A Universal Descriptor for the Entropy of Adsorbed Molecules in Confined Spaces

Abstract

Confinement of hydrocarbons in nanoscale pockets and pores provides tunable capability for controlling molecules in catalysts, sorbents, and membranes for reaction and separation applications. While computation of the enthalpic interactions of hydrocarbons in confined spaces has improved, understanding and predicting the entropy of confined molecules remains a challenge. Here we show, using a set of nine aluminosilicate zeolite frameworks with broad variation in pore and cavity structure, that the entropy of adsorption can be predicted as a linear combination of rotational and translational entropy. The extent of entropy lost upon adsorption is predicted using only a single material descriptor, the occupiable volume (Vocc). Predictive capability of confined molecular entropy permits an understanding of the relation with adsorption enthalpy, the ability to computationally screen microporous materials, and an understanding of the role of confinement on the kinetics of molecules in confined spaces.

Understanding solvent effects on adsorption and protonation in porous catalysts

“…Note that the weakened adsorption entropy loss in the liquid-phase has been observed in the literature, even to the extent where the entropy increases upon confinement 66 . In the vapor phase, adsorption is most commonly an exothermic process and the decrease in translational/rotational degrees of freedom typically leads to a decrease in entropy 67 . In liquid-phase adsorption, an increase in entropy and even endothermicity is more common than in the vapor phase.…”

Progress in Computational and Machine‐Learning Methods for Heterogeneous Small‐Molecule Activation

“…Dauenhauer et al developed a universal descriptor to account for the entropy of adsorbate in confined space (e.g., adsorbate in zeolite catalyst), which previously was only measurable using molecular dynamics simulation. [235] Another overlooked statistical phenomenon that has been recently addressed is the hindered translator for physisorbed molecules and hindered rotor for part of an adsorbate such as CH 3 group. [236] The recent publication by Bajpai et al shows that commonly used statistical mechanics methods such as harmonic oscillator, hindered translator, and the 2D ideal gas are not satisfactory in describing the energetics compared to the exact solution obtained by surveying the potential surface.…”

An approach for predicting intracrystalline diffusivities and adsorption entropies in nanoporous crystalline materials

“…30,35 The hopping rate k can be interpreted as a result of total contribution of translational, rotational, electronic, vibrational and nuclear motions, contributions. 44 We follow the dynamically corrected transition state theory (dcTST) 26,29,30 that has been widely used in the simulations of molecular diffusion in confined media, 26,29,30 and assume the molecules on top of the barrier are in equilibrium. Further to that, as current work focused on the molecular diffusion at low loading, we can consider the Maxwell-Boltzmann distribution can be considered as a simple yet accurate representation of velocity distribution of molecules on the basis of kinetic gas theory of dilute gas.…”

“…An alternative approach is to connect the confinement effect to the adsorption entropy of adsorbed molecules in nanoporous crystalline materials, as shown in Figure 1b. [42][43][44][45] Moor et al 42,43,46 found that confinement has impact on the free degree of molecular translational and rotational motion of molecules by density functional theory (DFT) simulations. They found the carbon number of C 1 -C 8 hydrocarbons is approximately a linear function of the adsorption entropy for FAU, BEA, MOR, MFI, and CHA zeolitic frameworks.…”

“…Actually Campbell et al 49 and Dauenhauer et al 44 found that the adsorption entropy could be related to the pre-factors in rate constants as well as desorption rate from the viewpoint of the transition state theory. Note that diffusion of guest molecules from one site to an adjacent site in nanoporous crystalline materials can be described by hops in the specified framework, 26,30 and the probability of molecules diffusing from one site to another site per unit time can be defined as hopping rate.…”