Isosteric Heats of Adsorption of Gases and Vapors on a Microporous

Article Cite This: J. Chem. Eng. Data XXXX, XXX, XXX−XXX

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Isosteric Heats of Adsorption of Gases and Vapors on a Microporous Carbonaceous Material S. Hadi Madani,†,‡ Francisco Rodríguez-Reinoso,§ Mark J. Biggs,‡,# and Phillip Pendleton*,‡ †

Australian School of Petroleum, The University of Adelaide, Adelaide, SA 5005, Australia School of Chemical Engineering, The University of Adelaide, Adelaide, SA 5005, Australia § Laboratorio de Materiales Avanzados, Departamento de Química Inorgánica, Universidad de Alicante, Apartado 99, Alicante E-03080, Spain Downloaded via DURHAM UNIV on July 13, 2018 at 12:29:45 (UTC). See https://pubs.acs.org/sharingguidelines for options on how to legitimately share published articles.

‡

S Supporting Information *

ABSTRACT: High-resolution, multiple temperature adsorption isotherms of ten adsorptives classified into highly polar (1.7 ± 0.1 D) and nonpolar (0 D) probes with increasing kinetic diameters were measured on a well-characterized poly(furfuryl alcohol)-based microporous carbon. The Clausius−Clapeyron equation was applied to each, resulting in isosteric heats of adsorption. Fluid−fluid interactions, nonspecific fluid−solid interactions, and specific fluid− high energy site interactions were identified and discussed as variables contributing to the total isosteric heat of adsorption. Each isosteric heat was compared against its position relative to adsorption heat by a flat surface, twice this heat, and adsorptive latent heat of condensation. The shape of each curve was analyzed via the contribution of each interaction to the total across the fractional filing range, leading to identification of fillings as Zero Coverage, Low Coverage, and High Coverage. This systematic investigation provided a detailed analysis of the influences of adsorptive size, its conformation, and polarity effects on micropore filling, and tabulation of the analyses gave a clear and comprehensive insight into the adsorption mechanisms.

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INTRODUCTION Gas and vapor adsorption on porous materials has a variety of scientific and industrial applications including but not limited to characterization of porous materials,1 separation and purification,2 chemical reaction and catalysis,3 and adsorption and storage of chemicals.4,5 Adsorption phenomena always involve interaction of adsorptive molecules with themselves, adsorptive molecules with high energy sites on the porous material surface, and adsorptive molecules with porous material surface. These interactions are usually exothermic followed by reduction in the system internal energy and heat release. The heat released per unit molecule added at constant loading and constant temperature is known as isosteric heat of gas (or vapor) adsorption.6 Isosteric heat of adsorption can be evaluated by either direct calorimetry or multiple temperature adsorption isotherm measurements followed by Clausius− Clapeyron calculations.7,8 A third, but infrequently used, method is due to Neimark and co-workers where a combination of molecular simulation (Quenched Solid Density Functional Theory, QSDFT) and experimental isotherm is used for analysis.9 Analysis of isosteric heat of adsorption is important from both scientific and industrial points of view. From a scientific perspective, isosteric heat of adsorption contains information about energetics of adsorption and its mechanism. From an industrial perspective, the analysis of the released energy can be used for process design to release extra heat and to control processes at desired temperatures. © XXXX American Chemical Society

Despite its importance, isosteric heat of gas/vapor adsorption on porous materials has been infrequently reported in the literature. Some reasons could be due to 1. The variety of adsorptives and of porous materials with different preparation methods and surface functionalities that are available; a systematic study of adsorption energetics requires a unique collection of adsorptives and a well-characterized porous structure. 2. The fact that adsorption calorimeters are not widely accessible for direct isosteric heat measurement, and when they are, their accuracy to record small quantities of heats of adsorption at small changes in loadings is challenging. 3 The fact that considerable demands are made of experimental precision to make meaningful highresolution adsorption isotherms, especially at accurately controlled multiple temperatures and sufficiently low relative pressures for consequential isosteric heat evaluation and analysis. Even when the data are collected, an insightful interpretation of the data is a second challenge. Adsorption isosteric heat is a summation of several individual heats contributing at different Received: May 8, 2018 Accepted: June 27, 2018

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DOI: 10.1021/acs.jced.8b00363 J. Chem. Eng. Data XXXX, XXX, XXX−XXX

Journal of Chemical & Engineering Data

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Table 1. Adsorptives Used for Adsorption Measurements physical properties

adsorptive argon (Ar) nitrogen (N2) methane (CH4) iso-butane (i-butane) sulfur-hexafluoride (SF6) water (H2O) dichloromethane (DCM) methanol (MeOH) iso-propanol (i-PrOH) 2-methyl, 2-butanol (2M2B)

condensation heat at average T qL (kJ/mol)15

enthalpy of adsorption on a flat graphitized surface, qf−s,1 (kJ/mol)16

polarity (Debye)17

ads. temp. (K)/ temp. control devicea

18

minimum kinetic diameter, σ (nm)

grade/supplierb

6.64 5.58 8.17 19.75

10.89 9.17 12.21 40.40

0.34 0.3618 0.3819 0.501

0.0 0.0 0.0 0.1

85,87,89/C 75,77,79/C 107,110,113/C 278,288,298/RC

>99.999%/BOC >99.999%/CG >99.999%/BOC >99.995%/SA

9.38

19.44

0.5520

0.0

273,283,293/RC

>99.75%/SA

44.22 28.30

19.23 30.51

0.2710 0.3310

1.8 1.8c

278,288,298/RC 278,288,298/RC

38.66

22.15

0.4310

1.7

278,288,298/RC

45.44

29.26

0.4710

1.7

278,288,298/RC

51.50

44.70

0.6010

1.9

278,288,298/RC

Milli-Q water CHROMASOLV Plus >99.9%/SA analysis grade >99.9%/M HPLC grade >99.9%/SA analytical standard >99.5%, SA

a

C = cryostat; LN2 = liquid N2 bath; RC = refrigerated circulator. bCG = Coregas, Australia; M = Merck, USA; BOC = BOC Gases, Australia; SA = Sigma-Aldrich, USA. cThe authors recognize this dipole moment is sometimes cited as 1.14 D and sometimes as 1.4 D.

Figure 1. Adsorptives used for adsorption experiments, their kinetic diameters, and dipole moments.

ranges of loadings; their detailed interpretation requires a deep knowledge of the adsorption phenomena and its energetics. In the current work, we report multiple temperature adsorption isotherms on a well-characterized PFA-based microporous carbon. The available detailed characteristics of this carbon enable us to better understand and interpret adsorption mechanisms and isosteric heats of adsorption.8,10−12 We used a unique collection of selected highly polar and nonpolar probes with increasing kinetic diameters to probe microporous structure.13 Previous studies have shown that the collected adsorption isotherm data on different samples include negligible uncertainty, endorsing experiments’ repeatability and reproducibility.13 Multiple temperature adsorption isotherm data were used to calculate isosteric heats of adsorption via the Clausius−Clapeyron equation, and the resulting data were qualitatively and quantitatively interpreted to support the various adsorption mechanisms.

The ensuing discussion significantly enhanced the current literature addressing adsorption and isosteric heat.

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MATERIALS AND METHODS

A well-characterized poly(furfuryl alcohol)-based, activated carbon was used in this study as an exemplar microporous adsorbent. Its synthesis and activation procedures were described in detail elsewhere,11,12 along with the surface chemistry and physical properties of the sample.14 Normal condition liquid and gas adsorptives were used in this study; grade and supplier details are given in Table 1. The kinetic diameter comparison with dipole moment for each molecule is made in Figure 1. The following criteria were tested against adsorptive selection: B



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Figure 2. PFA-based carbon PSD based on the QSDFT22 model on N2 adsorption at 77 K.

1. Which fixed-gas adsorptives are most widely used, viz., N2, Ar, and CO2, regardless of size, conformation, or polarity? 2. How might the probe molecules be classified based on polarity? Zero or negligible dipole moment (isobutane) compared with those with an appreciable dipole moment ranging from 1.7 to 2.2 D. 3. How might the probe molecules be classified via their size or kinetic diameter? Nonpolar probes ranging from 0.34 nm for Ar to 0.55 nm for SF6 and polar probes ranging from 0.27 nm for H2O to 0.60 nm for 2M2B. For all adsorption measurements, each sample was degassed thoroughly (250 °C, 4 h, 10−5 kPa). Ar and CH4 gas adsorption isotherms were measured using an ASAP-2020 apparatus (Micromeritics, Norcross, GA, USA) equipped with a cryostat (Cold Edge Technologies, Allentown, PA, USA). Helium was used for dead-space corrections (>99.999%, ex. BOC Gases, Adelaide, Australia). All other adsorption isotherms were obtained using a BELSORP-max gas adsorption apparatus (BEL, Osaka, Japan) equipped with a vapor adsorption kit combined with a Neslab refrigerated bath circulator. The manifold temperature and its connection to the sample holder were maintained at 313 K to suppress the possibility of vapor condensation during measurements. Again helium was used for dead-space measurement. Isotherms for each adsorptive were measured on separate samples, and for each measurement the only variable was the sample mass temperature with all other conditions reproduced and/or controlled within their uncertainty. Since slightly different masses were used in each measurement, equilibrium pressures were consequently slightly different for each predefined dosing pressure. Measurements at one temperature were repeated three times, allowing the isotherm uncertainty evaluation. Details of uncertainty evaluation were reported elsewhere.13 Each measurement was preceded by trial measurements to optimize measurement variables including dosage volume, excess dosage, equilibration time, and the maximum clearance to the target relative pressure. These trial measurements provided repeatable and reproducible data collection details

leading to high levels of confidence for precise isosteric heat analyses. The Clausius−Clapeyron equation for a single-component gas−adsorbate system was used to calculate isosteric heats of gas adsorption ÄÅ ÉÑ ÅÅÅ ∂ln p ÑÑÑ ÑÑ qst = −RÅÅÅ ÅÅÇ ∂(1/T ) ÑÑÑÖnE (1) where qst represents the isosteric heats of gas adsorption, R the universal gas constant, P the equilibrium pressure, and T the adsorption temperature. Detailed thermodynamic bases were explained elsewhere.8 A frequently used virial-type equation21 was applied to the adsorption data and extrapolated across the lowest measured equilibrium relative pressures to avoid experimental limitations frequently encountered at the limits of device sensitivity.7,8 Equation 1 presents isosteric heats of adsorption at constant amount adsorbed (Vads). For comparison between isosteric heat curves, the amounts adsorbed were normalized to fractional filling of total available pore volume thereby accounting for molecular size and conformation-induced molecular sieve effects. Fractional filling was thus defined as Vads/Vads,max. We used a cryostat to adjust the temperature for N2, Ar, and CH4 adsorption measurements permitting experiments to be measured at each adsorptives’ boiling point and promoted adsorption isotherm measurement up to saturation conditions. All other measurements were made using a refrigerated circulator at predefined, controlled temperatures. Due to the sample container and pressure limitations, i-butane and SF6 adsorption isotherms were measured up to atmospheric pressure, and their fractional pore filling was calculated by normalizing the amount adsorbed to an averaged calculated pore volume.13

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RESULTS AND DISCUSSION The porous material of interest in this study was a wellcharacterized, microporous, PFA-based activated carbon. Prior to a detailed interpretation and discussion of the isosteric heat results, it would be appropriate to develop a deeper C



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Figure 3. N2 (a) and Ar (b) adsorption isosteric heat on microporous PFA-based carbon: isosteric heat (qst), condensation heat (qL), heat of adsorption on a flat surface (qf−s,1), and twice the heat of adsorption on a flat surface (qf−s,2).

Figure 4. H2O (a) and DCM (b) adsorption isosteric heat on microporous PFA-based carbon: isosteric heat (qst), condensation heat (qL), heat of adsorption on flat surface (qf−s,1), and twice the heat of adsorption on a flat surface (qf−s,2).

understanding of the surface chemistry and physical properties of the adsorbent as they pertain to their influence on the calculated isosteric heat of adsorption of the various adsorptives. Furthermore, the adsorptives provide a range of chemical and physical property differences that lead to collective and dissimilar features in their adsorption properties, ergo, their adsorption enthalpy curves. Each of the N2 adsorption isotherms (75, 77, and 79 K) on the PFA-based carbons exhibited Type I shape (Supporting Information Figure S1a), characteristic of micropores with negligible contribution from mesopores, macropores, or the external surface. The relatively sharp knee implied a relatively narrow pore size distribution (PSD) of micropores, subsequently derived from a Quenched Solid Density Functional Theory (QSDFT) analysis22 (Figure 2). This PSD suggested a narrow distribution of micropores with a mean (wmean) centered at 0.57 ± 0.05 nm. Previous analyses showed that PSDs calculated using immersion calorimetry,10 adsorption isosteric heat,23 immersion calorimetry,10 and adsorption of different gases and vapors23 on similarly prepared samples were statistically consistent with that shown in Figure 2, confirming the distribution could be taken as a standard (on following the preparation method). The isosteric heat of adsorption, qst, is comprised of a linear combination of fluid−fluid and fluid−solid interaction enthalpies, with the latter consisting of specific qf−HES and nonspecific qf−s interaction contributions, summarized as8 qst = αqf − f + βqf − s + γqf − HES

Depending on the accessibility of adsorbent surface groups as isolated, geminal, or localized groupings of high energy sites and the size, conformation, and electron localization of the adsorptive (probe), the coefficients of the independent variables in eq 2 would contribute varyingly to an evaluated isosteric heat of adsorption. These three interactions would be expected to regulate the initial value and decay of enthalpy with the expectation that the highest free energy change (and hence enthalpy change) would be due to the initial interactions. A similar, preliminary interpretation was made elsewhere for pore filling enthalpy analyses:13 • Fluid−fluid interaction heat, qf−f, interactions between adsorptive molecules: (1) At initial or small-valued fractional fillings, there would be an insufficient number of adsorbate molecules present to make a meaningful contribution, an ideal gas-type system. With increasing pore filling, a departure from ideal behavior would occur leading to intermolecular interaction enthalpy up to that equivalent to a (latent heat of) condensation enthalpy contribution. Typical values would be 35 kJ/mol for hydrogen bonding probes (H2O, MeOH, iPrOH, and 2M2B). • Nonspecific fluid−solid interaction heat, qf−s, as van der Waals forces between an adsorptive and an adsorbent:

(2) D



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Figure 5. CH4 (a) and MeOH (b) adsorption isosteric heat on microporous PFA-based carbon: isosteric heat (qst), condensation heat (qL), heat of adsorption on flat surface (qf−s,1), and twice the heat of adsorption on flat surface (qf−s,2).

Figure 6. i-Butane (a) and i-PrOH (b) adsorption isosteric heat on microporous PFA-based carbon; isosteric heat (qst), condensation heat (qL), heat of adsorption on a flat surface (qf‑s,1), and twice the heat of adsorption on a flat surface (qf‑s,2).

(1) If the solid were a flat surface, the heat contribution would represent interaction between the two species. For porous materials, and the condition where the adsorptive (kinetic diameter) approached a pore of similar dimensions, the adsorptive molecule would encounter multiple concurrent interactions with the pore surface leading to significantly enhanced enthalpy. • Specific fluid−solid interaction heat, qf−HES, represented by interactions between permanent dipoles and (localized) High Energy Sites (HESs) on the adsorbent surface: (1) In this classification, the adsorptive would usually have a permanent dipole moment, and the surface might contain polarized or polarizable functional groups, typically oxygen-based, but other (implanted) electronegative atoms would behave in a similar manner. Induced dipole moments could be a result of the interaction. The number of HESs per unit area can be evaluated via adsorption,24,25 or surface titration,26 or calorimetry.27 If HESs were present within micropores, these would only contribute to the enthalpy of adsorption if no molecular sieve effects were present. Generally, specific fluid−solid interaction heat contributions would diminish sharply with filling resulting in negligible contribution at higher fractional fillings. The shape of the isosteric heat curve for each adsorptive might be classified into three distinct levels of pore filling or coverage, θ: (1) isosteric heat at Zero Coverage (θ ≅ 0); (2) isosteric heat at Low Coverage (0 < θ ≤ 0.1); and (3) isosteric heat at High Coverage (0.1 < θ).

Although the upper pore filling or coverage limit of θ < 0.1 appears to be arbitrary for the Low Coverage range, it is tacit acknowledgment of Dubinin’s previous observation of failure of the Theory of Volume Filling of Micropores (TVFM) to adequately define pore filling below this value.28 Second, from an experimental perspective, the reproducibility of very low amounts adsorbed or pore filling becomes poor due to sensitivity limitations of the apparatus employed. The definition of high coverage has a single-valued lower limit without reference to another intermediate coverage or pore filling range because properties distinguished as curve shape and enthalpy contributions defined in eq 2 would overlap the upper coverage or pore-filling component of the curve more than the lower limit. Zero Coverage. By definition, the surface would be completely devoid of adsorptive; however, since the focus is on curve analysis, zero coverage is defined here as first adsorptive (atom or molecule) contact with the pore surface and/or network, with the expectation that isolated adsorptive−surface interactions occur or at least minimal (as an unspecified number of) adsorbate−adsorptive enthalpy contributions due to localized adsorption. Of course, this mechanism would be more likely for interaction with HES. Assuming an inconsequential number of adsorptive molecules at the proposed (near-) zero coverage, no fluid−fluid interaction heat would be developed qf−f = 0. Zero coverage isosteric heat would represent only the energetics of fluid−solid interactions for nonpolar adsorptives, provided they do not respond to HES dipole induction. For those adsorptives susceptible to E



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those capable of hydrogen bonding, a significant increase in fluid−fluid interactions could occur with a simultaneous but not (usually) numerically equivalent decrease in fluid−HES interaction enthalpy released. Consequently, the shape of isosteric heat of adsorption curves at Low Coverage would depend on these as competitive effects: a resulting increase in isosteric heat would be due to Δqf−f > Δqf−HES and vice versa. The governing equation for the low coverage isosteric heat would be eq 2 as none of the contributing heats can be neglected over this range. High Coverage. This range of coverage is so defined to encompass the expected fluid−fluid interactions that would predominate pore filling and/or wide pore surface or multiple layer adsorption processes. Specific fluid−solid interactions would be complete, but any structure within the adsorbed phase due to dipole moment induction effects would possibly extend the upper limit of Low Coverage. The fluid−fluid enthalpy contributions to the isosteric heat of adsorption would become equivalent to the adsorptive latent heat of condensation. Overall, at high coverage qst = qL + βqf − s

where q L represents the adsorptive’s latent heat of condensation. Previous classifications based on the adsorption of the adsorptives in this work focused on the range of relative pressure encompassing pore filling.13 Apart from the aforementioned interaction contributions to the isosteric heat of adsorption, enhancement as adsorption enthalpy defined by the quotient of adsorptive kinetic diameter and pore width could also contribute to the initial (zero) coverage analysis. This contribution was made independent by comparing adsorptives with relatively similar kinetic diameters. The analyses made below were categorized into: (a) the classical adsorptives (N2 and Ar); (b) predominantly nonspecific interactions (H2O and DCM); and (c) similarly sized adsorptives as (i) small adsorptives (CH4 and MeOH); (ii) medium adsorptives (i-butane and i-PrOH); and (iii) large adsorptives (SF6 and 2M2B). The contrast in these size comparisons considered polarity contributions. For each adsorptive, multiple temperature adsorption isotherm data are presented as Supporting Information. The detailed information on the isotherm shape and pore filling mechanisms was also given elsewhere.13 Classical Adsorptives: N2 and Ar. Both N2 and Ar are accepted as standard probes for porous materials characterization. They are classified as nonpolar and almost nonpolarizable13 and possess sufficiently small kinetic diameters (0.34 nm for Ar and 0.36 nm for N2) to probe medium- and large-sized micropores. Calculated isosteric heats of adsorption for N2 and Ar were shown in Figure 3a and 3b. Since both adsorptives are nonpolar, isosteric heats of adsorption at zero coverage, qst,0, equate to nonspecific fluid−solid interactions. Enhanced zerocoverage isosteric heat was observed for both adsorptives compared to their heats of adsorption on a flat surface, qf−s,1, attributed to porosity; N2 and Ar adsorbates interact with multiple carbon walls. Due to the nonpolar nature of each adsorptive, contributions of both increasing fluid−fluid interactions and decreasing specific fluid−solid interactions are negligible, and the isosteric heat was relatively constant across the low-coverage range. As the coverage increases, more surface would be covered with adsorbate, and the heat of

Figure 7. SF6 (a) and 2M2B (b) adsorption isosteric heat on microporous PFA-based carbon: isosteric heat (qst), condensation heat (qL), heat of adsorption on a flat surface (qf−s,1), and twice the heat of adsorption on a flat surface (qf−s,2).

dipole moment induction, the additional fluid-HES enthalpy should also be considered. Zero coverage isosteric heat of adsorption analyses for nonpolar probes provide an estimate of pore size.23 Thus, at zero coverage For polar adsorptives: qst,0 = βqf − s + λqf − HES

(3)

where qst,0, qf‑s, and qf‑HES represent zero coverage isosteric heat and nonspecific and specific fluid−solid interactions, respectively. For nonpolar adsorptives: qst,0 = βqf − s

(5)

(4)

The coefficients are maintained in these expressions to demonstrate the possibility of nonlinear addition. For nonporous materials or microporous materials with relatively large pore size compared to the probe size, nonspecific fluid−solid interaction heat qf−s would be constant valued for a constant pair adsorptive−adsorbent. The values for each adsorptive are presented in Table 1 recognizing first or equivalent monolayer coverage qf−s,1 . For porous materials with pore sizes comparable with the adsorptive size, this heat would become enhanced due to interactions with multiple pore walls. The ultimate case would be interaction between an adsorptive molecule with the pores of the same size in which case the fluid−solid interaction heat would be twice the heat of adsorption on a flat surface qf−s = 2qf−s,1. Low Coverage. This definition considers that all, or almost all, of the HESs and any other surface reference point on which adsorption might commence would be available and contribute to the isosteric heat of adsorption as a combination of fluid− fluid and fluid−solid interactions. With the first and, in some instances, subsequent interactions between isolated or geminal, highly electronegative HES and polar adsorptives, enhanced by F



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nonspecific fluid−solid interaction would reach zero (qf−s = 0); isosteric heat at high coverage would equate to condensation heat qL. This convergence to condensation heat was clearly shown in Figure 3 for both adsorptives. Specific Adsorptives with Negligible Nonspecific Interactions: H2O and DCM. The classical adsorptive for assessing the presence of high energy surface sites on porous carbons is H2O. It has a small kinetic diameter (0.27 nm) and shows almost no affinity for nonspecific interactions with the carbon surface. Having a high polarity and potential for hydrogen bonding, H2O exhibits exceptional fluid−fluid (qf−f) and specific fluid−solid (qf−HES) interactions. The amount of H2O adsorbed at extremely low coverages has been used to quantify surface density or surface concentration of HESs, particularly surface oxygen groups.14,29 Similar to H2O, DCM has a relatively small kinetic diameter (0.33 nm) and high polarity, indicating its potential for specific fluid−solid (qf−HES) interactions. In contrast, DCM also offers nonspecific interactions with surface carbon atoms through its chlorine atoms, which have no hydrogen bonding capability; fluid−fluid (qf−f) and specific fluid−solid (qf−HES) interactions are weaker compared to H2O. Calculated isosteric heats of adsorption for these two adsorptives were shown in Figure 4. Since both adsorptives are polar, they exhibited large specific fluid−solid interactions (qf−HES) at zero coverage. This enhanced zero coverage enthalpy was significantly larger for H2O because of its additional hydrogen bonding with HESs, producing more than twice the heat of adsorption on a carbon flat surface, qst,0 > qf−s,2. In the Low Coverage range, both adsorptives showed decreasing trends, indicating the dominant effect of decreasing specific fluid−solid interactions (qf−HES) compared to fluid− fluid interactions (qf−f). As the coverage increased HESs became saturated, diminishing qf−HES. H2O had negligible affinity for the carbon surface at High Coverage adsorbing via condensation reflected in the isosteric heat equivalent to the latent heat of condensation. Unlike H2O, DCM contributed additional nonspecific fluid−solid interaction through chlorine atoms postponing the fractional filling heat reduction to qL until considerably higher fractions (Figure 4b). Small Adsorptives: Nonpolar CH4 vs Polar MeOH. The adsorptives CH4 and MeOH have similar conformation and small kinetic diameters (0.38 and 0.43, respectively) offering the ability to probe medium and large micropores. The alcohol group in MeOH provides the primary contrast between this pair suggesting it should exhibit hydrogen bonding interaction enthalpies as increased fluid−fluid and specific fluid−solid interaction enthalpies to qst compared with CH4. The results in Figure 5 showed substantially different isosteric heat responses to fractional filling, providing insight into and confirmation of their respective adsorption mechanisms. The physical properties in Table 1 indicate the kinetic diameter for CH4 ≅ 1.1 times those for Ar. Both have zero dipole moment, and the isosteric heat response to fractional filling CH4 was similar in conformation but ≈15% elevated to that for Ar. This modest increase at Zero Coverage was most likely due to improved packing in the smallest pores up to the mean pore size = 1.5σCH4, confirmed by comparing qst,0 with qf−s,1, interpreted as interaction with multiple pore walls.30 Applying these same arguments to compare MeOH with CH4, one would expect similar increases in nonspecific interaction

contributions to qst,0 and relatively large specific fluid−solid interactions via the OH, qf−HES. Overall, the Zero Coverage isosteric heat, qst,0,MeOH, would be a combination of specific and nonspecific interactions via OH and CH3 groups within the molecule. The Low Coverage fractional filling isosteric heat for CH4 was relatively constant up to 0.1 controlled by relatively small fluid−fluid interaction enthalpies, with negligible contributions from HES-induced polarity in the adsorbate, qf−HES → 0. Considerable contrast existed between these two adsorption enthalpies where, in the Low Coverage fractional filling by MeOH, the isosteric heat increased with filling. The dipole moment in the OH group led to hydrogen bonding in the adsorbed phase implying that the Low Coverage filling enthalpy was due to an increasing fluid−fluid interaction. Both adsorbates showed a gradual decrease in enthalpy in the High Coverage filling range. As the coverage increased, pores of similar dimensions to the probes would be occupied, and consequently enhancement due to multiple pore wall interactions disappears, resulting in a decrease in the isosteric heat at High Coverage. Medium-Sized Adsorptives: Nonpolar i-Butane vs Polar i-PrOH. Both i-butane and i-PrOH were considered as medium-sized adsorptives to probe microporous materials with the kinetic diameter of 0.5 and 0.47 nm, respectively. Previous immersion calorimetry analyses on the same PFA-based microporous carbon showed that although i-PrOH had critical dimensions close to the average pore size molecular conformation and size detracted from influences on packing efficiencies resulting in a reduced heat of immersion.10 The secondary OH group provides significant polarity promoting specific fluid−solid interactions and fluid−fluid interactions via hydrogen bonding. In contrast, i-butane has similar size and conformation, negligible polarity (0.1 D, Table 1), and no potential for hydrogen bonding. The isosteric heats of adsorption for these adsorptives were shown in Figure 6. The Zero Coverage i-butane isosteric heat, qst,0,i‑butane, was developed from enthalpy changes due to nonspecific fluid− solid interactions, with an expected negligible specific fluid− HES interaction contribution (based on its nominal dipolar property). The kinetic diameter was 0.88wmean suggesting not only that would this adsorptive have diffused readily into pores < wmean but also qst,0,i‑butane probably had contributions from interactions with multiple pore surfaces10 resulting in the enhanced enthalpy approaching qf−s,2.30 Although i-PrOH has dimensions similar to i-butane, the OH moiety provided a hydrogen bonding contribution via HES interactions. The three carbon alkyl backbone would have contributed (near) simultaneous nonspecific fluid−solid interaction enthalpy to the total Zero Coverage isosteric heat. The shape of the isosteric heat dependence on fractional filling up to 0.1θ clearly decreases from the qst,0,i‑butane value, suggesting that the contribution from the small-valued dipole moment (qf−HES) diminished with increasing filling. As fractional filling approached 0.1θ, the (van der Waals intramolecular) fluid−fluid interactions were enhanced by contributions from multiple fluid−solid interactions, as discussed above. In contrast, the isosteric heat for i-PrOH increased in value with Low Coverage indicating the HES interaction impact declined to a condition where contributions from qf−HES were equivalent in magnitude to qf−f.10 Maximum adsorbed phase density would only be achieved with incomplete packing in pores in the wmean range. G


large size

medium size

small size

specific; no nonspecific potential

hydrogen bonding: OH and HESs + small nonspecific f−s interactions

nonspecific f−s interaction + large porosity enhancement

hydrogen bonding: OH and HESs + relatively large nonspecific f−s interactions + large porosity enhancement nonspecific f−s interaction + significant porosity enhancement (perfectly fits pores)

hydrogen bonding: OH and HESs + large nonspecific f−s interactions + significant porosity enhancement (perfectly fits pores)

MeOH

i-butane

i-PrOH

2M2B

SF6

nonspecific f−s interaction + porosity enhancement

polarity-induced specific interation: DCM and HESs

DCM

CH4

hydrogen bonding: H2O and HESs

H2O


Ar

zero coverage mechanism


probe

N2

adsorptive group

classical

Table 2. Summary of the Adsorption Mechanism in Different Coverage Ranges low coverage mechanism

H

2D condensation + hydrogen bonding: OH and HESs + nonspecific f−s interactions + significant porosity enhancement

2D condensation + hydrogen bonding: OH and HESs + nonspecific f−s interactions + porosity enhancement multilayer adsorption + significant porosity enhancement + 2D condensation

condensation + hydrogen bonding: OH and HESs + small nonspecific f−s interactions condensation is dominant nonspecific adsorption + relatively large porosity enhancement + 2D condensation

condensation + hydrogen bonding: H2O and HESs latter is dominant polarity-induced specific interation: DCM and HESs + Condensation former is dominant multilayer adsorption + porosity enhancement + condensation

multilayer adsorption + porosity enhancement + condensation

condensation + multilayer adsorption + porosity enhancement

high coverage mechanism

condensation + multilayer adsorption + porosity enhancement latter disappears with coverage condensation + multilayer adsorption + porosity enhancement latter disappears with coverage condensation + multilayer adsorption + porosity enhancement latter disappears with coverage nonspecific adsorption + relatively large porosity enhancement + 2D condensation porosity enhancement disappears with coverage 2D condensation + multilayer adsorption + porosity enhancement nonspecific adsorption + relatively large porosity enhancement porosity enhancements continues with coverage 2D condensation + nonspecific f−s interactions + significant porosity enhancement porosity enhancements continues with coverage

condensation + multilayer adsorption + porosity enhancement latter disappears with coverage condensation + multilayer adsorption + porosity enhancement latter disappears with coverage condensation

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At High Coverage ≤0.8θ, the isosteric heat for both adsorptives remained elevated relative to qL and qf−s,1 for ibutane. For the latter, the low-pressure adsorption isotherm data in Figure S4a indicated that a wide relative pressure range (2 × 10−5 ≤ p/p0 < 0.17) was required for pore filling up to 0.8θ, substantiating that the qf−f interactions were supported by multiple wall interactions as porosity effects in increasingly larger pores were responsible for the elevated isosteric heat. The subsequent rapid decline toward qL was consistent with pores filled. Similar arguments describe the High Coverage response for i-PrOH, but the pore filling occurred over a considerably narrower relative pressure range (2 × 10−3 ≤ p/p0 < 0.012). The moderately increased amount of i-PrOH adsorbed over this narrower range would suggest that the intramolecular forces and associated heat via the OH group led to greater levels of structure or increased adsorbed phase density within the pores. Relatively Large Adsorptives: Nonpolar SF6 vs Polar 2M2B. In these comparisons, both SF6 and 2M2B were classified as relatively large kinetic diameter adsorptives (0.55 and 0.6 nm) appropriate to probe and characterize medium and large micropores.13 The former is spherical and nonpolar: the strongly electronegative fluorine atoms promote polarization of an S−F bond in the presence of surface HES. The latter has a 3D conformation with each axis of different length, the largest along the alkyl backbone. The secondary alcohol provides interaction with HES in a manner similar to i-PrOH, as well as fluid−fluid interactions through hydrogen bonding and van der Waals dispersion forces. These same interactions and conformations would be expected to contribute to packing effects and multiple pore-surface contact heats of adsorption. Immersion calorimetry analyses were interpreted as single-layer pore filling with maximum interaction between the probe and two pore walls for wmean, extending to multiple contacts with increasing pore widths.10 The isosteric heat for the two adsorptives was summarized in Figure 7. The spherical nature and kinetic diameter of SF6 suggested preferential adsorption in pores of width wmean provided the isosteric heat at Zero Coverage. The heat approached qf−s,2, interpreted as an optimized pore filling following the observations of Everett and Powl,30 which focused on nonpolar atoms adsorbed by slit-shaped pores, ignoring any specific adsorption effects. The average width in the PSD (0.57 ± 0.05 nm) suggests that statistically 2M2B (0.6 nm) would also be expected to adsorb preferentially in pores of width wmean and provide a Zero Coverage isosteric heat similar to that for SF6. The results in Figure 7b clearly showed that this was not the case. Although polarizability effects were discounted for SF6, the permanent dipole in 2M2B should have provided specific interactions with HES in competition with van der Waals dispersion force interactions with the carbon surface. The relatively smaller qst,0,2M2B compared with qst,0,i‑PrOH and qst,0,MeOH demonstrated that the principal interaction within the pores of width wmean was most probably dispersion force fluid−solid interactions, but specific fluid−HES contributions should not be ignored. The isothermal data for SF6 in Figure S5a indicated that there was appreciable uptake as pore filling occurred in the Low Coverage range over a relatively wide range of pressure (0.01 ≤ p, kPa < 1). The modest decrease in qst,0,SF6 indicated that the influences of qf−f and qf−HES remained subordinate to fluid−solid interactions during pore filling, with multiple wall

interactions increasing at the expense of a reducing packing density. In contrast, the isosteric heat for 2M2B increased slightly, akin to but significantly less than those for MeOH and i-PrOH. The slight increase again suggested that contributions from qf−f probably exceeded those from qf−HES. The High Coverage SF6 fractional filling in Figure 7a responded with elevated isosteric heats relative to qf−s,1 and remained constant up to the equilibrium pressure limitation equivalent to 0.7θ. This enhanced isosteric heat is interpreted as contribution of interaction with multiple pore walls plus condensation heat (qf−s + qL). The results terminated at 0.75θ because further filling would have exceeded the 101 kPa limit of the glass sample container. The large dipole moment of 2M2B (1.9 D) imposed by the OH group implied that strong fluid−fluid interactions via 3-D hydrogen bonding and condensation pore filling processes would be influential in this range of fractional filling. The adsorptive dimensions relative to the available pores tempered these processes, reducing pore filling to 2-D structures; consequently, qf−f < qL. The most likely mechanism of pore filling at High Coverage combined nonspecific fluid−solid interactions with incomplete fluid−fluid interactions in confined pore spaces.

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CONCLUSIONS The adsorption isotherms of a unique set of 10 nonpolar and highly polar adsorptives were obtained at multiple temperatures on a well-characterized, PFA-based, microporous carbon. The isotherms were statistically independent, but the temperatures were sufficiently close to provide linear plots of the Clausius−Clapeyron equation and thus unique values for isosteric heats. Fluid−fluid, nonspecific fluid−solid, and specific fluid−HES interactions were discussed as the underpinning components of the adsorption isosteric heats. The resulting heat curves were discretized into three ranges: Zero Coverage, Low Coverage (up to 0.1 fractional filling), and High Coverage. The ensuing results allowed a classification as summarized in the Table 2. The above adsorptives, their high-resolution multiple-T adsorption isotherms and subsequent isosteric heats, and the interpreted interaction discussions significantly enhance the current literature and the current understanding of the adsorption and isosteric heat. Although a specific adsorbent was used, it was clear that the methodologies and interpretations were quite general and could be extended to a wider combination of adsorptives and adsorbents.

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jced.8b00363.

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Multiple temperature adsorption isotherms for the ten adsorptives including the low-pressure adsorption data (PDF)

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Tel.: +61 (0)8 8313 1265. ORCID

Phillip Pendleton: 0000-0003-1031-8170 I



Article

Present Address

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College of Science & Technology, Nottingham Trent University, Nottingham NG1 4FQ, UK. Funding

The authors thank the Australian Research Council discovery program (DP110101293) for funding support. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The authors thank Prof Teresa Bandosz for fruitful discussions related to data analyses.

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REFERENCES

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Isosteric Heats of Adsorption of Gases and Vapors on a Microporous

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