Exact affinity distributions for linear polyampholytes and polyelectrolytes

Ising models have been used to describe acid-base behavior of linear polyampholytes and polyelectrolytes. Alternatively, such titration curves are often interpreted in terms of an affinity distribution (pK spectrum). Here we show that such affinity distributions exist if the zeros of the grand partition function of the corresponding Ising model are negative and real. Furthermore, we derive the exact affinity distributions for various Ising models of linear polyelectrolytes and polyampholytes. Applications of the Ising model to the titration behavior of poly(acrylic acid) and poly(ethylenimine) are discussed.