By Stuart A. Rice
This sequence offers the chemical physics box with a discussion board for severe, authoritative reviews of advances in each zone 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 info for Advances in Chemical Physics, Volume 131
110), we use the Kirkwood–Riseman approximation of replacing ann0 by the values asymptotically valid for large jnj and jn0 j, ann0 8 pﬃﬃ < 832 $ 1=2 : 2 dnn0 for n ¼ 0 ¼ n0 for n 6¼ 0 jnj ð113Þ It follows from Eqs. (103) and (108) that X 0 hrj i ¼ R_ X i fi i R_ N ¼ 2 0 ð1 dxfðxÞ À1 0 ^ ¼ R_ N f 0 ð114Þ 22 m. muthukumar ^ is given by Eq. (110) as f 0 1 ^ ¼ f pﬃﬃ 0 1 þ 832 h ð115Þ By combining Eqs. (98) and (114), the translational friction coefﬁcient is given by ft ¼ h ft ¼ h N pﬃﬃ i 1 þ 832 h N 1þ i pﬃﬃﬃ pﬃﬃ N 8 2 1=2 3Z0 ð12p3 ‘‘1 Þ ð116Þ ð117Þ In the free-draining limit of no hydrodynamic interactions, we have ft ¼ N ð118Þ When hydrodynamic interactions are present, we obtain 3Z ft ¼ p0ﬃﬃﬃ ð12p3 N‘‘1 Þ1=2 8 2 ð119Þ Recalling that ‘1 =‘ð¼ hR2 i=N‘2 Þ is the expansionp factor for ﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ ﬃ the mean-square end-to-end distance and the radius of gyration Rg is hR2 i=6 within the uniform expansion approximation, we have pﬃﬃﬃ 9 3=2 3 p ft ¼ p Z0 Rg ¼ ð6pZ0 Rg Þ 4 8 & N; low salt $ 3=5 high salt N ; ð120Þ ð121Þ Although ft $ N in both the non-free-draining limit for low salt solutions and the free-draining limit, the terms appearing as prefactors are qualitatively different.
295Þ Alternatively, Eq. (295) can be rewritten in terms of the intrinsic viscosity given by Eq. (216) as Z À Z0 ¼ c½Z þ kH c2 ½Z2 þ Á Á Á Z0 ð296Þ where ½Z ’ 1:616 cÃ ð297Þ 48 m. muthukumar and the Huggins coefﬁcient kH is kH ’ 1:57 ð298Þ This value of kH is actually low by an order of magnitude for dilute suspensions of charged spheres of radius Rg . This is due to the neglect of interchain correlations for c < cÃ in the structure factor used in the derivation of Eqs. (295)–(298). If the repulsive interaction between polyelectrolyte chains dominates, as expected in salt-free solutions, the virial expansion for viscosity may be valid over considerable range of concentrations where the average distance between chains scales as cÀ1=3 .
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.
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