Show description

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.