Exact matrix treatment of an osmotic ensemble model of adsorption and pressure induced structural transitions in metal organic frameworks.

Here we present an exactly treated quasi-one dimensional statistical mechanical osmotic ensemble model of pressure and adsorption induced breathing structural transformations of metal-organic frameworks (MOFs). The treatment uses a transfer matrix method. The model successfully reproduces the gas and pressure induced structural changes which are observed experimentally in MOFs. The model treatment presented here is a significant step towards analytical statistical mechanical treatments of flexible metal-organic frameworks.