Effect of Surface Chemistry on Confined Phase Behavior in ......and for MCM-41 with the adsorption of water.29 Other studies have focused on the industrial applications of surface

Effect of Surface Chemistry on Confined Phase Behavior inNanoporous Media: An Experimental and Molecular Modeling StudyEvan Lowry* and Mohammad Piri

College of Engineering and Applied Sciences, University of Wyoming, Laramie, Wyoming 82071, United States

*S Supporting Information

ABSTRACT: It is well accepted that nanopore size is acontrolling parameter in determining the phase behavior ofconfined adsorbate molecules. Despite this knowledge, thequantitative effect of surface chemistry on the confined phasebehavior is a factor that remains obfuscated. Obtaining acomplete understanding of the variables controlling confinedphase behavior is a critical step in developing more completeequations of state for predictive modeling. To this end, acombined experimental and molecular modeling study wasconducted to investigate the effects of surface chemistry andwetting on the confined phase behavior of propane and n-butane in modified and unmodified silica MCM-41. Isothermswere measured in four types of silica MCM-41 modified with varying sizes of alkyl groups to determine the effects of increasingsurface modification. Results showed that increased pore surface coverage of carbon resulted in a notable change in the capillarycondensation pressures, adsorption enthalpy, and confined critical temperature of the adsorbate. Correlations between thesurface coverage of carbon and the confined critical temperature were presented and supported by thermodynamic arguments.The primary conclusions were partially supported by hybrid molecular dynamics-Monte Carlo simulations of propaneadsorption in models of the four types of experimental adsorbents. Several differences were noted and explained between theexperimental and modeling results. Energetic heterogeneity on the surface of the modified MCM-41 adsorbents as well asdifferences in adsorbate entropy induced by surface features and chemistry were suggested as primary driving factors for theobserved trends. The results of this work have direct implications for improving understanding of confined phase behavior inmaterials of varying surface chemistries.

■ INTRODUCTIONThe effects of decreasing pore sizes within microporousadsorbents have been investigated at length in the recentliterature.1−4 This phenomenon is critically relevant to anumber of industrial applications and fundamental researchareas. Careful characterization of the type and extent of theeffects of confinement on phase behavior is vital forengineering design in areas such as catalysis, oil and gasapplications, and air pollution remediation.5−11 Previousstudies have suggested that confinement-induced phasebehavior, also termed and associated with capillary con-densation, appears when pore sizes are in the range of 2−100nm and when the pore diameters approach the mean free pathof the adsorbate molecules.1,2 This behavior results in a first-,or nearly-first-, order phase transition that often occurs atlower pressures than the bulk vapor−liquid phase transition.12Travalloni and colleagues produced a series of modifiedequations of state based on previous knowledge regardingcapillary condensation.13−15 The fundamental variables in theirmodels were based on the relationship between the moleculardiameter and the pore radius, with the effects of fluid−porewall interactions increasing as the pore size decreased. Thiscorrelative observation has been upheld in molecular dynamics

and Monte Carlo simulation studies.16−20 Using an empiricalapproach, Tan and Piri devised an equation of state forconfined fluids based on coupling of perturbed-chain statisticalassociating fluid theory and the Young−Laplace equations.21Despite these notable efforts, there remains a large amount ofuncertainty regarding the key variables controlling phasebehavior in confinement.Silica-based adsorbents have received much attention in

research associated with capillary condensation primarily dueto the relative ease of production via chemical templating andthe regular, nanometric pore sizes associated with suchmaterials.22 Adsorbents such as MCM-41 and SBA-15 havebeen routinely used to investigate confinement phenom-ena.23,24 Morishige et al. investigated the so-called capillarycritical points of argon, nitrogen, ethylene, and carbon dioxidein MCM-41. They showed that the capillary critical temper-ature of these confined gases is much lower than the bulkcritical point.3 In subsequent studies, the hysteresis temper-ature was differentiated from the confined critical temperature

Received: March 28, 2018Revised: June 12, 2018Published: July 14, 2018

Article

pubs.acs.org/LangmuirCite This: Langmuir 2018, 34, 9349−9358

© 2018 American Chemical Society 9349 DOI: 10.1021/acs.langmuir.8b00986Langmuir 2018, 34, 9349−9358

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pubs.acs.org/Langmuirhttp://pubs.acs.org/action/showCitFormats?doi=10.1021/acs.langmuir.8b00986http://dx.doi.org/10.1021/acs.langmuir.8b00986

by noting a change in the linearity of the plot of logarithmicpressure versus temperature over a series of measuredisotherms.4 The hysteresis temperature, confined criticaltemperature, and differential enthalpy of adsorption wereobserved to be dependent on the pore size in a number ofother studies as well.25−27

Although there is a relatively significant amount of dataavailable regarding the impact of pore size on capillarycondensation, the effects of variation in adsorbate−adsorbentinteractions are still poorly understood. The effects ofwettability on the qualitative shape of adsorption isothermswere codified in a recent IUPAC report.28 Isotherms aregenerally classified by type. A “wetting” isotherm (type IV) isindicated by a downward concave shape in the low-pressureregion, whereas nonwetting behavior (type V) is classified byan isotherm that exhibits upward concavity in the low-pressureregion. Despite having evidence of the effects of surfacechemistry on capillary condensation via isotherm shape, thereremains very little explanation of the fundamentals governingthis phenomenon. Attempts to model the effects of theseinteractions have been made by Gubbins et al. by introducing awetting parameter to the traditional expressions for the grandpartition function. This parameter is based on the ratiobetween the adsorbate−adsorbent and the adsorbate−adsorbate interactions. Although the parameter is ratheresoteric, it was shown to fit experimental data fairly well foradsorption in carbon nanotubes with a variety of adsorbatesand for MCM-41 with the adsorption of water.29 Other studieshave focused on the industrial applications of surfacemodification in MCM-41. One such study showed that ahybrid organic/inorganic MCM-41 matrix enhanced theloading and release characteristics of ibuprofen. The discussionincorporated an investigation of both pore size and surfacemodification with aminopropyl groups.30 The outcome showedthat the surface chemistry leveraged first-order effects onloading and desorption, whereas pore size was not a significantcontrolling factor. Mello et al. demonstrated that amino-modified MCM-41 served as a more efficient low-pressureadsorbent for CO2 capture due to the increased enthalpy ofadsorption compared to that of unmodified MCM-41.31 Thesurface groups induced chemisorption at lower pressure thatenhanced the low-pressure loading capacity of the modifiedMCM-41 material. Xu et al. demonstrated that adsorptioncapacity and kinetics are directly affected by the degree ofsurface modification in a silica MCM-41, which was modifiedwith polyethylenimine (PEI) to varying degrees. It wasobserved that although the PEI decreased the pore size, itled to greater loading capacity for CO2 compared to pureMCM-41 and pure PEI adsorbents.32

Several Monte Carlo studies have also investigated theeffects of interactions between surface and adsorbate. Puibassetet al. performed simulations in the grand canonical ensembleto determine the phase transition of a Lennard-Jones fluidwithin three different pore types. Using a regular, geometricallyundulated, and chemically undulated pore, the adsorptionbehavior and coexistence regions were extracted fromsimulation. Results indicated that the geometrical undulationdid not significantly impact the phase behavior of the fluid,whereas chemical undulations resulted in a larger hysteresisregion as well as created apparent intermediate phases withinthe vapor−liquid coexistence region.33,34 Other simulationsshowed that changes in the attractive parameters to make thesolid less wetting resulted in a shift of the phase behavior

toward the bulk behavior.35,36 Experimentally, most previousinvestigations of surface−fluid interactions have focused onmaximizing the adsorption capacity for the removal of volatileorganic compounds (VOCs) from industrial waste effluentstreams.37−41 Both Kim et al. and Wang et al. demonstratedthat MCM-41 and SBA-15 modified with organic surfacegroups showed superior adsorption performance with commonindustrial solvents, including hexane, gasoline, benzene, andtoluene.37,38

In spite of the aforementioned studies, there is still a lack ofunderstanding regarding the fundamental mechanisms anddriving factors that govern the interplay between adsorbent−adsorbate interactions and capillary condensation. To this end,experiments and simulations were conducted to develop abetter understanding of these complex interactions. In thefollowing section, the experimental methods and theory arepresented. This is followed by detailed presentation anddiscussion of the results, which lead to the major conclusionsof this work.

■ METHODSPreparation of Adsorbents and Fluids. Four types of

adsorbents were synthesized based on standard templated meso-porous silica MCM-41. Pure silica MCM-41 as well as silica MCM-41possessing surface modification with C1, C8, and C18 alkylfunctionalities were synthesized by Galantreo, Ltd. The adsorbentswere modified such that all had nearly the same pore diameter andresulted in alkyl bonding densities between 0.475 and 1.44 μmol/m2.Elemental analysis was provided by the manufacturer and was alsoindependently confirmed using electron-dispersive spectroscopy(EDS). EDS was conducted with a Bruker X-Flash detector with anenergy resolution of 121 eV. Measurements were taken over multiplesample particles with accelerating voltage of 10 kV and current of 0.4nA. Spectra were acquired and subjected to matrix corrections beforeintegrating and determining the averages. The results from Brunauer−Emmett−Teller (BET) and the average wt % of carbon fromelemental analysis for each adsorbent are listed in Table 1.

Pure n-butane and propane (99.995% purity) were obtained for useas the fluid phases during all experiments. The gravimetric adsorptionapparatus was designed and fabricated to produce highly accuratetemperature and mass measurements.42,43 Differential balancesmanufactured by Mettler Toledo were used to read the mass of theadsorption cells to an accuracy of 0.00001 g. Temperature wascontrolled within 0.1 K using a Thermotron environmental chamber.High-precision Rosemount pressure transducers monitored thepositive pressure of the fluid in contact with the titanium adsorptioncell, whereas Leybold vacuum gauges were used to read values belowatmospheric pressure. Data was digitally logged and recorded foraveraging after the experiment. More details about the apparatus usedin this study can be found elsewhere.43

Experimental Procedure. Four adsorption cells were firstcleaned and weighed before packing with each adsorbent andweighed again. The adsorption cells were installed into the apparatus,and the system was pressure tested at 400 psi to eliminate leaks.Special care was taken not to increase the temperature to a point

Table 1. Results of BET Analysis for Silica MCM-41 withVarious Surface Modifiers

MCM-41 surface modifier

none C1 C8 C18

surface area (m2/g) 596 345 183 122pore diameter (Å) 40 36 42 38pore volume (cm3/g) 0.49 0.34 0.22 0.15wt % C 0 6.15 12.3 17.3

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where the surface functional groups may be chemically altered orremoved from the pore surfaces. Jaroniec et al. performed a systematicstudy of the surface modification effects in silica MCM-41 usingorganosilane modification reactions. Thermogravimetric analysisshowed that, unlike standard MCM-41, the organo-modified MCM-41 had excellent thermal stability up to 100 °C, at which point theorganosilane bonds began to decompose.44 Therefore, the system wasregulated at 50 °C for 2 weeks while under high vacuum to removecontaminants from the surface of the adsorbents. The vacuum levelreached 1 mbar, at which point it became stable. The initial isothermsat 16 °C for propane in the unmodified MCM-41 were compared tothose recently published by Barsotti et al.45 The isotherms were foundto match nearly identically, and therefore it was concluded that nosignificant adsorbed water remained within the system. Experimentswere conducted at multiple different temperatures with propane andn-butane. To construct each isotherm, the pressure, temperature, andmass were recorded in real time while small amounts of fluid wereinjected to each adsorption cell. The pressure response was monitoredfor stability, which was taken as an indicator of thermodynamicequilibrium. Doses of fluid were progressively administered to eachcell until after the bulk condensation point of the fluid was observed.At this point, the desorption isotherm was established byprogressively placing the system under short periods of vacuumpressure to remove incremental amounts of fluid. The mass andpressure data points on the isotherm were extracted by taking anaverage over 100 time-series data points prior to the time at which adose was administered. By doing this, each isotherm point was takenas close to equilibrium as possible. Between experimental temper-atures, the system was placed under high vacuum (1 mbar) to returnthe adsorbents as close to the initial conditions as possible.NVT-Grand Canonical Monte Carlo (GCMC) Simulation. In

an attempt to verify the results obtained from experiments at themolecular level, coupled grand canonical Monte Carlo (GCMC) andmolecular dynamics (NVT) simulation was used to study theadsorption of propane on several different models of silica MCM-41. GCMC simulation uses traditional Monte Carlo moves as well asparticle insertion−deletion steps to match the model system to thethermodynamic characteristics of an imaginary reservoir. The grandcanonical ensemble fixes the chemical potential (μ), system volume,and temperature during particle insertion−deletion steps and followsthe metropolis criterion for determining probabilities in Monte Carlomoves.46 GCMC has been traditionally used for predicting phasebehavior and adsorption.47,48 By coupling GCMC with NVTsimulation, particles are allowed to translate and rotate according tothe traditional molecular dynamics framework between GCMCmoves. This allows the system to reach a minimum energy statemore quickly and provides for more complex particle−surfaceinteractions.Four different model pores were prepared to mimic the substrates

used in the experimental work. Initially, a base silica MCM-41 porewas prepared as described previously.49 An algorithm was used toplace different surface-modifying groups within the pores. First,undercoordinated silica was removed from the interior surface of thepore. Next, each undercoordinated surface oxygen atom wasconsidered for bonding to a surface-modifying group. The surface-modifying molecule with appropriate chain length was progressively“grown”, starting from an oxygen atom at the surface of the poretoward the central pore axis. Surface-modifying groups were placedrandomly with the constraint that each progressive addition must be amaximal distance from other nearby groups. The algorithm wasterminated once the desired level of surface carbon was reached, asdetermined by matching the characterization data in Table 1 asclosely as possible. This procedure was used to create four pore types:unmodified MCM-41 and MCM-41 with methyl, octyl, and octadecylgroup surface modifications.It was desirable to use a very simple model to approximate the

adsorbents to aid in determining the controlling effects in theadsorption process. As a result, charge effects were not considered andonly Lennard-Jones dispersive forces were used for simulation using aunited-atom approach. The TRAPPE-UA model was used for the

alkyl surface groups as well as for the propane adsorbate molecules.50

Once modified, each model was subjected to a 5 ns NVTequilibration sequence with a time step of 1 fs and temperaturecoupling every 10 steps to allow the surface alkyl chain molecules toachieve a minimum energy configuration. The void volume of eachmodel was calculated using simulated helium porosimetry with aprobe radius of 1.2 Å.51 To simulate adsorption, a hybrid NVT-GCMC framework was implemented using the LAMMPS platform.52

This framework allows the surface groups and the adsorbatemolecules to undergo translational and rotational motions betweenMonte Carlo steps. Each chemical potential and temperaturecondition was simulated for over 1 × 106 Monte Carlo steps untilequilibrium was reached, as implied by stability of the total insertedparticles. Isotherms, as well as thermodynamic data, were extractedfrom the raw simulation data and averaged over the last 50 000simulation steps. Only dispersion interactions were considered in thesimulations, and consequently surface hydrogen atoms were ignored.

■ RESULTS AND DISCUSSIONIsotherms were extracted from the raw data and are reported interms of the average fluid density within the pore. Thisquantity was calculated by first determining the pore volumefrom BET data in Table 1. Next, the amount of bulk phasefluid was subtracted from the total amount of fluid prior todividing by the pore volume. The bulk phase density wasextracted from data published by NIST at the equilibriumpressure for each point.53 By reporting the amount adsorbed interms of average fluid density within the pores, directcomparisons were possible between each isotherm.On first observation, it is clear that tests conducted on the

unmodified, C1-modified, and C8-modified MCM-41 adsorb-ents resulted in type IV isotherms for both propane and n-butane. All isotherms showed a downward concavity, whichindicates favorable or wetting adsorption.28 The C18-modifiedMCM-41 did not present classically type IV isotherm behavior.Instead, the C18 MCM-41 isotherms appeared to inducecontinuous condensation along the lower region of theisotherm prior to reaching a capillary saturation plateau.For all isotherms in the modified MCM-41, the general

trend appeared to be a decrease in the capillary condensationpressure as the degree of surface modification of the MCM-41increased.40 This is attributable to the increased adsorbent−adsorbate interactions resulting from the alkyl surface groups.Additionally, the unmodified MCM-41 induced the largestaverage density in the adsorbed fluid within the pores, followedby the C18-, C8-, and C1-modified MCM-41 adsorbents. Thisobservation is in agreement with the previous literature.54,55

One hypothesis for the lack of a distinct capillary condensationpoint in the C18-modified MCM-41 is that the adsorbateexperienced premature condensation during the pore-fillingregion across the entire pressure range preceding the poresaturation plateau and bulk condensation.One surprising result is the fact that the unmodified MCM-

41 substrate resulted in the lowest capillary condensationpressure for both the propane and n-butane adsorbates. Similarobservations were reported by Zhao and Lu for adsorption ofbenzene on MCM-41 and silylated MCM-4155 and by twoother studies with toluene and trifluoromethane adsor-bates.54,56 The explanation provided by Zhao and Lu wasrelated to increased diffusive resistance in the pore-fillingprocess due to the addition of methyl group surfacemodification.55 This is a plausible explanation for thedifference observed between the capillary condensationpressures in the modified MCM-41 and those of the

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unmodified MCM-41 in Figures 1 and 2. Another contributingfactor could be related to the smoothness of the interior poresurface in the modified versus unmodified MCM-41.57

Nonuniform modification of the surface with alkyl groupsmay have resulted in a less homogeneous adsorption surface

that did not favor uniform adsorbate nucleation andsimultaneous onset of capillary condensation in all areas ofthe adsorbent. These hypotheses are additionally supported bya qualitative review of the slope of the condensation step foreach adsorbent. Isotherms in the modified MCM-41

Figure 1. Propane isotherms for standard, C1-, C8-, and C18-modified silica MCM-41. Isotherms for MCM-41-C8, MCM-41-C18, and MCM-41are shifted vertically by 0.15, 0.3, and 0.45, respectively. MCM-41 isotherms are denoted by triangles, C1-modified MCM-41 is denoted by circles,C8-modified MCM-41 is denoted by squares, and C18-modified MCM-41 is denoted by pentagons. Open symbols denote desorption data.

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Figure 2. n-Butane isotherms for standard, C1-, C8-, and C18-modified silica MCM-41. Isotherms for MCM-41-C8, MCM-41-C18, and MCM-41are shifted vertically by 0.15, 0.3, and 0.45, respectively. MCM-41 isotherms are denoted by triangles, C1-modified MCM-41 is denoted by circles,C8-modified MCM-41 is denoted by squares, and C18-modified MCM-41 is denoted by pentagons. Open symbols denote desorption data.

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adsorbents appear to have a progressively smaller slope overthe condensation region. This would indicate that capillarycondensation in the modified substrates continuously occurredover a wider pressure range than in the unmodified MCM-41.Hysteresis was not pronounced for the propane isotherms

but was clearly present in experiments with n-butane. For n-butane, the C18-modified MCM-41 displayed a hysteresisregion at 2 °C, which extended to low-pressure, furthersupporting the hypothesis of adsorbate trapping and impedi-ment within the long alkyl chains on the surface. Hysteresisrapidly disappeared for the C8- and C18-modified MCM-41after 8 °C. The disappearance of hysteresis seemed to beweakly correlated to the degree of surface modification as well.The unmodified MCM-41 displayed some amount ofhysteresis even above the estimated pore critical temperature.To evaluate the driving thermodynamic factors for the

qualitative observations from the isotherms, the differentialenthalpy of adsorption was calculated between two subcriticaltemperatures for each adsorbent−adsorbate pair. Classically,the differential enthalpy of adsorption may be calculated usingthe following thermodynamic relation

ikjjj

y{zzz

∂∂

* = −Δ

Γ

Γ

TP

h

RTln( ) Tads ,2

(1)

where P* is the equilibrium pressure divided by the standardpressure. By integrating over paths of constant loading (Γ), thedifferential enthalpy may be estimated from several adsorptionisotherms. It is important to note that the estimate is only agood approximation over the low loading region of theadsorption isotherm because it is considered to bethermodynamically reversible. As such, the data in Figures 3and 4 are only reported for low loading.For both propane and n-butane, the unmodified MCM-41

resulted in the largest values of ΔadshT,Γ at loading prior to

capillary condensation. This indicates that the adsorbateexperienced stronger physisorption on the unmodifiedsubstrate, resulting in a larger reduction in entropy (asΔadssT,Γ0 = ΔadshT,Γ − R ln(P/P*)) of the confined fluidcompared to that of the other modified adsorbents. The lowerentropy was a result of favorable siting of the adsorbatemolecules in the pores of the unmodified surfaces. Althoughcounterintuitive, this phenomenon could be explained by thesmoothness of the interior pore surface of the unmodifiedsubstrate. The uniform decline with increased loading, which isobservable in all cases, is indicative of an energeticallyheterogeneous adsorption and is due to the progressive fillingof high-energy surface adsorption sites. A coupled effect oflarger decrease in entropy and greater change in enthalpy uponadsorption in the unmodified MCM-41 is the best explanationfor the lower condensation pressures observed in theexperimental isotherms for the unmodified MCM-41.58 Theresults of the GCMC simulation are also shown in Figure 3.The simulations did not match the experimental data for theunmodified MCM-41. For the modified adsorbents, themodeling results showed better agreement with the exper-imental counterparts but were not able to account for thesignificant heterogeneity that was present in the experimentalsystems.

Confined Critical Temperature. The depression of thecritical point in confinement is a phenomenon that has beenwell documented in the literature.3,4,25−27 As such, theconfined critical points of propane and n-butane werecalculated in all types of adsorbent materials used. Themethod of Nardon and Larher was used to calculate theconfined critical temperature (Tcp) based on the inverse slopeof pressure versus loading over the capillary condensationregion of the isotherm.3,59 The inverse slope changesdrastically once the critical point has been reached, allowingfor the estimation of the critical point from multiple isothermsover a temperature range that includes the critical point.59

Only the points that were decidedly above the critical point,

Figure 3. Differential enthalpy of adsorption for propane in MCM-41(triangles), MCM-41-C1 (circles), MCM-41-C8 (squares), andMCM-41-C18 (pentagons). Dashed line indicates the bulk value forthe standard enthalpy of vaporization of propane. The open symbolsare the values obtained from the GCMC simulation of propaneadsorption in the four model adsorbents (with linear fit line).

Figure 4. Differential enthalpy of adsorption for n-butane in MCM-41(triangles), MCM-41-C1 (circles), MCM-41-C8 (squares), andMCM-41-C18 (pentagons). Dashed line indicates the bulk value forstandard enthalpy of vaporization of n-butane.

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based on the inverse slope of the capillary condensation region,were used to fit the supercritical line.The Tcp estimates from the desorption branch for the n-

butane isotherms rendered values that were typically within 1°C of the adsorption branch. The critical temperatures ofpropane and n-butane in all of the adsorbent types are shownin Figure 5. From the figure, it is clear that there is a trend ofdecreasing confined critical temperature with increasing surfacemodification.

For both propane and n-butane, Tcp decreases with increasein surface modification. This observation is consistent withprevious GCMC simulation results.35,49 Tcp for propanefollowed a linear trend described by eq 2, whereas Tcp for n-butane was described by eq 3, where Xcarbon represents the wt% of surface carbon and Tcp,MCM‑41 is the confined criticaltemperature for unmodified MCM-41.

= −‐T T X0.565cp cp,MCM 41 carbon (2)

= −‐T T X0.982cp cp,MCM 41 carbon (3)

From Figure 5, there appears to be a correlation between theslope of the decline in Tcp with increased modification and thesize of the n-alkane adsorbate. Although more adsorption datafor larger n-alkanes would be needed to confirm a generaltrend, this observation may possess a qualitative explanation.One possible hypothesis is that n-butane presents a steeperdecline in Tcp as compared to propane due to the additionalpostadsorption entropy retained through conformationalisomerism. This additional, albeit small, rotational entropyretained by n-butane may become much more significant inconfinement where translational motion is restricted. As aresult, n-butane may advance toward confined criticality morequickly with the introduction of surface-modifying alkylgroups.

NVT-GCMC Simulations. Propane adsorption was simu-lated over a range of temperature and chemical potential valuesin the four types of model pores shown in Figure 6. A hybridNVT-GCMC scheme was used that allowed the surface groupsand the adsorbate molecules to move throughout thesimulations. The raw data from the simulations were used toextract the grand potential using eqs 4 and 520,49,60

ikjjjj

y{zzzz

ϕμ

∂∂

= −⟨ ⟩NT V

G

, (4)

Figure 5. Confined critical temperature of propane and n-butane insilica MCM-41 with as a function of the amount of surfacemodification (surface bonded carbon). Dotted lines are shown forreference.

Figure 6.Model silica MCM-41 pores with (a) no surface modification, (b) C1 surface groups, (c) C8 surface groups, and (d) C18 surface groups.Pores are shown during an NVT equilibration sequence.

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ikjjjj

y{zzzz

ϕμ

∂∂

= ⟨ − ⟩μ

T

TE N

/

1/V

G

, (5)

The grand potential was used to locate the phase transitionpoint using the relation in eq 6

ikjjjj

y{zzzz

ϕ∂∂

=μ

N0

T

G

, (6)

The critical temperature can be estimated from the grandpotential using methods previously presented in theliterature.60 The grand potential is related to the averagepressure for a homogeneous fluid by the relation in eq 7 andtherefore is a useful way to present isotherm data from GCMCsimulation.

ϕ = −⟨ ⟩P VG (7)Figure 7 shows simulated propane isotherms for all pore types.It can be noted that, with the exception of the unmodified

MCM-41 model, the simulated isotherms follow the sametrend as the experimental data. The capillary condensationpoint occurs at lower grand potential values for the poresystems with more alkyl group surface modification.The density of the fluid is larger in the C1-modified MCM-

41 compared to that in the C8- and C18-modified MCM-41,likely due to the better packing configurations achieved withthe lack of the long alkyl surface modifiers. The larger values ofnormalized grand potential in the vapor adsorption region ofthe unmodified MCM-41 simulated isotherms indicate acombination of higher entropy of the adsorbate and lowersurface interaction with the substrate, which is different fromwhat was observed experimentally. The fact that the simulatedisotherms for MCM-41 resulted in the largest capillarycondensation pressure of the four model pores, in contrastto the experiment, indicates that the potentials used to model

unmodified MCM-41 may not adequately represent the realmaterial. This discrepancy is also apparent in Figure 3 wherethe differential enthalpy of adsorption does not match wellwith the experimental data for the unmodified MCM-41. Thismight be attributed to the effects of Coulomb charge on thesurface of the unmodified MCM-41 in the adsorption process,which could not be adequately represented by the relativelysimple Lennard-Jones model employed here.The computed confined critical temperatures of propane are

presented in Figure 8 as a function of the pore type. The

experimental values are shown in the plot for reference. Bothexperimental and simulated data show the same, nearly linear,negatively sloped trend. The simulations produced generallylower values of Tcp for the modified MCM-41 models. This islikely due to the lack of heterogeneity in the model that waspresent in the actual substrates. The magnitude of thisdiscrepancy increased for the more modified surfaces,indicating that significant heterogeneity may have been presentin the modified MCM-41 materials used in the experiments.This heterogeneity, likely caused by uneven modification of thepore surfaces, would result in large energetic differences in theadsorption surface. The simulated value of Tcp for theunmodified silica, MCM-41, was interestingly similar to theexperimental value despite the differences in the qualitativeisotherm behavior and the differential enthalpy of adsorption.

■ CONCLUSIONSIn this study, both experimental and modeling techniques wereemployed to investigate the effects of surface chemistry on theadsorption and thermodynamic behaviors of propane and n-butane. Four types of MCM-41 were created with varyingdegrees of surface modification. The MCM-41 was modifiedusing silylation reactions to bond methyl, octyl, and octadecylgroups to the surface of pure MCM-41. These adsorbents wereused to measure adsorption isotherms of both propane and n-

Figure 7. Propane isotherms at 210 K from GCMC simulation withfour types of modified and unmodified silica MCM-41. Isotherms areplotted in terms of the normalized grand potential.

Figure 8. Confined critical temperature of propane estimated byGCMC in four types of model pores with varying surfacemodifications. Experimental results are shown for reference.

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butane at multiple temperatures. Additionally, hybrid NVT-GCMC modeling was used to simulate adsorption in fourmodel pores that were analogous to the experimentaladsorbents using a united-atom, Lennard-Jones interactionscheme. The surface modification directly impacted the shapeof the isotherms as well as the differential enthalpy ofadsorption. Interestingly, the unmodified MCM-41 presentedthe lowest capillary condensation pressures and the highestdifferential enthalpy of adsorption, pointing to energeticallyfavorable adsorption behavior and larger reductions in entropyupon adsorption. These findings were explained by diffusiveresistance caused by the surface-modifying groups andheterogeneity caused by nonuniform modification of thesurface. The combination of these two factors resulted in lessreduction in entropy upon adsorption as well as causingcapillary condensation to occur over a wider pressure range ascompared to that in the unmodified MCM-41. Theexperimental and simulated isotherms were used to calculatethe confined critical temperature (Tcp) of both fluids. Bothcalculations supported a negatively sloped trend of Tcp withincreasing alkyl surface modification. The slope of this trendalso appeared to be correlated to the adsorbate size; however,more data are needed to confirm a more general behavior. Theresults of the simulations did not closely agree with theirexperimental counterparts for the unmodified MCM-41 butshowed encouragingly similar results for the modifiedsubstrates in terms of qualitative capillary condensationpressure behavior and the calculated differential enthalpy ofadsorption. These results suggest that impacts of surface chargeeffects are non-negligible for adsorption on unmodified MCM-41, even when the adsorbate is a nonpolar molecule. Theresults presented in this work have direct implications fordeveloping a better understanding regarding the effects ofsurface chemistry on confined phase behavior.

■ ASSOCIATED CONTENT*S Supporting InformationThe Supporting Information is available free of charge on theACS Publications website at DOI: 10.1021/acs.lang-muir.8b00986.

Adsorption and desorption isotherms for propane and n-butane (PDF)

■ AUTHOR INFORMATIONCorresponding Author*E-mail: [email protected] Lowry: 0000-0001-5375-9852NotesThe authors declare no competing financial interest.

■ ACKNOWLEDGMENTSThe authors gratefully acknowledge the financial support ofSaudi Aramco and the School of Energy Resources at theUniversity of Wyoming.

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