Heat of Adsorption: A Comparative Study between the Experimental Determination and Theoretical Models Using the System CH₄-MOFs

Abstract

In this investigation, adsorption heats were determined using a direct method (adsorption calorimetry, Ad-Cal) and an indirect method (in which adsorption isotherms are measured at different levels of pressure and temperature) that makes use of thermodynamics, using the Clausius–Clapeyron (CC) equation, which is able to evaluate the isosteric heat. The results obtained from the two methods were compared determining the adsorption of CH4 on five normal structures of metal–organic frameworks (MOFs) synthesized in this investigation: zeolitic imidazolate framework (ZIF)-8, Hong Kong University of Science and Technology (HKUST)-1, isoreticular MOF (IRMOF)-1, MOF-177, and MgMOF-74, with the intention of establishing the similarities and differences between these methods. The experimental results of adsorption heats were fit at models: Dubinin–Astakhov (DA), and Toth, Unilan modified to determine the extent of each of the methods used in this analysis. This research has found a good agreement between the measured heat using the calorimetric method and model DA throughout the load range of CH4. Also, this study found that the model fits the least data obtained by adsorption calorimetry. The adsorption capacity of CH4 was also analyzed.

Identical Composition and Distinct Performance: How ZIF-8 Polymorphs’ Structures Affect the Adsorption/Separation of Ethane and Ethene

“…In fact, a linear fitting with all C2/C3 molecules’ data points yielded (note the actual uptake of C3 molecules in Figure a was multiplied by 5 for the sake of clarity; in the linear fitting, the actual uptake values were used so that all C2/C3 data points actually fall on the same line) where C is the adsorbed amount, K is the Henry coefficient, the linear fitting slope P = 9.3 Pa ( R 2 = 0.9983), very close to the equilibrium pressure, 0.01 kPa, which is consistent with Henry’s law. The uptake at 0.01 kPa also correlates with Q st 0 , although the correlation is not as good as with the Henry coefficient, as had been explained previously. , Further comparing ethene with other three molecules (ethane, propane, and propene), their 0.01 kPa uptake, the Henry coefficient, the Q st 0 , all show significant correlation among these molecules (Figures S3–S5). These correlations could be attributed to the fact that these four alkanes or alkenes share similar interactions with ZIFs.…”

“…The uptake at 0.01 kPa also correlates with Q st 0 , although the correlation is not as good as with the Henry coefficient, as had been explained previously. 36,85 Further comparing ethene with other three molecules (ethane, propane, and propene), their 0.01 kPa uptake, the Henry coefficient, the Q st 0 , all show significant correlation among these molecules (Figures S3−S5). These correlations could be S6 and S7.…”

Evaluation of amine-based solid adsorbents for direct air capture: a critical review

“…Experimentally, the heat (enthalpy) of adsorption (Δ H ads ) is evaluated by either direct or indirect methods. 160 In the direct method (usually called the calorimetric method), the heat released upon the contact between adsorbate and adsorbent is measured using a calorimeter (differential scanning calorimetry or microcalorimetry). In the indirect method, the enthalpy of adsorption is estimated from the adsorption isotherm data at multiple temperatures by fitting adsorption isotherms using Langmuir, Toth, or related thermodynamic models and then applying the Clausius–Clapeyron equation.…”

“…In the indirect method, the enthalpy of adsorption is estimated from the adsorption isotherm data at multiple temperatures by fitting adsorption isotherms using Langmuir, Toth, or related thermodynamic models and then applying the Clausius–Clapeyron equation. 160 The enthalpy of adsorption can also be expressed as isosteric heat of adsorption ( Q st ) at particular coverage. The isosteric heat of adsorption has the same magnitude as the enthalpy of adsorption but with an opposite sign (Δ H ads = − Q st ).…”

“…162 Among the two measurement methods, the isosteric heat measurement by the Clausius–Clapeyron equation is widely used compared to the calorimetric measurement. 160 However, the heat value calculated from the indirect method sometimes underestimates the actual heat value due to the inconsistency in adsorption fitting. Hence, for practical DAC application, the heat of desorption and the heat of regeneration, along with the heat of adsorption, are also calculated using calorimetry.…”