Diffusion of Polyelectrolyte Chains

Although the direct consequences of the Einsteinian dynamics of the center-of-mass diffusion of a polyelectrolyte chain in dilute solutions. 

The behavior of polyelectrolyte molecules cannot be interpreted as arising solely from the polymer. The coupled behavior of the chain and its counterion cloud must be treated together. The counterions exert an electric field, even in the absence of any externally imposed electric field, in the immediate environment of a charged segment. This field in turn modifies the collective diffusion coefficient of the polyelectrolyte. The polyelectrolyte molecule must be treated not as an individual particle but as a quasiparticle along with its counterion cloud. 

Let pp (r, t) be the local number density of polymer chains in the volume element r at time f. By addressing the induced electric field Eind (r) arising from the counterion cloud in the volume element r that acts on the polymer chains, 

Dc is the cooperative diffusion coefficient of the chain if the couphng to the counterion cloud were to be absent. In dilute solutions, Dc is inversely proportional to the radius of gyration, is the velocity of the polyelectrolyte chains and ii is the electrophoretic mobility of the polyelectrolyte chain (discussed in Section 7.4). From the Poisson equation (Equation 3.9), we get 

Defining the fluctuations in the concentrations of the polyelectrolyte chains and counterions. 

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