Langmuir 1998, 14, 935-943
935
Surface Complexation/Gouy-Chapman Modeling of Binary and Ternary Cation Exchange In H. Rhee† and David A. Dzombak* Department of Civil and Environmental Engineering, and Colloids, Polymers and Surfaces Program, Carnegie Mellon University, Pittsburgh, Pennsylvania 15213 Received January 9, 1997. In Final Form: December 8, 1997 The two-layer surface complexation model combined with the Gouy-Chapman model (SCGCM) was applied to describe and predict experimental data for cation adsorption and exchange on a synthetic resin. Knowledge of the surface properties of the sulfonate macroreticular cation-exchange resin was incorporated in the model. The data set included single, binary, and ternary cation adsorption involving Na, Mg, and Zn in single anionic media of chloride, perchlorate, and sulfate at 0.05 and 0.2 N in total cation concentration (TCC) and in their 1:1 binary mixtures at TCC ) 0.05 N. The SCGCM exhibited reasonably good agreement with binary and ternary cation exchanges in the different anionic backgrounds and ionic strengths, based on constants extracted from fits of single cation adsorption data and a small set of binary exchange data. Specific adsorption was predicted to be dominant for the cation adsorption and exchanges on the resin studied in this work. Na was specifically adsorbed on the sulfonate group of the resin to an equal to or greater extent than Mg and Zn, possibly because of reduced surface-binding energy of the divalent cations due to local electrostatic effects on short-range interactions resulting from very high surface charge density associated with the resin. The SCGCM provides insight into the ion-exchange processes and incorporates knowledge of the resin phase, unlike conventional mass action and thermodynamic models. In addition, the effect of electrolyte composition and solution complexation on cation exchange can be described with the SCGCM, allowing consideration of the adsorption of cation-anion complexes. The SCGCM can be applied to multicomponent systems and incorporated in general chemical equilibrium models, but has substantial data requirements for calibration.
1. Introduction A general model capable of describing and predicting cation exchange under a range of conditions does not exist at present. Conventional mass action models are limited because of the neglect of anion uptake,1 the arbitrary selection of the solid-phase activity coefficient,2 and the use of conditional constants.3 Thermodynamic equations for ion exchange cannot account explicitly for anion and specific adsorption effects and require solid-phase activity coefficients that cannot be measured.4 In the GouyChapman model,5 the Coulombic interaction considered between cations and negative exchanger sites makes no distinction in selectivity for cations of the same charge and specific adsorption is not considered. Recently, to account for anion uptake and specific adsorption in ion exchange, mass action models and electrical double-layer theory have been combined with surface complexation models to permit explicit consideration of chemisorption via ion pairing and complexation at surface sites, as well as sorption in the diffuse layer. The Vanselow6 mass action equation was adopted to * Author to whom correspondence should be addressed. † Current address: Korea Electric Power Research Institute, Taejeon, Korea. (1) Fletcher, P.; Sposito, G. Clay Min. 1989, 24, 375. (2) Duncan, J. F.; Lister, B. A. J. Faraday Discuss. 1949, 7, 104. (3) (a) Bolt, G. H. Neth. J. Agric. Sci. 1967, 15, 81. (b) Dzombak, D. A.; Hudson, R. J. M. Aquatic Chemistry: Interfacial and Interspecies Processes; Huang, C. P., O’Melia, C. R., Morgan, J. J., Eds.; Wiley: New York, 1995; Chapter 4. (4) (a) Kressman, T. R. E.; Kitchener, J. A. J. Chem. Soc. (London) 1949. part 2, 1190. (b) Kressman, T. R. E.; Kitchener, J. A. J. Chem. Soc. (London) 1949, part 2, 1201. (c) Meares, P.; Thain, J. F. J. Phys. Chem. 1968, 72, 2789. (d) Fletcher, P.; Townsend, R. P. J. Chem. Soc., Faraday Trans. 1985, 1, 1731. (5) (a) Eriksson, E. Soil Sci. 1952, 74, 103. (b) Bolt, G. H.; Page, A. L. Soil Sci. 1965, 99, 357. (6) Vanselow, A. P. Soil Sci. 1932, 33, 95.
account for the diffuse-layer sorption in some surface complexation models for metal sorption on clays.7 However, these models did not consider specific adsorption on the fixed charge sites; surface complexation reactions were considered only for the pH-dependent, variable charge sites. There also have been attempts to couple surface complexation reactions with Gouy-Chapman theory to describe ion-exchange data.3b,8 Application of such a model requires detailed knowledge of the surface properties and an extensive data set to determine the surface complexation constants between the surface sites and all relevant ions. Cation-exchange reactions exhibit various phenomena that are neither well-described nor predicted by conventional mass action or thermodynamic models for ion exchange, including nonconstancy of selectivity constants with changing solution chemistry, dependence of cationexchange capacity on the nature of the exchanging ions, changes in cation selectivity with changes in the electrolyte anion, and differences in cation selectivity in binary cation exchange relative to ternary cation exchange. A molecular-level model is needed for interpretation and prediction of these phenomena, as the semiempirical mass action models and thermodynamic models provide little insight into the physicochemical processes involved. The purpose of this study was to apply a surface complexation/Gouy-Chapman model for cation exchange3b to a consistent, extensive experimental data set to gain insight into anion and specific adsorption effects, and to evaluate the usefulness of such a model for the prediction of ternary cation exchange based on data for single cation sorption and binary cation exchange. To obtain the (7) (a) Schindler, P. W.; Liechti, P.; Westall, J. C. Neth. J. Agric. Sci. 1987, 35, 219. (b) Zachara, J. M.; Smith, S. C. Soil Sci. Soc. Am. J. 1994, 58, 762.
S0743-7463(97)00033-4 CCC: $15.00 © 1998 American Chemical Society Published on Web 01/31/1998
936 Langmuir, Vol. 14, No. 4, 1998
necessary data for the determination of binding constants, batch experiments for single cation adsorption were conducted with a synthetic cation-exchange resin bearing a sulfonate surface group (Amberlite 200) in contact with electrolyte solutions containing Na, Mg, or Zn as cations and chloride, perchlorate, and sulfate as anions over the concentration range of 0.005-1.0 N. For testing the predictive capability of the model, binary and ternary cation exchange data were also obtained. These experiments involved Na, Mg, and Zn in single anion media of chloride, perchlorate, and sulfate at two total cation concentrations (TCC) of 0.05 and 0.2 N and their 1:1 mixtures at TCC ) 0.05 N.9 2. Experimental Materials and Methods Amberlite 200 macroreticular cation-exchange resin (Rohm and Haas Co.) possesses only sulfonate functional groups which are separated by about 0.6 nm. The radius of the pores present in the resin bead is about 20 nm, which is adequate to ensure no diffuse-layer overlap for the ionic strengths examined in this work. The specific surface area of Amberlite 200 resin is 40 m2/g, the cation exchange capacity is 4.6 mequiv/g, and the surface charge density is 11 C/m2. Small-volume batch experiments were employed to measure cation adsorption and exchange. Single cation sorption experiments were performed with two-component electrolytes consisting of Na+, Mg2+, or Zn2+ as cations and Cl-, ClO4-, or SO42- as anions. The particular cations and anions were selected on the basis of their solution complexation properties and their charge. Na-form, Mg-form, and Zn-form resins attained with 1 N NaCl, MgCl2, and ZnCl2 were used for the study of the sorption of Na, Mg, or Zn, respectively, in chloride, perchlorate, and sulfate backgrounds. The concentration of these conditioned resins was maintained at 0.5 equiv/L. Then, 2.778 g (dry basis) of conditioned resin of the appropriate form were added into nine polyethylene bottles which contained 25 mL of 1.0 or 0.5 N electrolyte stock solutions for NaCl, NaClO4, Na2SO4, MgCl2, Mg(ClO4)2, MgSO4, ZnCl2, Zn(ClO4)2, and ZnSO4. Every suspension was diluted to the final concentration of 0.005 N, sequentially by removing a volume of the supernatant solution (e.g., 2.5 or 5 mL) and then adding the same amount of demineralized water. At each dilution step, the suspensions were allowed to equilibrate with gentle agitation for 12 h in a rotator, followed by gravity settling of the resin and analysis of the supernatant for the total element concentration by atomic absorption spectroscopy. The amount of cation adsorbed in the resin was obtained from the difference between the quantities of cation present in suspension and cation dissolved in solution. The removal of the matrix effect in the atomic absorption analyses was made with KCl for Na and with ethylenediaminetetraacetic acid and KCl for Mg and Zn. The data for binary and ternary cation exchanges were obtained from combinations of Na, Mg, and Zn in single anion backgrounds of chloride, perchlorate, and sulfate at total cation concentrations (TCC) of 0.05 and 0.2 N, and in their 1:1 mixtures at TCC ) 0.05 N. Ten 50-mL suspensions spanning 10 equivalent fractions ranging from 0.05 to 0.9 in the solutionphase cation concentration were prepared by combining the stock electrolyte solutions with the Na-form or Mg-form resins. After equilibration of the suspensions for 12 h with gentle agitation in the rotator was completed, the concentration of cations in the solution phase was measured. Adsorbed cation concentrations were obtained by subtracting solution concentrations from the total concentrations of cation added into the suspension. Additional details on the experiment materials and methods are available.9,10 (8) Nir, S.; Rytwo, G.; Yermiyahu, U.; Margulies, L. Colloid Polym. Sci. 1994, 272, 619. (9) Rhee, I. H. Ph.D. Thesis, Carnegie Mellon University, Pittsburgh, PA, 1996. (10) Rhee, I. H.; Dzombak, D. A. Langmuir, submitted for publication.
Rhee and Dzombak
3. Surface Complexation/Gouy-Chapman Model The common ion-exchange models do not account explicitly for the different classes of exchange sites or for the nature of the ion-surface interactions. In addition, most common models do not account for solution speciation. This limits understanding of ion exchange in terms of physicochemical processes and limits the general predictive capabilities of ion-exchange models. Surface charge sites, variable- as well as permanent-charge sites, are capable of reacting specifically and nonspecifically with cation and anion species. Ion-exchange processes are usually thought of in terms of nonspecific, Coulombic interactions in which the electric field created by charged surface species causes adsorption of oppositely charged ions. This surface charge neutralization concept of ion exchange is the basis for the traditional models10 in which ion exchange is described with mass law expressions related to equivalent exchanges of charge. The Gouy-Chapman diffuse layer theory can be employed to describe the effects of surface-related Coulombic forces on adsorption and desorption of ions, but site-specific surface complexation reactions also influence ion-exchange reactions, as evidenced by very high selectivity observed for some ions. Diffuse layer theory can be combined with surface complexation theory to describe the combined effects of specific and nonspecific adsorption phenomena.3b In the combined surface complexation and Gouy-Chapman model (SCGCM), the ions adsorbed on the solid are divided into two categories: a portion that is chemically bound to surface sites and another portion that is electrostatically sorbed in the diffuse layer. A two-layer description of the solid-water interface is simplest,11 but more complex interface models can be used. In the two-layer (or diffuse layer) model, both cations and anions may be sorbed specifically to form complexes with surface sites, and electrostatically in the formation of the diffuse layer. To apply the SCGCM, the nature, geometry, and quantity of charged sites need to be understood to establish reactions for their chemical binding with solution phase ions and to apply the GouyChapman theory. In a suspension with MgCl2 as the electrolyte and a resin with permanent charge surface sites (tSp-), surface complexation of Mg2+ can be described as reactions on the negatively charged surface:
surface complex: tSp- + Mg2+s ) tSpMg+
int KtSpMg
(1)
ion-pair surface complex: tSp- + Mg2+s + Cl-s ) tSpMgCl0
int KtSpMgCl (2)
where the subscript s is used to represent ions present in solution but at the surface. The electrostatic sorption of Mg and Cl ions in the diffuse layer can be represented by
[MgDL2+] ) gMg[Mg2+ ]
(3)
[MgClDL+] ) gMgCl[MgCl+]
(4)
[ClDL-] ) gCl[Cl-]
(5)
where [ ] represents molar concentration; [MgDL2+], [MgClDL+], and [ClDL-] are the excess and deficit molar concentrations of Mg2+, MgCl+, and Cl- in the diffuse layer; and gMg, gMgCl, and gCl are factors calculated with the Gouy-Chapman theory that relate diffuse layer ion concentrations to bulk solution ion concentrations.12 The generalized expression for gi developed by Borkovec and Westall,12 an integral equation, can be readily manipulated to make the variable of integration simply the surface potential, ψ, resulting in the following expression for gi: (11) Dzombak, D. A.; Morel, F. M. M. Surface Complexation Modeling: Hydrous Ferric Oxide; Wiley-Interscience: New York, 1990. (12) Borkovec, M.; Westall, J. J. Electroanal. Chem. 1983, 150, 325.
Surface Complexation/Gouy-Chapman Modeling
gi ) as
x
0
2RT
[Mg2+]sorbed ) [Mg2+DL] + [MgCl+DL] + [tSpMg+] + ×
∫
sign(-ψ0)
Langmuir, Vol. 14, No. 4, 1998 937
[tSpMgCl0] (11) exp(-ziFψ/RT) - 1
ψ0
0
x∑
dψ (6)
1000Cj,B[exp(-zjFψ/RT) - 1]
j
where a is the specific surface area (m2/g) of the charged solid, s is the mass concentration of the solid (g/m3), is the dielectric constant of water at 25 °C (78.54), 0 is the permittivity of free space (8.85 × 10-12 C2/J‚m), R is the molar gas constant (8.314 J/mol‚K), T is the absolute temperature (K), F is the Faraday constant (96485 C/mol), zi is the charge number for species i, Cj,B is the bulk solution concentration of species j (mol/L), and the summation runs over all bulk solution species, and from 0 to ψ0 in surface potential (V). The factor of 1000 is included for conversion of molar concentrations to mol/m3. The sign of gi is positive for surface excess and negative for surface deficit. int ) for a surface The intrinsic equilibrium constant (KtSpMg complexation reaction (e.g., eq 1) can be expressed via the law of mass action as follows:
int KtSpMg )
)
)
{tSpMg+}
(7a)
2+ {tSp }{Mg s}
{tSpMg+} 2+ {tSp }{Mg } exp(-2Fψ/RT)
[tSpMg+] 2+ [tSp ]γMg[Mg ]
exp(-2Fψ/RT)
(7b)
4. Parameter Optimization Approach for SCGCM (7c)
where { } and [ ] represent activity and molar concentration, respectively, and ψ is the surface potential. The exponential terms account for long-range electrostatic interactions and are introduced to relate the activity of Mg2+ in the diffuse-layer region to that in the solution phase.3b,11 The Gouy-Chapman theory is used to relate surface potential to surface charge density. The activities in eq 7b may be converted into the molar concentrations (eq 7c) by introducing the activity coefficient for Mg2+ in the bulk solution (γMg). Solution-phase activity coefficients can be calculated with the use of the Davies equation, a commonly used, practical approach for multicomponent equilibrium problems because no ion-specific parameters are required other than the charge number. The activity coefficients for the surface species are assumed equal.13 Equation 7c can be rearranged to give the concentration of the specifically sorbed Mg2+ species: int 2+ [tSpMg+] ) KtSpMg exp(-2Fψ/RT)[tSp )γMg[Mg ] (8)
The mole balance equation for the surface sites on the solid surface is given by + 0 [tSp ]Total ) [tSp ] + [tSpMg ] + [tSpMgCl ]
By writing diffuse-layer sorption and surface complexation reactions for all cations and anions in a system, and combining these with the relevant solution complexation reactions, ionexchange phenomena can be modeled.3b The integration involved with eq 6 can be performed numerically by use of the Simpson rule. In this work, solution of the equilibrium problem represented by the surface complexation and diffuse-layer sorption reactions (e.g., eqs 1-10) and the relevant solution-phase reactions (Table 1) was performed with the use of MINEQL+ 15 and Maple.16 For specified concentrations of free cations in the solution phase, MINEQL+ was used to calculate the aqueous-phase speciation. The concentrations of species electrostatically and specifically sorbed were then calculated with the use of Maple and with the calculated solution-phase species concentrations as inputs. Maple provides an efficient means of solving the set of equations related to the surface reactions, which is a complicated equation set because of the gi factor (eq 6) associated with the diffuselayer sorption.9 Although the ions in the diffuse layer and on the solid surface do not behave ideally due to ionic interaction, ion polarization, and dielectric saturation effects, the surface complexation/GouyChapman model (SCGCM) provides mechanistic insight into ion exchange. Variations in cation selectivity and in apparent exchange capacity can be interpreted due to the explicit consideration of anion imbibition and specific adsorption. While this model will be restricted in applicability due to the necessity of many parameters to cover surface inhomogeneity, it nevertheless can be useful in interpreting data for simple systems.
(9)
The surface complexation constants were determined by fitting the equilibrium model to the experimental data. Because of the complexity of the equation set resulting from the consideration of diffuse-layer sorption (i.e., the gi factor in eq 6), a directed search optimization approach could not be employed. Thus, brute force optimization involving trial of a large number of surface complexation constant combinations was used. The sum of the squares of the residuals between the values predicted and observed for the adsorbed amount of cation was calculated for every possible combination of binding constants over the ranges of feasible values specified. The optimization routine was written in Maple16 with a call of the surface adsorption algorithm as a subroutine.9 The sequence employed in the optimization program was as follows: (1) select values for two surface complexation constants; (2) calculate the concentration of the free charged sites with eq 9; (3) determine the surface potential with substitution into eq 10 of the concentration of free charged sites obtained from (2); (4) calculate the amount of cation adsorbed with eq 11; (5) calculate the sum of squares of residuals (SSR) between the observed (Yobs) and predicted (Ycal) equivalent fractions for an exchanging cation: SSR ) Σ(Ycal - Yobs)2; (6) repeat until residual is minimized. For the optimization of two surface complexation constants, local minima typically occurred for one of the constants, necessitating a search to find the global minimum.
5. Results and Discussion and the electroneutrality statement for the solid/water interface is
2[Mg2+DL] + [MgCl+DL] + [tSpMg+] ) [Cl-DL] + [tSp-] (10) Also, the total sorption of Mg from a solution of MgCl2 can be represented as (13) Chan, D.; Perram, J. W.; White, L. R.; Healy, T. W. J. Chem. Soc., Faraday Trans. 1 1975, 71, 1046.
The experimental data for single cation sorption and selected data for binary cation exchange were used in calculating free ion concentrations using MINEQL+, and the SCGCM was fitted to these data through an adjust(14) Smith, R. M.; Martell, A. E. NIST Critical Stability Constants of Metal Complexes Database; NIST Standard Reference Data: Gaithersburg, MD, 1993. (15) Schecher, W. D.; McAvoy, D. C. MINEQL+ Version 3.0; Environmental Research Software, Inc.: Hallowell, ME, 1994. (16) University of Waterloo. Maple. Brooks/Cole: Pacific Grove, CA, 1985.
938 Langmuir, Vol. 14, No. 4, 1998
Rhee and Dzombak
Table 1. Formation Constants for Major Solution Complexes Involving Na+, Mg2+, and Zn2+ and Cl-, ClO4-, and SO42Log Ka Na+ Mg2+ Zn2+
b
Cl-
ClO4- b
-0.5[NaCl0]
-0.7[NaClO4 0.4[Mg(ClO4)+] 0.25[Zn(ClO4)+]
0.6[MgCl+] 0.46[ZnCl+]
SO420]
-0.72[NaSO4-] 2.23[MgSO40] 2.34[ZnSO40] 3.28[Zn(SO4)22-]
a Values from Smith and Martell14 unless otherwise indicated. Estimated from the stability constants for NO3-, Cl-, and SO42-.9
Figure 2. Fits of the experimental data with the SCGCM for Na-Mg (s) and Na-Zn (- - -) exchanges in the chloride background at TCC ) 0.05 N on the sulfonate macroreticular cation-exchange resin.
Figure 1. Single cation sorption of Na (O), Mg (4), and Zn (0) in (a) chloride, (b) perchlorate, and (c) sulfate background on the sulfonate macroreticular cation-exchange resin. Fits of data with the SCGCM are shown (- - -).
ment of surface complexation constants. The optimal surface complexation constants were then used to predict ion exchange in other binary systems and in ternary systems. In each case, the calculated resin-phase speciation was examined to assess the contributions of electrostatic and site-specific sorption to cation exchange. 5.1. Experimental Data for Cation Adsorption and Exchange. The surface complexation/Gouy-Chapman model was calibrated with the cation adsorption data for two-component electrolytes (Figure 1), and with the data for Na-Mg and Na-Zn exchanges in chloride media at 0.05 N in total cation concentration (Figure 2). The calibrated SCGCM was then tested by making predictions of cation exchange for the other binary and ternary cation exchange data presented in Rhee and Dzombak.10 As shown in Figure 1, cation uptake increased in the order of Na < Mg < Zn and in the order of sulfate < perchlorate < chloride as the background anion. These trends are consistent with the solution complexation
capabilities and the charge of each cation. The difference between cation adsorption capacity and cation exchange capacity (4.6 mequiv/L) was small below 0.1 N in cation concentration in solution, but it increased above 0.5 N. The results in Figure 1 demonstrate that measurements of cation exchange capacity need to be conducted at lower concentrations with an electrolyte whose components are low in complexation capability. 5.2. Determination of Intrinsic Binding Constants. The experimental data in the chloride media for the single cation adsorptions of Na, Mg, and Zn and for Na-Mg and Na-Zn exchanges at 0.05 N in total cation concentration in solution were used to determine the intrinsic surface complexation constants for Na, Mg, and Zn. The parameter optimization was conducted with the data for the single cation sorption obtained below 0.5 N in total cation concentration (TCC) in solution for which the modeling for binary and ternary cation exchanges was performed in this work. Those surface complexation constant values that provided the best fits for both single cation adsorption and binary cation exchange were selected. The fitted surface reactions and intrinsic surface complexation constants are given in Table 2. Estimation of standard error in the parameter values, only possible by the bootstrap method, was not performed because of unmanageable computational requirements.9 The fits obtained are shown in Figures 1a and 2. With the fitted surface complexation constants for reactions 1, 5, and 9 in Table 2, the remaining constants for ion-pair-surface complexes of perchlorate and sulfate (reactions 3, 4, 7, 8, 11, and 12) were determined from the measured values for the single cation sorptions of Na, Mg, and Zn in the perchlorate and sulfate media. The magnitude of the surface complexation constants increased in the order of positive surface complexes (e.g., tSpMg+ and tSpZn+), neutral surface complexes (e.g., tSpNa0), and negative surface complexes (e.g., tSpNaCl-). The greater surface complexation constants extracted for Na relative to Mg and Zn are surprising but may be
Surface Complexation/Gouy-Chapman Modeling
Langmuir, Vol. 14, No. 4, 1998 939
Table 2. Surface Complexation Reactions and Equilibrium Constants for Sorption of Na+, Mg2+, and Zn2+ on Amberlite 200 Resin in Solutions with Chloride, Perchlorate, and Sulfate no.
surface complexation reactions
Log Kint
1 2 3 4 5 6 7 8 9 10 11 12
tSp- + Na+s ) tSpNa0 tSp- + Na+s + Cl-s ) tSpNaCltSp- + Na+s + ClO4-s ) tSpNaClO4tSp- + Na+s + SO42-s ) tSpNaSO42tSp- + Mg2+s ) tSpMg+ tSp- + Mg2+s + Cl-s ) tSpMgCl0 tSp- + Mg2+s + ClO4-s ) tSpMgClO40 tSp- + Mg2+s + SO42-s ) tSpMgSO4tSp- + Zn2+s ) tSpZn+ tSp- + Zn2+s + Cl-s ) tSpZnCl0 tSp- + Zn2+s + ClO4-s ) tSpZnClO40 tSp- + Zn2+s + SO42-s ) tSpZnSO4-
-1.42 0.630 0.630 3.58 -2.95 -1.25 -1.35 1.55 -2.85 -0.950 -1.05 1.95
explainable by the very high surface charge density associated with the Amberlite 200 cation-exchange resin. As noted earlier, the average separation of sulfonate groups on the resin surface is estimated to be approximately 0.6 nm. If the charge separation on the surface is not much greater than the hydrated radius of a sorbing cation, the bonding energy of the sorbing cation with a particular site may be influenced by localized electrostatic interactions with the neighboring fixed, negative charge sites. These localized attractive and repulsive forces may decrease bonding strength for positively charged surface complexes (e.g., tSpMg+ ) at particular negative sites, and may increase bonding strength for negatively charged surface complexes (e.g., tSpNaCl- ). A schematic illustration of ion-sulfonate group binding and the localized effects of neighboring charges is provided in Figure 3. Although the chemical bond of the surface complex formed from a divalent cation is, in general, stronger than that from a monovalent cation,11 the net binding energy may be affected by the local electrostatic interactions. Thus, the divalent cation may be less chemically bound to the singly charged site than the monovalent cation for this high charge density resin. 5.3. Fitting of Single Cation Adsorption and Binary Exchange Data. As described above, model calibration was performed by fitting single cation adsorption data obtained in chloride, perchlorate, and sulfate backgrounds, and Na-Mg and Na-Zn exchange data in chloride media. The SCGCM was able to fit reasonably well the single cation adsorption data over the moderate concentration range (below 0.5 N) (Figure 1) and to fit well Na-Mg and Na-Zn exchange data over the entire range of conditions at TCC ) 0.05 N (Figure 2). The adsorption in excess of the cation-exchange capacity was taken into account by consideration of the ion-pair surface complex involving the electrolyte anion as well as the cation. Calculated sum of squares of residuals for all fits are available in Rhee.9 According to the SCGCM modeling, the main component of cation adsorbed in the resin phase is the surface complex between the cation and the sulfonate group. The calculated percentage of cation residing in the diffuse layer over the total cation sorbed is 9-10%, 16-22%, and 1520% for Na, Mg, and Zn adsorptions, respectively, across all three electrolyte anions studied. As discussed earlier, the significant specific adsorption predicted for Na may be related to the very high surface charge density for the Amberlite 200 cation-exchange resin. With increasing surface coverage of divalent cations in Na-Mg and NaZn exchanges, the calculated contribution of specific adsorption to overall sorption increased from 66 to 79%
Figure 3. Schematic illustration of local electrostatic effects on a positively charged surface complex to a resin bearing negatively charged sulfonate groups: (a) inner-sphere and (b) outer-sphere surface complexes with positive formal charges.
for Mg and 71 to 81% for Zn. The slightly greater specific adsorption for Zn accounts for the slightly greater preference of the resin for Zn than for Mg relative to Na. 5.4. Predictions of Binary Cation Exchanges. The calibrated SCGCM was employed to predict the experimentally studied uni-bivalent and bi-bivalent cation exchanges in the different anion backgrounds. The accuracy of the SCGCM for predictions of cation exchange in systems not included in the calibration was investigated and compared to similar predictions made with conventional mass action and thermodynamic models.10 The sum of squares of residuals for all predictions are available in Rhee.9 5.4.1. Na-Mg Exchanges. Figure 4 shows the predictions for Na-Mg exchange isotherms in 1:1 mixtures of two anions, Cl-/ClO4-, ClO4-/SO42-, and Cl-/SO42- at TCC ) 0.05 N and in the single anion backgrounds of Cl-, ClO4-, and SO42- at TCC ) 0.2 N. The SCGCM provided reasonable agreement with the measured values. Also shown as Figure 4 is the Mg selectivity predicted by GouyChapman theory alone. The Mg selectivity observed was much lower than that calculated by the Gouy-Chapman theory. This agrees with the much lower value for the optimized surface complexation constant of the Mg surface complex compared to that for the Na surface complex. The total adsorbed amounts of cation calculated are in agreement with the measured values within (1%. The predicted resin-phase chemical speciation for NaMg exchange in Cl-/ClO4- at TCC ) 0.05 N is presented in Figure 5. The diffuse-layer concentrations for cations and anions are given by the surface excess and deficit, respectively. The main species are Na+ and Mg2+ in the diffuse layer and their surface complexes with sulfonate groups. The resin-phase species involving anions are predicted to be minor because the total amount of cation adsorbed is not much greater than the cation-exchange capacity. The anion species present in the resin phase are predicted to be mostly in the form of surface complexes.
940 Langmuir, Vol. 14, No. 4, 1998
Figure 4. Na-Mg exchanges in a 1:1 mixture of Cl-/ClO4(b), ClO4-/SO42- (9), SO42-/Cl- (2) at TCC ) 0.05 N and in the single anion background of Cl- (O), ClO4- (0), and SO42- (4) at TCC ) 0.2 N. The solid and dashed curves are model predictions. The calculated curves for Na-Mg exchanges in ClO4-/SO42- and SO42-/Cl- backgrounds are overlapped.
Figure 5. Resin-phase speciation predicted with SCGCM for Na-Mg exchanges in a 1:1 mixture of chloride and perchlorate at TCC ) 0.05 N. (×) distinguishes the plot for ClO4-DL from that for Cl-DL (O).
The selectivity reduction of Mg in Na-Mg exchange with increasing Mg surface coverage was predicted with consideration of Mg surface complex formation. According
Rhee and Dzombak
Figure 6. Na-Zn exchanges in a 1:1 mixture of Cl-/ClO4- (b), ClO4-/SO42- (9), and SO42-/Cl- (2) at TCC ) 0.05 N and in the single anion background of Cl- (O), ClO4- (0), and SO42- (4) at TCC ) 0.2 N. The solid and dashed curves are model predictions.
to the SCGCM, the contribution of Mg specific adsorption to overall Mg sorption increased from 65 to 80% at TCC ) 0.05 N and from 55 to 76% at TCC ) 0.2 N. As described earlier, the surface complexation constant for tSpMg+ is lower than that for tSpNa0. Thus, the overall preference of Mg for the sulfonate group against Na decreased with increasing fraction of Mg adsorbed. Also, this trend was greater for the lower TCC due to the higher contribution of specific adsorption. 5.4.2. Na-Zn Exchanges. The SCGCM predictions for Na-Zn exchange isotherms under the same conditions are given in Figure 6. As in the case of Na-Mg exchange, the SCGCM predictions are in good agreement with the experimental data. Also, the exchange isotherm curves predicted by SCGCM are much below those by GouyChapman theory alone, but consistent with the data. SCGCM predicted total adsorbed amounts of cations within (0.5% of measured values. The predicted chemical speciation plot in Figure 7 is very similar to that for Na-Mg exchange. The surface complexes of the sulfonate group with Na and Zn are the dominant species in the resin phase at low and high surface coverages of Zn, respectively. The fraction of charged sites specifically occupied by a cation is a little decreased with Zn surface coverage relative to Mg surface coverage (from 84 to 82% at TCC ) 0.05 N and from 84 to 80% at TCC ) 0.2 N). Zn sorbed in the diffuse layer is always greater than Na due to the higher affinity for the divalent cation in the Gouy-Chapman theory. Similar to Na-Mg exchanges, the fraction of the electrostatic sorption over the total sorption for Na is decreased from 3.4 to 2.0% at both TCC ) 0.05 N and from 5.0 to 1.7% at TCC ) 0.2 N, whereas for Zn, it is reduced from 32 to 19% at TCC ) 0.05 N and from 49 to 22% at TCC ) 0.2 N. The diffuselayer sorption is favored in the sulfate media and at the higher TCC because the sulfate causes the negative surface potential calculated to be increased by 3-5 mV at TCC ) 0.05 N and 5-7 mV at TCC ) 0.2 N, compared to chloride
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Figure 8. Mg-Zn exchanges in a 1:1 mixture of Cl-/ClO4- (b), ClO4-/SO42- (9), and SO42-/Cl- (2) at TCC ) 0.05 N and in the single anion background of Cl- (O), ClO4- (0), and SO42- (4) at TCC ) 0.2 N. The solid and dashed curves are model predictions. Figure 7. Resin-phase speciation predicted with SCGCM for Na-Zn exchanges in a 1:1 mixture of chloride and perchlorate at TCC ) 0.05 N. (×) distinguishes the plot for ClO4-DL from that for Cl-DL (O).
and perchlorate. This explains the variation of Zn selectivity with the surface coverage and the type of anion. 5.4.3. Mg-Zn Exchanges. The almost nonpreference bi-bivalent cation exchange data between Mg and Zn in the different anion backgrounds at two total cation concentrations of 0.05 and 0.2 N were predicted well with the SCGCM as shown in Figure 8. This is expected from the closeness of the surface complexation constants for Mg and Zn on the sulfonate group of the resin, even though the isotherm curves for Na-Mg and Na-Zn exchanges are slightly apart in the same anionic media and total cation concentration (Figures 4 and 6). The decreased selectivity of Zn in the sulfate background at TCC ) 0.2 N was well predicted. The predicted resin-phase speciation for Mg-Zn exchange in Cl-/ClO4- is presented in Figure 9 where it may be seen that both electrostatic and specific adsorptions for Zn increase, and for Mg decrease, with the increase in Zn surface coverage. Cations adsorbed are predominantly present as complexes with the charged sulfonate sites (about 81% out of total sulfonate groups on the resin). The predicted percentage of the electrostatic sorption relative to the total cation adsorption for Zn varied from 17 to 18.5% at TCC ) 0.05 N and 18.5 to 20% for Zn at TCC ) 0.2 N, while for Mg, it changed from 20 to 22% at TCC ) 0.05 N and from 23 to 24.5% at TCC ) 0.2 N. The contribution of specific adsorption to overall sorption in Mg-Zn exchange was less influenced by the surface coverage and the ionic strength than in heterovalent cation exchange. 5.5. Predictions of Ternary Cation Exchanges. The predictions for Na-Mg-Zn exchanges in the chloride and sulfate media at TCC ) 0.05 and 0.2 N are given in
Figure 9. Resin-phase speciation predicted with SCGCM for Mg-Zn exchanges in a 1:1 mixture of chloride and perchlorate at TCC ) 0.05 N. (×) distinguishes the plot for ClO4-DL from that for Cl-DL (O).
Figures 10 and 11. SCGCM generally provided good predictions of the experimental data. The predicted exchange isotherms agreed well with the measured values in the chloride media (Figures 10a and 11a). The slight
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Rhee and Dzombak
Figure 10. Na-Mg-Zn exchanges in (a) chloride and (b) sulfate media at TCC ) 0.05 (closed symbols) and 0.2 N (open symbols) in the presence of constant Mg in suspension. The equivalent factions of Na, Mg, and Zn adsorbed are represented by triangles (2, 4), squares (9, 0), and circles (b, O), respectively. The solid and dashed curves are model predictions.
Figure 11. Na-Mg-Zn exchanges in (a) chloride and (b) sulfate media at TCC ) 0.05 (closed symbols) and 0.2 N (open symbols) in the presence of constant Zn in suspension. The equivalent factions of Na, Mg, and Zn adsorbed are represented by triangles (2, 4), squares (9, 0), and circles (b, O), respectively. The solid and dashed curves are model predictions.
deviation in the sulfate media was consistent with the somewhat lower quality fits of the binary cation exchange data in the sulfate media (Figures 10b and 11b). Overall, the predictions of cation exchange in the ternary systems by the SCGCM were somewhat more accurate than those obtained with conventional thermodynamic and mass action models for cation exchange, though not greatly so.9,10 As expected from modeling the single and binary cation exchanges, specific adsorption was predicted to play a significant role in total cation sorption in the ternary systems as illustrated in Figure 12 which is the resinphase plot for Na-Mg-Zn exchange in the 1:1 mixture of chloride and sulfate at a constant total amount of Mg in suspension (constant TOTMg). Over 80% of the sulfonate groups at the surface were calculated to be occupied by adsorbed cations. The contribution of specific adsorption to overall sorption was slightly greater at TCC ) 0.05 N than at TCC ) 0.2 N due to the higher fraction of the diffuse-layer sorption of the divalent cation at the higher TCC. Under this condition, Na was predicted to be mostly present in the form of the surface complex in the resin phase (over 95%). 5.6. Comparison of SCGCM and Conventional Models. Ion-exchange phenomena are usually modeled with mass action equations, and sometimes with thermodynamic expressions.10 These models, unlike the SCGCM, generally do not consider effects on ion exchange of different types of charged surface groups, and account for the effect of anion type on cation exchange only with consideration of solution speciation and activity correction. Mass action models are largely empirical and applicable only for the calibration conditions. Thermodynamic models are more general but require many fitting pa-
rameters as the number of solution components increases. There are several criteria that may be used to compare the utility and accuracy of conventional models and the SCGCM, including scientific rigor, data requirements, ease of implementation, goodness of fit, and accuracy of predictions. The SCGCM has advantages but also some limitations in comparison to conventional models. First, the SCGCM is more scientifically rigorous in that it attempts to describe the physicochemical processes involved in cation exchange. While certainly not completely accurate in this regard, the SCGCM does provide mechanistic insight into cation exchange. The data requirements for the SCGCM are substantial, however, including data for adsorbent surface properties (surface area, surface site density, and surface site charging characteristics) and sufficient single cation and binary cation adsorption data for the determination of surface complexation constants. It must be noted, though, that data requirements are also substantial for conventional models, which must be calibrated with data for all solution conditions of interest. The SCGCM has the advantage that a nonredundant database can be developed for an adsorbent of interest, obviating the need for some experiments. The SCGCM is clearly a more complicated model to implement than the conventional models. With the development of software and an appropriate user interface, however, the complexity of implementation can be made transparent to the user. Finally, the SCGCM provides reasonably accurate predictions of cation exchange in multicomponent systems, and as demonstrated here the SCGCM is the only model that can account for and predict cation adsorption in excess of cation-exchange capacity.
Surface Complexation/Gouy-Chapman Modeling
Figure 12. Resin-phase speciation predicted with SCGCM for Na-Mg-Zn exchanges in a 1:1 mixture of sulfate and chloride at TCC ) 0.05 N in the presence of constant Mg in suspension. (×) distinguishes the plot for SO42-DL from that for Cl-DL (O).
6. Summary and Conclusions Mechanistic modeling of ion exchange, with consideration of specific adsorption and electrostatic adsorption in the diffuse layer, offers promise for enhanced understanding of ion-exchange processes. In this work, a combined surface complexation/Gouy-Chapman model was applied to a large data set for binary and ternary cation exchange on a synthetic cation-exchange resin bearing sulfonate surface groups. The surface complexation/Gouy-Chapman model (SCGCM) was first fitted to a set of single cation adsorption data and a small set of binary cation exchange data, and then used to make predictions of other binary and ternary cation exchange data obtained with the same resin. The SCGCM showed reasonably good predictions for binary and ternary cation exchanges in the different anion backgrounds and ionic strengths studied experimentally. Overall, the predictions of the SCGCM, especially for the ternary cation exchange data, were comparable or slightly more accurate than those obtained with conventional thermodynamic and mass action models applied to the same data in related work.
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According to the SCGCM, the specific adsorption of cations on the sulfonate groups of the resin was the dominant mechanism of cation adsorption and exchange. About 80% of sulfonate functional groups at TCC ) 0.05 N were predicted to be occupied by cations for the cation exchange data modeled in this work, and this fraction was only reduced by 2-4% at TCC ) 0.2 N. For the adsorption of single cations from two-component electrolytes, more anions were predicted to be present as surface complexes with increasing solution concentrations. Divalent cations (Mg and Zn) showed a somewhat weaker specific adsorption on the sulfonate resin than Na, perhaps because the surface bonding energy for positive surface complexes (e.g., tSpMg+) may be reduced by the localized electrostatic interaction with adjoining sulfonate groups on the resin studied which has a very high surface charge density. The significant specific adsorption of Na yielded decreased preference of the resin for the divalent cations, lower than predicted by Gouy-Chapman theory. The SCGCM provided some possible explanations for several cation-exchange phenomena. The selectivity sequence for the cations on the sulfonate resin appears to be related to the different specific adsorption intensities. The selectivity of the divalent cations (Mg or Zn) diminished with surface coverage due to increased specific adsorption which was more favorable for Na than Mg or Zn. In addition, the observed dependence of cation adsorption capacity on the ionic strength could be explained by the formation of cation-anion surface complexes at high ionic strength. Observed effects of anion type on cation selectivity could also be explained by surface reactions involving anions. The success of the SCGCM in modeling multicomponent systems other than those used for calibration demonstrates its potential usefulness. It distinguishes the electrostatic and specific adsorptions of ions, and can account for the effect of electrolyte composition on ion adsorption and exchange. Thus, it provides physicochemical insight into ion exchange. The success achieved with modeling cation-exchange data for a synthetic resin suggests that ion-exchange reactions on heterogeneous charged solids can be modeled with the SCGCM, given detailed knowledge of the surface characteristics and the surface complexation constants for the discrete-charged sites. Data requirements would be substantial for the application of the SCGCM to such systems, however. Acknowledgment. This work was supported by a Korea Electric Power Corporation Fellowship to In Rhee and by the National Science Foundation through a Presidential Young Investigator Award (Grant No. BCS9157086) to David Dzombak. LA9700331
