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

By Stuart A. Rice

ISBN-10: 0471445266

ISBN-13: 9780471445265

ISBN-10: 0471739456

ISBN-13: 9780471739456

This sequence offers 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 drinks 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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18 m. muthukumar where the proportionality factor  is to be determined below from a consideration of equilibrium. The correlation function h½Rðs; tÞ À Rðs0 ; t0 ފ2 i follows from its Fourier transform as ð ð dq 1 dq0 1 do h½Rðs; tÞ À Rðs ; t ފ i ¼ À1 2p À1 2p À1 2p ð1 do0 ÀiðqÀq0 ÞsÀiðoÀo0 Þt 0 0 0 ½e À 2eÀiqs À iot þ iq s þ io t À1 2p 0 0 ð1 2 0 0 0 ~ ðq; oÞ Á R ~ à ðq0 ; o0 Þi þ eÀiðqÀq Þs ÀiðoÀo Þt ŠhR ð85Þ Substituting Eq. (83) in Eq. (85) and by performing q0 and o0 integrals, we obtain ð1 dq h½Rðs; tÞ À Rðs ; t ފ i ¼ 2 À1 2p 0 0 2 ð1 do À1 2p 0 ½1 À cos½qðs À s0 ފeioðtÀt Þ Š ^ ^ ðqÞq ðqÞq ðio þ 3kB ‘T1DðqÞ ÞðÀio þ 3kB T‘1DðqÞ Þ ð1 dq ‘1 ðqÞ ¼ ^ ðqÞq2 2p 3kB T D À1 !

B. Translational Friction Coefficient The translational friction coefficient ft of the polymer chain at infinitelyPdilute solutions is calculated by equating the net force acting on the chain, À i hri i, 0 0 and Àft R_ , where R_ is the net drift velocity of the center of mass of the chain X i hri i ¼ ft R_ 0 ð98Þ 20 m. muthukumar If there is no velocity field in the absence of polymer (F ¼ 0), ri follows from Eq. (43) as X hri i ¼ hR_ i i À  hGðRi À R j Þ Á rj i ð99Þ j6¼i 0 Assuming that R_ i is the same as the center-of-mass velocity R_ for all i and invoking the preaveraging approximation, we get 0 hri i ¼  R_ À  X hGðRi À R j Þihrj i ð100Þ j6¼i With the assumption of uniform chain expansion due to potential interactions, we have ( ) 1 1 hGðRi À Rj Þi ¼ ð101Þ 6pZ0 jRi À Rj j  1=2 1 1 ð102Þ ¼ Z0 6p3 ‘‘1 ji À jj Defining hrj i  fi  R_ 0 ð103Þ Eq.

90Þ 19 polyelectrolyte dynamics The mean-square displacement of a labeled monomer is 0 2 h½Rðs; tÞ À Rðs; t ފ i ¼ 2   jtÀt0 j dq ‘1 ðqÞ À tq 1Àe p q2 ð1 0 ð91Þ When hydrodynamic interaction dominates, tq $ qÀ3n , so that 0 2 h½Rðs; tÞ À Rðs; t ފ i $ ð1 dq qÀð2nþ1Þ ð1 À eÀq 3n jtÀt0 j Þ ð92Þ 0 $ jt À t0 j 2=3 ð93Þ The incoherent dynamical structure factor is given by Sinc ðk; tÞ ¼ expðÀk2 h½Rðs; tÞ À Rðs; t0 ފ2 i=6Þ 0 2=3 $ expðÀk jt À t j 2 ð94Þ Þ where k is the scattering wave vector. Sinc ðk; tÞ is therefore of the form exp½Àðk3 jt À t0 jÞ2=3 Š ð95Þ so that the decay rate is proportional to k3 .

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


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