Electrophoretic Fluctuation Theory

In this section the foregoing analysis is applied to the analysis of concentration fluctuations (Freidhof and Berne, 1975). This section covers essentially the same ground as Section 9.2, but from the point of view of nonequilibrium thermodynamics. There are several different conclusions. 

Our starting point is Eqs. (13.7.8) and (13.3.8c) (with no reaction). Expanding V/r in terms of the molar concentration gives fik = HI(dfxk/dcl) cr When this is substituted into Eq. (13.7.8) the fluxes become 

Substitution of Eq. (13.8.1) into Eq. (13.3.8c) gives the generalized diffusion equation of electrophoresis 

This equation—the primary equation of this section—is treated along the lines proposed in Section 9.3. 

The field E in Eq. (13.8.2) consists of a homogeneous external part Eo and an internal part Ej, that is, 

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Chapter 13 includes a short introduction to the theory of nonequilibrium thermodynamics. A discussion of frames of reference in the definition of transport coefficients is given and a systematic theory of diffusion is presented. Fluctuations in electrolyte solutions are analyzed, and the parameters measured in electrophoretic light-scattering experiments are related to conductance and to the transference numbers—quantities usually measured in conventional electrochemistry. 

Duke, T., Viovy, J.-L., and Semenov, A.N., Electrophoretic mobUity of DNA in gels. I. New biased reptation theory including fluctuations. Biopolymers, 34, 239,1994. 

The photomicrographic measurements refer directly to polymer motion under the influence of an external force. However, measurements of migration velocity v as a function of applied electrical field E show that some of these electrophoretic measurements were made in a low-field linear regime, in which the electrophoretic mobility jx is independent of E. Linear response theory and the fluctuation-dissipation theorem are then applicable they provide that the modes of motion used by a polymer undergoing electrophoresis in the linear regime, and the modes of motion used by the same polymer as it diffuses, must be the same. This requirement on the equality of drag coefficients for driven and diffusive motion was first seen in Einstein s derivation of the Stokes-Einstein equation(16), namely thermal equilibrium requires that the drag coefficients / that determine the sedimentation rate v = mg/f and the diffusion coefficient D = kBT/f must be the same. 

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