By Stuart A. Rice
This sequence offers the chemical physics box with a discussion board for severe, authoritative reviews of advances in each region 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 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 features.
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Extra resources for Advances in Chemical Physics, Vol.131 (Wiley 2005)
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. (119) and (175) for dilute solutions ðxH ) Rg Þ.
222)–(225), gðkÞ becomes in the high salt limit, 1 1 Á gðkÞ ¼ À w þ wk2c cx2 ðk2 þ xÀ2 Þ ð226Þ and in the low salt limit, gðkÞ ¼ 1 k2 cwc x4 ðk4 þ xÀ4 Þ ð227Þ In infinitely dilute silutions, l1 is proportional to N and N 1=5 , and consequently 3 the radius of gyration Rg is proportional to N and N 5 , respectively, in low-salt ðk ’ 0Þ and high salt ðkRg ) 1Þ limits as already pointed out. In semidilute solutions, l1 is proportional to cÀ1=2 and cÀ1=4 , and consequently Rg is proportional to cÀ1=4 and cÀ1=8 , respectively, in low salt and high salt limits.
Coupled Diffusion Coefficient By accounting for the coupling between the dynamics of polyelectrolyte chains and their counterions and salt ions and assuming that small ions relax faster than polyelectrolyte chains, we have derived Df to be Df ¼ Dc þ 4p Qcm Ek2 N ð329Þ In dilute polyelectrolyte solutions containing monovalent salt ions, Df is given by 8 À Á T 1 kRg ( 1 > < Z0 1 þ N ; ! 2 ð330Þ Df $ T zp Nc 1 1:17 kRg ) 1 > : Z0 Àw þ 4plB Á1=5 N 3=5 1 þ ðz2c c þ 2cs Þ ðkRg Þ2=3 ; k2 Therefore we expect Df , identified as the fast diffusion coefficient measured in dynamic light-scattering experiments, in infinitely dilute polyelectrolyte solutions to be very high at low salt concentrations and to decrease to self-diffusion coefficient DðkRg ) 1Þ as the salt concentration is increased.
Advances in Chemical Physics, Vol.131 (Wiley 2005) by Stuart A. Rice