Computing the temperature dependence of adsorption selectivity in porous solids

Highlights

• Fast screen the selectivity performance of porous solids at broad range of conditions

• Expand the available data at different adsorption temperatures

• Validate IAST predictive results with direct multicomponent adsorption simulations

Abstract

We describe a method that computes gas adsorption equilibria in porous solids, at arrays of temperature and mixture compositions. The method uses an initial dataset of single component adsorption isotherms, obtained either from experiment or grand canonical Monte Carlo simulations. It utilizes the Clausius Clapeyron equation to expand the number of the available isotherms for the adsorbate components at a specified sequence of temperatures. It employs the ideal adsorbed solution theory (IAST) on the expanded data for the complete range of mole fractions in the mixture. We show case the method considering experimental isotherms of CO₂ and CH₄ adsorption at near ambient temperatures, for an activated carbon cloth, an ordered mesoporous carbon and on the alpha phase of magnesium formate. In the same context, we produce a set of simulated adsorption isotherms for a zeolitic imidazolate framework, namely ZIF69. The adsorbate mixture capacities of CO₂ and CH₄ on ZIF69, predicted by the IAST method are validated with explicit mixture adsorption simulations performed at the same conditions of interest. The method is appropriate for fast screening the selectivity performance of porous solids aiming to minimize the effort regarding experiments for multicomponent physisorption.

Introduction

Advanced adsorption studies and porous materials characterization, are performed almost routinely in commercially available adsorption instruments and pore size analysers [[1], [2], [3]]. Nowadays, single component adsorption data can be obtained at any temperature of interest even at cryogenic conditions (<200 K) using specially designed thermostats and pressure controllers [4]. On the other hand, mixed gas adsorption experiments are less amenable to automation and far more complex than the single component experiments [5]. They require custom equipment and an elaborate data analysis [6]. More important is that equilibrium conditions for adsorbate mixtures may need several hours to be detected or ensured. Considering the time and the resources required for multicomponent experimental adsorption, it is intractable to perform such experiments at lengthy arrays of temperatures, pressures and feeding compositions. To minimize the conceivable effort for thorough experimental investigations, we propose a computational method that combines the ideal adsorbed solution theory and the Clausius Clapeyron equation to estimate gas mixture adsorption at a range of conditions.

The ideal adsorbed solution theory (IAST) is developed by Myers and Prausnitz in 1965 [7]. It is a thermodynamic framework that predicts multi-component adsorption using only data from single component adsorption at the temperature of interest. IAST describes the adsorbed phase as a two dimensional layer along the solid surface, where the adsorbed species exert a spreading pressure π. The spreading pressure is the analogy of the pressure in two dimensions. A key assumption of IAST is that, although the individual adsorbate components behave non-ideally (i.e., adsorbate species may obey nonlinear isotherms like Langmuir, Freundlich etc.), their mixture along the solid surface is ideal [8,9]. The surface area occupied per mole, by an adsorbate, is the same regardless if other adsorbates are also present in the layer and the capacities of single and multi component adsorption obey the Raoult's law of gas mixtures. These approximations are reasonable for adsorbate mixtures having particles with similar size, shape and molecular interactions of equivalent strength.

The capability of IAST to predict multicomponent competitive interactions has been confirmed decades ago [[8], [9], [10]]. M. Benjamin has introduced a new IAST solution approach, allowing the model equations to be solved using a simple spreadsheet analysis [11]. Simon et al., provided a python package that performs IAST calculations, where the pure component isotherms can be characterized using appropriate fitting models or linear interpolation [12]. Likewise IAST, the Flory-Huggins theory has been also proposed as a binary mixture predictive model and validated with experimental binary adsorption data [13,14]. Comparison studies between IAST predictions and direct mixture adsorption simulations, have been reported, for many pore structural models, like carbons, porous crystallines and metal organic frameworks and for different number and types of adsorbate components [[15], [16], [17]].

CO₂ and CH₄ are typical gases in industrial applications omnipresent in feed and post-combustion streams of relevant processes. The reduction of greenhouse gas emissions and the purification of biogas and natural gas, demanded the development of technologies for separating the specific components. Adsorption based technologies using porous solids have been identified as an attractive option. Existing and newly developed porous materials have been considered for CO₂ capture or CO₂/CH₄ separation. Such materials include adsorbents like carbons, zeolites and metal-organic frameworks. A general overview of the advantages and limitations of such adsorbents can be found in the literature [18,19].

In this work we consider four representative solids, an activated carbon cloth an ordered mesoporous carbon, the alpha magnesium formate and ZIF69 (i.e, a zeolitic imidazolate framework). We use an initial dataset of CO₂ and CH₄ adsorption isotherms at three temperatures. We apply the Clausius Clapeyron equation to interpolate the available isotherms at an array of specified temperatures. We employ the ideal adsorbed solution theory to compute the mixture adsorption densities at the specified temperatures and for the full range of CO₂-CH₄ mixture compositions. The experimental CO₂ and CH₄ adsorption isotherms of the two carbons and the magnesium formate are taken from the literature [[20], [21], [22]]. Complementary, we perform grand canonical adsorption simulations to produce the relevant CO₂ and CH₄ isotherms of ZIF69. The IAST predictions for the adsorbate mixture capacities on ZIF69 are examined and validated after performing direct mixture component adsorption simulations at the same conditions.