The Effective Coordination Number Distribution: An Insightful Property to Understand Interaction Parameters

The coordination number has been an integral part of classical theories of polymer mixtures to describe the effective interaction parameters between different species. Building upon the pioneering concepts developed by Morse and co-workers on the effective coordination number z_inf, a quantity that includes correlation hole effects in the limit of infinite chain length, we formulate a new expression for the effective interaction parameter based solely on the properties of the distribution of z_inf. We have tested this theory in multiple coarse grained simulations with excellent results, both in transferability and universality. Furthermore, the interpretation of the different terms in this series becomes straightforward which lends itself to explain the origin of different terms of fitted incompatibility parameters. Also, we show how to exploit certain properties of this series to train neural networks to learn free energies on-the-fly. This work should be useful to clarify the origin of certain contribution to interaction parameters, as well as allow researchers to compare results across different models.