Lytle and Sing developed a more elaborate ion-pairing theory that they dubbed the 'transfer matrix model' of complex coacervation, which models the electrostatic interactions of a polyelectrolyte with its surroundings by mapping to a one-dimensional adsorption model. This mapping considered a test polyelectrolyte as a substrate, onto which the oppositelycharged species (i.e. salt and polymer) was adsorbed. This was able to be solved, in some cases analytically, by the transfer matrix method that is commonly used to solve (for example) the one-dimensional Ising model or the Zimm-Bragg model of coil-helix transitions. They proposed the following free energy: