Polyelectrolytic aspects of the titration curve. The semi-flexible model.
An analysis is given of the theoretical approach to the quantitative description of proton dissociation curves for weak polyacids. The basic model of the counterion condensation theory has been used, with the modification reported in the preceding study (S. Paoletti, A. Cesàro, C. Arce Samper and J.C. Benegas, Biophys. Chem. 34 (1989) 301). In this paper we demonstrate the effect of relaxing the hypothesis of a rigid conformation on the polyelectrolytic properties of weak polyacids. As an application of the present approach, a description is given of the titration curves for two weak polyacids, poly(DL-glutamic acid) (PDLGA) and poly(L-aspartic acid) (PLAA).
We will now develop the approximation theory appropriate for the finite elements developed in Chapter 3. We take a constructive approach, defining an averaged version of the Taylor polynomial familiar from calculus. The key estimates are provided by some simple lemmas from the theory of Riesz potentials, which we derive. As a corollary, we provide a proof of Sobolev’s inequality, much in the spirit given originally by Sobolev.