Microstructural Characterization of Adsorption and Depletion Regimes

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J. Phys. Chem. C 2007, 111, 15736-15742

Microstructural Characterization of Adsorption and Depletion Regimes of Supercritical Fluids in Nanopores† Gernot Rother,*,‡ Yuri B. Melnichenko,,| David R. Cole,‡ Henrich Frielinghaus,§ and George D. Wignall| Chemical Sciences DiVision, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831-6110, Neutron Scattering Science DiVision, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831-6393, and Forschungszentrum Ju¨lich GmbH, IFF, Neutronenstreuung, D-52425 Ju¨lich, Germany ReceiVed: May 14, 2007; In Final Form: August 13, 2007

Fluid accommodation in porous media has been studied over a wide range of pressures at three supercritical temperatures by small-angle neutron scattering. A new formalism gives for the first time the mean density and volume of the adsorbed fluid phase formed in the pores from experimental data; thus, excess, absolute, and total adsorption become measurable quantities without the introduction of further assumptions. Results on propane adsorption to a silica aerogel show the formation of a thin adsorption layer of high density at low bulk fluid pressures and densities. In that region, the density of the adsorption layer increases with increasing fluid density while its volume remains approximately constant. Depletion of the fluid from the pore space is found near and above the critical density, which leads to negative values of the excess adsorption. At high fluid densities, the pores are evenly filled with fluid of lower density than the bulk fluid. The total amount of fluid confined in the pore spaces increases with the fluid density below the critical density and remains approximately constant at higher fluid densities. Application of the new model also gives insight into the sorption properties of supercritical carbon dioxide in silican aerogel. The concept presented here has potential to be adopted for the study of numerous other sub- and supercritical fluids and fluid mixtures in a variety of micro- and nanoporous materials.

1. Introduction

ne )

Confinement of fluids to porous matrices results in a variety of interesting physical phenomena, including pore condensation effects,1,2 shifts in freezing and melting temperatures,3 and metastable microscopic phase separation.4 The formation of an adsorbed phase in porous media plays an important role in numerous processes including heterogeneous catalysis, chromatography, and fluid storage. The properties of pure fluids in pores of nanoscopic size are altered from the corresponding bulk fluid because of interactions with the pore walls and geometrical confinement. Interactions of the adsorbate fluid with a solid adsorbent lead to the creation of an adsorbed phase with properties different from those of the bulk fluid at similar thermodynamic conditions. Information on the physical properties of the adsorbed phase and their variation with pressure (P) and temperature (T) is fundamental to the successful development of separation technologies and optimization of reaction processes5 but is inaccessible to conventional experimental methods (volumetric, gravimetric, etc.), which measure solely the excess adsorption ne. The excess adsorption is defined by the integral over the local density deviations F(r) from the bulk density Fb over the sorption layer profile formed perpendicular to the adsorbent surface: †

Part of the “Keith E. Gubbins Festschrift”. * Corresponding author. E-mail: [email protected]. ‡ Chemical Sciences Division, Oak Ridge National Laboratory. § Forschungszentrum Ju ¨ lich GmbH. | Neutron Scattering Science Division, Oak Ridge National Laboratory.

∫0∞ [F(r) - Fb]dr

(1)

Alternatively, the absolute adsorption, na, is defined by the integral over the local densities in the inhomogeneous sorption layer of thickness l:

na )

∫0l F(r)dr

(2)

The absolute adsorption is an important quantity used for thermodynamical studies of sorption processes including the application of equation of adsorption isotherms, grand canonical Monte Carlo simulations, and density functional theory.6 The assumption of a constant density throughout the sorption phase (box model) gives the following relationship between excess and absolute adsorption:

ne ) na(1 - F2/F3) ) na - V3F2

(3)

Here F2 and F3 are the densities of the unadsorbed and adsorbed fluid phase, respectively, and V3 is the specific volume of the adsorbed phase in cm3/g. Equation 3 shows that the absolute adsorption can be rigorously calculated from ne only if the density or the volume of the adsorbed phase is known. Because this information is not readily available, different assumptions are usually made to calculate na, such as F3 . F2 at all pressures and temperatures, in which case na ≈ ne. Evidently, the inequality F3/F2 . 1 is valid only for adsorption of gases at low pressures when F2 f 0 or at temperatures below the liquidgas critical temperature Tc, where F3 is expected to be close to the density of the bulk liquid.7 The validity of these assumptions

10.1021/jp073698c CCC: $37.00 © 2007 American Chemical Society Published on Web 10/25/2007

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is unknown for near-critical fluids when a significant difference between na and ne is anticipated. Therefore, experimental information on the variation of F3 and V3 with P and T is essential for accurate determination of the actual amount of the adsorbed fluid under nanoscale confinement. Here we demonstrate that F3 and V3, and thus also na, can be determined simultaneously without additional assumptions. We apply the methodology to study the phase behavior of deuterated supercritical propane (d-propane) in mesopores of silica aerogel as a function of pressure. We also present the sorption phase properties of supercritical CO2 in the same silica aerogel as obtained from the adsorbed phase model. SANS has been widely used previously to characterize the structure of porous materials by saturating them with liquids or gases and applying contrast-variation methods (see for example ref 8 and references therein). It has also been applied to investigate the influence of confinement on the phase behavior of individual fluids and binary liquid solutions.9-15 The importance of analyzing the neutron transmission as a function of temperature and pressure and a method of determining the excess adsorption of supercritical fluids in porous media from the transmission data was first outlined and applied to measure the ne of supercritical carbon dioxide (CO2) in silica aerogel in ref 16. 2. Adsorbed Phase Model The following analysis is based on the assumption that the sorption phase is homogeneous; that is, the unknown density profile of the fluid perpendicular to the adsorbent surface is represented by a sorption phase of constant density (box model). This implies that the inhomogeneous F(r) versus r function is represented as a step function, which gives a first approximation to the true actual (MD) distribution function (see Figure 3 of ref 17). Consider a three-phase system that consists of the porous matrix (phase 1), unadsorbed fluid (phase 2), and adsorbed fluid (phase 3), characterized by their volume fractions φ1, φ2, and φ3 and mass densities F1, F2, and F3, respectively. The adsorption effects are expressed in deviations in the measured values of transmission tm and invariant Zm from their calculated counterparts tz and Zz, which account for the case of zero adsorption, that is, complete pore filling with unadsorbed fluid (φ3 ) 0). By definition, the neutron transmission (t) is the ratio of the transmitted beam intensity after attenuation by the sample to the incident neutron intensity. The transmission, tm, of fluid saturated aerogel is given by

tm ) t1 exp - FjCd

(4)

where t1 is the P- and T-independent transmission of a blank porous matrix (aerogel), Fj is the mean fluid density in the sample, C is the attenuation factor for the fluid, and d is the sample thickness. Defining the mean fluid density in the pores as

Fp ≡ Fj/(1 - φ1) ) (F 2φ2 + F3φ3)/(1 - φ1)

(5)

and taking into account that φ1 + φ2 + φ3 ) 1, we obtain the expression for the volume fraction of the unadsorbed phase:

φ2 )

F3 - Fp (1 - φ1) F3 - F 2

ments using eqs 4 and 5, and F2(P,T) is calculated using the appropriate equation of state of the fluid. In SANS experiments, the scattered intensity, I(Q), is measured as a function of the momentum transfer Q, given by Q ) 4π sin θ/λ, with λ being the wavelength of the neutrons and 2θ being the angle of scatter. The volume fraction of the adsorbed phase was obtained by analysis of the scattering invariant, which is defined as the integral over the second moment of the cross section: Z ) ∫∞0 Q 2I(Q)dQ, where I(Q) is the coherent cross section and Q is the momentum transfer. The scattering invariant for a two-phase system Zz, which describes the case of zero adsorption, is given by

Zz ) 2π2φ1(1 - φ1)(F/1 - F/2)2

(7)

where F/1 and F/2 are the coherent neutron scattering length densities of silica and unadsorbed fluid, respectively. The scattering invariant measured in the sorption experiment includes contributions from the adsorbed phase. The formula for the invariant of a three-phase system in terms of the volume fractions φj and coherent scattering length densities F/j of the constituting phases was proposed by Wu:18

Zm ) 2π2[φ1φ2(F/1 - F/2)2 + φ2φ3(F/2 - F/3)2 + φ1φ3(F/1 - F/3)2] (8) This formula is valid for ordered or disordered systems regardless of the specific structure of the sample and has been applied successfully to a variety of systems.19,20 The volume fraction of the adsorbed phase is obtained by combination of eqs 7 and 8

φ3 )

Zm - Zz 2

2π

[φ2(F/2

-

F/3)2

+ φ1(F/1 - F/3)2 - φ1(F/1 - F/2)2]

(9)

and through an alternative expression derived from eqs 5 and 6:

φ3 )

Fp(1 - φ1) - F 2φ2 Fp(1 - φ1) - F2 ) F3 F3 - F2

(10)

The unknown quantity φ3 is eliminated by equating eqs 9 and 10. The respective coherent scattering length densities of phase j are given by N

F/j )

bi ∑ i)1

Fj N A Mj

(11)

with bi as the bound coherent scattering length of atom i, N as the total number of atoms in the molecule, and Fj as the mass density. Mj is the molar mass, and NA ) 6.023 × 1023 mol-1, Avogadro’s constant.21,22 Equation 11 shows that the scattering length densities F/2 and F/3 vary with the mass densities F2,F3 ) f(P,T). The unknown φ2 is eliminated by expression through eq 6, such that F3 remains the only unknown parameter, which is calculated by solving this equation for the respective experimental data points at different T and P values. 3. Materials and Methods

(6)

In eq 6, only φ2 and F3 are unknown because the porosity of the adsorbent (1 - φ1) is determined a priori from porosimetry measurements, Fp is determined from the transmission measure-

Confining Matrix. We used base-catalyzed silica aerogels (Oscellus Technologies, Livermore, California) with a nominal density F (aerogel) ) 0.1 g/cm3, corresponding to a porosity of 96%, which consist of thin silica strands with mesh sizes of 60-70 Å and possess a high surface area of As ≈ 700 m2/g.23

15738 J. Phys. Chem. C, Vol. 111, No. 43, 2007

Figure 1. Transmissions of bulk d-propane at different densities, measured at T ) 92 °C (red circles) and T ) 100 °C (blue squares).

Because of its high porosity, the material comprises an open, fully accessible pore network. The porosity of the individual silica aerogel samples was controlled by weighing and measuring the dimensions of the samples. Under the assumption that the density of the silica skeleton is 2.0 g/cm3, as reported in ref 23, we calculate a porosity of 95-96 % for the aerogel sample used in this study. The corresponding neutron scattering length density for this mass density of the silica skeleton is F/1 ) 3.16 × 1010 cm-2. The aerogel sample has the form of a cylinder of 17 mm diameter, which corresponds to the inner diameter of a SANS stainless-steel high-pressure cell. The aerogel thickness was chosen to d ) 10 mm, and the optical path of the cell was adjusted to be equal to the aerogel thickness by inserting sapphire plugs. Thus, the entire volume of the cell was occupied by the absorber. Fluid. Deuterated propane (Cambridge Isotope Laboratories, Andover, MA) with a deuteration degree of 99.5% was used to minimize significant incoherent background from hydrogen in protonated propane, which would inhibit measurements of the coherent SANS signal from the fluid saturated aerogel. The cell was pressurized with d-propane using a screw-type pressure generator. The gas-liquid critical parameters of d-propane were determined by measuring the temperature variation of the correlation length of the density fluctuations of the bulk fluid by SANS. It was found that the critical temperature of the bulk fluid is Tc ) (91.0 ( 0.1) °C, which is ∼6.6 °C lower than the critical temperature of hydrogenated propane. The critical pressure of Pc ) 4.25 MPa24 is not influenced by deuterium substitution within experimental error. The density of unadsorbed d-propane, F2, at each P was calculated using the NIST12 software package for thermodynamical properties of pure fluids with the equation of state for h-propane, corrected for the 18% higher molar mass and shift in critical temperature of d-propane. This calculation gives a critical density for deuterated propane of Fc ) 0.27 g/cm3, as calculated from Fc ) 0.23 g/cm3 the tabulated value for protonated propane. The validity of the such constructed equation of state for d-propane was verified by measurement of the neutron transmission of the pure fluid as a function of the fluid pressure for two supercritical temperatures (T ) 92.0 °C and T ) 100.0 °C). A Sensotec AG-100 digital pressure indicator with a stated accuracy of (0.25 % was used to measure the pressure in the sample cell. The variation of the transmission with the fluid density is shown in Figure 1. Good agreement was achieved between the two data sets, which superimpose within the error bars of the measurements. Figure

Rother et al.

Figure 2. Scattering curve from empty aerogel, shown with Guinier approximation at low Q and Porod approximation at high Q. The inset shows a comparison of the aerogel scattering curves measured before the fluid sorption experiments started (open black circles) and after the fluid sorption experiments finished (red filled triangles).

1 also shows a fit to a exponential decay function, which agrees closely with the calculations and measured data, confirming that the modified equation of state for d-propane is valid in the studied pressure and temperature range. SANS. SANS Experiments were performed on the KWS2 instrument at the 20 MW FRJ2 reactor in FZ Ju¨lich, Germany, using the high-pressure setup described previously.16 The neutron wavelength was λ ) 6.3 Å with (∆λ/λ ) 0.1). The scattered neutrons were detected by a area detector of 60 × 60 cm2 in 128 × 128 channels. The scattering patterns were corrected for detector efficiency, background, and empty pressure cell scattering. The 2D scattering data were radially averaged, corrected for sample transmission, and normalized to absolute intensities. The calibration of the scattering vectors and absolute SANS intensities were verified by measurement of two calibration samples comprised of porous materials.25 The error of the absolute intensities with respect to the reference data was less than (4 %. The transmission at each pressure and temperature was measured continuously in situ using a He3 direct beam monitor positioned in the center of the beam stop. The absolute error of the transmission measurement is within (0.01. SANS data of fluid saturated silica aerogels were taken at sample-detector distances of 2 and 4 m with a constant neutron collimation length of 8 m. Figure 2 shows the SANS curves measured for empty aerogel before and after the sorption experiments. The data coincide within the errors of the measurement, which means that the pore structure of the silica aerogel was not permanently altered or destroyed by the series of fluid adsorption and desorption processes at different temperatures. The silica aerogel scattering curve shows Porod scattering at large Q with the I(Q) ∝ Q-4 decay characteristic for scattering from smooth interfaces. The low Q data are described well by a Guinier function. SANS and transmission data were taken as a function of pressure along several isotherms as well as a function of temperature along several isochors. The fluid pressure was changed in small increments in order to minimize the stress load on the aerogel. The fluid adsorption and desorption processes are fully reversible, which was confirmed by pressure jump experiments. The SANS and transmission measurements were started after the sample has equilibrated, which was indicated by a constant reading of the pressure gauge

Microstructural Characterization

Figure 3. Exemplary scattering curves for silica aerogels saturated with fluids of different bulk densities at T ) 91.2 °C. The incoherent scattering backgrounds have been subtracted from the plotted data.

Figure 4. D-propane in silica aerogel: Experimental transmissions for fluid saturated silica aerogel as a function of temperature and bulk fluid density, in comparison to calculated transmissions for pore filling with unadsorbed fluid (dashed line).

connected to the sample cell. Typical equilibration times were in the range of 20-30 min, while the actual SANS measurements took about 5-10 min at each sample-detector distance. In Figure 3, the SANS data for fluid-saturated silica aerogels for different F2 values at T ) 91.2 °C are shown. The scattering intensities change over several orders of magnitude with varying bulk fluid density, making SANS a very sensitive technique for these studies. 4. Results and Discussion Here we report the results obtained along the supercritical isotherms at three temperatures as a function of the bulk fluid density F2, which is calculated from the fluid pressure using the apporpriate equation of state. Figure 4 shows the variation of the neutron transmission of d-propane-saturated aerogel as a function of temperature and bulk fluid density. At small fluid densities, the measured transmission, tm, decreases with increasing density and is lower than the calculated transmission, tz, which accounts for the case that the pore space is evenly filled with unadsorbed fluid of density F2. This is due to the formation of a dense adsorbed phase, which leads to enrichment of the

J. Phys. Chem. C, Vol. 111, No. 43, 2007 15739

Figure 5. D-propane in silica aerogel: Measured invariants for different temperatures and fluid pressures. The dashed line corresponds to the invariant calculated for the case of zero fluid sorption.

aerogel matrix by d-propane. Conversely, for fluid densities above the critical density it remains constant at tm ≈ 0.4 and is always higher than tz, providing direct evidence that the aerogel matrix experiences fluid depletion. The transmission results show a weak temperature dependence at low F2, where the strongest adsorption effects are found for the near-critical temperature T ) 91.2 °C. The depletion effects at high F2 show no clear temperature dependence. The results of the SANS experiments are summarized in Figure 5, which shows the invariant as a function of F2 for three different temperatures. The evaluation of Zm was carried out by numerical integration in three parts because the data are only measured between the lower (l) and upper (u) Q values, Ql and Qu. The contribution to the invariant from the (unmeasured) cross section between Q ) 0 and Ql ) 0.01 Å-1 was estimated via the Guinier approximation, extrapolated from the measured cross section at the lowest Q values. The contribution to the invariant from the Q range between Qu ) 0.18 Å-1 and Q ) ∞ was estimated via the Porod approximation [I(Q) ) DQ-4 + B]. The incoherent background B resulted primarily from small amounts of hpropane in the fluid and was subtracted before Zm was calculated; the total contribution from the unmeasured Q regions amounted to less than 10% of the total invariant. The strongest deviations between Zm and Zz are found for fluid densities of F2 ≈ 0.2 g/cm3, indicating the formation of a sorption phase, which is most pronounced at the near-critical temperature. At F2 ≈ 0.4 g/cm3 Zm is approaching Zz, indicating the formation of effectively a two-phase system; that is, the pores are filled with the sorption phase. The invariant Zm determined from the SANS data, in addition to the mean pore fluid density determined from the transmission measurements, were used to calculate the density and volume fraction of the adsorbed phase, as described above. As is seen in Figure 6, in the low-pressure region the density of the adsorbed fluid phase increases almost linearly with the density of unadsorbed fluid. At the same time, the volume fraction of the adsorbed phase, shown in Figure 7, remains approximately constant. The density of the adsorbed fluid is nonmonotonic: just below Fc it reaches a maximum of F3 ≈ 0.5 g/cm3, which is close to the density of liquid d-propane. The thickness, l, of the adsorbed phase is calculated from the formula 3

l ) xMNA/F3 × V3 ÷ As

(12)

15740 J. Phys. Chem. C, Vol. 111, No. 43, 2007

Figure 6. D-propane in silica aerogel: Density of the adsorbed phase as a function of the density of unadsorbed fluid. The dashed line accounts for F2 ) F3.

Figure 7. D-propane in silica aerogel: Volume fraction of the adsorbed phase in dependence of the bulk fluid density.

with M ) 52.11 g/mol the molar mass of d-propane. We calculate a thickness of the adsorbed phase of 1-2 molecules in the region of F2 < Fc. At F2 > Fc, F3 decreases down to 0.2-0.22 g/cm3, becomes lower than the density of unadsorbed phase, and remains constant to F2 f 0.5 g/cm3 ≈ 2Fc. At the same time, φ3 increases monotonically with F2 and approaches 0.96 at F . Fc, which indicates that at high pressures the entire pore volume is filled with the adsorbed fluid with F3 < F2. The temperature effect on the density and volume of the adsorbed phase is rather small over the studied region. However, an increase of the temperature further into the supercritical region seems to shift the crossover from the high density adsorbed phase to the low-density depletion phase to lower bulk fluid densities F2. The excess adsorption, ne, was calculated from the transmission data following the scheme described previously.16 The total adsorption or total amount of fluid in the pore space is given by nt ) na + nu, where nu is the amount of unadsorbed fluid in aerogel pores. It was calculated from the mean fluid density and the total pore volume of aerogel Vp ) 9.6 cm3/g using nt ) FpVp. The absolute adsorption, na, is calculated via eq 3 or alternatively by na ) F3φ3Vp. The variation of ne, na, and nt as a function of F2 is shown for T ) 91.2 °C in Figure 8. The adsorption quantities are normalized to the mass of adsorbent.

Rother et al.

Figure 8. D-propane in silica aerogel: Variation of adsorption quantities with bulk fluid density at T ) 91.2°. Blue crosses, total adsorption nt; black triangles, excess adsorption ne; red circles, absolute adsorption na.

Figure 9. Physical properties of the adsorbed phase formed during CO2 adsorption in silica aerogel at T ) 35°. Blue squares, density of the adsorbed phase F3; red circles, volume fraction of the adsorbed phase φ3.

At F2 , Fc, all three parameters are increasing functions with maximum values reached at F2 ≈ 0.2 g/cm3 < Fc, where the pore fluid reaches a near-critical composition (as seen from the total adsorption, nt, given in Figure 8). In a narrow region, critical adsorption effects are present.26,27 At F2 > 0.2 g/cm3, the excess adsorption decreases rapidly and becomes negative, while nt and na always remain positive and constant above F2 ≈ 0.25 g/cm3. The slope of the isotherms at low fluid densities is similar to the type-III isotherm in the IUPAC classification, which indicates a weak affinity of the adsorbate for the adsorbent compared to the adsorbate-adsorbate interaction.28 The adsorption isotherms look similar for the two other temperatures, but critical adsorption effects with features are absent at the higher temperatures. Comparison with CO2 Behavior. The sorption behavior of supercritical CO2 in the same type of silica aerogel with 96% porosity was studied recently in our group.16 We analyzed the SANS data in terms of the adsorbed phase model and present the results for the physical properties of the adsorbed phase at one supercritical temperature (T ) 35 °C) in Figure 9. Strong sorption effects are found in the vicinity of the bulk critical

Microstructural Characterization point, which is located at Tc ) 31.1 °C and Fc ) 0.46 g/cm3. We find the formation of a high-density adsorbed layer at low fluid densities, with approximately constant volume and a maximum density of F3 ≈ 1.05 g/cm3. Schneider et al. reported a value of 1.07 g/cm3 for the maximum density of near-critical CO2 adsorbed to porous silica using Fourier transform IR spectroscopy.29 The adsorbed phase formed at low fluids densities consists of ca. 20-25 layers of CO2 molecules, as calculated by eq 12 with M(CO2) ) 44 g/mol. At F2 > Fc, a breakdown of the high-density adsorbed phase is observed and the pores become evenly filled with depleted fluid of density F3 ≈ 0.4 g/cm3, which is lower than the critical density of CO2. The main findings on the physical properties of the sorption phase formed in the CO2 + silica aerogel system are in good qualitative agreement with the properties of the sorption phase found for d-propane in silica aerogel. The results described above reveal new and to some extent unexpected features, the most striking of which being the fluid phase behavior at high fluid pressures and bulk densities. The depletion of pores in the liquid-gas critical region of the bulk fluid, that is, negative values of the excess adsorption at T f Tc was observed in refs 27 and 30 along near-critical isochores of SF6 in controlled pore glass. Unfortunately, these measurements were not extended to the region of bulk fluid densities above Fc. Evidence of critical depletion, in terms of decreased but still positive excess adsorption of N2O in silica gel along near-critical isotherms in the density range 0.74 eF/Fc e1.15 has also been reported.31 5. Conclusions In this work, supercritical fluid sorption in porous media has been studied by coupling of SANS and neutron transmission. The data were analyzed in terms of the adsorbed phase model, which correlates the sorption properties to the microstructure of the pore fluid. The properties of the adsorbed fluid (F3 and φ3) became accessible by application of a first-order approximation, in which we assume that the adsorbed phase is homogeneous in density. A similar model has been employed in ref 32 to visualize the sorption properties of binary liquids in porous CPG-10 materials of different pore sizes. It was shown that the adsorption properties in the strong adsorption region close to the two-phase coexistence line of the liquid mixture are linked to the pore morphology of the adsorbent; that is, the adsorption is not exclusively controlled by the surface area but may be limited by the pore size in narrow pores. The film thickness of the sorption layer could be calculated from excess sorption data under the assumption of a certain composition of the sorption phase. The box model, although not accounting for the full complexity of the system, provided valuable insight into the structure of the pore fluid. The adsorbed phase model presented here constitutes an improvement of the model applied in ref 32 because it requires no assumptions on either the density or the volume of the adsorbed phase. The experimental data for d-propane sorption in silica aerogel at three different temperatures show fluid adsorption at low bulk fluid densities and fluid depletion at high fluid densities. The underlying assumption of a uniform density throughout the adsorbed layer does not account for density inhomogeneities that may exist in the adsorbed phase. At low fluid densities, the highest density of the adsorbed layer will be found at the adsorbing surface. The mean density, F3, obtained from the adsorbed phase model will be somewhat lower than this maximum density, whereas in the transition region from the adsorbed fluid to bulk fluid fluid densities lower than

J. Phys. Chem. C, Vol. 111, No. 43, 2007 15741 F3 may be present. MD computer simulation studies are planned to model fluid density profiles perpendicular to the pore walls from our experimental data. The occurrence of critical fluctuations in the pore fluid is undesired because it would increase the small-angle scattering and lower the transmission of the sample, thus virtually increasing adsorption. However, critical scattering in bulk fluids is limited to a narrow region of pressures and temperatures around the critical point. It is safe to assume that scattering from critical fluctuations does not occur at the highest temperature studied, T ) 102 °C, which is more than 10 °C above the bulk Tc. The temperature dependencies of the transmissions and invariants of the confined fluid do not show the typical strong increase in small-angle scattering as Tc is approached, which would point to a significant contribution from critical scattering. Additionally, the resulting data for the adsorbed phase, given in Figures 6 and 7, show no unusual temperature dependence while Tc is approached. Therefore, we believe that critical fluctuations in the pore fluid are suppressed effectively by the confinement and sorption effects, as was already concluded from an independent analysis in ref 14. In refs 27 and 30, the critical depletion was explained by differences between the compressibility of confined and bulk fluid in the critical region, which should result in decreased mean pore density as T f Tc. Our data provide unequivocal experimental evidence for a tendency of a critical fluid to be expelled by a confining medium, which manifests in a significant decrease of the excess adsorption. This variation of na and ne is accompanied by a factor of 2 reduction of the density and a factor of 6 increase of the volume fraction of the adsorbed phase in the critical region. Additionally, our results demonstrate that the depletion of aerogel is not restricted to the critical region but extends over a wide range of pressures and densities above Fc. Negative values of the excess adsorption of supercritical argon, neon, krypton, nitrogen, and methane on activated carbon at high fluid pressures and densities were reported in ref 33, which may indicate that both critical and high-pressure depletion are universal phenomena dependent on the specifics of solid-gas interactions and the confinement topology. Computer simulation and theoretical studies of Lennard-Jones fluids in a single pore geometry inspired by refs 27 and 30 did not reproduce the depletion effects.34,35 The authors concluded that critical depletion might be restricted to fluids confined in matrices with connected pores. However, it should be noted that the results of computer simulation studies of fluids in pores depend crucially on the setup, for example, fluid-fluid and fluid-wall interaction parameters, pore size, morphology, and so forth.36 Recently, Brovchenko et al.17,37 found strong fluid depletion effects in a computer simulation study of high-density vapors of Lennard-Jones fluids near weakly attractive surfaces. In their study, fluid adsorption to the interface was found for low-density vapors, whereas a crossover to weak adsorption and eventually depletion is reported for increasing fluid vapor densities. The depletion effect is referred to as surface perturbations, that is, the missing neighbor effect and the short-range surface field. Our excess adsorption data, given in Figure 8, match the features of the Gibbs adsorption isotherms reported by Oleinikova et al.17 The order parameter profiles of critical adsorption processes in systems with weak surface fields have been studied for the Ising model in ref 38. Further experiments and theoretical studies will address the sorption behavior of high-density fluid vapors, which is much-less explored than the low density region. This may be due to the difficulties found in commonly used

15742 J. Phys. Chem. C, Vol. 111, No. 43, 2007 gravimetric techniques, which result from sample buoyancy effects at high fluid densities that cover the sorption effects in part or entirely. From a practical point of view, our data suggest that the assumption discussed in the Introduction, which is often used to calculate na from ne, may not always be valid because F3 may be a nonmonotonic function of pressure and become lower than the density of unadsorbed fluid at high pressures. Molecular simulation will provide more insight into more representative F(r) profiles to improve the proposed methodology. Acknowledgment. We congratulate Prof. Gubbins on his 70th birthday and for his pioneering work on fluids under confinement. We thank the editors of this special issue for the invitation to participate in honoring Keith. We thank Profs. G. H. Findenegg, M. Schoen, and Dr. A. Chialvo for fruitful discussions, the referees of this and an earlier version of this article for valuable comments, and FZ Ju¨lich for providing SANS beam time. Research sponsored by the Divisions of Materials Sciences and Engineering (to Y.B.M. and G.D.W) and Chemical Sciences, Geosciences and Biosciences (to G.R and D.R.C.), Office of Basic Energy Sciences, U.S. Department of Energy, under contract DE-AC05-00OR22725 with Oak Ridge National Laboratory, managed and operated by UTBattelle, LLC. References and Notes (1) Striolo, A.; Gubbins, K.; Gruszkiewicz, M. S.; Cole, D. R.; Simonson, J. M.; Chialvo, A. A.; Cummings, P.; Burchell, T.; More, K. Langmuir 2005, 21, 9457-9467. (2) Coasne, B.; Jain, S. K.; Gubbins, K. E. Mol. Phys. 2006, 104, 34913499. (3) Schreiber, A.; Ketelsen, I.; Findenegg, G. H. Phys. Chem. Chem. Phys. 2001, 3, 1185-1195. (4) Gelb, L. D.; Gubbins, K. E.; Radhakrishnan, R.; SliwinskaBartkowiak, M. Rep. Prog. Phys. 1999, 62, 1573-1659. (5) Sircar, S. Engineering Handbook; CRC Press: Boca Raton, FL, 1996. (6) Murata, K.; El-Merraoui, M.; Kanekoa, K. J. Chem. Phys. 2001, 114, 4196-4205. (7) Humayun, R.; Tomasko, D. AIChE J. 2000, 46, 2065. (8) Ramsay, J. D. F. AdV. Colloid Interface Sci. 1998, 77, 13-37. (9) Dierker, S. B.; Wiltzius, P. Phys. ReV. Lett. 1991, 66, 1185-1188. (10) Lin, M. Y.; Sinha, S. K.; Drake, J. M.; Wu, X.-I.; Thiyagarajan, P.; Stanley, H. B. Phys. ReV. Lett. 1994, 72, 2207-2210.

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