Langmuir 1997, 13, 1245-1250
1245
A General Model for Adsorption of Organic Solutes from Dilute Aqueous Solutions on Heterogeneous Solids: Application for Prediction of Multisolute Adsorption† Anna Deryło-Marczewska* Department of Physical Chemistry, Faculty of Chemistry, M. Curie-Skłdowska University, 20031 Lublin, Poland
Adam W. Marczewski‡ Department of Chemical Engineering, Kyoto University, Kyoto 606, Japan Received December 13, 1995. In Final Form: October 7, 1996X A general model describing the adsorption process from the single-component and multicomponent dilute aqueous solutions of dissociating organic substances on activated carbon is studied. The theoretical considerations are based on the theory of physical adsorption on energetically heterogeneous solids. The effect of solution pH and ionic strength is also taken into account. The theoretical considerations are illustrated by the experimental data for single-, bi-, and trisolute adsorption systems.
Introduction With regard to the great importance of problems connected with environment pollution and protection, studies of the adsorption process from dilute aqueous solutions on solid surfaces have become very important. Its usefulness in water and wastewater treatment requires many experimental and theoretical investigations. The complexity of adsorption process in such systems results in a relatively little progress in its theoretical description.1,2 The theory of localized physical adsorption on heterogeneous solids is one of the theoretical approaches used successfully to analyze the adsorption equilibria. Its great advantage is that it makes it possible to take it into account the effects of many factors on adsorption equilibria: solid surface charge established by solution pH and ionic strength; energetic heterogeneity; lateral interactions in adsorbed phase. From an engineering point of view the adsorption systems consisting of many solutes are of great importance. However, the description of such systems is very complicated because of a great number of substances with various physicochemical properties competing at a solid surface. In the literature several methods were proposed for the description of adsorption from multicomponent systems. Starting from the simple Langmuir model,3 many other more theoretically advanced approaches were discussed: the extension of the Polany’i potential theory;4 the ideal adsorbate solution (IAS) model;5-7 the vacancy solution theory.8 The theory of adsorption on energetically heterogeneous solids was also successfully applied for
description of the adsorption process from liquid mixtures;1,2,9-15 however, the assumptions concerning the relations between solute adsorption energies are necessary in this model. Methods based on a high correlation of adsorption energies or a lack of any correlation were considered.1,2,14,15 It is also possible to use a more general assumption about a qualitative similarity of adsorption forces for all mixture components.12,16 On the basis of this model, the attempts of taking into account the mutual interactions in adsorbed phase were also considered.1,15 The experimental investigations of multicomponent systems are very time-consuming. Thus, the possibility of estimation of multisolute adsorption using the parameters describing the simple systems seems to be very important. Many attempts of adsorption prediction were considered; however, the results were good in the case of only some specific systems.3-13 One of the main problems is a difficulty to assess the mutual interactions between mixture components and adsorbent in solvent media. Another problem is the fact that more general solutions which allow for taking such interactions into account are not analytical equations. The first step in the analysis of multisolute equilibria is to choose the physically realistic model describing the single-solute adsorption systems and to calculate exactly the parameter values characterizing these data. Then, it is necessary to investigate the possibilities of estimating adsorption values from multicomponent solutions by using the single-solute data. This simple procedure allows a definition of the deviations
† Presented at the Second International Symposium on Effects of Surface Heterogeneity in Adsorption and Catalysis on Solids, held in Poland/Slovakia, September 4-10, 1995. ‡ Current address: Laboratory of Adsorption and Interface Physicochemistry, Institute of Catalysis and Surface Chemistry, Polish Academy of Sciences, M. Curie-Skłdowska Pl 3, 20031 Lublin, Poland. X Abstract published in Advance ACS Abstracts, February 15, 1997.
(6) Jossens, L.; Prausnitz, J. M.; Fritz, W.; Schlu¨nder, E. U.; Myers, A. L. Chem. Eng. Sci. 1978, 33, 1097. (7) Fritz, W.; Schlu¨nder, E. U. Chem. Eng. Sci. 1981, 36, 721. (8) Fukuchi, K.; Kobuchi, S.; Ihara, Y.; Noda, K.; Arai, Y. Water Purif. Liquid Wastes Treat. 1983, 24, 789. (9) Jaroniec, M.; Deryło, A. J. Colloid Interface Sci. 1981, 84, 191. (10) Okazaki, M.; Kage, H.; Toei, R. J. Chem. Eng. Jpn. 1980, 13, 286. (11) Mu¨ller, G.; Radke, C. J.; Prausnitz, J. M. J. Colloid Interface Sci. 1985, 103, 466 and 484. (12) Marczewski, A. W.; Deryło-Marczewska, A.; Jaroniec M. Chem. Scr. 1988, 28, 173. (13) Marczewski, A. W.; Deryło-Marczewska, A.; Jaroniec, M. J. Chem. Soc., Faraday Trans. 1 1988, 84, 2951. (14) Rudzinski, W.; Charmas, R.; Partyka, S.; Bottero, J. Y. Langmuir 1993, 9, 2641. (15) Koopal, L. K.; Van Riemsdijk, W. H.; De Wit, C. M.; Benedetti, M. F. J. Colloid Interface Sci. 1994, 166, 51. (16) Deryło-Marczewska, A. Mh. Chem. 1994, 125, 1.
(1) Jaroniec, M.; Madey, R. Physical Adsorption on Heterogeneous Solids; Elsevier: Amsterdam, 1988. (2) Deryło-Marczewska, A.; Jaroniec, M., Surface and Colloid Science; Plenum Press: New York, 1987; Vol. 14. (3) Butler, J. A. V.; Ockrent, C. J. Phys. Chem. 1930, 34, 2841. (4) Manes, M.; Greenbank, M. Treatment of Water by Granular Activated Carbon; Advances in Chemistry Series 202; American Chemical Society: Washington, DC, 1983, p 9. (5) Radke, C. J.; Prausnitz, J. M. AIChE J. 1972, 18, 761.
S0743-7463(95)01536-8 CCC: $14.00
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Deryło-Marczewska and Marczewski
predicted from experimental values, to estimate their sources and the ways of eventual corrections. The aim of this paper is to study experimentally and theoretically the adsorption process from dilute aqueous solutions of dissociating organic solutes on solid surfaces. The theoretical analysis is based on the theory of adsorption on heterogeneous solids which allows an evaluation, in a simple way, of the effect of many factors on adsorption equilibria. A general model of weak electrolyte adsorption is considered by including the effect of energetic heterogeneity, the changes of solid surface charge and electrical potential connected with solution pH and ionic strength. The basic assumption is that the adsorption energies of all solution components change in an ordered way. The experimental data are measured for several single-, bi-, and trisolute adsorption systems over a wide range of pH and solute concentrations. The parameters characterizing single-component adsorption are used to estimate the values for multisolute adsorption. Theoretical Section The mechanism of adsorption from dilute solution of n dissociating organic substances may be described as a competition of water and organic molecules in neutral and ionic forms to the surface sites. Water as a solvent is treated as a reference substance “w” ) “n + 1” with constant concentration xlw = 1 ( xlw = 1 is the mole fraction of water in the liquid phase). The inorganic electrolytes (except for H+ and OH-) regulating solution pH and ionic strength are assumed not to participate in adsorption; they form only the diffuse double layer. The adsorbent is considered as an energetically heterogeneous solid; its surface sites are characterized by different values of adsorption potential. The differences between adsorption forces on ionic and neutral surface sites are taken into account through the dependence between ion adsorption and the electrical double layer potential connected with the ionic strength and surface charge established by solution pH. The simplifying assumptions are as follows: all solution components have identical molecular sizes; molecular interactions compensate in bulk and adsorbed phases. Thus, the basic integral equation describing multisolute adsorption on heterogeneous solid for the constant ionic strength may be written as follows:16 n
a(n)/am )
ai(n)/am ) ∑ i)1 n
∫∆E
gi[ci,pH,Ei] ∑ i)1
1+
n
χ(E) dE (1)
gi[ci,pH,Ei] ∑ i)1
gi(ci,pH,Ei) ) gi(w)(ci,pH,Ei(w) - Ew)
i ) 1, 2, ..., n
In the above, a(n) is the total adsorption of n organic solutes, ai(n) is the adsorption of the ith organic solute from an n-component mixture, am is the average maximum adsorbed amount, ci is the molar concentration, Ei ) i/RT is the reduced adsorption energy, where i is the adsorption energy, R is the ideal gas constant, and T is the temperature, E ) (E1, E2, ..., En) is the vector of reduced adsorption energies, χ(E) is the n-dimensional distribution function of adsorption energies, Ew is the adsorption energy of water, and gi(ci,pH,Ei) is the function describing the local adsorption on a homogeneous surface patch of constant energy and depending on adsorption mechanism.
With regard to the competition mechanism of adsorption from liquid systems, the process may be described by the solute-solvent (water) exchange reactions and the function gi depends on the values characterizing solute with respect to water (Ei ) Ei(w) - Ew). The dissociating organic substance may be treated as a mixture of ionic and neutral species. Thus, the function gi characterizing the adsorption process for the ith solute has the following form:
gi(ci,pH,Ei) ) gis(cis,pH,Eis) + gij (cij,pH,Eij)
(2)
In the above, the subscripts s and j denote the neutral and ionic form of organic substance. The concentrations of these forms are related by the dissociation constant Ka. In a simple case, when we can neglect the molecular interactions (or rather assume that they are equal) between the adsorbed species, the Langmuir-type model will be good for a local isotherm. Thus, for a neutral form we can assume that its adsorption does not depend on solution pH and we write
gis(cis,Eis) ) Kiscis,
Kis ) Kios exp(Eis)
(3)
where Kis is the equilibrium constant connected with adsorption energy for a neutral form and Kios is the preexponential factor. For dissociated solutes one should take it into account the electrostatic interactions between the charged adsorbent surface and organic ion. Mu¨ller et al.11,17 proposed the model of weak electrolyte adsorption based on the electrostatic theory and the classical Gouy-Chapman model of an electrical double layer. According to this model the function gi has the following form:16
gij(cij,pH,Eij) ) Kij fqcij,
Kij ) Kioj exp(Eij)
fq ) exp(-zi(Fφs/RT)
(4) (5)
In the above, Kij is the constant describing the ion adsorption on an electrically neutral surface, fq is the factor reflecting the effect of solid surface charge on adsorption, zi( is the charge of organic ion, F is the Faraday constant, φs(qsI) is the electric interfacial potential, qs is the surface charge density, and I ) (1/2)∑icizi2 is the ionic strength. The surface charge density qs(pH,I) is determined from the experimental data of potentiometric titration. However, the φs(qs,I) value may be estimated from the equation expressing the condition of system electroneutrality balancing qs by the charge density due to all adsorbed ions, qa, and by the charge density of the diffuse double layer qd(φs)
qs + qa + qd(φs) ) 0
(6)
and from the relation qd(φs)
(
-zdqd ) x8∈RTI sinh
)
|zd|φsF 2RT
(7)
where zd ) |z+| ) |z-| is the valence of ions in diffuse layer and ∈ is the solution dielectric permittivity. In the case of organic solute adsorption from dilute aqueous solutions on carbons the concentrations of adsorbed species in the surface phase can be very high. Thus, the lateral interactions between adsorbed molecules may play a significant role in adsorption equilibria. Because (17) Mu¨ller, G.; Radke, C. J.; Prausnitz, J. M. J. Phys. Chem. 1980, 84, 369.
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Langmuir, Vol. 13, No. 5, 1997 1247
of the complexity of regarded adsorption systems, it should be necessary to take it into account various types of interactions among different molecules in adsorbed phase. The function gi may be then expressed as a product of the term describing adsorption without lateral interactions and the function characterizing such interactions.1,18 For the random distribution of adsorption sites, gi is a function of the total surface coverage:
gi(ci,pH,Ei) ) Kicigint
(8)
where Ki ) Kis or Ki ) Kij fq The function gint can be expressed as a product of terms relating to various types of lateral interactions in the adsorbed phase. In the case of specific interactions, the association model of Kiselev can be used:1,18
gKis ) 1 + Kn(a(n)/am)
(9)
However, the dispersive interactions can be represented by the Fowler-Guggenheim equation
gFG ) exp[a(a(n)/am)]
(10)
where the constants Kn and R characterize the specific and dispersive interactions, respectively. The effect of energetic heterogeneity and lateral interactions in surface phase was analyzed by many authors.1,14,15,18 The mutual compensation of both effects was observed. Thus, we can say about a general deviation of adsorption system from ideality, though in systems of the type analyzed in this paper, heterogeneity is the prevalent effect. The integral eq 1 may be solved analytically or numerically only under some specific assumptions concerning the form of energy distribution function.1 Different methods were proposed by assuming special dependencies between the adsorption energies of system components. A more general way is to establish a qualitative similarity of adsorption interactions of all mixture components with an adsorbent surface. Let us assume that a certain correlation exists between the adsorption energies of solution components “i” and “k”:12
Ei ) Ei(Ek)
and
Ek ) Ek(Ei)
∫EE * χ(Ei) dEi ) ∫EE * χ(Ek) dEk ) i
k
k,min
F(Ei*) ) F(Ek*) ) F* (12) In the above F(Ei) ∈ 〈0,1〉 is the integral distribution function which is connected with the differential distribution function χ:
dF/dEi ) χ(Ei)
(13)
The assumption means that the same tendency of energy changes (decreasing or increasing) is observed for all solution components and surface sites. In Figure 1 the idea of such a correlation of adsorption energies for the solutes A and B is presented for the model distribution functions. After assumptions 11 and 12 are introduced, the n-dimensional integral eq 1 is transformed into a one(18) Deryło-Marczewska, A. Langmuir 1993, 9, 2344.
dimensional one: n
a(n)/am )
∫01
gi[ci,pH,Ei(f)] ∑ i)1
1+
n
df
(14)
gi[ci,pH,Ei(f)] ∑ i)1
Then, defining the variable zi describing the distance of adsorption energy from the mean energy E h i we obtain: n
a(n)/am )
∫0
1
gj i[ci,pH,E h i(f)] exp[zi(f)] ∑ i)1 n
1+
df
(15)
gj i[ci,pH,E h i(f)] exp[zi(f)] ∑ i)1
gj i ) gi(ci,pH,E h i);
zi(f) ) E h i(f) - E hi
(16)
(11)
It means that if the molecules of solute “i” and “k” adsorb on the surface site “*”, their adsorption energies and distribution functions are related as follows:
i,min
Figure 1. Correlation of adsorption energies for the mixture of solutes A and B for the model distribution functions of adsorption energies.
Equation 15 has a simple form of one-dimensional integral. It describes adsorption from an n-component mixture; however it is characterized by the functions zi(f) and the h io exp(E h i) obtained from the mean energy constants K hi)K experimental data of single-solute adsorption. Thus, it is possible to predict the parameters of multicomponent adsorption using the values characterizing the singlesolute adsorption. Experimental Section The experimental isotherms were measured for adsorption of single organics and their mixtures from dilute aqueous solutions on the granular activated carbon RIC from Norit n.v. (Amersfoort, Netherlands) at 293 K. In order to remove some inorganic impurities, the activated carbon was washed with HCl solutions of increasing concentration, and then it was rinsed with bidistilled water. The amounts of Ca2+ and Na+ ions in the extract were controlled by atomic absorption spectroscopy (AAS). Finally, the carbon was dried at 393 K to attain a constant mass. The purified RIC carbon is characterized by the BET specific surface area, SBET ) 990 ( 30 m2/g, and the total specific pore volume obtained from nitrogen adsorption, Vp ) 0.59 cm3/g. The surface charge density was determined by potentiometric titration of carbon in NaCl solutions of ionic strength I ) 0.01 and 0.1 mol/L. Prior to the experiment the activated carbon was dried at 393 K.
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The adsorption isotherms were measured for the constant ionic strength I ) 0.1 mol/L and over the pH range 1.7-10.5. The adsorbate solutions were prepared from bidistilled water and organic substances of commercially available quality. Benzoic acid (BA, pKa ) 4.2), salicylic acid (SA, pKa ) 2.98), and p-nitrophenol (NP, pKa ) 7.25) were used as adsorbates. Singlesolute adsorption of NP, bisolute adsorption of BA + NP and SA + NP and trisolute adsorption from BA + SA + NP solutions have been measured. (The single-solute data for BA and SA and bisolute data for BA + SA systems measured earlier16,18 in the same conditions are also used in the paper.) Before contacting with adsorbate solution a known amount of activated carbon was added to a known amount of bidistilled water and the mixture was degassed under vacuum in order to remove the air from the pores. The amount of water removed during this process was controlled. The ionic strength was established by addition of NaCl, and pH was established by addition of HCl or NaOH solutions. The isotherms for bi- and trisolute systems were established under the constant initial concentration of one component: 2, 4, 6, 8, and 10 mmol/L. In order to obtain the definite equilibrium pH and to choose the measured concentration range in the best possible manner, the simulation procedure was elaborated.18 The theoretical isotherms of Freundlich type were simulated for the assumed approximate parameters. The surface charge of activated carbon and the charge due to adsorbed organic ions and their relation to pH changes during adsorption process were taken into account in the simulation procedure. The compositions of adsorbate solutions and activated carbon amounts were prepared according to the simulated theoretical isotherms. After equilibrium was attained, the solute concentrations were measured by using the UV-vis spectrophotometer Specord M-40 (Carl Zeiss, Jena). The amount of adsorbed organic substance was calculated from the experimental data using the material balance.
Results and Discussion The experimental systems were analyzed by using the presented model including the effect of energetic heterogeneity and solid surface charge established by solution ionic strength and pH. The data of single-, bi-, and trisolute adsorption were analyzed by applying the suitable forms of eq 15 with the functions gi expressed by eqs 3 and 4. First, the parameters characterizing the single-solute adsorption isotherms were evaluated using the optimization procedure utilizing the optimization package MINUIT (CERN, Geneve).18 It was assumed in the calculations that the system heterogeneity was characterized by the Gauss distribution function of adsorption energies
f(z) )
[
(| |)]
1 z 1 + sin(z) erf 2 x2σ
σ2 )
(17)
∫01[E(f) - Eh ]2 df
where σ is the energy dispersion. The interfacial potential was calculated from eqs 6 and 7. The adsorption capacity was assumed to be equal for all systems, am ) 4.7 mmol/g; this value was obtained from the BET surface area and the average area occupied by a simple aromatic molecule (0.35 nm2/g). The best-fit parameters characterizing the single-solute adsorption for all investigated systems are presented in Table 1. The details of these calculations and their results for experimental data of benzoic and salicylic acid adsorption are presented in ref 18. The new experimental isotherms for p-nitrophenol adsorption are shown in Figure 2. The adsorption isotherms at the pH values below 6 coincide: for such pH values the dissociation degree of p-nitrophenol is below 6% (pKa ) 7.25) and according to the model, the adsorption of nonionized organics does not depend on the pH and the surface charge. However, the isotherms
Table 1. Values of Parameters Characterizing the Single-Solute Adsorption from Dilute Aqueous Solutions on Activated Carbon RIC at 293 Ka solute
log Ks
log Kj
σ
SDlog
L
benzoic acid (BA)* salicylic acid (SA)* p-nitrophenol (NP)
0.196 0.713 0.396
-1.705 -0.828 0.018
4.75 5.12 4.79
0.0263 0.0373 0.0478
71 70 47
L a SD 2 1/2 log ) [ ∑l)1 (log aopt,l - log aexp,l) /(L - 4)] , L, number of experimental points. σ, energy dispersion. *, ref 18. K h s and K h j in [L/mmol].
Figure 2. Experimental data of p-nitrophenol (NP) adsorption from dilute aqueous solutions on activated carbon RIC at 293 K. Lines are optimized isotherms (eq 15). Insert: the dependence qs ) f(pH) determined from the potentiometric titration data18 for I ) 0.1 mol/L.
measured at the pH > pKa differ strongly, because p-nitrophenol is highly dissociated and adsorption of its ionic form depends on the surface charge qs(pH,I). Good agreement between the experimental points and theoretical curves for this wide range of dissociable solute concentrations and solution pH values confirms the correctness and usefulness of the model used. Next, the parameters characterizing the single-solute adsorption were applied to estimate the adsorption values for bi- and trisolute systems by using the suitable forms of eq 15. In the numerical procedure the values of partial ai(n) and total summaric a(n) adsorption were estimated. In Figures 3 and 4 the comparison of experimental and predicted values for partial and total summaric adsorption is shown. The results are presented by using adsorptionadsorption and log(adsorption)-log(adsorption) plots, which allow an estimation of the prediction quality over the whole range of measured adsorption values. In Table 2 the deviations of predicted adsorption values from experimental data are given. Generally, good agreement between the experimental points and predicted dependencies is observed for total summaric adsorption in the case of all systems studied. However, for the partial isotherms greater deviations are found. Analyzing the data shown in Figures 3 and 4, we can state that the points representing the partial adsorption values for p-nitrophenol (NP), benzoic acid (BA), and salicylic acid (SA) can be grouped along the straight lines with the slopes different from the ideal behavior (slope equal to unity). These straight lines fitting the partial isotherms in a simple way (estimated using ai(n) but not log ai(n) data), are additionally drawn in both figures. For the system salicylic acid + p-nitrophenol (SA + NP) the straight line slopes have the following values: 1.40 (partial adsorption for salicylic acid) and 0.74 (partial adsorption for p-
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Figure 3. Comparison of experimental (exp) and predicted (pre) total summaric and partial values of adsorption from benzoic acid + p-nitrophenol (BA + NP) and salicylic acid + p-nitrophenol (SA + NP) solutions on activated carbon RIC at 293 K. Dashed and dotted lines represent linear best-fits (pre vs exp values) for partial adsorption data. Solid line refers to the perfect fit, exp ) pre.
Figure 4. Comparison of experimental (exp) and predicted (pre) total summaric and partial values of adsorption from benzoic acid + salicylic acid + p-nitrophenol (BA + SA + NP) solutions on activated carbon RIC at 293 K (lines as in Figure 3). Table 2. Deviations of Predicted Values from Experimental Partial Adsorption Values for the Bi- and Trisolute Systemsa solute
SD
L
benzoic acid (BA) salicylic acid (SA) p-nitrophenol (NP)
0.0329 0.0529 0.0847
175 175 72
a SD ) { ∑L [(a 2 1/2 i(n)pre,l - ai(n)exp,l)/am] /(L - 4)} . L, number of l)1 experimental points.
nitrophenol), whereas in the case of the system benzoic acid + p-nitrophenol (BA + NP) we obtain 1.15 (partial adsorption for benzoic acid) and 0.83 (partial adsorption for p-nitrophenol). For the three-component system (BA + SA + NP), we have slope coefficient values 1.08, 1.26, and 0.58 for benzoic acid, salicylic acid, and p-nitrophenol respectively. However, for the binary adsorption system benzoic + salicylic acid16 (BA + SA) the values of straight line slopes were much closer to unity: 0.94 (partial
adsorption for benzoic acid) and 1.02 (partial adsorption for salicylic acid). This particular system was characterized by little deviations from the ideal behavior as well for the total summaric and as for partial isotherms. This good result is evidence that components of this mixture are similar, so their molecules are not distinguished during adsorption process. The other systems show greater deviations for partial adsorptions; however, simultaneously their total summaric adsorptions are fitted quite well. Such deviation suggests that some interactions among adsorbed components take place, so the ratio of h j is different from the constant K h ij the constants K h i and K characterizing their binary mixture. In this case, the differences among mixture components are great and strong interactions in adsorbed phase during adsorption process can be expected. Though the values of slope coefficients seem quite varying from system to system, the ratios of respective coefficients seem to be more consistent. We have NP/BA (simple notation for respective
1250 Langmuir, Vol. 13, No. 5, 1997
ratio of slope coefficients) equal to 0.72 for binary mixture BA + NP and 0.53 for the BA + SA + NP system, NP/SA 0.53 for SA + NP and 0.46 for BA + SA + NP, and BA/SA is 0.93 for BA + SA and 0.85 in the BA + SA + NP system. The differences in values for given pairs of components can be attributed to differences in composition and adsorption range of involved systems, experimental deviationssespecially for the three-component systemsas well as oversimplification related to this line fitting. Quality of adsorption prediction in this modelsespecially for partial adsorption valuessdepends also on the agreement between the assumption about correlations of solute adsorption energies and proprieties of a real system. The simplest assumption that such a correlation exists for similar components finds a justification in the analysis of the BA + SA adsorption system. However, adsorption of p-nitrophenol, though its single component adsorption parameters and well estimated summaric adsorption in mixed systems do suggest a similarity to BA and SA adsorption systems, is chemically different enough to produce distinct deviations of partial adsorptions from those for SA and BA. As indicated above, this effect may be a result of the specific interactionssdifferent for BA/ SA and NP systems, but probably also in part it results from differences between the solute interactions with adsorption sites and subsequent, at least partial, nonvalidity of the assumption about perfect correlation of their adsorption energies. (For example, an organic acid and a base may well have similar energy distribution functions when adsorbed on a surface with both acidic and basic sites, however, the adsorption energies of their respective acidic/basic groups on such sites should have correlation coefficient close to -1, whereas for their hydrocarbon part this may be close to 1.12) Results of the simple tests discussed above suggest that corrections taking into account the mutual effect of interactions of system components should be considered. In a simple way a good adsorption estimation for practical applications may be obtained when some mixed adsorption data are used to “correct” the estimates of the multicomponent partial adsorption data based on predictions from single component adsorption data. These empirical coefficients are to compensate various differences between the model and experimental systems, although they are not necessary for some of them (e.g., BA + SA). Nevertheless, when such empirical corrections are introduced, the equations can be used to estimate adsorption within a very wide concentration and pH range, though they are then less sound theoretically. For practical purposes, a simple procedure may be proposed: (1) calculate partial adsorptions according to the single adsorption parameters; (2) correlate predictions with some experimental mixed adsorption data, determine “correction coefficients” for pairs of components (summaric adsorption remains constant); (3) estimate unknown adsorptions by calculations according to (1) and recalculate partial adsorptions by using coefficients obtained by (2). We hope, that more appropriate, theoretically sound corrections can be well accommodated in this flexible model after gathering more experimental evidence on the nature of the observed discrepancies through further studies of multicomponent systems. Some discrepancies are even
Deryło-Marczewska and Marczewski
to be expected if simplifying assumptions are not valid for a given adsorption system and here we would like to repeat the reasons why: The correlation between adsorption energies of components may be different than assumed (eq 11), although for organic adsorbates it is well documented;1,19 the lateral interactions should be taken into account by utilizing independent adsorption data on nonheterogeneous solids;20 to take into account both factors in a proper way, one would have to know also the topography of adsorption sites.1 Unluckily, effect of the lack of adsorption energy correlation is difficult to distinguish from that of lateral interactionssat least on the basis of analysis of adsorption data alone. The shape of energy distribution function used in the paper (Gauss f.) is well founded and widely used for the class of systems in question; however it is only an approximation of the real distribution function, though very useful and largely true in the range of medium adsorption values studied and, as good fitting of single component adsorption data confirm, should not be of primary concern. Although, other quasi-Gaussian distribution functions are often used. The so-called Langmuir-Freundlich distribution function,1 related to a simple analytical form of the adsorption isotherm, is an especially tempting choice; however this equation does not agree with Henry’s criterion resulting from the existence of minimum adsorption energy, and introducing a cut-distribution function form or lateral or ionic interactions cancel immediately this advantage. The Gauss function produces isotherms consistent with Henry law (though the distribution function does not have minimum or maximum energy itself19). Thus the most preferable, though difficult (and costly), solution would be to calculate energy distributions for all solution components from single adsorption data, which would undoubtfully improve prediction accuracy, but could not remedy the lack of siteenergy correlation data. Conclusions Summing up the above presented considerations we can state that the analyzed model of adsorption from dilute solutions of weak organic electrolytes describe satisfactorily the measured experimental data. The great advantage of this model is that it allows taking it into account the effect of many factors on adsorption equilibria: adsorbent heterogeneity and surface charge; lateral interactions in adsorbed phase. The model can be also used as a simple estimation of adsorption parameters for multicomponent systems by using the parameters found for the single-solute adsorption data. For the experimental systems containing the components which show similar behavior, the prediction results are very good. In the case of mixtures of components with different physicochemical properties some corrections should be introduced in order to take into account the interaction effects and component differentiation. LA951536E (19) Young, D. M.; Crowell, A. D. Physical Adsorption of Gases; Butterworths: London, 1962. (20) Marczewski, A. W.; Jaroniec, M.; Deryło-Marczewska, A. Mater. Chem. Phys. 1986, 14, 141.
