# An Ising Model for Metal-Organic Frameworks

## TL;DR

This paper introduces a 3D Ising model with a fixed framework structure to simulate condensation in metal-organic frameworks, showing similar phase behavior to real methane condensation in IRMOF-16.

## Contribution

It develops a minimal porous Ising model that captures the phase transition behavior of gas condensation in metal-organic frameworks, validated by Monte Carlo simulations.

## Key findings

- Both models exhibit a line of first-order phase transitions ending in a critical point.
- Critical behavior belongs to the 3D Ising universality class.
- Contrasts with other confinement phase transitions like capillary condensation.

## Abstract

We present a three-dimensional Ising model where lines of equal spins are frozen in such that they form an ordered framework structure. The frame spins impose an external field on the rest of the spins (active spins). We demonstrate that this "porous Ising model" can be seen as a minimal model for condensation transitions of gas molecules in metal-organic frameworks. Using Monte Carlo simulation techniques, we compare the phase behavior of a porous Ising model with that of a particle-based model for the condensation of methane (CH$_4$) in the isoreticular metal-organic framework IRMOF-16. For both models, we find a line of first-order phase transitions that end in a critical point. We show that the critical behavior in both cases belongs to the 3D Ising universality class, in contrast to other phase transitions in confinement such as capillary condensation.