Article pubs.acs.org/JPCC
Unusual Entropy of Adsorbed Methane on Zeolite-Templated Carbon Nicholas P. Stadie,*,† Maxwell Murialdo, Channing C. Ahn, and Brent Fultz W. M. Keck Laboratory, California Institute of Technology, Pasadena, California 91125, United States S Supporting Information *
ABSTRACT: Methane adsorption at high pressures and across a wide range of temperatures was investigated on the surface of three porous carbon adsorbents with complementary structural properties. The measured adsorption equilibria were analyzed using a method that can accurately account for nonideal fluid properties and distinguish between absolute and excess quantities of adsorption, and that also allows the direct calculation of the thermodynamic potentials relevant to adsorption. On zeolitetemplated carbon (ZTC), a material that exhibits extremely high surface area with optimal pore size and homogeneous structure, methane adsorption occurs with unusual thermodynamic properties that are greatly beneficial for deliverable gas storage: an enthalpy of adsorption that increases with site occupancy, and an unusually low entropy of the adsorbed phase. The origin of these properties is elucidated by comparison of the experimental results with a statistical mechanical model. The results indicate that temperature-dependent clustering (i.e., reduced configurations) of the adsorbed phase due to enhanced lateral interactions can account for the peculiarities of methane adsorbed on ZTC.
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applied Virial-type fitting equation 6 or the ideal gas approximation7). A general method for analyzing experimental adsorption equilibria based on a physically consistent model that is fundamentally very simple while incorporating the crucial features of real adsorption phenomena is needed (as addressed in this work and, e.g., elsewhere8−12). The primary quantity of interest for many adsorbent/adsorbate systems is the isosteric (differential) enthalpy of adsorption, −ΔHads, sometimes referred to as the “isosteric heat”, qst, which is directly related to the change in free energy upon adsorption at specific conditions of pressure, temperature, and adsorbed quantity. The dependences of −ΔHads on pressure, temperature, and adsorbed quantity can render a significant impact on adsorption-based properties such as the effective (“deliverable”) storage capacity of the material, and therefore should be a central objective of the analysis methodology. The assessment of −ΔHads(P,T) requires multiple steps, which are increasingly complicated in the limit of higher bulk fluid density where a number of simplifying approximations become invalid. In this nonideal limit, (a) the measured (“Gibbs excess”) quantity of adsorption is not the relevant thermodynamic quantity, (b) intermolecular interactions become significant, and (c) the adsorbed phase itself begins to occupy a significant (a priori unknown) volume within the system. A general methodology for the thermodynamic analysis of adsorption equilibria should
INTRODUCTION
A fundamental understanding of gas adsorption phenomena, especially the thermodynamic state properties, is relevant to a multitude of commercial and industrial processes, and increasingly in energy-related applications such as gas storage and gas separation. The gas−solid interface in particular plays a central role at many or all steps in various sustainable energy generation−storage−conversion processes that have been proposed: for example, the hydrogen cycle,1 the carbon-neutral carbon−hydrogen cycle (e.g., the production of synthetic fuels from carbon capture),2 or the hydrogen−ammonia cycle.3 Steps involving mixed gases or catalytically active surfaces demand even more rigorous tools for analysis due to the presence of multicomponent and variable-composition fluid phases and are rarely investigated in detailed equilibrium experiments. Despite the urgent demands, a comprehensive physical understanding of practical adsorption phenomena has not been achieved at present,4 and only limited, simple experimental systems can be adequately described by physical models over an appreciable range of pressure and temperature. A typical empirical approach, therefore, is to analyze (fit and interpolate) measured adsorption data with one or a number of phenomenological equations/models that may be partially or even wholly irrelevant to the experimental system. This choice is either by convention (e.g., the BET method5) or based on the best fit to a particular set of data. Such approaches often do not yield an insightful understanding of the system under investigation, and, worse, may not allow a physically meaningful analysis of the relevant thermodynamic properties (e.g., using the commonly © 2015 American Chemical Society
Received: May 26, 2015 Revised: November 4, 2015 Published: November 4, 2015 26409
DOI: 10.1021/acs.jpcc.5b05021 J. Phys. Chem. C 2015, 119, 26409−26421
Article
The Journal of Physical Chemistry C
performed using a least-squares residual minimization algorithm based on the Differential Evolution optimization method (in anticipation of a large number of local minima). Each search was performed in excess of 100 unique times per fit (by varying the random number seed) yielding extremely robust (“global”) minima even while allowing wide limits on the fitting parameters (0 < nmax < 100 mmol g−1, 0 < Vmax < 10 mL g−1, 0 < α < 1, 0 < Ei < 100 kJ mol−1, Ai > 0).
at least account for these three considerations, a−c, as we demonstrate in this work. First, we describe a generalized (multisite) Langmuir fitting equation and model of adsorption that accounts for the three most pertinent considerations encountered at high pressures (a−c) and a simple methodology for the determination of relevant thermodynamic quantities. We then apply this analysis method in the investigation of supercritical methane (CH4) adsorption between 238 and 526 K and 0.01−9 MPa on the surface of three carbonaceous materials with diverse and complementary physical properties. In this region of specific interest for the storage of natural gas among other applications, methane diverges significantly from ideal gas behavior, and an accurate methodology for analysis is crucial. In addition to the isosteric enthalpy of adsorption, the entropy of the adsorbed phase, a thermodynamic quantity with increasingly recognized importance,13 is directly accessed via a methodology that incorporates considerations a−c (in contrast, e.g., to models based on the Tóth or other nonanalytically differentiable equations). Finally, to demonstrate its validity, this experimentally derived approach is then compared to a simple theoretical approach based on statistical mechanics, where the role of each of the three considerations (a−c) is examined. The individual contributions to the total entropy of the adsorbed phase can be extracted from the statistical mechanical calculations to elucidate the role of material properties (e.g., surface homogeneity, pore size, etc.) in the corresponding thermodynamic properties of the adsorbed phase.
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ADSORPTION MODEL In general, raw adsorption uptake data must be converted to thermodynamically relevant quantities (such as absolute adsorption) before analysis, which necessitates the use of an appropriate fitting methodology and/or theoretical model of adsorption. A number of different methods and models have been compared in the course of this work to both determine the best quantitative fit to the measured data and achieve the most physically insightful and accurate depiction of the true thermodynamics of the system. The standard material MSC-30, whose properties are well reported in the literature,20 was chosen as the test sample in this comparative analysis due to its high surface area (rendering very low error in the uptake quantities) and diverse mixture of micro- and mesopores (lending it minimally- or non-structurally dependent adsorption properties). The details of the development of the following adsorption model based on methane adsorption on MSC-30 have been introduced elsewhere,21 and a detailed account of the methodologies and important considerations is given herein. The physical understanding of the measured adsorption quantity of real fluids is subject to, at least, three important considerations: (a) the concept of the excess quantity of adsorption, which is relevant to both volumetric and gravimetric adsorption measurements, (b) the well-known deviation of real gas properties from that of an ideal gas, which is especially relevant to adsorptive storage applications where high pressures must be applied, and (c) the effects of an increasing adsorbed phase volume in the system, which is a significant consideration that is almost categorically ignored in common practice. Gibbs Surface Excess (a). Measurements of adsorption by volumetric or gravimetric methods have the simple shortcoming that they cannot directly determine the absolute adsorbed amount.22 This is readily apparent at high pressures where it is observed that the measured uptake amount reaches a maximum and then decreases with increasing pressure, which is fundamentally inconsistent with the physical nature of adsorption. A simple geometrical explanation of the measured quantity of adsorption at the interface between two bulk phases was first given by Gibbs,23 and is referred to as the excess quantity of adsorption. Because the volume of the adsorbed phase is not measurable, a model must be employed to predict the absolute quantity of adsorption at high pressures. The implications of this consideration for the determination of thermodynamic quantities of adsorption have been discussed in great detail in other work.24−26 The Gibbs definition of excess adsorption, ne, as a function of absolute adsorption, na, is
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EXPERIMENTAL METHODS Methane adsorption uptake was investigated on three materials: two commercial activated carbons, referred to as MSC-30 and CNS-201, and a zeolite-templated carbon material prepared from a faujasite-type template, ZTC. Materials. Maxsorb MSC-30, a commercially available superactivated carbon, was obtained from Kansai Coke & Chemicals Co., Ltd. (Amagasaki, Japan). CNS-201, a commercially available activated carbon, was obtained from A. C. Carbone Inc. (Saint-Jean-Sur-Richelieu, Canada). A zeolitetemplated carbon, referred to here as ZTC, was synthesized by typical methods from a NaY zeolite template, previously referred to as “ZTC-3”.14 Materials’ Characterization and Methane Adsorption Measurements. Structural and chemical characterization of all three materials has been previously performed, including N2 adsorption measurements at 77 K, electron microscopy and electron energy-loss spectroscopy, X-ray diffraction, X-ray photoelectron spectroscopy, elemental analysis, and helium pycnometry at 298 K14 (where potential errors due to finite helium adsorption in narrow micropores15 have been disregarded in this work). Equilibrium methane adsorption isotherms were measured with a custom volumetric Sieverts apparatus, also described elsewhere.16 Methane gas densities were determined from the measured temperature and pressure using the 32-term modified Benedict−Webb−Rubin (mBWR) equation of state as implemented by the REFPROP Standard Reference Database,17 and the excess quantity of adsorption was determined by the Sieverts method.18,19 Methane Adsorption Data Analysis. The “raw data”, excess quantity of adsorption (mmol g−1) as a function of pressure (MPa) and isotherm temperature (K), were tabulated and imported into a Mathematica worksheet for further analysis. Fitting of the data to the adsorption model was
ne = na − Va(P , T )ρg (P , T )
(1)
To determine the absolute quantity of adsorption, the density of the bulk gas (or supercritical fluid), ρg, must be known, in addition to the total volume of the adsorbed phase, Va. 26410
DOI: 10.1021/acs.jpcc.5b05021 J. Phys. Chem. C 2015, 119, 26409−26421
Article
The Journal of Physical Chemistry C Gas-Phase Nonideality (b). Adsorption at high pressures and low temperatures (approaching the critical temperature) is marked by a significant deviation from adsorption in the dilute limit, where the ideal gas model is a satisfactory approximation for both the adsorbed phase and the gas above it. Therefore, it is vitally necessary to use “real gas” properties for the gas phase itself in all calculations of the excess and absolute adsorbed phase quantities, and to eschew any ideal gas approximations in subsequent thermodynamic analyses (this point is further emphasized in the following section). For the fitting methodology, this implies that the gas density, ρg, used in eq 1 (and in all subsequent equations) must be derived from a sufficiently accurate “real gas” model. In all calculations performed herein, including the initial Sieverts method calculations to obtain the raw data, we have chosen the mBWR equation of state as implemented by the REFPROP Standard Reference Database.17 Methane, despite its relatively weak intermolecular interactions, is already significantly nonideal at 2.5 MPa and ambient temperature (by ∼5% with respect to density). Attractive interactions are the dominant cause of the nonideality of methane in the region of the phase diagram investigated in this study;27 this results in a significantly higher gas density than the ideal gas (i.e., a compressibility factor of
