Study of entropy-driven self-assembly of rigid macromolecules

A simple model composed of two rigid macromolecules (adsorbents) immersed in a large number of small molecules (adsorbates) is used to study entropy-driven association processes. The surfaces of the adsorbents are capable of adsorbing the smaller adsorbates. The partition function of the model is obtained analytically. The probability of dimerization and the number of adsorbed molecules are shown to depend on the enthalpy and the entropy differences between the assembled and the disassembled states. Under certain conditions, dimerization of the macromolecules occurs with increasing temperature. This entropy-driven self-assembly is originated from an overall entropy gain due to the release of the adsorbed small molecules, leading to a large peak in the heat capacity due to the dimer formation. The desorption of the adsorbates induces a sharp change in the first-order derivative of the free energy, resulting in another large peak in the heat capacity. A temperature-induced re-entrance into the dimer state is also contained in the model.