By Stuart A. Rice
This sequence offers the chemical physics box with a discussion board for serious, authoritative reviews of advances in each sector 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 drinks 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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Additional resources for Advances in Chemical Physics, Volume 131
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.
For large values of kRg , m becomes m$ N0 Z0 knÀ1 1 ; kRg ) 1 ð173Þ While m is independent of N at all salt concentrations, it decreases with the salt concentration with an apparent power law, m $ N 0 kÀa ð174Þ where a changes smoothly from zero at low salt concentrations to 2=3 at high salt concentrations. In reaching these conclusions the role of hydrophobic effect is ignored. D. Coupled Diffusion Coefﬁcient As seen in the preceding section, the counterions play a crucial role in the mobility of the polyelectrolyte molecules.
In reaching these conclusions the role of hydrophobic effect is ignored. D. Coupled Diffusion Coefﬁcient As seen in the preceding section, the counterions play a crucial role in the mobility of the polyelectrolyte molecules. Even in the absence of an external electric ﬁeld, the counterions exert an induced electric ﬁeld in the immediate environment of a charged segment which in turn signiﬁcantly modiﬁes the collective diffusion coefﬁcient of the polymer. This additional contribution is absent for uncharged polymers, where the cooperative diffusion coefﬁcient Dc is given by the Stokes–Einstein law in dilute solutions, Dc ¼ kB T ft ð175Þ We discuss below how this law is modiﬁed by counterions for the case of polyelectrolyte solutions.