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By Stuart A. Rice
This sequence presents the chemical physics box with a discussion board for serious, authoritative reviews of advances in each quarter of the self-discipline. quantity 131 comprises chapters on: Polyelectrolyte Dynamics; Hydrodynamics and Slip on the Liquid-Solid Interface; constitution of Ionic drinks and Ionic Liquid Compounds: Are Ionic beverages real beverages within the traditional Sense?; Chemical Reactions at Very excessive strain; Classical Description of Nonadiabatic Quantum Dynamics; and Non-Born Oppenheimer Variational Calculations of Atoms and Molecules with Explicitly Correlated Gaussian foundation features.
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Additional resources for Advances in Chemical Physics, Vol.131 (Wiley 2005)
Sample text
For ^ 00 is identically zero so that k ¼ 0, A m¼ Q N0 $ Z0 ft ð172Þ ^ 00 cancels 1=ft exactly in the non-free-draining limit and the For k 6¼ 0, a part of A remainder is dependent on the structure factor of the polymer and the size exponent n. For large values of kRg , m becomes m$ N0 1 Z0 knÀ1 ; kRg ) 1 ð173Þ While m is independent of N at all salt concentrations, it decreases with the salt concentration with an apparent power law, m $ N 0 kÀa ð174Þ where a changes smoothly from zero at low salt concentrations to 2=3 at high salt concentrations.
258) for the segment density of the polyelectrolyte is coupled to the equation of motion for ri, q 4p X zi ri ðkÞ ri ðkÞ ¼ ÀDci k2 ri ðkÞ À ri0 mi qt E i ð259Þ where Dci and mi are the diffusion coefficient and the electrophoretic mobility of the ith species. The noise term is ignored in the above equation. Assuming that small ions, i 6¼ 1, relax faster than the polyelectrolyte chains, qtq ri ðkÞ ¼ 0, Eqs. (258) and (259) get decoupled to finally give ! q k21 M1 2 rðkÞ ð260Þ rðkÞ ¼ ÀDc k 1 þ 2 ðk þ k2 Þ qt where k21 ¼ 4p Q2 c EkB T N ð261Þ kB Tm QDc ð262Þ zi Dci kB T ð263Þ and M1 ¼ In obtaining Eq.
255), the cooperative coefficient Dc is given by ð kB T dj ½1 À ðk Á jÞ2 gðk þ jÞ ð282Þ Dc ¼ Z0 ð2pÞ3 ðj2 þ xÀ2 gðkÞ H Þ The scattering function gðkÞ is a function of static correlation length x as given by Eqs. (225)–(227). For semidilute solutions at high salt concentrations, Dc follows from Eqs. (226) and (282) in the k ! 0 limit, Dc ¼ kB T xH 6pZ0 x ðx þ xH Þ ð283Þ In infinitely pffiffiffi dilute solutions we have xH ! 1 and the static correlation x ¼ Rg = 3 as already discussed. In this limit, Dc of Eq.