Developing Electrolyte Perturbed-Chain SAFT Density Functional

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C: Surfaces, Interfaces, Porous Materials, and Catalysis

Developing Electrolyte Perturbed-Chain SAFT Density Functional Theory for CO2 Separation by Confined Ionic Liquids Gulou Shen, Aatto Laaksonen, Xiaohua Lu, and Xiaoyan Ji J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.8b04120 • Publication Date (Web): 10 Jun 2018 Downloaded from http://pubs.acs.org on June 11, 2018

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The Journal of Physical Chemistry

Developing Electrolyte Perturbed-Chain SAFT Density Functional Theory for CO2 Separation by Confined Ionic Liquids

Gulou Shen,1, 2* Aatto Laaksonen,3,4 Xiaohua Lu5 and Xiaoyan Ji2

1

Jiangsu Provincial Engineering Laboratory for Advanced Materials of Salt Chemical

Industry, Huaiyin Institute of Technology, Huaian 223001, China 2

Division of Energy Science/Energy Engineering, Lulea University of Technology, 97187

Lulea, Sweden 3

Department of Materials and Environmental Chemistry, Arrhenius Laboratory, Stockholm

University, SE-106 91 Stockholm, Sweden 4

Department of Chemistry, Ångström Laboratory, Uppsala University, Box 538,

SE-75121 Uppsala, Sweden 5

State Key Laboratory of Materials-Oriented Chemical Engineering, Nanjing Tech

University, Nanjing 210009, China ABSTRACT: The electrolyte perturbed-chain statistical associating fluid theory (ePC-SAFT) classical density functional theory (DFT) was developed to describe the behavior of pure ionic 1 ACS Paragon Plus Environment

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liquid (IL) and CO2/IL mixture confined in nanopores, in which a new ionic functional based on the ionic term from ePC-SAFT was proposed for electrostatic free energy contribution. The developed model was verified by comparing the model prediction with molecular simulation results for ionic fluids, and the agreement shows that the model is reliable in representing the confined behavior of ionic fluids. The developed model was further used to study the behavior of pure IL and CO2/IL mixture in silica nanopores where the IL-ions and CO2 were modeled as chains consisted of spherical segments with the parameters taken from the bulk ePC-SAFT. The results reveal that the nano-confinement can lead to an increased CO2 solubility, and the solubility increases with increasing pressure. The averaged-density of pure IL and solubility of CO2 are strongly dependent on pore sizes and geometries. In addition, the choice of IL-ions is very important for the CO2 solubility. In overall, the modeling results for silica confined systems are consistent with available molecular simulation and experimental results.

I. INTRODUCTION Ionic liquids (ILs) are salts with melting points below 100 °C. Recent research shows that ILs are promising liquid absorbents for CO2 capture and separation in fossil-fueled power plants or biofuel production because of their high CO2 solubility/selectivity and low energy requirement for regeneration.1-3 However, the viscosity of pure ILs is relatively high compared to common organic solvents, causing a decrease of the mass- and heat-transfer rates. Many studies have shown that using the ILs confined in nanoporous supports is an effective way to improve the mass transfer.4-6 However, most of these studies focus on experimental synthesis and characterization of solid confined IL materials for CO2 separation such as supported IL membranes or immobilized ILs on porous materials and the measurements of CO2 sorption/desorption kinetics.7-11 Due to the solid-fluid interaction and spatial confinement, the 2 ACS Paragon Plus Environment

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structures and physicochemical properties of the confined ILs are significantly different from those in the bulk phase. Considering the huge number of ILs that can be synthesized, it is particularly desirable to obtain fundamental understanding of the effect of confinement on the behavior of CO2/ILs in order to develop the CO2-separation technologies based on the hybrid material of IL and solid material. Recent studies have revealed that the solubility of gas in a confined solvent shows quite different characteristics compared to that in bulk phase.12-18 For example, Malani et al.19 used molecular dynamics simulations to study the solubility of NaCl in the confined water, and found that solubility of NaCl is lower compared to the water in the bulk phase. Ho et al.20 observed the enhanced solubilities of CO2 and H2 in the octamethylcyclotetrasiloxane (OMCTS) confined in MCM-41 by combining experiment and molecular simulation. Hu et al.21 studied CH4/benzene and H2/OMCTS in silica and graphite slit pores using classical DFT and molecular simulation, and both increased and decreased solubilities were observed, depending on the system conditions. However, only few experimental and simulation studies have addressed the confinement effect on the gas solubility in ILs. The experimental results of Banu et al.22 showed that the solubility and diffusivity of CO2 are enhanced in the ILs confined in the ceramic porous film compared to those in the bulk ILs. Shi et al.23 found increased solubilities and self-diffusivities of CO2, H2, and N2 in [C6mim][Tf2N] confined in silica slit pores by molecular simulation, and CO2 solubility is lower in a large pore than that in a small pore. Budhathoki et al.24 simulated CO2 separations from CH4 and H2 using [C4mim][Tf2N] confined in graphite slit pores, and observed that the CO2 solubility is higher in a large pore than that in a small pore, which is opposite to the trend observed by Shi et al.23. Very recently, Shen et al.25 simulated the CO2 sorption in deep

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eutectic solvent (DES), choline chloride and ethylene glycol confined in graphite and rutile silt pores, and the results showed that the average number density of CO2 dissolved in the confined ethylene glycol is smaller than the value in the bulk ethylene glycol, but the overall average number density of CO2 (dissolved in confined ethylene glycol, adsorbed at the pore wall and at the gas/liquid interface) is larger than what is observed in the bulk DES. On the basis of the above studies, it can be concluded that confinement has a significant, yet complex impact on the CO2 solubility in ILs which is an important property for the selection of materials for CO2 separation. Considering a large number of porous materials and ILs could be synthesized, theoretical modeling for CO2 absorption in the confined ILs is required for the purpose of screening and optimizing the hybrid of ILs and porous materials. In our previous work, ePC-SAFT was extended to accurately represent the densities of pure ILs in a wide temperature and pressure range,26,

27

allowing for reliable predictions of gas

solubility in the bulk ILs. Moreover, a PC-SAFT-DFT model has been developed to obtain the properties of fluid confined in nanopores.28 The developed PC-SAFT-DFT model can reliably describe the behavior of a confined fluid. It is of great importance to develop an ePC-SAFT-DFT model to the confined IL systems. The goal of this work is to develop further the ePC-SAFT model in order to describe the property of the IL and CO2/IL confined in nanopores by incorporating an ionic functional into the PC-SAFT-DFT model for electrostatic interactions. The developed model will be used to predict the density distributions of model ionic fluids in charged pores, and the predicted results will be compared with the molecular simulation results for model and method verification. Moreover, the developed model will be used to investigate the effect of pressure, IL-ions and solid-fluid interaction on the properties of the confined pure IL and CO2/IL mixture.


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II. THEORY We considered an IL system confined in a nanopore. Following the modeling of the bulk IL systems using ePC-SAFT,26 an IL is assumed to be composed of an IL-cation and an IL-anion. Each individual IL-ion is modeled as a non-spherical species with repulsion, dispersive attraction and electrostatic interactions. Although this coarse-grained model does not give a detailed description of intramolecular interactions of a real substance as provided by all-atom molecular simulation, it enables accurate modeling of the density of ILs and quantitative prediction of the solubility of CO2 in bulk ILs without any binary parameter.

Figure 1. Schematic of an IL-ion comprised of mi spherical segments. Specifically, each IL-ion is modeled as a chain consisted of spherical segments as shown in Figure 1. The nonelectrostatic interaction between segments is decomposed into a soft repulsion and a Lennard-Jones attraction. This requires three pure IL-ion parameters, i.e. non-integer segment number mi, segment diameter σi and dispersion-energy parameter εi/kB. The electrostatic interaction between two charges of IL-ions with distance r is described by Coulomb’s law

β uij = λB zi z j / r

(1)

In eq. (1) β = 1/kBT, where kB is Boltzmann constant and T is the absolute temperature in kelvins; zi is the valence and the valences of IL-cation and IL-anion are +1 and -1, respectively; and λB is the Bjerrum length, i.e. λB= e2/(4πε0εrkBT), e is the unit charge, ε0 is the permittivity of vacuum and εr is the relative permittivity which is assumed to be unity. According to DFT, in the presence of a solid surface, at a fixed µi , V and T, the grand 5 ACS Paragon Plus Environment


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potential Ω is given by the equation

Ω[ρ i (r )] = A[ρ i (r )] − ∑ ∫ dr ' ρ i (r ' )( µ i − miVi , ext (r ' ))

(2)

i

where A is the Helmholtz free energy, ρi (r ) is the molecular density of component i, µ i is the chemical potential, mi is the number of segments in a chain for component i, and Vi , ext (r ) is the external potential acting on the segment of component i. Following ePC-SAFT, the Helmholtz free energy A for the ionic systems can be expressed as A[ρ i ( r ) ] = Aid [ρ i ( r )] + A hs [ρ i ( r )] + A chain [ρ i ( r ) ] + A disp [ρ i ( r ) ] + Aion [ρ i ( r ) ]

(3)

where Aid is the ideal free energy, and Ahs, Achain, Adisp and Aion are the excess free energies due to the hard sphere repulsions, chain connectivity, dispersive and electrostatic interactions, respectively. A. Ideal, hard chain and dispersion terms The extension of Aid, Ahs, Achain and Adisp of PC-SAFT to inhomogeneous fluid has been described in our previous work. Here we only briefly show the key equations. Following our previous work, the model developed by Tripathi and Chapman29 was used to represent the ideal and chain terms. The free energy of the reference ideal atomic gas mixture is

βAid [ρi ] = ∑ ∫ drmi ρi (r )(ln ρi (r ) − 1)

(4)

i

The excess Helmholtz energy functional for chain connectivity can be expressed as

 

βAchain [ρ ] = ∑ − (mi − 1)∫ drρi (r ) ln yiicont [ρi (r ), di ]∫ dr ' i

 

  δ ( r − r ' − di ) ρ r ( ' )  − 1 i 2 4πdi  

(5)

This model implicitly assumes that each segment in the chain is identical. yiicont [ρi (r ), d i ] is the value of cavity correlation function at contact, and it is a function of weighted densities, i.e.


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yiicont [ρ i ( r ), d i ] =

d i (ζ 2 ) 2 1 3d i ζ 2 , + + 1 − ζ 3 2(1 − ζ 3 ) 2 2(1 − ζ 3 ) 3 2

(6a)

and

π  k ζ k = ∑ 6 mi d i ρ i (r )  i   ρ i (r ) = 3 dr ' ρ i ( r ' ) 3  4πd i ∫r −r ' Rc − σ i / 2

∞ 0

β Vext , i ( r ) = 

r < Rc − σ i / 2

(25)

where r is the radial distance of the ion from the center of the pore, the ion diameter σ+ = σ- = σ is 0.425 nm, and the pore radius Rc is 4.2125 nm. In the ePC-SAFT-DFT prediction, only the hard sphere (Eq. 7) and Debye–Hückel electrostatic (Eq. 18) free energies were considered. The surface charge and bulk concentration are the same as those used in MC simulation41. Figure 3 shows the model predictions of the ionic concentration profiles using ePC-SAFT-DFT. For comparison, the corresponding results from the MC simulation41 are also shown. For 1:1 electrolytes, the model prediction agrees with MC data quantitatively. For 2:2 electrolytes, Peng and Yu42 predicted the ionic concentration distributions by DFT using MFMT (Eq. 7) and MSA (Eq. 17) for the hard sphere and electrostatic correlation terms, respectively, and their results are also included in Figure 3b. The predicted concentration of co-ion from present DFT (MFMT+DH) matches the MC results41 better than that from the MFMT+MSA. For counterion, the prediction of the present DFT is slightly worse than that from the MFMT+MSA.


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Figure 3. (a) Concentrations for 1:1 electrolyte inside a charged cylindrical pore. The bulk concentration of the electrolyte solution is 0.1002 mol/L and the surface charge density is 0.0711 C/m2. Lines: ePC-SAFT-DFT model predictions; Symbols: MC simulation data.

(b)

Concentrations for 2:2 electrolyte inside a charged cylindrical pore. The bulk concentration of the electrolyte solution is 0.0515 mol/L and the surface charge density is -0.1422 C/m2. Solid lines: predictions of present ePC-SAFT-DFT model; dashed lines: predictions of MFMT+MSA from reference42; Symbols: MC simulation data.

B. Distributions of polyelectrolyte solutions near a charged planar surface In this section, the model was applied to study polyelectrolyte solutions in order to evaluate the performance of the combination of hard chain and electrostatic functional terms. The residual electrostatic terms in Eq. 17 and Eq. 18 can be simply extended to calculate the electrostatic energy of charges in polyelectrolyte solutions, and the detailed expressions are provided in the Supporting Information. The developed model was used to predict the density profiles of polyelectrolyte solutions near a charged planar surface. The nonelectrostatic interaction between the surface and a polymer segment or a small ion is expressed as



∞ 0

β Vext , i ( z ) = 

z < σi z > σi

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(26)

where z is the perpendicular distance between fluid and surface.

Figure 4. Density profiles of (a) polyion segments and (b) cations near a charged surface. The reduced surface charge density is Qσ2/e = 0.125. Solid lines: ePC-SAFT-DFT predictions; Dashed lines: PC-SAFT/MSA-DFT predictions; Symbols: MC simulation data. In the polyelectrolyte, a polyion is represented by a chain consisted of charged hard sphere, and a small ion is modeled as a charged hard sphere. Each polyion has 10 negatively charged segments (mi = 10). The polyion segments and small ions have the same size, and the valence is 1 for a polymer segment, +1 for a small cation, and -1 for a small anion. Figure 4 displays the density profiles of the polymer segments and small cation at different polyion segment bulk densities, i.e. 0.06, 0.1, 0.15 and 0.2. The concentration of anions in the bulk is small and has negligible influence on the polyion distribution. At high concentrations, polyions are accumulated near the surface due to the electrostatic attraction from the oppositely charged surface. The ePC-SAFT-DFT successfully captures the secondary peak (at z ≈ 2σ) of polyion density profile, which suggests a layering structure of polyions. In general, the predictions of ePC-SAFT-DFT and PC-SAFT/MSA-DFT are similar and are in good agreement


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with MC data43, 44. Based on the above results, it is clear that the prediction of the developed ePC-SAFT-DFT model agrees with the molecular simulation data and the prediction of PC-SAFT/MSA-DFT, which indicates the model’s reliability.

C. IL systems in nano slit-like and cylindrical pores 1. Pure IL in slit pores In this section, the model was used to study the real IL systems. We first consider the pure IL in slit pores, and the IL is represented as an asymmetric electrolyte using our coarse-grained model. The bulk concentrations of cation and anion are the same.

Figure 5. (a) The averaged density of [C6mim][Tf2N] in silica slit pores (with pore size H = 2.0, 3.0, 4.0, 5.0 nm) at 333 K and 10 bar. Solid line is for IL in silica slit pore, dashed line is for the bulk IL. (b) The density distribution of [C6mim]+ in silica slit pores (with pore size H = 3.0, 5.0 nm) at 333 K and 10 bar. Solid line is for 3.0 nm pore. Dotted line is for 5.0 nm pore, dash-dot line is for the bulk IL. The profile of H = 3 nm was shifted right by 1 nm. Only half of the profiles are shown since the other half is its mirror image. Figure 5(a) shows the averaged density of [C6mim][Tf2N] confined in the silica slit pore with pore width H = 2.0, 3.0, 4.0, 5.0 nm, at 333 K and 10 bar. The densities of the IL confined in



silica slit pores were found to be lower than those of the bulk IL, and the averaged density increases with increasing pore width. A similar trend was observed for other ILs in the slit pore. It is expected that the density of the confined IL will approach the bulk density value for a larger pore. Figure 5(b) shows density profiles of the cation in 3 and 5 nm. Due to the strong solid-fluid interaction, the density of IL adjacent to the wall is very much higher. Long-range oscillatory density profiles were observed for both narrow and large pores. In the large pores, the densities at the pore center tend to be very close to the bulk value. Similar layering structures of the confined fluids have been observed in many simulation works.39, 45 2. CO2/IL in slit pores The solubility of CO2 in the bulk IL was predicted by ePC-SAFT. For example, Figure 6 shows the calculated CO2 solubility in the bulk [C6mim][Tf2N], and the experimental results46, 47 were included for comparison. It can be observed that the CO2 solubility increases with increasing pressure. Compared to the experimental data, the model prediction shows slight deviations at 30-90 bars. More detailed analyses of model prediction of bulk solubility of CO2 are available elsewhere.26

Figure 6. Saturated concentration of CO2 in the bulk [C6mim][Tf2N] at 333 K. Symbols: experimental data. Lines: prediction of ePC-SAFT.


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Figure 7. (a) Solubility of CO2 in the [C6mim][Tf2N] confined in silica at 333 K. Symbols, MC simulation data, filled circles are for the IL in 2.5 nm silica and open circles are for the bulk IL. Lines: prediction of ePC-SAFT-DFT, solid line, dashed line and dash-dot-dot line are for the IL in the silica with pore size H = 2.5, 5 nm, and the bulk IL, respectively. (b) Density profiles of CO2 and IL in the silica slit pore at 333 K and 16.1 bar. ePC-SAFT-DFT model was further used to study the properties of CO2/IL mixture in the silica slit pore. Figure 7 (a) shows the calculated absorption isotherms of CO2 in the [C6mim][Tf2N] confined in the silica slit pore. The solubility of CO2 is higher in the IL confined in narrow pore than in the corresponding bulk IL, and it generally decreases with increasing pore size. The trends are the same as that observed by Shi and Luebke23 through isostress-osmotic Monte Carlo simulations. The solubility data of CO2 in the [C6mim][Tf2N] confined in 2.5 nm silica slit pore and that in the bulk [C6mim][Tf2N] from simulation by Shi and Luebke23 were also included in Figure 7 (a) as filled and open symbols. The predicted CO2 solubility from ePC-SAFT-DFT is higher than that from simulation. The difference may be partially from the difference of the predicted bulk solubility and the difference on the confined systems (in our modeling, the system is open which means fluids in the nanopore are in equilibrium with a bulk reservoir). Another reason may be that the fluids are represented by coarse-grained model in our ePC-SAFT-DFT



model which is different from that by force field in molecular simulation. To get a further understanding of difference on the CO2 solubility in silica confined IL and bulk IL, we analyzed the density distributions of components in the pore. Figure 7 (b) shows the density distributions of CO2 and IL-ions in the silica pore. We can find that some CO2 molecules are located near the wall, and other CO2 molecules are absorbed inside the IL. The amount of CO2 absorbed in the first two layers of the IL near the surface is much larger than that in bulk IL. It suggests two competitive mechanisms affect the solubility in nanopore, one is adsorption near the pore surface, and the second is absorption inside the IL. These mechanisms can also be found in the uptake of gas in organic solvent confined in nanopore by both experiment and molecular simulation.20 The IL-ions play an important role in determining the CO2 solubility. For example, the strong dependence of CO2 solubility on anions has been reported by some experimental studies.48 In this work, the influences of alkyl chain length and the choice of anion on the CO2 solubility in the IL confined in nanopore were investigated. Figure 8(a) displays the model results of the CO2 solubility in the ILs with the same anion [Tf2N]- in 2.5 nm pore. The results show that the CO2 solubility in the confined IL increases with increasing alkyl chain length of the cation, i.e. [C2mim][Tf2N]

Developing Electrolyte Perturbed-Chain SAFT Density Functional

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