Article pubs.acs.org/JPCC
Sorption Phase of Supercritical CO2 in Silica Aerogel: Experiments and Mesoscale Computer Simulations Gernot Rother,*,† Lukas Vlcek,*,†,‡ Miroslaw S. Gruszkiewicz,† Ariel A. Chialvo,† Lawrence M. Anovitz,† José L. Bañuelos,† Dirk Wallacher,§ Nico Grimm,§ and David R. Cole∥ †
Chemical Sciences Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831-6110, United States Joint Institute for Computational Sciences, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831-6173, United States § Helmholtz-Zentrum Berlin fur Materialien und Energie GmbH, Hahn-Meitner Platz 1, D-14109 Berlin, Germany ∥ School of Earth Sciences, The Ohio State University, Columbus, Ohio 43210, United States ‡
ABSTRACT: Adsorption of supercritical CO2 in nanoporous silica aerogel was investigated by a combination of experiments and molecular-level computer modeling. High-pressure gravimetric and vibrating tube densimetry techniques were used to measure the mean pore fluid density and excess sorption at 35 and 50 °C and pressures of 0−200 bar. Densification of the pore fluid was observed at bulk fluid densities below 0.7 g/cm3. Far above the bulk critical density, near-zero sorption or weak depletion effects were measured, while broad excess sorption maxima form in the vicinity of the bulk critical density. The CO2 sorption properties are very similar for two aerogels with bulk densities of 0.1 and 0.2 g/cm3, respectively. The spatial distribution of the confined supercritical fluid was analyzed in terms of two nanodispersed phases with sorption- and bulk-phase densities and their volumes by means of the adsorbed phase model (APM), which used data from gravimetric sorption and small-angle neutron scattering experiments. To gain more detailed insight into supercritical fluid sorption, large-scale lattice gas GCMC simulations were utilized and tuned to resemble the experimental excess sorption data. The computed three-dimensional pore fluid density distributions show that the observed maximum of the excess sorption near the critical density originates from large density fluctuations pinned to the pore walls. At this maximum, the size of these fluctuations is comparable to the prevailing pore sizes.
1. INTRODUCTION Anthropogenic carbon dioxide emissions into the atmosphere can be reduced by carbon capture and geologic carbon storage, CO2 utilization as green solvent, or its catalytic conversion to fuels. In geologic carbon storage, CO2 is stored as a supercritical (sc) fluid in porous rock formations.1 Estimation of the sorption capacity of storage sites and understanding sorption and capillary trapping mechanisms are important prerequisites for safe, efficient, and permanent large-scale carbon storage. Common potential storage rocks contain large fractions of nanometer-sized pores.2−5 The physical properties of fluids confined in these narrow pores are altered by physical interactions with the pore walls and the effect of confinement; especially the local densities of supercritical fluid are sensitive to even small external perturbations.6,7 An intriguing demonstration of confined fluid behavior complexity are the phenomenon of pore fluid condensation and depletion, driven by the balance between the fluid−solid interactions, pore size, and fluid correlation length. An especially intriguing phenomenon is critical depletion reported for certain porous materials and observed in computational models.8−10 Adsorption is commonly quantified in terms of the excess sorption, which gives the extra amount of fluid stored in the © 2014 American Chemical Society
sorption layer with respect to the hypothetical situation of an interfacial fluid with bulk density. The desired outcome of adsorption studies is ultimately to understand the molecular and nanoscale properties of the interfacial fluid and the impacts of adsorbent structure and thermodynamic conditions. The excess sorption yields no direct information about the morphology of the sorption phase, but this information can be gleaned from complementary scattering experiments. For instance, sorption processes in adsorbents with complex pore morphology have been studied extensively with small angle neutron scattering (SANS). Recently, Erko et al. have shown using SANS that during pore condensation pores of equal size fill in random order while obeying the Kelvin equation.11 Broseta et al. used SANS to study water condensation in sandstone with nanoscale surface fractal properties, and showed that smaller surface cavities fill up with a condensed water phase at lower relative pressure, in agreement with the Young− Laplace equation.12 Scattering studies have also illuminated Received: April 16, 2014 Revised: June 18, 2014 Published: June 18, 2014 15525
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system size due to computing limitations. Classical molecular models can offer a highly realistic description of fluid properties but are limited to systems sizes of up to a few tens of nanometers, i.e., they are only suitable for confinement studies in very narrow and simple pore morphologies. Fluids confined in larger and more irregularly shaped pores, such as those found in silica aerogel, have been represented by simple lattice gas, and simulated using GCMC and mean field density functional (DFT) methods.22 Despite their simplicity, lattice gas simulations, which represent a discretized model of fluid, provide useful insights into the critical phenomena of real fluids because they follow the same scaling laws as real liquid−gas transitions, i.e. they belong to the same universality class.23 This aspect makes them suitable for larger scale near-critical sorption studies and for the investigation of interference effects of the two length scales intrinsic to the system: pore size and correlation length of the fluid. As a result, a number of lattice gas simulations have been performed to study adsorption of fluids in porous materials in general, and also specifically in silica aerogel structures.22,24−26 The goal of this study is to provide a detailed, experimentally verified, molecular-level description of the properties of sc CO2 confined in silica aerogel. Of primary interest is the fluid distribution in the open pore space with fractal properties that is created by the aerogel matrix. Here, we examine the contributions of large critical fluctuations to fluid sorption in pores of different sizes and morphologies and in particular their effect on critical condensation and depletion. Different theoretical and simulation models of fluid adsorption in pores are evaluated. The paper is structured as follows. In sections 2 and 3 experimental details and the mesoscopic lattice models and methods used for simulations are described. In section 4 we present our results and discuss their implications for the studies of near-critical fluid sorption. We conclude with a Summary and Outlook.
pore-filling mechanisms in porous materials with complex hierarchical pore morphologies.13 Experimental and molecular dynamics (MD) simulation results show that sorption layers formed by supercritical fluids exhibit gradual density changes from the surface density to the bulk density, and the properties of the density profile are controlled by temperature, fluid density, pore morphology, and the character of the fluid−solid interactions.14,15 However, the detailed structure of the pore fluid density profile could not hitherto be measured. Sub- and supercritical pore fluids have recently been investigated by SANS techniques that rely on the evaluation of the scattering invariant.16,17 In these studies, the inhomogeneous fluid density profile near the adsorbing surface was approximated by a sorption phase with constant density and thickness (a box model). The scattering invariant at different conditions of fluid saturation and temperature describes three-phase systems composed of porous matrix, unadsorbed pore fluid, and adsorbed pore fluid, in which each phase is characterized by its volume and neutron coherent scattering length density (SLD). A formula developed by Wu is utilized to link the volumes and SLD’s of these three phases to the scattering invariant.18 The volume fractions of the unadsorbed and adsorbed pore fluid phases are unknown a priori, as is the density of the sorption phase. A second measure of the pore fluid composition, i.e., excess sorption or mean pore fluid density, is therefore needed to calculate the density and volume of the sorption phase using a mass balance consideration of the pore fluid distribution between the adsorbed and unadsorbed phases. For a detailed description of the adsorbed phase model (APM) and its use for the calculation of adsorbed phase density and volume, see Rother et al.16 Here, the APM will be used to examine experimentally derived sorption phase properties of sc CO2 in aerogel through a combination of SANS and gravimetric excess sorption data. The APM interpretation of the experimental data yields the mean density and the volume fraction of the adsorbed phase, but cannot resolve finer structural features, i.e., the density gradient and lateral inhomogeneity within the sorption phase. This is due to the limited spatial resolution of the SANS instrument and the inherent volume averaging effect of the technique. The SANS technique and APM interpretation yield the mean density and volume of the sorption phase, averaged over the entire sample. The sorption phase will take up a larger fraction of the pore volume in smaller pores as compared to larger pores. Therefore, the average pore fluid densities in small pores will differ from those in large pores. The APM and the underlying three-phase model make no assumption about the size or shape of the nanodispersed sorption phase, and account for sorption in both small and large pores. Molecular level computer simulations are powerful tools for complementing the experimental information and gaining insight into the relation between pore space morphology and fluid densification. The two critical factors determining the modeling accuracy are the quality of the porous matrix reconstruction and the realism of the model in describing the confined fluid. The aerogel matrix is known to possess a complex fractal structure with its parameters defined by the method of preparation. 19 The aerogel matrix can be reconstructed in silico using the diffusion-limited cluster− cluster aggregation (DLCA) algorithm and its variants,20,21 which mimic the physical process of gradual aggregation of basic silica building blocks into a fractal network of the gel.19 The choice of the fluid model often depends on the simulated
2. EXPERIMENTAL SECTION Base-catalyzed silica aerogels (Oscellus Technologies, Livermore, CA) with bulk densities of 0.1 and 0.2 g/cm3 were used in excess sorption and SANS measurements of sc CO2 in silica aerogel. The skeleton density of silica strands is 2.0 g/cm3, based on neutron scattering data.16 For the 0.1 g/cm3 silica aerogel, the porosity is 95%, while it is 90% for the 0.2 g/cm3 aerogel.20 Gravimetric measurements of the excess sorption were performed at a temperature of T = 35 °C and pressures of 0−200 bar using the Rubotherm magnetic suspension balance at the DEGAS laboratories at the Helmholtz Zentrum Berlin. Carbon dioxide with >99.999% purity was purchased from Linde. The temperature at the sample was controlled to ±0.02 °C by electrical resistance heaters wrapped around the outside of the pressure vessel and a calibrated Pt-100 sensor placed directly underneath the sample bucket. Pressure was measured using a temperature-corrected Keller Preciseline piezoelectric pressure transducer with a calibrated range of 0−300 bar. Pieces of silica aerogel with a total mass of ca. 200 mg were placed in the measurement cup. The measurement vessel was closed, sealed, and evacuated with a turbo-molecular pump until sample mass constancy. Compressed CO2 was added by means of a manual high-pressure piston pressurizer. Temperature, pressure, and sorption equilibria were typically attained within 20−30 min after changing the pressure. Equilibrium pressure data were recorded with ±0.1 bar accuracy and mass data with 15526
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Figure 1. Structure of the silica aerogel matrix: seen in a TEM image (left), and as a computer model (middle), and a magnified view of the modeled structure with depth cueing (right).
±0.02 g accuracy. The raw data were corrected for sample and balance buoyancy effects; error bars are within the size of the data points.27 Experimental details of the vibrating tube and SANS measurements are given elsewhere.17,28
3. INTERACTION MODEL AND SIMULATION METHODS 3.1. Aerogel Matrix Reconstruction. To create a realistic reconstruction of the aerogel matrix, we used a two-step procedure based on the chemically limited cluster−cluster aggregation (CLCA) algorithm29,30 followed by surface annealing guided by transmission electron microscopy (TEM) images (see Figure 1). In CLCA simulations, the basic units (spherical silica particles) diffuse through space, and may form a bond with the sticking probability p when they collide.29 This procedure is a generalization of the more common diffusion limited cluster−cluster aggregation (DLCA)10,11 algorithm, in which case p = 1. The sticking probability was treated as an adjustable parameter, with p = 0.9 found to produce the best match between the simulated and experimental SANS spectra. The CLCA simulations started from random configurations of nonoverlapping spheres, whose sizes were drawn from the Gaussian distribution with mean, m = 4 nm, and standard deviation, σ = 1 nm, first determined from the TEM images and further adjusted on the basis of SANS results, while the pore volume fraction was kept at the experimental value of 0.95. The size of the simulation box was set to 0.4 μm3, which was deemed adequate to cover the size range probed by the SANS data. Since the TEM images show that the silica beads are mostly fused together and the surface is annealed, we followed the CLCA reconstruction of the fractal framework by an annealing procedure that allowed the spherical particles to fuse. To achieve the annealed effect we divided the simulation box into a regular grid with a cubic unit cell with a side length of 0.4 nm, corresponding approximately to the size of a SiO2 unit or a CO2 molecule. Each lattice unit was assigned either to silica or to pore space, depending on its overlap with the silica beads. The annealed effect observed in the TEM image was achieved by reducing the surface energy through moving under-bonded surface sites (with 1 or 2 nearest neighbors) to more favorable positions. A magnified view of the modeled aerogel structure is shown in Figure 1c. Figure 2 shows a comparison between experimental and simulated SANS data. The position and width of the correlation peak resulting from the quasi-periodic arrangement of silica
Figure 2. Comparison of experimental (blue) and simulated (red) SANS data of silica aerogel with density of 0.1 g/cm3.
strand are very well reproduced, indicating that the nanoscale structure of the aerogel is modeled with high accuracy. At smaller length scales, i.e., Q > 0.1 Å−1, the modeled scattering intensity is higher than the experimental value. This deviation is attributed to the failure of the CLCA model to allow for structural relaxations through tangential movements of silica beads upon network formation. Additional surface roughness was also introduced into the model structure by less than complete annealing of silica beads (see Figure 1). Improvements of the CLCA model beyond the scope of this study are needed to improve structure refinement at small scales. At large scales, weak artifacts resulting from the periodicity of the simulation box are indicated by excess scattering from the modeled aerogel structure. These features do not impact fluid sorption, which takes place on shorter length scales. Overall, the quality of aerogel reproduction was deemed sufficient for the purposes of this study, but fluid adsorption at low fluid density may be exaggerated because of the additional surface area. 3.2. Grand Canonical Lattice Gas (LG) Simulations. 3.2.1. Interaction Model. The distribution of sc CO2 within the reconstructed aerogel matrix was modeled using GCMC simulations with an LG model implemented on a simple cubic lattice with 10243 grid points and periodic boundary conditions. The grid points are separated by 0.4 nm, which roughly corresponds to the direct correlation length of CO2.31 The Hamiltonian, H, of the system can be written as H = −μ ∑ nif − wff i
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∑ nif njf i,j
− wfs ∑ nif nks i,k
(1)
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where μ is the fluid chemical potential, wff is the energy parameter of fluid−fluid interaction, wfs is the energy parameter of fluid−solid interaction, nfi is the occupancy (either 0 or 1) of the fluid site, nsk is the occupancy of the solid site, the first summation runs over all lattice sites, and the remaining two summations run over all nearest neighbor pairs of lattice sites. This discrete approximation of the fluid was necessary to accommodate the large size of the system, which corresponds to approximately 109 CO2 molecules for the dense fluid case. The correspondence between the LG model and real CO2 was established by matching their critical-point properties (i.e., temperature Tc = 31.1 °C, pressure Pc = 73.77 bar, and density ρc = 0.4676 g/cm3)32, and the use of reduced units for temperature, pressure, and density. Figure 3 compares the near-
the best match obtained for wfs = 0.9. In each cycle, the occupancy nfi of each site i was changed with the “switching” probability Pswitch determined from the following expression: i ⎧ ⎡ ⎪ 1 (1 − 2nif )(μ + wff Piswitch = min⎨1, exp⎢ − ⎢⎣ kBT ⎪ ⎩ + wfs ∑ k
∑ njf j/i
⎤⎫ ⎪
nks)⎥⎬ ⎥⎦⎪ ⎭
(2)
where kB is the Boltzmann constant. The fluid chemical potential was varied between values corresponding to bulk densities 0.1ρc and 0.9ρc. At each chemical potential the system was first equilibrated until the total fluid density between MC cycles did not change by more than 10−6ρc, and was then was simulated for additional 100 equilibrated cycles to calculate average densities at each lattice site. These averages were collected and analyzed.
4. RESULTS AND DISCUSSION Macroscopic excess sorption data are presented and the sorption behavior analyzed, followed by the microscopic characterization of the sorption phase using the APM. Computer modeling techniques utilized to reconstruct silica aerogel in silico, and adsorption studies of a lattice gas calibrated to mimic sc CO2 in this structure are presented and discussed in section 4.3. 4.1. Excess Sorption and Mean Pore Density of CO2 from Gravimetric Experiments. Figure 4 shows the gravimetric excess sorption isotherms for supercritical CO2 adsorption to silica aerogel with density of 0.1 g/cm3 at temperatures of 35 and 50 °C.
Figure 3. Peng−Robinson equation of state for CO2 (solid)33,34 and its LG representation (dashed) in reduced units at reduced temperature Tr = 1.013.
critical bulk fluid isotherm of the LG model with the Peng− Robinson equation of state at the experimental temperature of 35 °C (i.e., reduced temperature Tr = 1.013).33,34 The two isotherms agree reasonably well at lower densities, but deviate more significantly above the critical density. This is a result of the simplistic description of the LG interactions. For symmetry reasons, the model’s maximum density, at which its pressure reaches infinity, is equal to twice the critical density. This is not true for real CO2, whose solid density (ρs = 1.562 g/cm3 at −78.5 °C) is more than three times the critical density. Near ρc, however, the LG isotherm exhibits much flatter density dependence, which corresponds to large density changes with small pressure or chemical potential variations. These differences between the model representation and the real fluid behavior are reflected in the size of critical fluctuations. The CO2 correlation length at the critical density and Tr = 1.013 is 25 Å,35 while LG predicts 30 Å (as we determined from the long-range decay of the site−site pair correlation function). To achieve the same correlation length, the LG model would have to be simulated at Tr = 1.020. It follows that critical phenomena caused by critical density fluctuations will be more enhanced in the LG model than in the real fluid at the same reduced temperature. 3.2.2. Grand Canonical Monte Carlo Simulations of Fluid Sorption. GCMC simulations were used to calculate the adsorption isotherm of the model system. For the modeling of sc CO2 sorption in silica aerogel, the reduced fluid−fluid interaction parameter was set to unity, wff = 1. The fluid−solid parameter was optimized to approximate the experimental CO2 adsorption isotherm in 0.1 g/cm3 silica aerogel at 35 °C, with
Figure 4. Gravimetric excess sorption isotherms of CO2 interacting with silica aerogel of density 0.1 g/cm3.
Positive values of the excess sorption are measured at low fluid density, followed by broad excess sorption maxima and decreasing and finally near-zero and negative values of the excess sorption at high fluid density above the bulk critical density. The excess sorption maximum is found at a bulk fluid density of ρb ≈ 0.38 g/cm3. A pronounced inverse temperature dependence of the excess sorption is found in the vicinity of the excess sorption maxima, while the temperature effects at low and high fluid densities are weak. The mean pore density of fluid, ρp, is calculated from the pore volume normalized excess sorption by ρp = ρb + ρe, with 15528
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ρb the bulk fluid density and ρe the excess density of fluid in the pores. The pore fluid densities were calculated under the assumption that the pores are fully accessible to the fluid. Gruszkiewicz et al. recently reported the pore density and excess sorption of CO2 in silica aerogel with a bulk density of 0.2 g/cm3 from vibrating tube densimetry and gravimetric excess sorption.28 Quantitative agreement between the results obtained from the different techniques was observed, indicating full accessibility of the internal pore spaces in silica aerogel. The pore density isotherms obtained from gravimetric data are shown for the two aerogels in Figure 5. The same
using gravimetric and vibrating tube techniques differ from the pore densities measured by neutron transmission, which is due to several artifacts in the neutron transmission method. Although it was shown that the neutron transmission method works well for bulk fluids away from the critical point,16 the presence of critical fluctuations in the bulk fluid interferes with the neutron transmission method for measurement of excess sorption. Increased small-angle scattering originating from fluid density fluctuations results in smaller values of the neutron transmission when approaching the critical point, although the fluid density in the sample remains constant. The situation becomes more complex for pore fluids, where a number of scattering contrast changes occur at internal surfaces. As fluid molecules enter the pores, the scattering contrast between pores and matrix changes, i.e., is usually reduced. Therefore, the scattering power and transmission of the sample change as well, wherein for evenly distributed fluid pore filling the scattering contrast is reduced and the transmission increases. At high fluid densities, this effect leads to strongly diminished scattering from the porous matrix, mimicking strong pore depletion effects. If the fluid forms a sorption phase with very different density from the bulk fluid, scattering will increase and transmission will decrease. These additional complexities were not accounted for in the earlier studies using the transmission measurements and led to unreliable data for the excess sorption or pore density in these publications.16,17 Here, the CO2 sorption phase properties in aerogel with density of 0.1 g/cm3 were reassessed by combining the SANS data recorded by Melnichenko et al.17 with the gravimetric excess sorption data presented and discussed above. We use the formalism laid out in ref 9., but use the pore density data shown in Figure 5. Note that relatively large error bars are introduced by the addition of individually small uncertainties in pressure and temperature control of the separate excess sorption and neutron measurements using different pressure transducers and temperature sensors. Data close to the critical point have the largest errors due to larger changes in fluid density with even small uncertainties in P and T. Simultaneous measurements of excess sorption and SANS data would greatly reduce the uncertainties in density and volume fraction of the sorption phase, and are planned for future studies. The calculated data for density and volume of the CO2 sorption phase in aerogel at T = 35 °C are shown in Figure 6. At low fluid densities, a dense sorption phase forms at the
Figure 5. Pore density isotherms of CO2 in silica aerogels, T = 35 °C.
adsorption behavior is found in both samples, i.e., sc CO2 adsorption is only weakly if at all perturbed by small changes in the aerogel structure. SANS measurements yielded very similar volume-fraction normalized scattering patterns for the two aerogel samples, suggesting presence of very similar nanoscale structures in our samples despite the difference in bulk density. 4.2. SANS and APM. Using the APM,16 the volume and density of the sorption phase of sc CO2 in the silica aerogel nanopores were calculated from scattering and sorption data under the assumption of a uniform density of the adsorbed fluid (adsorbed phase or box model). The SANS data used here were previously analyzed using a neutron transmission method for the measurement of excess sorption, which relies on the Lambert−Beer law.17 However, we have since determined that the CO2 excess sorption and pore densities in aerogel measured
Figure 6. Density (left) and volume (right) of the sorption phase formed by CO2 in silica aerogel, at a temperature of T = 35 °C. 15529
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aerogel walls. At fluid densities ρb ≈ 0.2 g/cm3, the density of the sorption phase reaches values of ρa ≥ 1 g/cm3 and exhibits only limited additional densification with further increases in the bulk fluid density. The highest value for the sorption phase density, which is observed in a narrow range of bulk fluid densities near the bulk critical density, is close to the solid density of CO2 (dry ice). These values for adsorbed CO2 are in significant agreement with FTIR results reported by Schneider et al., although the authors note possible impacts of surface species on their results and speculate that the interfacial density of CO2 could be somewhat lower.36 The volume of the sorption increases with increasing bulk density up to ρb ≈ 0.46, i.e., the maximum of the excess sorption. At densities above the bulk critical density, the density of the sorption phase is reduced to the bulk fluid density or slightly below. This density change is also indicated in the excess sorption isotherms, which abruptly drops at densities above the critical density. At ρb ≈ 0.7 g/cm3, the excess sorption (Figure 4) is reduced to values close to zero, realized by a shrinking density difference between the adsorbed and unadsorbed fluid phases and low volume of the sorption phase. A drop in the sorption phase fluid density to values around the bulk fluid density is found near the bulk critical density. The sorption phase volume increases rapidly for ρb < 0.3 g/ cm3, and then remains approximately constant until the sorption phase vanishes at high pressure. The overall low values of the sorption phase volumes compared to the accessible pore volume indicate that the sorption phase formation is not hindered by the geometrical confinement under the conditions studied. 4.3. Lattice Gas Simulations. The simple lattice gas model allows us to investigate two competing forces influencing the adsorption of fluids in porous environments: (a) the strength of fluid-surface interactions and (b) the impact of geometrical confinement imposed by the aerogel on fluid density fluctuations. While the former effect can be thought to be localized at the fluid−solid interface and dominating fluid adsorption at conditions far from the critical point, the latter effect depends on the relative magnitudes of the confining pore size and the fluid correlation length, and becomes increasingly more important for fluid sorption near the critical conditions. Before analyzing the microstructural properties of CO2 adsorbed in silica aerogel, it is necessary to evaluate how closely the LG model reproduces the results of the excess sorption experiments. As mentioned in section 3.2.1, the only adjustable parameter (wfs,) controlling the relative strength of fluid−fluid and fluid−solid interactions was optimized such that the modeled adsorption isotherm closely resembles the experimental one. In Figures 7 and 9, we illustrate comparison between the experimental and simulated excess sorption data for the optimized model with wfs = 0.9. The overall agreement between the two curves is semiquantitative, with the largest deviations at low bulk densities. This behavior suggests that the fluid-surface interactions are underestimated. However, the increase of the value of wfs leads to exaggerated adsorption at higher densities. To achieve an overall reasonable agreement, the strength of the solid−fluid interactions has to be regarded as an effective parameter that balances adsorption at both low and high pressures. The excess sorption peak position is in excellent agreement with the experimental data, while its height is about 15% overestimated. This enhanced critical condensation is a direct result of larger critical fluctuations of the LG fluid compared to real CO2, as discussed in section 3.2.1. Both
Figure 7. Mean pore densities of sc CO2 confined in silica aerogel with density of 0.1 g/cm3 as a function of bulk CO2 density from experiments and simulations.
experimental and simulated excess density curves approach zero or slightly negative values at approximately 0.75 g/cm3. For the model system this behavior is a result of weaker fluid−solid interactions with wfs = 0.9 compared to fluid−fluid interactions with wff = 1.0. Consequently, fluid sites are preferentially surrounded with other fluid sites rather than those corresponding to the solid surface. The inability of the LG fluid to precisely reproduce the experimental excess sorption data originates from the model’s two main imperfections: the assumption of uniform interaction strengths of surface sites, and the inherent limitations underlying the simplicity of the LG model. As Figure 8
Figure 8. Molecular dynamics snapshot of CO2 adsorbed at a flat amorphous silica surface at bulk fluid density 0.01 g/cm3. Color-coding of atoms: silicon (yellow), oxygen (red), and carbon (cyan). Carbon dioxide oxygen atoms strongly bind to under-coordinated surface silicon atoms, whereas other surface configurations are only weakly attractive.
(obtained from an independent molecular dynamics simulation of CO2 adsorption at a flat amorphous silica surface, using Harris and Yang model of CO2,37 and ClayFF model of silica38) illustrates, the surface exposes a mixture of strongly and weakly interacting sites, where Si atoms with distorted bonding configurations cause the stronger interactions. The more strongly interacting sites are occupied first, which results in strong adsorption at low densities. The weakly interacting sites are occupied only at higher fluid densities, effectively lowering the interaction energies at these higher densities. Strong fluid adsorption at low densities is observed in the experiments and 15530
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Figure 9. 2D density profiles (in g/cm3) of lattice gas CO2 confined in silica aerogel matrix corresponding to different stages of pore filling. The letters (A, B, and C) indicate corresponding states in the 2D profiles and in the plot of excess sorption as a function of bulk density (bottom left) obtained from experiment (red) and modeling (green) for CO2 in silica aerogel with density of 0.1 g/cm3 and T = 35 °C.
model (Figure 6). As the density approaches the bulk critical value, the fluid condenses in increasingly larger confined spaces. The plot corresponding to the maximum excess sorption shows that pores as large as 50 Å are filled with denser fluid. Such pore sizes are equal to about the twice the correlation length of the LG (30 Å) or real CO2 (25 Å) fluid at T = 1.013 Tc (35 °C). All points in such pores are within the correlation length of a surface site, and therefore directly influenced by the surface. Once the amount of the adsorbed phase reaches its maximum, further increases of the bulk density lead to decreasing excess sorption. When the adsorbed and bulk phases reach equal density at about 0.75 g/cm3, the main distinction between the adsorbed and bulk phases disappears and, consequently, scattering from fluid−fluid interfaces is not detected by neutron scattering experiments. Similarly, the APM model (Figure 6) indicates the disappearance of the adsorbed phase at these densities. As mentioned in the Introduction, some computational representations (including the LG model) are known to exhibit critical depletion in certain porous environments.9 While the overall adsorption curve (Figure 7) only shows enhanced excess adsorption, it may be possible that critical depletion occurs locally but is overwhelmed by condensation in the macroscopic average. To explore this possibility, we analyzed the simulated 3-dimensional density to see whether any region of the pore space exhibits local density below the bulk average. We were not able to detect such regions and conclude that the investigated silica aerogel (0.1 g/cm3) does not induce critical depletion of CO2 on the local scale. However, we did observe critical depletion in the same aerogel structure at different model settings (e.g., for LG with first and second nearest neighbor interactions as opposed to just the first nearest neighbors used in our optimized model). A more detailed study needed to address these issues is beyond the scope of the work presented here.
also expressed in the APM model results (Figures 4 and 6). Assignments of different interaction strengths wfs to these different surface sites could improve the modeling accuracy but was not pursued here to simplify the interpretation. The second, more fundamental limitation stems from the character of LG interactions. While in real fluids the average interaction energy between nearest neighbors depends on density and becomes increasingly less attractive as the average distance between particles decreases, interactions between nearest neighbors in an LG fluid are density independent. This behavior accounts for the differences between CO2 and LGbased equations of state at above-critical densities (Figure 3), and will similarly influence fluid−solid interactions, which become less attractive in real fluids at higher densities. This density dependence can be explained as a result of orientational ordering and shortening of average intermolecular distances. For example, at low bulk densities, even at a uniform surface, CO2 molecules will be adsorbed in favorable molecular orientations, which will become less favorable and less attractive at higher densities. This limitation can only be resolved by employing a more flexible fluid representation that explicitly or implicitly accounts for the density dependence of average fluid−solid interactions. While such a behavior cannot be reproduced by the simple LG model adopted in the present study, it can be captured in the effective interactions used by some versions of the lattice Boltzmann method.39 We note that the simple model employed here captures the general behavior of the experimental excess sorption isotherms and is suitable for the following molecular-level interrogation of the sorption process. In Figure 9, the CO2 density distribution within aerogel pores at different bulk densities is shown as a density map. The two-dimensional sections through the porous matrix show that at low bulk densities the fluid adsorbs on the surface in a monolayer, as could be expected and indicated by the APM 15531
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5. SUMMARY AND CONCLUSIONS We have studied the adsorption of sc CO2 in silica aerogel through a combination of excess sorption experiments, neutron scattering, and computer modeling techniques with the goal of quantifying the microstructure of the pore fluid. Excess sorption and pore fluid density data show fluid adsorption at low density, formation of a sorption maximum, and vanishing adsorption and weak depletion effects at fluid densities above the bulk critical density. The CO2 excess sorption isotherms in silica aerogel exhibit a similarity to our previously reported results for CO2 sorption in mesoporous Controlled Pore Glass (CPG-10).27 CPG-10, which comprises interconnected single pores with local cylindrical geometry, was found to show excess sorption maximum shifts to higher bulk fluid density with increasing pore width. The position of the excess sorption maximum of amorphous silica aerogel is close to the one observed for CPG-10 with a nominal pore width of 35 nm, which indicates that confinement effects in aerogel are not as strong as in single pores of similar dimension (i.e, CPG-10−75 with 9 nm pores). The sorption phase density and volume, calculated from experimental data, show complex variations with the bulk fluid density. At the sorption maximum, we determined that the sorption phase is up to ca. 3 times denser than the corresponding bulk fluid. The sorption phase is significantly denser than the bulk fluid at low pressures, but of equal or lower density than the bulk fluid at high pressures. The volume of the sorption phase initially increases with increasing pressure, but drops toward zero at higher pressures. The silica strands with mesh-like nanometer structure provide a random network of adsorption sites, acting as anchor points for a continuous sorption phase. Since the boundaries between the sorption and bulk phases of a supercritical fluid are diffuse, the APM results, which assume sharp boundaries, have to be interpreted with care for near-critical fluid sorption scenarios. Modeling of the experimental excess sorption isotherms with a simple lattice gas model was successful in reproducing the main sorption features using a weakly attractive fluid−solid interaction potential. Fluid density maps, calculated for different bulk fluid densities, provide a valuable visualization of the molecular scale mechanism of the buildup of the sorption phase. The strongest local fluid enrichments are found in small cavities at the silica aerogel surface and narrow pores. Both the experimental and simulation data show variations of the sorption phase density with bulk fluid density, i.e., the concept of a constant sorption phase density is not supported by our data, and may indeed only be valid for subcritical fluid adsorption. Our results are in agreement with simulation studies of supercritical fluid adsorption for weakly attractive solid−fluid interactions by Brovchenko and Oleinikova.40−42 Our excess sorption and mean pore fluid density results are also comparable to those computed by De et al.43 and LópezAranguren et al.44 Central findings of that paper were pressure shifts and density enhancements of the pore fluid as a function of porosity. Our study of two aerogels with very similar structures did not reproduce those findings, which were most pronounced in the comparison of aerogels with porosities of 95% and 80%. However, we recently reported very similar pore size effects in an excess sorption study of sc CO2 sorption in CPG-10 mesoporous silica.20 For the dilute aerogels studied here we conclude, based on the fluid density maps and fact that the pore volume is much larger than the sorption phase volume,
that the geometric confinement of the porous matrix does not significantly impede the formation of the sorption phase. The consistence of the results reported in ref 44 with our experimental results obtained for CPG-10 indicate that nanoporous solids with low internal surface area to pore volume ratios are most likely to limit pore fluid adsorption. This effect may present itself in pores with very different geometric shapes (for instance, cylindrical single pores and pore networks). The new combination of advanced experimental and simulation tools presented here may hold potential for other sorption investigations, including the study of temperature and pore size effects.
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AUTHOR INFORMATION
Corresponding Authors
*E-mail:
[email protected]. *E-mail:
[email protected]. Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS This material is based upon work supported as part of the Center for Nanoscale Control of Geologic CO2, an Energy Frontier Research Center funded by the U.S. Department of Energy, Office of Science, Office of Basic Energy Sciences.
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