## 2 Background
### Outline of the VTIR Spectroscopic Method  
The variable-temperature IR method, recently developed, is an instrumental technique particularly well suited to gain access to gas-solid physisorption thermodynamics while simultaneously obtaining the IR spectroscopic signature of the adsorption complex [38], provided that either the solid adsorbent or the molecule being adsorbed from the gas phase has an IR active mode that undergoes a change brought about by the adsorption process. Should that be the case, let Equation (1) below represent the adsorption equilibrium:  
\[\mathrm{S}_{(s)}\ +\ \mathrm{M}_{(g)}\leftrightarrows\ \mathrm{S}\cdots\mathrm{M}_{(at)} \tag{1}\]  
where S stands for the adsorption site and M for the adsorbed molecule. If adsorption follows the Langmuir model, the characteristic frequency of the IR absorption band being monitored does not change during adsorption measurements, and its integrated intensity is proportional to surface coverage, \(\theta\), according to the Lambert Beer law, thus giving information on \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Structure Type-Code** & **Selected Isotypes** & **Dimensionality** & **Pore Size (Å)** \\ \hline Small pore & & & \\ STI & Stilbite, Stellerite & 1D & \(2.7\times 5.6\) \\ ERI & Erionite & 3D & \(3.6\times 5.1\) \\ CHA & Chabazite & 3D & \(3.8\) \\ LTA & Linde A & 3D & \(4.1\) \\ Medium pore & & & \\ FER & Ferrierite, ZSM-35 & 2D & \(4.2\times 5.4\) \\ MTT & ZSM-23, EU-13 & 1D & \(4.5\times 5.2\) \\ MFI & Silicalite, ZSM-5 & 3D & \(5.5\) \\ Large pore & & & \\ MOR & Mordenite, LZ-211 & 2D & \(6.5\times 7.0\) \\ LTL & Perlialite, L & 1D & \(7.1\) \\ FAU & Faujasite, X, Y & 3D & \(7.4\) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Examples of zeolites showing the structure type-code and details on the pore system. Figure 2: Framework type LTL, MFI and FER images (adapted from [[http://www.iza-structure.org/](http://www.iza-structure.org/)]([http://www.iza-structure.org/](http://www.iza-structure.org/)) databases/). the activity (in the thermodynamic sense) of both the adsorbed species and the empty sites, 1-\(\theta\). Simultaneously, the equilibrium pressure, \(p\), gives the activity of the molecules in the gas phase. Hence, by measuring IR absorbance and equilibrium pressure at any given temperature, \(T\), the equilibrium constant \(K\), of the gas adsorption process (at that temperature) can be determined. Assuming that changes in specific heat are negligible [60], the variation of \(K\) with temperature, \(T\), is related to the standard adsorption enthalpy, \(\Delta H^{0}\), and entropy, \(\Delta S^{0}\), through the van't Hoff equation:  
\[K(T)\ =\ e^{\frac{-\Delta H^{0}}{KT}}e^{\frac{\Delta S^{0}}{K}} \tag{2}\]  
Combination of Equation (2) with the Langmuir Equation (3) leads to Equation (4) below:  
\[\theta=\frac{K(T)p}{1+K(T)p} \tag{3}\]  
\[ln\frac{\theta}{(1-\theta)p}=\frac{-\Delta H^{0}}{RT}+\frac{\Delta S^{0}}{R} \tag{4}\]  
Alternatively, Equation (4) can be written as:  
\[ln\frac{A}{(A_{M}-A)p}=\frac{-\Delta H^{0}}{RT}+\frac{\Delta S^{0}}{R} \tag{5}\]  
where \(A\) is the actual IR absorbance being measured and \(A_{\text{M}}\) stands for the maximum absorbance, which corresponds to \(\theta=1\). It should be clear that after determining \(\theta\) (or relative IR absorbance) as a function of \(T\) and \(p\) over a temperature range, Equations (4) or (5) provide direct access to the corresponding values of \(\Delta H^{0}\) and \(\Delta S^{0}\) involved in the adsorption equilibrium process. Notably, the IR spectra should be recorded over a sufficiently wide temperature range, otherwise a spurious correlation between \(\Delta H^{0}\) and \(\Delta S^{0}\) can appear [61]. Further details regarding the applicability of the VTIR method can be found elsewhere [38]. On the experimental side, the VTIR method can easily be implemented by using an IR cell which allows IR spectra to be recorded over a (relatively) wide temperature range while simultaneously measuring temperature and gas equilibrium pressure.