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Cite This: ACS Appl. Mater. Interfaces XXXX, XXX, XXX−XXX
Renormalization of Ionic Solvation Shells in Nanochannels Ke Zhou and Zhiping Xu* Applied Mechanics Laboratory, Department of Engineering Mechanics and Center for Nano and Micro Mechanics, Tsinghua University, Beijing 100084, China
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S Supporting Information *
ABSTRACT: Recently, experimental studies on selective ion transport across nanoporous membranes or through single nanochannels have unveiled interesting behaviors of dissolved ions under nanoconfinement. However, the exploration was limited by the resolution of experimental characterization. In this work, we present an atomistic simulation-based study, showing how the nanoconfinement and surface functionalization of graphene and graphene oxide nanochannels renormalize the solvation of ions (Na+, K+, Mg2+, Ca2+, Cl−). We find that the spatial distribution of dissolved ions demonstrates a layered order in nanochannels. The 1st hydration shell structures of cations are well defined in channels with width beyond ∼1.0 nm, although the rotational degree of freedom is constrained, while the 2nd hydration shells could be destructed. In the graphene oxide nanochannels, oxygen-containing functional groups can participate in the hydration shells of univalent ions but not for the divalent ions, and the valencedependent reduction in the ionic diffusivity offers good selectivity between the divalent and univalent ions with the interlayer spacing of ∼1.0 nm, which is absent in the graphene nanochannels. With these findings, we conclude that the assessment of permeability and selectivity of ions has to take the renormalized nature of ionic solvation shells into account in the design of nanoporous membranes or nanofluidic devices for energy and environmental applications. KEYWORDS: solvation shells, ion transport, nanochannels, nanoconfinement, surface functionalization
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assumed molecular-sieving criterion,6,14−16 but also the strength of ionic solvation shells and their interaction with the channel surfaces can be inferred from the transport measurements.7,16−18 Several studies concluded with an apparent correlation between the hydration radii of ions and their mobility.14−17 However, the applicability of hydration radii measured in the bulk solution in the nanoconfined environment has not yet been assessed, and the reported data of hydration radii in the literature are too scattering to make sound conclusions on size sieving.24,25 Moreover, contradicting results on the ion-transport processes in the graphene oxide (GO) membranes were reported due to the lack of information on parameters such as the surface charges, functional groups, sizes and geometries of the GO sheets, and the microstructures as controlled by the fabrication processes; some studies show that the permeability decreases with the hydration radii while others do not.6,14−17,19−21 Nanoengineering the nanochannels could boost the performance of selective ion transport by controlling the microstructure and surface chemistry of nanochannels through intercalation26 and surface modification,27 respectively. For example, tuning the interlayer spacing of GO membranes elevates the ion−water selectivity to nearly 100%.14,18 Molecular-level insights into the structural and
INTRODUCTION Aqueous solvation of metal cations and dynamical behaviors of dissolved ions are of critical importance for a wide spectrum of physicochemical processes ranging from ion separation to electrochemical reaction.1,2 The remarkable effects of solvation on the molecular structures and dynamical properties of the solvation complex were discussed with a focus on the entropy of hydration, viscosity, and water exchange through the structure-breaking and structure-formation-based arguments.3−5 Compared to dissolving ions in the bulk solution, confining ions in a limited space comparable to their hydrated sizes offers opportunities to probe the nature of ion solvation and the ion−surface interaction.6,7 However, since the early efforts made to understand ionic solvation in the 1950s,8 the effect of spatial confinement on the behaviors of dissolved ions has been rarely discussed,9−11 and the mechanisms of selective ion transport under nanoconfinement are yet to be quantitatively elucidated from the possible ones, including dehydration,12,13 steric exclusion,6,14,15 electrostatic interaction,16 and Donnan exclusion.17 Confining ions in nanochannels are also of practical interest. Laminated membranes of two-dimensional (2D) materials or constructed nanofluidic devices were applied for filtration and separation.14−22 With the recent advances in nanomaterial synthesis and nanofluidic techniques, the mobility of ions confined in nanochannels has been measured,23 where not only the size of dissolved ions can be extracted according to the © XXXX American Chemical Society
Received: June 4, 2018 Accepted: July 30, 2018 Published: July 30, 2018 A
DOI: 10.1021/acsami.8b09232 ACS Appl. Mater. Interfaces XXXX, XXX, XXX−XXX
Research Article
ACS Applied Materials & Interfaces dynamical behaviors of ions dissolved under nanoconfinement are thus urged. In this work, molecular dynamics (MD) simulations were conducted to probe the structures and dynamics of dissolved ions (Na+, K+, Mg2+, Ca2+, Cl−) confined within graphene or GO nanochannels with width corresponding to the intercalation of n (=1, 2, 3, and 4) water layers, denoted as G(GO)/nL, according to evidences reported from experimental studies.6,14,18−21 We find that the 1st hydration shell (1HS) structures of most ions (Na+, K+, Mg2+, Ca2+) are well defined for n > 1, although their rotation is constricted. The 2nd hydration shell (2HS), however, could be destructed. The spatial distribution of ions shows preference in the depletion region of water molecules, and the strength and stability of hydrated ions determines the selectivity and mobility of ions. Ionic diffusion in GO nanochannels is weakened by steric hindrance and electrostatic interaction from the oxygencontaining functional groups, which, however, result in improved divalent/univalent ionic selectivity compared to that in the graphene nanochannels. The solvation complex could be perturbed by the surface functional groups in GO channels, which capture univalent cations with weak 1HSs. These findings clarify the molecular mechanisms of selective ion transport in nanochannels and offer essential understandings for developing relevant applications in high-performance membranes and functional nanofluidic devices.
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RESULTS Hydrated Shells under Nanoconfinement. The width d of a nanochannel is critical for the molecular structures of confined matter. Previous studies show that one to three water layers appear at d ≤ 1.15 nm.28 While immersed in water, the interlayer spacing of GO membranes increases from 0.6 to 6−7 nm before disintegration,29 which could be further controlled, for example, by enforcing physical confinement (0.64−0.97 nm)14 or cationic pinning (ca. 1.12−1.14 nm).18 We thus model graphene and GO nanochannels with d ranging from 0.68 to 1.50 nm (Table S1). To measure the spatial correlation between the ions and water molecules, we plot the ion (M)− water (O) pair distribution functions (PDFs) in Figure 1. The distinct peaks (p) and valleys (v) indicate the formation of HSs, also known as the solvation or coordination shells. The 1HS is defined from the origin to the first valley v1 in the PDF, and the 2HS is defined from the first valley v1 to the second one v2. It was known that water intercalated in the G/1L channel features a solidlike structure (Figure S1),28,30 and thus the ion can be considered as a point defect embedded in the quasi-square lattice. The 1HS and 2HS are distinct, especially for n = 1, although the structure of 2HS is relatively weaker. With the increase of d, the position of p1 remains intact for all of the ions confined in nanochannels with n > 1, consistent with previously reported results for Na+ and K+ ions confined within the carbon nanotubes.31 The coordinate number Nc defined as the number of water molecules in the 1HS is almost a constant for all of the ions in the G/nL channels with n > 1, which is close to the value in the bulk solution (Figure 2a). However, the number of water molecules in the 2HSs (Figure 2b) increases with n, gradually converging to the bulk value. The renormalization of hydrogen shells for ions is attributed to the spatial confinement comparable to the size of hydrated shells, which are universal for all of the ions, and thus the relevant HS stabilities of ions in the nanochannels are expected to be similar to those for ions in bulk solvents.
Figure 1. Ion−water (the oxygen atom) pair distribution functions measured in the G/1−4L nanochannels and the bulk solution.
The topology of 1HSs can be measured by the coordination and orientation of the water molecules with dipole p in the hydrated complex (Figure 2c,d). The distribution functions of the angles O−M−O (θ1) and M−O−p (θ2), which are P(θ1) and P(θ2), respectively, measure the local order of solvation. For Na+ and Mg2+, the distribution P(θ1) exhibits two major peaks near θ1 = 180 and 90° for the octahedral32 and prismatic antitrigonal structures, while the two peaks of Ca2+ at 72 and 142° indicate the square antitrigonal and dodecahedral trigonal configurations. Our results are shown to be the same as those in the CNT for Na+ and K+31,33 and consistent with previous studies based on the polarizable atomic potential33 and quantum mechanical/molecular mechanical models34 for Mg2+ and Ca2+. The 1HS for K+, however, does not display any specific geometry.35 The distribution P(θ2) exhibits a single peak near 180° for all of the cations, with p aligning to the M−O direction. The peak in P(θ2) for Mg2+ lies most closely to 180°, followed by that for Ca2+, Na+, and K+; this order indicates the contrast in the strength and stability of 1HSs. The spatial distribution of ions in the nanochannels shows preference for the regions with a low density of water (Figures 2e,f, 3, and S2). In the G/2L channel, divalent cation ions are intercalated between the two water layers, while the univalent cations either reside within the water layers with a halftruncated octahedral structure or be intercalated with a quasispherical configuration. For the G/3L channels, most of the ions are located in the water-depletion region except for K+ that prefers to be embedded in the central water layer with a spherical 1HS or near the wall with a truncated octahedral structure, less preferably. This specific spatial distribution of ions results from the layered order of water and the ion−water B
DOI: 10.1021/acsami.8b09232 ACS Appl. Mater. Interfaces XXXX, XXX, XXX−XXX
Research Article
ACS Applied Materials & Interfaces
Figure 2. (a) 1HS coordination number of ions confined in the graphene and GO nanochannel. (b) average numbers of H and O atoms located in the shell [r, r + dr] measured from the ions. (c, d) Distribution of angles θ1 (O−M−O) and θ2 (M−O−p), as defined in the inset of (c). (e, f) Spatial distribution of ions along the channel width.
Figure 3. Schematic illustrations of the 1HS of ions in the bulk solution and water confined in the G/2L (d = 1.02 nm) and G/3L (d = 1.28 nm) nanochannels. The snapshots of hydrated ions are instantaneous configurations near local free-energy minima that are determined from the spatial distribution profiles of the ions (Figure 2e,f). The depth of background color illustrates the density of water. The water molecules are shown as red (O) and white (H) balls surrounding the ions, and the carbon atoms in graphene layers are shown in gray.
direction for both divalent and univalent ions, while the dimensions in the in-plane directions are reduced only for the divalent ions (Figure S3). For ions entering or exiting the
interaction. The topology of the 1HSs is robust, but their molecular structures are distorted under nanoconfinement. The cation−water solvation complex is squeezed in the z C
DOI: 10.1021/acsami.8b09232 ACS Appl. Mater. Interfaces XXXX, XXX, XXX−XXX
Research Article
ACS Applied Materials & Interfaces
Figure 4. (a) Residence time correlation functions (RTCF) measured for ions confined in the G/2L nanochannel. (b) Normalized RTCFs calculated for all of the ions in G/2−4L nanochannels and the bulk solution.
Figure 5. (a−f) Schematic illustration of the 1HS that can be captured by hydroxyl groups in GO/2L and GO/3L nanochannels. (a, b, d) Na+ or K+ ions captured by one hydroxyl group. (e) Na+ or K+ ions captured by two neighboring hydroxyl groups. (c, f) Cl− ion weakly interacting with one hydroxyl group. The snapshots of hydrated ions are instantaneous configurations near local free-energy minima that are determined from the spatial distribution profiles of the ions (Figure 2e,f). (g) Normalized RTCFs for Na+ and K+ ions captured by the functional groups in the GO channels. (h) Mean-square distance (MSD) curves measured for K+ and Mg2+ ions confined in the GO/2L channels. The colored background indicates the range of standard error.
D
DOI: 10.1021/acsami.8b09232 ACS Appl. Mater. Interfaces XXXX, XXX, XXX−XXX
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lifetime of native and temporary capturing events, as well as the weighting parameters w and 1 − w, respectively. The native binding has much longer lifetime τ1 = ∼100 ps than τ2 = ∼10 ps for the temporary binding that displays lower strength.39 We also define a factor p to measure the relative period for a cation to be captured in thermal equilibrium. The simulation results show that for all cations, the values of τ1, τ2, w, and p increase with the strength of nanoconfinement, from GO/3L to GO/2L (Table S4), which indicates an enhanced feasibility to be captured by the functional groups. The perturbation by hydroxyl features a longer lifetime τ1 than epoxy due to the higher negative charge on the oxygen, while epoxy is sterically more accessible to cations than the hydroxyl group with a folded structure (θC−O−H = 113°), causing the epoxy captured more likely to be native. Mobility and Selectivity of Hydrated Ions. The selectivity of a nanochannel is endowed by both the sizesieving effect and the contrast in ionic diffusivities. The hydrated size of ions can be related to the permeability through the Renkin equation,40 as extracted from the ion-transport process across the GO,14−16,18 MoS2,17 and polymer films.41 However, although the 1HSs of ions are intact in the nanochannels with n > 1, the 2HSs can be significantly perturbed. Consequently, the hydration radius measured in the bulk solution may not apply under nanoconfinement, not to mention the scattered nature of data reported in the literature.24,25 On the basis of the definition of the effective hydration radius proposed by Zhou et al.,37 where HSs are considered to be spherical, we find that the univalent ions are smaller than the divalent ions. To account for the polydispersity in the hydrated ions, we update the definition by considering the packing states identified for the HSs to discuss the steric exclusion of ions by the nanochannels (see Methods for definition). The results show that the effective size of ions follows the order K+ < Na+ < Ca2+ < Mg2+ (Figure 6). The effective width of the graphene and GO channels can be defined as de = d − dG (dGO) by excluding the width of depletion regions near the wall. With dG = 0.34 nm and dGO = 0.48 nm,42 the value of de is 0.68 nm for G/2L, which is larger than the diameters 2re of all cations calculated following our definition (Table S5). Our simulation results show that the univalent ions could diffuse in the G/2L channels with wellpreserved 1HSs while the divalent ions only diffuse with distorted ones. In contrast, the effective width of the GO/2L channel is 0.52 nm, larger than the value of 2re of the univalent cations but smaller than that of the divalent ions, which could offer high selectivity. The less-confined GO/3L channel with de = 0.77 nm could accommodate all of the cations. For GO membranes immersed in water with d = ∼1.3 nm and de = 0.82 nm,19−21 the embedded nanochannels allow transport of all of the cations under investigation and thus could fail for separation in the molecular-sieving regime, while the contrast in the ionic diffusivities may play a central role in determining the selectivity. To probe the nature of ionic diffusion under nanoconfinement, we calculate the van Hove distribution function Gs(r, t) from the simulation trajectories (Figure S6).43 In our 10 ns simulations, Gs(r, t) is in the Gaussian form for ions confined in graphene nanochannels, but not for the GO nanochannels where cations are locally trapped by the functional groups and long-range transport can only be activated by intersite “hops”.44 The deviation from Brownian behavior results from the dynamical heterogeneity and can be quantified by the non-
nanochannels, there are thus both enthalpic and entropic penalties in the free energy concerning the changes in HSs in addition to the ion−wall interaction, especially the 2HS. Strength and Stability of Hydrated Shells. In Figure 1, we find that the 1st peaks in the PDFs for divalent cations are higher and narrower than those for the univalent cations, and the values between the 1st and 2nd peaks, p1 and p2, are close to 0 for the divalent cations. This signature of shorter M−O bond lengths and higher structural order suggests that the HSs for divalent cations are stronger. This contrast in the structural stability of HSs can also be confirmed by the fact that the 1HS coordination number for Mg2+, Nc = 6, is an integer and that for Ca2+ fluctuates between 7 and 8, with a mean value of ∼7.95, while the Nc values of Na+ and K+ ions are ∼5.5 and ∼6.5, respectively, indicating the less well-defined topology and frequent exchange of water molecules in 1HS (Figure S4). The distribution of Nc for K+ is wider than that for Na+ and Ca2+, indicating a less stable hydration complex. We thus conclude that the order of 1HS strength or stability is Mg2+ > Ca2+ > Na+ > K+, which is also evident by measuring the thermal fluctuation of HSs through the increasing rattling range that is defined as the average distance between the cation and the mass center of the 1HS (Table S2).11,36 For Cl−, the HSs are weaker and larger compared to the cations as the anions attract positively charged hydrogen atoms in the water molecules,37 which differs from the cations that attract negatively charged oxygen atoms instead. As a result, the 1HS of Cl− could even be destructed in nanochannels with n = 2. To assess the dynamical stability of 1HSs in the solution, we calculate the residence time correlation function (RTCF)38,39 (see Methods for definition) for cations in the G/2L channels (Figure 4). The RTCF for Mg2+ is a constant of 6 during our 10 ns MD simulations, demonstrating the fidelity of water molecules in the 1HS against exchanging with exterior ones. This long lifetime compared to the simulation time scale echoes with the fact that the 1HS for Mg2+ is the strongest and the most stable one among the four cations under exploration. In comparison, the RTCF for Ca2+ decreases linearly with time, while that for the univalent ions decays exponentially and can be fitted to extract the finite lifetime. The lifetime of the 1HSs thus follows the same order as their stabilities, Mg2+ > Ca2+ > Na+ > K+. Moreover, the calculation results also indicate that nanoconfinement extends the lifetime of 1HSs (Table S3). Hydrated Shells Perturbed by Surface Functional Groups. In GO, the graphene sheets are functionalized by oxygen-containing groups, such as hydroxyl, epoxy, and carbonyl. The negatively charged hydrophilic surfaces of GO have high affinity to the cations. As a result, the HSs of cations could be perturbed by substituting water molecules in the HSs with the oxygen-containing groups (Figures 5a−f and S5). Our simulation results show that this mechanism works for the univalent ions with weaker HSs (Na+, K+), but not for the divalent cations (Mg2+ and Ca2+), where the stronger HSs could screen the ion−wall interaction. The 1HS for Cl− can also be perturbed, as captured by the H atoms in hydroxyl groups. To quantify the cationic affinity of functional groups, we calculate the RTCFs for the oxygen-containing functional groups that participate in the HSs (Figure 5g), which are then fitted to a double-exponential model (see Methods for definition) with two lifetime constants, τ1, τ2, to measure the E
DOI: 10.1021/acsami.8b09232 ACS Appl. Mater. Interfaces XXXX, XXX, XXX−XXX
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ACS Applied Materials & Interfaces
plane diffusion constant D increases with n, and the values in the graphene channels with ultralow wall friction are much higher than those in the GO channels. We also find that the univalent ions are more diffusive than divalent ones due to their weaker 1HSs, with DK+ > DNa+ > DMg2+ ≈ DCa2+, which is consistent with the order of effective ionic sizes. We then define a self-diffusion-specific selectivity as SA/B = D(A)/D(B) between cations A and B (Table S6). The simulation results show that the divalent/univalent selectivity in graphene nanochannels is not significant, with SK+/Mg2+ = 2.43 and SNa+/Ca2+ = 2.00 in the G/2L channel, which are reduced to 1.88 and 1.82 for G/3L, respectively. The GO nanochannels, however, exhibit elevated selectivity, although the ionic diffusivity is reduced. For the GO/2L channel with d = 1.0 nm, we have SNa+/Mg2+ = 5.57, SNa+/Ca2+ = 7.08, SK+/Mg2+ = 6.79, and SK+/Ca2+ = 8.83, which echo the excellent selectivity reported recently for the physically confined GO membrane with d = ∼0.98 nm.14 This role of functional groups in elevating the ionic selectivity is reminiscent with the ion channels in living or bioinspired systems.47,48
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DISCUSSION Although outstanding permeation and separation performance have been reported for the GO membranes consisting of both graphene and GO nanochannels, an understanding of the molecule-level selectivity is still lacking, mainly due to their microstructural complexities. Contradicting results on the ionic mobilities were reported. Specifically, some experimental studies conclude that the diffusivity of Mg2+ is higher than that of K+,20,21 as the former has a stronger HS, which is opposite to another set of experimental results showing the order K+ > Mg2+,14,17 as the effective hydration radii of the latter is larger. In the experiments with nanochannel width d < 1 nm,14,17 the ion-transport process is limited by dehydration of the 1HSs. The activated energy for dehydration depends on the strength of the hydration shell, resulting in the order Mg2+ > K+. While for wider channels with d > 1 nm,20,21 our simulation results show that the 1HSs of the cations are well retained, resulting in a limited dehydration effect, and the oxygen-containing functional groups in GO could participate in the 1HS of univalent ions but not for the divalent cations. The functional groups could thus be regarded as steric hinders only for the divalent cations, while for the univalent cations they further perturb the HSs by natively capturing ions such as K+. Our simulation results thus explain the contradicting results identified from experimental data, which are attributed to the lack of information on the structure and chemistry of GO sheets and microstructures of the GO membranes. Consequently, the microscopic mechanisms are of critical importance to extract reliable understandings form the measured permeation and selectivity through GO membranes. The diffusivity of K+ is higher than that of Mg2+ in the GO nanochannels in the dilute solution; however, at high concentration, K+ could be captured within the channel and block the transport pathway, reducing the effective space for diffusion. Our previous experimental results show that the rejection of KCl will increase with concentration.20,21 The π− cation interaction18,20,36 that is not considered in classical MD simulations could further enhance the ion−wall interaction, especially for the univalent cations with pyramid 1HSs near the graphene wall. These effects may be negligible for Mg2+ with a highly stable 1HS that could shield the surface interaction effectively. Auger electron spectroscopy measurements20
Figure 6. (a) Self-diffusion coefficients of cations confined in graphene and GO nanochannels. The dashed horizontal line means the D for bulk water. The D values for ions in all of the cases are smaller than the D’s of water. (b) Effective channel width and diameter of hydrated ions.
Gaussian parameters α2.45 The Einstein relation can be applied to evaluate the self-diffusion coefficients of ions only in the condition that the value of α2 becomes negligible (Figure 6), and this criterion can be met in a much longer time scale for the GO nanochannels than graphene due to the enhanced heterogeneity from the surface functional groups. The order of self-diffusion coefficients among cations is K+ > Na+ > Ca2+ ≈ Mg2+, which is consistent with the order of effective size re, and the strength and stability of hydrated shells are the same in G channel. The perturbation on the HSs and steric hindrance by the oxygen-containing functional groups in GO channels is significant for ionic diffusion. Specifically, for the K+ ion with a weak HS and Mg2+ with a strong one in the GO/2L channel, we find that the presence of surface functional groups leads to notable contrast in the ionic diffusivities (Figure 5h). The diffusivity of Mg2+ in epoxy-functionalized channels is higher than that with hydroxyl-functionalized ones due to the less remarkable steric hindrance. With this weakened hindrance, the diffusivity of K+ in the hydroxylfunctionalized GO/2L and GO/3L channels shows little difference. In the G/1L channel, water is solidlike at room temperature,28 and the ions embedded in the lattice can only diffuse with water layer collectively,46 while in the GO/1L channel, the trapped cations are almost immobile because of their strong electrostatic interaction with the GO surface. As the confinement is relaxed, in the G(O)/2L and G(O)/3L channels, self-diffusion of the cations is activated. The inF
DOI: 10.1021/acsami.8b09232 ACS Appl. Mater. Interfaces XXXX, XXX, XXX−XXX
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ACS Applied Materials & Interfaces
fixed during the simulations as the local lattice flexibility does not yield a notable effect. Periodic simulation boxes with ion and water intercalated between two graphene or GO sheets are constructed by using the PACKMOL package.60 The system is first equilibrated for 3 ns after simulating annealing to release the pressure. Production simulations are carried out at 300 K using a Nosé−Hoover thermostat with a damping time constant of 1 ps. The total simulation time is 10 ns, which is long enough to obtain converged results for thermodynamic analysis. The diffusion constant is calculated from the mean-square distance (MSD) extracted from atomic trajectories by using the Einstein relation. Time averaging and statistical error analysis are performed based on a set of 5−10 independent MD runs. The solvation of ions in this work is discussed in the dilute limit, by ignoring the ion-pairing effect.7 The range of ion concentration is ∼0.06 mol/L for the G/1L channel, which decreases to ∼0.02 mol/L for G/4L. The molecular structures are visualized in the OVITO package.61 It should be noted that our equilibrium MD approach neglects dynamical effects, such as reconstruction or perturbation of HSs, exchange of water molecules, and ion aggregation, which remain to be explored in the future work, although the equilibrium MD simulation results presented here are expected to apply for the relatively low-rate processes in experiments. Calculation of the Residence Time Correlation Function. The RTCF was used in the literature to study the solvation of proteins,38,39 which can be fitted to a single- or double-exponential function to extract the lifetime constants.39 Here, we use a singleexponent model for water in the HSs and a double-exponent model for the ion−wall interaction, according to the characteristic features identified in the simulation results. We define an instantaneous set of states S(t) = [s1, s2,..., sN] with Boolean variables si = 1:0 indicating the presence/absence of water molecule i in the 1HS of an ion at time t, where the 1HS is defined through the PDFs (Tables S8 and S9). The RTCF is calculated from the thermodynamic average R(t) = ⟨S(t)· S(0)⟩. The value of R(0) measured the coordinate number Nc in the 1HS, and fitting R(t) by the single exponential function yields R(0) exp(−τ1/t). A second set of states U(t) = [u1, u2,..., uM] is defined with ui = 1:0 meaning that the ion is captured by the functional group i or not. The RTCF for ion capturing is defined as F(t) = ⟨U(t)· U(0)⟩, where F(0) measures the probability of capturing. Fitting F(t) by the double-exponential function yields F(0)[w exp(−τ1/t) + (1 − w) exp(−τ2/t)] with τ1 > τ2.39 The period to collect data from simulation trajectories (10 ns) is 50 fs, which is short enough to assure the convergence of all of the calculations. Effective Size of the Hydration Ion. The hydration state of an ion depends on not only the distance between the water molecules in the HSs and the ion but also the configuration of the complex. Zhou et al.37 proposed that only water molecules in the 1HS with θ2 > θc can be considered for the hydration. The critical orientation θc = 150° is the average value determined from the distribution P(θc) (Figure S7). The hydration factor and number are then defined as h = ∫ 180 θc P(θ2)dθ2 and Nh = h × Nc, while the effective radius of an ion re can be extracted from the volume of 1HS
verified this conclusion by showing that K+ but not Mg2+ remained in the GO membranes after usage. These facts thus explain the high mobility of Mg2+ compared to K+. Additional effects, such as the ion−ion interaction at high concentration49 and the surface charge effects, could further modulate the selective ion-transport process in nanochannels,49 which await further exploration. Moreover, our discussion on the stability of HSs could also advise the cationic pinning control of nanochannels in lamellae GO membranes,18 which show that the 1HS lifetime of K+ increases from ∼30 ps in the G/2L channel to ∼400 ps in GO/2L, suggesting that K+ can be a better choice for cationic control than Na+, Ca2+, and Mg2+.
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CONCLUSIONS In brief, we explored the structure, stability, and mobility of ions confined in graphene and GO nanochannels, demonstrating the penalty for ion dissolution under nanoconfinement and the perturbation from surface functional groups, which determines the ionic selectivity in the nanoscale fluidic transport process. Although the discussion is focused on ions within the 2D nanochannels, their entry and exit in the pathway of dissolution can also be critical for transport across the membranes of nanochannels. Under strong nanoconfinement (n = 1), dehydration of the 1HS could be necessary, while as the confinement is relaxed (n ≥ 2), water molecules in the strongly bound 1HSs will be intact but the 2HSs could be distorted or destructed, resulting in additional free-energy cost for the ions to fit the nanoconfinement and surface chemistry of the channel walls.
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METHODS
Molecular Dynamics Simulations. We use the large-scale atomic/molecular massively parallel simulator50 to perform the MD simulations.51 The all-atom optimized potentials for liquid simulations52 are used for the graphene and GO sheets. The SPC/E model is used for water, which is widely adopted for MD simulations of water transport as it predicts reasonable static and dynamic propensities.53 The van der Waals interactions are modeled in the Lennard-Jones 12-6 form with heteroatomic parameters determined following the Lorentz−Berthelot mixing rules. The GO structures are constructed by functionalizing graphene sheets with hydroxyl or epoxy groups. The GO structures with hydroxyl groups are more stable in the aqueous solution and are used for discussion without specification. The interaction between carbon atoms in graphene or GO and oxygen atoms in water is modeled with parameters εC−O = 4.063 meV and σC−O = 0.319 nm, which predict a water contact angle of 98.4° for graphene, consistent with the value measured experimentally.54 We use the force-field parameters developed by Kenneth’s group55,56 for the ions, which are optimized for the free energy and shell structure of ion solvation, with long-range electrostatics treated by the particle mesh Ewald method. The parameters are validated by the experimental data for the bulk solution (Table S7). It should be noted that the use of classical potentials is limited by neglecting charge transfer31,57 and the cation−π interaction between cations and the sp2 regions of the GO sheets.18,20,36 These effects, however, can only be captured in models at the electronic structure level, for example, by the firstprinciples calculations with much higher computational cost.58 In our work, we choose the density of water in the nanochannel and the channel width to minimize the pressure of confined water, approaching zero (|pz| < 100 MPa, |px| < 50 MPa, and |py| < 50 MPa), to avoid the effect of lateral pressure on the dynamical properties of the confined solvent.59 The time step for integrating Newton’s equations is 1 fs, and the SHAKE algorithm is applied for hydrogenrelated energy terms to avoid computation of the high-frequency vibrations that require much shorter time steps. The carbon atoms are
VHS =
4 3 4 4 3 πre = Vwater + Vions = Nh πrw3 + πrM 3 3 3
(1)
Here, the radius of the ion is defined as rM = rMO − rw, where rMO is the ion−water distance and rW = 0.138 nm is the diameter of water.3,5 To account for polydispersity in the packing state of HSs,5 we introduce another definition based on the value of hydration factor, re = rM + 2rW × h, which predicts the correct order of ionic diffusivity in the bulk solution.
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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/acsami.8b09232. Interlayer spacings of graphene and GO nanochannels; rattling ranges of the solvation complexes; lifetime G
DOI: 10.1021/acsami.8b09232 ACS Appl. Mater. Interfaces XXXX, XXX, XXX−XXX
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ACS Applied Materials & Interfaces
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constants of the 1HSs; properties of HSs; ion selectivity; Lennard-Jones potential parameters; PDF parameters measured for dissolved univalent ions; schematic illustration of cations in the G/1L channel; spatial distribution of ions; spatial extent of 1HSs; distribution of Nc; schematic illustration of 1HSs captured by epoxy groups; PDFs of atomic displacements and nonGaussian parameters; and orientational distribution of water molecules (PDF)
AUTHOR INFORMATION
Corresponding Author
*E-mail:
[email protected]. ORCID
Ke Zhou: 0000-0003-2239-4381 Zhiping Xu: 0000-0002-2833-1966 Author Contributions
Z.X. conceived and directed the research. Both authors analyzed data and wrote the manuscript. Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS This study was supported by the MIT-China seed fund, the National Natural Science Foundation of China (Grant No. 11472150), and the National Key Basic Research Program of China (Grant No. 2015CB351900). The computation was performed on the Explorer 100 cluster system of Tsinghua National Laboratory for Information Science and Technology.
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