ISING-MODELS AND ACID-BASE PROPERTIES OF WEAK POLYELECTROLYTES

Ionization equilibria of weak polyelectrolytes and their oligomeric an alogs are discussed in terms of the Ising model. Within the Ising mode l one treats the thermal statistics of a collection of interacting sit es, which can be either protonated or deprotonated. The basic paramete rs of the model are microscopic pK values of individual groups and var ious interaction parameters between pairs and possibly triplets of sit es. By performing the appropriate thermal average, one can obtain the titration curve of the system considered. For systems with finite numb er of ionizable sires, we recover the classical description in terms o f successive protonation equilibria. Thereby one can express the ioniz ation constants in terms of the interaction parameters. For system wit h infinite number of sites, such as Linear polyelectrolytes, the titra tion curves fan be also calculated explicitly. We discuss three illust rative examples in more detail: (i) a simple model for linear, weak po lyelectrolytes; (ii) a refined model for same type of system which des cribes poly(ethylene imine) and its oligomeric analogs quantitatively; (iii) simple mean-filed model for polymeric interfaces, such as the s urface carboxylated latex particles.