Phase Behavior and Capillary Condensation Hysteresis of CarbonDioxide in MesoporesSilvio Dantas,† Katie Cychosz Struckhoff,‡ Matthias Thommes,*,§ and Alexander V. Neimark*,†

†Department of Chemical and Biochemical Engineering, Rutgers, The State University of New Jersey, 98 Brett Road, Piscataway,New Jersey 08854, United States‡Anton Paar Quantatec Inc., 1900 Corporate Drive, Boynton Beach, Florida 33426, United States§Department of Chemical and Bioengineering, Institute of Separation Science and Technology, Friedrich-Alexander UniversityErlangen-Nurnberg, 91058 Erlangen, Germany

*S Supporting Information

ABSTRACT: Carbon dioxide adsorption on micro- and meso-porous carbonaceous materials in a wide range of temperatures andpressures is of great importance for the problems of gas separations,greenhouse gas capture and sequestration, enhanced hydrocarbonrecovery from shales and coals, as well as for the characterization ofnanoporous materials using CO2 as a molecular probe. Weinvestigate the influence of temperature on CO2 adsorption focusingon the capillary condensation and hysteresis phenomena. Wepresent experimental data on the adsorption of CO2 on CMK-3,ordered carbon with mesopores of ∼5−6 nm, at various temper-atures (185−273 K) and pressures (up to 35 bars). Using MonteCarlo (MC) simulations in the grand canonical and mesocanonical ensembles, we attempt to predict the transition fromreversible capillary condensation to hysteretic adsorption−desorption cycles that is experimentally observed with the decrease oftemperature. We show that although the desorption at all temperatures occurs at the conditions of pore vapor-liquidequilibrium, the capillary condensation is a nucleation-driven process associated with an effective energy barrier of ∼43 kT,specific to the sample used in this work. This barrier can be overcome at the equilibrium conditions in the region of reversiblecondensation at temperatures higher than 240 K. At lower temperatures, the regime of developing hysteresis is observed withprogressively widening hysteresis loops. The position of capillary condensation transition is estimated using the pressuredependence of the energy barrier calculated by the thermodynamic integration of the van der Waals-type continuous canonicalisotherm simulated with the gauge cell MC method. These findings lay the foundation for developing kernels of CO2 adsorptionand desorption isotherm for calculating the pore size distribution in the entire range of micropore and mesopore sizes from onehigh-pressure experimental isotherm.

■ INTRODUCTION

Specifics of CO2 adsorption on nanoporous materials,especially, on micro- and mesoporous carbons, have beenattracting continuous interest of interdisciplinary scientificcommunities due to pressing problems of CO2 separation,capture, and sequestration, as well as the use of CO2 inenhanced gas recovery from shales and coal.1,2 Carbon dioxidehas been proven to be a suitable probe molecule tocharacterize microporous carbons due to its ability to beadsorbed at ambient temperatures, allowing for faster diffusionrates and penetration into the narrowest micropores notnormally accessible by cryogenic adsorbates.3,4 Recenttechnological advances in adsorption instrumentation technol-ogy have enabled reliable gas adsorption experimentsperformed with automated adsorption instruments usingcarbon dioxide at high pressures and temperatures.5 As aresult, the appraisal of the pore size distributions (PSD) overthe full micro- and mesopore range from one experimentalCO2 isotherm becomes available. The quantitative interpreta-

tion of measured isotherms requires a better understanding ofthe CO2 adsorption and phase behavior in micro- andmesopores, most importantly, of the mechanisms of capillarycondensation and hysteresis. The main challenge resides inpredicting the pressure of condensation in the so-called regimeof developing hysteresis6 as a function of the pore size andtemperature. Here, we report experimental adsorption data ofCO2 on ordered mesoporous carbons of CMK-3-type over thewide ranges of temperatures (from 273 down to 185 K) andpressures up to the saturation (∼35 bar at 273 K). Theexperimental observations are explained using the Monte Carlo(MC) simulations harnessed with the theoretical analysis ofthe nucleation phenomena during capillary condensation.The use of carbon dioxide as a probe molecule for

adsorption measurements was proposed at temperatures

Received: June 9, 2019Revised: July 31, 2019Published: August 5, 2019

Article

pubs.acs.org/LangmuirCite This: Langmuir 2019, 35, 11291−11298

© 2019 American Chemical Society 11291 DOI: 10.1021/acs.langmuir.9b01748Langmuir 2019, 35, 11291−11298

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close to 273 K,7 as a way to overcome critical limitationsobserved with traditionally used cryogenic adsorbates (e.g., N2:77 K and Ar: 87 K). Due to nitrogen’s quadrupole momentand strong interactions with carbon surfaces, diffusion intosmaller pores is effectively inhibited. Argon facilitates theresolution of smaller micropores (∼0.5 nm) at higher relativepressures than N2.

7,8 However, activated carbons may containsignificant amounts of ultra-micro-pores (<0.5 nm), and accessto these micropores is further limited by diffusion. Carbondioxide, with a slightly smaller kinetic diameter and hightemperature of adsorption, enables higher diffusion rates,ultimately producing a better resolution of ultra-micro-pores.9

With access to a wide range of relative pressures, from theultrahigh vacuum (P/P0 = 10−7) to pressures up to more than80 bar, one can measure full subcritical CO2 adsorptionisotherms. The application of modern methods based on MCand density functional theory (DFT) simulations for theinterpretation of adsorption measurements allows for accurateevaluation of the pore size distributions of nanoporousmaterials within the whole micro- and mesopore range.With high microporosity, carbon-based materials are widely

used for many applications including capture and sequestrationof gases,10 filtration processes,11 energy storage,12 catalysis.13

In the search for new structures, advanced templatingprocedures have been developed leading to the synthesis ofordered mesoporous carbon materials.14 In 2000, Ryoo and co-workers15 reported the synthesis the first CMK-3, an orderednanoporous carbon material that retains the same structuralsymmetry as its template, SBA-15,16 a well-known orderedmesoporous silica molecular sieve. The ability to tune thewidth of the primary group of pores on such well-orderedstructures enables the synthesis of materials with large poresurface area and pore volume. Understanding the texturalproperties (e.g., surface area, pore size, porosity) of thesematerials is key to perfecting their use in catalysis, separations,and many other applications.8 With most of the pores in CMK-3 carbons being in the mesopore range, a better understandingof the process of capillary condensation and the possiblehysteresis behavior that can be observed under certainconditions is required.Capillary condensation represents a phenomenon of gas

condensation in pores into a liquid-like phase at a pressuresmaller than the saturation pressure, P0, of the bulk fluid. Dueto the influence of pore confinement, the vapor−liquidtransition occurs below the pore critical temperature, Tcp,which is smaller than the bulk critical temperature.17 Providedthe pores are sufficiently large, capillary condensation isaccompanied by hysteresis. In the absence of pore networkeffects, the hysteresis in cylindrical pore channels is solelydetermined by the effect of delayed condensation (due to themetastable pore fluid), whereas the desorption branch reflectsthe liquid−vapor equilibrium transition.18 The hysteresisphenomenon depends on temperature and pore size: theincrease in temperature has a qualitatively similar effect as thedecrease in the pore size, leading to a reduction in the width ofthe hysteresis loop. For a given pore size, the hysteresis loopeventually disappears at a so-called hysteresis critical temper-ature Th, which is below Tcp.

6,19 For a given temperature, thepositions of phase transformations depend on the pore size,and the hysteresis appears in pores wider than a certainhysteresis critical pore size. From the comparison of thecanonical ensemble van der Waals-type isotherms generated bythe mesocanonical ensemble gauge cell MC simulation and

classical DFT simulations with the experiments, the authors6

have classified the adsorption isotherms into four regimes. (1)Supercritical sorption without phase separation above the porecritical temperature, T > Tcp; (2) reversible capillarycondensation between the pore critical temperature and thehysteresis critical temperature, Th < T < Tcp; (3) irreversiblecapillary condensation with developing hysteresis loop astemperature reduces below the hysteresis critical temperature,T < Th; and (4) irreversible capillary condensation with adeveloped hysteresis loop upon further decrease of temper-ature. A hysteresis loop is considered developed, whencapillary condensation occurs at the limit of metastability ofthe vapor-like state (vapor-like spinodal), and developing, ifcapillary condensation occurs between the equilibrium and thevapor-like spinodal. Similar regimes are observed for theisotherms at a fixed temperature and varying pore sizes. It isworth noting that the nucleation-driven phase transitionsdepend on temperature, pore size, and fluid−solid pair.20

The use of molecular simulations can be invaluable to thecharacterization of materials such as CMK-3 materials, as theycan exhibit all of the capillary condensation regimes describedabove. Under subcritical conditions, grand canonical MonteCarlo (GCMC)21 simulations allow for calculations of theadsorption and desorption branches that form the hysteresisloop, bounded by the condensation and evaporationstransitions in the system. Among several methods that havebeen developed22−25 to determine the equilibrium transitionbetween states under confinement, the gauge cell method26,27

has been proven to be useful and reliable.28−36 Themesocanonical ensemble gauge cell MC method allows forcalculating the equilibrium transition and the spinodal limits ofstability of the vapor-like and liquid-like metastable states, andfurthermore, for estimating the energy barriers that separatethem. The key aspect of this method is the use of a gauge cellset in chemical and thermal equilibrium with the system cellthat contains the adsorbent. The gauge cell method allows forcalculating the chemical potential of the adsorbed phase andconstructing the continuous van der Waals-type adsorptionisotherm.26,27 Of special interest is the recent work,31 wherethe gauge cell simulations were used to calculate the nucleationbarriers for capillary condensation of Ar and analyze thedifferent capillary condensations regimes observed experimen-tally at three temperatures and for two different MCM-41samples.In the present study, we explore the phase behavior of CO2

under the confinement of micro-mesoporous carbon materialsat various temperatures through high-pressure CO2 adsorptionexperiments and MC simulations in the grand canonical andmesocanonical ensembles. Experimental adsorption data at185−273 K is obtained on a CMK-3 sample with microporesof about 1 nm and mesopores of about 6 nm. As thetemperature decreases, a gradual transition is observed fromreversible to hysteretic isotherms, and below the triple point, toreversible isotherms limited by desublimation. Theoreticalisotherms are obtained at 210, 220, 240, and 273 K using theTraPPE model37 for CO2 and a Lennard-Jones (LJ) solid−fluid potential to implicitly represent the carbon pore of 6 nmin diameter. Using both grand canonical and mesocanonicalensembles, we accurately identify the positions of equilibriumvapor−liquid transition and of the vapor and liquid transitionsthat correspond to the limit of stability of respective vapor-likeand liquid-like phases. To properly predict capillary con-densation, we calculate the pressure dependence of the

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nucleation barrier for condensation. From the comparisonbetween experiments and simulations, we estimate a character-istic energy barrier of ∼43 kT, which represents the criticalbarrier that has to be overcome to transit from vapor tocondensed states. This finding allows us to predict theexperimentally observed features of CO2 capillary condensa-tion and reproduce the adsorption isotherms in the regime ofdeveloping hysteresis.

■ METHODOLOGYExperimental Measurements: High-Pressure CO2

Adsorption. Ordered mesoporous carbon samples38,39 wereoutgassed at 423 K for 12 h under turbomolecular pumpvacuum. Ar (87 K) and N2 (77 K) adsorption measurementswere performed on a high-resolution low-pressure nanometricadsorption equipment (Quantachrome Instruments Autosorb-iQ MP). CO2 high-pressure adsorption measurements wereexecuted on a Quantachrome Instruments iSorb HP. Temper-atures below 263 K were maintained by using a QuantachromeInstruments’ CryoCooler.Molecular Modeling. The modeled pore structure for the

carbon adsorbent is composed of perfectly smooth, rigid, andinfinitely long cylindrical pores. The simulations are performedin a cubic cell with periodic boundary conditions on all threeaxes with “padding” of half of the cutoff distance added to thesides of the pore. Carbon dioxide is modeled by using theTraPPE model37 with 15 Å cutoff, Ewald summation, and tailcorrections, to reproduce bulk properties properly in the rangeof temperatures of interest (see the Supporting Information,Section A). All simulations were performed using the MCCCSTowhee software package40 with the addition of the cylindricalsolid−fluid potential, eq 1.41 In eq 1, r is the distance betweenthe fluid atom and the center of the cylinder; R represents halfof the diameter of the cylindrical potential that differs from theinternal pore diameter by σs = 0.34 nm; ρA is the area densityof carbons atoms in the pore surface; σsf and ϵsf are the LJsolid−fluid interaction parameters; F(a,b,c,d) is the hyper-geometric function. The Lennard-Jones (LJ) parametersemployed are as follows: σO−O = 0.305 nm, ϵO−O/kb = 79 K,σs−O = 0.3225 nm, ϵs−O/kb = 46.184 K, σC−C = 0.28 nm, ϵC−C/kb = 27 K, σs−C = 0.31 nm, and ϵs−C/kb = 27 K with ρA = 38.19nm−2. The solid−fluid interaction parameters, ϵsf and σsf, arecalculated using Lorentz−Berthelot mixing rules with thefluid−fluid TraPPE parameters and solid−solid parameters,σs−s = 0.34 nm and ϵs−s/kb = 27 K, determined from fitting tothe experimental data.42

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The densities of the adsorbate both in bulk and in confinedspace are calculated using the GCMC method. In this method,the grand thermodynamic potential of the system at a fixedpressure, which is correlated to the chemical potential,temperature, and volume, is minimized over the course ofthe simulation using the Metropolis algorithm. Simulation

moves include: insertion/deletion (50%), center-of-masstranslation (25%), and rotation about the center-of-mass(25%). The density of the system is calculated by averagingover a minimum of 2 × 106 steps after the equilibration stagefor at least 4 × 105 steps. For simulations in the bulk, thesimulation box has a volume of (45 Å)3. The system simulationbox has dimensions of 30.5 Å × (2 × R + 7.5) Å × (2 × R +7.5) Å.The mesocanonical ensemble Gauge Cell MC method26,27 is

applied here to calculate the chemical potential of theadsorption system at different densities, in the vicinities ofthe capillary condensation step. The simulation is performed intwo cells of fixed volume, the system cell representing the pore(the same from GCMC simulations) and the gauge cellrepresenting the gas phase. Simulation moves include moleculeinterbox transfer (20%), center-of-mass translation (40%), androtation about the center-of-mass (40%). Simulation results arecalculated by averaging over N × 104 steps after beingequilibrated for at least N × 103 steps, where N is the numberof CO2 molecules in the system at each point.This method provides access to metastable states by

suppressing density fluctuations, allowing for the constructionof the canonical ensemble isotherm in the form of the van derWaals loop (see Figure 1). This isotherm identifies: (i) the

region, −∞ < μ < μsv, of vapor-like states, Nv(μ,T), terminatingat the vapor-like spinodal, μsv; (ii) the region, μsl < μ < 0, ofliquid-like states, Nl(μ,T), terminating at the liquid-likespinodal, μsl; (iii) the backward trajectory of transient states,μsl < μ < μsv. The transient states are unstable if the system isopen; they are stabilized due to reduced fluctuations in thegauge cell method. The continuity of this isotherm allows forthe estimation of the equilibrium pressure and the energybarrier that separates the vapor-like and liquid-like states bythermodynamic integration. The equilibrium pressure iscalculated by applying Maxwell’s rule of equal areas (eq 2)to find a chemical potential, μVLE, to which the shaded area tothe left is equal to the shaded area to the right. Nv, Nt, and Nl

are the amount adsorbed within the vapor (v), transient (t) orliquid (l) regions, respectively.

Figure 1. Canonical ensemble van der Waals-type adsorptionisotherm. The positions of vapor−liquid equilibrium and vapor andliquid spinodals are shown by red broken lines. Green broken linerepresents the chemical potential at which the energy barrier is beingcalculated.

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Here, Nt and Nv are the densities calculated frommesocanonical ensemble MC simulations for transient statesand vapor states, respectively. The dotted green line in Figure1 represents the chemical potential μ′ in which the energybarrier is being calculated. As the energy barrier is proportionalto the shaded area to the right of the green line, it peaks at theequilibrium chemical potential, μVLE, and diminishes at thevapor spinodal, μsv. The energy barrier E is estimatednormalizing ΔWvl by the aspect ratio of the modeled pore,L* = pore length/pore diameter, to allow for comparisonacross systems of different sizes

μ μ μ μ′ = Δ * ≤ ′ <E W L( ) / , for LEvl V sv (5)

Capillary condensation should occur at equilibrium if thesystem is able to surpass the energy barrier E at the chemicalpotential μVLE of the reversible capillary condensation.Otherwise, capillary condensation should take place at a

chemical potential, μ′ > μVLE, at which the system canovercome the energy barrier.

■ RESULTS

Experimental Adsorption Data. When analyzing theadsorption behavior, one must consider the specifics of thepore size distribution (PSD) for a given material. Determinedfrom the low-temperature adsorption isotherms of N2 and Ar(Figure 2a), the PSDs (Figure 2b) of the sample of CMK-3considered here indicate the presence of well-defined regularprimary mesopores in the range of 5−6 nm, a fraction ofmicropores centered around 0.8 m, and a group of wider (>7nm) disordered secondary mesopores, as indicated by arelatively small but clearly visible shoulder. The Ar and N2 PSDcurves, obtained by using appropriate quenched solid densityfunctional theory slit-cylindrical models,43 are in perfectagreement and also in line with what has been reportedpreviously.39,44

To assess the correlation between temperature and capillarycondensation regimes of CO2 adsorption on the sampledescribed earlier, a set of experimental measurements wereperformed from 185 up to 273 K. Figure 3 shows the data involume adsorbed (cm3 of CO2 per g of CMK-3) as a functionof absolute pressure in a semilog (Figure 3a) and relativepressure in a linear plot (Figure 3b). The semilog plot allowsfor highlighting the adsorption and micropore filling region inthe low-pressure range.The isotherms at 185 and 195 K (only on Figure 3a) show

the filling of micropores, but no pore filling of the mesoporescould be observed although the adsorption isotherms weremeasured up to the corresponding saturation pressure of thesolid (bulk desublimation), i.e., here it was not possible withinexperimental resolution to differentiate between a phasetransition in the pore and in the bulk. Contrary to this, at210 K, still below the bulk triple point of CO2 (216.6 K), the

Figure 2. (a) Adsorption isotherms of N2 (77 K) and Ar (87 K). (b) Pore size distribution analysis of each isotherm using QSDFT kernels.

Figure 3. (a) Semilog plot of CO2 high-pressure adsorption isotherms in the wide range of temperatures from 185 up to 273 K. (b) Linear plot ofthe adsorption isotherms from 210 up to 273 K.

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adsorption isotherm shows a clear capillary condensation withH1-like hysteresis, same as seen in Ar (87 K) and N2 (77 K)experiments. A similar, but narrower, hysteresis loop isobserved at 220 K, however it is absent at 240 K for themain capillary condensation step (associated with capillarycondensation into the main mesopores). On the other hand, asmall, yet discernible, hysteresis loop is still present at relativepressures larger than 0.7, representing capillary condensationinto the secondary mesopores, indicated by the beforemen-tioned shoulder between 6 and 10 nm in the PSD curvesshown in Figure 2b.For temperatures above 240 K, the hysteresis is no longer

present, as shown in the reversible isotherm at 273 K.Remarkably, the observation of reversible capillary condensa-tion over an extremely wide range of bulk-subcriticaltemperatures, i.e., from 304.25 K (CO2 bulk critical temper-ature) down to below 240 K, indicates a significant shift of thephase diagram of CO2 confined to mesopores. The porecritical temperature and, consequently, the hysteresis criticaltemperature are shifted to lower temperatures, as well as thetriple point region, as indicated by the observation of capillarycondensation at 210 K, ca. 6 K below the bulk triple pointtemperature. Qualitatively similar observations have beenmade for the adsorption of argon in narrow silica mesopores.45

GCMC Simulations. The MC simulations were performedfor a pore width of 6 nm that corresponds to the effectivediameter of primary mesopores in CMK-3. To draw aquantitative comparison between the experimental andsimulated data, the simulated isotherms in mesopores are tobe augmented to account for the contribution of micropores.The theoretical isotherms presented in Figure 4 are calculatedaccording to the following expression

ρ ρ= × + ×N T V T V T( ) ( ) ( )lmi me

MC(6)

where the micropore volume, Vmi = 0.35 cm3/g, and thevolume of primary mesopores, Vmi = 1.06 cm3/g, are estimatedby minimizing the difference between the simulated andexperimental data at pressures well below, and just above, thecapillary condensation step. ρl(T) and ρMC(T) represent thebulk liquid CO2 density and the pore fluid density calculatedfrom MC simulations, respectively. The quantitative relation ofthe isotherms for each temperature is only significant within acertain range of pressures, starting from low pressures (0.3−0.4P/P0) and up to after capillary condensation (0.65−0.85 P/P0). Below this range, the micropores are not completely filled,which is reflected in the higher values of the theoretical data.Above such range, capillary condensation occurs on thesecondary mesopores, leading to higher loadings than thepredicted by simulations. Within the range of interest, goodagreement is achieved for all temperatures with the exceptionof the capillary condensation step, which is predicted to occurat higher pressures than what is observed in experiments.Another aspect of comparison is the steepness of the capillarycondensation step, which is more accentuated in simulationsdue to the ideal nature of having one pore size, rather than apore size distribution.Figure 4 shows the contrast between experimental

adsorption isotherms (circles) and rescaled theoreticalisotherms (squares) at 273, 240, 220, and 210 K. Thesimulated data is composed by the adsorption branch,calculated using GCMC, and desorption step, defined by theequilibrium pressure calculated using the gauge cell MCmethod (shown by the red line). Although the hysteresis isabsent from both experiments and simulation at 273 K, it ispresent in the simulated data for lower temperatures. Furtheranalysis of the comparison reveals good agreement of theequilibrium pressure from simulations compared to theinflection point of the desorption curve from the experimentaldata. On the other hand, the experimental condensationpressures are not reproduced by GCMC simulations, exceptfor the highest temperature (273 K). At 240 K, the simulatedisotherm exhibits a prominent hysteresis, whereas theexperimental isotherm is reversible. This observation indicatesthe difference in the hysteresis/pore critical temperatures inthe experiments and in the simulations. This effect can beattributed to the striking difference in the observation time inreal and simulated experiments and inability to cross thenucleation barrier in GCMC simulation that occurs near thevapor spinodal. The gauge cell MC isotherms at all pressureexhibit a s-shaped van der Waals behavior indicating thereversible vapor−liquid equilibrium determined by theMaxwell rule. Furthermore, points near equilibrium reflectthe average density at the two states (vapor-like and liquid-like), shown in more details in the Supporting Information,Section B.

Condensation Pressure Estimation from EnergyBarriers. To investigate the condensation pressure discrep-ancies between experimental and simulated data, energybarriers for each simulated gauge cell MC isotherm atpressures ranging from equilibrium to vapor spinodal werecalculated using eq 5. The results, in Figure 5, show thedecrease of the energy barrier with pressure for eachtemperature, where the maximum is at equilibrium andapproaches 0 at the vapor spinodal. At 210 K, the experimentalcondensation pressure is about 0.62 P/P0, the calculated

Figure 4. Comparison of experimental (circles) and GCMCsimulated (squares) data at (a) 210 K, (b) 220 K, (c) 240 K, and(d) 273 K. The simulation data is composed by adsorption (grayclosed squares), desorption (gray open squares). The canonical vander Waals-type isotherm simulated with the gauge cell MC is shownwith the gray dashed line and equilibrium pressure with the red solidline. Isotherms at 240, 220, and 210 K are shifted to avoid overlap.

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energy barrier of the system at that pressure is Ec = 43 kT,which is taken to be the critical energy barrier, a referencevalue for the experimental system. The critical energy barrierrepresents the maximum barrier that the real system canovercome, disregarding the temperature. Therefore, it isassumed that the condensation in experiments occurs at thepressure corresponding to the critical nucleation barrier Ec. Ifthis pressure is larger than the equilibrium pressure, the systemwill exhibit hysteresis. In other words, the condensation step isdelayed in the systems with the energy barrier at equilibriumlarger than the critical energy barrier, E(μVLE) > Ec. Ec = 43 kTdetermined at 210 K is used to calculate the predictedcondensation pressure for other temperatures. At 210 and 220K, the energy barrier at equilibrium is above 43 kT, thusindicating the presence of a hysteresis loop at bothtemperatures. Remarkable that at 240 K, when theexperimental isotherm is reversible, the calculated barrier atequilibrium is around 43 kT, within the accuracy of thecalculation. This leads us to suggest that this temperature canbe considered as the critical temperature of the hysteresis ofthe given system. At 273 K, the lack of the hysteresis in bothexperimental and simulation data can be explained by the factthat the calculated energy barrier at equilibrium, 5 kT, is notonly smaller than the critical experimental energy barrier Ec butalso smaller than the critical barrier achievable within thesimulation. Such a small energy barrier allows the system tojump back and forth between vapor-like and liquid-like statesin the vicinity of equilibrium.Figure 6 further illustrates the comparison of the

experimental and simulated adsorption isotherms. All iso-therms are normalized by the maximum theoretical amountadsorbed in a 6 nm wide cylindrical pore.The snapshots displayed in Figure 7 show the final state of

the simulated system at the three equilibrium characteristicpoints, vapor-like state (Figure 7a−d), metastable (Figure 7e−h), and liquid-like state (Figure 7i−l). Some trends can beidentified from this representation, on the left column (vapor-like states), the density increases with the increase intemperature, opposite of what is observed on the right column(liquid-like) states. Furthermore, the unstable states (middlecolumn) display an increase in density from 210 to 240 Kfollowed by a density decrease at 273 K.

■ CONCLUSIONSA combination of the experiments and MC simulations revealsthe specifics of phase behavior of CO2 under confinement. Theadsorption and desorption isotherms on a sample of CMK-3,an ordered mesoporous carbon material, are measured in therange of temperatures from 185 to 273 K. Two regimesassociated with the condensation of the pore into mesoporesare found: reversible condensation at T > 240 K and capillarycondensation hysteresis at 210 K < T < 240 K. The isothermsat 185 and 195 K are associated with filling of micropores only,as the adsorption isotherms were measured up to thecorresponding saturation pressure of the solid (bulkdesublimation); it was not possible within experimental

Figure 5. Energy barriers for condensation. Red solid lines indicateequilibrium conditions. Orange dotted lines represent the predictedpressures of condensation at 210 and 220 K, at which the barrier isequal to the critical value of Ec = 43 kT.

Figure 6. Comparison between experimental and simulatedadsorption isotherms at (a) 210 K, (b) 220 K, (c) 240 K, and (d)273 K. Both equilibrium pressures (red solid line) and estimatedcondensation pressures (yellow dashed line) are illustrated by verticallines.

Figure 7. Snapshots of the simulated system at different temperaturesshowing the three different states at equilibrium pressure: (a−d)vapor-like state, (e−h) unstable state, (i−l) liquid-like state. The porewalls are not shown. CO2 atoms are represented as spheres withoxygens in red and carbons in black.

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resolution to differentiate between phase transitions in thepore and in the bulk.The grand canonical and mesocanonical (gauge cell)

simulations are performed in the model carbon cylindricalpore of 6 nm at the same temperatures, as measuredexperimentally. To evaluate the conditions of experimentallyobserved hysteresis, the nucleation barriers for the condensa-tion are estimated from the continuous gauge cell MCisotherms. Assuming that the condensation may occurprovided the nucleation barrier is smaller than a certain criticalenergy barrier Ec, the positions of experimental condensationare calculated. Ec = 43 kT is chosen as equaled the calculatedenergy barrier at the experimental condensation pressureobserved at 210 K. With this value, the experimentallyobserved hysteresis at low temperatures is fairly predicted.Moreover, it is found that at 240 K, when the experimentalisotherm is reversible, the calculated barrier at equilibrium isaround 43 kT. This leads us to suggest that 240 K can beconsidered as the critical temperature of the hysteresis of thegiven system, which separates the temperature region ofequilibrium adsorption at T > 240 K and the region ofdeveloping hysteresis at T < 240 K.With the accuracy of the predictions obtained in this work,

the method developed can be used to estimate the conditionsof delayed capillary condensation in pores of different sizes andat different temperatures. This allows one to determine thecondensation pressures in the regime of developing hysteresisthat is necessary for building the adsorption kernels for poresize distribution calculations from high-pressure CO2 adsorp-tion data.

■ ASSOCIATED CONTENT*S Supporting InformationThe Supporting Information is available free of charge on theACS Publications website at DOI: 10.1021/acs.lang-muir.9b01748.

Bulk properties of CO2; the evolution of the number ofmolecules; histogram of the number of molecules (PDF)

■ AUTHOR INFORMATIONCorresponding Authors*E-mail: matthias.thommes@fau.de (M.T.).*E-mail: aneimark@rutgers.edu (A.V.N.).ORCIDSilvio Dantas: 0000-0001-7168-4938Alexander V. Neimark: 0000-0002-3443-0389NotesThe authors declare no competing financial interest.

■ ACKNOWLEDGMENTSThis work is supported in part by the National ScienceFoundation (grant No 1834339).

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