In this last step, we assumed that all of the monomers were equivalent. The form of the expression in the natural log can be thought of as the single-site partition function, where the ion can be in two 'states'; the near-chain state is described by the integral term, while the away-from-chain state is given by the one. This is reinforced by the θ s,± factor, which enforces locality in the second, integral term. We then use the binomial theorem to rewrite as: