6)

with ˇ=

−1

+2

(7)

In Eq. (6), 2 is an adjustable parameter that is estimated from the experimental external obstruction factor for = 0, = 0, and k1 = 0 (non-porous particles). From this same equation, the expression of  e = Deff /Dm is given by: e =

2(1 − 2 /2) 3 − e (1 + 2 )

(8)

The measurements were made after having completely filled the mesoporous volume of the column with liquid n-nonane. They provided an obstruction factor 2 = 0.59 for a 4.6 mm × 150 mm column packed with non-porous 5.0 ␮m Luna-C18 (2) particles of external porosity 0.36 [36]. Thus, the value of 2 given by Eq. (8) is 0.627. The reduced B coefficient in Eq. (5) can then be written [34]: B = 2(1 + k1 )

Deff

(9)

Dm

2.2.2. Eddy dispersion HETP The term A() is the overall reduced eddy dispersion term; its expression is based on the one derived in the coupling theory of eddy dispersion by Giddings [32]: A() =

The reduced interstitial linear velocity, , is [33]:

37

1 1 + + hTC () 1/21 + 1/ω1  1/22 + B/2e ω2 

(10)

where 1 , ω1 , 2 , and ω2 are the eddy dispersion parameters that predict the sample band dispersion in the homogeneous, random, bulk region of the bed packed with impermeable solid spheres under asymptotic conditions [30]. These parameters were obtained as functions of the bed porosity (e ) and for different packing protocols. Finally, in Eq. (10), hTC is the pre-asymptotic transcolumn eddy dispersion HETP term in classical analytical columns. It accounts for the wall effects (trans-column velocity biases) and for the inlet/outlet border effects [11]. 2.2.3. The solid–liquid mass transfer resistance term The general expression of the solid–liquid mass transfer resistance coefficient due to the finite sample diffusivity across the particles (Cp ) is given by [32,37]: Cp =

1 e 30 1 − e

 k 2 1 1 1 + k1



(11)

In this equation, was estimated from Torquato model of effective diffusion by combining Eqs. (9), (6), and (7).

(5)

The physico-chemical descriptions and the mathematical expressions of each of these four HETP terms are recalled in the next subsections.

2.2.4. The adsorption–desorption mass transfer resistance term This HETP term is relevant when the number of adsorption–desorption steps is small, e.g., when the average residence time of analyte molecules in the stationary phase is very

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F. Gritti, G. Guiochon / J. Chromatogr. A 1332 (2014) 35–45

large [16]. Let consider a first order slow adsorption–desorption kinetics. Then, (12)

second after the column. The total volume of these two tubes is 4.8 ␮L. • A small volume detector cell, V() = 0.6 ␮L, 10 mm path. The cell volume is about 1.4 ␮L.

where kads is the adsorption constant (unit s−1 ), Cs is the sample concentration in the stationary phase (the reference volume of the stationary is (1 − t )VC , where VC is the column tube volume), and Cp is its concentration in the stagnant bulk eluent inside the pores. The general expression of the HETP associated with a slow adsorption–desorption kinetics (Ca ) is given by the Laplace transform [37,38]:

No solvent heat exchanger was used in the experiment. The total extra-column volume is close to 8.4 ␮L. When the column is replaced with a ZDV union connector, this volume generates an estimated extra-column volume variance that varies between 7 and 18 ␮L2 for trans-stilbene molecules when the flow rate is increased from 0.1 to 2.5 mL/min (injection volume 1 ␮L, methanol/water eluent, 90/10, v/v).



∂Cs Cs = kads Cp − Ka ∂t





e 1 k1 Ca = 2 1 − e 1 − p 1 + k1

 2  k 2 1 p 1 + kp

D

(13)

where D is the dimensionless constant D=

kads dp2

(14)

Dm

and kp is given by kp =

1 − p

p

Ka

(15)

When either D or kads is very large, Ca tends towards zero and the adsorption–desorption kinetics can be considered as being fast. 3. Experimental 3.1. Chemicals The mobile phase was either pure methanol, a mixture of methanol and water (90/10, v/v), or a mixture of acetonitrile and water (75/25, v/v). Tetrahydrofurane (THF) was used in small amounts. All these solvents were HPLC grade from Fisher Scientific (Fair Lawn, NJ, USA). Acetonitrile was filtered before use on a surfactant-free cellulose acetate filter membrane, 0.2 ␮m pore size (Suwannee, GA, USA). The eleven polystyrene standards (MW = 590, 1100, 3680, 6400, 13,200, 31,600, 90,000, 171,000, 560,900, 900,000, and 1,870,000) were purchased from Phenomenex (Torrance, CA, USA). Toluene, naphthalene, potassium chloride (KCl), tri-tert-butylbenzene (TTBB), and the racemic mixture of trans-stilbene were also purchased from Fisher Scientific, with a minimum purity of 99%. 3.2. Apparatus All the measurements were performed with a 1290 Infinity HPLC system (Agilent Technologies, Waldbroon, Germany) liquid chromatograph. The system includes a 1290 Infinity Binary Pump with Solvent Selection Valves and a programmable auto-sampler. The injection volume is drawn into one end of the 20 ␮L injection loop. The instrument includes a two-compartment oven and a multidiode array UV–vis detection system. The system is controlled by the Chemstation software. The sample trajectory in the equipment involves the successive passage of its band through the series of: • A 20 ␮L injection loop attached to the injection needle. The design of the First In-Last Out (FILO) injection system is such that the entire volume of sample drawn into the loop is injected into the column. This ensures an excellent injection repeatability. • A small volume needle seat capillary (115 ␮m I.D., 100 mm long),  1.0 ␮L, located between the injection needle and the injection valve. The total volume of the grooves and connection ports in the valve is around 1.2 ␮L. • A 120 ␮m × 220 mm and a 115 ␮m × 220 mm long capillary tubes were used. The first one is placed before the column and the

3.3. Column The 4.6 mm × 150 mm column packed with 5 ␮m Lux Cellulose1 particles was given by Phenomenex (Torrance, CA, USA). In order to fairly estimate the long-range eddy dispersion HETP of this column, a standard 4.6 mm × 150 mm column packed with 5.0 ␮m Luna-C18 (2) particles was also provided by the same manufacturer. Table 1 lists the physico-chemical properties of these two columns, according to the manufacturer data and to data acquired in our laboratory. 3.4. Measurement of the column porosities The porosities of the Luna-C18 (2) column were measured from inverse size exclusion chromatography (ISEC) using pure THF as the mobile phase. The Lux chiral stationary phase used in this work is prepared by coating silica gel with the cellulose-1 polymer derivative. The use of a solvent like THF or dichloromethane must be avoided to avoid damaging the stationary phase. Standard ISEC experiments and pycnometry measurements that require the use of dichloromethane cannot be made to determine the external and total porosities, respectively. The total porosity of the Lux column was measured by injecting potassium chloride and recording its elution time at 210 nm (using the slight UV absorption of the chloride anion). The KCl concentration was manually adjusted until the peak did not front anymore and the retention time of its apex remained unchanged. The external porosity was measured from the specific permeability of the column, assuming a Kozeny–Carman constant equal to Kc = 160 [31]: k0 =

3e dp2

(16)

Kc (1 − e )2

k0 was measured according to the following equation: k0 = L

1 rc2 (Ptot − Pex )/Fv

(17)

where  is the eluent (methanol–water, 90/10, v/v) viscosity at room temperature (0.836 cP), L is the column length (15 cm), rc is the inner column radius (2.3 mm), Ptot is the total pressure drop including the system contributions, Pex is the pressure drop generated by the HPLC system in absence of the chromatographic column replaced by a zero dead volume (ZDV) connector. The maximum flow rate (1.0 mL/min) was set so that the corrected pressure drop does not exceed 60 bar, the effect of pressure on the viscosity is negligible, and the column temperature remains constant. The internal porosity (p ) was derived from:

p =

t − e (1 − e )

(18)

All the results for the total, the external, and the internal porosities are listed in Table 1.

F. Gritti, G. Guiochon / J. Chromatogr. A 1332 (2014) 35–45

39

Table 1 Physico-chemical property of the chiral and non-chiral chromatographic columns used in this work. Column

Column’s serial number

Column’s dimension I.D. [mm] × length [mm]

Total porosity (εt )a

External porosity (εe )

Particle/shell porosity (εp )

Permeability [cm2 ] (k0 )

5.0 ␮m Lux Cellulose-1 5.0 ␮m Luna-C18 (2)

613442-1 233517

4.6 × 150 4.6 × 150

0.658a 0.628c

0.380b 0.363d

0.448 0.416

2.24 × 10−10 e 1.84 × 10−10 f

a

Measured from the elution time of KCl in methanol/water, 90/10 (v/v) at 1 mL/min. Measured from the slope of the plot of the corrected back pressure vs. the flow rate. Eluent: methanol/water, 90/10 (v/v) at 1 mL/min. T = 24 ◦ C. The Kozeny–Carman constant was taken at Kc = 160. c Measured from the elution time of toluene in THF at 0.48 mL/min. d Measured from ISEC using polystyrene standards and pure THF as the eluent. e Measured from the corrected pressure drop (> 40. Eq. (13) was applied to extract the kinetic constant kads , which is written: kads = 2



e 1 k1 1 − e 1 − p 1 + k1

 2  k 2 1 D p m 1 + kp

Ca dp2

(33)

Accordingly, kads = 955 and 1202 s−1 for trans-stilbene 1 and 2, respectively. Following the same approach with pure methanol (see Figs. 6A–C), we found that kads decreases to 608 and 747 s−1 , respectively. Once again, the two h plots of TTBB overlay nearly perfectly within the experimental errors. Thus, the rate constant decreases slightly with increasing diffusion coefficient, a result consistent

43

h 4

trans-stilbene 1 2

0

10

20

30

Reduced velocity ν B/ν +Cpν +A(ν) Experimental h data

6

h 4

trans-stilbene 2 2

0

10

20

Reduced velocity ν

30

B/ν +Cpν +A(ν) Experimental h data

6

h 4

TTBB 2

0

10

20

30

Reduced velocity ν

40

Fig. 5. Comparison between the plots of the experimental total reduced plate height h (full red circles) and of the sum of the experimental B/, Cp , and A() reduced plate height terms (full black squares) vs. the reduced velocity . Test compounds: transstilbene enantiomers (top and middle graphs) and TTBB (bottom graph). Mobile phase: methanol/water (90/10, v/v). Column: 4.6 mm × 150 mm column packed with Lux 5 ␮m Cellulose-1 particles. Room temperature. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of the article.)

with the observations made in Fig. 4A and B and their interpretations. According to the results on the mass transport properties calculated from a microscopic description of band broadening in packed beds [17] or to collision theories, if each collision between

44

F. Gritti, G. Guiochon / J. Chromatogr. A 1332 (2014) 35–45

B/ν +Cpν +A(ν) Experimental h data

6

Longitudinal diffusion Short-range eddy dispersion Long-range eddy dispersion Solid-liquid mass transfer resistance : Dp Solid-liquid mass transfer resistance : kads

6

h

Total HETP

h

4

4

2

trans-stilbene 1

2 0

10

20

0

B/ν +Cpν +A(ν) Experimental h data

6

0

4

1.0

trans-stilbene 2

0

10

20

30

Longitudinal diffusion Short-range eddy dispersion Long-range eddy dispersion Solid-liquid mass transfer resistance : Dp Solid-liquid mass transfer resistance : kads

h

2

ν

10

hi /htotal

20

0.5

Reduced velocity ν B/ν +Cpν +A(ν) Experimental h data

6

h 0.0 0

4

10

ν

20

30

Fig. 7. Relative reduced plate height contributions of longitudinal diffusion, shortrange eddy dispersion, long-range eddy dispersion, and solid–liquid mass transfer resistances due to a slow diffusion across the particle (Dp ) and to a slow adsorption–desorption process (kads ), to the total HETP recorded in chiral RPLC. Column: 4.6 mm × 150 mm column packed with Lux 5 ␮m Cellulose-1 particles. Mobile phase: methanol/water mixture (90/10, v/v). Chiral analyte: trans-stilbene 1. Room temperature.

2

0

10

20

30

Reduced velocity ν Fig. 6. Same figure as in Fig. 5, except the mobile phase is pure methanol.

the analyte molecules and the stationary phase leads to an adsorption event, kads should be typically four orders of magnitude larger, around 1.6 × 107 , for a retention factor k = 5 [15]. 4.3. Deconvolution of the total HETP in chiral RPLC Fig. 7A–B summarize our experimental results regarding the relative contributions of longitudinal diffusion, short-range eddy dispersion, long-range eddy dispersion, and solid–liquid mass transfer resistances due to a slow diffusion across the particle (Dp )

and to a slow adsorption–desorption process (kads ), to the total HETP recorded in chiral RPLC for the Lux Cellulose-1 used with a methanol-rich aqueous eluent (90/10, v/v), and trans-stilbene 1. The temperature was room temperature (24 ◦ C). At the optimum velocity (opt = 3.5), the mass transfer mechanism is essentially controlled by longitudinal diffusion and long-range eddy dispersion. The solid–liquid mass transfer resistances (Cp  and Ca ) have a minor impact on the optimum performance of the column. In contrast, at large reduced velocities the solid–liquid mass transfer resistances due to a slow diffusion rate across the particle (Dp ) and to a slow adsorption–desorption process (small kads value) account respectively for 19% and 28% of the total reduced plate height. The relative contribution of long-range and short-range eddy dispersion are 43 and 9%. Finally, longitudinal diffusion is

F. Gritti, G. Guiochon / J. Chromatogr. A 1332 (2014) 35–45

45

almost negligible since it represents less than 2% of the total plate height.

Laboratory. We thank Tivadar Farkas (Phenomenex, Torrance, CA, USA) for the generous gift of the four Kinetex columns.

5. Conclusion

References

This work elucidates completely the mass transfer mechanism in chiral RPLC columns using a Lux Cellulose-1 CSP. The accurate measurement of each individual contribution to the total HETP, including the longitudinal diffusion term (peak parking data), the solid–liquid mass transfer resistance term due to the finite diffusion rate across the particle (peak parking data + Torquato’s model of effective diffusion along a packed bed), the short-range eddy dispersion term (statistical analysis of mass transport in packed beds), and the long-range eddy dispersion term (adjusted long-range eddy dispersion HETP data obtained with a reference RPLC-C18 column of the same dimension and packed with particles of the same size) permits the accurate measurement of the adsorption rate constant kads . It was found that kads is large for non chiral compounds (107 s−1 , a result consistent with those of calculations based on a microscopic description of these mass transport phenomena or on collision theories). On the column used, it is about four orders of magnitude smaller for the chiral trans-stilbene probes than for the achiral TTBB (kads 103 s−1 ). kads was about 25% larger for the more retained than the lesser retained enantiomer, with a selectivity factor ˛ = k 2 /k 1 = 1.40. The relative decrease of kads when the methanol content in the mobile phase decreases from 90 to 100% was about −35%. This result agrees well with the theory, which predicts the adsorption rate constant to be inversely proportional to the bulk diffusion coefficient Dm (+50%). These initial results are encouraging for a more general study of mass transfer mechanisms in chiral chromatography. So far, little efforts had been devoted to this study, due to a lack of suitable kinetic models and of physical interpretation of chromatographic data. The impact of temperature, mobile phase composition, nature of the mobile phase components and additives, and of the nature of the CSP on the different HETP terms should be investigated using the robust and accurate experimental protocol described in this work. This should refine our understanding of mass transfer mechanisms in chiral columns. This could also speed up the optimization of the experimental conditions for maximum resolution based on a solid physico-chemical description of column efficiency in chiral chromatography. For instance, it could be possible to optimize the acetonitrile or methanol concentrations in aqueous mobile phases to maximize the speed and the resolution, when acetonitrile or methanol is required in the mobile phase. A forthcoming report will discuss whether columns packed with CSP core–shell particles may help to improve the resolution factors above those achieved with classical fully porous CSPs.

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Acknowledgements This work was supported in part by the cooperative agreement between the University of Tennessee and the Oak Ridge National