Environ Sci Pollut Res (2014) 21:3134–3144 DOI 10.1007/s11356-013-2263-z

RESEARCH ARTICLE

Statistical thermodynamics of adsorption of dye DR75 onto natural materials and its modifications: double-layer model with two adsorption energies M. Khalfaoui & A. Nakhli & Ch. Aguir & A. Omri & M. F. M’henni & A. Ben Lamine

Received: 22 February 2013 / Accepted: 21 October 2013 / Published online: 8 November 2013 # Springer-Verlag Berlin Heidelberg 2013

Abstract In this article, adsorption modelling was presented to describe the sorption of textile dye, Direct Red 75 (DR75), from coloured wastewater onto the natural and modified adsorbent, Posidonia oceanica. The formulation of the doublelayer model with two energy levels was based on statistical physics and theoretical considerations. Thanks to the grand canonical ensemble in statistical physics some physicochemical parameters related to the adsorption process were introduced in the analytical model expression. Fitting results show that the dye molecules are adsorbed in parallel position to the adsorbent surface. The magnitudes of the calculated adsorption energies show that the DR75 dye is physisorbed onto Posidonia. Both Van der Waals and hydrogen interactions are implicated in the adsorption process. Despite its simplicity, the model fits a wide range of experimental data, thereby supporting the underlying data that the grafted groups facilitate the parallel anchorage of the anionic dye molecule. Thermodynamic parameters, such as adsorption energy, entropy, Gibbs free adsorption energy and internal energy were calculated according to the double-layer model. Results suggested that the DR75 adsorption onto Posidonia was a spontaneous and exothermic process. Keywords Double-layer adsorption model . Wastewater treatment . Statistical physics . Functionalised biomass-derived material . Adsorption thermodynamics Responsible editor: Michael Matthies M. Khalfaoui (*) : A. Nakhli : A. Omri : A. Ben Lamine Quantum Physics Laboratory, Faculty of Sciences of Monastir, University of Monastir, Monastir 5000, Tunisia e-mail: [email protected] C. Aguir Ch. Aguir: •M. M.F.F.M’henni M’henni Applied and Environmental Chemistry Laboratory, Faculty of Sciences of Monastir, University of Monastir, Monastir 5000, Tunisia

Introduction Given their toxicity, dyes are of considerable environmental concern. Indeed, industrial effluents discharged from dyeing industries are highly coloured. These effluents can be toxic for aquatic and terrestrial life including humans (Bae and Freeman 2007; Chen 2002; Gottlieb et al. 2003; Lee and Pavlostathis 2004; Michaels and Lewis 1985). Several techniques have been proposed and attempted for the removal of such pollutants (Aksu 2005; Burlica et al. 2004; Horacek et al. 1994; Liu et al. 2007; Shakira et al. 2010). Among these numerous methods of pollutants removal, it is now recognised that adsorption, using solid supports, is an effective and useful technique. Removal of organic and inorganic compounds from wastewaters is well documented. Recently, the quality of water has been adversely affected by factors associated with the tremendous growth in the production of industrial chemicals. Indeed, it is well known that in literature there are many publications interested in wastewaters treatment, especially by means of the adsorption of pollutants onto numerous adsorbents. Conventional materials have been used with success. However, their widespread use is restricted due to their high cost. For this reason, alternative non-conventional materials, such as waste materials from agriculture and industry, have been proposed as adsorbents for the removal of organic and inorganic pollutants (Chong et al. 2010; Churchley et al. 2000; Couillard 1994; McKay et al. 1987; Nemr et al. 2009). The challenge for adsorption is to promote non-conventional materials mainly in term of high adsorption capacity and low cost. The use of aquatic plants as low cost materials, for the removal of organic and inorganic pollutants from wastewaters gained high interest (Aguir et al. 2009; Boaventura et al. 2002; Cengiz et al. 2012; Kousha et al. 2012; Ncibi et al. 2009; Wahab et al. 2011). In one of our previously published works, it was demonstrated that Posidonia oceanica is widely distributed and can be obtained very economically on a large scale from the

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Mediterranean Sea (Aguir et al. 2009). It was also demonstrated that waste biomass of Posidonia can be used as effective adsorbents for both heavy metal ions and dyes form aqueous solution (Aguir et al. 2009). This aquatic plant has an important capacity of adsorption thanks to the presence of phenol moieties and hydroxyl function in this vegetal material. In order to further improve the retention capacity of such material, carboxylic groups were introduced to Posidonia using a cheap methodology as it was described in our previous paper (Aguir et al. 2009). To understand and analyse the adsorption process, an approach of several isotherm models was developed in this work. It depends on the assumptions that are used to derive each model. However, all mathematical analyses of experimental adsorption data were found to be useful in characterising and interpreting the adsorption process based on the magnitudes of the fitting parameters. The main goal of the present paper is to give physical interpretations at microscopic level of dye (Direct Red 75 (DR75)) adsorption onto raw and modified Posidonia at four temperatures ranged from 30 to 80 °C. Our approach is based on a quantum statistical consideration of sorption using a double-layer model with two energy levels. We considered an adsorption of dye onto natural and modified materials taking into account steric and energetic conditions (requirements) of the process, as well as calculating its thermodynamic parameters.

Materials and methods Waste Posidonia was collected form Tunisian coasts. After an experimental procedure, the Posidonia was chemically modified by introducing succinic anhydride acid as functional groups. The reaction occurring between Posidonia component and succinic anhydride acid was detailed in one of our previous works (Aguir et al. 2009). As the hydroxyl groups are disposed towards reaction, lignin and hemicellulose, in addition to cellulose, may participate in the esterification of Posidonia . Furthermore, the chemically modified and raw biomasses were saturated with Pb2+ and this is to improve the adsorption capacity already noticed for the raw Posidonia. The experimental details have been reported elsewhere in our previous work (Aguir et al. 2009). The direct dye used in the experiments was DR75. The adsorbate was supplied by Industrial Society of Textile SITEX-Tunisia and was used without any purification in their commercially available from blended with mineral salts to adjust their dyeing power. The chemical structures of this dye are depicted in Fig. 1. The sorption of DR75 onto raw and modified Posidonia was carried out by batch sorption and the variables studied were initial sorbate concentration, contact equilibrium time, pH and temperature. Different quantities of raw and modified

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Posidonia in a given solution of sorbate were shaken at desired temperatures (30, 40, 60, and 80 °C) using a rotary operating (AHIBA NUANCE; SALVIS SA, Zollhausstrasse 2, CH-6015 Reussbühl) at 45 rpm. The concentrations were determined by an UV/visible spectrophotometer (CECIL, CE 2021, 2000) series) at wavelength corresponding to the maximum absorbance of the dye solution (λ max =511.5 nm). Several grafting rates were tested. It was found that the optimal rate is equal to 39.2 %. This grafting rate 39.2 % cannot be exceeded in experimental term. Indeed, after this grafting rate, the solubility of Posidonia increases as the grafting rate increases. At a grafting rate of 100 %, Posidonia becomes totally soluble and it cannot be used as adsorbent. Thus, in our work, two supports, such as raw and modified Posidonia, denoted P0 and MP, corresponently, were studied. For adsorption of DR75 dye, a binary interaction between dye and supports (P0 and MP) was tested. Furthermore, a binary system metal/support has been obtained in which the electron pairs of oxygen atoms in succinyl act as ligands for the complexation of the metal ion. The presence of functional groups and electron donor in the structure of the dye allows it to build complexes with metal ions. Then an analogous interaction including dye/metal/support must be suitable for the adsorption of such pollutants. Possibilities of ternary complex formation between the two supports (P0 and MP), direct red 75 and the mentioned metal ion were also investigated (Pb2+/P0 and Pb2+/MP). It was noticed that the adsorption capacities of the chemically modified biomasses. The same remark was deduced for the saturated biomasses with Pb2+. The pH of the aqueous solution was clearly an important parameter that controlled the adsorption process. Indeed, solution pH affects both aqueous chemistry and surface binding sites of the adsorbents which are negatively charged due to the presence of carboxylic groups. Depending on pH, these groups may change their charge. As it was mentioned previously, the adsorption is influenced by the surface charged that in turn is influenced by the solution pH. It was concluded in our previous work that the optimum uptake was obtained at pH 2 (Aguir et al. 2009). The investigation conducted at this pH value shows that optimum adsorptions of all materials used were achieved within the first 15–20 min and remained fairly stable thereafter. Figure 2 depicts the experimental adsorption isotherms of DR75 onto various studied substrates mentioned above. As it is observed from this figure, the adsorption capacity increased with the increase in temperature.

Theoretical background of studies The mathematical development of analytical expression of the double-layer model with two energy levels will be presented using a statistical physics approach. It will be seen that such a treatment provides expressions for all the model parameters,

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Fig. 1 Chemical structure of DR75

thereby enabling physical interpretations according to the experimental conditions. To apply statistical physics treatment, some assumptions will be considered. It is assumed that the adsorbate molecules are anchored onto receptor sites in two successive layers with different energy levels ε 1 and ε 2, respectively. Each receptor site can be empty or occupied once or twice. Adsorption involves an exchange of particles from free state to the adsorbed one. Its investigation cannot be performed without employing the grand canonical ensemble to take into account the particle number variation through the introduction of a Z gc ðT ; μÞ ¼

X

variable chemical potential, μ, in the adsorption process. The internal degree of freedom of the adsorbate molecules may be neglected in aqueous solution thereby allowing only the most important degree of freedom, i.e. the translational one, to be taken into account. This arises because the electronic degree of freedom cannot be excited thermally and the rotational degree of freedom is hampered in solution. The vibrational degree of freedom can be neglected in comparison with the translational one. According to these assumptions, the grand canonical partition function of one receptor site may be expressed as (Khalfaoui et al. 2012):

expð−β ð−εi −μÞN i Þ ¼ 1 þ expðβðε1 þ μÞÞ þ expðβ ðε1 þ ε2 þ 2μÞÞ

ð1Þ

N i ¼0;1;2

With the number of occupations of identical N m receptor sites at equilibrium being: ∂ln Z gc N o ¼ k BT ∂μ


N m

expðβ ðε1 þ μÞÞ þ 2expðβ ðε1 þ ε2 þ 2μÞÞ ¼ Nm 1 þ expðβ ðε1 þ μÞÞ þ expðβ ðε1 þ ε2 þ 2μÞÞ

ð2Þ Generally, the adsorption reaction should include a stoichiometric coefficient n: n ⋅ A þ S↔An S

ð3Þ

Where A represents the adsorbate molecule and S is the receptor site. The parameter n is an average number, which represents either the number of molecules anchored on one site (n ≻1) or the fraction of molecule per site (n ≺1). Therefore, the adsorbed quantity is written as a function of adsorbate concentration:

and

c2 ¼ cs exp − ΔE a1 þ ΔEa2 =RT

With c s is the solubility of adsorbate in aqueous solution, R is the ideal gas constant and T is the isotherm temperature. (−ΔE a1 ) and (−ΔE a2 ) are the adsorption energies at the first layer and the second one, respectively. As the first layer is used as a receptor site for the second one, the adsorption reaction at the second layer can be written: n ⋅ A þ An S↔A2n S

ð7Þ

This last reaction can also be written as: 2n ⋅ A þ S↔A2n S

ð8Þ

If we note that K 1 and K 2 are the equilibrium constants for the first and the second adsorbed layers respectively, we get: ½A2n S Š Qa2 a1 K 1 ¼ ½½SAŠ½nASŠŠn ¼ ðQ Q−Q Þcn and K 2 ¼ ½S Š½AŠ2n ¼ ð2Q −Q Þc2n asat1

Qa ¼ nN m

ðc=c1 Þn þ 2ðc=c2 Þ2n 1 þ ðc=c1 Þn þ ðc=c2 Þ2n

ð4Þ

ð6Þ

a

asat1

a

Where Q a1 and Q a2 are the adsorbed quantities at the first and the second layer respectively, while Q asat1(=nN m ) is the monolayer adsorbed quantity at saturation. The total adsorbed quantity is then:

where
c1 ¼ cs exp − ΔE a1 =RT

ð5Þ

Qa ¼ Qa1 þ Qa2 ¼ nN m

K 1 cn þ 2K 2 c2n 1 þ K 1 cn þ K 2 c2n

ð9Þ

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40

Fig. 2 Experimental adsorption isotherms of DR75 onto Pb2+-P0, Pb2+-EP3, EP3 and P0 as described by Aguir et al. (2009)

P0-DR75

2+

40

P0/Pb -DR75

30

Qa (mg/g)

Qa (mg/g)

30

20

30°C 40°C 60°C 80°C

10

0

20

10

0 0

50

100

150

30°C 40°C 60°C 80°C

200

0

50

100

C(mg/L)

Qa (mg/g)

60

MP-DR75

30°C 40°C 60°C 80°C

150

Qa (mg/g)

80

150

200

C (mg/L)

40

30°C 40°C 60°C 80°C

2+

MP/Pb -DR75

100

50 20

0

0

50

100

150

200

250

0 0

300

50

100

C (mg/L)

By equalising Eq. (4) and (9), the two equilibrium constants are related to the adsorption energies as:

K 1 ¼ ð1=cs Þn exp −n −ΔEa1 =RT ð10Þ

K 2 ¼ ð1=cs Þ2n exp −2n −ΔEa1 −ΔEa2 =RT

ð11Þ

The analytical model (Eq. 4) contains four parameters which can be deduced after fitting the experimental data. N m represents the receptor sites density per surface unit, n is a stoechiometric coefficient indicative of the anchorage manner of one adsorbed molecule onto the solid surface, c 1 is the halfsaturation concentration of the first adsorbed layer and c 2 is the concentration at half-saturation of the global isotherm. The adsorbed quantity at saturation, which is related to n and N m , is an important factor which characterises the adsorption system. It is about a steric parameter which gives us information on the adsorption capacity of the material. It is a very interesting parameter for the industrial dyeing as well as for the wastewaters depollution. The double-layer model with two energy levels was applied to fit all studied experimental data and shows a relatively highcorrelation coefficient R 2. The obtained results were also compared with those given by other models (Table 1), namely, monolayer and simple double-layer published elsewhere (Khalfaoui et al. 2002, 2003, 2006; Knani et al. 2012) where their expressions are written as:

150

200

250

300

C(mg/L)

Qa ¼

nN m
n 1 þ c1=2 =c

ð12Þ

Table 1 Comparison between the correlation coefficients obtained for each used model Adsorbent

T (°C)

Monolayer

Simple double-layer

Double-layer with two energy levels

P0-DR75

30 40 60 80 30 40 60 80

0.98229 0.98058 0.96722 0.96722 0.97843 0.96556 0.96802 0.9631

0.9806 0.98278 0.96992 0.96992 0.98035 0.96817 0.97106 0.97901

0.98088 0.982 0.97529 0.97529 0.9846 0.96975 0.97149 0.98621

30 40 60 80 30 40 60 80

0.98171 0.98261 0.95235 0.95866 0.98825 0.99341 0.98463 0.98366

0.98333 0.98385 0.95505 0.96137 0.98825 0.99429 0.98661 0.98471

0.98978 0.98981 0.97073 0.96855 0.99153 0.99607 0.97925 0.97214

P0/Pb2+-DR75

MP-DR75

MP/Pb2+-DR75

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2n þ 2 c=c1=2 Qa ¼ nN m
n
2n 1 þ c=c1=2 þ c=c1=2 c=c1=2


n

ð13Þ

n represents the number or the fraction of adsorbed molecule(s) per site, N m is the receptor sites density and c1/2 which is related to the adsorption energy represents the adsorbate concentration at half-saturation. These two last simple models have only one energy level which is related to the concentration at half-saturation. It could be seen that the Eq. (13) can be deduced from Eq. (4) or simply by writing the grand canonical partition function with the assumption that the adsorbate molecules are anchored onto receptor sites in two successive layers with the same energy. The fitting criterion in the present work is the well-known correlation coefficient R 2. The ideal fitting is obtained when the value of R 2 is close to the unit. The values of R 2 obtained from various models are not much spread (Table 1). However, the interpretation is based on the results given by the double-layer model with two energy levels. To reinforce the choice of the double-layer model with two energy levels, two physical reasons are taken into account. The first is an electric neutrality reason. Indeed, the adsorbent surface is positively charged while the solution contains the adsorbed molecules which are negatively charged. Thus, an electrostatic attraction occurs and the molecules are adsorbed onto the surface in the first layer. The second is to equilibrate the chemical potential. Indeed, the solution is still more concentrated although the first layer is adsorbed and more layers can be adsorbed. From the second layer, an electrostatic repulsion occurs which decreases the adsorbed quantity at the following layers. Consequently, the number of adsorbed layers will be limited. However, the interpretation is based on the results given by the double-layer model with two energy levels. The choice of such model is

reinforced by the two reasons of electric neutrality and chemical potential equilibrium as explained previously. Furthermore, it will be easy to interpret the microscopic adsorption process with a double-layer model in our case. Two different energy levels will be attributed respectively to the two adsorbed layers since the first is directly in contact with the adsorbent surface and the second is about an adsorbate–adsorbate interaction. The investigation of the adsorption process using the grand canonical partition function is a powerful tool because it is often possible to write the grand canonical partition function as a product of independent contributions. Thus, a complicated problem can be simplified by solving several independent problems. According to the statistical physics treatment, thermodynamic properties can be evaluated to reinforce the interpretations of the adsorption systems. These thermodynamic functions are entropy, Gibbs free adsorption energy and internal energy. The configurational entropy is given (Khalfaoui et al. 2012) by: Ja ¼ −

∂ lnZ gc −T ⋅ S a ∂β

where J a is the grand potential. The Gibbs free adsorption energy is given as follow: Ga ¼ μ⋅ N o The internal energy is expressed as:   ∂lnZ gc μ ∂lnZ gc þ E int ¼ − β ∂β ∂μ

E int ¼ −N m

ð16Þ

ð17Þ

ð18Þ

i 8h < ð1=βÞ⋅ðc=c1 Þn ⋅lnðc=c1 Þn þ 2⋅ðc=c2 Þ2n ⋅lnðc=c2 Þ2n :

ð15Þ

According to the double-layer model with two energy levels, the three thermodynamic parameters can be written as:

 8 9 < ðc=c1 Þn ⋅lnðc=c1 Þn þ ðc=c2 Þ2n ⋅lnðc=c2 Þ2n  = Sa ¼ −N m þ ln 1 þ ðc=c1 Þn þ ðc=c2 Þ2n : ; kB 1 þ ðc=c1 Þn þ ðc=c2 Þ2n


ðc=c1 Þn þ 2ðc=c2 Þ2n Ga ¼ Nm ⋅1n c=zg ⋅ kBT 1 þ ðc=c1 Þn þ ðc=c2 Þ2n

ð14Þ

1 þ ðc=c1 Þn þ ðc=c2 Þ2n

As it can be seen, the expressions of the three thermodynamic parameters depend on the equilibrium concentration of

h þμ

i9 ðc=c1 Þn þ 2ðc=c2 Þ2n =

1 þ ðc=c1 Þn þ ðc=c2 Þ2n ;

ð19Þ

adsorbate allowing thereby the investigation of their evolution during the whole adsorption process.

Environ Sci Pollut Res (2014) 21:3134–3144

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1.2

and understand the physical process at molecular level. It follows that two interpretations, steric and energetic, are derived.

P 0 -DR75 2+

P0/Pb -DR75 MP -DR75 2+

MP/Pb -DR75

0.9

n

Steric interpretations

0.6

0.3

30

40

50

60

70

80

T(°C)

Fig. 3 Evolution of the mean number of adsorbed molecules of DR75 per site as a function of temperature

The information given by the entropy is very important in the characterisation of the behaviour of adsorbed molecules. This parameter is due to various arrangements of the adsorbed molecules at the surface. In general, any reaction for which the change in the Gibbs free adsorption energy ΔG is negative should be favourable or spontaneous. Thus, its investigation is important to understand the physical adsorption process. The internal energy concept is an indispensable tool for the understanding of the physicochemical phenomena such as the case of adsorption process.

Results and discussion The nonlinear fit of the experimental data with the analytical model described by equation 4, allowed us to estimate the physicochemical parameters related to the adsorption process. The evolution of such parameters as a function of experimental conditions will be investigated in great details to interpret

Figure 3 depicts the evolution of the number or the fraction of adsorbed molecule(s) per site as a function of temperature. The interpretation of such results can be conducted by referring to the chemical structure of the dye DR75. Indeed, when this dye is dissolved in aqueous solution, four negative charges appear which contribute to the interaction with Posidonia’s receptor sites via electrostatic forces. It can be noticed from Fig. 3 that the number of adsorbed molecules per site is always lower than the unit and therefore the dye molecule is multi-anchored in parallel position onto the solid surface (Fig. 4). The same results was obtained in the case of the adsorption of the cyanine dye with their chromophores parallel to the solid surface (Jacob, 1980). For the raw Posidonia, the value of n is almost equal to the unit at 30 °C and then it decreases with the increase of temperature. This fact can be easily understood where the increase of the temperature can induce the swelling of Posidonia (Batzias and Sidiras 2007) and then some hidden receptor sites appear. As a result, the distance between receptor sites decreases and the dye molecule can be anchored with more than one receptor site. The same remark can be concluded for the other supports. The only difference between raw and modified Posidonia is that the anchorage of DR75 is parallel to the surface for the second case, which means more adequation between negative charges of the dye and the adsorbent surface. Another interesting result can be derived from the value of n. Indeed, in the case of adsorption of DR75 onto raw Posidonia at 30 °C, the value of n is equal to 0.975, i.e. a mean value is situated between 0.5 and 1 or an anchorage number situated between 1 and 2. This means that the dye molecule will be anchored either as one molecule per site or two molecules per site with the respective percentages x and (1–x) determined by

Dye DR75

Substrate

Dye DR75

DyeDR75

Fig. 4 Anchorage scheme for the dye DR75. The representation of the dye molecule is only symbolic

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P0 - DR75 2+

P0/Pb - DR75

45

N m (mg/g)

40 35 30 25 20 15 30

40

50

60

70

80

T ( °C)

MP - D R 7 5 2+ MP/Pb - DR75

N m (mg/g)

1200

800

400

0 30

40

50

60

70

80

T( °C ) Fig. 5 Behaviour of the effectively occupied receptor sites density in the case of raw and modified Posidonia (P0 and MP) and loaded supports (P0/Pb2+ and, MP/Pb2+) as a function of temperature

the value of n as demonstrated by Khalfaoui et al. (2002). In such case, the relationship between these percentages is x·1+ (1–x)·0.5=0.975. This gives 95 % of the adsorbed molecules as being anchored to one anchorage point and 5 % of the adsorbed molecules as anchored to two points involving two of the four negative charges of the dye molecule. In the case of the ternary system MP/Pb2+/DR75, 12 % of adsorbate molecules are anchored by three anchorages and the rest, i.e. 88 % are adsorbed by four anchorages. In the light of these results, it can be deduced that the anchorage of the dye molecule depends on its size as well as its structure. Furthermore, the adequation between the negative charges of the dye and the receptor sites is an important factor determining the anchorage position. Figure 5 depicts the evolution of the effectively occupied receptor sites, N m , as a function of temperature. In all cases, it appears that the loaded supports have a higher receptor sites density. It can also be noticed that when the temperature varies, the density N m notably increases and this is probably

due to the swelling of the adsorbent. This result is in good agreement with that found when studying the anchorage number mentioned earlier. The increase in temperature shows additional receptor sites that have been hidden at room temperature. Comparing the raw and the loaded Posidonia, it is obviously clear that the loaded adsorbents have more attractive receptor sites. This phenomenon was well investigated in literature in the case of the adsorption of basic red 18 and reactive 198 dyes by MgO-loaded porous carbons (Czyzewski et al. 2012). In such case, despite the relatively low specific surface area, substantially high adsorption capacity of dyes on MgO-loaded carbons was observed. Figure 6 shows the variation of the adsorbed quantity at saturation related to all investigated adsorbents. This steric parameter increases with the increase of temperature. This is easily understood since the increase in temperature has to give rise to an increase in the effectively occupied receptor sites. This result is confirmed by the fact that the evolution of Q asat is similar to the one of N m . Consequently, the parameter N m has a promising contribution to the adsorbed quantity at saturation and this is easily proved via our theoretical approach where Q asat =2·n·N m . Thus, it will be interesting to work at high temperature to get best dyeing yield and/or depollution of wastewaters. Another remark is that the loaded supports are more beneficial in terms of adsorption capacity. The steric interpretation determines average positions of the dye molecules on the adsorbent surface and whether the molecule is aligned parallel to the surface. Furthermore, the knowledge of the average positions can explain the behaviour of the adsorption capacity. Energetic interpretation The energetic investigation is fundamental to study in deep the adsorption process. For this reason, we propose a subsequent

P0 -DR75 2+

P0/Pb - DR75

600

MP - DR75 2+

MP/Pb - DR75

Q asat (mg/g)

50

450

300

150

0 30

40

50

60

70

T(°C)

Fig. 6 Change in the adsorbed mass of dye with its heating

80

Environ Sci Pollut Res (2014) 21:3134–3144

3141

Table 2 Adsorption energies for the first and the second adsorbed layer of DR75 onto raw and modified Posidonia Adsorption energies adsorbents

−ΔE a1 (kJ/mol)

−ΔE a2 (kJ/mol)

P0 P0/Pb2+ MP MP/Pb2+

−7.221 −14.100 −68.756 −13.280

−7.005 −8.098 −49.190 −10.490

study of some energy quantities characterising the adsorbate– adsorbent system. These energetic parameters allow us to interpret all the experimental results. Referring to the expression of our model, two parameters are related to the adsorption energies of the two respective layers (Eqs. 5 and 6). As the value of c s at the desired temperature is not well known, the mean values of ΔE a1 and ΔE a2 were determined by fitting the values of c 1 and c 2 in a function of temperature where the general form is written as: Fig. 7 Behaviour of the entropy versus the adsorbate concentration

C 1;2

   a b ¼ exp − T T

ð14Þ

All results are illustrated in Table 2. It can be noticed that all the values of adsorption energy are negative which means an exothermic process. It could be seen from Table 2 that the first adsorbed layer has the high adsorption energy, thus the affinity of the receptor sites located on this layer is more important. This means that the adsorbate–adsorbent interactions are stronger than those of adsorbate–adsorbate. Nevertheless, for the raw Posidonia, the inverse phenomenon occurs. Indeed, for raw Posidonia the interaction with surface takes place via Van der Waals or hydrogen bonds as there are no grafted receptor sites, and thereby there is no ion-exchange adsorption. As a result, the adsorbent–adsorbate energy is lower than the adsorbate-adsorbate one. It is obviously noticed from the values of adsorption energies that the dye DR75 gives energy to the solvent to be adsorbed, i.e., it is about exothermic process. Furthermore, all adsorption energy values indicate

30 °C 40 °C 60 °C 80 °C

45

P0-DR7 5

30

30 °C 40 °C

40

60 °C 80 °C

35

22

2+

Sa /kB

Sa / kB

P0/Pb -DR75 25 20 15 10

0 5

1

10

1

100

10

100

log(C), mg/L

log(C), m g / L 1200

30 °C

400

30 °C 40 °C

MP-DR75

40 °C

1000

60 °C

60 °C

80 °C

80 °C

300

800 2+

S/kB

Sa / kB

MP/Pb -DR75 200

600

400 100

200

0

0 1

10

log(C),m g /L

100

0,1

1

10

log(C ), m g / L

100

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Fig. 8 Behaviour of the Gibbs free adsorption energy as a function of the adsorbate concentration in the case of retention of the DR75 onto Posidonia

0

-20 -10

ΔG / kBT

ΔG / kBT

30 °C

-20

2+

P0/Pb -DR75

-40

P0 - DR75

T = 3 0°C T = 4 0°C T = 6 0°C T = 80°C

-60

-80

40 °C 60 °C

-100

80 °C -120 -30 0

50

100

150

0

200

50

C (mg/L)

100

150

200

C (mg/L)

0

0

-50

-100

30 °C

T = 30 °C T = 40 °C T = 60 ° C T = 80 °C

-150

ΔG / kBT

ΔG / kBT

MP/Pb2+-DR75

-500

MP-DR75

40 °C

-1000

60 °C 80 °C

-1500 -200

-2000

-250

0

50

100

150

200

250

300

C (mg/L)

that it is about physical adsorption and no dissociative adsorption took place. Similar results were found in the case of the 0.0

250

200

250

300

C (mg/L)

coccine dye onto sludge ash (Weng Ch 2002). Indeed, the experimental data were correlated well to the non-linear multilayer adsorption isotherm and the thermodynamic parameters indicated the ash adsorption was exothermic process as well as physical.

The grand canonical partition function can be further exploited and allows us to calculate other thermodynamic parameters involved in the adsorption process. These thermodynamic parameters are entropy, Gibbs free adsorption energy and internal energy which will be thereafter investigated. Using the grand canonical partition function, the theoretical expression of the entropy according to the double-layer model with two energy levels was given by the Eq. 17. Figure 7 depicts the evolution of the entropy of all studied adsorption systems as a function of the adsorbate concentration at various temperatures. Two different behaviours of entropy below and above the half-saturation are observed. The entropy increases

100 4

50

4

150

150

-1.0x10

0

-1.5x10 -2 10

100

Thermodynamics study Q a (mg/g)

E int /k B T

Eint/kBT

50

200

Qa

3

-5.0x10

0

3

10

log C

Fig. 9 Comparison between theoretical behaviours of adsorbed quantity and internal energy according equations 4 and 19 at 30 °C (n =0.988, N m =113.760 mg/g, c 1 =0.619 mg/L and c 2 =27.648 mg/L)

Environ Sci Pollut Res (2014) 21:3134–3144

3143

few receptor sites are empty. Close to the saturation, the free adsorption energy is near zero and then the adsorption is almost impossible. In term of temperature there is no significant effect on the spontaneity of DR75 adsorption onto Posidonia. To understand the phenomenon observed for the retention of the DR75 onto the adsorbent surface, the behaviour of internal energy was studied. Such study was conducted according to the theoretical double-layer model with two energy levels. For all experiments, internal energy was calculated using Eq. 19. To understand the behaviour of the internal energy along the adsorption isotherm, a theoretical illustration was proposed in Fig. 9. It can be observed that all the values of internal energy are negative. Conversely, the internal energy is correlated with the adsorbed quantity as it is shown in Fig. 9. This result seems to be logical since it is considered with the definition of internal energy. This could be explained by the fact that the potential energy is derived from all internal forces. Furthermore, the internal energy follows this increase because it is about an extensive quantity, i.e. it is proportional to the material amount. Figure 10 shows no clear difference between the values of internal energies at various temperatures. However, a significant difference appears at high adsorbate concentrations. The internal energy increases in module as the temperature increases and this is probably due to the increase of thermal collision.

with the adsorbate concentration before the half-saturation and decreases after this particular point. Indeed, at the beginning of adsorption the disorder increases when the adsorbed molecules become onto the solid surface and this is due to the fact that they have a lot of possibilities to find an empty site. After the half-saturation, the adsorbed molecule has low probability to choose adsorbent site since the surface tends toward the saturation and therefore tends toward the order. Figure 7 shows that for the same adsorbed quantity, the value of the entropy increases with the increase in temperature. This is probably due to the thermal agitation which increased with temperature and consequently the disorder increases. Thanks to the grand canonical formalism in statistical physics, the Gibbs free adsorption energy values were calculated by referring to Eq. 18 and then illustrated in Fig. 8. It can be observed from the last figure that all the values of Gibbs free adsorption energies are negative, i.e. the adsorption reaction occurs spontaneously. It can also be noticed that the variation in the Gibbs free adsorption energy is important at low concentration, i.e., at the beginning of adsorption. This result is foreseeable since at low coverage the adsorbed quantity increases greatly due to the high adsorption energy surface. When the coverage increases, the adsorption energy surface decreases where the number of empty sites is becoming increasingly weak. When the saturation is nearly reached, the adsorption reaction becomes more or less difficult since

Fig. 10 Behaviour of internal energy as a function of adsorbate concentration for all studied adsorption isotherms

0

0

30°C 40°C 60°C 80°C

2+

P0/Pb -DR75

30°C P0-DR75

40°C 60°C 80°C

-1000

E int /k

E int / k

B

B

T

T

-1500

-3000 -2000

0

50

100

150

200

0

50

100

C(mg/L)

200

0

0

-1x10

/k B T

-5000

30°C 40°C 60°C 80°C

-10000

0

50

E int

E int /k

B

T

150

C(mg/L)

DR75/ PM3

2+

MP/Pb - DR75

-2x10

-3x10 100

150

C (mg/L)

200

250

300

4

30°C 40°C 60°C 80°C

4

4

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100

150

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C(mg/L)

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300

3144

Conclusions The theoretical approach presented within this paper leads us to conduct new interpretations of the adsorption process of the DR75 dye onto raw, modified Posidonia and saturated with Pb(II). The model predictions were compared with those results obtained from experimental tests for dye adsorption and a close agreement was achieved. The investigation on the evolution of the fitting parameters shows that (1) the DR75 dye is multianchored to Posidonia surface, (2) additional receptor sites are highlighted through the intervention of van der Waals forces and/or hydrogen bonds, (3) the evolution of the adsorbed quantity at saturation can be explained regarding the experimental conditions and (4) the adsorption of DR75 onto Posidonia biomass is about exothermic process. Furthermore, a thermodynamic study was conducted and then consequent interpretations are raised such as the disorder and the degree of spontaneity at the adsorbent surface during the adsorption process. All these results were conducted thanks to the double-layer model with two energy levels based on statistical physics treatment. Thus, the new theoretical approach seems to be a powerful tool providing a good description of the adsorption process.

References Aguir C, Khalfaoui M, Laribi N, M’henni MF (2009) Preparation and characterization of new succinic anhydride grafted Posidonia for the removal of organic and inorganic pollutants. J Hazard Mater 172: 1579–1590 Aksu Z (2005) Application of biosorption for the removal of organic pollutants: a review. Process Biochem 40:997–1026 Bae JS, Freeman HS (2007) Aquatic toxicity evaluation of new direct dyes to the Daphnia magna. Dyes Pigments 73:81–85 Batzias FA, Sidiras DK (2007) Simulation of methylene blue adsorption by salts-treated beech sawdust in batch and fixed-bed systems. J Hazard Mater 149:8–17 Boaventura D, Alexander M, Santina PD, Smith ND, Ré P, Fonseca LCD, Hawkins SJ (2002) The effects of grazing on the distribution and composition of low-shore algal communities on the central coast of Portugal and on the southern coast of Britain. J Exp Mar Biol Ecol 267:185–206 Burlica R, Kirkpatrick MJ, Finney WC, Clark RJ, Locke BR (2004) Organic dye removal from aqueous solution by glidarc discharges. J Electrost 62:309–321 Cengiz S, Tanrikulu F, Aksu S (2012) An alternative source of adsorbent for the removal of dyes from textile waters: Posidonia oceanica (L.). Chem Eng J 189–190:32–40 Chen BY (2002) Understanding decolorization characteristics of reactive azo dyes by Pseudomonas luteola: toxicity and kinetics. Process Biochem 38:437–446 Chong MN, Jin B, Chow CWK, Saint C (2010) Recent developments in photocatalytic water treatment technology: a review. Water Res 44: 2997–3027 Churchley JH, Greaves AJ, Hutchings MG, James AE, Phillips DAS (2000) The development of a laboratory method for quantifying the

Environ Sci Pollut Res (2014) 21:3134–3144 bioelimination of anionic, water soluble dyes by a biomass. Water Res 34:1673–1679 Couillard D (1994) The use of peat in wastewater treatment. Water Res 28:1261–1274 Czyzewski A, Karolczyk J, Usarek A, Przepiorski J (2012) Removal of two ionic dyes from water by MgO-loaded porous carbons prepared through one step process from poly(ethylene-terephthalate)/magnesium carbonate mixtures. Bull Mater Sci 35:211–219 Gottlieb A, Shaw C, Smith A, Wheatley A, Forsythe S (2003) The toxicity of textile reactive azo dyes after hydrolysis and decolourisation. J Biotechnol 101:49–56 Horacek J, Soukupova L, Puncochar M, Slezcak J, Drahos J, Yosida K, Tsutsumi A (1994) Purification of waste waters containing low concentrations of heavy metals. J Hazard Mater 37:69–76 Jacob S (1980) Organized monolayers by adsoeprion. 1. Formation and structure of oleophobic mixed monolayers on solid surfaces. J Am Chem Soc 102:92–98 Khalfaoui M, Baouab MHV, Gauthier R, Ben Lamine A (2002) Dye adsorption by modified cotton. Steric and energetic interpretations of model parameter behaviours. Adsorpt Sci Technol 20:33–47 Khalfaoui M, Knani S, Hachicha MA, Ben Lamine A (2003) New theoretical expressions for the five adsorption type isotherms classified by BET based on statistical physics treatment. J Colloid Interface Sci 263:350–356 Khalfaoui M, Baouab MHV, Gauthier R, Ben Lamine A (2006) Acid dye adsorption onto cationized polyamide fibres. Modeling and consequent interpretations of model parameter behaviours. J Colloid Interface Sci 296:419–427 Khalfaoui M, Nakhli A, Knani S, Baouab MHV, Ben Lamine A (2012) On the statistical physics modeling of dye adsorption onto anionized nylon: consequent new interpretations. J Appl Polym Sci 125:1091–1102 Knani S, Khalfaoui M, Hachicha MA, Ben Lamine A, Mathlouthi M (2012) Modelling of water vapour adsorption on foods products by a statistical physics treatment using the grand canonical ensemble. Food Chem 132:1686–1692 Kousha M, Daneshvar E, Sohrabi MS, Jokar M, Bhatnagar A (2012) Adsorption of acid orange II dye by raw and chemically modified brown macroalga Stoechospermum marginatum. Chem Eng J 192: 67–76 Lee YH, Pavlostathis SG (2004) Decolorization and toxicity of reactive anthraquinone textile dyes under methanogenic conditions. Water Res 38:838–1852 Liu CH, Wu JS, Chiu HC, Suen SY, Chu KH (2007) Removal of anionic reactive dyes from water using anion exchange membranes as adsorbers. Water Res 41:1491–1500 McKay G, Ramprasad G, Mowli P (1987) Desorption and regeneration of dye colours from low-cost materials. Water Res 21:375–377 Michaels GB, Lewis DL (1985) Sorption and toxicity of azo and triphenylmethane dyes to aquatic microbial populations. Environ Toxicol Chem 4:45–50 Ncibi MC, Mahjoub B, Ben Hamissa AM, Ben Mansour R, Seffen M (2009) Biosorption of textile metal-complexed dye from aqueous medium using Posidonia oceanica (L.) leaf sheaths: mathematical modelling. Desalination 243:109–121 Nemr AE, Abdelwahab O, El-Sikaily A, Khaled A (2009) A removal of direct blue-86 from aqueous solution by new activated carbon developed from orange peel. J Hazard Mater 161:102–110 Shakira K, Elkafrawyb AF, Ghoneimya HF, Beheira SGE, Refaata M (2010) Removal of rhodamine B (a basic dye) and thoron (an acidic dye) from dilute aqueous solutions and wastewater simulants by ion flotation. Water Res 44:1449–1461 Wahab MA, Ben Hassine R, Jellali S (2011) Posidonia oceanica (L.) fibers as a potential low-cost adsorbent for the removal and recovery of orthophosphate. J Hazard Mater 191:333–341 Weng CH (2002) Adsorption characteristics of new coccine dye onto sludge ash. Adsorpt Sci Technol 20:669–681