ELECTROPHORETIC MOBILITY OF WORMLIKE CHAINS .2. THEORY

The theoretical reduced electrophoretic mobility u' of a wormlike cylinder having discrete sites along its axis is proportional, in the long-chain limit, to the average electrostatic potential <psi> on the surface of shear. The proportionality constant is the same as that for the uniformly charged cylinder (UCC). Short chains are predicted to have somewhat smaller u' values due to end effects. The treatment, which neglects ion-atmosphere relaxation, uses the Burgers method and the Yamakawa-Fujii chain model. As for the latter, the adjustable parameters are the Kuhn length, A(K), and the cylinder radius, a, which can be determined independently from hydrodynamic data evaluated in terms of the same model. The computed value of u' then depends only on linear charge density along the chain contour and the method chosen to evaluate the surface potential. Numerical integration with use of the Debye-Huckel assumptions for the hyaluronate polyion (a = 0.55 nm) leads to predicted u' values for unperturbed (A(K) = 8.7 nm), expanded (or "frozen-worm"), and rodlike models of the polyion. Corrections for the nonlinear effects of the Poisson-Boltzmann potential and ion-atmosphere relaxation, as computed for the UCC, lead to good agreement for the expanded model with experimental results for hyaluronate. Use of the same chain parameters leads to similarly good agreement with experiment for polysaccharides (polygalacturonate, alginate, and chondroitin 4-sulfate) having one charge per monosaccharide unit. The UCC model having the same value of a gives slightly lower results for u'. The discrete-site wormlike model predicts more accurately than the UCC model the ratio of u' to the slope m = (DELTA-pK/DELTA-alpha)I of plots of the apparent dissociation constant pK against degree of dissociation alpha from potentiometric titration. The discrepancy results from inclusion of self-energy of charge formation in the charging free energy traditionally used to interpret m in terms of the UCC model.