By Stuart A. Rice
This sequence presents the chemical physics box with a discussion board for severe, authoritative reviews of advances in each quarter of the self-discipline. quantity 131 contains chapters on: Polyelectrolyte Dynamics; Hydrodynamics and Slip on the Liquid-Solid Interface; constitution of Ionic beverages 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 services.
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Extra resources for Advances in Chemical Physics, Vol.131 (Wiley 2005)
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. (260), the condition mi ¼ 43 polyelectrolyte dynamics valid for small ions i 6¼ 1 has been used. It readily follows from Eq. (262) that the time correlation function hrðk; tÞrðÀk; 0Þi decays exponentially with time with rate Df k2 , hrðk; tÞrðÀk; 0Þi $ expðÀDf k2 tÞ ð264Þ where the ‘‘coupled diffusion coefficient’’ Df is given by Df ¼ Dc 1 þ k21 M1 ðk2 þ k2 Þ !
This requires (a) gathering of experimental data on well-characterized polyelectrolyte solutions and (b) obtaining the relationships between the various transport coefficients. Such data are not currently available, and experiments of this type are out of fashion. In addition to these experimental challenges, there are many theoretical issues that need further elaboration. A few of these are the following: 1. Although the coupling of counterion dynamics and polyelectrolyte dynamics has been accounted for at the mean field level, the relaxation of counterion cloud needs to be included in comparing with experimental data.
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. (287) for the cooperative diffusion coefficient Dc and with Eq. (272) for the translational diffusion coefficient D. In the Rouse regime at high salt concentrations, xH $ cÀ3=4 and R2g $ NcÀ1=4 so that Eq. (289) yields pﬃﬃﬃ Zp2 c T Df $ Z0 ðZc2 c þ 2cs Þ ð291Þ The coupled diffusion coefficient Df decreases from the value of Eq.