Download Advances in Chemical Physics, Volume 131 by Stuart A. Rice PDF

By Stuart A. Rice

This sequence presents the chemical physics box with a discussion board for serious, 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 real drinks 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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Additional info for Advances in Chemical Physics, Volume 131

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Substitution of Eq. (239) for R_ j in Eq. (238) enables us to write a phenomenological equation for rðkÞ: X q qU rðkÞ ¼ À þ fr ðkÞ þ fE ðkÞ Lkk0 qt qrðk0 Þ k0 ð244Þ where fr ðkÞ ¼ nX ik Á f vj eikÁRj  j ð245Þ and fE ðkÞ ¼ À X m ik Á Eðk0 Þrðk À k0 Þ N k0 ð246Þ polyelectrolyte dynamics 41 The Onsager coefficient Lkk0 is given by the fluctuation–dissipation theorem: h fr ðk; tÞfr ðk0 ; t0 Þi ¼ 2kB TLkk0 dðt À t0 Þ ð247Þ h fr ðk; tÞi ¼ 0 ð248Þ and Combining Eqs. (35), (242), (243), (245), (247), and (248), we obtain ð L kk0 ¼ dj k Á ð1 À ^j ^j Þ Á k0 rðk þ jÞrðk0 À jÞ ð2pÞ3 ½Z0 j2 1 þ Æðjފ ð249Þ Upon preaveraging, we obtain Lkk0 ¼ dðk þ k0 ÞLk ð250Þ ð c dj k2 ½1 À ðÀ^k Á ^j Þ2 Š Lk ¼ gðk þ jÞ  ð2pÞ3 ½Z0 j2 þ Æð jފ ð251Þ where with gðkÞ being the scattering function per segment, gðkÞ ¼  hrðkÞrðÀkÞi c ð252Þ Within the effective medium theory, the potential functional can be written as [3] U  X rðkÞrðÀkÞ ¼ kB T 2c k gðkÞ ð253Þ Substituting the results of Eqs.

Even in semidilute solutions, Eqs. (278)–(281) show that m is independent of N: ( 0 0 kRg ( 1 c N ; m $ N0 ð322Þ pffiffi ; kRg ) 1 c In addition, we predict that m is independent of polyelectrolyte concentration c at low salt concentrations and decreases with c as the salt concentration is polyelectrolyte dynamics 53 increased. There is also an additional salt concentration dependence of m as shown in Eq. (281). It is to be remarked that in the Rouse regime, the Hu¨ckel law of electrophoretic mobility is valid, m¼ QD kB T ð323Þ whereas in dilute solutions this law is significantly modified, m¼ QD MðkRg Þ kB T ð324Þ where MðkRg Þ is defined in Eq.

1. Self-Translational Diffusion Coefficient Equations (116) and (271) give D in dilute and semidilute limits. For low polyelectrolyte concentrations, we have ( D$ ; kRg ( 1 kRg ) 1 ð325Þ c0 N; 1 ffiffi p ; N c kRg ( 1 kRg ) 1 ð326Þ 1 N ; 1 N 3=5 In the Rouse regime we have derived ( D$ The numerical prefactors for the relations in the above two equations are given in Eqs. (116) and (271).

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