By Stuart A. Rice
This sequence presents the chemical physics box with a discussion board for serious, authoritative reviews of advances in each quarter of the self-discipline. quantity 131 comprises 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, Vol.131 (Wiley 2005)
229) and (38), the viscosity change in the Rouse regime becomes Z À Z0 1 ¼ c2 ll31 L Z0 24 ð300Þ Using the concentration dependence of l1 under different salt conditions, we get & Z À Z0 c5=4 N; kRg ) 1 ð301Þ $ kRg ( 1 c1=2 N; Z0 E. Frequency Dependence The theory given above can be readily extended  to the frequency o dependence of shear viscosity ZðoÞ and shear modulus GðoÞ ¼ ioZðoÞ. 1 ð3nÀ1Þ 1 coÀ 3n coÀ2=3 coÀ4=9 co1=3n co1=3 co5=9 cN 3nÀ1 cN 2 cN 4=5 ocN 3nÀ1 ocN 2 ocN 4=5 cð3nÀ1Þ N c1=2 N c5=4 N oc1=3nÀ1 N oc1=2 N oc5=4 N 3n oÀ1=2 c2ð3nÀ1Þ oÀ1=2 c3=4 oÀ1=2 c9=8 1=2 3n=2ð3nÀ1Þ o c o1=2 c3=4 1 o2 c9=8 Note that n is the radius of gyration exponent in infinitely dilute solutions.
35), (242), (243), (245), (247), and (248), we obtain L kk0 ¼ ð dj k Á ð1 À ^j ^j Þ Á k0 rðk þ jÞrðk0 À jÞ ð2pÞ3 ½Z0 j2 1 þ ÆðjÞ ð249Þ Upon preaveraging, we obtain Lkk0 ¼ dðk þ k0 ÞLk ð250Þ ð c dj k2 ½1 À ðÀ^k Á ^j Þ2 Lk ¼ gðk þ jÞ ð2pÞ3 ½Z0 j2 þ Æð jÞ ð251Þ where with gðkÞ being the scattering function per segment, gðkÞ ¼ hrðkÞrðÀkÞi c ð252Þ Within the effective medium theory, the potential functional can be written as  U X rðkÞrðÀkÞ ¼ kB T 2c k gðkÞ ð253Þ Substituting the results of Eqs.
232)–(235), we now calculate the diffusion coefficients, electrophoretic mobility, and viscosity of semidilute polyelectrolyte solutions. Using G and Æ, the translational friction coefficient and the electrophoretic mobility can be calculated by simply replacing G by G in the respective formulas. Before we proceed to do this, we present the collective dynamics of monomer density and counterions. Following the method of Ref. 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.
Advances in Chemical Physics, Vol.131 (Wiley 2005) by Stuart A. Rice