# Thermodynamics of Guest-Induced Structural Transitions in Hybrid Organic-Inorganic Frameworks

## TL;DR

This paper introduces a thermodynamic framework based on experimental adsorption isotherms to analyze guest-induced structural transitions in hybrid organic-inorganic frameworks, enabling the determination of free energy differences and understanding transition mechanisms.

## Contribution

It presents a novel thermodynamic approach to quantify free energy differences in guest-induced transitions, applicable to flexible hybrid materials, and classifies transition types based on adsorption thermodynamics.

## Key findings

- Derived conditions for double structural transitions and two-step isotherms.
- Validated the model with three case studies on different hybrid frameworks.
- Showed the model's robustness and wide applicability.

## Abstract

We provide a general thermodynamic framework for the understanding of guest-induced structural transitions in hybrid organic-inorganic materials. The method is based on the analysis of experimental adsorption isotherms. It allows the determination of the free energy differences between host structures involved in guest-induced transitions, especially hard to obtain experimentally. We discuss the general case of adsorption in flexible materials and show how a few key quantities, such as pore volumes and adsorption affinities, entirely determine the phenomenology of adsorption, including the occurrence of structural transitions. On the basis of adsorption thermodynamics, we then propose a taxonomy of guest-induced structural phase transitions and the corresponding isotherms. In particular, we derive generic conditions for observing a double structural transition upon adsorption, often resulting in a two-step isotherm. Finally, we show the wide applicability and the robustness of the model through three case studies of topical hybrid organic-inorganic frameworks: the hysteretic hydrogen adsorption in Co(1,4-benzenedipyrazolate), the guest-dependent gate-opening in Cu(4,4'-bipyridine)(2,5-dihydroxybenzoate)2 and the CO2-induced "breathing" of hybrid material MIL-53.