Dynamics of Propane in Nanoporous Silica Aerogel: A Quasielastic

Article pubs.acs.org/JPCC

Dynamics of Propane in Nanoporous Silica Aerogel: A Quasielastic Neutron Scattering Study Siddharth Gautam,*,† Tingting Liu,† Gernot Rother,‡ Niina Jalarvo,§,∥ Eugene Mamontov,∥ Susan Welch,† Julie Sheets,† Michael Droege,⊥ and David R. Cole† †

School of Earth Sciences, The Ohio State University, 275 Mendenhall Laboratory, 125 S Oval Mall, Columbus, Ohio 43210, United States ‡ Geochemistry and Interfacial Science Group, Chemical Sciences Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831-6110, United States § Jülich Centre for Neutron Science (JCNS-1), Outstation at Spallation Neutron Source (SNS), Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831-6473, United States ∥ Chemical and Engineering Materials Division, Neutron Sciences Directorate, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831-6473, United States ⊥ Ocellus Inc., 450 Lindbergh Avenue, Livermore, California 94551-9552, United States ABSTRACT: Molecular motion of hydrocarbons under confinement exhibits several peculiarities and has important implications in industries like gas recovery. A quasielastic neutron scattering (QENS) study of the dynamics of propane in nanoporous silica aerogel was carried out to quantify its molecular mobility. The dynamical properties of propane were studied as a function of temperature, pressure and presence of CO2. The effects of pressure, i.e., fluid density and composition, are found to be more pronounced than the effects of temperature. At low pressures of propane, many propane molecules are adsorbed onto the pore surfaces and are thus immobile. As the pressure of propane loading is increased, more molecules become available to take part in the diffusional dynamics and thus enhance the diffusivity. At low pressure the propane molecules take part in a continuous diffusion, while at higher pressures, the diffusion of propane molecules within the aerogel occurs via the mechanism of jumps. Presence of CO2 enhances the jump rate of propane molecules, thereby increasing the diffusion coefficient. This study aims to aid in understanding the complex processes involved in hydrocarbon migration in porous quartz-rich rocks and enhanced hydrocarbon recovery. mesoporous nature.1,2,4,5,7 As many reservoir rocks are quartzrich, mesoporous silica material can act as a proxy to the terrestrial rocks to understand their effects on the motion of hydrocarbons through them. Whereas microporous media impose a severe geometrical restriction on the confined species, in mesoporous media, the geometrical space available to the confined species can extend to several times the molecular size of the confined species. This milder confinement imposed by the mesoporous media can give rise to an opportunity for the confined species to simultaneously exhibit bulk like and interfacial behavior. Although there have been many studies on the dynamics of single confined species, in natural environments, mesoporous Earth materials are seldom occupied by only a single species. Several fluids are often found confined in the pores of materials at the same time, and the presence of one fluid may influence

I. INTRODUCTION Behavior of fluids confined in porous media is known to exhibit anomalous features.1−7 Dynamical features of the confined species are affected too. For example, a severe geometrical confinement has been shown to give rise to peculiar behavior like single file diffusion,8,9 anomalous dependence of diffusivity on the concentration10,11 and size12 of the confined species. In addition to this fundamental interest, a study of molecular motion under confinement has practical implications in industries like catalysis and gas recovery. This has resulted in an extensive study of molecular dynamics under confinement.9−28 Of particular interest is the dynamics of hydrocarbons confined in porous media10−12,20−28 due to their application in catalytic cracking reactions and hydrocarbon recovery. Porous media is classified according to IUPAC as microporous with pores smaller than 2 nm and mesoporous with pores larger than 2 nm in size.29 Studying the dynamics of hydrocarbons in mesoporous materials is interesting as it provides an ideal model to understand the migration of hydrocarbons through porous rocks which often exhibit a © 2015 American Chemical Society

Received: April 9, 2015 Revised: July 14, 2015 Published: July 14, 2015 18188

DOI: 10.1021/acs.jpcc.5b03444 J. Phys. Chem. C 2015, 119, 18188−18195

Article

The Journal of Physical Chemistry C

B. QENS Measurements. Quasielastic neutron scattering measurements were carried out at the Backscattering Instrument BASIS at the BL-2 beamline of the Spallation Neutron Source (SNS) facility at the Oak Ridge National Laboratory (ORNL), Oak Ridge, TN.30 The instrument uses a set of crystal analyzers to resolve an elastic line up to 3.5 μeV at full width of half-maximum when the signal is averaged over all detectors, with a momentum transfer range of 0.2 to 2.0 Å−1. An energy transfer window of ±100 μeV was used. The silica aerogel sample was loaded in a TZM (titanium−zirconium− molybdenum) sample cell and evacuated to remove any residual protonated volatiles, predominantly water from ambient moisture, which might give rise to an undesired quasi-elastic signal. The aerogel sample was made just to fit the sample can used for neutron scattering measurements and was inserted as a monolith in the sample can. The sample fit the can quite well leaving an empty space of no more than 0.1 mm. The height of the sample was covering the height of the beam. Spectrum was recorded for the evacuated silica aerogel. C3H8 gas was then pumped into the sample cell using a high-pressure syringe pump. Because of the tight fitting of the sample monolith in the sample cell, the amount of the fluid in the sample cell not absorbed by the aerogel is expected to be less than 10%. The quasielastic scattering of neutrons from the C3H8 in silica aerogel was measured at two temperatures (337 and 365 K), and two pressures of C3H8 loading (8 and 58 bar) at each temperature. The silica aerogel used in the experiments reported here is similar in its physical properties to the one used by Gruszkiewicz et al. in their measurements of pore fluid density by vibrating tube densimetry.31 Referring to Figure 4 in ref 31, we estimate a mass of propane adsorbed in the aerogel ranging between 0.14 to 0.76 g/g for the temperature and pressure conditions probed in our experiment. To study the effect of CO2 on the dynamics of confined C3H8, CO2 gas was loaded over the C3H8 at 8 bar already in the aerogel sample to result in two different total pressures (43 and 75 bar), while the content of C3H8 remained the same. The pressure of the loaded gases was controlled by a gas regulator attached between the gas cylinders containing the gases and the sample cell. Pure CO2 in the aerogel without C3H8 was also measured at two different pressure settings corresponding to gaseous and liquid states of CO2. As CO2 was observed to exhibit very fast motion, measurements involving it were limited to room temperature only. The raw data were reduced using standard BASIS routines. A vanadium standard was used to measure the instrumental resolution. In a quasielastic neutron scattering experiment, the measured quantity of interest is the double differential scattering crosssection (∂2σ/∂Ω∂ω).32 This quantity is proportional to the scattering law (S(Q,ω)) which contains information about the dynamic and structural correlations in the sample being measured. Here, Q and ℏω are the momentum and energy, respectively, that are transferred in a neutron scattering event. In principle, both coherent and incoherent scattering processes contribute to the detected signal. Whereas the former is a result of interference of scattering waves from different particles in the material under study, the latter has no contribution from scattering wave interference from different particles. Thus, while the coherent scattering is sensitive to collective motion of the particles, the incoherent scattering is sensitive to the motion of a single particle. The scattering law is then a sum of the incoherent and coherent scattering laws weighted with the

the behavior of the other. Attempts have been made recently to study the dynamical properties of more than one fluid confined in porous materials. For example, Chathoth et al. investigated the effect of CO2 and N2 on the diffusivity of methane confined in mesoporous carbon aerogel.27 They found that the selfdiffusivity of methane in carbon aerogel increases with the addition of CO2. A recent study of the diffusion properties of CH4−CO2 mixtures in microporous metal−organic framework (MOF) type solids found that the diffusivity of methane in MIL-47 (V) decreases as a function of the total loading; however this decrease is less pronounced in the case of a mixture of methane and CO2 as compared to pure methane.28 From this, the authors conclude that the presence of CO2 in the mixture enhances the diffusivity for methane in MIL-47 (V) for a given loading compared to the single component diffusivity. Thus, in both studies cited above, the presence of CO2 was thought to be responsible for an enhancement in the diffusivity of methane confined in micro- as well as mesoporous materials. Methane is the smallest hydrocarbon and possesses a tetrahedral structure. The effects of CO2 on the properties of larger confined hydrocarbons are less studied but are of great interest. In this paper, we present QENS studies on the dynamics of propane (C3H8), the third most abundant natural alkane, confined in silica aerogel that serves as an analogue for silica-rich porous rocks. The range of temperatures and pressures chosen correspond to the conditions found in the subsurface terrestrial environment. The temperatures chosen correspond approximately to the conditions at a depth of about 2 kms assuming a geothermal gradient of 20 °C/km. Although the pressure values chosen correspond to shallower depths, higher pressures were not measured to avoid higher density of propane that would contribute to multiple scattering events in the neutron spectra, making the analysis ambiguous. We will focus on the impacts of temperature and pressure of C3H8 loading, as well as impact of addition of CO2 on the single molecule dynamics of confined C3H8.

II. EXPERIMENT A. Materials. Cylindrical shaped silica aerogel blocks were prepared by mixing 28.0 g of tetramethylorthosilicate (0.184 mol) with 16.0 g of methanol (0.500 mol), followed by 16.0 g of 0.01 N ammonium hydroxide (0.00016 mol). The resulting sol−gel solution was poured into stainless steel molds with cylindrical cavities of 5.0 mm diameter × 50.0 mm high. The dried silica aerogel cylinders were obtained by supercritical extraction using methanol. Densities of the dried aerogel rods ranged from 0.31 to 0.33 g/cm3. The silica aerogel rods were kept in a furnace and were slowly heated to 873 K for several hours to remove any organic species such as methoxy groups. The pore size measurements were carried out with N2 adsorption using a Micromeritics ASAP 2020 gas sorption instrument. Silica aerogel material (0.0719 g) was degassed at 25 °C for 960 min to remove the impurities and gas inside the pores, and was backfilled with N2 as protective gas. Complete adsorption and desorption isotherms were obtained using N2 as the adsorbate. Secondary electron images of the aerogel material were acquired at an accelerating voltage of 15 kV, spot size 2.5, and working distance of 6 mm using an FEI Quanta Field Emission Gun (FEG) 250 scanning electron microscope (SEM). For these observations, samples were prepared by immersing small fragments of the aerogel in silver conductive paint on aluminum stubs and allowing them to airdry before sputter coating with Au−Pd alloy. 18189


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scattering intensity was lower in the case of pure CO2, and longer measurement periods were needed to obtain counting statistics similar to those for the C3H8-containing samples. The spectra of the three principal samples (C3H8, CO2, and C3H8 + CO2) have different profile shapes. The stochastic molecular motion in the sample leads to broadening of an elastic line. This quasielastic (QE) broadening appears as the wings of an elastic line, and flatter quasielastic wings of the elastic peak indicate larger QE broadening, which in turn indicates faster dynamics. The quasielastic wings in the CO2 spectrum are much flatter than the spectra from the C3H8 containing samples and the flattening was further enhanced at higher Q values. The flattening is too severe to retrieve any quantitative information at Q values higher than 0.35 Å−1, so only data at low Q values were used in the analysis for the sample with pure CO2. Another important feature is the relative distribution of scattering intensity in the energy space (Figure 2). In the case of the C3H8−CO2 mixed sample, the scattering intensity is more evenly distributed between the elastic peak and the quasielastic wings as compared to that in the other two samples. Stronger intensity in the quasielastic wings indicates higher scattering from mobile atoms, or in other words, more atoms take part in the dynamics in the case of the mixture. This effect will be quantified and discussed in the next section. No quasielastic broadening was observed for the silica aerogel spectrum. This spectrum, however, was not subtracted from the individual spectra in the analysis because its contribution was significant at the elastic line. Thus, the subtraction was not made in order to avoid an undesirable increase in the uncertainty of the experimentally determined data points.

corresponding scattering cross sections, and the double differential scattering cross-section becomes ∂ 2σ ∝ [σcohScoh(Q , ω) + σincSinc(Q , ω)] ∂Ω∂ω

(1)

where σ is the scattering cross-section, and the subscripts coh and inc denote coherent and incoherent quantities, respectively. Because the incoherent scattering cross section for hydrogen is an order of magnitude larger than the coherent or incoherent scattering cross sections of any other element, the measured scattering signal is dominated by the incoherent scattering from hydrogen in hydrogen-bearing samples. In the present case, therefore, the scattering intensity is proportional to the incoherent scattering law of hydrogen atoms in C 3 H 8 molecules. In the case of pure CO2 in the aerogel, the main scattering contribution is coherent due to carbon and oxygen both being purely coherent scatterers. In the case of a mixture of C3H8 and CO2, incoherent scattering from the C3H8 dominates the signal.

III. EXPERIMENTAL RESULTS Figure 1 shows a representative SEM micrograph of the silica aerogel fragments. The micrograph shows some surface

IV. DATA MODELING AND DISCUSSION A. Modeling. Quantitative information is obtained by utilization of the general scattering law, which is composed of a sum of an elastic term represented by a delta function, a quasielastic term represented by a Lorentzian, and a background. The effect of the instrument resolution is accounted for by convoluting this general scattering law with the instrument resolution R(ω). The instrument specific scattering law is S(Q , ω) = [A(Q )δ(ω) + (1 − A(Q ))L(Γ(Q ), ω) + B(Q , ω)] ⊗ R(ω)

(2)

Here, A(Q) is the fraction of the total scattering law that is elastic. It is called the elastic incoherent structure factor (EISF). L(Γ(Q),ω) is a Lorentzian function and its half-width at halfmaximum (HWHM) is Γ(Q). B(Q,ω) is the background. The experimental data were modeled with the scattering law in eq 2 above. This resulted in fits of sufficient quality shown in Figures 3 (for C3H8 in the aerogel) and 4 (C3H8 and CO2 in the aerogel). The individual contributions of the three terms in eq 2 are shown together with the experimental data and the total function fitted. The variation of the Lorentzian width over different experimental conditions and samples can be seen in addition to changes in the relative contributions of the elastic and the quasielastic terms. The parameters determined from these fits are the EISF, the HWHM of the Lorentzian, and the background. The significance of the EISF lies in its representation of the fraction of molecules which remain immobile on the time scale accessible to the instrument. Note that the EISF values obtained here are approximate and include elastic contribution

Figure 1. SEM micrographs of silica aerogel. The rough surfaces (arrows) are the highly fractal pore walls. The dark regions circled are the pores.

roughness, even on relatively flat areas on the fragments. Clusters of primary particles can be seen, as indicated by arrows in the figure. The rough morphology generates depressions (dark gray) and pores (black; encircled in the figure), which can be seen within the depressions. The pore features were further characterized by N2 adsorption. The adsorption isotherms obtained indicate the presence of mesopores with a size range of 15−25 nm. This estimate is in good agreement with the length scales of the pores observed in the SEM images, see Figure 1. A specific surface area of about 325 m2/g was estimated for the silica aerogel. Figure 2 shows the QENS spectra of silica aerogel filled with C3H8, CO2, and a mixture of C3H8 + CO2 at the lowest scattering angle. Because CO2 is a purely coherent scatterer, the 18190


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Figure 2. QENS spectra measured at the lowest scattering angle for silica aerogel filled with propane (8 bars), CO2 (liquid) and a mixture of propane and CO2 (75 bar). The width of QE broadening is a measure of the energies involved in the motion. A larger QE broadening appears as flatter wings of the elastic line.

Figure 3. Fits of the experimental data at Q = 0.9 Å−1 to eq 2 for pure propane. The experimental data collected for propane in silica aerogel at different conditions of temperature and pressure in the panels are denoted by circles, solid curves represent (i) the total fit function (red), (ii) the elastic term (blue), (iii) the Lorentzian representing the quasielastic term (magenta), and (iv) the flat background term (dark yellow).

from the silica aerogel and the sample cell as these contributions were not subtracted from the individual spectra. At low pressures, the aerogel and empty can together are estimated to make an average contribution of about 40% to the elastic intensity over the entire Q range. What is important to note, however, is the Q independence of the EISF values obtained here. There exist molecular motions in which a part of the molecule remains immobile, whereas the remaining portion exhibits motion. This happens for example with rotational motion in which the center of mass may remain immobile and

the peripheral atoms constituting the molecules continue to move around. In such a case an elastic contribution comes from the immobile atom and is a function of Q. The EISF then is a function of Q. However, if the elastic contribution comes from completely immobile molecules, then it is independent of Q and the EISF is a constant. In the present case, we observed that the EISF remained constant over Q indicating the presence of C3H8 molecules that remain immobile on the time scale of the instrument. On the other hand, the rotational motions of C3H8 molecules are likely too fast to be detected in the 18191


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Figure 4. Fits of the experimental data at Q = 0.9 Å−1 to eq 2 for CO2 and CO2 + propane in silica aerogel. The experimental data collected for the various samples at room temperature are denoted by symbols, while the solid curves represent (i) the total fit function (red), (ii) the elastic term (blue), (iii) the Lorentzian representing the quasielastic term (magenta), and (iv) the flat background term (dark yellow).

variation with Q gives important information about the type of motion involved. The spectra for samples containing CO2 showed very large broadening, which even falls out of the energy window at larger Q values. The fits to these spectra were therefore meaningful at low Q values only where the broadening was relatively small. In case of pure CO2 in the aerogel, this meant limiting the analysis to just two Q values, i. e., up to Q = 0.35 Å−1. The spectra for the mixture of C3H8 and CO2 were analyzed up to Q = 0.7 Å−1. The HWHM values obtained from these fits are shown as a function of Q2 in Figure 5. B. Diffusion Model. The variation of HWHM can be modeled to resolve the underlying dynamical process. In the case of molecules diffusing freely through Brownian motion, their motion is hindered only by collisions. The QE broadening

accessible energy transfer window. Propane is a small hydrocarbon, and the energy involved in the rotational motion for this molecule falls in the range of a few meV. For example, Mukhopadhyay et al. studied the rotational motion of propane in Na−Y zeolite which has a pore size of 1 nm, much smaller than the pore size of the silica aerogel used in our study.33 Using a triple-axis instrument with an elastic resolution of 3 meV (FWHM), they obtained the corresponding HWHM values ranging between 2 and 6 meV. In a recent MD simulation study34 on propane in mesoporous TiO2, we have also observed very fast rotation of propane with the time scales involved of ∼0.3 ps corresponding to an energy of about 2 meV. This is clearly out of the energy window of BASIS, and thus a rotational contribution is expected to appear as a flat background in the BASIS spectrum. For C3H8 at low pressures, EISF values ranged between 0.8 and 0.6. As the pressure is increased, the EISF values decrease below 0.1, indicating an increase in the fraction of molecules that are mobile under these conditions. The presence of CO2 also lowers the EISF values. The values of EISF averaged over all Q values are summarized in Table 1. The other physically significant parameter obtained from the fits is the HWHM of the Lorentzian, which is inversely proportional to the time scales involved in the dynamics, and its Table 1. EISF Values for Different Samples and Experimental Conditions sample propane

propane + CO2

experimental condition 8 bar; 337 K 8 bar; 365 K 58 bar; 337 K 58 bar; 365 K 43 bar; 300 K 75 bar; 300 K

average EISF 0.7 0.65 0.05 0.05 0.2 0.2

± ± ± ± ± ±

0.2 0.15 0.05 0.04 0.1 0.1

Figure 5. Variation of Γ obtained from fitting of the spectra to eq 2. The solid lines show the fits of the Γ variation to the jump diffusion model. The symbols denote the data for a mixture of propane and CO2 at 43 bar (red ●) and 75 bar (blue ●); CO2 gas (pink ●) and liquid (olive green ●). 18192


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available with the present BASIS instrument configuration. Mamontov et al. reported a similar unresolved component of the proton dynamics in a protic liquid using the BASIS spectrometer.36 The HWHM data obtained for low pressures of C3H8 in silica aerogel were fitted with eq 3 with addition of a constant, and data to higher pressures were fitted with eq 4. The resulting fits are included in Figure 6, and the parameters are listed in Table 2. In the Singwi−Sjolander jump model, where the motion occurs via discrete jumps between two sites, the mean jump length between two consecutive sites is given by

exhibited by such a sample has a Lorentzian profile with a HWHM following a linear relation with Q2. The HWHM is then given by Γ = DQ 2

(3)

where D is the diffusion coefficient. In the presence of stronger intermolecular interactions, this linearity breaks down and the HWHM values plateau at high Q values. The HWHM variation then follows a jump diffusion model. For fluids confined in noncrystalline media, jump diffusion usually follows the Singwi−Sjolander model, which assumes that the molecule sits at a site for some time called the residence time (τ), and then jumps to another site.35 In this case, the variation of HWHM has the following Q dependence; Γ=

DQ 2 1 + DQ 2τ

l 2 = 6Dτ

(5)

The values of the mean jump length calculated using eq 5 are also presented in Table 2. C. Discussion. Inspection of results in Table 2 shows several interesting features of C3H8 dynamics in silica aerogel. Most striking is the strong variation of the diffusion coefficient of C3H8 in aerogel as a function of pressure. At high pressure, the diffusion coefficient of C3H8 in the aerogel is greater than that at low pressure whereas the diffusivity is less affected by an isobaric variation within the temperature range investigated. Schmid et al.37 have measured the self-diffusion coefficients of bulk C3H8 at various temperatures and pressures using the spin echo technique with pulsed field gradients. At 323 K, they obtained a diffusion coefficient of 123 × 10−10 m2/s at 25 bar; and 99.9 × 10−10 m2/s at 50 bar. This latter diffusion coefficient is of the same order of magnitude as the one found for confined C3H8 at high pressure. Thus, the confinement due to the silica aerogel has an effect on the diffusion coefficient of C3H8 only at low pressures, becoming nearly negligible at the higher pressure of 58 bar. To compare the diffusion coefficient of confined C3H8 in other studies we can consider the work of Sayeed et al.20 who have reported a diffusion coefficient of C3H8 confined in Na−Y zeolite using MD simulations and QENS experiments (D ∼ 30 × 10−10 m2/s). This value lies between the two values reported here. However, in comparison to silica aerogel, Na−Y zeolite is expected to impose a stronger geometrical confinement due to a smaller pore size of about 1.2 nm. Another confining medium with a comparable pore size is carbon aerogel employed in the studies of confined methane by Chathoth et al.26,27 The diffusivity of C3H8 in silica aerogel at low pressure obtained here is smaller than that for methane in carbon aerogel (D = 7.29 × 10−10 m2/s) at a comparable pressure of 9.65 bar,26,27 as is expected for a larger molecule. At the higher pressure though, the diffusion coefficient obtained for C3H8 in silica aerogel here is an order of magnitude higher than that obtained by Chathoth et al. for methane in carbon aerogel at a comparable pressure of 61.7 bar (D = 6.07 × 10−10 m2/s). However, at this high pressure, C3H8 in the silica aerogel behaves more like a bulk fluid.

(4)

For the CO2−C3H8 mixture, a deviation from linearity in the variation of HWHM with Q2 is found (Figure 5) when least squared fitting of the data with error weighting is attempted. Therefore, the Singwi−Sjolander model was used for this sample. The variation of HWHM for single fluid C3H8 in the aerogel is shown in Figure 6. A striking feature is the qualitative change

Figure 6. Variation of Γ for propane in silica aerogel, obtained from the fitting of the spectra to eq 2. The solid lines are fits to continuous and jump diffusion models.

in the behavior of HWHM with pressure. At low pressures, the HWHM varies linearly with Q2, but at higher pressures a clear deviation from that behavior is observed. Although the variation of HWHM at low pressure is linear, it does not follow eq 3 and a positive y-axis intercept is needed to account for this variation. This could be due to another faster component of the dynamics which is not resolved explicitly within the energy window

Table 2. Parameters Obtained from a Fit of the HWHM with Eqs 3 and 4 sample propane

propane + CO2

experimental condition 8 bar; 337 K 8 bar; 365 K 58 bar; 337 K 58 bar; 365 K 43 bar; 300 K 75 bar; 300 K

diffusion coefficient D ( × 10−10 m2/s) 3.06 5.01 75.90 64.13 113.10 129.56

± ± ± ± ± ±

0.36 0.43 12.14 8.45 7.40 17.60

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residence time τ (ps) − − 5.32 4.64 1.52 2.42

± ± ± ±

0.21 0.18 0.34 0.70

mean jump length (Å) − − 4.92 4.22 3.21 4.33

± ± ± ±

0.49 0.47 0.40 0.87


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However, the jump length of C3H8 molecules remains low because of overcrowding. Thus, the net effect of CO2 addition is to enhance the jump rates of C3H8 molecules, resulting in a higher diffusion coefficient.

The jump lengths obtained for pure C3H8 at high pressures in the silica aerogel are comparable to the size of a C3H8 molecule, indicating a more crowded environment compared to low pressure. After CO2 addition to the low pressure C3H8 in the aerogel sample at room temperature to generate a total pressure comparable to the high pressure sample of C3H8, the diffusion coefficient of C3H8 was observed to increase, and the residence time decrease, signaling higher jump rates. This translates to smaller jump lengths on addition of CO2, documented in Table 2. In a small angle neutron scattering experiment with deuterated C3H8 in silica aerogel, Rother et al.38 have found that C3H8 forms a thin adsorption layer on the pore walls, and the density in this layer increases with increasing fluid density until a critical density is reached. At lower pressure loadings of C3H8, as the number of C3H8 molecules in the pores is small, many of these molecules are adsorbed at the pore walls and are immobile due to weak but nonzero intermolecular binding forces. The remaining molecules are able to overcome the binding forces from the surface walls and remain mobile. As the total number of molecules in the pores is small, the intermolecular interactions among the C3H8 molecules are weak, enabling the molecules that are not bound to the surface to take part in continuous diffusion motion. As the C3H8 loading is increased, more C3H8 molecules occupy pore space farther away from the pore walls. As these molecules are no longer under the influence of the surface forces, they are more mobile and exhibit an increase in their diffusion coefficient. However, the intermolecular interactions among C 3 H 8 molecules become important at higher loadings, and the diffusion mechanism changes from continuous diffusion to jump diffusion. The number of molecules in the central portion of the pores increases with increasing pressure, thereby reducing the ratio of immobile to mobile propane molecules, which reduces the EISF. Addition of CO2 has the same effect of crowding of the central portions of the pore, however, in the presence of C3H8, the contribution of CO2 molecules to the QENS signal remains negligible. Thus, the QENS signal is still dominated by the dynamics of C3H8 molecules alone. Silica surface often has a nontrivial presence of silanol groups that are a result of the interaction of the SiO2 surface with the atmospheric moisture even after heating and evacuating the silica. These groups interact with polar molecules via hydrogen bonds and make the surface hydrophilic.39 Thus, due to preferential affinity of the silanol groups for polar molecules, there would be a selective replacement of nonpolar propane molecules by quadrupolar CO2 molecules. Quadrupole moment of CO2 has been found to play an important role in the adsorption of CO2 on nanoporous metal terepthalates MIL-53 and MIL-47.40 In a preliminary computational study, Thu Le et al.41 found that in the case of C3H8 and CO2 mixture in mesoporous SiO2 the CO2−SiO2 interactions play a dominant role. Therefore, it could be expected that in the case of a C3H8−CO2 mixture in silica aerogel, CO2 replaces C3H8 molecules at the pore walls. This makes more C3H8 molecules available away from the pore-walls, which would decrease the EISF. However, the total number of scatterers (C 3 H 8 molecules) is lower for C3H8−CO2 mixture than in the case of pure C3H8 at high pressure, and therefore the fraction of immobile scatterers is higher. The EISF values are thus higher for the C3H8−CO2 mixture compared to the pure C3H8 case. The presence of CO2 makes the C3H8 molecules more excitable with higher jump rates by replacing them from the pore surface.

V. CONCLUSIONS Quasielastic neutron scattering was used to study the dynamical properties of C3H8 gas confined in nanoporous silica aerogel as a function of temperature, pressure and presence of CO2. The effect of pressure on the dynamical properties is found to be more pronounced than the effects of temperature over the range of temperature and pressures interrogated. At low pressures, many C3H8 molecules are bound to the pore walls and remain immobile while at higher pressures more C3H8 molecules are in the center of the pores increasing the fraction of mobile molecules. The mechanism of the molecular motion changes from a continuous diffusion at low pressure to jump diffusion at higher pressure. Diffusion coefficients and residence times have been obtained and compared with other studies. Confinement by the silica aerogel is found to affect the diffusion coefficient of C3H8 at low pressures only. The effect of CO2 on the C3H8 dynamics is to enhance the jump rate of C3H8 molecules, thereby increasing its diffusivity. This might have implications for the recovery of hydrocarbons from silica rich porous rocks.

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AUTHOR INFORMATION

Corresponding Author

*(S.G.) E-mail: [email protected]. Telephone: (+1) 614292-7365. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This research at Oak Ridge National Laboratory’s Spallation Neutron Source was sponsored by the Scientific User Facilities Division, Office of Basic Energy Sciences, U.S. Department of Energy. Research at OSU was sponsored by the U.S. Department of Energy, Office of Basic Energy Sciences, Chemical Sciences, Geosciences, and Biosciences Division for S. G. (Contract No. DE-SC0006878) and the Sloan Foundation-funded Deep Carbon Observatory for D.R.C. and J.S. G.R. was sponsored by the U.S. Department of Energy, Office of Basic Energy Sciences, Division of Chemical Sciences, Geosciences, and Biosciences.

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REFERENCES

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Dynamics of Propane in Nanoporous Silica Aerogel: A Quasielastic

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