Development of an equation for potentiometric titration of polyelectrolytes using a periodic lattice model. A numerical analysis of interactions among ionizable groups.

A numerical method is presented for analysing the potentiometric titration behavior of linear polyelectrolytes. A polyelectrolyte molecule is treated as a one-dimensional lattice containing a large number of lattice points, each of which has an identical ionizable group. In this method, the polyelectrolyte model lattice is divided into identical repeating unit cell systems with a finite number of ionizable groups to calculate the thermodynamic partition function of the system of polyelectrolyte solution. The electrostatic interaction between ionized groups adopted in the present study is given by the Debye-Hückel type screened Coulombic potential. The titration behavior as well as several thermodynamic quantities is derived by making a canonical ensemble summation of all states in a unit cell system under an appropriate periodic boundary condition. This method serves as a model of the two-step ionization often appearing in polyions with strong neighboring interactions such as homo- and copolymers of maleic acid. Several characteristics of the titration behavior of these polyelectrolytes are well reproduced by using a lattice model with pairwise intervals, including the effects of hydrogen bond formation and change in dielectric constant of the medium around an ionizable group. In addition, this method is valid for a more detailed analysis of the titration behavior of polyelectrolytes with various kinds of arrangements of charged groups.