Role of Confinement on Adsorption and Dynamics of Ethane and an

Subscriber access provided by TEXAS A&M INTL UNIV

Article

Role of Confinement on Adsorption and Dynamics of Ethane and an Ethane-CO Mixture in Mesoporous CPG Silica 2

Sumant Shreedhar Patankar, Siddharth Gautam, Gernot Rother, Andrey Podlesnyak, Georg Ehlers, Tingting Liu, David Robert Cole, and David L. Tomasko J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.5b09984 • Publication Date (Web): 10 Feb 2016 Downloaded from http://pubs.acs.org on February 22, 2016

Just Accepted “Just Accepted” manuscripts have been peer-reviewed and accepted for publication. They are posted online prior to technical editing, formatting for publication and author proofing. The American Chemical Society provides “Just Accepted” as a free service to the research community to expedite the dissemination of scientific material as soon as possible after acceptance. “Just Accepted” manuscripts appear in full in PDF format accompanied by an HTML abstract. “Just Accepted” manuscripts have been fully peer reviewed, but should not be considered the official version of record. They are accessible to all readers and citable by the Digital Object Identifier (DOI®). “Just Accepted” is an optional service offered to authors. Therefore, the “Just Accepted” Web site may not include all articles that will be published in the journal. After a manuscript is technically edited and formatted, it will be removed from the “Just Accepted” Web site and published as an ASAP article. Note that technical editing may introduce minor changes to the manuscript text and/or graphics which could affect content, and all legal disclaimers and ethical guidelines that apply to the journal pertain. ACS cannot be held responsible for errors or consequences arising from the use of information contained in these “Just Accepted” manuscripts.

The Journal of Physical Chemistry C is published by the American Chemical Society. 1155 Sixteenth Street N.W., Washington, DC 20036 Published by American Chemical Society. Copyright © American Chemical Society. However, no copyright claim is made to original U.S. Government works, or works produced by employees of any Commonwealth realm Crown government in the course of their duties.

Page 1 of 38

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48

The Journal of Physical Chemistry

ACS Paragon Plus Environment


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 2 of 38

Role of Confinement on Adsorption and Dynamics of Ethane and an Ethane-CO2 Mixture in Mesoporous CPG Silica Sumant Patankar1, Siddharth Gautam2, Gernot Rother3, Andrey Podlesnyak4, Georg Ehlers4, Tingting Liu2, David R. Cole2 and David L. Tomasko*,1 1

William G. Lowrie Department of Chemical and Biomolecular Engineering, The Ohio State University, 151 W Woodruff Ave., Columbus, OH 43210, USA

2

School of Earth Sciences, The Ohio State University, 125 South Oval Mall, Columbus OH 43210, USA

3

Geochemistry and Interfacial Science Group, Chemical Sciences Division, Oak Ridge National Laboratory, Oak Ridge, TN 37831-6110, USA

4

Quantum Condensed Matter Division, Oak Ridge National Laboratory, Oak Ridge, TN 378316110, USA

*Email address: [email protected], Phone no.: 614-247-6548


1

Page 3 of 38

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Abstract Ethane is found confined to mineral and organic pores in certain shale formations. Effects of confinement on structural and dynamic properties of ethane in mesoporous controlled pore glass (CPG) were studied by gravimetric adsorption and quasi-elastic neutron scattering (QENS) measurements. The obtained isotherms and scattering data complement each other by quantifying the relative strength of the solid-fluid interactions and the transport properties of the fluid under confinement, respectively. A magnetic suspension balance was used to measure the adsorption isotherms at two temperatures and over a range of pressures corresponding to a bulk density range of 0.01-0.35 g/cm3. Key confinement effects were highlighted through differences between isotherms for the two pore sizes. A comparison was made with previously published isotherms for CO2 on the same CPG materials. Behavior of ethane in the smaller pore size was probed further using quasi-elastic neutron scattering. By extracting the self-diffusivity and residence time, we were able to study the effect of pressure and transition from gaseous to supercritical densities on the dynamics of confined ethane. A temperature variation QENS study was also completed with pure ethane and a CO2-ethane mixture. Activation energies extracted from the Arrhenius plots show the effects of CO2 addition on ethane mobility. Keywords: supercritical, confinement, nanoporous, excess adsorption, dynamics. 1. Introduction Shale gas has reinvigorated petrochemical and manufacturing industries in the American midwest, partly due to the relative abundance of higher hydrocarbons along with methane in some shale formations (Marcellus and Utica formations). Ethane is one of the fluids being recovered


2


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 4 of 38

on a relatively large scale. Cracking of shale gas ethane to ethylene provides cheap access to crucial raw materials for polyethylene and related polymer manufacturing industries.1,2 The term ‘tight gas’ refers to natural gas that is trapped in low permeability bedrocks such as shales, sandstones, carbonates and coal beds.3 For generation of economic gas flow rates and reservoir exploitation, the extraction conditions as a function of pressure, temperature and composition of bedrock need to be optimized. Hydrodynamic trapping, confinement and adsorption also influence hydrocarbon properties in unconventional reservoirs which consist predominantly of nanoporous solid matrices.4,5 Confinement causes changes in properties of fluids relative to the bulk phase which need to be understood for their relevance to geofluid extraction and other applications6-8. Confinement effects are a consequence of both restricted space as well as interactions between the fluid and the internal pore surfaces of the confining media, and these effects need to be delineated for a complete understanding. The richness and complexity of fluid behavior (e.g. phase transitions, molecular orientation and relaxation, diffusion, adsorption, wetting, capillary condensation, etc.) in confined geometries underscores a need for a multidisciplinary approach when attempting to quantify this behavior regardless of the fluid type or nature of the porous medium. The effects of confinement have previously been studied using diverse tools such as computational9-12, spectroscopic13-19, gravimetric20 and calorimetric21,22. Gravimetric adsorption and spectroscopic methods such as inelastic neutron scattering have the benefit of being both non-invasive and nondestructive and are suitable to study microstructural wetting properties and dynamics of confined hydrocarbon fluids.23,24 Adsorption of hydrocarbons in nanoporous materials such as activated carbons25, zeolites26,27 and modified organic frameworks28,29has been studied. While spectroscopic studies measure dynamics of confined fluids, it is their combination with adsorption measurements that reveals


3

Page 5 of 38

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


the role of the fluid microstructure, which is dictated by fluid–substrate interactions. Thus, an adsorption measurement coupled with a spectroscopic study gives a much more detailed insight into the effects of fluid substrate interactions on the dynamics of confined fluid. A majority of the studies mentioned above have been conducted under the modest temperature and pressure conditions relevant to catalysis and separation. The high pressure and temperature conditions at reservoir environments often imply presence of supercritical hydrocarbon fluids. Fluids exhibit unique behavior near the critical point as parameters such as isothermal compressibility exhibit divergent behavior.30 Thus, it becomes important to extend the studies of hydrocarbons in nanoporous materials to supercritical phases. Minerals have a wide variety of pore sizes, shapes, surface chemistries and solid composition, and hence we have used Controlled Pore Glass (CPG) materials as a proxy confining media. Use of synthetic proxies in our study greatly facilitates control over these parameters and observation of their effects on fluid behavior. Studies have targeted controlled pore glasses to assess interfacial and confinement effects due to their well-defined pore structures31,32. The interplay between solid-fluid and fluid-fluid interactions on adsorption behavior has been explored in our study by varying pore size, temperature, pressure and fluid composition. We can observe the competition between various interactions through excess adsorption isotherms at varying fluid densities. This information is complemented by quasi-elastic neutron scattering measurements that are used to obtain the self-diffusivity of ethane as a function of its density in the CPG and the effect of a second fluid (i.e. the presence of CO2). Combined analysis of these data yields correlations between the fluid-solid interactions and transport properties. 2. Experimental Methods


4


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 6 of 38

2.1 Material Two synthetic mesoporous CPG materials in coarse powder form were acquired from Millipore CPG75 and CPG350, in which the numbers denote the nominal pore sizes in angstroms. The CPG is composed of amorphous silica with sponge-like pore network morphology (Figure 1). Rother et al. have performed contrast variation small angle neutron scattering (SANS) on the material and report a skeletal density of 2.2 g/cm3, which is close to that of cristobalite (2.33 g/cm3).

33

The CPG used in our study has been recognized as a suitable proxy for naturally

occurring silica rich rocks such as sandstone and portions of some shales.34,35

Figure 1: SEM images of the CPG silica (a) CPG75 (b) CPG350 Pore properties (size, volume, and surface area) were determined using an ASAP Micromeritics® 2020. Materials were degassed at 25°C for 960 minutes to remove the impurities and gas inside the pores. Complete adsorption and desorption isotherms were obtained for the two samples using nitrogen as the adsorbate, shown in Figures 2a and 2c. Pore distribution plots are presented as insets in Figures 2b and 2d. The pore distribution results were based on the Barrett-Joyner-


5

Page 7 of 38

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Halenda (BJH) method using desorption data. The Brunauer-Emmett-Teller (BET) method was used to determine the surface area. The pore volume was obtained using the first data point of the desorption limb of the isotherm. Nirogen gas adsorption derived pore properties are summarized in Table 1.


6


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 8 of 38

Figure 2: Pore property measurement using N2. (a) and (c) are the measured isotherms for CPG75 and CPG350, respectively. The insets - (b) and (d) are the pore distribution plots using BJH adsorption data. Table 1: Pore features of CPG75 and CPG350 samples used in this study. Dominant pore size (nm)

BET surface area

Total pore volume

BJH adsorption

(m2/g)

(cm3/g)

CPG75

11.1

148.5 ± 1.0

0.59

CPG350

41.5

65.5 ± 0.5

0.92

2.2 Adsorption Measurements Gravimetric adsorption is a direct way of gaining a quantitative understanding of interactions between solid surfaces and fluids. We have measured the adsorption isotherms for ethane on two CPGs at two different temperatures (308 K and 323 K), well above the critical temperature (Tc=305.3 K). Measurements were carried out using a high-pressure magnetic suspension balance (MSB) manufactured by Rubotherm, Germany with integrated measurements of the bulk fluid density.36 Large errors may occur in the isotherms close to the bulk critical density due to high sensitivity of fluid density to temperature gradients in the system. This error was moderated using a method described by Pini et al. which recommends measurement of fluid density by running the empty sample holder in the MSB instead of relying on the integrated density measurement, especially close to the critical point.37 After sample loading, the balance was evacuated with a GE (General Electric) Duo-seal vacuum pump and allowed to equilibrate to desired temperature overnight. Temperature in the sample cell was controlled using a Julabo (F-25 ME) circulator. This pre-treatment removes gaseous and


7

Page 9 of 38

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


physisorbed water but not surface hydroxyl groups.20 The mass and volume of the solid sample were estimated using helium pycnometry (Praxair Inc., Grade 5.0 Ultra High Purity). Assuming that helium does not adsorb on the material at moderate pressures (0-60 bar), the actual sample mass (Ms) and volume (Vs) of the sample were determined using the buoyancy relation – Mm = Ms - VsρHe

(1)

where Mm is the measured value of sample mass and ρHe is the measured helium density. A linear plot of Mm versus ρHe (which is measured in situ) yields the mass and volume of the sample. Liquid ethane (purity 99.99%) purchased from Praxair was pressurized using an ISCO 500 HL syringe pump. The pressure range was chosen to ensure variation across phase space starting from gas to supercritical ethane (Pc = 49 bar). At each pressure point the sample was allowed to equilibrate for 45-60 min beyond achievement of a steady mass reading. The quantity obtained from these measurements is the Gibbs excess adsorption. Excess adsorption (ne) is defined as the excess amount of fluid in the adsorbed phase region over the bulk density, i.e. the integral over the local difference between the adsorbed fluid density and the bulk density in the direction normal to the surface (z-direction, where z=0 identifies the solid surface)∞

ne = ∫ [ ρ ( z ) − ρb ]dz

(2)

0

The value of excess adsorption, which is measured in volumetric or gravimetric experiments, indicates the relative strength of solid-fluid over fluid-fluid interactions. A larger value of ne indicates a stronger affinity between the fluid and the surface. At low pressures, surface wetting systems follow Henry`s law, i.e. the rise in excess adsorption is almost linear with respect to pressure. Below the bulk critical temperature (Tc), due to rising pressure, a confined fluid phase


8


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 10 of 38

(e.g inside a pore) can undergo condensation earlier than the bulk, causing the excess adsorption to increase rapidly and then decrease sharply above bulk condensation.35 The excess adsorption isotherms for supercritical fluids (T > Tc) typically exhibit a broad peak when plotted against bulk density. Variations in peak height and peak position occur due to different relative strengths of fluid-solid and fluid-fluid forces, pore size and size of the fluid molecules, as will be discussed below.

2.3 Quasi-Elastic Neutron Scattering (QENS) The wavelength and energies of cold neutrons are suitable for the studies of structural dimensions and energies involved in the motions of confined hydrocarbon molecules. Combined with the high penetration power, which allows use of high pressure cells, this makes neutrons an ideal probe for comparing properties of bulk fluids and fluids in confined geometries. The large neutron incoherent scattering cross-section of hydrogen allows study of systems dominated by hydrogen-containing species in quasi-elastic (QENS) and inelastic (INS) experiments.38 Neutrons are detected as a function of momentum (ħQ) and energy (ħω) transfers after scattering by the sample, with ħ being the reduced Planck`s constant. The measured quantity is proportional to the scattering law S(Q,ω) which contains structural and dynamic information about the sample. Measured data are convoluted with the instrument`s resolution. In a QENS measurement, information about dynamics is extracted from broadening of the elastic peak caused by stochastic motions of hydrogen atoms. In addition to a background, the spectra in a QENS experiment consists of an elastic line due to atoms immobile on the time scale accessible by the spectrometer and a quasi-elastic component which is a broadening of the former and can be written as -


9

Page 11 of 38

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


, = { + 1 − Γ, + , } ⊗ ,

(3)

Here, is a delta function representing the elastic line centered at zero energy transfer. is the elastic fraction of the total scattering, called the elastic incoherent structure factor (EISF). The quasi-elastic broadening is represented, in the second term on the right hand side, by a Lorentzian function Γ, with half width at half maximum (HWHM) of Γ. , is the background. The quantity in the {} curly braces on the right side of Equation (3) contains information about the sample whereas the instrument resolution , is a property of the instrument alone. QENS measurements were carried out on the Cold Neutron Chopper Spectrometer (CNCS) at the Spallation Neutron Source (SNS) facility of the Oak Ridge National Laboratory (ORNL).39 CNCS is a multi-chopper direct geometry inelastic spectrometer with a large energy range suited to study molecular dynamics. For our experiment, the instrument was optimized to a resolution of 55 µeV at the elastic line by choosing incident neutron energy of 3 meV. The CPG sample was loaded into a cylindrical aluminum can with an inner diameter of 6 mm, designed to minimize multiple scattering events. Awarded beam time was sufficient for investigation of only one pore size of the CPG and the smaller pore size was chosen as it exhibits stronger confinement effects. The granular sample was loaded into an aluminum cell, evacuated, and spectra of the solid matrix were measured. Ethane (Air Liquide, Grade 2.0) was pressurized by means of a Helium head and loaded into the sample cell. The sample cell was filled with liquid ethane, pressurized by pushing helium on top of the ethane and heated to desired temperature. Pressure and temperature of the sample cell were monitored continuously. Spectra were collected for ethane loaded CPG sample for 5


10


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 12 of 38

different pressure readings ranging from 38 bar to 80 bar at 323 K and 5 different temperatures at 38 bar. Pressure variation from 38 bar to 80 bar at 323 K corresponds to a change from gas to supercritical ethane. A mixture of CO2 and ethane (with composition of 27 mol% CO2) was also studied at 38 bar and four different temperatures. A vanadium sample was used to measure the instrument resolution and the detector efficiency.

3. Results and Discussion 3.1 Adsorption Isotherms Measured excess adsorption isotherms are presented normalized to pore volume in Figure 3a and normalized to pore surface-area Figure 3b. These normalizations facilitate comparison between two different pore sizes to, which will allow us to discriminate between surface and confinement effects.


11

Page 13 of 38

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Figure 3: Excess adsorption isotherms for ethane in CPG normalized to (a) pore volume and (b) pore surface area

3.1.1 Pore Volume Normalization The excess adsorption isotherms normalized to pore volume are plotted in Figure 3a. These normalized quantities indicate the relative enrichment of the adsorbed fluid density over the bulk fluid density. The maxima in the isotherms occur at densities below the bulk critical density of


12


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 14 of 38

ethane (which is 0.203 g/cm3), and at roughly the same bulk density for both pore sizes. The excess sorption values decrease with increasing temperature for both pore sizes. Adsorption effects are more pronounced in the smaller pores, which contain a larger fraction of near-surface densely packed fluid layers. The stronger adsorption effects in the narrower pores extend out to the highest measured fluid densities. In contrast, the excess adsorption maximum is much lower for the larger pore size of the CPG, and approaches zero or slightly negative values at high density.

3.1.2 Pore Surface-Area Normalization Excess sorption values normalized to pore surface area are plotted in Figure 3b. At low bulk densities, an approximately equal numbers of adsorbed layers are present inside pores of both sizes. This is an indication that at low fluid densities, interaction with the internal pore surface controls adsorption and not pore size/confinement. As the bulk density increases, however, pore size control on the peak heights becomes more visible, with larger values of excess adsorption found in the larger pores. We attribute this finding to pore confinement effects, i.e. geometrical restriction of the growth of the adsorbed fluid layer by overlapping of fluid layers formed on opposite pore walls. The lower peak values for the smaller pore size in Figure 3b reflect this confinement effect. Above the bulk critical density, the adsorbed fluid layer in the smaller pores appears to remain more densified.

3.1.3 Comparison to excess adsorption of CO2 CO2 and ethane represent molecules with similar size but contrasting intermolecular interactions with itself, and with both hydrophobic and hydrophilic surfaces. The low degree of polarizability


13

Page 15 of 38

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


and large quadrupole moment of CO2 are contrasted against the high degree of polarizability and no moment for ethane. These two molecules also represent a sizeable fraction of fluid phase interactions (except H-bonding) observed in subsurface sedimentary basin reservoirs. A qualitative comparison between excess sorption isotherms of ethane and CO2 on the CPG is made using data published previously20, with raw data for the CO2 being renormalized using to the pore volume values in Table 1. Isotherms of CO2 and ethane normalized to pore volume for the CPG material with wider pores are plotted in Figure 4a, and for the narrower pores in Figure 4b. The isotherms are plotted against reduced density, which defined as the ratio of bulk fluid density to the bulk critical density of the fluid, to facilitate a direct comparison. A reduced density value of 1 corresponds to the bulk critical density of the fluid. In Figure 4a, a distinct difference can be seen between the sorption isotherms, more prominently at 308 K. The peak value for CO2 is larger than for ethane and also occurs at a larger value of reduced density. This indicates a stronger interaction between the CO2 and the solid surface, as compared to ethane. The adsorbed CO2 phase continues to become denser regardless of increased bulk fluidfluid interactions. However, the excess sorption for ethane drops off well before its bulk critical density. At 323 K, the peak heights are similar. However, the pore space is enriched relative to the bulk up to a higher value of reduced density of CO2. This difference in sorption behavior is vanishes in the smaller pores (Figure 4b). Geometric confinement restricts on the number of adsorbed layers that can be accommodated inside the narrower pores. Hence, the extent of both CO2 and ethane layering on the solid surface is restricted. The sorption layer formed by supercritical CO2 will extend further into the pore space, if geometric conditions permit.


14


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 16 of 38

Figure 4: Excess sorption isotherms for Ethane and CO2 normalized to pore volume (a) CPG350, (b) CPG75. Another feature of the CO2 isotherms is the shift in the position of the excess sorption maxima to a lower value of reduced density with decrease in the pore size from Figure 4a to Figure 4b. Such a shift in peak position was predicted from simulation studies of supercritical fluids and


15

Page 17 of 38

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


attributed to change in pore curvature leading to a high surface area to volume ratio due to decreasing pore size.40,41 CO2 follows this predicted trend but the position of the maxima for ethane is unaffected. On account of its stronger interaction with the substrate, it may be argued that changes in curvature are expected to change the position of the excess sorption maxima more for CO2 and less for ethane.

3.2 QENS 3.2.1 Data Analysis and Effect of Pressure Figure 5 shows the QENS spectra collected for evacuated CPG75, ethane confined to the CPG75 material and the vanadium sample measured at room temperature. While the spectra for the ethane-loaded CPG exhibit significant quasi-elastic broadening, the empty CPG spectrum is congruent with the Vanadium spectrum, indicating an absence of quasi-elastic broadening for the pure sample, i.e., absence of mobile H in empty CPG.


16


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 18 of 38

Figure 5: Comparative QENS spectra for Vanadium, empty (evacuated) CPG75 and CPG75 loaded with ethane The elastic intensity for the empty CPG sample is quite significant as seen in Figure 5. However, the empty CPG sample does not exhibit any quasi-elastic broadening as evacuation at room temperature could have caused elimination of mobile impurities that contribute to it. Thus the measured background will not represent true sample background. Also, addition of ethane causes significant multiple scattering/self-shielding events which lead to a reduction of the elastic intensity. As a result, attempting to subtract the background leads to over-subtraction. Thus, we choose to not subtract the empty CPG background from our spectra. This approach has been adopted previously. 14,42,43 Elastic scattering by the empty CPG sample is accounted for in the δ term in equation 3. Analysis of QENS data was carried out using DAVE software.44 The first step in QENS data analysis involves the separation of elastic and quasi-elastic components of the spectra by fitting the experimental spectra with equation 3. However, fit quality was unsatisfactory at low energy transfers close to the elastic line. At the scale of energy transfers measured in this experiment, a contribution by rotational motion to quasi-elastic broadening is probable. Mukhopadhyay et al. observed rotation of propane molecules in Na-Y zeolite using an elastic resolution of 1.6 meV (HWHM).45 In a pore of TiO2 (4 nm) larger than the Na-Y, MD simulations have indicated that rotation of propane occurs at time scales corresponding to about 2 meV.46 We therefore attempted to model the experimental data with a scattering law composed of a convolution of translation and rotational motion. This attempt did not result in good quality fits either. In the present case, the guest (ethane) size is smaller and the host pore dimension is larger. Consequently, the rotational motion can be expected to have higher energy which will lead to a


17

Page 19 of 38

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


broadening too wide to be resolved by the current instrument settings, i.e., the rotational component would appear as a flat background in the spectra. To improve the quality of fits, we included a second Lorentzian in our model, which implies that the quasi-elastic width represents molecular motions at two different time scales. Fitting the experimental data with two Lorentzians resulted in good quality fits shown in Figure 6a.


18


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 20 of 38

Figure 6: (a) Reduced QENS data, overall fit and individual Lorentzian components for P = 49.5 bar and Q = 0.7 Å -1 (b) Structure factor versus energy transfer and corresponding fits for all 5 pressures at a fixed wave vector transfer Since there is no quasi-elastic contribution by the solid matrix (Figure 5), all quasi-elastic broadening originates due to the ethane mobility. The two Lorentzian terms in the fit imply the presence of two populations of ethane molecules with motions at two different time scales. The origin and nature of these two populations is rationalized by the assumption of two distinct populations of ethane – bulk and adsorbed. The CPG used in this study has a grain size in the range of 0.2-0.4 mm.20 It is reasonable to expect the presence of bulk-like ethane in the interstitial space between grains. The larger pores in the CPG will also contain a fraction of bulk-like ethane molecules that do not interact with the surface and contribute to the faster motions. The HWHM (Half-Width at Half Maximum) values


19

Page 21 of 38

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


for this faster motion (broader Lorentzian) when plotted against the Q2 values (shown in Figure 7a) fit well with the Fickian diffusion model represented by Equation (4)

=

(4)

where D is the self-diffusion coefficient. Figure 8b shows these values along with values quoted for bulk ethane at higher pressures (greater than 200 bar).47 This observed behavior of selfdiffusivity as a function of pressure is characteristic for bulk fluids. We therefore infer that the faster component represents contributions from bulk-like ethane molecules, which do not interact with the CPG. The variation of HWHM as a function of Q2 for the slower component (narrower Lorentzian) shows a deviation from linearity at higher Q values (Figure 7b) and exhibits a plateau which is characteristic of jump diffusion, modeled by Equation (5)48

=

! "

(5)

In this model, diffusion occurs via jumps; a molecule spends a finite amount of time, called residence time (τ), at a given site before jumping to another site. The diffusion coefficient of the adsorbed and confined species (Dc) obtained from this component and plotted in Figure 8a has the same order of magnitude as observed for ethane in silicalite21 and is substantially slower than the bulk diffusion.


20


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 22 of 38

Figure 7: HWHM vs Q2 at 38 bar and 80 bar for (a) faster (bulk-like) and (b) slower (confined) ethane. Data for other pressures are not shown for the purpose of clarity.

Figure 8: Comparison between (a) measured bulk and confined ethane self-diffusion coefficients for ethane and (b) measured bulk-like and previously published47 bulk self-diffusion coefficients (published data were measured using spin-echo NMR) Thus, the narrower Lorentzian represents contributions from the molecules interacting with the surface within the pores whereas the broader Lorentzian describes the bulk-like molecules in the


21

Page 23 of 38

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


space between the CPG particles and in the pore centers. The measured parameters associated with the ethane diffusion are reported in Table 2. Table 2: Experimentally obtained transport parameters for ethane in CPG75 at 323 K Pressure

D (x 109 m2/s)

τ (ps)

(bar)

Self-diffusion coefficient

Residence time

Bulk-like (Db)

Confined (Dc)

Confined

38

40.48±1.70

12.27±0.93

1.56±0.07

50

38.20±1.73

10.04±0.80

1.76±0.09

60

38.20±0.88

5.74±0.54

1.45±0.14

70

36.65±0.84

8.92±1.51

1.07±0.16

80

32.78±0.35

8.44±1.07

0.72±0.11

3.2.2 Self-Diffusion Coefficient Self-diffusion coefficient values for confined ethane, Dc, are much slower than the bulk-like values, Db. As seen in Table 2, the values for Dc vary between 5.6 and 12 x 10-9 m2/s. These values are higher than the values reported for ethane confined to silicalite and Na-ZSM-5 at 300 K, as well as those in microporous silica at 270 K, listed in Table 3. However, those studies involved porous matrices with much smaller pore size than the CPG and lower temperatures.

Table 3: Reported self-diffusion coefficients for hydrocarbons in other nanoporous materials. D (x 109 m2/s)

Temperature

Fluid

Material

Pore size

Source

(nm)


22


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

1.25 - 3

300 K

Ethane

Silicalite

Role of Confinement on Adsorption and Dynamics of Ethane and an

Recommend Documents