Free energy distribution between interaction

The equilibrium state is determined by a minimization of the free energy. The total interaction in colloidal systems is mainly determined by electrostatic interactions and can be divided in three components. The first component occurs at interactions between net charged molecules or molecules with asymmetric charged distribution. These charge distributions can often be described by multipole expansions, i.e., a combination of monopole, dipole, quadrupole, etc., and is a fruitful approach if each multipole expansion can be described by one or two terms. The interaction is given by the sum of interactions between the terms, where the first contribution is the interaction between ions and is given by Coulomb s law and is the main contribution in systems with... 

Once solved Laplace s equation for the bounded problem, we are able to determine the potentials within the cavity, c, and in the bulk, e. The charges within the cavity induce a polarisation in the dielectric, giving rise to a reaction potential, OR(ri), which acts back on the dissolved charges. Once determined the analytical expression for R(rt), Helmholtz s free energy of this interaction is just the difference between the reversible work of assembling the charge distribution in the presence of the dielectric and under vacuum, and simply reads ... 

The distribution coefficient is an equilibrium constant and, therefore, is subject to the usual thermodynamic treatment of equilibrium systems. By expressing the distribution coefficient in terms of the standard free energy of solute exchange between the phases, the nature of the distribution can be understood and the influence of temperature on the coefficient revealed. However, the distribution of a solute between two phases can also be considered at the molecular level. It is clear that if a solute is distributed more extensively in one phase than the other, then the interactive forces that occur between the solute molecules and the molecules of that phase will be greater than the complementary forces between the solute molecules and those of the other phase. Thus, distribution can be considered to be as a result of differential molecular forces and the magnitude and nature of those intermolecular forces will determine the magnitude of the respective distribution coefficients. Both these explanations of solute distribution will be considered in this chapter, but the classical thermodynamic explanation of distribution will be treated first. 

The Distribution of Standard Free Energy Between Different Types of Molecular Interactions... 

In contrast to apportioning the standard free energy between different groups in the solute molecule, the standard free energy can also be dispensed between the different types of forces involved in the solute/phase-phase distribution. This approach has been elegantly developed by Martire et al. [13]. In a simplified form, the standard free energy can be divided into portions that result from the different types of interaction, e.g.,... 

The Self-Consistent Reaction Field (SCRF) model considers the solvent as a uniform polarizable medium with a dielectric constant of s, with the solute M placed in a suitable shaped hole in the medium. Creation of a cavity in the medium costs energy, i.e. this is a destabilization, while dispersion interactions between the solvent and solute add a stabilization (this is roughly the van der Waals energy between solvent and solute). The electric charge distribution of M will furthermore polarize the medium (induce charge moments), which in turn acts back on the molecule, thereby producing an electrostatic stabilization. The solvation (free) energy may thus be written as... 

It is easy to understand the lower reactivity of non-ionic nucleophiles in micelles as compared with water. Micelles have a lower polarity than water and reactions of non-ionic nucleophiles are typically inhibited by solvents of low polarity. Thus, micelles behave as a submicroscopic solvent which has less ability than water, or a polar organic solvent, to interact with a polar transition state. Micellar medium effects on reaction rate, like kinetic solvent effects, depend on differences in free energy between initial and transition states, and a favorable distribution of reactants from water into a micellar pseudophase means that reactants have a lower free energy in micelles than in water. This factor, of itself, will inhibit reaction, but it may be offset by favorable interactions with the transition state and, for bimolecular reactions, by the concentration of reactants into the small volume of the micellar pseudophase. 

As mentioned above, the PCM is based on representing the electric polarization of the dielectric medium surrounding the solute by a polarization charge density at the solute/solvent boundary. This solvent polarization charge polarizes the solute, and the solute and solvent polarizations are obtained self-consistently by numerical solution of the Poisson equation with boundary conditions on the solute-solvent interface. The free energy of solvation is obtained from the interaction between the polarized solute charge distribution and the self-... 

The difference between GB0 and Gsc resides in their second terms, which comprise the interaction free energy between the solute charge distribution and the solvent electronic polarization. In particular, the matrix elements of V are the cavity surface integrals... 

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