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Modeling CO Transport and Sorption in Carbon Slit Pores Abby Kirchofer, Mahnaz Firouzi, Pete Psarras, and Jennifer Wilcox J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.7b06780 • Publication Date (Web): 28 Aug 2017 Downloaded from http://pubs.acs.org on September 3, 2017

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The Journal of Physical Chemistry

Modeling CO2 Transport and Sorption in Carbon Slit Pores Abby Kirchofer†, Mahnaz Firouzi†, Peter Psarras‡, and Jennifer Wilcox‡* †

Department of Energy Resources Engineering, Stanford University, 367 Panama Street,

Stanford CA 94305, USA; ‡

Department of Chemical and Biological Engineering, Colorado School of Mines, 1613 Illinois

Street, Golden CO 80401, USA.

1 ACS Paragon Plus Environment


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ABSTRACT: The need to reduce carbon dioxide (CO2) emissions is one of the most significant environmental challenges facing society. Carbon Capture and Storage (CCS) has the potential to mitigate gigatons of anthropogenic CO2 emissions, and is regarded as a key method for globalscale CO2 emissions reduction. Understanding CO2 adsorption and transport is crucial to the development of successful carbon capture and storage technologies. This work investigates the use of an improved potential model to directly treat CO2 electrostatic and geometric properties, thereby more accurately describing the fluid-fluid and fluid-wall interactions that determine adsorption capacity and dynamics. Non-equilibrium molecular dynamics (NEMD) simulations are conducted to investigate pore entrance effects on transport through carbon pores. CO2 interactions with pure and hydroxyl-functionalized slit and step carbon pores are simulated to investigate pore entrance effects and tradeoffs between pore size, chemistry, capacity, and transport. The relative importance of 1) CO2 geometry and flexibility, 2) electrostatic interactions, and 3) pore surface chemistry is investigated. The transport investigations of CO2 through carbon pores suggest that fluid density, diffusivity, and permeability are sensitive to the potential model used to describe molecular interactions, pore size, pore geometry, and surface chemistry. The differences in capacity and dynamic properties between the step and slit cases show the importance of investigating transport using models that account for different types of mass transfer resistance. The current work highlights the importance of the potential and structure models in molecular simulations of adsorption and dynamics. These fundamental studies indicate the significance of molecular-scale phenomena in carbon dioxide transport in the confined spaces for carbon capture and sequestration applications.


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1. Introduction The need to reduce carbon dioxide (CO2) emissions is one of the most significant environmental challenges facing society. Carbon Capture and Storage (CCS) has the potential to mitigate gigatons of anthropogenic CO2 emissions, and is regarded as a key method for global-scale CO2 emissions reduction. However, the feasibility of wide-scale deployment of CCS hinges on improving the economic and environmental viability of CCS technologies. Understanding CO2 adsorption and transport is crucial to the tuning adsorbent material properties to optimize capture processes, and therefore the development of cost-effective and efficient CCS technologies. More generally, developing an improved understanding of transport in confined spaces is necessary for the advancement of myriad technologies, including gas-solid reactions, separation processes, gas storage and heterogeneous catalysis.

The current work investigates CO2 transport in porous carbon materials (that could be also a representative of the carbon-based kerogen porous structure of shale), consists of slit and step pores using DCV-GCMD simulations, with the aim of developing an improved understanding of mass transfer resistance in nanopores.

Previous work suggests that the type, shape and chemistry of the pore model used for molecular simulations can significantly impact adsorption results,1 and that such material properties could be used to enhance sorbent capacity, selectivity or uptake.

2-3

However, investigations of

adsorption dynamics tend to rely on simplified potential and structure models; to date, little work has investigated the transport of CO2 on carbon materials using realistic models for fluids and solids. More so than investigations of adsorption and capacity, most of the literature regarding



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transport and kinetics treats CO2 as a spherical molecule or as a rigid linear molecule.4-12 Nonetheless, recent work supports the need for more accurate structural and potential models. Cai et al.13 investigated the effect of the pore wall model on equilibrium and non-equilibrium MD investigations of transport in graphitic slit pores, and found that the results can vary significantly depending on which pore wall model (e.g., smooth or structured) is used to describe a given pore. Skoulidas et al.10 investigated CO2 diffusion in carbon nanotubes with diameters from 1.1 to 5.4 nm using equilibrium MD (EMD), and compared results based on spherical (1CLJ) and linear (EPM2) models for CO2. However, the investigation did not account for CO2 flexibility, possible defects or surface functionality on the carbon surface, or pore entrance and exit effects. Newsome and Sholl14

investigated mass transfer resistances for gas transport

through carbon nanotube membranes, and estimate the relative importance of surface resistance (i.e., interfacial resistance to diffusion through the pore entrance or exit) in comparison to intracrystalline resistance (i.e., resistance to diffusion inside the pore). Previous work by Newsome and Sholl15 suggests that surface resistances for a permeating species will increases with increasing adsorption strength of that species, or with decreasing temperature. Previous work highlights the need to account for structural heterogeneity and pore connectivity to accurately predict transport properties of porous materials.9,

16

Firouzi et al.16 investigated

transport and separation of supercritical CO2-alkane mixtures in carbon molecular sieve (CMS) membranes using a composite pore model which included three connected graphitic slit pores with heights of 10, 23, and 77 Å. The pore wall C atoms and CO2 and CH4 molecules are treated as 1C-LJ spheres, while the larger alkanes are treated as flexible chains of CH2 and CH3 unitedatom (UA) centers. Additionally, Firouzi and Wilcox17 investigated the transport of CO2 in a carbon-based 3-D pore-network model, and show that morphological characteristics such as


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porosity play a significant role in determining the flow and transport properties of fluids. The authors conclude that transport properties can be dependent on pressure gradient and direction, depending on the porous material under consideration and discussed the mass transfer mechanisms and dominating mass transfer resistances that can vary in different pore size. Zimmermann et al.18 studied surface effects on equilibrium transport of hydrocarbon gases in zeolite pores. Depending on the conditions, material, and gases, the importance of surface effects ranges from negligible to dominating in terms of limiting mass transfer. Depending on the system investigated, the mass transfer mechanisms and dominating mass transfer resistances can vary widely. Such a range is promising, in that it suggests that material and molecular properties could be tuned to enhance mass transfer for a given process; however, to take advantage of such properties will require an improved mechanistic understand of adsorption dynamics at the nanopore scale. As Zimmermann et al.18 point out for zeolites, confusion remains about the basic processes of adsorption and transport in micropores, despite the great number of studies investigating adsorption and transport in zeolites. For porous carbon materials, a similar state of confusion exists, and further work is required to determine the influence of various material properties and conditions on transport and mass transfer resistances. Lim et al.12 investigated CO2 permeability in carbon slit pores, using EMD and GCMC to predict diffusivity and permeability. The authors compare results for spherical (1C-LJ) and linear (3-site LJ with point charges) models of CO2, and report that diffusion of CO2 in small pores is underestimated by the spherical model, because such a model does not fit in small pores as well as the linear model. Additionally, Lim et al.12 report permeabilities that are three times greater than those reported based on macroscopic measurement, and suggest that the discrepancy between simulation and experimental results exists because the simulations do not account for the rate-limiting step of



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mass transport through the pore mouth, or for pore connectivity and tortuosity, which can play an important role in limiting mass transfer in real porous systems. The authors state that diffusion in CMS adsorbents is limited by pore-mouth resistance and estimate that pore mouth resistance is roughly 2 orders of magnitude greater than pore intracrystalline resistance, so theoretical simulations that do not take into account entrance effects would predict increased permeability and diffusivity compared to experiment/reality. As Lim et al.12 note, both adsorption and diffusion impact flux and permeability in microporous systems; therefore, flux and permeability do not increase monotonically with pore width.

Previous work supports the need for additional work investigating the complex nature of mass transfer through nanoporous materials. Specifically, given the importance of porous structure properties in influencing kinetics, there is need to develop an improved understanding of pore entrance effects,9-10,

12, 16

which is addressed in the current work. In the current work, the

relationship between surface resistance, adsorption effects, and temperature will be investigated by considering the effect of temperature, fluid-fluid and gas-fluid potentials, surface chemistry, and pore structure. Additionally, the current work considers the effect of using more realistic potential models for the fluid and solid components of the system. The potential model EPM2 developed by Harris and Yung19 successfully reproduces the vapor-liquid coexistence curve, and has been modified previously to include bond angle flexibility.20-21 Babarao and Jiang22 investigated diffusion and separation of CO2 and CH4 in carbon (C168 schwarzite) and non-carbon (silicalite and IRMOF-1) sorbents using EMD. CO2 was modeled using the 3-site model, fitted to experimental data by Hirotani et al.,23 with point charges, rigid C-O bonds, and, for the noncarbon sorbents only, flexibility. The authors do not discuss the impact of accounting for


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molecular flexibility on adsorption dynamics. To the author's knowledge, potential models incorporating CO2 bond flexibility have only been used to investigate transport in non-carbon systems such as silicates or clays.20, 22 Finally, the effect of pore surface chemistry on transport is investigated, to determine how functional groups affect mass transfer. In order to develop optimal sorbents, more accurate models are required to explore and develop understanding of adsorption and transport, especially in regards to tradeoffs associated with key material properties such as surface chemistry and/or pore size. For instance, functional groups may be used to increase (or optimize) the adsorption energy, but functional groups also act to physically narrow the pore by occupying a certain volume of pore space. In confined space adsorption and diffusion are coupled, and transport may be controlled by activated diffusion or molecular sievelike mechanisms, dependent on sorption behavior, sorbent pore morphology, and sorbate molecular geometry.24 This work attempts to develop an improved understanding of the tradeoff between capacity and kinetics, and to highlight the importance of kinetics in optimizing sorbents for CCS.

The accuracy of MD simulations hinges on the accuracy of the potential models used to describe the system under investigation. Furthermore, numerous studies have shown that predicted adsorption behavior could depend strongly on whether chemical heterogeneity, molecular geometry, or electrostatic interactions are accounted for. This work investigates the use of the flexible quadrupole model for CO2, an improved potential model to more accurately describe fluid-fluid and fluid-wall interactions by directly treating CO2 electrostatic and geometric properties. The flexible quadrupole (FQ) model is based on the EPM2 model developed by Harris and Yung,19 but modified to include bond angle flexibility. Additionally, we consider pure



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and hydroxyl-functionalized slit and step pores in the micro- to mesopore range, to investigate pore entrance effects and tradeoffs between pore size, chemistry, capacity, and transport.

Transport of molecules in confined systems (i.e., in microporous materials) differs greatly from that of bulk-phase transport, as adsorption and diffusion are coupled, and diffusion may be hindered by strong adsorption or activation barriers (e.g., pore entrance effects). For systems that include charged or polarizable sorbents, or sorbents with dipole or quadrupole moments, electrostatic interactions can play an important role in sorption and transport. The current work addresses this, by investigating CO2 transport using the flexible quadrupole model for CO2, which directly accounts for the point charges and flexibility of CO2.

In this study, non-equilibrium molecular dynamics (NEMD) simulations were conducted to investigate pore entrance effects on transport through carbon pores. CO2 transport in various graphitic pores was simulated using the dual control-volume grand canonical molecular dynamics (DCV-GCMD) method to apply an external pressure gradient.8-9, 16-17, 25-27 The DCVGCMD simulation was combined with configurational-bias Monte Carlo method, an approach first implemented by Firouzi et al.25 to investigate the transport of CO2 molecules treated with the FQ model. To determine the significance of electrostatic interactions on CO2 transport through pore entrances, simulations were conducted using potential models of varying levels of sophistication. The relative importance of 1) CO2 geometry and flexibility, 2) electrostatic interactions, and 3) pore surface chemistry is investigated. To the authors’ knowledge, the current work is novel and contributes to the literature in the following ways: First, previous investigations of CO2 transport through carbon nanopores have not included such a realistic


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potential model, which directly treats the geometry, flexibility, and quadrupole moment of CO2. Second, the investigation of entrance effects including a direct treatment of fluid-fluid and fluidwall electrostatic interactions is novel. Third, the impact of surface functional groups on CO2 transport through carbon nanopores has not been investigated previously. The plan of this paper is as follows. In the next section, we describe the pore models. Next, the molecular models of CO2 and the interaction potentials are described. We then describe the molecular dynamics simulation details. The results are then presented and analyzed. The paper is summarized in section VI.

2. Pore Models Porous carbon materials have been modeled extensively as idealized independent slit pores with smooth graphitic walls and infinite connectivity. Everett and Powl28 described carbon pores as the absence of one, two, or three graphene layers from bulk graphite (corresponding to pore sizes of 7, 11, and 14 Å), and theorized that the microporosity of carbon materials is accurately described by slit-pore models. While numerous molecular simulations of CO2 adsorption and transport in porous carbons have been conducted, to date accurate prediction of adsorption dynamics remains challenging.

In this paper, we focus on pore entrance effects on transport through carbon pores. Investigations were carried out for graphitic step pores, which consist of slit pores in series with inner (small) pore heights of 10, 15, 20, 25 and 50 Å. Figure 1 provides a schematic of the step pore model, and shows the location and relative size of the control volumes for two example structures with varying pore heights. In the current work, periodic boundary conditions are applied in the y



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direction (i.e., perpendicular to the plane of this page). The pore wall consists of three graphene layers throughout the system, and an additional three graphene layers create the step and form the inner pore walls. In such a model, the outer pore height z1 varies as a function of the inner pore height z2, such that z1 = z2 + 20.1 Å, as depicted in Figure 1. For most cases, the inner pore is centered in the transport region, and the inner pore length is two-thirds the length of the transport region. For select cases, variations of inner pore location or length were considered, to investigate the effect of the small pore length and position on CO2 transport properties.

FIGURE 1. Schematic of the carbon pore model used in the simulations. The P1 and P2 represent the high pressure and low pressure in the control volumes, respectively.

To investigate the effect of surface chemistry, pure and hydroxyl-functionalized graphene layers were tested. The structures are based on DFT-relaxed structures by Liu and Wilcox2 multiplied to generate the overall step pore. For the hydroxyl-functionalized structures, only the inner graphene layers of the small pore are functionalized with OH-groups on the basal plane of the


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graphene layer, as detailed in Figure 2. Traditional slit pore structures were investigated to determine the relative importance of entrance versus intra micropore resistance. Figure 3 shows the 20 Å slit pore structure in comparison to the 20 Å step pore structure; as the figure shows, the entire slit pore structure is similar to the small pore of the step pore structure, and the total system dimensions are equal.

FIGURE 2. Location of hydroxyl functional groups in the pore model.



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FIGURE 3. Slit versus step pore model.

3. CO2 Molecular Models and Interaction Potentials In order to accurately model fluid behavior and transport, it is imperative that realistic potential models are used to describe molecular interactions. In this work, CO2 molecules are represented using the either the simple one-site Lennard Jones potential model or the Flexible Quadrupole potential model.

While the effective molecular parameters attempt to account for electrostatic interactions, the single-site per molecule limits the ability of the 1C-LJ model to accurately describe electrostatic interactions of molecules with dipole or quadrupole moments, such as CO2. In comparison to the 1C-LJ model, the flexible quadrupole (FQ) model accounts for the geometry, flexibility, and intrinsic quadrupole moment of CO2. The FQ model is more computationally expensive, but will allow a more realistic model of CO2 transferring in confined spaces. The details for the one-site Lennard Jones (1C-LJ) and FQ models are provided in Supporting Information. Table 1 provides 12 ACS Paragon Plus Environment

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the potential parameters and charges for the materials investigated in the current work.

In the previous works author modeled smooth homogeneous graphene surface using the Steele 10-4-3 potential to predict CO2 transport properties in carbon pores. In the current work, the atoms comprising the graphitic pore walls are treated explicitly as 1C-LJ sites to address the problem of representing the morphology of a carbon surface by a realistic model including discrete carbon atoms. We used the LJ potential for the interactions between CO2 and the

individual carbon atoms on the walls, arranged as in graphite with a cutoff distance of 3.9σC.

In simulations where CO2 is treated using the FQ model, the charges of the individual wall atoms are included to describe the electrostatic interactions between CO2 and the pore wall. Table 1. Potential parameters ()

(Å)

1C–LJ model CO2 He C(pore wall)

240 10.9 28

3.75 2.64 3.4

OH(pore wall)

85.27

3.034

FQ model C(CO2) O(CO2) C(pore wall) O(pore wall)

28.999 82.997 28 85.27

2.785 3.064 3.4 3.034

Atom or molecule

Q (E)

0.6645 –0.33225 ±0.0498 –0.3



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4. Molecular Dynamics Simulation The dual control-volume GCMD technique (DCV-GCMD),29-30 which has been used extensively in the past by several research groups,4-9, 16-17, 25-27, 31-34 and described in details in the previous works by Firouzi et al.8-9, 16-17, 25-27, 31 was employed to investigate the transport properties of CO2 molecules. In the MD simulations, the Verlet velocity algorithm was used to integrate the equations of motion with a dimensionless time step, ∆t*=5 equations of motion were integrated with up to 1

X

X

10-3 (i.e., ∆t =0.00685 ps). The

107 time steps to ensure that steady state has

been reached, after which the properties, such as concentration and velocity profiles, fluxes, etc., were calculated and averaged over the last one million time steps. More details for MD simulations are provided in Supporting Information. In this work the walls are rigid. We computed several quantities of interest, including the density profiles of the component i along the x- and z-directions, ρ iz (x) and ρ ix (z), respectively. As discussed next in greater detail, these quantities are important in understanding the gas transport properties in nanoconfined pore systems. In addition, for each component i the flux, Ji, in the direction of the applied pressure gradient was calculated by measuring the net number of gas molecules crossing a given yz plane. The permeability, Ki, of component i was then calculated using: =

= , (1) ∆ ⁄ ∆

where ∆ = ∆ is the partial pressure drop for component i along the pore, with xi being the mole fraction of component i, ∆P the total pressure drop imposed along the pore, and nL the pore length in the transport direction. In the current work, the pore length is defined as the distance from the upstream CV to the downstream CV, which includes both the large and small pore segments of the transport region, and equals 148 Å. Time-averaged density profiles for a given case are computed using the bin method for the x and z directions, in which the simulation cell is 14 ACS Paragon Plus Environment

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divided into bins along a given axis, and the number of molecules in each bin is recorded. The transport diffusivity Di is calculated as a function of flux and the concentration gradient across the transport region: = −

∆

, (2)

where is the length of the transport region and ∆ is the change in density across the transport region (#/cm3), defined as the density difference between the upstream and downstream control volumes. In what follows, we present and discuss the results of our simulation.

5. Results and Discussion Impact of different potential models

For the LJ simulations, flux data were collected at different locations along the transport pore to ensure that the fluxes are equal for a given pore height at different locations. More details are provided in Supporting Information. Snapshots of CO2 in corresponding LJ and FQ cases are shown in Figure 4 as projections in the y-direction (perpendicular to the transport direction), to provide a visual comparison of the distribution of fluid particles inside pores simulated using the LJ and the FQ model. The depth of the snapshots equals the length of the simulation cell in the ydirection, 85.4 Å. The snapshots show higher density in the upstream CV (where P = 50 atm) than the downstream CV (where P = 10 atm). As the snapshots highlight, for both FQ and LJ cases the CO2 density is highest near the pore walls. To gain further insight into the differences between LJ versus FQ cases, density profiles along the z direction were considered at various positions along the x (transport) direction, since such profiles depict how the density changes as the fluid progresses through the pore. Figure 5 provides density profiles along the z direction for 15 ACS Paragon Plus Environment


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LJ and FQ 10 and 20 Å cases at 75°C. Figure 6 provides select profiles for 25Å FQ and LJ cases at 25 and 75°C. As expected, for both the LJ and FQ cases, the density profiles reflect the higher density in the lower temperature (25°C) cases. In all cases, the density profiles reflect the higher density in the LJ cases than the FQ cases of corresponding pore size and conditions. The CO2 molecules are primarily located in layers adjacent to the pore wall, and the CO2 molecules must shift closer to the pore center in the z direction in order to transition into the inner pore. In all cases, the density increases just before the inner pore entrance; however, this increase is more dramatic for LJ cases. Furthermore, the density profiles in the inner pore entrance for the LJ cases show very small density, while for the FQ cases the density throughout the inner pore height is significant. The differences in the LJ and FQ profiles suggest that the FQ fluid is able to transition through the pore entrance more readily than the LJ fluid. Pore model chemistry and structure effects Transport through slit pores was investigated to provide context for the step pore results. The results from a given slit case can be considered a baseline for the corresponding step case results, and the difference in density, flux, and diffusivity are a measure of the significance of pore entrance effects. Furthermore, by contrasting the slit pore LJ and FQ cases we gain insight to the importance of using a more realistic potential model to accurately predict


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FIGURE 4. Projections of CO2 at 25°C and 50-10 atm in the y-direction for a) Pure-FQ (linear CO2 model) and b) Pure-LJ (spherical CO2 model) 20 Å step pores; the projection depth equals 85.4 Å.

FIGURE 5. Z density profiles for 10 and 20 Å cases at 75°C and 50 - 10 atm.



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FIGURE 6. Z density profiles for 25 Å cases at 25°C or 75°C and 50 - 10 atm.

transport properties. Figure 7 provides snapshots of CO2 in LJ and FQ pure and OH 20 Å cases, shown as projections in the y-direction (perpendicular to the transport direction). The depth of the snapshots equals the length of the simulation cell in the y-direction, 85.4 Å. The snapshots show the higher density in the upstream CV (where P = 50 atm) than the downstream CV (where P = 10 atm). As the snapshots highlight, the density in the inner pores of the OH cases fluctuates due to the location of OH groups. Figure 8 provides density profiles along the z direction for pure and OH 20 Å cases at 75°C. The profiles for the pure and OH cases are similar, although the density peaks for each position in the pore are slightly lower for the OH case than the pure case. Additionally, there is slight asymmetry in the OH entrance and inner pore profiles, due to the asymmetry in the position of OH groups on opposing pore walls. Future work should include the investigation of different functional groups and different surface coverage. It is important to note that the densities in the upstream CVs are higher in the step cases than the corresponding slit 18 ACS Paragon Plus Environment

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cases, despite the equal dimensions of the CV for corresponding step and slit cases; this effect is likely because the CV in the step cases is influenced by the inner pore, and the density is higher because of pressure

FIGURE 7. Projections of CO2 in at 25°C and 50-10 atm in the y-direction for a) Pure-FQ, b) OH-FQ, c) Pure-LJ, and d) OH-LJ 20 Å step pores; the projection depth equals 85.4 Å



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FIGURE 8. Z density profiles for pure and OH 20 Å cases at 75°C.

buildup at the pore entrance. This effect decreases with increasing pore height, likely because the significance of the entrance effects decreases with increasing pore height. Transport Properties The flux, diffusivity, and permeability for each case were determined based on the simulation results. The direct output from the simulations includes the number of passing molecules at the transport region entrance and exit at a given time step. Figure 9 provides the number of passing CO2 molecules for FQ and LJ step pores at 25 or 75°C and 50 - 10 atm. As expected, the number of passing CO2 molecules is greater at 25°C than 75°C for a given pore height and potential model. It is interesting to note that the difference between the low and high temperature cases decreases with increasing pore height, presumably because temperature effects are greater for the adsorbed-phase (i.e., molecules forming a higher density layer adjacent to the pore wall) than the bulk phase molecules in the pore center, and the ratio of adsorbed to bulkphase decreases with increasing pore height. Additionally, for a given pore height, the LJ cases have lower passing numbers than the corresponding FQ cases, and this difference increases with increasing pore height. Likely this is because for pure graphene pores the difference between the


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LJ versus FQ fluid-wall interactions is less significant than the difference between the LJ versus FQ fluid-fluid interactions, and the

FIGURE 9. Number of passing CO2 molecules in step pores at 25 or 75°C and 50 - 10 atm.

importance of fluid-fluid interactions increase with increasing pore height. From the flux and density results, diffusivity and permeability for each case was determined. Table 2 summarizes diffusivities for 20 and 50 Å cases. In general, diffusivity increases with increasing temperature; however, this effect is more significant for FQ cases than for LJ cases. This effect may be due to the relationship between density and temperature: at higher temperature, the density is lower and there is less resistance to motion because the pore is less packed. Permeability, on the other hand, tends to decrease with increasing temperature, largely due to the decrease in density with increasing temperature.

Previous results predict collective diffusivities for CO2 in carbon slit pores of 5.96 × 10-5 to 1.29 ×



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10-4 cm2/s at 25°C and 5 atm, and 6.27 × 10-5 to 1.38 × 10-4 cm2/s in slit pores at 45°C and 5 atm (Lim et al., 2010). The results are in agreement with previous investigations of transport using molecular simulation, which predict permeabilities for CO2 in carbon step pores at 55°C and 45 atm of 6.1 × 10-7 to 5.5 × 10-6 mol-cm/min-cm2-atm,9, 16 and in carbon slit pores at 35°C and 5 atm of 4.0 × 10-5 to 6.5 × 10-5 mol-cm/min-cm2-atm.12 A more detailed comparison is not possible because of the differences in potential model, structure model, and thermodynamic conditions simulated in the current work and previous investigations from the literature. In order for more explicit and detailed comparison, future work should include combined experimental and theoretical investigations. This would enable benchmarking simulation results, for instance to confirm that the computationally expensive FQ model (in comparison to the LJ model) provides a more realistic depiction of CO2 adsorption dynamics. TABLE 2. Diffusivity and permeability for select cases at 50 - 10 atm

Case Step–20 (25℃) Step–20 (75℃) OH–Step–20 (25℃) OH–Step–20 (75℃) Slit–20 (25℃) Step–50 (25℃) Step–50 (75℃) OH–Step–50 (25℃) OH–Step–50 (75℃) Slit–50 (25℃)

Diffusivity (cm2/s) LJ FQ 0.0027 0.0050 0.0030 0.0063 0.0010 0.0014 0.0011 0.0011 0.0217 0.0294 0.0036 0.0075 0.0046 0.0110 0.0021 0.0035 0.0030 0.0037 0.0157 0.0155

Permeability*105 (mol–cm/min–cm2–atm) LJ FQ 2.28 5.41 1.78 2.34 0.84 1.91 0.68 0.52 25.8 54.5 2.14 3.72 2.01 3.21 1.29 2.22 1.35 1.27 10.6 11.0

Figure 10 shows permeabilities for pure LJ and FQ step and slit pores at 25 or 75°C and 50 - 10 atm. As expected, permeabilities for slit pore cases are drastically higher than permeabilities for


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the corresponding step pore cases, because the slit pore cases do not involve transfer through a pore entrance. In other words, the slit cases do not include the resistance to mass transfer due to the step through the pore entrance; therefore, permeability through the step cases would only approach permeability through the slit cases if there was no barrier or resistance to mass transfer through the pore entrance. Given the difference in predicted permeabilities and diffusivities for slit and step cases, the results highlight the importance of pore entrance effects in limiting CO2 transport through carbon nanopores. Figure 11 provides the permeabilities for pure LJ and FQ step pores at 25 or 75°C and 50 - 10 atm or 10 - 5 atm. The FQ cases appear more sensitive to temperature and pressure conditions than the corresponding LJ cases.

FIGURE 10. Permeabilities for LJ and FQ pure 50 - 10 atm cases.



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FIGURE 11. The effect of ∆P and T on permeabilities for pure LJ and FQ step cases: a) 25°C and 50 - 10 atm or 10 - 5 atm, and b) 50 - 10 atm and 25°C or 75°C.

Figure 12 shows the permeabilities for pure and OH LJ and FQ step pores at 25 or 75°C and 50 10 atm. Regardless of pore height, potential model, or temperature, the OH cases have lower permeability than the corresponding pure cases. As with the pure cases, the FQ 25°C cases gave markedly higher permeabilities than the cases investigated. Figure 13 shows the diffusivities for pure LJ and FQ step pores at 25 or 75°C and 50 - 10 atm or 10 - 5 atm. For comparison, the Knudsen and molecular diffusivities, DK and DM, respectively, are plotted. In general, the diffusivity

FIGURE 12. The effect of surface functionality on permeabilities for LJ and FQ step cases at a) 24 ACS Paragon Plus Environment

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50 - 10 atm and 25°C or 75°C, and b) 25°C and 50 - 10 atm or 10 – 5 atm.

FIGURE 13. Diffusivities for LJ and FQ pure step cases.

is higher for the 50 - 10 atm cases than for the corresponding 10 - 5 atm cases, and higher for the 75°C cases than the corresponding 25°C cases. However, the effect of pressure appears greater for the LJ cases, and the effect of temperature appears greater for the FQ cases. Furthermore, as pore size decreases, the effect of temperature appears to decrease for both LJ and FQ cases.

As expected and shown in Table 2, the diffusivities for slit cases, which do not account for pore entrance effects, are higher than the diffusivities for the corresponding step cases, which include mass transfer resistance due to the step into the inner pore. It is interesting to note that the diffusivity for step cases tends to increase with increasing pore height, likely because the mass transfer resistance due to the step into the inner pore plays a less significant role as the inner pore height increases, while the diffusivity for slit cases tends to decrease with increasing pore height in the micropore range (i.e., for pore heights less than 20 Å). Recalling that diffusivity is the



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proportionality constant for the concentration gradient and the flux, this result is due to the relative changes in the concentration gradient and flux as pore height increases: for the 10 - 20 Å cases, the ratio of the change in flux to the change in concentration gradient decreases with increasing pore height, therefore the diffusivity decreases with increasing pore height. For the micropore slit cases, the density throughout the system is greater than the critical density, and the concentration gradient throughout the system is small; there is a significant increase in concentration gradient for the 20 Å cases, and thereafter the concentration gradient decreases with increasing pore height. Given this increase in concentration gradient in the micropore cases, which outweighs the change in flux, the diffusivity decreases. The difference in trends and quantitative results between the step and slit cases highlights the importance of investigating transport using models that account for different types of mass transfer resistance.

6. CONCLUSIONS The current work highlights the importance of the potential and structure models in molecular simulations of transport properties. The DCV-GCMD investigations of CO2 transport through carbon pores suggest that fluid density, diffusivity, and permeability are sensitive to the potential model used to describe molecular interactions, pore height, pore type, and surface chemistry. The difference in trends and quantitative results between the step and slit cases shows the importance of investigating transport using models that account for different types of mass transfer resistance. The LJ cases predict significantly higher densities than the corresponding FQ cases, and show heightened sensitivity to pore height. On the other hand, the capacity and kinetic results for FQ cases are more sensitive to changes in temperature and pressure. For both LJ and FQ cases, the pore entrance and exit effects decrease with increasing pore height, because as the pore height increases the importance of the step diminishes. The pore entrance and exit effects, 26 ACS Paragon Plus Environment

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specifically the density peaks, are more significant for the LJ cases. Also, the transition region for the inner pore entrance, where the density profile changes due to the inner pore entrance, is shorter for the FQ cases than the LJ cases. The results suggest the FQ fluid transitions through the pore entrance more readily than the LJ fluid. The current work on CO2 transport provides a preliminary step forward in understanding the tradeoffs between adsorption and dynamics and in providing the molecular results required for improved process modeling. For CCS, as well as other emerging technologies, there is great need for molecular simulation of adsorption and transport to link material properties to the process scale, so that material properties can be optimized for a given process. Future work at the molecular scale should consider mixtures of CO2, CH4, H2O and other gases relevant to capture processes. Future work should also include the investigation of different functional groups, different surface coverages, and pores entrance effects as a function of step height. Depending on the application of the work, functional groups could be tailored to represent chemical heterogeneity of natural carbons such as coal, or to represent synthetic materials functionalized to improve capture properties.

SUPPORTING INFORMATION Description of potential models for sorbate representation, flux data collection locations, example flux data results

ACKNOWLEDGEMENTS The computations were carried out on the Center for Computational Earth & Environmental Science (CEES) cluster at Stanford University. We would like to thank Dennis Michael for his administration of CEES and assistance in the installation of our simulation codes.



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TOC Graphic

Projections of CO2 at 25°C and 50-10 atm in the y-direction for a) Pure-FQ (linear CO2 model) and b) Pure-LJ (spherical CO2 model) 20 Å step pores.


Modeling CO2 Transport and Sorption in Carbon ... - ACS Publications

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