Thermodynamics of Self-Assembly and Supramolecular Transitions Using Enhanced Sampling

Computational studies of self-assembly have the potential to provide rich insights into their underlying thermodynamics and identify optimal system conditions for applications such as nanomaterial synthesis or drug delivery. However, both self-assembly and supramolecular transitions can be hindered by free energy barriers, rendering them rare events on molecular time scales and making it challenging to sample them. Here, we show that the use of enhanced sampling techniques, when combined with a judiciously chosen set of order parameters, offers an efficient and robust route for characterizing the thermodynamics of self-assembly and supramolecular transitions. Specifically, we show that transitions between states with different periodicities or symmetries can be reversibly sampled by biasing a relatively small number of Fourier components of the particle density. We illustrate our approach by computing the free energy required to cleave a liquid slab and estimating the corresponding liquid-vapor surface tension. We also characterize the free energetics of the transition between spherical and rod-shaped droplets. These results serve as a first step toward the development of a systematic computational framework for exploring transitions in diverse supramolecular systems, such as surfactants or block copolymers, and characterizing the thermodynamics of their self-assembly.