By Stuart A. Rice
This sequence offers the chemical physics box with a discussion board for serious, authoritative reviews of advances in each zone 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 actual 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, Vol.131 (Wiley 2005)
186) reduce to Qdck þ zc drc;k ¼ ðk2 k2 Qdck þ k2c Þ ð190Þ Substituting this result in Eq. (186), we obtain ! qdck 4p "cmQ ¼ À Dc þ dck qt E ðk2 þ k2c Þ ð191Þ Therefore, we can write the equation for the time evolution of fluctuations of polymer concentrations as qdck ¼ ÀDf dck qt ð192Þ 32 m. muthukumar where Df is the effective diffusion constant. Let us call Df as the coupled diffusion coefficient to contrast with the cooperative diffusion coefficient Dc . In general, Df depends on k. Df ¼ Dc þ 4p "cmQ E ðk2 þ k2c Þ ð193Þ 4p "cmQ E k2c ð194Þ In the limit of k !
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 ð6pZ0 Rg Þ ft ¼ p Z0 Rg ¼ 4 8 & N; low salt $ 3=5 N ; high salt 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.
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.