By Stuart A. Rice
This sequence presents the chemical physics box with a discussion board for severe, authoritative reviews of advances in each sector of the self-discipline. quantity 131 contains chapters on: Polyelectrolyte Dynamics; Hydrodynamics and Slip on the Liquid-Solid Interface; constitution of Ionic drinks and Ionic Liquid Compounds: Are Ionic beverages actual 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 capabilities.
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Additional info for Advances in Chemical Physics, Volume 131
On the other hand, in the Rouse regime, Eq. (283) yields Dc $ T $ c3=4 Z0 x ð284Þ 46 m. muthukumar since xH $ x $ cÀ3=4 . For semidilute solutions at low salt concentrations, Dc follows from Eqs. (227) and (282): Dc ¼ ð 2kB T dj 1 ðk þ jÞ2 ðk4 x4 þ 1Þ 4 4 3Z0 ð2pÞ3 ðj2 þ xÀ2 k2 H Þ ½ðk þ jÞ x þ 1 ð285Þ The cooperative diffusion coefﬁcient in the salt-free limit is thus strongly k-dependent. In this limit the equilibrium scattering function gðkÞ exhibits a peak at kÃ ¼ xÀ1 . Approximating gðkÞ in Eqs.
265) and (266) dominates, Df becomes Df ¼ 4pQcm Ek2 N ð288Þ Writing m explicitly in terms of Rg and xH , Df is given by Df ¼ Zp2 c kB T NxH 2pZ0 ðZc2 c þ 2cs Þ R2g ð289Þ where salt ions are taken to be monovalent. In the salt-free limit, xH $ cÀ1=2 and R2g $ NcÀ1=2 so that Df $ T N 0 c0 Z0 ð290Þ Therefore, remarkably, the coupled diffusion coefﬁcient becomes independent of N and c in the Rouse regime of salt-free polyelectrolyte solutions. This is to be 47 polyelectrolyte dynamics contrasted with Eq.
Q 1 Rg 2 2 m¼ M À k xH MðkRg Þ 6pZ0 Rg ð1 À k2 x2H Þ xH ð277Þ polyelectrolyte dynamics 45 This reduces to Eq. (156) in the inﬁnite dilution limit ðxH ! 1Þ. In the Rouse regime (xH small ), the electrophoretic mobility becomes Q Rg M m¼ ð278Þ 6pZ0 Rg xH Substituting the asymptotic form of MðRg =xH Þ, we obtain m¼ QxH 2pZ0 R2g ð279Þ Noticing the expression for D in the Rouse limit, Eq. (270), we see that m becomes m¼ QD kB T ð280Þ in the Rouse regime. The power laws of m on N and polyelectrolyte concentration c follow from Eq.