Statistical Mechanical Model of Gas Adsorption in a Metal-Organic Framework Harboring a Rotaxane Molecular Shuttle

Abstract

Metal-organic frameworks (MOFs) are modular and tunable nano-porous materials with applications in gas storage, separations, and sensing. Flexible/dynamic components that respond to adsorbed gas can give MOFs unique or enhanced adsorption properties. Here, we explore the adsorption properties that could be imparted to a MOF by a rotaxane molecular shuttle (RMS) in its pores. In the unit cell of an RMS-MOF, a macrocyclic wheel is mechanically interlocked with a strut of the MOF scaffold. The wheel shuttles between stations on the strut that are also gas adsorption sites. At a level of abstraction similar to the seminal Langmuir adsorption model, we pose and analyze a simple statistical mechanical model of gas adsorption in an RMS-MOF that accounts for (i) wheel/gas competition for sites on the strut and (ii) gas-induced changes in the configurational entropy of the shuttling wheel. We determine how the amount of gas adsorbed, position of the wheel, and differential energy of adsorption depend on temperature, pressure, and the interactions of the gas/wheel with the stations. Our model reveals that, compared to a rigid, Langmuir material, the chemistry of the RMS-MOF can be tuned to render gas adsorption more or less temperature-sensitive and to release more or less heat upon adsorption. The model also uncovers a non-monotonic relationship between the temperature and the position of the wheel if gas out-competes the wheel for its preferable station.

Dynamic network of intermolecular interactions in metal-organic frameworks functionalized by molecular machines

“…Inspired by living cells, where multiple nanoscale machines interplay and work together to perform specific and comprehensive tasks, the implementation of molecular machines into artificial and hierarchical architectures has become a major task due to the potential to achieve emergent functionality by molecular cooperativity. In recent years, several theoretical and experimental studies on the incorporation of molecular machines into well-defined molecular interfaces have been reported (9)(10)(11)(12)(13)(14)(15)(16)(17)(18)(19)(20)(21). Corresponding intelligent materials, which could act as a response to external physical and chemical stimuli, offer a substantial impact for applications ranging from medicine (19,22) over chemistry (23) to environmental technologies (22,24).…”