Solvent friction

The elementary condition for obtaining conductivity in solutions is obviously the dissolution of electrolyte and considerable charge separation. The most common and important conduction mechanism relates to the motion of separated ions in the liquid medium, retarded by friction (solvent-solute and ion-ion interactions). The ions thus reach a constant drift speed (S) under the electric field ... 

There are, in principle, two ways in which solvents can affect the reaction rates of homogeneous chemical reactions through static, or equilibrium, solvent effects and through dynamic, or frictional, solvent effects [463, 465, 466]. 

At the same time, AV(, is invariably positive for electrode reactions in organic solvents, signaling rate control by solvent friction. Solvent dynamics dominate electrode kinetics in non-aqueous media even when the corresponding self-exchange reactions clearly conform to the TST model. In short, pressure effects reveal that electrode reactions are subject to solvent dynamical effects in non-aqueous media at least, but the corresponding self-exchange reactions are not, regardless of the solvent. 

With use of obtained parameters, the extended SM theory is employed to predict the ET rates beeause the experimental rates are measured in a strong friction solvent. 

Lee et al. investigated the photoisomerism of fran.y-stilbene in supercritical ethane to observe the so-called Kramer s turnover region where the solvent effects are in transition from collisional activation (solvent-promoting reaction) to viscosity-induced friction (solvent-hindering reaction) (76). In the experiments the Kramer s turnover was observed at the pressure of about 120 atm at 350 K. (See Scheme 2.)... 

Discuss the dependence of the friction phase diagram on temperature, mono-layer density, velocity, load and solvent vapor. Explain why each of these variables will drive one to the right or left in Fig. XII-8. 

In the sections below a brief overview of static solvent influences is given in A3.6.2, while in A3.6.3 the focus is on the effect of transport phenomena on reaction rates, i.e. diflfiision control and the influence of friction on intramolecular motion. In A3.6.4 some special topics are addressed that involve the superposition of static and transport contributions as well as some aspects of dynamic solvent effects that seem relevant to understanding the solvent influence on reaction rate coefficients observed in homologous solvent series and compressed solution. More comprehensive accounts of dynamics of condensed-phase reactions can be found in chapter A3.8. chapter A3.13. chapter B3.3. chapter C3.1. chapter C3.2 and chapter C3.5. 

As is inversely proportional to solvent viscosity, in sufficiently viscous solvents the rate constant k becomes equal to k y. This concerns, for example, reactions such as isomerizations involving significant rotation around single or double bonds, or dissociations requiring separation of fragments, altiiough it may be difficult to experimentally distinguish between effects due to local solvent structure and solvent friction. 

Predicting the solvent or density dependence of rate constants by equation (A3.6.29) or equation (A3.6.31) requires the same ingredients as the calculation of TST rate constants plus an estimate of and a suitable model for the friction coefficient y and its density dependence. While in the framework of molecular dynamics simulations it may be worthwhile to numerically calculate friction coefficients from the average of the relevant time correlation fiinctions, for practical purposes in the analysis of kinetic data it is much more convenient and instructive to use experimentally detemiined macroscopic solvent parameters. 

In the Smoluchowski limit, one usually assumes that the Stokes-Einstein relation (Dq//r7)a = C holds, which fonns the basis of taking the solvent viscosity as a measure for the zero-frequency friction coefficient appearing in Kramers expressions. Here C is a constant whose exact value depends on the type of boundary conditions used in deriving Stokes law. It follows that the diffiision coefficient ratio is given by ... 

Multidimensionality may also manifest itself in the rate coefficient as a consequence of anisotropy of the friction coefficient [M]- Weak friction transverse to the minimum energy reaction path causes a significant reduction of the effective friction and leads to a much weaker dependence of the rate constant on solvent viscosity. These conclusions based on two-dimensional models also have been shown to hold for the general multidimensional case [M, 59, and 61]. 

To conclude this section it should be pointed out again that the friction coefficient has been considered to be frequency independent as implied in assuming a Markov process, and that zero-frequency friction as represented by solvent viscosity is an adequate parameter to describe the effect of friction on observed reaction rates. 

The key quantity in barrier crossing processes in tiiis respect is the barrier curvature Mg which sets the time window for possible influences of the dynamic solvent response. A sharp barrier entails short barrier passage times during which the memory of the solvent environment may be partially maintained. This non-Markov situation may be expressed by a generalized Langevin equation including a time-dependent friction kernel y(t) [ ]... 

Because of the general difficulty encountered in generating reliable potentials energy surfaces and estimating reasonable friction kernels, it still remains an open question whether by analysis of experimental rate constants one can decide whether non-Markovian bath effects or other influences cause a particular solvent or pressure dependence of reaction rate coefficients in condensed phase. From that point of view, a purely... 

The relation between the microscopic friction acting on a molecule during its motion in a solvent enviromnent and macroscopic bulk solvent viscosity is a key problem affecting the rates of many reactions in condensed phase. The sequence of steps leading from friction to diflfiision coefficient to viscosity is based on the general validity of the Stokes-Einstein relation and the concept of describing friction by hydrodynamic as opposed to microscopic models involving local solvent structure. In the hydrodynamic limit the effect of solvent friction on, for example, rotational relaxation times of a solute molecule is [ ]... 

Haynes G R and Voth G A 1993 The dependence of the potential of mean force on the solvent friction consequences for condensed phase activated rate theories J. Chem. Phys. 99 8005... 

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