Solvent frictional forces

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... 

Including solvent in a molecular dynamics simulation creates a frictional force that damps some motion of the solute. This affects in particular the motions of exposed side chain in proteins. 

Langevin dynamics simulates the effect of molecular collisions and the resulting dissipation of energy that occur in real solvents, without explicitly including solvent molecules. This is accomplished by adding a random force (to model the effect of collisions) and a frictional force (to model dissipative losses) to each atom at each time step. Mathematically, this is expressed by the Langevin equation of motion (compare to Equation (22) in the previous chapter) ... 

Second, we take account of the frictional drag as the solute molecule moves through the solvent. The frictional force is taken to be proportional to the velocity of the particle, with a proportionality constant called the friction coefficient... 

In the equation of motion (13), the friction force with the solvent... 

Under the influence of a gravitational (centrifugal) field, a solute particle of mass m — M/Ni immersed in a solvent of density p at a distance r from the rotor axis experiences three forces. Within the frame of reference of the rotor, spinning with angular velocity co, these are the centrifugal force Fc, the buoyant force Fb, and the frictional force Ff. 

In substitutional metallic solid solutions and in liquid alloys the experimental data have been described by Epstein and Paskin (1967) in terms of a predominant frictional force which leads to the accumulation of one species towards the anode. The relative movement of metallic ion cores in an alloy phase is related to the scattering cross-section for the conduction electrons, which in turn can be correlated with the relative resistance of the pure metals. Thus iron, which has a higher specific resistance than copper, will accumulate towards the anode in a Cu-Fe alloy. Similarly in a germanium-lithium alloy, the solute lithium atoms accumulate towards the cathode. In liquid alloys the same qualitative effect is observed, thus magnesium accumulates near the cathode in solution in bismuth, while uranium, which is in a higher Group of the Periodic Table than bismuth, accumulated near the anode in the same solvent. 

First, consider the solvent. The characterization of the solute-solvent coupling by a relaxation time is based on analogy to Brownian motion, and the relaxation time is called the frictional relaxational time Xp. It is the relaxation time for momentum decay of a Brownian motion in the solute coordinate of interest when it interacts with the solvent under consideration. If we call the subject solute coordinate s, then the component of frictional force along this coordinate may be written as... 

Let us make some connections to the results which came from the previous model development. First, if we compare (3.19)-(3.22) with (3.11)-(3.15), a natural identification of the solvent coordinate s in Sec. 3 is in fact just the fluctuating force SF on x at the transition state. (Note especially that this choice associates the solvent coordinate with a direct measure of the relevant solute-solvent interaction.) The solvent mass, force constant and frequencies in Sec. 3 would then be given molecular expressions via (3.19)-(3.21), while the solvent friction i (t) of Sec. 3 would be the friction per mass for Sf (3.22),... 

In the case of charged molecules, an additional friction force should be introduced as a result of the induced polarization of the surrounding solvent molecules. 

In the case of an immobile macromolecule in solution it is possible to estimate a value of the frictional force (F) developed between the solvent and polymer molecules by assuming the macromolecule to consist of a number (n) of solid spherical entities and applying the Stokes formula in a modified form (Eq. 5.8). 

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... 

For brevity, only -components are considered in the following. The force fXti is assumed to be in equilibrium with the friction force exerted by the flowing solvent. One assumes ... 

The frictional coefficient, f, depends on the size and shape of the particle, as well as the viscosity of the solvent. The frictional force increases with the velocity of the particle until a constant velocity is reached. At this point, the two forces are balanced (Equation 7.6). 

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