Onsager studies

Two important contributions to the study of solvation effects were made by Bom (in 192( and Onsager (in 1936). Bom derived the electrostatic component of the free energ) c solvation for placing a charge within a spherical solvent cavity [Bom 1920], and Onsagi extended this to a dipole in a spherical cavity (Figure 11.21) [Onsager 1936]. In the Bor... 

Molecules do not consist of rigid arrays of point charges, and on application of an external electrostatic field the electrons and protons will rearrange themselves until the interaction energy is a minimum. In classical electrostatics, where we deal with macroscopic samples, the phenomenon is referred to as the induced polarization. I dealt with this in Chapter 15, when we discussed the Onsager model of solvation. The nuclei and the electrons will tend to move in opposite directions when a field is applied, and so the electric dipole moment will change. Again, in classical electrostatics we study the induced dipole moment per unit volume. 

Only in the last decades has the thermodynamics of open systems been treated intensively and successfully. The thermodynamics of irreversible systems was studied initially by Lars Onsager, and in particular by Ilya Progogine and his Brussels school both studied systems at conditions far from equilibrium. Certain systems have the capacity to remain in a dynamic state far from equilibrium by taking up free energy as a result, the entropy of the environment increases (see Sect. 9.1). 

The time relaxation corresponds to the change in the initial entropy state. As it has been established by one of the present authors (6), it is possible to derive generalized thermodynamic forces and fluxes in the sense of Onsager s theory and to study e.g. stability problems of tubular reactors. 

As soon as the concentration of the solute becomes finite, the coulombic forces between the ions begin to play a role and we obtain both the well-known relaxation effect and an electrophoretic effect in the expression for the conductivity. In Section V, we first briefly recall the semi-phenomenological theory of Debye-Onsager-Falkenhagen, and we then show how a combination of the ideas developed in the previous sections, namely the treatment of long-range forces as given in Section III and the Brownian model of Section IV, allows us to study various microscopic... 

In nonequilibrium steady states, the mean currents crossing the system depend on the nonequilibrium constraints given by the affinities or thermodynamic forces which vanish at equihbrium. Accordingly, the mean currents can be expanded in powers of the affinities around the equilibrium state. Many nonequilibrium processes are in the linear regime studied since Onsager classical work [7]. However, chemical reactions are known to involve the nonlinear regime. This is also the case for nanosystems such as the molecular motors as recently shown [66]. In the nonlinear regime, the mean currents depend on powers of the affinities so that it is necessary to consider the full Taylor expansion of the currents on the affinities ... 

Historically, one of the central research areas in physical chemistry has been the study of transport phenomena in electrolyte solutions. A triumph of nonequilibrium statistical mechanics has been the Debye—Hiickel—Onsager—Falkenhagen theory, where ions are treated as Brownian particles in a continuum dielectric solvent interacting through Cou-lombic forces. Because the ions are under continuous motion, the frictional force on a given ion is proportional to its velocity. The proportionality constant is the friction coefficient and has been intensely studied, both experimentally and theoretically, for almost 100... 

Ab initio SCRF/MO methods have been applied to the hydrolysis and methanol-ysis of methanesulfonyl chloride (334). ° The aminolysis by aromatic amines of sulfonyl and acyl chlorides has been examined in terms of solvent parameters, the former being the more solvent-dependent process.Solvent effects on the reactions of dansyl chloride (335) with substituted pyridines in MeOH-MeCN were studied using two parameters of Taft s solvatochromatic correlation and four parameters of the Kirkwood-Onsager, Parker, Marcus and Hildebrand equations. MeCN solvent molecules accelerate charge separation of the reactants and stabilize the transition... 

An important result of the theoretical studies of the multipair effects is that the recombination kinetics in a cluster of ions, in which the initial separation between neighboring cations is 1 nm, is faster than the corresponding decay kinetics of a single ion pair [18]. Furthermore, the escape probability is lower than the Onsager value [Eq. (15)], and decreases with increasing number of ion pairs in the cluster (a relative decrease of about 30% for two ion pairs, and about 50% for five ion pairs). The average electron escape probability in radiation tracks obviously depends on the distribution of ionization events in the tracks, which is determined by the type of radiations and their energy. 

Studies on multicomponent systems have been mainly restricted to relatively simple ternary systems containing a solvent as component 1 and-solutes as components 2 and 3. For such a system, under zero-volume flow conditions (Eq. (3)), exact expressions for the fluxes of the components 2 and 3 may be written as independent quantities of the forces involved so that the linear laws to which the Onsager reciprocal relationship applies may be written as follows341 ... 

More than half a century ago, Bawden and Pirie [77] found that aqueous solutions of tobacco mosaic virus (TMV), a charged rodlike virus, formed a liquid crystal phase at as very low a concentration as 2%. To explain such remarkable liquid crystallinity was one of the central themes in the famous 1949 paper of Onsager [2], However, systematic experimental studies on the phase behavior in stiff polyelectrolyte solutions have begun only recently. At present, phase equilibrium data on aqueous solutions qualified for quantitative discussion are available for four stiff polyelectrolytes, TMV, DNA, xanthan (a double helical polysaccharide), and fd-virus. 

The problem of relative permittivity of mixed solvents (denoted by e for simplicity) was theoretically studied by Debye and Onsager [34], Onsager derived the following equation ... 

This study was undertaken to determine whether or not the electrolytic conductance of the lithium bromide-bromosuccinic acid-acetone system can be described by the Fuoss-Onsager-Skinner equation (FOS equation)—Equation 2—by treating the system as lithium bromide in a mixed solvent, and to establish values for Ao and KA for lithium bromide in anhydrous acetone with the same equation. The equation requires knowledge of the concentration and corresponding equivalent conductance along with the dielectric constant and viscosity of the solvent and the temperature that is,... 

This connection is further discussed in Sect. 2.3. (The prescribed diffusion method of solution of this problem has been used by Mozumder [76], but it was shown to be unsatisfactory by Hong and Noolandi [72].) Recently, Clifford et al. [322] have shown that the diffusion and drift equation can be re-cast in a form which is symmetric to the sign of the coulomb potential. Consequently, the care necessary to define the sign of the Onsager distance, rc, is no longer required and it is sufficient to solve for an attractive potential. This is particularly valuable when performing numerical studies, as only attractive potentials need be considered (and such situations are more easily solved numerically than repulsive cases). 

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