Abstract
A new semi-analytical mean-field model is proposed to rationalise breathing of MIL-53 type materials. The model is applied on two case studies, the guest-induced breathing of MIL-53(Cr) with CO2 and CH4, and the phase transformations for MIL-53(Al) upon xenon adsorption. Experimentally, MIL-53(Cr) breathes upon CO2 adsorption, which was not observed for CH4. This result could be ascribed to the stronger interaction of carbon dioxide with the host matrix. For MIL-53(Al) a phase transition from the large pore phase could be enforced to an intermediate phase with volumes of about 1160–1300 Å3, which corresponds well to the phase observed experimentally upon xenon adsorption. Our thermodynamic model correlates nicely with the adsorption pressure model proposed by Coudert et al. Furthermore the model can predict breathing behaviour of other flexible materials, if the user can determine the free energy of the empty host, the interaction energy between a guest molecule and the host matrix and the pore volume accessible to the guest molecules. This will allow to generate the osmotic potential from which the equilibria can be deduced and the anticipated experimentally observed phase may be predicted.
Highlights
Breathing materials are a fascinating class of flexible porous frameworks
The methodology section consists of two parts, first the expression of the Helmholtz free energy is introduced and second a Legendre transform is conducted to transform the free energy towards the thermodynamic potential Xin the osmotic ensemble
The model is applied to MIL-53(Cr) with methane and carbon dioxide
Summary
Breathing materials are a fascinating class of flexible porous frameworks. They may undergo a substantial volume change up to 40 % under influence of external stimulus such as temperature, mechanical pressure, or gas adsorption, maintaining their crystallographic connectivity[1,2,3,4]. An exemplary breathing metal-organic framework (MOF) is the MIL-53 family of materials, first synthesized in 2002 in the Ferey group.[5] The network of metal clusters Depending on the specific nature of the material, various stimuli were found to induce the breathing such as temperature[6,7,8], pressure[7, 9], guest molecules[5, 7, 10], .
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