Advances in Chemical Physics, Volume 131 by Stuart A. Rice PDF
By Stuart A. Rice
This sequence offers the chemical physics box with a discussion board for serious, authoritative reviews of advances in each region 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 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 features.
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83) in Eq. (85) and by performing q0 and o0 integrals, we obtain ð1 dq h½Rðs; tÞ À Rðs ; t Þ i ¼ 2 À1 2p 0 0 2 ð1 do À1 2p 0 Â½1 À cos½qðs À s0 ÞeioðtÀt Þ ^ ^ ðqÞq ðqÞq ðio þ 3kB ‘T1DðqÞ ÞðÀio þ 3kB T‘1DðqÞ Þ ð1 dq Â‘1 ðqÞ ¼ ^ ðqÞq2 2p 3kB T D À1 ! ÀjtÀt0 j 1 À cos½qðs À s0 Þe tq 2 2 ð86Þ The equal time correlation function, ð1 dq Â‘1 ðqÞ ½1 À cosðqLÞ h½RðL; tÞ À Rð0; tÞ2 i ¼ ^ ðqÞq2 0 p 3kB T D ð87Þ is the equilibrium result h½RðL; tÞ À Rð0; tÞ2 i ¼ L‘1 ð88Þ By comparing Eqs. (87) and (88), we get the following expression for Â: ^ ðqÞ Â ¼ 6kB T D ð89Þ Therefore, h½Rðs; tÞ À Rðs0 ; t0 Þ2 i follows as 0 0 2 h½Rðs; tÞ À Rðs ; t Þ i ¼ 2 ð1 0 jtÀt0 j dq ‘1 ðqÞ À tq 0 1 À cos½qðs À s Þe p q2 !
The concentration dependence of D in this limit can be obtained by assuming that D is proportional Ã to RÀ1 g fe ðc=c Þ and that the N-dependence of D should be consistent with the reptation law, ( 1 1 pﬃﬃ 2 ; kRg ( 1 cN D$ ð317Þ 1 1 ; kRg ) 1 c7=5 N 2 For concentrations between the Rouse and reptation regimes, D can depend more sensitively on N due to the entropic barrier mechanism [6, 64]. In this crossover region, D can be written as D $ N Àd ð318Þ where d can be 3 or even higher, depending on the concentration range and the system.
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.
Advances in Chemical Physics, Volume 131 by Stuart A. Rice