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Soil Chemistry

Hydration Energy Determines Isovalent Cation Exchange Selectivity by Clay Minerals

^a Dep. of Crop and Soil Sciences and Environmental Science and Policy Program, 283 Plant and Soil Sciences Bldg., Michigan State University, East Lansing, MI 48824-1325
^b Dep. of Crop, Soil and Environmental Sciences, Univ. of Arkansas, Fayetteville, AR 72701

^* Corresponding author (teppen{at}msu.edu)

	ABSTRACT

TOP ABSTRACT INTRODUCTION Selectivity Due to Hydrated... Eisenman Model for Selectivity Selectivity Due to Complexation MATERIALS AND METHODS RESULTS AND DISCUSSION CONCLUSIONS REFERENCES

 
Cation exchange is one of the most venerable concepts in soil science, yet it needs rethinking. This paper presents an extremely simple conceptual framework for interpreting many observed trends in cation exchange. Taking the example of Cs-K exchange, the methods of computational molecular mechanics found that Cs-montmorillonite is considerably higher in energy than K-montmorillonite at constant water content, in agreement with inferences from a new thermodynamic cycle representation of cation exchange. Since montmorillonite selects Cs⁺ over K⁺ in real experiments, these results mean that alkali cation-exchange selectivity is controlled by selectivity of the solution phase for the more strongly hydrated cation. Thus the clay does not "select" for Cs⁺ over K⁺ in any positive sense and it may be more useful to consider cation exchange as a partitioning reaction: Given two cations of equal valence, the more weakly hydrated will tend to partition into the "subaqueous" smectite interlayer phase. This concept seems not only parsimonious, but also more accurate than other hypotheses for cation exchange selectivity that impute more favorable interactions between smectite surfaces and the selected cations; such theories err by ignoring energy changes in the solution phase. This simple partitioning concept rationally explains the alkali and alkaline earth selectivity sequences as well as the selectivities of smectites for organic cations over inorganic, for larger organic cations over smaller, and for organometallic complexes over the uncomplexed metal.

	INTRODUCTION

TOP ABSTRACT INTRODUCTION Selectivity Due to Hydrated... Eisenman Model for Selectivity Selectivity Due to Complexation MATERIALS AND METHODS RESULTS AND DISCUSSION CONCLUSIONS REFERENCES

 
CATION EXCHANGE at charged clay mineral surfaces is a preeminent, unifying concept in soil science (Arnold, 1977). The fates of major plant nutrients (NH₄⁺, K⁺, Ca²⁺), many micronutrients, and industrial pollutants in soils are strongly influenced by cation exchange, so it is one of the first examples of adsorption taught to students of soil and environmental science. Many empirical results are cataloged in the literature of cation exchange phenomenology, but a clear description of the underlying forces that govern selectivity is lacking. Knowledge of these fundamental forces is desirable, because predictive ability enables rational management of soils.

Cation exchange is by definition a selectivity of the adsorbent phase for one cation over another, and previous efforts to describe the reasons for cation exchange selectivity have most often focused on the well-studied selectivities of pure clay minerals for alkali cations. It was 70 yr ago that Hans Jenny showed (Jenny, 1932, 1936) that the selectivity of a purified swelling clay mineral for alkali cations followed the lyotropic series

[1]

Explanations for this ranking are myriad. An early hypothesis that was derived on a theoretical basis and shown to have quantitative predictive ability was that of Jenny (Jenny, 1936) who asserted that if the clay selects ion b over ion w, then "b has a smaller oscillation volume than w, which implies that b is more strongly attracted by the surface." That is, cation exchange occurs because less strongly held ions wander too far from the surface, providing opportunities for more strongly bound ions to take their places near charged sites. Thus, cation exchange selectivity has been explained on the basis of favorable clay-cation interactions since the inception of the concept.

In efforts to compute these attractive forces between a clay and an ion, soil chemists came to recognize this task as very complex owing to contributions from hydrated Gouy-Chapman diffuse-layer cations (Schofield, 1947; Eriksson, 1952; Bolt, 1955) and more strongly adsorbed cations in a Stern-type monolayer directly adjacent to the clay surface (Kerr, 1928; Vanselow, 1932). By the 1960s, several authors (Gaines and Thomas, 1953; Heald et al., 1964; Bolt, 1967; Shainberg and Kemper, 1966b, 1967) had formulated the formidable task of computing equilibrium constants from the contributions of electrostatic versus specific energies of adsorption as a function of cation valence, distance from the surface, and changing hydration status. Basic conceptual overviews of the driving forces controlling cation-exchange selectivity were lost, having foundered on the shoals of complexity.

	Selectivity Due to Hydrated Radius

TOP ABSTRACT INTRODUCTION Selectivity Due to Hydrated... Eisenman Model for Selectivity Selectivity Due to Complexation MATERIALS AND METHODS RESULTS AND DISCUSSION CONCLUSIONS REFERENCES

 
One mechanistic concept that did survive and has come to dominate the discussion argues that selectivity is due to the "effective" radius of the cation in soils (i.e., the hydrated radius): A larger hydrated radius means that the cationic center of charge is farther from the clay surface so the clay-cation electrostatic interaction is weaker (Pauley, 1953; Shainberg and Kemper, 1966b). This concept fits the lyotropic series very well if one considers only cation-clay interactions, and is presented as the key explanation of cation-exchange selectivity by smectites in many reviews (Gast, 1977, p. 44; McBride, 1989, p. 58) and textbooks (Bohn et al. 1985, p. 158ff; Stumm, 1992, p. 133; Sparks, 1995, p. 143; Evangelou, 1998, p. 208). This mechanism is also invoked to explain the selectivity of alkali cations by ion-exchange resins (Cotton et al. 1999, p. 102–103). Operation of selectivity by this mechanism alone assumes that the adsorbed cations are fully hydrated (i.e., as hydrated as they would be in aqueous solution where the hydrated radii were estimated), which may be true on external surfaces but is clearly not true in the interlayer regions of swelling clays. Evangelou (Evangelou, 1998, p. 208) points out that the selectivity rule based on the smallest hydrated radius is equivalent to saying that the cation with the "least negative heat of hydration" is preferred.

Xu and Harsh (Xu and Harsh, 1990b) argue that the hydrated radius is a poor predictor of cation-exchange selectivity, even within the lyotropic series: Although the hydrated radius of Li⁺ is larger than that of Na⁺, there is not much difference in the selectivity of montmorillonites for Li⁺ versus Na⁺ (Kinniburgh and Jackson, 1981; Xu and Harsh, 1990a). On the other hand, Cs⁺ is strongly selected over Rb⁺ (Bruggenwert and Kamphorst, 1982; Maes and Cremers, 1986), even though their hydrated radii are similar.

	Eisenman Model for Selectivity

TOP ABSTRACT INTRODUCTION Selectivity Due to Hydrated... Eisenman Model for Selectivity Selectivity Due to Complexation MATERIALS AND METHODS RESULTS AND DISCUSSION CONCLUSIONS REFERENCES

 
The concept of electrostatic attraction to the surface is refined by the Eisenman model (Eisenman, 1962), originally developed to explain the behavior of ion-specific glass electrodes. Here, the energy gained by moving an ion to direct contact with the surface is viewed as an electrostatic term involving the ionic radius of the cation and an effective radius for the surface charge site, less the energy required to remove the water intervening between the cation and the surface. Application of this concept to cation exchange has been nicely presented in the textbook by McBride (McBride, 1994, p. 73ff). The Eisenman model explains selectivity for the lyotropic series Eq. [1] because the more weakly hydrated ions are easier to dehydrate and therefore more likely to be specifically adsorbed to the surface (Shainberg and Kemper, 1966b). Since the depth of a mineral charge site beneath the surface can be related to an effective radius for the site, the Eisenman model can further rationalize the observations (Maes and Cremers, 1978) that smectites with charged sites arising from octahedral substitution exhibit larger selectivity differences along the lyotropic series than do smectites with more tetrahedral substitution.

Eberl (Eberl, 1980) also draws heavily on Eisenman's (Eisenman, 1962) work, extending it to point out that clay layer charge and interlayer hydration status are important variables influencing selectivity. Using reasonable guesses for the interlayer hydration of smectites saturated with different alkali cations, Eberl was able to compute free energies of cation exchange that agreed fairly well with measured values. He showed that this Eisenman-based treatment predicts that selectivity among the lyotropic series should become more pronounced as the clay dries and also predicts that (at constant water content) selectivity differences should decrease as clay layer charge increases. Maes and Cremers (Maes and Cremers, 1986) point out that the latter prediction is opposite to the observed trend (Maes and Cremers, 1978), since reducing the charge on a smectite was seen to decrease its selectivity for Cs⁺ over Na⁺. These experiments and the predictions of the Eisenberg model can perhaps be reconciled by considering that, as smectite layer charge increases, the tendency to dehydrate interlayer cations also increases (Maes and Cremers, 1986).

Maes and Cremers (1986) point out that proper modeling of exchange reactions must include changes in the solution phase as well as those on the mineral surface. Even so, they confine their discussions to the hydration of cations in the clay interlayer: Changes that tend to dehydrate the interlayer region, such as increasing the charge density of the clay or increasing the ionic strength of the bulk solution phase, should enhance selectivity differences within the lyotropic series.

Laird and Shang (Laird and Shang, 1997) advanced the concept (Eberl, 1980; Maes and Cremers, 1986) that interlayer hydration status is a key determinant of cation-exchange selectivity. Their analysis recognizes that the hydration of smectite quasicrystals changes as the mix of exchangeable cations changes. Within quasicrystals, each hydrated interlayer with one, two, three, or four discrete layers of water between the clay lamellae can be described as a separate phase (Laird and Shang, 1997), because the properties of interlayer water depend on interlayer thickness (Sposito and Prost, 1982). Each separate phase might be expected to have different cation-exchange selectivity coefficients, so this approach explains the frequently observed changes in selectivity coefficients as a function of clay cation composition to be the result of smectite (quasi-) crystalline swelling.

This concept (Laird and Shang, 1997) is able to explain why selectivity for K⁺ over Ca²⁺ (Shainberg et al., 1987) and for Cs⁺ over K⁺ (Maes and Cremers, 1986) both increase as clay layer charge increases: Increasing the layer charge increases the tendency toward interlayer collapse (whatever the cation), and the consequent decrease in the number of layers of water causes an increase in selectivity of the clay for the more weakly hydrated cation. This concept (Laird and Shang, 1997) implies that a given cation is most likely to adsorb into an interlayer hydration phase like that of its homoionic clay end-member. Thus, Laird and Shang (1997) demonstrate that, for a smectite that has a three-layer hydrate for its Mg-saturated end member and a two-layer Ba-saturated end-member, the selectivity for Ba²⁺ increases sharply when the two-layer hydrate forms.

Xu and Harsh (1990b) criticized all electrostatics-based models for not explicitly including energy terms describing inner-sphere complexation reactions between polarizable cations and surface functional groups. However, Maes and Cremers (1986) had clearly invoked polarizability differences as another key qualitative feature to explain how surface dehydration (in the Eisenman sense) governs cation exchange selectivity by enhancing the electrostatic interaction between cation and surface.

	Selectivity Due to Complexation

TOP ABSTRACT INTRODUCTION Selectivity Due to Hydrated... Eisenman Model for Selectivity Selectivity Due to Complexation MATERIALS AND METHODS RESULTS AND DISCUSSION CONCLUSIONS REFERENCES

 
It had long been pointed out (Heald et al., 1964; Rice and Harris, 1956; Shainberg and Kemper, 1966a) that, in contrast to the models focusing on simple ion-ion or ion-dipole electrostatic interactions, the lyotropic series [1] follows the polarizability series of the cations, with smectites selectively adsorbing the more polarizable cations. The dominant hypothesis for interpretation of this trend has been that the siloxane ditrigonal cavities on the basal surfaces of clay minerals act as rather polarizable Lewis bases and thus preferentially form inner-sphere complexes with more polarizable (softer) Lewis acids (Heald et al., 1964; Shainberg and Kemper, 1967; Sullivan, 1977; Sposito, 1984). This treatment for clay surface complexation follows the hard and soft acid-base (HSAB) theory of Pearson (Pearson, 1963, 1990) for the formation of solution-phase complexes. That is, the likelihood of inner-sphere complexation between alkali cations and smectites is the basis for differences in adsorption selectivity (Shainberg and Kemper, 1966b; Sposito, 1984, p. 131), rather like Maes and Cremers' (1986) interpretation of the Eisenman model. This HSAB model means that cation-exchange selectivity is again defined in terms of attractive forces between the cations and the clay surface, but now the operant forces are polarizability-based electrostatic, van der Waals, and even covalent interactions. Again, this concept for cation-exchange selectivity is presented in several leading soil chemistry textbooks (Sposito, 1984, p. 129ff; Evangelou, 1998, p. 209). In addition, the HSAB concept has been taken farther and used to quantitatively derive thermodynamic equilibrium constants for cation exchange from electronegativities and softness parameters (Xu and Harsh, 1990b) Indeed, these quantitative predictions have been "verified" (Xu and Harsh, 1990a) for series [1] interacting with several clay minerals, and the computed parameters used to posit specific adsorption mechanisms operant in the exchange reactions (Xu and Harsh, 1992). For example, Xu and Harsh (1990a) assert that 80% of the free energy release when Cs⁺ replaces Na⁺ on montmorillonite SWy-1 is due to covalent interactions between Cs⁺ and the smectite surface while the remaining 20% is due to electrostatic contributions. Thus, the reasons for selectivity were again seen to originate in positive interactions between the clay surface and the more selected cation.

In light of this debate, the present study attempts to apply the tools of computational chemistry to investigate the mechanisms underlying cation exchange selectivity. In particular, the goal is to determine whether cation exchange selectivity is indeed caused by increased attraction of the more selected cation to the clay mineral surface. Specifically, free energy changes are computed for K⁺ Rb⁺ Cs⁺ exchange on a model montmorillonite, and compared with experimental determinations of free energies for this exchange.

	MATERIALS AND METHODS

TOP ABSTRACT INTRODUCTION Selectivity Due to Hydrated... Eisenman Model for Selectivity Selectivity Due to Complexation MATERIALS AND METHODS RESULTS AND DISCUSSION CONCLUSIONS REFERENCES

 
Molecular simulations of K⁺ Rb⁺ and Rb⁺ Cs⁺ exchange were performed on an alkali (X⁺) cation-saturated idealized montmorillonite of composition X₄·Si₃₂(Al₁₂Mg₄)O₈₀(OH)₁₆ (CEC = 135 cmol_c kg^–1) at a water content of 0.15 g g^–1 (approximately equivalent to monolayer coverage). This model montmorillonite was created from the crystal structure of muscovite mica (Comodi and Zanazzi, 1995; Liang and Hawthorne, 1996) to mimic the "Camp Berteau" montmorillonite, for which experimental free energy measurements are available (Martin and Laudelout, 1963; Maes and Cremers, 1978) for cation exchange and which exhibits a larger selectivity among the alkali cations than do other smectites with smaller layer charge or more tetrahedral substitution. Octahedral substitution was random, except that no two Mg atoms were placed in neighboring octahedra.

All molecular simulations of the hydrated clay systems employed force field methods (Teppen et al., 1997) that have proven reasonably successful in modeling the structural properties of hydrated clay interlayers (Teppen et al., 1998; Yu et al., 2000a, 2000b; Boyd et al., 2001; Sheng et al., 2002). The hydrated systems used in the present study were created by expanding the interlayer, adding enough water molecules to the interlayer space so that a monolayer was formed, and then equilibrating the system very well before undertaking the present study. All simulations employed periodic boundary conditions, the isothermal-isobaric ensemble (constant NPT: number of atoms N, pressure P, and absolute temperature T). This allowed the system volume to change freely at 1 x 10⁵ Pa (1 bar) external pressure and 298 K. These fully dynamic simulations employed Ewald summation to compute both electrostatic potentials and dispersive van der Waals interactions. Each simulation was equilibrated for volume and potential energy over 50 ps using a 0.5-fs time step.

The force field parameters used for the alkali cations were created for this study and are listed in Table 1. Testing of the parameters in pure water according to the method of Åqvist (Aqvist, 1990) resulted in cation-oxygen peaks in the aqueous radial distribution function centered at 2.8, 2.95, and 3.1Å for K⁺, Rb⁺, and Cs⁺, respectively. These are in reasonable agreement with the observed values (Ohtaki and Radnai, 1993) near 2.80 and 3.15 Å for K⁺ and Cs⁺, respectively. The values for G of hydration (relative to K⁺) from our simulations in pure water were 17 and 39 kJ mol^–1 for Rb⁺ and Cs⁺, respectively, which compare with 21 and 54 kJ mol^–1 from experiment (Burgess, 1978). Equilibrium swellings of the homoionic montmorillonite systems were reasonable but 3 to 4% below experimental values: The equilibrated d₀₀₁ was 9.74 ± 0.03 Å for the dry K-montmorillonite, 12.09 ± 0.05 Å for the hydrated K-montmorillonite, 12.14 ± 0.04 Å for the hydrated Rb-montmorillonite, and 12.23 ± 0.05 Å for the hydrated Cs-montmorillonite. Thus it can be seen that the parameters used for the cations interacting with water and the clay were reasonably good but far from perfect. We will attempt to show below that the conclusions of this paper do not at all depend on perfection of the simulation parameters.

To investigate whether cation exchange selectivity is indeed determined by increased attraction of the more selected cation to the clay mineral surface, we computed free energy changes for the reactions in the clay interlayer

[2]

with G_clay the overall Gibbs free energy change for the reaction.

To calculate G_clay we used the technique of free energy perturbation, which is commonly employed to compute Gibb's free energy differences in organic systems (Bash et al., 1987; Jorgensen and Ravimohan, 1985; Straatsma et al., 1986). Indeed, Eisenman himself used similar methods late in his career to explore the cation selectivity of proteins (Eisenman et al., 1991, 1992; Aqvist et al., 1992). Free energy differences cannot be directly computed, but are calculated indirectly during perturbations in which the parameters that characterize the initial system are changed incrementally into those characterizing the final system. The number of steps, n, required to complete the mutation process is determined by the convention (Bash et al., 1987; Jorgensen and Ravimohan, 1985; Straatsma et al., 1986) that the free energy differences between consecutive steps should be < 2RT, or < 2.5 kJ mol^–1 for the current study conducted at 298 K. In our study, appropriate values of n were determined by trial and error to be 10 for K⁺ Rb⁺ exchange and 16 for Rb⁺ Cs⁺ exchange. The value of n was then used to define a so-called coupling parameter, , according to the equations

[3]

where i referred to the step number (i = 0, 1,... n). At the ith step of the mutation from, for example, K⁺ into Rb⁺, the potential energy of the system was calculated using parameters, P, defined by the equation:

[4]

where P_Rb and P_K were rubidium and potassium parameters, respectively. The cation parameters used in each step of the present study are given in Table 1.

To calculate the overall free energy changes of the Reaction [2], it was necessary to compute and sum the relative free energy differences between adjacent mutation steps. Again, free energy differences cannot be computed directly, but the free energy perturbation technique (Bash et al., 1987; Jorgensen and Ravimohan, 1985; Straatsma et al., 1986) computes G via the potential energy differences U, which are computed directly. For the isothermal-isobaric ensemble,

[5]

Expectation values of exp(–U/RT) were calculated by performing 14 separate molecular dynamics (MD) simulations, performed on SGI workstations using the Discover module of the Insight II molecular modeling suite by Accelrys, Inc., San Diego, CA. Five hundred molecular configurations or "snapshots" were randomly selected from the second half of each MD run and used as an approximate statistical mechanical ensemble of states. For each ensemble, Eq. [5] and spreadsheet software were used to compute G for each of the 26 subintervals (  + or  – ) along the mutation path. Summing the G for each interval gave the overall G_clay for reaction [2].

	RESULTS AND DISCUSSION

TOP ABSTRACT INTRODUCTION Selectivity Due to Hydrated... Eisenman Model for Selectivity Selectivity Due to Complexation MATERIALS AND METHODS RESULTS AND DISCUSSION CONCLUSIONS REFERENCES

 
The simulated free energy changes for the clay phase during the cation exchange reaction of Eq. [2] are displayed in Fig. 1 . In this figure, the value of the coupling parameter (here referred to as the reaction coordinate) is plotted on the abscissa and relative Gibb's free energy is plotted on the ordinate. At = 0 the interlayer cation is K⁺, at = 1 the ion is Rb⁺, and at = 2 the ion has become Cs⁺.

View larger version (11K): [in this window] [in a new window]   Fig. 1. Free energy changes computed during the simulated transformation of K+ Cs+ in the interlayer of a smectite clay.

This concept is illustrated by a thermodynamic cycle in Fig. 2 . The top reaction of this cycle is the experimental cation exchange reaction, and is labeled –7 kJ mol^–1 according to the free energy change measured for K-Cs exchange on the Camp Berteau montmorillonite (Maes and Cremers, 1978). In a thought experiment, this overall cation exchange reaction can be decomposed into the sum of two separate reactions, one occurring in the clay phase and one in the aqueous phase, as shown in Fig. 2. Since the free energy is a state function, its sum for these two component reactions must equal the free energy change for the overall experimental reaction. There are reliable experimental measurements available for the "exchange" of K⁺ for Cs⁺ in the aqueous phase; this free energy change is given by the difference in free energies of hydration between K⁺ and Cs⁺ and accepted values in textbooks range from –46 (Marcus, 1985; McBride, 1994) to –58 kJ mol^–1 (Cotton et al., 1999) and even up to –93 kJ mol^–1 (Evangelou, 1998). Inserting a typical value of –54 kJ mol^–1 (Burgess, 1978) into the thermodynamic cycle (Fig. 2), we can compute by inference that the free energy change for exchanging Cs⁺ for K⁺ on the clay phase must be +47 kJ mol^–1. This estimate, based on the difference between two experimental values, is reasonably close to the +54 kJ mol^–1 estimate by our molecular simulations (Fig. 1). Based on the agreement of these two methods that the G_clay >> 0 for Eq. [2], we assert that cation-exchange selectivity of these three monovalent cations on montmorillonite is determined by the relative hydration energies of the ions, not by the affinities of the ions for the smectite surface. That is, Cs⁺ is most strongly selected by the clay in spite of its unfavorable adsorption energy, because the free energy gained by having K⁺ in aqueous solution more than compensates for the unfavorable free energy of placing Cs⁺ on the clay. This can be rationalized by observing that the interlayer region of smectites must contain cations but allows only partial hydration of those cations, so the more strongly hydrated cations (K⁺) will tend to stay in the solution phase where they can remain fully hydrated. On the other hand, less strongly hydrated cations (Cs⁺) will suffer less of an energy penalty for incomplete hydration within the clay interlayer region, so the overall system free energy will be lowest when Cs⁺ partitions into the clay interlayer phase and K⁺ partitions into the aqueous phase. That is, the interlayer region is a separate phase (Laird and Shang, 1997) from the bulk solution phase, so cations will partition between the bulk (aqueous) and interlayer (subaqueous) phases according to their hydration energies. The interlayer region is here termed "subaqueous" to denote that the orientational freedom of interlayer water molecules is strongly restricted by the high ionic strength of interlayer solution and by the close proximity of up to two siloxane surfaces. The preferred orientations of interlayer water (Sposito and Prost, 1982) result in the entropy of adsorbed water being lower than that of bulk water (Keren and Shainberg, 1980; Fu et al., 1990). In addition, the diffusion and dielectric relaxation rates of water molecules in smectite interlayers tend to be slower than in bulk solution (Sposito and Prost, 1982). Furthermore, smectite interlayer regions are often only 3 to 9 Å thick, which may not be room for complete hydration shells to form around cations. Through a combination of these factors, cations in the interlayer region cannot be hydrated as efficiently as they can in bulk solution.

View larger version (15K): [in this window] [in a new window]   Fig. 2. A thermodynamic cycle that allows cation exchange energies (top) to be assigned to clay-phase (left) and solution-phase (right) contributions at 298 K and 1 x 105 Pa (1 bar) pressure.

Implications for Inner-Sphere Adsorption of Monovalent Cations by Clay Minerals and the Hypothesis that Complexation Phenomena Determine Selectivity
Note that smectite selectivity (as measured by free energy of cation exchange) for Cs⁺ over Na⁺ is about 10 kJ mol^–1, only a bit larger than that for Cs⁺ over K⁺ (Gast, 1969, 1972; Maes and Cremers, 1978, 1986), despite the fact that the Na-Cs hydration energy difference is more than twice as large as that for K-Cs. This implies that Na⁺ is very strongly favored over Cs⁺ in the clay phase (Fig. 3 ) by roughly 120 kJ mol^–1. An adsorption energy difference this large might arise in two ways: First, both ions could be almost fully hydrated, but somewhat imperfectly, so that the energy of exchanging them in the clay interlayer would be a bit less than the difference in their hydration energies. We know this is not true for Cs⁺, as the monolayer of water in wet Cs-smectites (MacEwan and Wilson, 1980; Suquet et al., 1975, 1977; Suquet and Pezerat, 1987; Kawano and Tomita, 1991; Berend et al., 1995) forces the interpretation that Cs⁺ forms inner-sphere complexes with hydrated smectite siloxane surfaces. Second, even a relatively strongly hydrated cation like Na⁺ may adsorb to the smectite surface largely as an inner-sphere complex, and the electrostatic energy for converting inner-sphere Na⁺ to inner-sphere Cs⁺ would be large and positive, helping to account for the very large difference between the clay adsorption energies of Na⁺ and Cs⁺. Molecular mechanics simulations (Chang et al., 1995; Boek et al., 1995) show a strong tendency for Na⁺ to form inner-sphere complexes on hydrated smectite interlayer surfaces, and Miller and Low (1990) used several lines of indirect thermodynamic evidence to argue that Na⁺ forms mostly inner-sphere complexes on smectites, so the present study adds one more indirect supporting argument.

View larger version (14K): [in this window] [in a new window]   Fig. 3. Thermodynamic cycle that describes cation exchange energies (top) for Na+ Cs+ exchange and quantifies the clay-phase (left) and solution-phase (right) contributions at 298 K and 1 x 105 Pa (1 bar) pressure.

The essential error of most previous attempts at descriptions of cation exchange energetics is that they concentrate on the energies of cation-clay interactions, while the measured thermodynamic values include energy changes in both the clay and solution phases. When both phases are included in the discussion (Fig. 2), it becomes clear that the origin of cation exchange selectivity is the selectivity of the bulk aqueous phase for the more strongly hydrated cation.

Implications for Effect of Interlayer Hydration on Cation Exchange
Cesium-smectites in aqueous suspension are almost always reported to adsorb a monolayer of interlayer water, while K-smectites sometimes adsorb a monolayer (high-charged smectites and those with dominantly tetrahedral substitution), sometimes a bilayer of water (especially lower-charged smectites), and sometimes more (Suquet et al., 1975, 1977; Suquet and Pezerat, 1987; Kawano and Tomita, 1991; Berend et al., 1995). One wonders how much a potential change in interlayer hydration status might contribute to the cation exchange energy. Dry homoionic K-smectite (Wyoming montmorillonite) has a total heat of immersion of 3 to 4 kJ (mol water)^–1 (Berend et al., 1995). Due to interstratification of the partially hydrated K-smectites, it is difficult to separate components, but a reasonable estimate is that the K-smectite sorbs its first layer of interlayer water with an enthalpy of –2 to –3 kJ mol^–1 and further water with an enthalpy less than –1 kJ mol^–1. Desorbing the second layer of water would therefore result in an enthalpy change +1 kJ mol^–1. When Cs-saturated, this smectite adsorbed only one layer of water, again with an average enthalpy of –3 to –4 kJ mol^–1 (Berend et al., 1995). We know of no entropic measurements for K- or Cs-smectites, but the entropy change (–TS) for desorbing the second layer of water from a Na-montmorillonite (leaving a monolayer hydrate) is about –1 kJ mol^–1 at 298 K (Fu et al., 1990). Assuming that the entropy of adsorbed water is reasonably similar in Na- and K-smectites at a given layer spacing, the entropic change for desorbing a potential second layer of water from K-smectite as it is converted to a Cs-smectite during ion exchange is approximately equal in magnitude but opposite in sign to the enthalpic change, so the net free energy change due to a bilayer-monolayer transition should be close to zero for K-smectites. This is in accord with observations (listed above) that wet K-smectites may be found in either state. (Indeed, even for Na-montmorillonite the overall free energy for desorption of the second layer of water is only about +0.2 kJ mol^–1 (Keren and Shainberg, 1980) to +0.7 kJ mol^–1 (Fu et al., 1990), and one would expect the magnitude of this value to be smaller for K-montmorillonite since the positive component is the enthalpy, which is smaller for K-smectites). This explains the great similarity in water adsorption among K-, Rb-, and Cs-smectites (Berend et al., 1995), which all readily adsorb a monolayer of water from the vapor phase but will adsorb more only grudgingly and even then only near saturation. Since the number of water molecules per hydration layer in a montmorillonite is roughly seven to ten per monovalent cation (Keren and Shainberg, 1980; Tardy and Touret, 1985; Johnston et al., 1992; Berend et al., 1995), the potential bilayer to monolayer transition for a K-smectite is expected to result in a free energy change of only about +1 kJ (mol cations)^–1, and certainly less than +7 kJ (mol cations)^–1. Thus, if a transition from a bilayer to a monolayer of interlayer water occurred during the exchange of Cs⁺ for K⁺ in the interlayer, then a maximum of +7 kJ mol^–1 would be due to the change in hydration status, while about +40 kJ mol^–1 would be due to exchange of the more favorable K-smectite interaction for the less favorable Cs-smectite interaction (Fig. 2).

Consider the extreme case in which the K-smectite contains a bilayer of water but the Cs-smectite totally dehydrates in the interlayer region (as is conceivable for moderately high-charged smectites). An upper limit on the associated energy changes can be estimated: Two careful studies (Keren and Shainberg, 1980; Fu et al., 1990) both found the overall free energy of adsorption for the first layer of water in Na-montmorillonite to be –2 to –3 kJ mol^–1. This serves as an upper limit for K- and Cs-smectites since Na-smectites are considerably more hydrophilic (Berend et al., 1995). Again, typical smectites contain 7 to 10 water molecules per monovalent cation per layer of hydration (Keren and Shainberg, 1980; Tardy and Touret, 1985; Johnston et al., 1992; Berend et al., 1995), so an upper limit on the free energy change due to dehydration would be +20 to 30 kJ (mol cations)^–1. From above, loss of the second layer of water would cost less than +7 kJ (mol cations)^–1, for a total dehydration energy of +27 to +37 kJ (mol cations)^–1. Thus, even in this most extreme case of dehydration and in the case where the overall selectivity of Cs⁺ is highest (Fig. 2), there would still be a significantly unfavorable free energy term of (at minimum) +10 to +20 kJ mol^–1 for replacement of K⁺ by Cs⁺ in the clay interlayer. Thus there can be little doubt that the source of cation exchange selectivity is found in the aqueous phase, since the free energy for exchanging Cs⁺ for K⁺ in the clay phase seems unfavorable under all circumstances.

Note that, for a given increase in free energy for the substitution of Cs⁺ for K⁺ in the interlayer, loss of water from the smectite interlayer would increase the unfavorable energy change in the clay phase (Fig. 2), resulting in a less negative free energy change (or even a positive, unfavorable one) for the overall cation exchange reaction. This is offered as an explanation for observations (Maes and Cremers, 1978) that selectivity for Cs⁺ over K⁺ is enhanced for smectites with octahedral rather than tetrahedral substitution, since tetrahedral substitution would tend to enhance interlayer collapse (Suquet et al., 1975, 1977). In addition, we hypothesize that tetrahedral substitution would increase the energy required to replace K⁺ by Cs⁺ on the clay (Fig. 1), thus making the overall free energy of exchange less favorable.

On the other hand, the selectivity of Cs⁺ over K⁺ tends to be greater for smectites with greater overall layer charge (Maes and Cremers, 1978, 1986). This can perhaps be explained by the tendency of K-smectites to swell less as their layer charge increases: If the K-smectite contains a monolayer of adsorbed water, then Cs-exchange will probably not cause a change in the hydration status, so there will be no positive contribution to the free energy of cation exchange from loss of interlayer water, so the free energy of cation exchange will be as negative as possible.

Implications for Adsorption of Monovalent Organic Cations
The concepts outlined above for the origins of alkali cation exchange selectivity can also be used to provide a simple explanation for the strong selectivity of smectites for organic cations over inorganic (Maes et al., 1980; Maes and Cremers, 1986), and for larger organic cations over smaller (Maes et al., 1980; Mizutani et al., 1995). For example, trimethylammoniumalkane cations of alkane chain length n (TMA-n) readily replace monovalent inorganic cations such as Na⁺ (Maes et al., 1980) and even replace divalent cations such as Ca²⁺. The free energy change when TMA-2 exchanges for Ca²⁺ on the Camp Berteau montmorillonite is –17 kJ mol^–1, respectively, and rises to –22 kJ mol^–1 for TMA-10 (Maes et al., 1980). The hydration free energy of N(CH₃)₄⁺ (i.e., TMA-1) is approximately –219 kJ mol^–1 (Ford and Wang, 1992), and would be expected to be less negative for larger organic cations. For example, if four more methylene carbons are added to make N(C₂H₅)₄⁺, the free energy of hydration rises to about –183 kJ mol^–1 (Ford and Wang, 1992). Thus, the hydration free energies of even small organic cations (with the probable exception of the smallest alkylammonium cations such as CH₃NH₃⁺) are more than 50 kJ mol^–1 less negative than even the most weakly hydrated inorganic cations such as Cs⁺ (–284 kJ mol^–1; Burgess, 1978). Thus, again, there is a very strong driving force to move the inorganic cations into bulk aqueous solution, and to move the organic cations into the subaqueous clay interlayer.

The same reasoning allows a simple explanation for why smectites select larger organic cations over smaller: The larger cation with the least favorable hydration energy again has a greater likelihood of partitioning into the subaqueous interlayer phase. Support for the simple nature of this explanation is found in experiments with different solvents: Mizutani et al. (1995) showed that smectites selected for the largest organic cation from aqueous suspension, but reversed their selectivity and favored the smallest organic cation from organic solvents. Thus, the selectivity sequence must be controlled by the solvent and not by interactions with clay surfaces.

Implications for Alkaline Earth Cation Selectivity
Divalent alkaline earth cations tend to be selected by smectites in the sequence (Evangelou, 1998)

[6]

This sequence is consistent with the main hypothesis of this paper in that the more strongly hydrated cation is always favored in the solution phase. Selectivity differences along sequence [6] are less pronounced than those among the alkali cations (Eq. [1]). This is rational, since the interlayer regions of smectites saturated by divalent cations are more hydrated, and therefore more like bulk solution, than those of alkali-saturated smectites. Furthermore, the average interlayer hydration changes less among the alkaline earths than among the alkali cations, in that Ba-smectite interlayers tend to contain a bilayer of water while Mg-smectites tend to contain a trilayer (Laird and Shang, 1997).

Implications for Adsorption of Organic Complexes of Inorganic Cations
Complexation of an inorganic cation (such as Cu²⁺) by an organic ligand (such as neutral ethylenediamine [en]) results in a very strong selectivity of smectites for the Cu(en)₂²⁺ complex over Cu²⁺ (–14 kJ mol^–1, Maes et al., 1982). In addition, higher-charged smectites exhibit the strongest such selectivity (Maes and Cremers, 1981). Maes and coworkers (Maes et al., 1982) have already pointed out that the changes in hydration energy for Cu(en)₂²⁺ versus Cu²⁺ must play some role in the exchange selectivity, though the magnitude of the change is not known. However, their review of the subject (Maes and Cremers, 1986, p. 271) again concentrates on hydration changes in the clay phase, and concludes that "the selectivity enhancement on complexing is enthalpy driven and may be ascribed to enhanced charge dependent (primarily Coulombic) interactions with the surface as compared with the aqueous ions." Continuing with the emphasis of the present paper, we can see that, since Cu(en)₂²⁺ must be solvated at a much higher (probably at least 100 kJ mol^–1 less negative) free energy than Cu²⁺ in bulk solution, then an exchange free energy of –14 kJ mol^–1 (Maes et al., 1982) implies that Cu²⁺ must actually be very strongly favored on the clay phase over Cu(en)₂²⁺ (Fig. 2). Again, the overall exchange reaction must be driven by the strong preference of the aqueous solution for Cu²⁺. All else being equal, the clay too, would rather adsorb Cu²⁺, but the energy penalty for the clay taking Cu(en)₂²⁺ is less than the penalty for the solution phase taking it.

	CONCLUSIONS

TOP ABSTRACT INTRODUCTION Selectivity Due to Hydrated... Eisenman Model for Selectivity Selectivity Due to Complexation MATERIALS AND METHODS RESULTS AND DISCUSSION CONCLUSIONS REFERENCES

 
The methods of computational molecular mechanics found that Cs-montmorillonite is considerably higher in energy than K-montmorillonite at constant water content, in agreement with inferences from a new thermodynamic cycle representation of cation exchange. Since montmorillonite selects Cs⁺ over K⁺, these results mean that alkali cation-exchange selectivity is dominantly controlled by selectivity of the solution phase for the more strongly hydrated cation. Thus the clay does not "select" for Cs⁺ over K⁺ in any positive sense and it may be more useful to consider cation exchange as a partitioning reaction: Given two cations of equal valence, the more weakly hydrated will tend to partition into the "subaqueous" smectite interlayer phase. This concept seems not only parsimonious, but also more accurate than other hypotheses for cation exchange selectivity that impute more favorable interactions between smectite surfaces and the selected cations; such theories err by ignoring energy changes in the solution phase. This simple partitioning concept rationally explains the alkali and alkaline earth selectivity sequences as well as the selectivities of smectites for organic cations over inorganic, for larger organic cations over smaller, and for organometallic complexes over the uncomplexed metal.

	ACKNOWLEDGMENTS

 
The authors thank Lothar Schäfer and Ching-Hsing Yu for discussions of the free energy perturbation calculations reported here.

Received for publication June 28, 2004.

	REFERENCES

TOP ABSTRACT INTRODUCTION Selectivity Due to Hydrated... Eisenman Model for Selectivity Selectivity Due to Complexation MATERIALS AND METHODS RESULTS AND DISCUSSION CONCLUSIONS REFERENCES

 

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