By Stuart A. Rice
This sequence presents 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 beverages 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, Vol.131 (Wiley 2005)
Muthukumar so that both the real and imaginary parts are proportional to ð 1 ½Z $ o dq 6n q þ o2 $ oÀð3nÀ1Þ=3n ð309Þ Equation (307) gives the intrinsic modulus as ½G $ o1=3n 2. 1 ð314Þ These apparent strange results are to be contrasted with the results at high salt concentrations (n ! 1 51 ð316Þ The above general results and the asymptotic values for high and low salt concentrations are included in Table II. Although several experimental studies [22, 62, 63] have been reported on Z, G, and the compliance of polyelectrolyte solutions, systematic investigations on the frequency dependence is still lacking.
At low salt conditions, D is independent of polyelectrolyte concentration. The crossover between these asymptotic results is described by Eq. (271). B. Electrophoretic Mobility Analogous to the derivation in dilute solutions, m is given by m ¼ QðG00 þ A00 Þ ð273Þ Combining Eqs. (228) and (144), AðrÞ is given by AðrÞ ¼ r 1 k2 x2H ðeÀkr À eÀxH Þ 6pZ0 r ðk2 x2H À 1Þ ð274Þ Substituting this result in Eq. (148), A00 becomes A00 ! 1 k2 x2H Rg MðkRg Þ À M ¼ xH 6pZ0 Rg ðk2 x2H À 1Þ ð275Þ where the function M is defined as ð N À1 X N À1( ÀxRij ) Rg X e 2Rg 1 k2 SðkRg Þ ¼ dk 2 MðxRg Þ 2 N i¼0 j¼0 Rij pN 0 ðk þ x2 Þ ð276Þ Using Eqs.
266Þ The coupled diffusion coefficient Df is calculated using Eqs. (255)–(263). We now present the key results of the above equations. A. Translational Friction Coefficient The translational friction coefficient is given by ft ¼ N À1 X N À1 X hGÀ1 ðRi ; Rp Þi ð267Þ i¼0 p¼0 The self-translational diffusion coefficient D is related to ft by the Stokes– Einstein relation and is given by D¼ N À1 X N À1 kB T kB T X kB TG00 ¼ 2 hGðRi À Rp Þi ft N i¼0 p¼0 Using Eqs. # R2 g kB T 2xH 2 xh xH Rg x2 1 À pﬃﬃﬃ þ D¼ 1 À e H erfc Rg xH 6pZ0 Rg Rg p Rg ð268Þ ð269Þ This reduces to the result of Eqs.