Potential medium-induced

Flexible polyelectrolytes exhibit conformational variations when the interaction strength (ZB) or the density of a system is changed. Hence, the structure factor is no longer an a priori known quantity but has to be determined in a self-consistent manner. This is achieved by casting the underlying multichain interactions into a medium-induced interaction potential among the... 

To elucidate the structure of a solution of flexible polyelectrolytes, we again use the integral equation theory approach of Sect. 2.2. The necessary structure factor is determined self-consistently using the reference chain (9) of the last section. The intermolecular interactions are taken into account by a medium-induced intramolecular potential [35, 47,48]... 

The monomer-monomer correlation functions of flexible polyelectrolytes exhibit qualitatively the same behavior as those for rod-like molecules. The conformational changes, however, result in more pronounced and shifted peaks. From Fig. 8 we deduce a shift of the peaks of flexible chains to larger distances compared to those of rod-like chains. This is a consequence of a smaller overlap between flexible chains compared to the one between rodlike molecules. Naturally, the effect is most pronounced for densities larger than the overlap densities. The increased peak intensity corresponds to a more pronounced order in the system of flexible chains, and is a result of the more compact structure of a polymer coil. (The structural properties of flexible polyelectrolytes without medium-induced potential have been studied in [48].)... 

Chandler and co-workers constructed a tractaUe medium-induced potential in the context of the solvated electron problem [93,94]. Their self-consistenc pair approximation also applies to real polymeric fluids, and for homopolymers with neglect of explicit chain end efi s approximation one has [92-94]... 

This result can be deduced from a number of perspectives such as renormalized perturbation theory [93], polymer density fimctional theory [95,96], and Per-cus functional expansion methods [97]. The medium-induced pair potential is determined by the direct correlation function and collective density fluctuations which are both functionally related to the intramolecular pair correlations via the PRISM equation. Hence, a coupled intramolecular/intermolecular theory is obtained. 

This approximate form can be derived many ways from renormalized second-order perturbation theoryGaussian (linear response) density field theory,or via density functional expansions. Pictorially, the medium-induced potential between a pair of tagged sites is determined by coupling to the surroundings via an effective potential (direct correlation function), which is mediated by density fiuctuations of the condensed phase. The integrated strength of the medium-induced potential is... 

Figure 32. Typical high-density (po lj = 1) medium-induced potential between...

The final and less commonly dealt-with member of the family of electrokinetic phenomena is the sedimentation potential. If charged particles are caused to move relative to the medium as a result, say, of a gravitational or centrifugal field, there again will be an induced potential E. The formula relating to f and other parameters is [72, 77]... 

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