Hindered Gas Transport through an Aqueous Salt Solution Interface

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Hindered Gas Transport through Aqueous Salt Solution Interface Gang Fang, and Jige Chen J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.8b05495 • Publication Date (Web): 24 Aug 2018 Downloaded from http://pubs.acs.org on September 4, 2018

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The Journal of Physical Chemistry

Hindered Gas Transport through Aqueous Salt Solution Interface Gang Fang1, 3, Jige Chen1, 2, * 1

Division of Interfacial Water and Key Laboratory of Interfacial Physics and

Technology, Shanghai Institute of Applied Physics, Chinese Academy of Sciences, Shanghai 201800, China 2

Computational Science and Engineering Laboratory, Department of Mechanical and Process Engineering, ETH Zurich, Zurich 8092, Switzerland 3

University of Chinese Academy of Sciences, Beijing 100049, China

ABSTRACT Gas transport through water plays an important role in various natural processes and applications as the most common form in liquid-gas transport. Conventionally, it is expected that the flux of gas through water would be determined by the gas solubility and diffusion in water. However, it is still unclear whether such behavior holds in aqueous salt solutions. In this paper, we find that the methane transport is heavily hindered through the aqueous salt solutions by molecular dynamics simulations. Surprisingly, the hindrance to methane is not caused by the methane solubility or the diffusion change in aqueous salt solutions, but by the gas concentration barrier at the liquid-gas interface. Our simulation results show that the gas concentration barrier originates from the variance of mass density profile in aqueous salt solutions. Furthermore, it is found that the flux of methane is negative linear dependent upon the gas concentration barrier at the liquid-gas interface by investigating various salt solutions with different cations and anions, e.g., Na+, K+, Mg2+, Ca2+, Cl-, Br-, and in different concentrations and at different temperatures. Our work implies the gas

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accumulation at the liquid-gas interface as the deciding factor for gas transport through liquid and would be helpful in liquid-gas transport applications like shale gas and flammable ice exploitation.

INTRODUCTION Gas transport through water, as the most common form of gas transport phenomenon across liquid-gas interface,1-3 plays an essential role for the living matter and the nature of its interactions with various physical, chemical, biological systems continues to be at the forefront of current research in many fields of science.4-8 For example, gas transport in the blood circulation is one of the key physiological activities in the process of metabolism,9 and gas molecules would spontaneously accumulate on certain positions of proteins in cells and disable some biochemical functions, which is known as air anesthesia in medical applications.10 During the exploitation of shale gas and flammable ice, natural gas molecules, particularly methane molecules, are collected through the liquid-gas interface,11-13 and the interfacial gas transport efficiency is the key factor that determines the exploitation rate. Since gas transport through water is usually regarded as a typical diffusion processes, therefore the conventional thought about the flux of gas through water is that it is determined by the gas solubility and its diffusion coefficient in water.14-17 Meanwhile, water in nature always contains salt ions and thus exhibits quite different properties comparing with pure water.18-19 The existence of salt ions exhibits strong interactions with the water molecules around them and forms hydration shells,20-22 which brings a huge change in the hydrogen bond network,22-28 viscosity,29 electrical


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conductivity,30 density,31 etc., in the aqueous salt solutions, and leads to different behavior in chemical reactions, protein folding, and many other processes in water.32-34 For example, anomalous crystallization, spacing control between graphene oxide membranes and enhanced stability of graphene oxide membrane would be realized in aqueous salt solutions due to the cation-π interactions,35-37 a S-shaped velocity profile would be induced by the viscosity change in aqueous salt solutions flow,38 etc. Furthermore, compared to the pure water, ions in aqueous salt solutions, particular on the air/water interface, would also induce the specific properties and phenomena.39-41 For example, heavier halogen anions have a propensity for the interface that is proportional to their polarizability, ions at the air/water interface are important for atmospheric chemistry involving ocean surfaces and seawater aerosols, many salts (such as NaCl) tend to inhibit bubble coalescence.42 Despite the significant influence of salt ions upon the structure and transport properties of water, there is still a lack of studies about the gas transport through the aqueous salt solutions and across the aqueous salt solution-gas interface. In particular, it remains an open question, instead of gas solubility and diffusion coefficient, whether other changes in the aqueous salt solutions would influence the flux of gas. In this paper, we study the methane transport through the aqueous salt solutions by molecular dynamics simulations. Comparing with pure water, the flux of methane is heavily hindered up to only 12-56% of the original value through the aqueous salt solutions. It is found that the methane permeation across the liquid-gas interface is sensitive to the mass density profile of the aqueous salt solutions and it leads to



excessive methane accumulation at the interface that hinders the methane transport through the aqueous salt solutions. A negative linear correlation of the methane flux upon the gas concentration barrier at the liquid-gas interface is obtained.

METHODS

Figure 1. Snapshots of typical simulation systems around 0 ns and 100 ns: (a) NaCl system (b) pure water system.

Figure 1a and 1b show the snapshots of NaCl and pure water systems around 0 ns and 100 ns. Both of them are consisted of a solution layer with the thickness of ~10.0 nm at z axis, 150 gas molecules (methane) and 4 fixed solid sheets. The left and right sheets, with the horizontal distance of 20.0 nm at z axis, are used to prevent the periodic diffusion of gas. The middle sheets, with the vertical distance of 4.0 nm at y axis, are boundaries of the solution layer. The detailed snapshot of the pure water simulation system with the periodic boundary condition lines is shown in PS1 in the supplementary material. Water layer in each kind of aqueous salt solutions contains single kind of chloride salts (e.g., NaCl, KCl, MgCl2, CaCl2) with the typical


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concentration of 1.76 mol/L (M) (1.0 u). Two NaCl systems with the different NaCl concentrations of 0.88 M (0.5 u) and 3.52 M (2.0 u) are also considered. The whole system is divided into three regions as high-density region (of gas), solution region, and low-density region (of gas). The high-density region and low-density region are 5.0 nm long at z axis. Initially, gas molecules are randomly distributed in the high-density region and no gas molecule is in the low-density region. In our simulation, we chose methane as the typical example of the gas molecule because it is a simple and common type of gas and is known as the main components of natural gas, shale gas and flammable ice. The simulation box is 5.042 × 4.260 × 20.000 nm3 in x, y, z directions and the periodic boundary condition is applied to all x, y, z three directions. The simulation is performed in the NVT ensemble at 300 K by Gromacs 4.5.5.43 GMX force field is used to describe the interactions between different molecules.44 We chose GMX force field because this force field is one of the most common force fields used in the molecular dynamics simulations, and it is a reliable force field to model both methane molecule and aqueous salt solutions.11, 45-46 The SPC/E water model is used and the long-range electrostatic interaction is treated with Particle-Mesh Ewald (PME) method with a real space cutoff of 1.2 nm. The cutoff distance of the van der Waals (vdW) interaction is set up to be 1.2 nm as well. The Lennard-Jones parameters of the carbon atom of the left and right solid sheets are εcc = 0.000 kcal/mol and σcc = 3.374 Å. While the Lennard-Jones parameters and charges of other atoms (C, O, H) and ions (Na+, K+, Mg2+, Ca2+, Cl-, and Br-) are set according to the forcefield. The total



simulation time is 200 ns with a time step of 2 fs and 5 simulations from different initial conditions are performed to obtain the ensemble averages. The output data is collected per 500 steps.

RESULTS AND DISCUSSION

Figure 2. Gas transport through solution layer. (a) Transported number of gas molecule NL through the solution layer of pure water (red line) and NaCl (green line), KCl (blue line), MgCl2 (cyan line), CaCl2 (pink line), NaCl (0.5 u) (yellow line), NaCl (2.0 u) (brown line) systems. (b) Density profile of gas ρG(z) and the overall mass density ρM(z) in the typical NaCl system at z axis. The dark blue line represents the location of liquid-gas interfaces. S1 and S2 are the gas accumulation area of ρG(z) and they are colored pink and blue. (c) Density of gas ρG(z,y) at z-y plane in the typical NaCl system around 100 ns.

The whole transport of gas through solution layer can be divided into four parts: adsorption, dissolution, diffusion and desorption. We define NH, NS and NL as the


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numbers of gas molecules in the corresponding high-density region, solution region and low-density region, respectively. The liquid-gas interface at z axis is defined according to the relative density of water at 50% of the density value in bulk water. The solubility of gas NS is defined as the number of gas molecules in the solution layer between two liquid-gas interfaces. The transported number of gas molecule through solution layer is represented by NL. The flux of gas is presented by the increasing rate of NL as dNL/dt. Figure 2a shows the transported number of gas NL in the pure water and NaCl, KCl, MgCl2, CaCl2, NaCl (0.5 u), NaCl (2.0 u) systems. We find that NL in the pure water system is highest, increasing rapidly with the simulation time from 0 at 0 ns to 22.3 at 200 ns. For the NaCl and KCl system, NL increases slower, reaching 9.5 and 12.5 at 200 ns, which are only 42% and 56% of the original value NL in the pure water system. For the MgCl2 and CaCl2 systems, NL is even much lower at the values of 4.8 and 2.7 at 200 ns, which are only 21% and 12% comparing with the pure water system. To investigate the influence of different concentrations of the salt solution, we also calculate the NL in the NaCl (0.5 u) and NaCl (2.0 u) systems at 200 ns to be 12.4 and 6.6, as only 55% and 29% of the original value NL in the pure water system. The results indicate the flux of gas would be heavily hindered by replacing the pure water into aqueous salt solutions. We also check the effect of the thickness of the solution layer on the gas flux by taking the pure water system as a typical example and the result is shown in PS2 in the supplementary material.



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In order to understand the microscopic origin of the hindrance, we tend to study the gas distribution and its relative transport properties in the aqueous salt solutions. First, we define the gas density in the z-y plane to be ρG(z,y) as, t0 + t2

ρG ( z , y ) =

∑N

G

( z, y)

t0 + t1

SG ( z , y ) × (t2 − t1+1)

(1)

where NG(z,y) is the sum of the number of gas molecules presented in per block at z-y plane over the system samples, t0 corresponds to the system sample in the typical time we chosen to calculate the ρG(z,y) which is 100 ns, t1=0 and t2=1000 corresponds to the system samples at 100 ns and 101 ns , SG(z,y) is the area of this block which is 0.1 nm × 0.1 nm, and (t2-t1+1) is the total number of the samples to do the summation. The corresponding gas density at z axis ρG(z) can be calculated as, t = t2

ρG ( z ) =

∑N

G

( z)

t = t1

l ( z ) × (t2 − t1 + 1)

(2)

where NG(z) is the number of gas molecule in per slice at z axis, t1=100,000 and t2=200,000 correspond to the system samples in the corresponding times to calculate the summation which are ranging from 100 ns to 200 ns, l(z) is the length of this slice at z axis which is 0.1 nm in our calculation, (t2-t1+1) is the total number of the samples to do the summation. Similarly, to understand the overall density profiles in the aqueous salt solutions, the mass density of aqueous salt solutions ρM(z) could be calculated as, t = t2

ρM ( z) =

∑[N

G

( z )mG + N S ( z )mS + N Ions ( z )mIons ]

t =t1

l ( z ) ×（t2 - t1 +1）


(3)

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where NG(z), NS(z), NIons(z) are the numbers of gas molecules, water molecules and ions in per slice at z axis and mG, mS, mIons are the molar mass of gas, water and ions, t1=100,000 and t2=200,000 correspond to the system samples in the corresponding times to calculate the summation which are ranging from 100 ns to 200 ns, l(z) is the length of this slice at z axis which is 0.1 nm in our calculation, (t2-t1+1) is the total number of the samples to do the summation. Figure 2b shows the ρG(z) in the typical NaCl system and we find that ρG(z) in the high-density region has an accumulated structure at liquid-gas interface. Two accumulation peaks, which are located at z=4.7 nm and z=5.3 nm, show high density of adsorbed gas near the liquid-gas interface with the values of 43.3 nm-1 and 67.3 nm-1. S2 is the gas accumulation region near the solution layer at the liquid-gas interface, and S1 is the gas accumulation region near the gas phase at the liquid-gas interface. Later it shows that the gas concentration barrier (∆S=S2-S1) behaves like a barrier for the gas molecules to permeate into the solution layer, which plays a dominant role in the hindrance to the overall flux of gas through the aqueous salt solutions. Correspondingly, the mass density ρM(z) in the typical NaCl system is also illustrated. It implies that the gas accumulation peak near the solution layer corresponds to the initial position of the mass density profile increase in the solution region, where the value of ρM(z) keeps stable at 30 u/nm in the high-density region and increases to 1200 u/nm in the solution region. Figure 2c shows the ρG(z,y) in the typical NaCl system around 100 ns. The ρG(z,y) for other systems (pure water, KCl, MgCl2, CaCl2 and NaCl (0.5 u), NaCl (2.0 u)) around



100 ns are illustrated in PS3 in the supplementary material. For the NaCl system, we find that ρG(z,y) in the high-density region is >5.0 nm-2, while ρG(z,y) in the low-density region is 10.0 nm-2), which provides the 2D view of the gas accumulation behavior, as well as the snapshot of the NaCl system in Figure 1a and the ρG(z) results in Figure 2b.

Figure 3. Dissolution and diffusion behavior of gas molecule in aqueous salt solutions. (a) Time variation and average value of the gas molecules number in the solution region NS of pure water (red line/bar), NaCl (green line/bar), KCl (blue line/bar), MgCl2 (cyan line/bar), CaCl2 (pink line/bar), NaCl (0.5 u) (yellow line/bar) and NaCl (2.0 u) (brown line/bar) systems. (b) Relation between dNL/dt and NS. (c) MSD (2) and diffusion coefficient d of gas molecule in the solution region of pure water (red line/bar) and NaCl (green line/bar), KCl (blue line/bar), MgCl2 (cyan


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line/bar), CaCl2 (pink line/bar), NaCl(0.5 u) (yellow line/bar) and NaCl(2.0 u) (brown line/bar) systems. (d) Relation between dNL/dt and d.

In order to reveal the microscopic origin of the gas transport hindrance, we first calculated the number of dissolved gas molecules in the solution region NS to check the effect of gas solubility. As shown in Figure 3a, the numbers of gas molecules NS in all solution systems are stable with simulation time that correspond to their respective solubility. The average values of NS are 8.25, 7.16, 8.57, 6.43, 5.24, 9.03, 6.72 in the pure water, NaCl, KCl, MgCl2, CaCl2, NaCl (0.5 u) and NaCl (2.0 u) systems. The relation between dNL/dt and NS is shown in Figure 3b. The variation of gas flux value is non-monotonic by changing the solubility value, which is against the conventional idea that a large solubility means a proportional increase of gas molecules releasing into the low-density region. Meanwhile, the variance of the solubility is quite small from 6.72-9.03 with only 25% difference, and the corresponding flux of gas varies from 2.7-22.3 with a magnitude difference. Therefore, the slightly difference in the solubility of gas cannot be the microscopic mechanism leading to the heavy hindrance to the gas flux. Second, we consider the influence of gas diffusion in the solution region upon the total flux of gas. In Figure 3c, the time variations of the mean square distance (MSD) of gas molecule in the solution region are calculated as 2. It shows that gas molecule diffuses more quickly in the aqueous salt solutions than in the pure water. The diffusion coefficient d is used as a quantitative measure for the gas diffusion capability by linearly fitting the MSD curve. It is found that the values of d are



1.628×10-5 nm2/ps, 1.995×10-5 nm2/ps, 2.050×10-5 nm2/ps, 2.200×10-5 nm2/ps, 2.283×10-5 nm2/ps, 1.950×10-5 nm2/ps, 2.150×10-5 nm2/ps for the corresponding systems of pure water, NaCl, KCl, MgCl2, CaCl2, NaCl (0.5 u) and NaCl (2.0 u). To make it clearer, we also compared the diffusion coefficient d of gas molecule in both pure water and NaCl systems with an enlarged simulation box (10.000 × 10.000 × 10.000 nm3) and the similar values of d are obtained (see details in PS4 in the supplementary material). In Figure 3d, the relation between dNL/dt and d is illustrated. The variance of diffusion is also very small from 1.628-2.283×10-5 nm2/ps, with only 28% difference. More importantly, it reveals an unexpected opposite dependence against the conventional thoughts, where a higher diffusion coefficient value corresponds to a lower flux of gas. Therefore, it infers that the change in gas diffusion cannot be the microscopic mechanism of the hindrance to the gas flux.

Figure 4. Diffusion behavior of gas molecule in the solution region. (a) Number of hydrogen bonds NHB in pure water (red bar) and NaCl (green bar), KCl (blue bar), MgCl2 (cyan bar) and CaCl2 (pink bar), NaCl (0.5 u) (yellow bar), NaCl (2.0 u) (brown bar) systems. (b) Relation between NHB and the diffusion coefficient of gas d


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in the solution region. (c) Gas density ρG(z) in pure water (red line) and NaCl (green line), KCl (blue line), MgCl2 (cyan line), CaCl2 (pink line), NaCl (0.5 u) (yellow line) and NaCl (2.0 u) (brown line) systems. (d) Relation between diffusion coefficient of gas d and the gradient of ρG(z) along z axis dρG(z)/dz in pure water (red bar) and NaCl (green bar), KCl (blue bar), MgCl2 (cyan bar), CaCl2 (pink bar), NaCl (0.5 u) (yellow bar), NaCl (2.0 u) (brown bar) systems.

In order to understand the diffusion coefficient change and its influence upon the transport of gas, we consider the number of hydrogen bond and the flux of gas in the solution region. Based on the geometric criterion, the hydrogen bond between two water molecules is defined as the O-O distance is less than 3.5 Å and the angle H-O⋅⋅⋅O is less than 30°. The gas diffusion would be dependent upon the interactions in the solution, which could be measured by the hydrogen bond network between the water molecules. Figure 4a shows the average number of hydrogen bonds (HB) NHB of per water molecule in both pure water and NaCl, KCl, MgCl2, CaCl2, NaCl (0.5 u), NaCl (2.0 u) systems. It is found that NHB in the pure water is largest with the value of 1.705. While in the other aqueous salt solutions, NHB is smaller, with the values of 1.547, 1.538, 1.365 and 1.300, 1.618, 1.430 for the corresponding NaCl, KCl, MgCl2 and CaCl2, NaCl (0.5 u), NaCl (2.0 u) systems. The reduced NHB in the aqueous salt solutions indicates that the HB network is not as stable as the HB network in the pure water system, which would enhance the diffusion of gas molecules across them. Figure 4b confirms such relationship that a smaller NHB results to a higher diffusion coefficient d.



The frequent breaking process of HB network in the aqueous salt solutions suggests instability of the water structure and provides more probability for gas molecules to diffuse in the solution region. In Figure 4c, the flux of gas in the solution region is illustrated separately, where the gas molecule transports faster in the salt solutions than in the pure water. In Figure 4d, it illustrates the relation between diffusion coefficient of gas d and the gradient of ρG(z) along z axis (dρG(z)/dz) in pure water and NaCl, KCl, MgCl2, CaCl2, NaCl (0.5 u), NaCl (2.0 u) systems. The positive dependence of dρG(z)/dz upon d confirms the faster gas transport in the solution region due to the enhanced gas diffusion.

Figure 5. (a) Gas accumulation at the liquid-gas interface of ρG(z) in pure water (red line) and NaCl (green line), KCl (blue line), MgCl2 (cyan line), CaCl2 (pink line), NaCl (0.5 u) (yellow line) and NaCl (2.0 u) (brown line) systems. The dashed line


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represents the position of gas accumulation peak near the solution phase. S1 and S2 are the gas accumulation area of ρG(z) near the gas phase and near the liquid phase respectively. (b) Total mass density ρM(z) in pure water (red line) and NaCl (green line), KCl (blue line), MgCl2 (cyan line), CaCl2 (pink line), NaCl (0.5 u) (yellow line) and NaCl (2.0 u) (brown line) systems. (c) Approximate linear relation between the flux of gas dNL/dt and the gas concentration barrier ∆S=S2-S1. Simulation results of NaCl model systems and pure water system at different temperatures and NaBr systems are also included.

As illustrated in Figure 2b, the mass density change at the liquid-gas interface leads to gas accumulations S1 near the gas phase and S2 near the solution phase. In Figure 5a and 5b, they illustrate the gas density profiles ρG(z) and mass density profiles ρM(z) in all solution systems to represent the different gas accumulations. Similarly, it is found that the peaks of the gas accumulation S2 near the solution phase correspond to the respective initial positions of mass density increase. As a typical diffusive process from high-density region to the low-density region, the larger gas accumulation S2 near the solution phase would spontaneously cause a negative effect of flux to the smaller gas accumulation S1 as a hindrance effect. In order to confirm that such negative effect at the liquid-gas interface is the deciding factor of the hindrance to the overall flux of gas, we consider the gas concentration barrier according to the ρG(z) at the liquid-gas interface as, z2

z1

z1

z0

∆S = S 2 − S1 = ∫ ρ G ( z )dz − ∫ ρ G ( z )dz


(4)


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where ρG(z) is the density of gas molecules along z axis, the integration limits z0=4.4, z1=4.9, z2=6.4 are determined according to the location of ρG(z), where ρG(z) reaches the stable values in the high-density/solution region as well as the trough between two peaks which corresponds to z1=4.9. The integration limits z0=4.4 and z2=6.4 are determined according to deviation between the former and the later values of ρG(z) less than 5%. Figure 5c reveals an approximate negative linear correlation between dNL/dt and the ∆S as,

dN L = −k × ∆S + b dt

(5)

where k=0.0381 ns-1, and b=0.1644 ns-1. The negative linear correlation in all solution systems implies that the hindrance is determined by the excessive gas accumulation at the liquid-gas interface. To transport through the aqueous salt solutions, gas molecules have to permeate into the solution phase, and the gas accumulation acts as a barrier that heavily hinders such process. The microscopic mechanism of this gas accumulation behavior could be attributed to the extra potential energy barrier for gas due to the concentrations of ions (please see PS8 in the supplementary material). Furthermore, in order to verify such microscopic mechanism under different conditions, we tend to investigate the effect of cations and temperature. Simulations with model NaCl system by varying the valence number of Na to be +2, +3 and +4, and simulations with the pure water system by varying the temperature of water from 280 K to 340 K, and simulation with the NaBr system with the concertation of 1.76 mol/L are performed (please see PS5, PS6 and PS7 in the supplementary material). It


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is found that the dependence of the gas flux dNL/dt upon the gas concentration barrier

∆S also fits well with the negative linear correlation in Figure 5c.

CONCLUSION In summary, we used molecular dynamics simulations to study the transport of gas through various aqueous salt solutions like NaCl, KCl, MgCl2, CaCl2, NaBr, etc, in different concentrations and at different temperatures. The flux of gas would be heavily hindered up to 12-56% of the flux value in pure water. Unlike the conventional thoughts, the gas solubility and diffusion in solution are not the microscopic origin of such hindrance. It is found that gas molecules would be accumulated at the liquid-gas interface due to interfacial mass density change that leads to the hindrance effect. The reduction of the flux of gas is found to be linearly dependent upon the gas concentration barrier at the interface. Our work reveals the microscopic process of gas transport process across the aqueous salt solutions, which implies the deciding role of gas accumulation at the liquid-gas interface. It provides new ideas to manipulate the process of liquid-gas transport process and might be helpful in liquid-gas transport applications like shale gas and flammable ice exploitation.

Supplementary Material Snapshot of the typical pure water system with the periodic boundary condition line, Gas flux through pure water layer of different thicknesses, Density distribution of gas



ρG(z,y) in pure water, KCl, MgCl2, CaCl2, NaCl(0.5 u) and NaCl(2.0 u) systems around 100 ns, Compared diffusion coefficient of methane in enlarged simulation box of both pure water and NaCl systems, Results of the NaCl model systems by varying the valence number of Na to be +2, +3 and +4, Results of the pure water systems by changing the water temperature to be 280 K, 320 K, 340 K, Results of the NaBr system, Extra potential energy barrier due to the concentrations of ions.

AUTHOR INFORMATION * Address correspondence to [email protected].

NOTES The authors declare no competing financial interests.

ACKNOWLEDGMENTS This work was supported by National Natural Science Foundation of China (#11405245), and Schweizer Bundes Exzellenz Stipendium of Switzerland (#2017.0475), and the Key Research Program of Chinese Academy of Sciences (#KJZD-EW-M03). The authors also thank the China Scholarship Council, Shanghai Supercomputer Center of China, and Supercomputing Center of the Chinese Academy of Sciences.

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TOC Graphic

The flux of methane molecule across the aqueous salt solutions would be heavily hindered due to the gas concentration barrier at the liquid-gas interface. A negative linear correlation of the flux of methane upon the gas concentration barrier is obtained.


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Hindered Gas Transport through an Aqueous Salt Solution Interface

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