A graph theory-based statistical mechanics approach for nucleation of nano-porous materials

Understanding the nucleation of weak electrolytes from solution is critical for the design and synthesis of crystalline nano-porous materials such as metal-organic frameworks (MOFs) and zeolites. However, existing simulation approaches to model nucleation are often extremely limited when applied to weak electrolytes. We developed a novel graph theory-based sampling approach that overcomes limitations of existing approaches, especially, for bulk solvent systems. Our method seeks to exploit the property of materials whose crystal structure exhibit directional bonding and thus can be described as a "graph" of connected monomers. By utilizing a rigorous statistical-mechanics approach, we generate a nucleus of size N+1 from size N by performing a Monte Carlo type attachment of a solute to the surface of a nucleus followed by a thermodynamic integration step to turn on interactions. A "bootstrapping" approach in the nucleus size (N) is then used to generate an ensemble of representative nuclei and their corresponding free energies. To validate our approach, we begin with an ideal system of non interacting particles and evaluate the free energy dependence with nucleus size. The free energies show excellent agreement with reference values obtained from a GCMC (Grand Canonical Monte Carlo) approach. Subsequent work will extended our approach to treat systems with more complex interactions and geometries.