Computational Investigation of Correlations in Adsorbate Entropy for Pure-Silica Zeolite Adsorbents

The Entropy of van der Waals Fluid

Thermodynamic state functions are fundamental quantities in many fields. In this work, the van der Waals (vdW) equation of state and calculation formulas of state functions are derived with statistical thermodynamic method in three-dimensional (3D) and two-dimensional (2D) spaces. The heat capacity at constant volume (CV,m ) or area (CA,m ) is exactly the same as that of ideal gas, but the heat capacity at constant pressure (Cp,m ) and other state functions are different from those of ideal gas. The vdW equation of state is a cubic equation, which leads to the fact that the entropy and free energy changes of vdW fluid can be expressed as explicit expressions of volume rather than pressure. Therefore, the adsorbate entropy at constant area can still be theoretically proven to have a linear relationship with the gas-phase entropy at constant volume. However, the linear correlation between it and gas-phase entropy at constant pressure is no longer strictly true in theory. In addition, since the vdW equation of state is applicable to both gas and liquid, the linear correlation between adsorbate entropy and liquid-phase entropy can also be found. At last, the reference state for real gas or fluid at a constant molar volume is suggested.

Transition-state correlations for predicting thermochemistry of adsorbates and surface reactions

Estimating thermochemical properties from linear correlations may provide a pathway to circumvent expensive density functional theory (DFT) calculations for quantities such as pre-exponentials and temperature corrections to DFT energies. Here, we construct thermochemical scaling relations between C₁-C₆n-alkanes in the gas phase and adsorbed alkyl chains extending from several transition metal surfaces, and examine changes in the slope and fit between metals and adsorption sites. We subsequently add -OH, -NH₂, CO, and CC functional groups to the C₁-C₆ molecules and demonstrate strong linear correlations for thermochemistry across all species. We broaden the correlations to incorporate transition states of C₁-C₆n-alkane dehydrogenation reactions, where thermochemistry for computationally prohibitive transition-state calculations can be quickly assessed. Additionally, we rationalize the linearity of thermochemical correlations based on the composition of the homologous series and theoretical assessments. As an application of the correlations, we estimate pre-exponentials for elementary surface reactions of ethane and propane hydrogenolysis on Ru(0001), which is of relevance to plastic hydrogenolysis. Depending on kinetically important steps, entropic contributions may be necessary to include in certain reaction mechanisms; in contrasting examples, entropies are found to be relatively insignificant for ethane hydrogenolysis but pertinent for propane hydrogenolysis.