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Predicting Neopentane Isosteric Enthalpy of Adsorption at Zero Coverage in MCM-41 Carmelo Herdes,*,† Carlos Augusto Ferreiro-Rangel,‡ and Tina D€uren‡ † ‡
vora, Departamemto de Química, Universidade de E vora, 7000-671 E vora, Portugal Centro de Química de E Institute for Materials and Processes, School of Engineering, The University of Edinburgh, Edinburgh EH9 3JL, United Kingdom ABSTRACT: The isosteric enthalpy of adsorption for neopentane at relative pressures down to 3 108 in MCM-41 was predicted for the temperature range from 15 to 0 C. At such low pressures and temperatures, experimental measurements become problematic for this system. We used an atomistic model for MCM-41 obtained by means of a kinetic Monte Carlo method mimicking the synthesis of the material. The model was parametrized to represent experimental nitrogen adsorption isotherms at 77 K using grand canonical Monte Carlo simulations. The simulated isosteric enthalpy of adsorption shows very good agreement with available experimental data, demonstrating that GCMC simulations can predict heats of adsorption for conditions that are challenging for experimental measurements. Additional insights into the adsorption mechanisms, derived from energetic analysis at the molecular level, are also presented.
1. INTRODUCTION The isosteric enthalpy of adsorption (IEA) at low pressures is an important indicator of adsorbent heterogeneity, because its magnitude and variation as a function of the adsorbate loading is a measurement more sensitive to the adsorbent pore structure than adsorption isotherms. Experimentally, there are two common ways of determining this quantity. It can be measured directly using calorimetry studies and indirectly by analyzing adsorption isotherms using the isosteric method.1 Gas adsorption calorimetry, although being a direct method, combines the difficulties of gravimetric experimental setup with the calorimetric experimental setup, and it is also the most expensive option. On the other hand, the isosteric method is easy to apply but, for accurate and reliable results, requires the determination of a set of close isotherms at different temperatures (as a rule of thumb, it is advised to work at a maximum ΔT = 10 C between the isotherms) and low pressures down to near zero coverage (in Henry’s law region, usually down to 107 in relative pressure). The necessity to determine adsorption isotherms over a range of temperatures for the isosteric method might introduce additional challenges. For example, for the determination of the IEA for the system neopentane (2,2-dimethylpropane)/MCM-41, it is found that the temperature range, in which neopentane is in the liquid phase, is narrowed to less than 30 C. In a previous experimental work, it was highlighted that a better determination of this important quantity for hydrocarbon adsorption in this type of material was necessary because of the low quality of the linearity of the neopentane isosteres at low pressure.2 Molecular simulation provides a complementary tool to determine the IEA experimentally. It is not only able to qualitatively r 2011 American Chemical Society
predict macroscopic properties, such as adsorption isotherms or isosteric enthalpies of adsorption, but also able to provide a detailed picture on the molecular scale, which is not easily accessible by experimental methods, thus allowing us to interpret and elucidate macroscopic properties from the microscopic perspective. There are many examples in the literature demonstrating how experimental and theoretical tools work hand in hand to understand the fundamentals of adsorption.39 Specifically, molecular simulation studies have yielded quantitative predictions of the IEA.1014 MCM-41 is a highly ordered mesoporous silica material that shows long-range order but is amorphous on the atomistic scale. Whereas, for crystalline materials, the model of the adsorbent can be produced from crystallographic information, a realistic model of MCM-41 has to be created for the adsorption simulations. Several different approaches have been employed to model MCM-41,1518 and a recent comparison of different MCM-41 models can be found elsewhere.19 For a reliable prediction of the low loading IEA, the MCM-41 model has to capture, in particular, the roughness of the experimental material, because it has been shown that a simulation approach in which the solidfluid interaction potential is treated by a homogeneous surface cannot reproduce the form of the adsorption isotherms, particularly at low pressures.15 Neopentane is an interesting nonpolar probe molecule for the characterization of mesoporous materials. Specifically, in MCM41, its hysteresis critical temperature, Tch, the temperature above Received: December 10, 2010 Published: May 05, 2011 6738
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Langmuir which hysteresis is not observed, was estimated to be in the range of 195205 K,2 and it was also confirmed that neopentane adsorbs, without hysteresis, in the range of 258278 K.2 This represents energetic advantages over other fluids commonly used for the characterization of porous solids, such as nitrogen at 77 K or argon at 87 K. This work focuses on the prediction of IEA for the system neopentane/MCM-41 and demonstrates that molecular simulation is a useful tool to quantify the IEA in situations where its experimental determination is difficult. In contrast to experimental studies, pressure and temperature can be easily controlled over the desired ranges in the simulations, because they are input parameters. The paper is organized as follows: in section 2, the descriptions of the experimental and theoretical methodologies are given. Section 3 highlights the results along with the discussion. The last section is dedicated to conclusions and remarks for future work.
2. METHODOLOGY 2.1. Experimental Studies. The experimental nitrogen and neopentane adsorption isotherms used here for comparison were obtained in a MCM-41 sample of pore diameter ∼3.46 nm. The experimental isotherms as well as further characteristics of the experimental sample, such as the total surface area, external surface area, mesopore volume, and X-ray diffraction, are given in ref 2. 2.2. Molecular Models. To create our model pore, we followed the methodology described by Schumacher and co-workers based on a kMC method, which mimicks the hydrothermal synthesis of the material.20 It has been shown previously that the resulting atomistic model pores result in accurate predictions of adsorption in MCM-41 for simple fluids, such as methane, ethane, or nitrogen.20 The hexagonal model pore used in this work (R = β = 90 and γ = 120; a = 3.886 nm, b = 1.945 nm, and c = 4.008 nm) has an average pore diameter of 3.40 nm and contains 525 oxygen atoms and 240 silicon atoms. More details about the simulations to obtain the model pores is given below. To describe the fluidfluid interaction of nitrogen21 and neopentane,22,23 we selected transferable force fields that correctly describe the vaporliquid equilibrium. Nitrogen molecules were modeled by a pairwise additive effective potential, composed of two noncharged LennardJones (LJ) sites.21 This model has been used previously by Schumacher and co-workers20 to quantitatively predict the adsorption of nitrogen in MCM-41. For neopentane, we selected the optimized intermolecular potential functions for liquid hydrocarbons,22 with the modification proposed by de Pablo and co-workers.23 It is worth noting that the system neopentane/MCM-41 had been studied by other authors with a similar approach.14 However, the adsorption isotherm presented in that work lacks in describing the low-pressure range, and consequently, the IEA was calculated at high relative pressures, p/p0 > 0.78, reporting a value of 41.1 kJ/mol at 273 K in a pore of 3.2 nm in diameter.14 In line with previous simulation studies, the interactions between the silicon atoms in the MCM-41 model pore and the fluid molecules are not taken into account, because their influence on the amount adsorbed is negligible. Potential parameters ranging from 118 to 1313 K for the LJ parameter ε for oxygen are reported in the literature.15 Here, we fitted this parameter to capture the experimental nitrogen adsorption isotherm measured at 77 K obtaining a parameter of 146.81 K for the oxygen atoms for the best fit. This parameter is then held constant for the simulation of neopentane adsorption. Full details of the fitting process as well as adsorption isotherms simulated with different parameters can be found in the Results and Discussion.
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The LorentzBerthelot mixing rules (arithmetic mean for the LJ parameter σ and geometric mean for the LJ parameter ε) are applied to calculate the interaction of heteroatomic pairs, by the effective values for the homoatomic pairs.
2.3. Synthesis of the MCM-41 by Kinetic Monte Carlo (MC). Periodic mesoporous silicas are formed in solutions containing water, a silica precursor [e.g., tetraethoxysilane (TEOS)], and a surfactant. The surfactant in the solution will form micelles, whose shape will depend upon the synthesis conditions (i.e., pH, concentration, temperature, etc.). The silica monomers present in the solution will then condense around those micelles containing the surfactant molecules and, upon further polymerization, will lead to the formation of a silica network, which is the material structure. The kMC methodology focuses on the synthesis interactions leading to the formation of the silica network, which means that the main energy contributions come from the positions and bonding of the atoms and from the interaction between the silica monomers and the present model micelle. Full details on the methodology can be found elsewhere;20 only a brief description of some key aspects of the method will be given here. First, the reaction path to be mimicked by the simulation contains the following basic stages: (a) first layer silica formation, (b) further silica condensation, (c) aggregation of silica-covered micelles, (d) micelle deformation, and (e) calcination. To this end, the method allows for the following MC moves to take place: monomer insertion, shaking, swapping, condensation, and hydrolysis. The first needs no further comment; the other four however are worth a few words. Shaking is an important move to keep the system from being trapped into metastable states for too long, which is likely to happen because they are usually formed of hundreds of atoms. Swapping will allow for the evolution of the silica ring size throughout the simulation, and it has an important effect on the final topography of the pore (it arises from quantum mechanical simulations, because they indicate that swapping is analogous of the real diffusion mechanism in amorphous silica). The last two types of moves, condensation and hydrolysis, refer to the random formation and breaking of bonds, respectively, and are the core of the simulation. After each MC move, a process of steepest descent minimization is undertaken, which means that the method is, in essence, not ergodic and will favor a low-energy-configuration path. It is important to mention that the model micelle is a model of exact geometry. No explicit surfactants are present in the system, and the micelleatom interactions are then given by a soft structureless potential (which allows for the silica monomers to slightly penetrate the geometric surface of the micelle). In the calcination stage, however, the model micelle is removed, while the simulation is allowed to continue, and the system keeps its relaxation until equilibration of the system is attained. The importance of this arises in the fact that, during this stage, a shrinkage of the unit cell could be observed, given rise to a slightly smaller pore than the one expected given the micelle radius at the end of the “micelle deformation” stage, as observed experimentally. This presents an unavoidable trial-and-error scheme for the production of a given real pore size; however, a energetic parametrization scheme for the oxygen atoms can be adopted over a close-enough model size (see section 3). As for the pressure contribution, this is taken into account only in the deformation stage, when the unit cell size (and the micelle radius) is allowed to vary during the energy minimization process. A kMC simulation for the MCM-41 synthesis takes from several days up to a few weeks (depending upon the system size) on dual-core CPU machines, each with 32 GB of RAM and AMD Opteron processors (4 GB per core). The cores are clocked at 2.4 or 2.6 GHz. All machines are part of the CLX cluster run by the School of Engineering and Electronics at the University of Edinburgh.
2.4. Modeling Adsorption Isotherms by Grand Canonical MC. Grand canonical MC simulations were carried out using the multipurpose simulation code MuSiC.24 In the simulations, MCM-41 6739
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Table 1. LJ Geometric (σ) and Energetic (ε) Parameters for Nitrogen (N) and Oxygen (O), along with the Mean Absolute Error (MAE) between the Experimental and Simulated Nitrogen Adsorption Isothermsa set
σN (nm)
εN/kB (K)
σO (nm)
230.00
2.174
16
185.00
1.235
20
172.27
1.032
159.54
0.991
146.81
0.922
0.331
37.3
bO = 0.27 nbO = 0.30
5
is considered as a rigid structure. The sampling protocol includes four types of moves, specifically bias insertions and deletions, random rotations, and translations with equal distribution of weights among the moves. At least 1 107 GCMC (for nitrogen) and 2 107 GCMC (for neopentane) steps were performed for each adsorption point (each step being an attempt to insert, delete, rotate, or translate a molecule), with half of the steps taken to equilibrate the system and the other half taken to sample the data, while for the pressure points located in the vicinity of the capillary condensation region, further GCMC steps were needed (up to 6 107 for nitrogen and 8 107 for neopentane). The number and spacing between consecutive relative pressure points varies depending upon the desired resolution of the pressure range, with more points devoted to low pressures up to the region of capillary condensation. Adsorption data are presented as the excess fluid density adsorbed (mmol/g) in a MCM-41 sample versus relative pressure p/p0 of the bulk phase, where p0 is the bulk saturation pressure at the set temperature. Fugacities and gas-phase densities at the particular bulk conditions (temperature and pressure) were calculated using the PengRobinson equation of state.
2.5. Isosteric Enthalpy of Adsorption from Simulations. The IEA is calculated using the method by Vuong and Monson, which is appropriate for the comparison to the experimental results,10 applying the theory of fluctuations with direct results from the GCMC simulations25 IEA ¼ hres, bulk þ RTð1 zÞbulk
ÆN a U a æ ÆN a æÆU a æ ÆN a2 æ ÆN a æÆN a æ
ð1Þ
where hres,bulk and zbulk are the residual enthalpy and the compressibility factor of the bulk phase, respectively. The fluctuation term is composed of appropriate ensemble average, denoted by the angular brackets, of the number of adsorbed molecules, Na, and their potential energy, Ua.
reference
2 4
Figure 1. Experimental (blue line) and simulated nitrogen adsorption isotherms in MCM-41 at 77 K for different sets of the LJ parameter ε for the oxygen atoms (black circles, ε/kB = 230 K; green squares, ε/kB = 185 K; purple diamonds, ε/kB = 172.27 K; orange invert triangles, ε/kB = 159.54 K; and red triangles, ε/kB = 146.81 K). The inset presents the same data with a logarithmic pressure axis. The dashed lines for the simulated data were added as a guide to the eye.
MAE (mmol/g)
1 3
a
εO/kB (K)
this work
kB is the Boltzmann constant.
3. RESULTS AND DISCUSSION Selected nitrogen adsorption isotherms obtained at 77 K for the pore model and the experimental sample are depicted in Figure 1, from 1 109 (for the simulation) and 5 105 (for the experiments) up to 0.98 in relative pressure. These results were obtained with five different values of ε for the oxygen atoms in the pore wall ranging from ε/kB = 146.81 to 230 K summarized in Table 1 (values in the range of 1181313 K for this parameter had been reported in other simulation studies of adsorption in MCM-4115). All simulated adsorption branches presented similar behavior for adsorption and capillarity condensation; i.e., the load increases continuously, in a multilayer regime fashion, until the point of capillarity condensation is reached. The pressure logscale inset of Figure 1 shows that all of the curves have the same trend, with slight differences in the low-pressure range between the simulation and experiments. However, a clearly differentiated capillary condensation step is found for each set of parameters. The best overall agreement (i.e., the smallest mean absolute error) between experiments and simulations was found for the set number 5, with a LJ energetic parameter of 146.81 K for the oxygen atoms (see set 5 in Table 1 and red solid triangles in Figure 1). This value has been used for the rest of the study. The corresponding simulated nitrogen adsorption/desorption isotherms compared to the experimental results are depicted in Figure 2. The capillary condensation step for the experimental sample was found between ∼0.26 and ∼0.31 in relative pressure, and no hysteresis was observed.2 The simulated isotherm presented a narrow hysteresis loop type H1 (adsorption branch at 0.21/desorption branch at 0.15 relative pressures). The presence of hysteresis in the simulated isotherm could be an artifact of the GCMC method because of the sub-critical state of the nitrogen in the pore and the finite number of attempted configurations to mimic it, as previously pointed out by other researchers.15,26,27 Hypothetically, this hysteresis loop might be composed of longlife metastable states and would vanish if longer simulations or better sampling schemes were adopted.27 Then, the equilibrium transition would correspond to a truly continuous one. Four snapshots, at different relative pressure levels, are embedded on Figure 2, showing that initially nitrogen molecules adsorb in the small cavities, resulting from the surface roughness of the model pore. At higher relative pressure, nitrogen adsorption follows a layer-by-layer process. After the energetic parameters for the oxygen atoms in the MCM-41 model pore were determined using the experimental/ 6740
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Figure 2. Experimental (blue line) and simulated set 5 (ε/kB = 146.81 K) nitrogen adsorption (solid triangles) and desorption (open triangles) isotherms in MCM-41 at 77 K. The dashed line was added to guide the eye. The four snapshots correspond to the relative pressures of 1 105, 0.21, 0.28, and 0.96 in the adsorption branch highlighted in red circles.
Figure 3. Experimental (green line) and simulated (red circles) neopentane adsorption isotherms in MCM-41 at 258 K. The inset presents the same data with a logarithmic pressure axis. The dashed line was added to guide the eye.
simulated nitrogen adsorption isotherms, we predicted, without further modification of the parameters, the adsorption of neopentane. Figure 3 depicts the neopentane adsorption isotherms from the simulation and experiments at 258 K. The simulations predict the experimental data remarkably close but slightly underestimate the relative pressure of capillary condensation
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Figure 4. Experimental (lines) and simulated (symbols) neopentane adsorption isotherms in MCM-41 at 263 K (green and triangles) and 273 K (orange and circles). Adsorptions isotherms for 273 K were shifted by 2 mmol/g for clarity.
(simulated 0.11 compared to experimental 0.13). It is worth noting that the simulated isotherm is a full prediction, in a single pore, of the hydrocarbon adsorption capacity in MCM-41. An overall average deviation of þ2% is found between the simulated adsorption branch and experimental data for the whole isotherm at 258 K. Analogous predictions for neopentane adsorption at 263 and 273 K were performed. The model was able to describe both temperatures in a very good overall agreement with the experiments, with an average deviation of þ3% from the whole experimental isotherm; these results are shown in Figure 4. For all three temperatures, the agreement between the simulated and experimental neopentane adsorption isotherms is excellent in the low-pressure range. This allows us to further explore the adsorption behavior at lower pressures and, in particular, to obtain an accurate description of the IEA, which is the main goal of this paper. Figure 5 presents the comparison of the theoretical calculation of the neopentane IEA using the fluctuation theory as described in section 2.5 at 258 K (green circles), 263 K (red squares), and 273 K (blue diamonds), with the results of the isosteric method applied over the experimental adsorption isotherms, using three temperatures (solid orange line).2 The neopentane molar enthalpy of condensation, 24.6 kJ/mol, is also plotted for comparison. The three simulated curves are decreasing monotonically with loading, always above the molar enthalpy of condensation. For higher pressures, the simulated IEA agrees very well with the experimental values.2 However, there is a certain degree of uncertainty in the experimental results because of the quality of the linearity of the isosteres at low pressure. The dashed orange line represents the points of uncertainty in Figure 5. In contrast to this, the IEA at zero coverage can be reliably 6741
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Figure 5. Experimental (solid orange) and simulated (258 K, circle; 263 K, squares; and 273 K, diamonds) isosteric enthalpy of adsorption of neopentane in MCM-41. The dashed lines for the simulations are just to guide the eye. The dashed orange line represents the points of uncertainty for the experimental data. The molar enthalpy of condensation for neopentane, 24.6 kJ/mol, is plotted in a dashed black line.
Figure 7. Solidfluid energy histogram and preferential adsorption sites at 258 K and a relative pressure of 3 105. Snapshots of ZX and a single microcavity, where the MCM-41 structure is depicted in gray space-filling mode. In the ZX view, the green points show the preferential sites of neopentane molecules.
Figure 6. Potential energy of the system as a function of the loading split into solidfluid (red line with open circles) and fluidfluid (blue line with open circles) contributions. Snapshots are given at loadings of 1.75 and 5 mmol/g to illustrate the arrangement of the fluid molecules.
calculated from the simulation results and is 50 kJ/mol from the average of the simulation results. It is worth mentioning that, for other hydrocarbon adsorptives, such as toluene and methylcyclohexane, the experimental IEA is monotonically decreasing over the whole pressure range in a MCM-41 sample of similar pore size, and that the IEA value predicted for neopentane lies in between these two adsorptives as expected.2
To investigate the neopentane adsorption mechanisms in MCM-41 at the molecular level in the low-pressure region in more detail, the potential energy of the system was split in the fluidfluid and solidfluid contributions for the simulation at 258 K (see Figure 6). Figure 6 clearly shows that the solidfluid interaction is the predominant contribution to the total potential energy of the system up to 2 mmol/g. The fluidfluid interaction increases linearly, and its contribution is modest until saturation is reached (5 mmol/g), when it becomes larger than the solidfluid interaction. The snapshots in Figure 6 illustrate that the neopentane molecules are initially located close to the pore wall until capillary condensation results in complete pore filling. Moreover, the two first points of the solidfluid interaction curve, in Figure 6, correspond to the highly attractive microscopic cavities in the surface that are filled at low pressures. To identify these microscopic cavities, with high interaction energy, on the rough pore surface and to study their impact on the amount adsorbed and the IEA, an energy histogram was produced for a relative pressure of 3 105 (Figure 7). The average contribution was 46.70 kJ/mol. The surface roughness of the MCM-41 model pore induces energetic heterogeneity, differentiated by the adsorptive molecules at each relative pressure in the low range. This distinction plays an important role at very low pressures; however, it decreases very quickly because the few high interaction sites are occupied very quickly 6742
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Langmuir (see the solidfluid profile in Figure 6). The preferential sites for a given energy/load and a close-up of a filled microcavity can be seen in the snapshots at the bottom of Figure 7. This snapshot illustrates that the highest interaction energies, which are responsible for the high values of the IEA at very low pressures, are located in the microcavities of the pore wall, which exhibits considerable surface roughness on the atomistic scale.
4. CONCLUSIONS AND FUTURE WORK In summary, we combined experiments and simulations to describe nitrogen and neopentane adsorption behavior in MCM41 at different temperatures. Our simulations were carried out in a single model pore and yielded accurate prediction of the amount adsorbed of two different adsorptives in MCM-41 with a mean absolute error of less than 3% compared to reliable experimental data. We have shown that molecular simulation can predict the IEA at zero coverage, which is difficult to obtain experimentally for the system neopentane/MCM-41. An average value of 50 kJ/mol was obtained for the three temperatures in this work (258, 263, and 273 K). Moreover, molecular simulation can provide additional insights into the adsorption mechanisms. The same procedure can be applied to study/predict the adsorption behavior of other nonpolar hydrocarbons of interest (toluene, methylcyclohexane, etc.) in MCM-41 materials.
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’ AUTHOR INFORMATION Corresponding Author
*E-mail:
[email protected].
’ ACKNOWLEDGMENT This work was supported financially by the Fundac-~ao para Ci^encia e a Tecnologia (FCT, Portugal), Plurianual Finance vora (619), and Project Project Centro de Química de E FCOMP-01-0124-FEDER-007145. The authors thank Dr. Andres Mejia, for the access to the clusters at Chemical Department, Universidad de Concepcion, Chile, and the resources provided by the School of Engineering at the University of Edinburgh (CLX cluster), Dr. Claudia Prosenjak, Dr. David Fairen-Jimenez, and Dr. Manuela L. Ribeiro Carrott, for helpful discussions. ’ REFERENCES (1) Rouquerol, F.; Rouquerol, J.; Sing, K. Adsorption by powders and porous solids principles. Methodology and Applications; Academic Press: New York, 1999. (2) Russo, P. A.; Ribeiro Carrott, M. M. L.; Carrott, P. J. M. Adsorption 2008, 14, 367. (3) Ravikovitch, P. I.; Odomhnaill, S. C.; Neimark, A. V.; Schuth, F.; Unger, K. K. Langmuir 1995, 11 (12), 4765. (4) Sonwane, C. G.; Bhatia, S. K.; Calos, N. Ind. Eng. Chem. Res. 1998, 37 (6), 2271. (5) Gelb, L. D.; Gubbins, K. E.; Radhakrishnan, R.; Sliwinska-Bartkowiak, M. Rep. Prog. Phys. 1999, 62 (12), 1573. (6) Steele, W. Appl. Surf. Sci. 2002, 196, 3. (7) Do, D. D.; Do, H. D. Adsorpt. Sci. Technol. 2003, 21 (5), 389. (8) Ferey, G. Chem. Soc. Rev. 2008, 37 (1), 191. (9) D€uren, T.; Bae, Y. S.; Snurr, R. Q. Chem. Soc. Rev. 2009, 38 (5), 1237. (10) Vuong, T.; Monson, P. A. Langmuir 1996, 12, 5425. (11) Kowalczyk, P.; Tanaka, H.; Kaneko, K.; Terzyk, A. P.; Do, D. D. Langmuir 2005, 21 (12), 5639. (12) Gigras, A.; Bhatia, S. K.; Kumar, A. V. A.; Myers, A. L. Carbon 2007, 45 (5), 1043. 6743
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