Algorithms for Partition Function Calculation Applied to Self-Assembly of Patchy Particles

The direct calculation of partition functions can be useful in understanding the thermodynamics of self assembly. We present algorithms to efficiently calculate both the energies and entropies of clusters of building blocks. Our methods rely on shape-matching techniques [1] to distinguish clusters and numerical integration of vibrational and rotational entropic contributions of each cluster to the partition function. The assembly pathways we obtain by constructing a network of connected ensembles are then used to inform building block design.

[1] Keys AS and Iacovella CR and Glotzer SC, Annual Reviews of Condensed Matter Physics, 2 (2011)