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 comprises chapters on: Polyelectrolyte Dynamics; Hydrodynamics and Slip on the Liquid-Solid Interface; constitution of Ionic drinks 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 capabilities.
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Extra resources for Advances in Chemical Physics, Volume 131
102). ð162Þ 28 m. muthukumar For a polyelectrolyte chain that has non-Gaussian statistics, exact analytical expression for B is not feasible. To get some insight, we notice that the static structure factor has the limiting behavior, ( k 2 R2 Nð1 À 3 g þ Á Á ÁÞ; kRg ( 1 SðkÞ ¼ ð163Þ $ 11=n ; kRg ) 1 ðk‘Þ Therefore we construct an approximate interpolation for SðkÞ as SðkÞ ¼ N 2 2 1 þ 2n 3 k Rg 1=2n Substituting this expression for SðkÞ, Eq. 0 $ 1 : 1=n 1=nÀ1 ; kRg ) 1 ð164Þ ð165Þ ð166Þ ZRg k This result reduces to 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. (290) to that of Eq. (291) as the salt concentration is increased. D. Viscosity The virial series of viscosity in polyelectrolyte concentration c can be obtained from Eq. (229) by iterating ÆðkÞ to the desired order in c and then combining with Eq.
59, we write the equation of motion for the collective coordinate of local segment density rðrÞ, rðrÞ ¼ n X N À1 X dðr À Rai Þ ð236Þ a¼1 i¼0 When we deﬁne the Fourier transform as rðkÞ ¼ N À1 nX eikÁRj j¼0 ð237Þ 40 m. muthukumar the evolution of rðkÞ follows as qrðkÞ n X ¼ ik Á R_ j eikÁRj qt j ð238Þ Analogous to the derivation of the effective Langevin equation for the chain in dilute solutions, we get in semidilute solutions R_ i ¼ À N À1 X GÀ1 ðRi À Rj Þ Á j¼0 qU m þ f vi þ E qRj N ð239Þ where N À1 qU X 3kB T ¼ ð2di; j À di; jþ1 À di; jÀ1 ÞRj þ =Ri VðRi À Rj Þ qRi l2 j¼0 !