Dr. Michael Katz - Porous Materials

# Isosteric Enthalpies of Adsorption

The isosteric heat of adsorption is the amount of energy that is emitted when a gas adsorbes onto a surface (at least when we are talking about gas adsorption in MOFs). The most common method to determine this is to measure the gas adsorption isotherm at three temperatures. The three temperatures should be within 5-10 °C; this is to ensure that the mechanism of adsorption doesn't change. Fitting these isotherms to a model (see below) allows us to determine the isosteric enthalpies of adsorption. There are several different models that can be utilized. In our experience, a low degree of residuals is key to determining the enthalpies of adsorption. Even a seemingly good fit with residuals of 0.02 may not give the optimal results. Furthermore, global refinement of some parameters is critical.

Data input is easy. Select your model, input the temperature of the three isotherms (in Kelvin), and then select your data file. Your data file should be a csv file where the first row contains the unit of the column (e.g., KPa, mmol/g, KPa, mmol/g, KPa, mmol/g). The remaining rows contain your data. At present, please make sure that your last line in your CSV is not blank (we hope to fix these bugs in the near future).

No data is stored on our end, so feel comfortable to try out the different models for your work. The plots are all interactive, and they can be saved. We are working on exporting the data for your records.

We have implemented several models below. To reduce the "black box" nature of this, the models and constraints we have put upon them are described below. One constant to every fit is that we add an error shift parameter at the end of the equations. This accounts for various factors associated with the data collection. In general, this parameter should refine close to zero. Each isotherm will have a different shift.

The enthalpies of adsorption are all exothermic. The data her presents the enthalpies as the absolute value.

## Single Site Langmuir

The single site Langmuir equation is shown below. We have two versions of the model. In the unrestricted model, each isotherm is fit to a different saturation value and equilibrium constant. In the global fit, the saturation value is identical for every fit. The latter model is prefered. constraining a global saturation value states that for your system the number of adsorption sites doesn't change. The only change is temperature and that changes the equilibrium constant.

$q = q_{sat}{KP \over 1+KP} + C$

The enthalpies of adsorption are determined by the following equation. For a derivation of this, we recommend the work by Long et al.

Isotherm Model:

Temp 1 (K): Temp 2 (K): Temp 3 (K):

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### Contact Details

Department of Chemistry,
Memorial University,
St. John's, NL
Canada

Phone: 1-709-864-8745
Email: mkatz@mun.ca
Website: www.KatzResearchGroup.com