Free energy cation-exchange reaction

A acAange = change in free energy for a binary cation exchange reaction,... 

The layered silicate nanoparticles are usually hydrophilic and their interactions with nonpolar polymers are not favorable. Thus, whereas hydrophilic polymers are likely to intercalate within Na-activated montmorillonite clays [24-29], hydrophobic polymers can lead to intercalated [23,30-32] or exfoliated [33] structures only with organophilized clays, i.e., with materials where the hydrated Na+ within the galleries has been replaced by proper cationic surfactants (e.g., alkylammonium) by a cation exchange reaction. The thermodynamics of intercalation or exfoliation have been discussed [34-37] in terms of both enthalpic and entropic contributions to the free energy. It has been recognized that the entropy loss because of chain confinement is compensated by the entropy gain associated with the increased conformational freedom of the surfactant tails as the interlayer distance increases with polymer intercalation [34,38], whereas the favorable enthalpic interactions are extremely critical in determining the nanocomposite structure [39]. 

The measured equilibrium constants for this stepwise deprotonation scheme for Mo and W have been collected from the literature in [56]. They show that Mo is more hydrolyzed than W, and that the deprotonation sequence for Mo and W at pH = 1 reaches the neutral species M02(0H)2(H20)2. Assuming the deprotonation processes for the Sg compounds to be similar to those of Mo and W, Equations (6-9), V. Pershina and J.V. Kratz performed fully relativistic density-functional calculations of the electronic structure of the hydrated and hydrolyzed structures for Mo, W, and Sg [56]. By use of the electronic density distribution data, relative values of the free energy changes and by use of the hydrolysis model [29,30], constants of hydrolysis reactions (6-9) were defined [56]. These results show hydrolysis of the cationic species to the neutral species to decrease in the order Mo>W>Sg which is in agreement with the experimental data on hydrolysis of Mo and W, and on Sg [55] for which the deprotonation sequence may end earlier with a cationic species such as SgO(OH)3(H20)2+ that is sorbed on the cation-exchange resin. 

Surface complexation is a typical multi-component reaction, similar to cation exchange. The database for surface complexation includes complexation constants for major elements in groundwater such as and S04 , but not for and HCOs". In the first instance, constants for these ions can be estimated with linear free energy relations (LFER s) in which the properties of similar chemical systems are compared and interpolated (Dzombak and Morel, 1990). Thus, the surface complexation constant for is expected to lie in between the ones for and for Zn, in line with the known differences of the association constants of these heavy metals with OH in water. For the weak sites, the LFER gives ... 

Figure 3.2. Dependence of f-values of adsorbed cations on the mole fraction of exchange sites occupied by Rb and Na in the NaV b and Li+/Na+ exchange reaction on smectite. Adapted from R. G. Cast. 1969. Standard free energies of exchange for alkali metal cations on Wyoming bentonite. Soil Sci. Soc. Am. Proc. 33 37-41 1972. Alkali metal cation exchange on Chambers montmorillonite. Soil Sci. Soc. Am. Proc. 36 14-19.)...

Eyring and Wadsworth (50) and Little (51) present spectroscopic evidence that thiols bond to ZnO surfaces and xanthates bond to PbS surfaces by way of hydroxyl-exchange reactions in which metal-sulfide bonds are formed, and metal-hydroxyl bonds are broken during adsorption. We expect that trends exhibited in the relative stabilities of amino acid and hydroxo complexes of various dissolved cations should parallel trends in the relative reactivities and adsorption free energies, should this type of bonding control adsorption. 

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