Separable Equilibrium Solvation

The most useful theoretical framework for studying chemical reactions in solution is transition state theory. Building on the material presented in the introduction, we will begin by presenting a general theory called the equilibrium solvation path (ESP) theory of reactions in a liquid. We then present an approximation to ESP theory called separable equilibrium solvation (SES). Finally we present a more complete theory, still based on an implicit treatment of solvent, called nonequilibrium solvation (NES). All three... 

The simplest way to include solvation effects is to calculate the reaction path and tunneling paths of the solute in the gas phase and then add the free energy of solvation at every point along the reaction path and tunneling paths. This is equivalent to treating the Hamiltonian as separable in solute coordinates and solvent coordinates, and we call it separable equilibrium solvation (SES) [74]. Adding tunneling in this method requires a new approximation, namely the canonical mean shape (CMS) approximation [75]. 

If the reaction path and dividing surface are optimized in the gas phase, but the rate constant is calculated with the equilibrium solvation Hamiltonian, the resulting rate constant is called separable equilibrium solvation (SES) [57]. However, if the reaction path and dividing surface are optimized with the equilibrium solvation potential, the result is labeled equilibrium solvation path (ESP) [57,78]. 

However, if the van t Hoff plots are linear, it indicates that the retention and/or selective processes governing the separation are unchanged over the temperature range studied. Furthermore, it can be assumed that a separation is a) thermodynamically reversible, b) (AH) and (AS) values are temperature independent, c) the enantiomers are retained in single associative mechanism, and d) a solvation-desolvation equilibrium does not obscure the association process of the enantiomers with the... 

As shown in Table 12, in polar media highly syndiotactic PMMA is formed for free ions and with lithium and sodium as counterions for sodium, syndiospeci-licity is observed only in more polar solvents such as dimethyoxyethane or in the presence of strongly solvating ligands such as cryptands. Lithium is the smallest alkali metal cation and the most strongly solvated the equilibrium constants for formation of free ions and solvent-separated ion pairs are largest for lithium and... 

In a solution an equilibrium "solvate-separated ionic pair - contact ionic pair" evidently exists [73] ... 

The general formula for the initiator species can be written H B, where the degree of separation or ion pairing depends on the polarity of the medium and the possibility of specific solvation interactions. If we represent the equilibrium constant for the reactions in (6.DD) and (6.EE) by K, the initiator concentration can be written as... 

The normal pressure Pn In the fiuld confined between the walls varies with wall separation and Is not. In general, equal to the bulk pressure P3 of fiuld at the same chemical potential. The difference Pn - Pb Is the solvation force per unit area, fg, and can be calculated from the equilibrium density profiles by... 

Equation (31) is true only when standard chemical potentials, i.e., chemical solvation energies, of cations and anions are identical in both phases. Indeed, this occurs when two solutions in the same solvent are separated by a membrane. Hence, the Donnan equilibrium expressed in the form of Eq. (32) can be considered as a particular case of the Nernst distribution equilibrium. The distribution coefficients or distribution constants of the ions, 5 (M+) and B X ), are related to the extraction constant the... 

In order to obtain the ion concentrations in the pure solvent, we can consider the equilibrium constant K w of the overall reaction 4.3, as separation step 4.1 is followed almost instantaneously by solvation step 4.2, and so... 

Solvent-separated ion pairs, in which the first solvation shells of both ions remain intact on pairing may be distingnished from solvent-shared ion pairs, where only one solvent molecule separates the cation and the anion, and contact ion pairs, where no solvent separates them (Fig. 2.6). The parameter a reflects the minimum distance by which the oppositely charged ions can approach each other. This eqnals the sum of the radii of the bare cation and anion pins 2, 1, and 0 diameters of the solvent, respectively, for the three categories of ion pairs. Since a appears in Eq. (2.49), and hence, also in Q(b), it affects the value of the equilibrium constant, K s- The other important variable that affects K ss is the product T and, at a given temperature, the value of the relative permittivity, e. The lower it is, the larger b is and, hence, also K s-... 

Extensive literature has developed related to the preferential interaction of different solvents with proteins or peptides in bulk solution.156-5X1 Similar concepts can be incorporated into descriptions of the RPC behavior of peptides and employed as part of the selection criteria for optimizing the separation of a particular peptide mixture. As noted previously, the dependency of the equilibrium association constant, /CassoCji, of a peptide and the concentration of the solvent required for desorption in RPC can be empirically described1441 in terms of nonmechanistic, stoichiometric solvent displacement or preferential hydration models, whereby the mass distribution of a peptide P, with n nonpolar ligands, each of which is solvated with solvent molecules Da is given by the following ... 

In dlfluorenylstrontlum Itself the solvation Is a stepwise process, l.e., Fl, Sr++,Fl- <— Fl",Sr F1" += Fl 11Sr4 11Fl (31). In the n - 2 bolaform salt the first separation step Is difficult, but once bound THF molecules force Sr to separate from the first Fl Ion, the cyclic structure probably opens up due to the shortness of the (CH2>2 chain. This would leave a free Fl Ion on one end of the chain. Since the conductance of the salt Is known to be very low, this latter species most likely will rapidly dimerize to form a non-conducting cyclic aggregate consisting of loose Ion pairs only,as shown In reaction 14. This aggregation shifts the equilibrium In favor of the loose Ion pairs. 

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