Friction virial coefficient

Thus one must rely on macroscopic theories and empirical adjustments for the determination of potentials of mean force. Such empirical adjustments use free energy data as solubilities, partition coefficients, virial coefficients, phase diagrams, etc., while the frictional terms are derived from diffusion coefficients and macroscopic theories for hydrodynamic interactions. In this whole field of enquiry progress is slow and much work (and thought ) will be needed in the future. 

There are a number of quantitative features of Eq. (14) which are important in relation to rapid diffusional transport in binary systems. The mutual diffusion coefficient is primarily dependent on four parameters, namely the frictional coefficient 21 the virial coefficients, molecular weight of component 2 and its concentration. Therefore, for polymers for which water is a good solvent (strongly positive values of the virial coefficients), the magnitude of (D22)v and its concentration dependence will be a compromise between the increasing magnitude of with concentration and the increasing value of the virial expansion with concentration. 

A difference in volume between cyclic and linear polymers leads to different solution properties of the cyclic polymers compared to the linear polymers, such as higher GPC elution volume [233], lower intrinsic viscosity [234], lower translational friction coefficient [235], neutron scattering functions more rapid decrease of second virial coefficient with molecular weight [236], and higher critical solution temperature [237]. 

The hydrodynamic virial coefficient, Iq, is defined as the concentration coefficient in D=Dq(1+Jcj)C+...) Dq is the value of D at infinite dilution kj)= 2A2M - kf-V2 where M is the polymer molecular weight and kf describes the concentration dependence of the friction coefficient, f where f=fQ(l+k ) and V2 is the partial specific volume, kj) is thus the sum of a static factor, proportional to the second virial coefficient, A2, and the concentration dependence of the friction coefficient. Expressions for kf have been... 

Sedimentation Coefficients, Diffusion Coefficients, Partial Specific Volumes, Frictional Ratios, and Second Virial Coefficients of Polymers in Solution, ... 

To overcome the divergence of the variance (V2(t)), we introduce into Eq. (121) the velocity-dependent dissipative nonlinear form y(V) for the friction coefficient [101,105]. We require y(V) to be symmetric in V [105], assuming the virial expansion up to order 2N... 

It is not easy to predict the osmotic pressure 11 and the friction coefficient / When 0 is not too large, a virial expansion can be sufficient, i.e.. 

The macromolecular friction coefficient in dilute solution can be written as a virial expansion ... 

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