pubs.acs.org/Langmuir © 2010 American Chemical Society
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NMR Studies of Cooperative Effects in Adsorption Iain Hitchcock,† John A. Chudek,§ Elizabeth M. Holt, John P. Lowe,‡ and Sean P. Rigby*,†,^ Department of Chemical Engineering, and ‡Department of Chemistry, University of Bath, Claverton Down, Bath BA2 7AY, United Kingdom, §Division of Biological Chemistry and Molecular Microbiology, School of Life Sciences, University of Dundee, Dundee DD1 4HN, United Kingdom, and Johnson Matthey Technology Centre, P.O. Box 1, Belasis Avenue, Billingham, Cleveland TS23 1LB, United Kingdom. ^ Present address: Department of Chemical and Environmental Engineering, University of Nottingham, University Park, Nottingham NG7 2RD, United Kingdom )
†
Received May 26, 2010 The conversion of gas adsorption isotherms into pore size distributions generally relies upon the assumption of thermodynamically independent pores. Hence, pore-pore cooperative adsorption effects, which might result in a significantly skewed pore size distribution, are neglected. In this work, cooperative adsorption effects in water adsorption on a real, amorphous, mesoporous silica material have been studied using magnetic resonance imaging (MRI) and pulsed-gradient stimulated-echo (PGSE) NMR techniques. Evidence for advanced adsorption can be seen directly using relaxation time weighted MRI. The number and spatial distributions of pixels containing pores of different sizes filled with condensate have been analyzed. The spatial distribution of filled pores has been found to be highly nonrandom. Pixels containing the largest pores present in the material have been observed to fill in conjunction with pixels containing much smaller pores. PGSE NMR has confirmed the spatially extensive nature of the adsorbed ganglia. Thus, long-range (g40 μm) cooperative adsorption effects, between larger pores associated with smaller pores, occur within mesoporous materials. The NMR findings have also suggested particular types of pore filling mechanisms occur within the porous solid studied.
Introduction The pore size distribution (PSD) is a key void space descriptor used to understand the performance of heterogeneous catalysts. Any potential inaccuracy in this descriptor would greatly undermine efforts to understand the inter-relationship between catalyst structure and performance. Gas adsorption is often used to obtain the PSD. The theoretical data analysis methods used for converting the adsorption isotherm into a PSD make two major assumptions. First, it is necessary to assume a theory for the fundamental physics underlying gas adsorption, particularly capillary condensation. Second, since gas adsorption is an indirect method, it is commonly necessary to assume a void space geometry, such as a parallel bundle of cylindrical pores. These two assumptions are not necessarily independent. Much recent work1 has been devoted to obtaining better descriptions of capillary condensation using nonlocal densityfunctional theory (NLDFT), rather than the traditional Kelvin equation. This is because the macroscopic thermodynamic description of capillary condensation given by the Kelvin equation is known2 to become less accurate for nanoporous materials. This work has been greatly facilitated by the development of templated mesoporous solids with apparently more regular void space structures than is typical for common heterogeneous catalyst support materials, such as aluminas. Related to the assumption of a particular void space geometry is the idea of thermodynamically independent pores. This is equivalent to treating the individual “pores” within an irregular, interconnected void space as if they were located within a hypothetical parallel pore bundle. Even assuming it is possible to obtain a *To whom correspondence should be addressed. Telephone: þ44 (0)115 9514078. E-mail:
[email protected]. (1) Ravikovitch, P. I.; Neimark, A. V. J. Phys. Chem. B 2001, 105, 6817. (2) Neimark, A. V.; Ravikovitch, P. I. Microporous Mesoporous Mater. 2001, 44-45, 697.
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physically meaningful definition of a “single pore” within an interconnected void space, this assumption neglects the possibility of interactions between neighboring pores, or even over much larger length scales. It is not particularly useful to study these effects in templated porous solids because their pores are nonintersecting (MCM-41),3 corrugations within the major pores are not controllable (SBA-15),4 the interconnecting pores are microporous (e.g., SBA-15),4 or the unit cell of interconnecting pores of different sizes is unrealistically small compared to amorphous materials (MCM-48).5 Possible alternative regular porous solids include electrochemically etched alumina6 or silicon7 materials. While it is possible to actively introduce corrugations or more abrupt changes in pore size in these materials, these materials still contain undetermined degrees of disorder sufficient to adversely impact clear interpretation of the adsorption data. In addition, the unit cell of relative order tends to be quite small. It is thus doubtful whether these materials capture all of the phenomena relevant to adsorption in industrially relevant materials, such as sol-gel silica, or γ-alumina mesoporous catalyst supports. Cooperative pore-pore interaction phenomena during adsorption have been studied to some extent. The advanced condensation theory of Esparza et al.8 is similar to proposals put forward originally by de Boer.9 It proposed that, for a through (3) Kruk, M.; Jaroniec, M.; Sayari, A. Langmuir 1997, 13, 6267. (4) Gommes, C. J.; Friedrich, H.; Wolters, M.; de Jongh, P. E.; de Jong, K. P. Chem. Mater. 2009, 21, 1311. (5) Morishige, K.; Tateishi, N.; Fukama, S. J. Phys. Chem. B 2003, 107, 5177. (6) Casanova, F.; Chiang, C. E.; Li, C.-P.; Schuller, I. K. Appl. Phys. Lett. 2007, 243103. (7) Coasne, B.; Grosman, A.; Ortega, C.; Simon, M. Phys. Rev. Lett. 2002, 256102. (8) Esparza, J. M.; Ojeda, M. L.; Campero, A.; Dominguez, A.; Kornhauser, I.; Rojas, F.; Vidales, A. M.; Lopez, R. H.; Zgrablich, G. Colloids Surf., A 2004, 241, 35. (9) de Boer, J. H. The shapes of capillaries. In The structure and properties of porous solids; Everett, D. H., Stone, F.S., Eds.; Butterworths Scientific Publications: London, 1958; p 68.
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(open) ink-bottle pore geometry, if the radius of the two shielding pore necks is greater than half that of the intermediate pore body, then all will fill at the same pressure. In this case, the pressure required is equivalent to that given by the Cohan10 equation for a cylindrical meniscus in the pore neck. This is because once condensate has filled the pore neck, filling of the pore body may then proceed via ingress of the, now hemispherical, meniscus from the end of the pore neck. If the pore neck radius is over half that of the pore body, then the pressure for condensation within the pore body, for a hemispherical meniscus, is exceeded by the pressure required to condense in the neck with a cylindrical meniscus. The general picture suggested de Boer9 has been confirmed by grand canonical Monte Carlo simulations of Ar adsorption in model, unconnected silica and alumina pores possessing corrugations.11,12 Detcheverry et al.13 conducted mean-field density functional theory (MFDFT) simulations of adsorption in disordered models for silica aerogels. They found that an initially localized condensation event can trigger further collective condensation in neighboring cavities, such that the independent pore model is completely inappropriate. The potential presence of advanced adsorption effects has significant implications for the interpretation of gas adsorption data for pore systems undergoing structural evolution. If an inkbottle pore geometry was being generated by progressive pore mouth blocking by coke deposition in a catalyst, then, in the presence of advanced adsorption, the pattern of adsorption (and hence data analysis necessary) would change as the neck radius declined below half that of the noncoked pore body. However, in addition, the strength of the adsorbate-catalyst and adsorbate-coke interactions may be different, and some suggestion that the critical ratio of pore body-to-neck sizes for the onset of advanced condensation is dependent on adsorbate-adsorbent interaction strength has been obtained using MFDFT studies.14 Advanced condensation has been invoked to explain the shape of hysteresis loops in various experimental studies of adsorption in regular15 and amorphous16 materials. However, direct observations of the effect are more limited. Casanova and coworkers6,17 have made experimental studies of advanced condensation of hexane in model funnel- and ink-bottle-shaped pores within anodized alumina using optical interferometry. These workers observed that, in a funnel-shaped model pore system, sorption in the externally directly accessible, larger pore section occurred without hysteresis. They observed that initial capillary condensation within the neck of the funnel lowered the relative pressure for condensation in the larger pore body (presumably by generating a dead end, and a hemispherical meniscus) but not simultaneous filling of the pore neck and body, as envisaged above using classical Cohan10 theory, presumably because the ratio of pore body to neck size was ∼4, rather than being less than 2. However, the size ratio was ∼2 for the model ink-bottle pores but advanced condensation with single step filling of both pore segments was not observed, though there was a small second step in the adsorption isotherm for the pore necks at a pressure closer to that of the pore (10) Cohan, L. H. J. Am. Chem. Soc. 1938, 60, 433. (11) Coasne, B.; Galarneau, A.; Di Renzo, F.; Pellenq, R. M. J. Phys. Chem. C 2007, 111, 15759. (12) Bruschi, L.; Mistura, G.; Liu, L.; Lee, W.; G€osele, U.; Coasne, B. Langmuir 2010, 26, 11894. (13) Detcheverry, F.; Kierlik, E.; Rosinberg, M. L.; Tarjus, G. Langmuir 2004, 20, 8006. (14) Rigby, S. P.; Chigada, P. Adsorption 2009, 15, 31. (15) Kleitz, F.; Berube, F.; Guillet-Nicholas, R.; Yang, C.-M.; Thommes, M. J. Phys. Chem. C 2010, 114, 9344. (16) Morishige, K. Langmuir 2009, 25, 6221. (17) Casanova, F.; Chiang, C. E.; Li, C.-P.; Roshschin, I. V.; Ruminski, A. M.; Sailor, M. J.; Schuller, I. K. Nanotechnology 2008, 19, 315709.
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bodies than the first step. This difference from classical theory may be because the critical ratio varies with adsorbate-adsorbent interaction strength, as suggested by previous MFDFT studies.14 NMR methods, specifically relaxometry, have been used to study cooperative effects in sorption experiments, but only poreblocking on the desorption isotherm. Porion et al.18 used NMR relaxometry to show that the relaxation time of water adsorbed in silica gels was the same, at the same fractional saturation level, irrespective of whether this was on the adsorption or desorption branch of the isotherm. They interpreted this finding to imply that pore-blocking effects were not occurring on the desorption branch. If pore-blocking effects were occurring, this would give rise to a different geometrical configuration of the adsorbed ganglia within the void space at the same saturation level on the adsorption and desorption branches leading to differences in average surface area to volume ratio. Hence, it would be expected that the relaxation times should differ between the hysteresis branches if poreblocking was occurring. However, this reasoning neglects the possibility of advanced condensation on the adsorption branch. In ink-bottle pore geometries where the pore body size does not exceed the critical value, the pore body and pore neck should fill and empty at the same time on both the adsorption and desorption branches if both advanced condensation and pore-blocking effects were occurring. Hence, the results of Porion et al.18 do not necessarily imply the absence of pore-blocking if advanced condensation was occurring too. Therefore, these results indicate the necessity of detecting advanced condensation effects before interpreting sorption data. Since cooperative adsorption effects are intrinsically spatial and longer range (at least compared to pore size) in character, then this suggests they need to be studied using a technique that is capable of providing spatially resolved information on the adsorption process. Magnetic resonance imaging (MRI) can be used to obtained spatially resolved maps of spin density, relaxation time, and diffusivity, which probe voidage fraction, pore size, and pore connectivity (tortuosity), respectively, of porous media over length scales of >10 μm.19 It has been used to show that “amorphous” mesoporous catalyst support pellets possess macroscopic heterogeneities in the spatial distribution of these parameters with correlation lengths exceeding ∼100 μm.19 However, while MRI has been used to study adsorption processes,20 it has not been used to probe more fundamental aspects. MRI has been used to study the kinetics of adsorption in packed beds21 and whole pellets.22 Simple imaging (without relaxation or diffusional preconditioning) has been used to obtain a spatially resolved isotherm, from which the spatial distribution of the Brunauer-Emmett-Teller (BET) surface area and interaction parameter have been obtained.20 However, to our knowledge, (relaxation) preconditioned imaging pulse sequences have not been used to study adsorption, particularly in materials that possess long-range correlations in pore size visible in MRI. In contrast to MRI, other techniques used to study the fundamental processes of adsorption, such as small angle X-ray scattering (SAXS) and small angle neutron scattering (SANS), generally give rise to data that is averaged over the whole sample.23 (18) Porion, P.; Faugere; Levitz, P.; Van Damme, H.; Raoof, A.; Guilbaud, J. P.; Chevoir, F. Magn. Reson. Imaging 1998, 16, 679. (19) Hollewand, M. P.; Gladden, L. F. J. Catal. 1993, 144, 254. (20) Beyea, S. D.; Caprihan, A.; Glass, S. J.; DiGiovanni, A. J. Appl. Phys. 2003, 94, 935. (21) Prado, P. J.; Balcom, B. J.; Jama, M. J. Magn. Reson. 1999, 137, 59. (22) Koptyug, I. V.; Khitrina, L. Y.; Aristov, Y. I.; Tokarev, M. M.; Iskakov, K. T.; Parmon, V. N.; Sagdeev, R. Z. J. Phys. Chem. B 2000, 104, 1695. (23) Hoinkis, E.; Rohl-Kuhn, B. J. Colloid Interface Sci. 2006, 296, 256.
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While scattering methods are generally used to study pore-scale phenomena (10 μm) processes, pulsed-field gradient (PFG) NMR can be used to study adsorption over some of the intermediate size range (∼1-10 μm). Hence, PFG NMR is a useful complementary technique. Ardelean and co-workers24 have used MRI without preconditioning and magnetization grid rotating frame imaging (MAGROFI) to study the spatial distribution of liquid within partially saturated silica samples. Partial saturation of the sample with condensate was achieved by halting a kinetic vapor adsorption experiment, above pure water, at a given weight. This technique may give rise to a different spatial arrangement of ganglia of condensate than would be achieved by equilibrium adsorption. MRI studies demonstrated a heterogeneous spatial distribution of liquid on macroscopic length scales. MAGROFI studies indicated that the water diffusivity at partial saturation exceeded that at pore filling due to the contribution from the vapor phase. However, when a pulsed-gradient stimulated-echo (PGSE) NMR technique was used, the apparent diffusivity appeared to decrease and then increase with decreasing saturation level. The difference in findings was due to condensate with low T2 being invisible to the PGSE NMR method. Naumov et al.25 have studied the spatial arrangement of condensate within the void space, on the adsorption and desorption branches of the hysteresis loop region of the isotherm, for cyclohexane sorption in Vycor porous glass. They found that the diffusivity differed between the boundary adsorption and desorption branches of the hysteresis loop at the same degree of pore filling. In addition, they also found that the spatial arrangement of condensate at the same saturation level differed for scanning loops, when compared with the boundary curves. These results suggested that the spatial arrangement of condensate within pores was dependent upon the adsorptiondesorption history of the sample. In this work, studies of advanced adsorption effects for water adsorption on a macroscopically heterogeneous, mesoporous silica using MRI and PFG NMR will be described. It will be shown that advanced adsorption can occur in pore bodies that are up to five times larger than their neighboring necks, and that these effects can extend over macroscopic length scales. From the results obtained here, it will be shown how a consideration of advanced condensation effects can be used to increase the information derived from gas adsorption.
Theory PFG NMR. For more details on the PFG NMR method, the reader is referred to earlier work by Hollewand and Gladden.26 In PFG NMR, the echo attenuation, R, is defined as the ratio of the echo intensity in the presence of a gradient (M(g)) to the echo intensity in the absence of a gradient (M(0)). For the NMR pulse sequence (detailed below) used in this work, the echo intensity is given by " # MðgÞ δ τ 2 2 2 ¼ exp - Dγ g δ Δ - ð1Þ R ¼ Mð0Þ 3 2 where D is the diffusion coefficient, γ is the gyromagnetic ratio, g is the pulsed-field gradient strength, δ is the duration of the pulsed gradient, Δ is the diffusion time, and τ is the correction time between bipolar gradients. A range of echo attenuations are obtained by varying g, and a plot of ln R against γ2δ2g2(Δ - δ/3 - τ/2) yields the diffusion coefficient from the slope of the straight line fit to the (24) Farrher, G.; Ardelean, I.; Kimmich, R. Appl. Magn. Reson. 2008, 34, 85–99. (25) Naumov, S.; Valiullin, R.; Monson, P. A.; K€arger, J. Langmuir 2008, 24, 6429. (26) Hollewand, M. P.; Gladden, L. F. Chem. Eng. Sci. 1995, 50, 309.
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data. Since the observed signal contains a contribution from the spin density, which is directly related to voidage, the diffusion coefficient measured by PFG NMR, DPFG, is given by26 DPFG ¼
Dw τp
ð2Þ
where Dw is the free diffusion coefficient for bulk water at the temperature at which the PFG NMR experiment is conducted and τp is the tortuosity of the pore space occupied by the fluid.
Experimental Section The porous material studied in this work, denoted G2, is a batch of mesoporous, sol-gel silica spheres of diameter ∼3 mm. The voidage fraction is 0.70 ( 0.02, the modal pore diameter is ∼30 nm, and the specific pore volume is 1 mL g-1. Previous work27 has shown that, when pore shielding effects are removed by fragmentation of the pellets to a powder of particle size ∼30 μm and the raw mercury porosimetry data is analyzed using semiempirical alternatives to the Washburn equation (calibrated independently to remove contact angle hysteresis effects), the pore size distribution for pellets from batch G2 is unimodal. Water Sorption. Water adsorption and desorption isotherms were obtained for a sample of two pellets and were carried out using a Dynamic Vapor Sorption Advantage apparatus, modified with a temperature preheater. Samples were initially presoaked in pure water and heated to 100 C to dehydrate the samples, but care was taken not to dehydroxylate the silica surface. Water adsorption to 90% humidity was performed at 296 ( 0.1 K in intervals of 10%, and an equilibration time of 4 h was used for each step. Upper points in the isotherm were obtained gravimetrically by suspension of similarly sized pellet samples above large reservoirs of sodium hydroxide solutions (see below). The sample preparation of pellets for gravimetric measurement of the isotherm and for MRI experiments was identical. MRI. Samples were suspended above solutions of sodium hydroxide with different concentrations such that they gave rise to various relative pressures of water vapor; it was assumed that no concentration change would occur during the adsorption experiment as the sodium hydroxide solution reservoir was “large”. The samples were sealed and left to equilibrate for 2 weeks at 296 K. Prior to the MRI experiment, the sample was transferred to a 5 mm NMR tube and suspended above the same concentration of sodium hydroxide solution to maintain the established equilibrium. A 10% H2O in D2O phantom was included in the NMR tube as a reference concentration; Cu(II), in the form copper sulfate, was added to make a 2.0 10-3 M solution to prevent T1 saturation. The NMR tube was then sealed with parafilm to minimize vapor exchange to the atmosphere. MRI experiments were carried out on a Bruker AVANCE NMR system with static field strength of 7.05 T, yielding a resonance frequency of 300.05 MHz for the 1H nucleus. Temperature stability of (0.5 K was maintained throughout all data acquisitions. The 5 mm NMR tube was placed into a 10 mm birdcage resonator and spin-spin relaxation time (T2) and spin density maps were acquired together using the Bruker sequence “m_msme”, and employed 90 selective and 180 nonselective pulses. A T2 preconditioned imaging sequence with an echo time of 4 ms was used. Three-dimensional (3D) images were acquired using the “m_se3d” sequence. The acquisition time for one data set was ∼100 h. Data acquisition, initial data transformation, two- and three-dimensional data processing, and workup were handled on an Aspect X32 workstation, running the Paravision suite of software (Bruker Analitische Messtechnik Gmbh, Karlsruhe, Germany). The in-plane pixel resolution was 79 μm, and the slice thickness was 130 μm. 3D spin-echo data were subsequently worked up using the AMIRA software package. Pixels were considered (27) Rigby, S. P.; Edler, K. J. J. Colloid Interface Sci. 2002, 250, 175.
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Figure 1. (a) Water adsorption ([) and desorption (9) isotherms obtained at 296 K for G2. The inset shows a solid line which is a fit of the adsorption data in the relative pressure range 0-90% to the fractal BET equation. (b) Expanded view of the hysteresis loop region of the water isotherms shown in (a). The line shown on the expanded view is to guide the eye. occupied by capillary condensed phase where signal intensities for all echo times exceeded the noise level, and hence, the pixel occupancy level was consistent with the water adsorption isotherm (see below). PFG NMR. PFG NMR experiments were carried out on a Bruker Avance 400 MHz spectrometer with a static field strength of 9.4 T yielding a resonance frequency of 400.13 MHz for the 1H nucleus. The samples were prepared as stated above for MRI and suspended in 5 mm NMR tubes. They were not, however, suspended above a sodium hydroxide solution, as the positioning of the receiver coil made this difficult. The pulse sequence used was a stimulated echo with bipolar longitudinal eddy current delay (BPLED). The values of δ and τ were 0.002 and 0.0001 s, respectively, and Δ was 0.05 or 0.1 s. Eight data points were taken at increasing gradient strengths between 0.674 and 32.030 G cm-1, and each point was obtained with 16 scans. This particular technique was chosen because, in this study, it is required to examine the spatial distribution of the condensate in regions where pore filling exceeds a thin film. As described by Ardelean and co-workers,24 thin films with low T2 values are likely to be invisible in PGSE NMR experiments.
Results Water Adsorption and Desorption Isotherms. Figure 1 shows the water adsorption and desorption isotherms for batch G2. It can be seen that uptake is very low until a relative pressure of ∼95% when there is a marked increase in uptake, as capillary condensation commences. Figure 1a also shows a fit of the data in the relative pressure range 0-90% to the fractal BET isotherm 18064 DOI: 10.1021/la103584k
equation derived by Mahnke and M€ogel.28 The coefficient of determination for the fit was 0.9997. The BET constant, monolayer capacity, and fractal dimension thereby obtained were 4.3, 1.56 mass % and 2.58, respectively. Also shown in Figure 1 is an extrapolation of the fitted fractal BET model to higher relative pressures. It can be seen that there is a significant deviation from the fractal BET model at relative pressures of ∼95%. Figure 1b shows an expanded view of the hysteresis loop region of the isotherm. The hysteresis loop is of type H2. The sharp knee in the desorption isotherm is characteristic of a percolation type transition. MRI Studies of Water Adsorption. Figures 2-4 show the data derived from porosity and spin-spin relaxation time images for arbitrary equatorial slices through a single pellet sample from batch G2 during equilibrium water adsorption at relative pressures of 0.960, 0.965, and 0.980, respectively. Due to the short relaxation time of molecules confined to liquid layers nearest the pore wall, regions of the pellet containing just multilayer adsorption will be invisible to MRI with the echo times possible to use. Further, as explained in earlier studies,29 even for regions of the void space that are pore-filled, some of the water in layers near the pore wall will be “invisible” to NMR. The invisible fraction is due to spins in water bound, or close, to the pore surface that are not averaged over the pore volume by diffusion during the echo time. These are likely to be molecules in the earliest layers of water next to the surface and thus present from the very lowest pressure points of the isotherm. This “invisible’” fraction can be determined by comparing the overall average voidage fraction determined from a calibrated spin density image of a fully saturated pellet, and the value obtained from helium-mercury pycnometry. For G2, the discrepancy was found to be 0.10 ( 0.02, which is similar to the corresponding value found in earlier MRI studies of catalyst support pellets.19,29 Since the typical pore size of G2 is 30 nm and the thickness of one layer of adsorbed water is ∼0.3 nm,30 then, averaged over the whole void space, the 10% invisible fraction corresponds to ∼2.6 layers of adsorbed water. According to the fitted multilayer isotherm, at relative pressures of 0.960 and 0.965, the multilayer thickness was ∼3.8 and ∼4 monolayers, respectively, which is very thin, and thus these would be invisible to MRI. Thus, assuming a voidage fraction of 0.1 occupied by water is invisible to MRI in each pixel occupied by capillary condensed phase, then, at relative pressures of 0.960 and 0.965, the mass uptakes calculated from the MR spin density image data are 23.5 ( 1.1% and 25.7 ( 1.2% of the pore-filled value, respectively, where the quoted error allows for experimental uncertainty in the pellet total porosity. The corresponding values from the water adsorption isotherm are 20.7 ( 1.2% and 27.0 ( 1.6%, respectively. Hence, the values estimated from the MRI data are consistent with the water isotherm data, within the known errors. Figure 5 shows the histograms of pixel spin-spin lattice relaxation times for the pellet slices shown in Figures 2-4. From the histograms, it can be seen that, at a given vapor pressure, the main part of the number distribution of relaxation times consists of a rough bell-shape, but at the lower two relative pressures there is also a long tail of higher relaxation times. At relative pressures of 0.960 and 0.965, the high-end tails consisted of relaxation times in excess of 40 and 50 ms, respectively. As the vapor pressure of water increases, the modal peak of the distribution shifts to larger values of relaxation time and values in the high-end tail increase in frequency. At the highest relative pressure (0.980), the lowest (28) Mahnke, M.; M€ogel, H. J. Colloids Surf., A 2003, 216, 215–228. (29) Hollewand, M. P.; Gladden, L. F. Chem. Eng. Sci. 1995, 50, 327. (30) D’Orazio, F. D.; Bhattacharja, S.; Halperin, W. P.; Eguchi, K.; Mizusaki, T. Phys. Rev. B 1990, 42, 42.
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Figure 2. Spin density (a) and spin-spin relaxation time (T2/ms) (b) images for an arbitrary equatorial slice through a pellet from batch G2 exposed to a relative pressure of water vapor of 0.960. The spin density is given as the fraction of sample volume occupied by water.
values of relaxation time that were present in the distributions for the lower pressures are absent and the modal peak is sited in the range of values of relaxation time previously making up the highend tails. A sensitivity study demonstrated that the high-end tails were present irrespective of the acceptable level chosen (in the range 1-10%) for error in pixel T2 values. The images themselves have been used to determine the spatial characteristics of the adsorption process. In the images, each pixel has eight nearest neighbors, including diagonal directions. For relative pressures below 0.980, image pixels containing adsorbed water tended to occur in clusters of other occupied nearest Langmuir 2010, 26(23), 18061–18070
neighbor pixels, separated from other clusters by a continuous sea of unoccupied pixels. The relaxation time for liquid in the surface layers of any adsorbed thin film is so short that the liquid is invisible in MRI. Cluster sizes ranged from single isolated pixels upward. From a consideration of the values of relaxation time among the particular nearest neighbors of each pixel, within its own cluster, it has been found that pixels from the high-end tail of the number distributions are statistically unlikely to be entirely segregated from pixels with values from the main (bell-shaped) body of the distribution. For example, in the spin-spin relaxation time image obtained at a relative pressure of 0.965, no pixel with a DOI: 10.1021/la103584k
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Figure 3. Spin density (a) and spin-spin relaxation time (T2/ms) (b) images for an arbitrary equatorial slice through a pellet from batch G2 exposed to a relative pressure of water vapor of 0.965. The spin density is given as the fraction of sample volume occupied by water.
value from the high-end tail of the number distribution was a member of a contiguous cluster within which there were absolutely no pixels with relaxation times from the main body of the number distribution. However, pixels with spin-spin relaxation times from the main body of the number distribution 3.1% were totally isolated. This value suggested that the corresponding result for the tail was less than the fraction that might otherwise be anticipated by chance alone. Hence, voxels in the tail are more likely to have an association with a voxel with a T2 from the peak in the distribution than chance would suggest. The spatial distributions of occupied pixels in the MR images have been compared with the random Poisson model. The area of each MR image occupied by the pellet was divided up into squares of size 3 3 pixels, or 4 4 pixels, ignoring squares which bridged the pellet boundary and beyond. The number of pixels occupied by condensate in each square was counted. The observed distribution in square occupancy thus obtained was compared with that expected for a Poisson model with the same overall average 18066 DOI: 10.1021/la103584k
occupancy rate. For the image of the pellet exposed to a relative pressure of 0.960 (Figure 2), it was found that the mode of the observed distribution was shifted to higher occupancy levels than expected for a random distribution, and this difference between the observed and expected distributions was found to be statistically significant in a χ2 test (p < 0.05). The spatial distribution of pixel intensities for an image obtained at a relative pressure of 0.965 was found to be significantly underdispersed (nonrandom) (p < 0.05) following tiling with squares of 4 4 pixels. PFG NMR Studies of Water Adsorption. The PFG NMR values obtained for the partially saturated samples gave rise to logattenuation plots that were closely approaching a linear form and were thus fitted to single component diffusion models. Table 1 shows the variation of tortuosity (for two diffusion times, Δ) with relative pressure. It can be seen that, at any given relative pressure, the tortuosities obtained at the two different diffusion times, differing by a factor of 2, are insignificantly different from each other. This suggests that diffusion is not completely restricted, since, if it were, Langmuir 2010, 26(23), 18061–18070
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Figure 4. Spin density (a) and spin-spin relaxation time (T2/ms) (b) images for an arbitrary equatorial slice through a pellet from batch G2 exposed to a relative pressure of water vapor of 0.980. The spin density is given as the fraction of sample volume occupied by water.
the apparent tortuosity would be expected to halve (or at least substantially decline) as diffusion time is doubled. This suggests that the ganglia of water are continuous over at least length scales of the order of the root mean square (rms) displacement of the water molecules (>∼10 μm). This is consistent with the imaging data that suggest that connected clusters of occupied voxels extend over length scales approaching the order of the size of the pellet. It can also be seen that as the relative pressure is varied from 95 to 98.5%, corresponding to the region of the steep increase in mass uptake, the tortuosity first increases as far as a relative pressure of ∼96.5% and then decreases again. Langmuir 2010, 26(23), 18061–18070
Discussion The fractal BET equation, used to fit the water adsorption isotherm, is based on the principle that in fractal systems, or any other systems with concavities, the number of potential adsorption sites will be reduced as the multilayer thickens. Rather than necessarily attributing any fractal nature to our material, the fractal dimension is used here as a way of characterizing, using a numerical parameter, the relative importance of preferential adsorption in concavities for a particular adsorbent-adsorbate system. The BET constant obtained from the fit of the water adsorption DOI: 10.1021/la103584k
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Hitchcock et al. Table 1. Average Tortuosity Values, for Self-Diffusivity of Water within Pellets from Batch G2, Obtained at Different Relative Pressures and Diffusion Times, Δ, Using PFG NMR relative pressure
Figure 5. (a) Frequency histogram for voxels from the spin-spin relaxation time (T2/ms) image obtained of an arbitrary slice through a pellet from batch G2 exposed to a relative pressure of water vapor of 0.960 shown in Figure 2b. (b) Frequency histogram for voxels from the spin-spin relaxation time (T2/ms) image obtained of an arbitrary slice through a pellet from batch G2 exposed to a relative pressure of water vapor of 0.965 shown in Figure 3b. (c) Frequency histogram for voxels from the spin-spin relaxation time (T2/ms) image obtained of an arbitrary slice through a pellet from batch G2 exposed to a relative pressure of water vapor of 0.980 shown in Figure 4b.
isotherm to the fractal BET model is 4.3, suggesting that water has only a relatively weak interaction with the surface of G2 at the temperature the isotherm was carried out. The surface fractal dimension of 2.58, obtained from the water adsorption isotherm for G2, is the same, within experimental error, as the value of 2.597 ( 0.023 obtained previously31 from a fit of the fractal BET equation to nitrogen adsorption isotherms for several samples from batch G2. The similarity in the values for water and nitrogen suggests that the molecules adsorb on potential energy surfaces of similar overall (31) Watt-Smith, M. J.; Edler, K. J.; Rigby, S. P. Langmuir 2005, 21, 2281–2292.
18068 DOI: 10.1021/la103584k
Δ/s
0.953
0.960
0.965
0.971
0.977
0.985
0.05 0.10
1.70 1.77
1.98 1.98
2.14 2.16
2.11 2.13
1.96 2.00
1.44 1.45
form. Both water (via hydrogen bonding) and nitrogen (via its quadrupole moment) are likely to interact particularly, and maybe quite strongly, with the polar hydroxyl groups on the surface of the silica. However, it is also noted that results31 obtained using the SAXS method suggest the surface fractal dimension of G2 is 2.30 ( 0.05. Hence, the apparent fractal dimensions obtained for water and nitrogen are significantly larger than this value. This positive discrepancy would arise if there was an additional decrease in the adsorption sites in higher adsorbed layers due to preferential initial adsorption in concavities. The MRI data presented above suggest that cooperative adsorption effects can take place between neighboring pores that differ in size by a factor of 5, and not just the upper limit of 2 suggested by the Kelvin equation, when the adsorbate-adsorbent interactions are relatively weak. By using the integrated gas sorption and mercury porosimetry technique to isolate the condensation pressure for pores of particular size in a sol-gel silica, previous work14 has shown that the interaction between nitrogen and the dehydroxylated surface of some sol-gel silica spheres is very weak, supporting the above suggestion from the analysis of multilayer adsorption. Hence, it seems likely that pore size distributions determined by nitrogen adsorption are more significantly influenced by cooperative adsorption effects than was generally thought. This may explain the often observed discrepancies between the shapes of the pore size distributions obtained by gas adsorption and (deshielded) mercury porosimetry. The statistical analysis of the MR images suggested a nonrandom spatial distribution of condensed phase, as might be expected if correlations in condensation events, due to pore-pore interactions, were occurring. Moving to the PFG NMR data, Naumov et al.25 have studied the adsorbed phase using PFG NMR during cyclohexane adsorption on Vycor porous glass. They observed a variation in the self-diffusivity of cyclohexane as the adsorbed amount was increased. It was found that the self-diffusivity went through a maximum. They attributed this pattern to the presence of three different phases within the sample with different diffusivities that contribute to the measured average diffusivity. First, a slow diffusion contribution from fluid in close contact with the pore walls which makes its largest fractional contribution to the average diffusivity at low pressures. A second fast diffusion contribution comes from the gaslike fluid at the center of the pores away from the pore walls, making its largest fractional contribution to the average diffusivity over an intermediate range of pressure. Finally, a slow diffusion contribution from fluid in liquid-like states at the center of pores that makes its contribution at higher pressure. In contrast, for adsorption of water studied here, there is a variation in observed average self-diffusivity with a minimum (corresponding to a maximum in tortuosity in Table 1) at intermediate relative pressures in the range covered. In Table 1, the values of tortuosity measured at relative pressures below that required for complete pore filling all exceed that at complete pore filling. It is conceivable, certainly at lower relative pressures, that the void space in G2 pellets might consist of isolated liquid droplets surrounded by a continuous vapor phase. Calculations, based upon the kinetic theory of gases, suggest that, for water at Langmuir 2010, 26(23), 18061–18070
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296 K, if the surface area for exchange between condensed liquid droplet and vapor phases approached the internal surface area of the pore space of G2, then all of the condensate could have time to exchange with vapor during the course of a PFG NMR experiment. However, in contrast, if the free meniscus area for exchange with vapor approached the external geometric surface area of a pellet from batch G2, then negligible liquid will exchange with the vapor. If rapid exchange occurs between pore condensate and pore vapor then the observed diffusion coefficient would be a composite value for both media. Maxwell (cited in Crank32) showed that, in a two (diffusion) phase system consisting of a suspension of spheres of one phase, a (e.g., water), so sparsely distributed in a continuum of the second phase, b (vapor), such that any interaction between them is negligible (i.e., water is not contiguous), the effective diffusion coefficient of the composite medium, Dw, can be written in the form: Dw - Db Da - Db ¼ νa ð3Þ Dw þ 2Db Da þ 2Db where νa is the volume fraction of the dispersed phase. The coefficient Dw is the diffusion coefficient of a hypothetical homogeneous medium exhibiting the same steady-state behavior as the two-phase composite. Equation 3 would suggest that, if significant exchange was occurring between condensed liquid and vapor, the observed diffusivity would be significantly higher than the purely liquid phase diffusivity at pore filling, even if liquid were the continuous phase. However, as seen in Table 1, the diffusivity at partial pore filling remains below that at complete pore filling. This suggests that the vapor phase is not making any significant contribution to the observed diffusivity (and thus tortuosity), since, otherwise, it would be expected that diffusion would be enhanced relative to solely liquid-phase diffusion. This suggests that the observed variation in tortuosity in Table 1 is due to variations in the average tortuosity of the regions making up the void space occupied by liquid at different relative pressures. Given that the MR images suggest that the distribution of condensed water is highly heterogeneous (correlated), and clusters of occupied pixels are macroscopic in dimension, then it seems likely that the area for liquid-vapor exchange is relatively low, and this is why there is no significant contribution of gas phase mass transport to the observed diffusivities. As noted above, at the highest relative pressure (0.980) imaged, the lowest values of relaxation time present in the distributions for the lower pressures are absent and the modal peak is sited in the range of values of relaxation time previously making up the highend tails. The lack of the lower values of T2 in the frequency histograms for higher relative pressure suggest that these values must correspond to partially filled pores, since if they had corresponded to completely filled smaller pores, they would still be present in the distribution for images obtained at complete pore filling. However, the lack of restricted diffusion in the corresponding PFG NMR suggests that the water ganglia in the partially filled pores do not occur in isolated blobs of lateral spatial extents less than ∼10 μm. Previous findings by Valiullin et al.33 suggest that the quite linear form of the log-attenuation plots for the PFG-NMR data found here suggest that diffusion components are not experiencing significant exchange with vapor phase regions. The above findings are thus consistent with the condensed phase, at lower relative pressures, existing as a highly thickened surface layer, with relatively little void space left at the center of the pores. A progressive thickening of this layer would be consistent with the (32) Crank, J. The Mathematics of Diffusion; Clarendon Press: Oxford, 1975. (33) Valiullin, R. R.; Skirda, V. D.; Stapf, S.; Kimmich, R. Phys. Rev. E 1997, 55, 2664.
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migration of the modal peak in the distribution of image T2 values toward higher values. At a relative pressure of 0.960, the modal peak in values of T2 occurred at ∼20-25 ms, while at pore-filling the modal peak occurred at ∼60 ms. If values of T2 of ∼20-25 ms at a relative pressure of 0.960 corresponded to the characteristic size of the film (its thickness) and the values of T2 of ∼60 ms at pore-filling correspond to the typical size of a pore, then the relative sizes of these values suggest a thick film of at least ∼1/3 of the pore size at a relative pressure of 0.960. In contrast, the long tail of highest values of T2 in the frequency histograms, present even at relative pressures of 0.960, included even some voxels with the maximum values of T2 present in the frequency histogram for the images of the completely saturated (and thus certainly pore-filled) pellet. This suggests that the largest pore containing condensed phase becomes completely pore-filled at lower pressure than the smaller pores, and thus there is potentially a filling mechanism dependent on pore size or configuration. Previous work34,35 using 1H solid-state NMR to study hydrogen bonding of water confined in MCM-41, SBA-15, and controlled-pore glass has suggested two different pore filling mechanisms in water adsorption. Gr€unberg et al.34 suggested that the mechanism of pore-filling in SBA-15 involved, after initial coverage of the surface, a radial growth in the surface film toward the pore axis. However, for MCM-41, the proposed mechanism of pore-filling involved initial wetting of the surface, then a coexistence of filled pores, or pore segments, with wetted pores, or pore segments, and then further filling occurs as a growth of the filled pores involving an axial filling of the pores. Gr€unberg et al.34 suggested that the difference in pore-filling mechanism arose because of the difference in pore sizes between SBA-15 and MCM-41. Subsequently, Vyalikh et al.35 suggested, based upon 1H-MAS solid state NMR data, that pore filling during the adsorption of water in controlled-pore glass also occurs by radial growth toward the pore axis. For G2, the migration of the position of the modal peak in the T2 distribution toward higher values with increased relative pressure suggests that the pore-filling mechanism for G2 is similar to that for SBA-15 and controlled-pore glass. However, contrary to earlier work,34,35 for G2, it is the largest pores, rather than the smallest, that have a filling mechanism that is similar to that of MCM-41. These findings suggest that it may not be (just) pore size that dictates the pore-filling mechanism. Studies of the pore structure of SBA-15 suggest that it possesses features such as mesoporous connectivity, pore corrugations, hairpin bends, and microporous walls (the so-called “corona”) that (at least some) may be shared with controlled-pore glass but not by MCM-41 (at least not to the same degree). Hence, the differences in filling mechanism observed between SBA-15 and controlled-pore glass on the one hand and MCM-41 on the other may be due to other differences between these porous solids besides, or in addition to, pore size.
Conclusions This work has shown that the knowledge of the particular spatial juxtaposition of pores of different sizes provided by spatially resolved techniques, like MRI, is essential for understanding cooperative adsorption processes. MRI data have shown that cooperative adsorption effects can happen in neighboring pores that differ in size by a factor of 5, rather than just up to a factor of (34) Gr€unberg, B.; Emmler, T.; Gedat, E.; Shenderovich, I.; Findenegg, G. H.; Limbach, H. H.; Buntkowsky, G. Chem.;Eur. J. 2004, 10, 5689. (35) Vyalikh, A.; Emmler, T.; Gr€unberg, B.; Xu, Y.; Shenderovich, I.; Findenegg, G. H.; Limbach, H. H.; Buntkowsky, G. Z. Phys. Chem. 2007, 221, 155.
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2 as suggested by the Kelvin equation. The variation in the distribution function of T2 taken from the image data with relative pressure suggests that water adsorption occurs in pores of intermediate and smaller sizes by progressive thickening of an adsorbed film. PFG NMR data have shown that this thick
18070 DOI: 10.1021/la103584k
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adsorbed film has an extensive lateral spatial extent, and thus adsorption is not occurring in isolated ganglia. Acknowledgment. S.P.R. and I.H. would like to thank the EPSRC and Johnson Matthey for financial support.
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