On the Use of Water and Methanol with Zeolites for Heat Transfer

Reducing carbon dioxide emissions has become a must in society, making it crucial to find alternatives to supply the energy demand. Adsorption-based cooling and heating technologies are receiving attention for thermal energy storage applications. In this paper, we study the adsorption of polar working fluids in hydrophobic and hydrophilic zeolites by means of experimental quasi-equilibrated temperature-programmed desorption and adsorption combined with Monte Carlo simulations. We measured and computed water and methanol adsorption isobars in high-silica HS-FAU, NaY, and NaX zeolites. We use the experimental adsorption isobars to develop a set of parameters to model the interaction between methanol and the zeolite and cations. Once we have the adsorption of these polar molecules, we use a mathematical model based on the adsorption potential theory of Dubinin–Polanyi to assess the performance of the adsorbate-working fluids for heat storage applications. We found that molecular simulations are an excellent tool for investigating energy storage applications since we can reproduce, complement, and extend experimental observations. Our results highlight the importance of controlling the hydrophilic/hydrophobic nature of the zeolites by changing the Al content to maximize the working conditions of the heat storage device.

Section S1. Structural model of zeolites.
All zeolites were generated following the same procedure regardless the Si/Al ratio. The unit cell of the pure silica FAU contains 192 Si atoms. We substitute some Si atoms by Al atoms to reproduce the experimental chemical composition (Si/Al ratio of 100, 2.61, and 1.06, HS-FAU, NaY, and NaX, respectively). HS-FAU, NaY, and NaX contain 2, 56, and 88 Al atoms, respectively.
We generated the structures following the methodology described in previous works [1,2]. We started from the crystallographic positions of the pure silica zeolite from the International Zeolite Association (IZA) database [3] to construct the aluminosilicates. For each structure, we created a set of 50 configurations by randomly substituting some silicon atoms by aluminum atoms within the constraint of Löwenstein's rule and selected the most energetically favorable configuration. Then, we compensated the net negative charge of the adsorbents by placing sodium extra-framework cations in the most probable crystallographic positions reported in the literature. A detailed description of these extra-framework cations is given in references [4][5][6]. Once we added the extra-framework cations to their preferential location, we optimized the structures with energy minimization simulations using Baker's [7] method and a full-flexible core-shell potential. [8,9] Section S2. Parameterization of methanol-zeolite interactions.
Interactions parameters between the molecules of water and the HS-FAU and NaX zeolites were developed in our previous work [10] using experimental adsorption isobars as reference data. In this work, we also computed the adsorption isobar of water in NaY, showing that the water-zeolite interactions are transferable in the whole range of Si/Al substitutions. Here we followed a similar procedure to obtain the methanolzeolite interactions. Starting from the cross-term Lennard-Jones parameters for each pseudo atom of the methanol-zeolite pairs, we iteratively modify the ε and σ parameters, creating a matrix of values smaller and larger than the initials. The partial charges for the adsorbates and zeolites are kept fixed and given in Table S1. For each set of parameters, we computed five values of an adsorption isobar from the low to the high coverage regime. We first compare with experimental data for NaX to narrow the search of adequate parameters to reproduce the adsorption in the zeolite with the highest content of extra-framework cations. Then, we compare with the measured data for HS-FAU and finally for NaY. We repeated the process until we found reasonable agreement between experiments and simulations using the same set of Lennard-Jones parameters regardless the Si/Al ratio. The optimal values are provided in Table S2 and the validation against experimental values is shown in Figure 2 of the manuscript. a reported in reference [11], b reported in reference [12], and c reported in reference [13], Table S2. Lennard-Jones parameters to describe the interactions between the zeolite and the water and methanol molecules.
Section S3. Thermodynamical and mathematical model.
We used the mathematical model based on the Dubinin-Polanyi theory [14,15] to obtain the energy storage properties of the zeolite-fluid working pairs. We first convert the adsorption isobars into their corresponding characteristic curves. The characteristic curve relates the volumetric uptake ( ) (volume of fluid adsorbed in the micropores [ml/g]) and the adsorption potential ( ) [kJ/mol]. The adsorption potential is the molar free energy of adsorption with opposite sign ( ).
where ( ), is the temperature-dependent vapour saturation pressure of the working fluid, ( ), the loading of adsorbed fluid per mass of adsorbent, [g/g], and ( ), the density of fluid confined within the micropores [g/ml]. We use the Peng Robinson equation of state to calculate the saturation pressure of each fluid. [16] We obtained the loading of fluid from QE-TPDA experiments and GCMC simulation. We used the model of Hauer to obtain the density of S5 confined fluids within the micropores. [17,18] This model gives a linear relationship between the density of a fluid confined within the pores of an adsorbent and the operational temperature: where is the free liquid density at the reference (283.15 K for water [15] and 298 K for methanol [19]).
is the free liquid thermal expansion coefficient of each working fluid at the reference temperature and 100 MPa [18,19] (3.871 10 -4 K -1 for water and 8.026 10 -4 K -1 for methanol).
One of the properties of interest for an adsorption-based heat storage application is the thermochemical storage density or simply storage density (SD). For a given pressure, the SD can be obtained by integrating the loading dependence of the specific enthalpy curves within two selected adsorption and desorption temperatures ( Figure S1): where the relation between loading and temperature (adsorption isobars) can be obtained from the characteristic curve and is the specific adsorption enthalpy. The specific adsorption enthalpy, also referred as differential adsorption enthalpy, isosteric adsorption enthalpy, differential heat of adsorption, or isosteric heat of adsorption, is the amount of heat released or required during adsorption/desorption cycles. It should be noted that in this context, is a positive value, even the enthalpy change related to adsorption processes is defined as a negative value. Figure S1. Schematics of storage density calculation (SD) from the integration of the specific adsorption enthalpy over adsorption-desorption cycles.

S6
The Dubinin-Polanyi theory also allows determining the specific adsorption enthalpy , which is defined as [19][20][21][22][23][24]: where is the enthalpy of vaporization, is the adsorption potential and is the differential entropy variation. As mentioned above, is a positive quantity, as well as the three terms in eq. 5. The enthalpy of vaporization is the energy change to transform a substance in liquid phase to gas phase, which is a positive value. This term can be also found in the literature as heat of condensation, usually, when the adsorption enthalpy is referred as heat of adsorption. It should be noted, that in eq. 5, enthalpy of vaporization (or heat of condensation), which depends on the temperature, should express a positive magnitude. The adsorption potential A, is a positive quantity for pressure values below the vapour saturation pressure, and the entropy change for an adsorption process is negative. The two latter terms in eq. 5 account for the total adsorption enthalpy changes during adsorption processes, which can be related with the adsorption potential (molar free energy, ) as:

(6)
It should be noted that enthalpy is a magnitude that does not depend on the entropy change. As can be inferred from eq. 6, the entropic term in eq. 5 and its negative sign are introduced to cancel the entropic contribution of the molar Gibbs free energy. Finally, the entropy variation [25] is related with the slope of the characteristic curve as: where is the thermal expansion coefficient of the fluid in the adsorbed phase, obtained from the density model.
In summary, the mathematical model based on the Dubinin-Polanyi theory allows obtaining the storages densities of adsorbent-fluid working pairs, just from an adsorption isotherm or isobar and some physicochemical properties of the fluids. These properties are the enthalpy of vaporization, bulk liquid density, thermal expansion coefficient, and saturation pressure.
Another advantage of the characteristic curve is that it can be reverted to obtain the adsorption isobars or isotherms at different conditions. In addition to the adsorption isobars, we also computed the adsorption isotherms to check the validity of the Dubinin-Polanyi theory. Figure  S2 shows the adsorption isotherms of both working fluids in the three zeolites.