Molecular Dynamics Simulations of Noble Gas Fractionation during

Dec 4, 2018 - Previous studies suggested that the incorporation of noble gas atoms is dependent upon the structure rather than the environment. In thi...
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Molecular Dynamics Simulations of Noble Gas Fractionation during Diffusion through Silica Nanopores Xin Ding,*,†,‡ Zongyang Qiu,†,§ Kun Qu,∥ and Zhenyu Li§ ‡

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Chinese Academy of Sciences (CAS) Key Laboratory of Crust−Mantle Materials and Environments, School of Earth and Space Sciences, §Hefei National Laboratory for Physical Science at the Microscale, and ∥Division of Molecular Medicine, Hefei National Laboratory for Physical Sciences at the Microscale, CAS Key Laboratory of Innate Immunity and Chronic Disease, CAS Center for Excellence in Molecular Cell Sciences, School of Life Sciences, University of Science and Technology of China, Hefei, Anhui 230026, People’s Republic of China S Supporting Information *

ABSTRACT: Ne retention and slight enrichment of Kr−Xe relative to atmospheric levels have been found in biogenic chert samples. Previous studies suggested that the incorporation of noble gas atoms is dependent upon the structure rather than the environment. In this study, we perform molecular dynamics simulations of dissolved noble gas atomic diffusion through 1−4 nm diameter silica pores. Bulk-liquidlike water does not exist in the 1 nm diameter nanopores, which hinder noble gas diffusion into or out of the pores. In ≥2 nm diameter nanopores, noble gas atoms transport with bulk-liquid-like water into the center of the pores but sizecontrolled diffusive separation occurs at the layer of surface water and in the interior of the silica structure. The motion of large atoms (Kr and Xe) in surface water is governed by significant adsorption. Relatively small Ne atoms are able to cross the surface water layer and diffuse into the crystal interior. As a result of its moderate size and the negligible interaction with the interfacial surface, Ar lies beyond the adsorption and silica structure diffusion regimes. Therefore, our simulation results indicate that noble gas entrapment is expected to occur in nanoscale fluid circulation during sediment-to-chert lithification. KEYWORDS: biogenic chert, diffusive separation, fluid circulation, lithification, noble gas entrapment

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INTRODUCTION Dissolved noble gases (Ne, Ar, Kr, and Xe) are used as natural tracers in aquatic systems to reconstruct the continental paleoclimate,1,2 track fluid transportation and mixing processes,3,4 and identify the source of groundwater contamination.5,6 However, the determination of relative parameters in bulk liquid water is not straightforward. Taking the diffusion coefficient as an example, experimental studies7−10 have determined the diffusion coefficients of Ne, Kr, and Xe in bulk liquid water, but the Ar diffusion coefficient in bulk liquid water has never been successfully measured. Holocher et al.11 estimated the Ar diffusion coefficient by extrapolation of other noble gas diffusion coefficients. Bourg and Sposito12 performed molecular dynamics (MD) simulations to investigate the diffusion coefficients of noble gases in liquid water; their results were consistent with the experimental data of Jähne et al.7 and the extrapolated Ar diffusion coefficient. However, fluid flow depends upon the characteristic of migration pathways. The transport of dissolved gases in carbon capture and storage,13−15 radioactive waste storage,16,17 and shale extraction18,19 occurs in a low-permeability environment generally involving nanopore structures. In contrast to the system of bulk liquid water, in which dissolved gases act as © XXXX American Chemical Society

insert tracers, studies in the past few years have indicated that dissolved gases in nanoporous media are affected by the hygroscopic effect and hydrophobic characteristics.20−22 Gadikota et al.23 presented MD simulation of noble gases partitioning into clay interlayer nanopores and suggested that the affinity of dissolved noble gases for clay surfaces is related to the size of the adsorbed molecules and the structure of the interfacial water by the clay surface. This finding may shed light on the mechanism of dissolved noble gas transportation in the context of fine-grained sedimentary rocks. Figure 1 illustrates noble gas concentrations and fractionation factors relative to the atmosphere. Young ocean sediment samples are composed of amorphous silica derived from skeletons,24−26 which display absolute F(Ne) depletion and F(Kr)−F(Xe) enrichment. As a result of the dehydration and recrystallization of amorphous silica, biogenic chert samples collected from limestone beds27,28 show variable degrees of F(Kr)−F(Xe) enrichment. Note that biogenic chert is also Received: Revised: Accepted: Published: A

September 25, 2018 December 3, 2018 December 4, 2018 December 4, 2018 DOI: 10.1021/acsearthspacechem.8b00136 ACS Earth Space Chem. XXXX, XXX, XXX−XXX

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ACS Earth and Space Chemistry

Figure 1. Noble gas concentrations reported in the literature.24−28 (a) Noble gas concentrations in young ocean sediments, (b) fractionation pattern of noble gases in young ocean sediments, (c) noble gas concentrations in biogenic cherts, and (d) fractionation pattern of noble gases in biogenic cherts. The solid green line depicts air-saturated seawater assuming a 10% porosity. The elemental abundance patterns of noble gases are expressed by the fractionation factor F(i) = (i/36Ar)sample/(i/36Ar)air, where i represents a noble gas element and air represents atmosphere air.

Figure 2. MD simulation model of a water-filled silica nanopore. (a) Cross section of the simulation box. The dished circle indicates the curved nanopore surface. (b) Side view of the simulation box. Water layers that cover both sides of the silica slab are partially shown as a result of the large length in the z direction. Atoms are color-coded as follows: silicon, yellow; oxygen in silica, red; oxygen in water, blue; and hydrogen in water, cyan.

characterized with F(Ne) ∼ 1. Matusubara et al.29 and Mitchell et al.30 found that the noble gas concentrations in biogenic chert are not influenced by different environments. Because the observed Ne concentration is consistent with 3−10% contribution of air-saturated seawater, Ne retention is not affected by the precursor of amorphous silica. Torgerson and Kennedy31 attributed the noble gas variations to fluid circulations during sedimentary lithification. Because the diffusion coefficient in bulk liquid water is a strong function of atomic mass, incomplete diffusion filling of lithic grains produces Ne enrichment and incomplete emptying of lithic grains generates a Kr- and Xe-enriched residual. However, this explanation31 requires another independent mechanism for noble gas entrapment into the chert structure; the authors suggested the potential role of angstrom-scale adsorption. As a follow-up to diffusion-controlled noble gas separation in sedimentary rocks, this study assesses the possible fractionation of dissolved noble gases by diffusion through silica nanopores. Because of the existence of solid−fluid interface interactions in the nanoscale regime, this paper employs MD simulations,

which can distinguish fluid transport characteristics at various pore size conditions. In combination with the geological history of fluid-circulating-related lithification, this study aims to explain Ne retention and Kr−Xe enrichment in biogenic cherts.

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MD SIMULATION Our simulation model consists of a ∼6 nm thick SiO2 glass slab featuring a cylindrical nanopore with a diameter of 1, 2, or 4 nm (Figure 2). The simulation cell is 31.646 × 36.541 × 190.0 Å3 for the 1 and 2 nm diameter pores and expanded twice in the x and y dimensions (63.291 × 73.083 × 190.0 Å3) for the 4 nm diameter pores. Undercoordinated surface O and Si atoms are saturated with H or OH groups.32,33 Detailed information on the SiO2 glass slab has been presented by Bourg and Steefel.34 Then, water molecules with a density of 1 g/cm3 are added to each simulation cell to fill the nanopore and form a thick water film on both sides of the glass slab. To simulate noble gas diffusion, single-component gas molecules (Ne, Ar, Kr, or Xe) are initially randomly placed. Ten noble gas atoms B

DOI: 10.1021/acsearthspacechem.8b00136 ACS Earth Space Chem. XXXX, XXX, XXX−XXX

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ACS Earth and Space Chemistry are placed outside of the 1 and 2 nm diameter nanopores, and 40 noble gas atoms are placed inside and outside of the 4 nm diameter nanopores. Following the choice of Bourg and Sposito12 and Bourg and Steefel,34 SiO2 and water are described by the CLAYFF35 and SPC/E model,36 respectively. The O−H bonds and H−O−H angle in water molecules are constrained by the SHAKE algorithm.37 The Lennard−Jones potential is used to calculate the interaction between atoms with arithmetic rules. Longrange Coulomb interactions are also treated and calculated by the Ewald summation method with 99.99% accuracy. A large cutoff (15.0 Å) is configured in the long-range interaction calculation. MD simulations are carried out in the NVT ensemble realized by the Nosé−Hoover thermostat at 298 K with a 1 fs time step. LAMMPS38 and VMD39 packages are used for simulation and visualization. Finally, sufficiently long MD trajectories are generated to observe and analyze the diffusion of water and noble gas (20, 20, and 6 ns simulation of 1, 2, and 4 nm nanopores, respectively).

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RESULTS AND DISCUSSION Density Distribution. Because the diffusion of noble gas atoms depends upon the behavior of the solvent system, the density distributions of water molecules in and outside the 1, 2, and 4 nm diameter pore systems are evaluated. Our calculation shows that the densities of water O atoms (ρOw) outside of 1− 4 nm diameter silica nanopores are 0.032−0.033 atoms/A3, similar to the value of bulk liquid water. Plots of ρOw versus distance from the curved silica pore surfaces (Figure S1 of the Supporting Information) reveal that the water density is bulkliquid-like at the center of ≥2 nm diameter pores but the adsorption peak lies ∼2.5 Å from the curved silica surface. Our observation is consistent with the MD simulation results of Bourg and Steefel,27 where the interaction between the silica surface and water molecules triggers the distortion of interfacial water. In the 1 nm diameter pores, ρOw exhibits strong oscillations reflecting the absence of bulk-liquid-like water. The decrease in pore diameter prevents optimal water− water bonding and enhances the steric effect. The analysis of noble gas density shows that noble gas atoms are difficult to diffuse into 1 nm diameter pores (Figure 3). Considering that the pore diameter is only ∼2.3−3.2 times larger than that of noble gas atoms, the 1 nm diameter pore performs as a constriction to filter noble gas atoms. The blocking of noble gas atoms at the pore entrance causes noble gas atoms to accumulate on both sides of the silica slab. Metadynamic simulations are performed to quantify the difficulty of noble gas atom diffusion into a 1 nm diameter nanopore. Detailed descriptions can be found in the Supporting Information. Our results indicate that there exist distinct energy barriers of about 2.0 kcal/mol for Ne atoms to diffuse into a 1 nm diameter nanopore. The disappearance of bulk-liquid-like water in the 1 nm diameter pores challenges the assumption that dissolved gas behaves as an insertion tracer in the water system. If a noble gas atom is trapped in a 1 nm diameter pore, then stagnant behavior is expected. With the increase in pore diameter (Figure 3), noble gas atoms are associated with the movement of bulk liquid water and start to diffuse into and diffuse out of ≥2 nm diameter pores. Figure 4 shows the noble gas density versus distance from the curved silica pore surfaces. In the 2 nm diameter pores, noble gas density patterns indicate the existence of adsorption peaks. These adsorption peaks for Ne, Ar, Kr, and Xe lie ∼2.5

Figure 3. Comparison of noble gas density profiles of 1−4 nm diameter pore systems along the z coordinate. The dashed lines indicate the position of the silica slab in the z direction.

Å from the curved silica surface, which is consistent with the position of the strongest ρOw oscillation. The interaction between the noble atom and silica surface is the origin of the adsorption on the silica surface. On the basis of the Ne density profile, Ne atoms can be divided into three expression forms: (1) adsorption close to the curved silica surface, (2) settlement in small “pockets” of the silica surface,12,32 and (3) transportation into the interior of the silica slab. The expression of Ar atoms is relatively simple, where Ar atoms are adsorbed on C

DOI: 10.1021/acsearthspacechem.8b00136 ACS Earth Space Chem. XXXX, XXX, XXX−XXX

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Figure 4. Density profiles of Ne, Ar, Kr, and Xe as a function of the distance from the curved silica surface of 2 and 4 nm diameter pores, calculated for z = 75−115 Å. The dark gray area represents the interior of the silica slab, and the light gray area represents the adsorption zone.

heterogeneous system. Two components of the diffusion coefficient, D∥ and D⊥ are calculated from the following equations:

the curved silica surface and ensconced in small pockets of the silica surface. Kr and Xe exhibit only adsorption to the silicate surface. The difference in density distributions can be attributed to the different sizes of noble gas atoms (radii of Ne, ∼0.51 Å; Ar, ∼0.88 Å; Kr, ∼1.03 Å; and Xe, ∼1.24 Å). When the size of a noble gas atom is as small as that of Ne, such an atom can traverse the adsorption layer and diffuse into the SiO2 crystal structure. In the 4 nm diameter pores (Figure 4), prominent adsorption peaks do not appear for Ne and Ar. The Ne atoms show a relative smooth density distribution at ∼6−16 Å from the curved silica surface, and the Ar atoms show a smooth density distribution at ∼6 Å from the curved silica surface toward the pore center. This finding is in agreement with the increased amount of bulk-liquid-like water, which reflects the tendency of small noble gas atom transportation with bulkliquid-like water. In contrast, Kr and Xe atoms produce the adsorption peaks. The location of these peaks lies ∼2.5 Å from the curved silica surface, which is the same position of the noble gas adsorption peaks in the 2 nm diameter pores and the strongest ρOw oscillation in the 4 nm diameter pores. It is clear that the large-sized noble gas atoms are controlled by the interaction between the noble atom and silica surface. In terms of the Ne density distribution, Ne atoms are not only associated with bulk liquid water but also stay inside the SiO2 structure. In comparison to the 2 nm diameter pore system, the increase in the surface area results in more chances to trap Ne atoms in the interior of the SiO2 crystal structure. Similarly, Ar atoms can be divided into two groups: (1) transporting with bulk liquid water and (2) settlement in small pockets of the silica surface. However, Kr and Xe atoms cannot diffuse into the silica crystal structure or become ensconced in small pockets of the silica surface. Water and Noble Gas Diffusion. The molecular-scale diffusion coefficient D is commonly calculated using the wellknown Einstein relation. However, Liu et al.40 proposed a modified method for calculating diffusion coefficients in the

D (zi ) = lim

t →∞

⟨[Δx 2(t ) + Δy 2 (t )]Si(t )⟩ ⟨Δz 2(t )Si(t )⟩ or lim i t →∞ 2dt ⟨S (t )⟩ 2dt ⟨Si(t )⟩

2 ⟨ψ i(t )ψni(0)Si(t )⟩ iLy D⊥(zi) = −jjj zzz lim n ⟨Si(0)⟩ k nπ { t →∞

(1)

(2)

Equation 1 calculates D∥ parallel to the silica slab surface outside the nanopore or D∥ parallel to the curved nanopore surface, in which Si(t) equals 1 if the molecule remains in the interested layer during the interval [0; t] or otherwise equals 0. Equation 2 calculates D⊥ perpendicular to the silica slab surface outside the nanopore, in which ψin(t) = sin(nπ(z(t) − zimin)/L), with n = 1 and L = (zimax − zimin). zimax and zimin are the boundaries of the ith layer. Each 1 ns trajectory is used, and D values are averaged from 5 to 20 ns in the case of 1 and 2 nm diameter nanopore systems and from 4 to 6 ns in the case of the 4 nm diameter nanopore system. Calculated diffusion coefficients from the Einstein relation and equations of Liu et al. are listed in Tables S1 and S2 of the Supporting Information. Both methods give similar D values for water molecules (DOw) and noble gas atoms (DNG) outside of 1−4 nm diameter silica nanopores. Because of the requirements to calculate area-specific diffusion coefficients, DOw and DNG in the nanopore are approached merely by equations of Liu et al. DOw values outside of 1−2 nm diameter silica nanopores have D∥ of (3.25 ± 0.11) × 10−9 m2 s−1 and D⊥ of (2.57 ± 0.06) × 10−9 m2 s−1. DOw values outside of 4 nm diameter silica nanopores have D∥ of (2.90 ± 0.06) × 10−9 m2 s−1 and D⊥ of (2.53 ± 0.14) × 10−9 m2 s−1. These results are close to previous studies41,42 of the self-diffusion coefficient of bulk liquid SPC/E water of ∼2.84 × 10−9 m2 s−1. The DOw values in D

DOI: 10.1021/acsearthspacechem.8b00136 ACS Earth Space Chem. XXXX, XXX, XXX−XXX

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ACS Earth and Space Chemistry silica nanopores (calculated for z = 75−115 Å) show a strong dependence upon the pore size and location. In the 1 nm diameter pores (Figure 5), water molecules do not possess the

Figure 5. Diffusion coefficients of water molecules (DOw) in and outside 1, 2, and 4 nm diameter pores. DOw values in nanopores are plotted as a function of the distance from the curved silica pore surface, calculated for z = 75−115 Å. DOw values in different areas are separated by the vertical lines. Figure 6. Diffusion coefficients of noble gas atoms (DNG) along the z direction in and outside (a) 2 nm and (b) 4 nm diameter pores. DNG values in nanopores are plotted as a function of the distance from the curved silica pore surface. DNG values of entrapped atoms in silica slab are calculated for z = 65−125 Å. DNG values of adsorbed atoms and those in bulk-liquid-like water are calculated for z = 75−115 Å.

property of bulk-liquid-like water, where water molecules move very slowly in the confinement with D∥ of (0.18 ± 0.03) × 10−9 m2 s−1. In the 2 and 4 nm diameter pores (Figure 5), the bulk-liquid-like water at the center of the pores (>5 Å from the curved silica surface) have diffusion coefficients D∥ of (1.83 ± 0.08) × 10−9 and (2.01−2.42) × 10−9 m2 s−1, respectively. However, the remaining water molecules close to the curved silica surface become relatively immobile on diffusive time scales. Our calculations show that the noble gas diffusion coefficient outside of the pores follows the sequence of DNe > DAr > DKr > DXe, which is consistent with a mass-dependent inverse power law in bulk liquid water.12,43,44 However, the simulation systems are not pure liquid water, yielding the slightly higher noble gas diffusion coefficient values of DNe ∥ = (5.48 ± 0.51) × −9 10−9 m2 s−1, DAr m2 s−1, DKr ∥ = (3.22 ± 0.15) × 10 ∥ = (2.76 ± −9 0.04) × 10−9 m2 s−1, and DXe m2 s−1. ∥ = (2.27 ± 0.03) × 10 The corresponding D⊥ values are close to D∥, where the detailed calculation results can be found in the Supporting Information. Figure 6 illustrates the variations in diffusion coefficients along the distances to the curved nanopore surfaces. In the 2 nm diameter pores, Ne atoms can transport back and forth between the adsorption area (0 < d < 5 Å) and pore center (5 −9 < d < 10 Å), where DNe and 4.39 × 10−9 ∥ values are 0.88 × 10 m2 s−1, respectively. Once Ne atoms diffuse into the small pocket of the silica surface or the interior of the silica slab, DNe ∥ decreases to approximately 0.039 × 10−9 m2 s−1. The DAr profiles are similar to those of Ne atoms, where adsorbed and dissolved Ar show diffusion coefficients from 0.60 × 10−9 to 1.58 × 10−9 m2 s−1, and the ensconced Ar atoms show immobility. In contrast, Kr and Xe appear only as the combination of adsorption and dissolution that are charac−9 terized with DKr m2 s−1 and DXe ∥ ≈ (0.49−1.73) × 10 ∥ ≈ −9 2 −1 (0.41−0.95) × 10 m s , respectively. It is clear that the interaction with the interfacial surface decreases the mobility of noble gas atoms. Relative to the noble gas behavior outside the pores, the adsorbed−dissolved noble gas atoms diffuse relatively slowly but still obey the diffusion coefficient sequence of DNe > DAr > DKr > DXe. In the 4 nm diameter pores, the Ne and Ar atoms show the preference as non-adsorbed species and the diffusion

coefficients of the atoms distributed close to the pore center −9 (0 < d < 5 Å) are DNe m2 s−1 and DAr ∥ ≈ 4.16 × 10 ∥ ≈ 2.39 × −9 2 −1 10 m s , respectively. Kr and Xe atoms close to the pore −9 2 −1 center have diffusion coefficients DKr m s and ∥ ≈ 1.99 × 10 −9 2 −1 Xe D∥ ≈ 1.69 × 10 m s , respectively. These calculated diffusion coefficients are less than the values outside the pore, which reflect the attractive and/or repulsive forces from the surrounding silica surface. Moreover, a major difference exists between Ne and Ar in the distribution of atoms trapped in the silica slab. Ne atoms in the pore prefer to diffuse into the SiO2 structure, exhibiting a diffusion coefficient of DNe ∥ ≈ 0.102 × 10−9 m2 s−1. A small amount of Ar atoms in the pore settles in −9 the pockets of the silica surface with DAr m2 ∥ ≈ 0.012 × 10 −1 s . For the case of the larger Kr and Xe atoms, adsorption −9 2 −1 results in diffusion coefficients of DKr m s and ∥ ≈ 0.31 × 10 D∥Xe ≈ 0.22 × 10−9 m2 s−1, respectively. The diffusion coefficients of Kr and Xe in the nanopore are roughly consistent with a simple “core−shell” model, where the adsorption layer is immobile and the remaining atoms at the pore center diffuse much faster. Comparison of Simulation Concepts and Literature Data. Biogenic cherts as a sedimentary rock are mostly formed in a marine environment. The noble gas signature of biogenic cherts is therefore compared to young ocean sediments, from which they often transform. For the young ocean sediment-tochert sequence, the sediment system must reduce the noble gas abundance. The variable degrees of F(Kr) and F(Xe) enrichments in biogenic cherts indicate the retention of Kr and Xe from the precursor of amorphous silica; alternatively, fluid circulation induces Kr and Xe enrichment. In contrast, observed F(Ne) ∼ 1 in biogenic cherts can be attributed merely to fluid circulation during sediment lithification. At different stages of lithification, fluid paths may involve (a) bulk flow through a grain framework of sediments, (b) fluid transport along micro- and nanostructured channels, and (c) recrystallization into quartz that interlocks crystal boundaries E

DOI: 10.1021/acsearthspacechem.8b00136 ACS Earth Space Chem. XXXX, XXX, XXX−XXX

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ACS Earth and Space Chemistry and retains residual fluids. If the system starts with bulk flow filling, the fastest Ne must first enter the sediment grain framework, producing F(Ne) enrichment. If the system switches to bulk flow emptying, the slowest Xe atoms are possibly left behind and F(Xe) enrichment is expected. However, two prominent characteristics should be highlighted at the stage of bulk flow. First, the bulk flow that caused enrichment and depletion in noble gas signals is expected to be temporary. Second, bulk flow tends to be expulsed because compaction is the dominated process in lithification. Because “trapping” from bulk water cannot explain F(Ne) retention in biogenic cherts, the entrapment of noble gas into the chert structure is necessary. We predict that structural entrapment occurs during the stage of nanoscale flow. First, our MD simulation results indicate that F(Xe) enrichments can be achieved by adsorption along the curved silica pore surfaces. Such adsorption can occur at either the filling or emptying process but is critically dependent upon the appearance of a “core−shell” structure. When the compaction reduces the sediment porosity in the nanoregime,41,45−47 the pore water is divided into a core of “free” water with bulk-liquid-like properties and a shell of “surface” water with distinct properties. Our MD simulation results of the 4 nm diameter pore system indicate that noble gas atoms tend to follow the bulk-liquid-like water into the pore center, but the interaction with the interfacial silica surface can induce atomic-radius-dependent adsorption. If the permanent noble gas capture of adsorbed atoms is by interlocking grain boundaries, then less well bound Kr atoms that show faster movement in surface water are pushed along the surface by step motion but more tightly bound Xe atoms that show slower movement in surface water behave as impurities that remain fixed, ultimately becoming buried within the crystal. The discrepancy between observed Kr and Xe in cherts is consistent with the role of surface adsorption, which favors larger and heavier noble gases. Second, our MD simulation results indicate that F(Ne) retention can be achieved by trapping into the interior of the SiO2 crystal structure. The Ne concentrations do not show variations from young ocean sediments to cherts, but Ne is the fastest species in bulk-liquid-like water at the center of ≥2 nm diameter pores, which would imply that the apparent Ne retention is actually a balance of compaction-introduced loss and entrapment from the circulating water. In the 4 nm diameter pore system, Ne atoms do not exhibit the form of adsorption on the curved silica surface. Instead, the silica slab incorporates small Ne atoms. This structural diffusion is fundamentally different from transportation in bulk-liquid-like water or surface water, which relies strongly upon the interaction between silica and Ne atoms. If a Ne atom partitions into the interior of the silica slab, the Ne atom is almost immobile. In this light, the signature of F(Ne) retention is created as long as the mechanism of silica structure trapping is unique to Ne atoms. From a quasi-crystal perspective, Ne atoms in the 2 nm diameter pore are probably influenced by the confinement of a narrower structure, which leads to adsorbed Ne atoms on the curved silica surface in addition to structure diffusion. Therefore, we propose that Ne incorporation into the silica interior is an inevitable process during nanoscale fluid circulation. Finally, Ar should be treated as a special case. According to the simulation results in the 4 nm diameter pore, Ar atoms principally concentrate at the center of the pore. Despite the

existence of Ar atoms ensconced in small pockets of the silica surface, the Ar atom is too large to slip into the silica structure and the interaction with the interfacial surface is not strong enough to make Ar atoms adsorbed on the silica surface. The amount of ensconced Ar atoms is insufficient to influence the average loss during sediment compaction, which leads to the observed variable degrees of F(Kr)−F(Xe) enrichment during fluid circulation in sediment compaction. Ultimately, Ar atoms tend to be adsorbed as the porosity reaches the scale of ≤2 nm. The interlocking process during recrystallization into quartz plays a role in entrapping the adsorbed and ensconced Ar atoms. Implications. These simulation results reveal anomalous diffusive transport behavior that mediates noble gas fractionation. Because bulk-liquid-like water does not exist in 1 nm diameter pores, noble gas atoms show difficulty in 1 nm diameter pores. This finding lies in contrast to the relative selfdiffusion of noble gas atoms associated with bulk-liquid-like water at the center of ≥2 nm diameter pores. Our results agree with the “core−shell” conceptual model, where noble gas atoms show distinct properties in the shell of surface water. In 2 nm diameter pores, noble gas atoms are adsorbed to the curved silica surface. In 4 nm diameter pores, Kr and Xe atoms tend to be adsorbed on the curved silica surface. These noble gas atoms in the surface water show substantially reduced diffusion coefficients. In addition to adsorption, a certain amount of Ne atoms is entrapped in small pockets of the silica surface and the interior of the silica slab and a small amount of Ar atoms is ensconced in small pockets of the silica surface. Once the small-sized Ne and Ar atoms are trapped, the DNe and DAr profiles display the effects of immobility. The simulation results provide a potential explanation for the Ne retention and Xe enrichment observed in biogenic cherts. During the transition from young ocean sediment to chert, the first stage of bulk flow dominated by compaction induces the loss of noble gas atoms. The observed F(Ne) retention and some degree of F(Xe) enrichment are expected to occur during the second stage of nanoscale fluid circulation. Small Ne atoms most likely follow structural diffusion to become incorporated into the SiO2 crystal structure. In contrast, the large noble gas atoms Kr and Xe are controlled by surface adsorption under a different diffusion coefficient regime. Our computations imply that the nanostructure does not detectably influence the behavior of Ar atoms. Most Ar atoms diffuse at the center of nanopores along with bulkliquid-like water. The third stage of recrystallization into quartz interlocks the trapped noble gas atoms.

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acsearthspacechem.8b00136. Water molecule density profiles from curved nanopore surfaces (Figure S1), metadynamic simulation of noble gas atom diffusion into 1, 2, and 4 nm diameter nanopores (Figures S2 and S3), diffusion coefficient of water molecules in 1, 2, and 4 nm diameter nanopore systems (Table S1), and diffusion coefficient of noble gas atoms in 1, 2, and 4 nm diameter nanopore systems (Table S2) (PDF) F

DOI: 10.1021/acsearthspacechem.8b00136 ACS Earth Space Chem. XXXX, XXX, XXX−XXX

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. ORCID

Xin Ding: 0000-0001-9460-2050 Zhenyu Li: 0000-0003-2112-9834 Author Contributions †

Xin Ding and Zongyang Qiu contributed equally to this work.

Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The authors thank Dr. Ian Bourg, Dr. Mack Kennedy, and Dr. Bin Li for helpful discussions. This work was supported by the National Natural Science Foundation of China (41773003 to Xin Ding), the Anhui Provincial Natural Science Foundation (1808085MD95 to Xin Ding), and the “100 Talents Plan” of Anhui Province (to Xin Ding). The authors thank the University of Science and Technology of China (USTC) Supercomputing Center and the School of Life Science Bioinformatics Center for providing supercomputing resources for this project. The authors thank Dr. V. Faye McNeill and two anonymous reviewers for comments that greatly improved the manuscript.

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DOI: 10.1021/acsearthspacechem.8b00136 ACS Earth Space Chem. XXXX, XXX, XXX−XXX