Perturbations to water, both by ions and confining media, have been the focus of numerous experimental and theoretical studies. Yet, several open questions remain, including the extent to which such perturbations modify the structural and dielectric properties of the liquid. Here, we present a first-principles molecular dynamics study of alkali cations in water (Li+, Na+, and K+) as well as of water and LiCl and KCl solutions under confinement within carbon nanotubes (CNTs) of small diameter (1.1–1.5 nm). Our simulations support the view that the water structure is only modified locally in the presence of cations. We found that molecular polarizabilities are fingerprints of hydrogen bonding modifications, which occur at most up to the second solvation shell for all cations in bulk water. Under confinement, we found that the overall value of the molecular polarizability of water molecules near the surface is determined by the balance of two effects, which are quantitatively different in CNTs of different radii: the presence of broken hydrogen bonds at the surface leads to a decrease in the polarizabilities of water molecules, while the interaction with the CNT enhances polarizabilities. Interestingly, the reduction in dipole moments of interfacial water molecules under confinement is instead driven only by changes in the water structure and not by interfacial interactions. As expected, confinement effects on water molecular polarizabilities and dipole moments are more pronounced in the case of the 1.1 nm CNT.

The chemistry of water and aqueous salt solutions has been an active area of research for decades.1,2 However, the effect of external perturbations, including the presence of ions and nanoscale confinement, on the structure and electronic properties of water is not yet fully understood. While the way ions modify the structure of water within the first solvation shell of ions is well established, the effect of ions outside the first solvation shell is more controversial.3,4 Some experimental studies, including dielectric relaxation5 and neutron diffraction6 measurements, support the view in which ions significantly affect global water properties, such as diffusion, viscosity, and hydrogen bonding.1,7 Other experiments employing x-ray absorption spectroscopy,8 fs-IR,9 and terahertz spectroscopy10 point instead at negligible global effects of ions on the surrounding liquid. Such discrepancies have motivated numerous simulation studies; however, even first-principles simulations have differed in their assessment of the global effect of salt properties, with some studies finding significant global structure making/breaking effects,11 while others reporting primarily local effects.12–14 A recent first-principles study by Gaiduk and Galli,14 based on statistically robust molecular dynamics trajectories of NaCl solutions, found that while Cl anions have structure-breaking effects beyond the second solvation shell of water, albeit weak, the Na+ cation has negligible structure-making effects beyond the first shell. Furthermore, the study found a direct correlation between local hydrogen bonding strength and molecular polarizabilities.

In addition to ions, nanoscale confinement is expected to perturb water. Many interesting and unusual behaviors of the liquid have been reported under confinement, including enhanced diffusion,15,16 elevated proton conductivity,17 the formation of one-dimensional water chains,18 square ice phases,19,20 and diameter-dependent elevated phase transition temperatures.21–23 Several recent studies of confined water have found anomalous and anisotropic dielectric properties.24–30 The remarkable properties of confined water have led to proposals for using carbon nanotubes (CNTs) in water filtration and desalination technologies as single molecule sensors, supercapacitors, and model biological systems.31,32 While many classical simulations have been employed30,33,34 to better understand such phenomena, first-principles simulations of water confined at the nanoscale are still relatively rare.18,35–37 In particular, the effect of confinement on the molecular polarizability of water remains an open question, and it is crucial to understanding the behavior of water at surfaces.38–41 

In this work, we present first principles simulations of bulk water and three hydrated cations, Li+, Na+, and K+, and of water and LiCl and KCl solutions under confinement. In order to analyze the trends in structural and dielectric properties with statistically significant trajectories, we chose a semi-local functional [Perdew, Burke, and Ernzerhof (PBE42)], which is computationally less expensive than, e.g., hybrid functionals, and an elevated temperature (400 K) to model the structural properties of water under ambient conditions.43 Motivated by the necessity of multiple independent trajectories to resolve statistical uncertainty,44,45 we computed 10 independent trajectories with a total trajectory time of ∼0.45 ns for each bulk cation solution. The total simulation time of the calculations reported here amounts to ∼1.4 ns, which was possible to span using a relatively simple functional as PBE, but it would have been prohibitively difficult to obtain with more sophisticated density functionals. We present an analysis of hydrogen bonding changes in the presence of ions and under confinement, and we relate structural changes to variations of dielectric properties, in particular, molecular polarizabilities, which we find to be key fingerprints to understand water modifications both in the presence of ions and under confinement.

The rest of this paper is organized as follows: After summarizing our simulation methodology (Sec. II), we describe our results for alkali ions in bulk water with specific focus on molecular polarizabilities (Sec. III). We then examine how molecular polarizabilities are modified under confinement (Sec. IV) both for water and in LiCl and KCl solutions. Section V concludes this paper.

The bulk salt solutions were modeled by periodic cubic cells consisting of a single ion and 63 water molecules, with the excess charge compensated by a uniform background charge. For all the models, the size of the cell was chosen to yield the experimental density of liquid water under ambient conditions. The salt concentration corresponds to 0.87M.

In addition to the bulk solutions, we considered water confined in carbon nanotubes (CNTs) with two different diameters, including 1.5 nm and 1.1 nm, which correspond to the (19 × 0) and (14 × 0) semiconducting CNTs. Specifically, the liquid confined in CNTs was modeled using supercells of dimension a = b = 21.17 Å, c = 17.0 Å and a = b = 17.25 Å, c = 25.56 Å, respectively. Our simulation model contained 54 water molecules for the 1.5 nm CNT, whereas 34 water molecules were included for the 1.1 nm CNT. We also considered confined salt solutions in the 1.1 CNT using a supercell that contained one cation–anion pair and 32 water molecules. The concentration of the confined solutions is higher than in the bulk (1.63M), but it can still be considered close to a dilute limit case. The number of water molecules was chosen so as to obtain the experimental equilibrium density of water under ambient conditions. In particular, we estimated the thickness of the exclusion volume present at the interface between water and the CNT wall to be ∼2 Å.35 This thickness was employed to determine the number of molecules needed to fill up the tubes in order to obtain a density of ∼1 g/cm3. All samples were equilibrated for 100 ps using the SPC/E classical potentials for water molecules, and the final structure was then used as input for the first-principles simulations. For the salt solutions under confinement, the initial configurations were obtained by replacing two water molecules with one cation and one anion.

Our first-principles simulations were carried out using Born–Oppenheimer molecular dynamics simulations with the Qbox code,46,47 with the interatomic forces derived from density functional theory (DFT) with the Perdew, Burke, and Ernzerhof (PBE)42 approximation for the exchange-correlation energy functional. The interaction between valence electrons and ionic cores was represented by norm-conserving pseudopotentials,48 and the electronic wave functions were expanded in a plane-wave basis set truncated at a cutoff energy of 85 Ry. All hydrogen atoms were replaced with deuterium to maximize the allowable time step, which was chosen to be 10 a.u. We note that the PBE functional was employed in this work as we are mainly interested in trends among the ions and in strength of confinement, and the use of this functional allows for statistically robust simulations at a manageable computational cost.14,44

We equilibrated the bulk and confined solutions at a constant temperature of T = 400 K for at least 10 ps. An elevated temperature was chosen, as the use of the PBE approximation is known to yield an overstructured liquid under ambient conditions, and the use of a simulation temperature of ∼400 K was shown to recover the experimental liquid structure and water diffusion coefficient at T = 300 K.43 Statistics were collected over 45 ps for each microcanonical simulation of the bulk solutions, for which we propagated 10 independent trajectories for each cation and one trajectory for Cl. We ran single 25 ps simulations for the confined solutions due to their higher computational cost.

We begin by examining the solvation properties of the ions in the bulk solutions using the radial distribution functions (RDFs) between the solvated ions and oxygen atoms of water molecules (Fig. S1 of the supplementary material). As expected, the position of the RDF first maximum follows the ion size, Li+ < Na+ < K+ < Cl, yielding a value of 1.97 Å, 2.44 Å, 2.81 Å, and 3.10 Å for Li+, Na+, K+, and Cl, respectively. We also report in Fig. S1 of the supplementary material the average oxygen coordination number in the first ion solvation shell for which we obtained values of 4.0, 5.2, 6.8, and 6.0 for Li+, Na+, K+, and Cl, respectively. Overall, these results are consistent with those of several previous first principles simulations49–52 as well as with experimental studies.53,54 We also found that oxygen–oxygen and oxygen–hydrogen RDFs (Fig. S2 of the supplementary material) of all solutions do not show any notable change relative to the corresponding ones of pure water, pointing to minor effects of the ions on the structure of water at the concentration considered here.

To better understand ion effects on the water structure, we investigated hydrogen bonding of the salt solutions. The subtleties of ion effects on hydrogen bonding require attention to statistical uncertainty. We used 10 independent trajectories for each cation solution to obtain statistically robust results with error bars on hydrogen bond averages, which were computed using Student’s t-test for 95% confidence intervals, as in earlier studies.14,44 Here, two water molecules were considered to be hydrogen bonded if their oxygen–oxygen separation was less than 3.35 Å, while the O⋯OH angle was equal to or less than 30°.55 The average hydrogen bond per water molecule in the first and second solvation shells of the ions is shown in Fig. 1 and is compared to the results obtained for liquid water using the PBE400 dataset.44 Our results clearly show a substantial suppression of hydrogen bonds in the first solvation shell for all the cations, with the extent of the reduction decreasing with the ion size: Li+ < Na+ < K+. In addition, we found that the presence of the cations leads to a weak enhancement in the number of hydrogen bonds in the second solvation shell relative to pure liquid water. However, beyond the second shell, our results show that the hydrogen bonds of none of cation solutions differ from those of liquid water. Our findings are consistent with the results reported by Gaiduk and Galli14 for Na+ and indicate that the effect of all cations on the water structure is rather localized.

FIG. 1.

Number of hydrogen bonds per molecule in bulk solutions as a function of solvation shells. “Bulk” refers to the region outside the second solvation shell. The boundaries of the 95% confidence interval for pure water (dotted horizontal line) were computed using the (PBE400 pure water dataset44). The inset shows a closer view of the data for the second shell and bulk regions.

FIG. 1.

Number of hydrogen bonds per molecule in bulk solutions as a function of solvation shells. “Bulk” refers to the region outside the second solvation shell. The boundaries of the 95% confidence interval for pure water (dotted horizontal line) were computed using the (PBE400 pure water dataset44). The inset shows a closer view of the data for the second shell and bulk regions.

Close modal

In addition to the analysis of hydrogen bonds, we investigated the diffusion coefficient of water in the presence of the ions, which was computed from the oxygen mean-squared displacement. We find that the presence of cations does not affect water diffusion in a statistically significant manner (see Table 1 of the supplementary material for specific values) at the concentration considered here, consistent with our hydrogen bonding analysis.

We now turn to examine the ion effects on the dielectric properties of water molecules. In particular, the dipole moments of water molecules in the solutions were computed using maximally localized Wannier functions,56–58 and their average values are shown in Fig. 2 (left panel). We find that, for all the ions other than Li+, the water molecules in the first ion solvation shell yield an average dipole moment reduced by at most ∼0.15 D, i.e., less than 10% relative to the rest of the liquid. In contrast, water molecules in the first solvation shell of Li+ exhibit a relatively weak enhancement of the dipole moment by ∼0.04 D. Most importantly, we found that ion effects on the water dipole moment are negligible beyond the first solvation shell, consistent with a previous study by Gaiduk and Galli, where the authors concluded that water dipole moment is insensitive to the long-range effects introduced by the solute (see Fig. S3 of the supplementary material). Our results are also in agreement with a previous first-principles study,11 which similarly concluded that the effect of ions on the dipole moment of water molecules is confined to the first solvation shell for aqueous solutions with the same cations, at a similar concentration.

FIG. 2.

(Left panel) The molecular dipole moments of water molecules in the bulk aqueous solutions. (Right panel) The molecular dipole moments of water molecules in the confined solutions. “Ion SS” and “Cation SS” denote water molecules within the first solvation shell of the ion/cation, while “Non-SS” denotes all water molecules outside the first solvation shell of the ions. In the abscissa, “W” denotes pure water.

FIG. 2.

(Left panel) The molecular dipole moments of water molecules in the bulk aqueous solutions. (Right panel) The molecular dipole moments of water molecules in the confined solutions. “Ion SS” and “Cation SS” denote water molecules within the first solvation shell of the ion/cation, while “Non-SS” denotes all water molecules outside the first solvation shell of the ions. In the abscissa, “W” denotes pure water.

Close modal

The study of Ref. 14 on NaCl has shown that the molecular polarizability of water molecules is a useful fingerprint of ion effects. We investigate here whether this conclusion is general and applies to all alkali halide cations. In Ref. 14, an effective molecular polarizability (αieff) of water molecules was employed, which is defined through the polarization Pi of the ith molecule as Pi=αieffE, where E is an applied (external) electric field. In this work, we instead employed the intrinsic water molecular polarizability αi, which is related to the total polarization through the local field Eloc acting on the molecule: Pi = αiEloc, where Eloc = EEenv, and Eenv is the field induced by the polarization Pj(j ≠ i) of the rest of the system on the ith molecule via multipolar interactions. More specifically, we used the method developed by Pan et al.59 to compute Eenv, and thus, the calculated αi includes multipolar interactions at all orders. A comparison of αi and αieff for water is given in Fig. 3, where we found that αi has lower values and narrower distributions; however, the relative ordering of the projections over molecular axes is the same for both quantities. For the purpose of comparing water molecules under different environments, it is more appropriate to consider the intrinsic polarizability. Indeed, in the definition of intrinsic polarizabilities, induced fields from the environment are subtracted (Eenv), and hence, polarizabilities under different environments can be directly compared. In addition, we emphasize that the use of the method introduced in Ref. 59 enables the inclusion of not only dipolar but also all the multi-polar effects in the calculation of the polarizability at the DFT level of theory.

FIG. 3.

Comparison of the molecular polarizability, αi, and the effective molecular polarizability, αieff, for pure water. “Bis” indicates the component of molecular polarizability that bisects the HOH angle; “PIP” indicates the component perpendicular to Bis in the molecular plane; “POP” indicates the component perpendicular to and out of the molecular plane.

FIG. 3.

Comparison of the molecular polarizability, αi, and the effective molecular polarizability, αieff, for pure water. “Bis” indicates the component of molecular polarizability that bisects the HOH angle; “PIP” indicates the component perpendicular to Bis in the molecular plane; “POP” indicates the component perpendicular to and out of the molecular plane.

Close modal

Our results for the average molecular polarizabilities [αi¯=13Tr(αi)] of bulk ionic solutions using 140 snapshots extracted equally spaced in time from our simulations are reported in Fig. 4 (left panel). Snapshots used for the calculations were extracted from the entire trajectories with at least ∼0.24 ps interval in between. We note that results obtained with 80 and 140 snapshots were indistinguishable. In particular, we compared the average water molecular polarizability in the first ion solvation shell (SS) to all molecules outside the first solvation shell (defined as non-SS) for all ion solutions. We found that the average αi¯ of the first SS is smaller than that of non-SS for all cations, following the ion size trend Li+ < Na+ < K+. The most significant change in polarizabilities between SS and non-SS was obtained for Li+, with ∼6% difference, whereas Na+ and K+ yield a more modest difference of ∼2% and ∼1%, respectively. Our result indicates that the trend of αi¯ among the cations is consistent with that found for the number of hydrogen bonds (Fig. 1). In addition, consistent with Ref. 14, we found that the cations and Cl have different effect on the polarizability of water. The perturbation induced on the water structure by the cations is local, whereas that of Cl can extend beyond the second solvation shell, leading to an overall reduction in the water polarizability (Fig. 4, left panel). We, therefore, expect that introducing Cl to the solutions would slightly reduce the overall polarizability of water molecules in the solution.

FIG. 4.

(Left panel) Average molecular polarizability, αi¯, of water molecules in the bulk solutions. (Right panel) Average molecular polarizability, αi¯, of water molecules in the confined solutions. “Ion SS” and “Cation SS” denote water molecules within the first solvation shell of the ion/cation, while “Non-SS” denotes all water molecules outside the first solvation shell of the ions. In the abscissa, “W” denotes pure water.

FIG. 4.

(Left panel) Average molecular polarizability, αi¯, of water molecules in the bulk solutions. (Right panel) Average molecular polarizability, αi¯, of water molecules in the confined solutions. “Ion SS” and “Cation SS” denote water molecules within the first solvation shell of the ion/cation, while “Non-SS” denotes all water molecules outside the first solvation shell of the ions. In the abscissa, “W” denotes pure water.

Close modal

In addition to the average water molecular polarizability, we investigated the component of αi in the direction perpendicular to and out of the molecular plane (αiPOP), which has been shown to be the most affected by the hydrogen bonding environment and even sensitive to changes outside the second solvation shell of sodium.14 We show the long-range effect of ions on αiPOP in Fig. 5, where “bulk” refers to all water molecules outside the second solvation shells of ions. We found that both αi¯ (see Fig. S4 of the supplementary material) and αiPOP show the same trend as a function of ion type. Importantly, we found that αiPOP of water molecules outside the second ion solvation shell is different relative to the corresponding average value in pure water, outside statistical error bars. Our results indicate that polarizabilities are sensitive to changes induced by ions even beyond the second ion solvation shell of the liquid. Hence, we confirm and generalize the findings of Gaiduk and Galli, who found that polarizabilities are fingerprints of long-range effects in the case of Na+, though in Ref. 14 only values of αieff were computed, in contrast to intrinsic polarizabilities in this work.

FIG. 5.

Perpendicular out-of-plane (POP) dimension of molecular polarizability (αiPOP) for bulk solutions. “Ion SS” denotes molecules within the first solvation shell of the ions, while “Bulk” denotes molecules outside the second solvation shell of the ions. In the abscissa, “W” denotes pure water.

FIG. 5.

Perpendicular out-of-plane (POP) dimension of molecular polarizability (αiPOP) for bulk solutions. “Ion SS” denotes molecules within the first solvation shell of the ions, while “Bulk” denotes molecules outside the second solvation shell of the ions. In the abscissa, “W” denotes pure water.

Close modal

We now turn to discuss the perturbation to water induced by confinement. In particular, we examined liquid water and salt solutions confined in carbon nanotubes with the diameter of 1.1 nm. This specific diameter was chosen due to a unique balance between permeability and salt rejection, making it the “Goldilocks diameter” for desalination applications.60 In addition, it has been shown that the 1.1 nm CNTs exhibit a pronounced local minimum in the diameter-dependent diffusion16 and anomalous phase transitions.23 For comparison, we also considered liquid water confined in a 1.5 nm CNT; as we show below, water molecules can be effectively considered all interfacial in the 1.1 nm CNT, whereas a demarcation between interior and interfacial water molecules may be made in the 1.5 nm CNT. In this regard, the use of 1.1 nm and 1.5 nm CNTs provides proper models for understanding surface effects under confinement.35,36

Our initial examination of the structure of water confined in the CNTs was based on the radial density distribution function. As expected, we find that water molecules do not occupy the central region of the 1.1 nm CNT, and therefore, all water molecules can be considered to be interfacial in this geometry (Fig. S5 of the supplementary material). This is in contrast to the 1.5 nm CNT, which exhibits both well-defined interior and interfacial water layers. A rendering of the two nanotube configurations showing these properties is given in Fig. S6 of the supplementary material. In addition, we found a strong preferential alignment of water molecules inside in the 1.1 nm CNT, as indicated by the (20°) maximum in the dipole–dipole angle distribution function (Fig. S7 of the supplementary material). We found some preferential alignment of water molecules in the larger CNT as well; however, the effect is less pronounced. Finally, over the time scale of our simulations, we found no evidence of the square ice formation under the ambient conditions, consistent with previous reports.35 

The average water dipole moments of the confined systems, as obtained by averaging over 100 snapshots, are shown in Fig. 2 (right panel) (also see Fig. S8 of the supplementary material for the distribution function). We found that water molecules under confinement exhibit reduced molecular dipole moments relative to the bulk value, with a greater reduction in the smaller tube (9% and 7% for 1.1 nm and 1.5 nm CNTs, respectively). A better understanding of this reduction may be inferred from Fig. 6 (left panel), where we present the radial dependence of the water dipole moment, which is shown to decrease as a function of the distance from the tube center. In particular, we found that dipole moments of water molecules in the interior of the 1.5 nm CNT remain close to those of bulk water, while the molecules belonging to the interfacial region exhibit a monotonic reduction of their dipole moment, as a function of the distance from the interface. In the case of the 1.1 nm CNT, all molecules are interfacial and exhibit a significant reduction of their dipole moment at all distances from the interface, except for a limited number of molecules residing the closest to the center of the CNT. Overall, our results for confined liquid water are consistent with those of Ref. 35.

FIG. 6.

(Left panel) The radial dependence of molecular dipole moments of water molecules in confined aqueous solutions. (Right panel) The radial dependence of the average molecular polarizability of water molecules in confined aqueous solutions. All distances are measured along the nanotube axis, from the tube center, and the distances on the abscissa are the results of a histogram with bins of width 0.5 Å.

FIG. 6.

(Left panel) The radial dependence of molecular dipole moments of water molecules in confined aqueous solutions. (Right panel) The radial dependence of the average molecular polarizability of water molecules in confined aqueous solutions. All distances are measured along the nanotube axis, from the tube center, and the distances on the abscissa are the results of a histogram with bins of width 0.5 Å.

Close modal

Interestingly, we found that the changes in the molecular polarizability of water molecules under confinement are more complex than those of the dipole moment. We found that the average water polarizability in the 1.1 nm CNT, where all water molecules are interfacial, is enhanced by ∼3% relative to the bulk value, whereas the average water polarizability in the 1.5 nm CNT is unchanged relative to the bulk (Fig. 4, right panel). The radial dependence of the molecular polarizabilities is shown in Fig. 6 (right panel), where all systems exhibit enhancement at the interface. Molecular polarizability in the 1.5 nm CNT is being balanced between lower interior polarizabilities (by ∼15% relative to the bulk) and enhanced ones (by ∼23% relative to the bulk) in the interfacial region.

To further understand the change in the water molecular polarizability under confinement, we considered the Cartesian components of αi: αiXX, αiYY, and αiZZ, where X, Y and Z denote the axes of the simulation cell (Fig. S9 of the supplementary material). We found that αiZZ is primarily responsible for the reduction of αi¯ in the interior of the 1.5 nm CNT as well as the enhancement in the interfacial region; specifically, αiZZ increases by ∼88% between interior and interfacial water molecules, compared to a value of ∼14% obtained for the other components. In addition, our results show that while αiZZ is the most affected component in the 1.1 nm CNT as well, the anisotropy between the three polarizability components is much weaker than for the 1.5 nm CNT.

In order to investigate the reasons for the enhancement of αi near the interface, we computed dipole moments and molecular polarizabilities in the presence and absence of the confining CNT for the same exact configurations obtained from simulations where the CNTs are present. We found that the dipole moments are unchanged in the presence of the confining surface (see Fig. S10 of the supplementary material), indicating that the reductions in dipole moments under confinement are driven by the changes in the water structure, i.e., broken hydrogen bonds, and not by interfacial effects. The results for molecular polarizability are given in Fig. 7, showing significant reductions of ∼0.1 Å3 in all solutions when the CNT is absent: molecular polarizabilities are reduced by ∼6% to 7% relative to bulk values. These results indicate that the variation in the water polarizability confined in a CNT is due to competing structural and interfacial effects. In particular, the polarizability decreases relative to bulk water due to broken hydrogen bonds at the interface; such a decrease is counterbalanced by that of the interaction with the confining surface, which is responsible for a polarizability increase. In the 1.1 nm CNT case, where all water molecules are at the interface, the effect due to the interaction with the CNT is dominant, leading to an overall increase in the molecular polarizability in confinement. In the 1.5 nm CNT case, the balance of interfacial and broken hydrogen bond effects leads to the same average polarizability as in the bulk.

FIG. 7.

Average molecular polarizability, αi¯, of water molecules in confined solutions. The points in the unshaded region are reproduced from Fig. 4, while the data in the shaded region correspond to the same solutions, where polarizabilities were computed in the absence of the CNT. “Cation SS” and “Cl SS” denote water molecules within the first solvation shell of the cation and chloride, while “Non-SS” denotes all water molecules outside the first solvation shell of the ions. In the abscissa, “W” denotes pure water.

FIG. 7.

Average molecular polarizability, αi¯, of water molecules in confined solutions. The points in the unshaded region are reproduced from Fig. 4, while the data in the shaded region correspond to the same solutions, where polarizabilities were computed in the absence of the CNT. “Cation SS” and “Cl SS” denote water molecules within the first solvation shell of the cation and chloride, while “Non-SS” denotes all water molecules outside the first solvation shell of the ions. In the abscissa, “W” denotes pure water.

Close modal

Overall, our findings on water dipole moment and polarizabilities point to the important effects of nanoconfinement on the electronic properties of liquid water. These results are further corroborated by investigating the bandgap of the confined liquid. In particular, we obtained a value of 3.87 (0.06) eV and 3.88 (0.04) eV for water confined in the 1.1 nm and 1.5 nm CNTs, respectively, by using 200 water snapshots extracted from the simulations. Here, the numbers reported in parentheses are limits of the 95% confidence error using Student’s t-test. The bandgaps under confinement are reduced by less than 10% relative to that of bulk water, consistent with other studies that found reductions in the water’s bandgap at the surface of the liquid.61 We note that the absolute value of the computed gaps largely underestimates experimental values due to the limitation of the PBE functional; however, we expect to obtain the same trends at higher levels of theory.62,63 Finally, we found that the gaps obtained using the whole systems, inclusive of the tube, yielded an additional reduction due to the hybridization between water and carbon states and to carbon states falling in the gap of the liquid.

We now turn to examine the combined effects induced in the presence of solvated ions and confinement on water by examining LiCl and KCl solutions in the 1.1 nm CNT. We found that Li+ resides closest to the tube center, followed by K+ and Cl (see Fig. S5 of the supplementary material). In addition, we found clear evidence of ion disruption to the dipolar orientations of liquid water reported in Sec. IV A. In particular, we found that the dipole–dipole angle distribution of both confined salt solutions has a reduced intensity at low angles (e.g., higher dipolar alignment) relative to pure water. The presence of ions also decreases the hydrogen bond lifetime in the confined solutions (Fig. S11 of the supplementary material). These results are consistent with experimental x-ray diffraction studies by Ohba et al.,64 who attributed increased intermolecular water distances and weakened hydrogen bonding of NaCl solutions in 2 nm diameter CNTs to the disruption introduced by the solvated ions. Our findings are also supported by recent classical MD simulations on Na+, K+, and Cl ion solutions confined in CNTs of diameters up to ∼1 nm,34 which found disruptions to the hydrogen bond structure across all ions.

The confinement of pure water at 1.1 nm caused a reduction in the average dipole moment by ∼9% relative to the bulk. We find that this reduction is enhanced by the presence of solvated ions, as the dipole moment of water molecules outside the first cation solvation shell is reduced by ∼13% and ∼12% relative to pure bulk for the LiCl and KCl solutions, respectively. This is consistent with the structural modifications leading to smaller dipolar alignments and disrupted hydrogen bonding due to the ions. Similarly, while αi¯ of pure water at 1.1 nm was enhanced by ∼3% relative to bulk water, in the LiCl and KCl solutions, polarizabilities were both enhanced ∼4%. These results show that at the concentration considered here, the solvation of ions moderately amplifies the effects of confinement on dipole moments and molecular polarizabilities. Furthermore, given the similar effects found for LiCl and KCl, these results suggest minimal effects of the cation identity (e.g., Li+ vs K+) past the first solvation shell, consistent with our findings for the bulk solutions. Our results also show that the effect of counterions on the water structure is more complex under confinement. While the introduction of Cl in the bulk solutions reduces the polarizability of water molecules, we do not observe any reduction in the case of confined solutions.

Notably, we find that the Li+ solvation shell is structurally resilient under confinement, maintaining a tight tetrahedral coordination. The structural resilience of the confined Li+ solvation shell was recently reported by using experimental XRD,65 finding that the hydration number of Li+ in the 2 nm CNT to be much more bulk-like than that of larger cations. We also found that the water dipole moment in the Li+ solvation shell (see Fig. 2, right panel) under confinement is similar to the bulk; specifically, the water dipole moment is enhanced in the first solvation shell relative to the rest of the liquid. Likewise, the qualitative behavior of the polarizability of the Li+ solvation shell molecules (see Fig. 4, right panel) is similar to that of the bulk: αi¯ is suppressed relative to its non-SS counterpart.

In the case of K+ and Cl under confinement, we find that K+ and Cl are desolvated relative to the bulk. In particular, the oxygen coordination of K+ decreases from 6.8 in the bulk to 5.4 under confinement, whereas that of Cl decreases from 6.0 to 4.7 and 5.5 in the KCl and LiCl solutions, respectively. In contrast to Li+, for these larger ions, we found no difference in the dipole moment between water inside and outside the first ion solvation shell. This differs from their corresponding bulk behavior, where water dipole moments in the K+ and Cl solvation shell are reduced relative to the bulk value. Similarly, the αi¯ of water molecules in the first solvation shell of K+ is indistinguishable from that of non-SS water molecules, again in contrast to the bulk behavior. Collectively, we found that water molecules in the solvation shell of Li+ preserve their bulk patterns due to the rigidity of the ion solvation, whereas those belonging to the solvation shell of larger ions do not.

In summary, we investigated the effect of ions and confinement on the structural and dielectric properties of water by carrying out first principles molecular dynamics simulations of several solutions containing alkali ions and alkali halides. In the case of bulk water, we found that Li+ and K+ have a local effect on the water structure and that molecular polarizabilities are fingerprints of hydrogen bond changes, generalizing the findings reported by Gaiduk and Galli14 in the case of Na+. We also computed diffusion coefficients of water, finding no cations to affect water diffusion in a statistically significant manner at the concentration considered here (0.87M). This is consistent with the picture that emerged from hydrogen-bonding analysis, showing that none of the cations studied here are global structure maker/breakers, and all have a similar effect on the structure of water.

We found that under confinement, two competing effects influence the value of the polarizability of water molecules: we observed a reduction due to broken hydrogen bonds and an enhancement caused by the interaction of water molecules with the CNT interface. The latter dominates in the narrow CNT (1.1 nm) where all water molecules are interfacial, resulting in ∼3% enhancement in the molecular polarizability relative to bulk water. In the wider CNT (1.5 nm) that contains both interior and interfacial water molecules, the broken hydrogen bonds and interfacial effects offset each other, yielding a total polarizability unchanged from that of the bulk. We also note that, under confinement, the polarizability of water molecules is highly anisotropic, with enhancements and reductions observed primarily in the component of the polarizability along the nanotube axis. The effect of confinement also led to a small reduction of bandgaps for both CNTs. We found that ion solvation leads to a slight amplification of confinement effects on water molecular polarizabilities and dipole moments in the 1.1 nm CNT. Several trends observed for the properties of ion solvation in the bulk were found to be the same under confinement, including the local effect of cations. In addition, we found that the Li+ solvation shell is structurally resilient under confinement, with similar modifications of water dipole moments and polarizabilities in the ion solvation shell as in the bulk. In contrast, the larger cation K+ is desolvated under confinement and does not maintain the bulk trends in ion solvation shell dipole moments and polarizabilities.

Overall, our findings demonstrate the sensitivity of molecular polarizability to the perturbation introduced by both solvated ions and confinement on liquid water. Our work provides a set of statistically robust reference data on ion solvation in pure water and under confinement for future studies using more sophisticated exchange-correlation functionals beyond the PBE approximation. Our results highlight the importance of the inclusion of polarizability for realistic simulations of water in complex environments and may assist with parameterization of future interatomic potentials.

See the supplementary material for the following figures: (S1) pair correlation functions and (S2) coordination number distributions for bulk solutions, (T1) a table of diffusion coefficients of bulk solutions, (S3) molecular dipole moment distributions for bulk solutions, (S4) average molecular polarizability in the ion solvation shell and beyond the second solvation shell for bulk solutions, (S5) radial density distributions for confined solutions, (S6) visualizations of the confined systems, (S7) dipole–dipole angle distributions for confined solutions, (S8) molecular dipole moment distributions for confined solutions, (S9) radial dependencies of molecular polarizability in confined system coordinates, (S10) dipole moments of confined solutions without the nanotube, and (S11) hydrogen bond existence correlation functions for confined solutions.

We are grateful to Alex Gaiduk, Ding Pan, Eric Schwegler, and Francois Gygi for useful discussions. V.F.R. acknowledges support from the Department of Energy National Nuclear Security Administration Stewardship Science Graduate Fellowship under Award No. DE-NA0003864. Part of this work was performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under Contract No. DE-AC52-07NA27344. T.A.P. was supported as part of the Center for Enhanced Nanofluidic Transport, an Energy Frontier Research Center funded by the U.S. Department of Energy, Office of Science, Basic Energy Sciences under Award No. DE-SC0019112. G.G. acknowledges support from AMEWS (Advanced Materials for Energy-Water System Center) funded by the U.S. Department of Energy, Office of Science, Basic Energy Sciences. This work was completed with resources provided by the University of Chicago’s Research Computing Center and the Lawrence Livermore National Laboratory Institutional Computing Grand Challenge Program.

1.
Y.
Marcus
, “
Effect of ions on the structure of water: Structure making and breaking
,”
Chem. Rev.
109
,
1346
1370
(
2009
).
2.
A. A.
Hassanali
,
J.
Cuny
,
V.
Verdolino
, and
M.
Parrinello
, “
Aqueous solutions: State of the art in ab initio molecular dynamics
,”
Philos. Trans. R. Soc., A
372
,
20120482
(
2014
).
3.
J. L.
Skinner
, “
Following the motions of water molecules in aqueous solutions
,”
Science
328
,
985
986
(
2010
).
4.
D.
Paschek
and
R.
Ludwig
, “
Specific ion effects on water structure and dynamics beyond the first hydration shell
,”
Angew. Chem., Int. Ed.
50
,
352
353
(
2011
).
5.
M.
Kondoh
,
Y.
Ohshima
, and
M.
Tsubouchi
, “
Ion effects on the structure of water studied by terahertz time-domain spectroscopy
,”
Chem. Phys. Lett.
591
,
317
322
(
2014
).
6.
R.
Mancinelli
,
A.
Botti
,
F.
Bruni
,
M.
Ricci
, and
A.
Soper
, “
Hydration of sodium, potassium, and chloride ions in solution and the concept of structure maker/breaker
,”
J. Phys. Chem. B
111
,
13570
13577
(
2007
).
7.
F.
Rull
, “
Structural investigation of water and aqueous solutions by Raman spectroscopy
,”
Pure Appl. Chem.
74
,
1859
1870
(
2002
).
8.
L.-Å.
Näslund
,
D. C.
Edwards
,
P.
Wernet
,
U.
Bergmann
,
H.
Ogasawara
,
L. G.
Pettersson
,
S.
Myneni
, and
A.
Nilsson
, “
X-ray absorption spectroscopy study of the hydrogen bond network in the bulk water of aqueous solutions
,”
J. Phys. Chem. A
109
,
5995
6002
(
2005
).
9.
A. W.
Omta
,
M. F.
Kropman
,
S.
Woutersen
, and
H. J.
Bakker
, “
Negligible effect of ions on the hydrogen-bond structure in liquid water
,”
Science
301
,
347
349
(
2003
).
10.
S.
Funkner
,
G.
Niehues
,
D. A.
Schmidt
,
M.
Heyden
,
G.
Schwaab
,
K. M.
Callahan
,
D. J.
Tobias
, and
M.
Havenith
, “
Watching the low-frequency motions in aqueous salt solutions: The terahertz vibrational signatures of hydrated ions
,”
J. Am. Chem. Soc.
134
,
1030
1035
(
2011
).
11.
T.
Ikeda
,
M.
Boero
, and
K.
Terakura
, “
Hydration of alkali ions from first principles molecular dynamics revisited
,”
J. Chem. Phys.
126
,
034501
(
2007
).
12.
J. A.
White
,
E.
Schwegler
,
G.
Galli
, and
F.
Gygi
, “
The solvation of Na+ in water: First-principles simulations
,”
J. Chem. Phys.
113
,
4668
4673
(
2000
).
13.
M.
Śmiechowski
,
J.
Sun
,
H.
Forbert
, and
D.
Marx
, “
Solvation shell resolved THz spectra of simple aqua ions–distinct distance- and frequency-dependent contributions of solvation shells
,”
Phys. Chem. Chem. Phys.
17
,
8323
8329
(
2015
).
14.
A. P.
Gaiduk
and
G.
Galli
, “
Local and global effects of dissolved sodium chloride on the structure of water
,”
J. Phys. Chem. Lett.
8
,
1496
1502
(
2017
).
15.
M.
Majumder
,
N.
Chopra
,
R.
Andrews
, and
B. J.
Hinds
, “
Nanoscale hydrodynamics: Enhanced flow in carbon nanotubes
,”
Nature
438
,
44
(
2005
).
16.
A.
Barati Farimani
and
N. R.
Aluru
, “
Spatial diffusion of water in carbon nanotubes: From Fickian to ballistic motion
,”
J. Phys. Chem. B
115
,
12145
12149
(
2011
).
17.
D. J.
Mann
and
M. D.
Halls
, “
Water alignment and proton conduction inside carbon nanotubes
,”
Phys. Rev. Lett.
90
,
195503
(
2003
).
18.
L.
Wang
,
J.
Zhao
,
F.
Li
,
H.
Fang
, and
J. P.
Lu
, “
First-principles study of water chains encapsulated in single-walled carbon nanotube
,”
J. Phys. Chem. C
113
,
5368
5375
(
2009
).
19.
K.
Koga
,
G.
Gao
,
H.
Tanaka
, and
X. C.
Zeng
, “
Formation of ordered ice nanotubes inside carbon nanotubes
,”
Nature
412
,
802
(
2001
).
20.
J.
Chen
,
A.
Zen
,
J. G.
Brandenburg
,
D.
Alfè
, and
A.
Michaelides
, “
Evidence for stable square ice from quantum Monte Carlo
,”
Phys. Rev. B
94
,
220102
(
2016
).
21.
D.
Takaiwa
,
I.
Hatano
,
K.
Koga
, and
H.
Tanaka
, “
Phase diagram of water in carbon nanotubes
,”
Proc. Natl. Acad. Sci. U. S. A.
105
,
39
43
(
2008
).
22.
M.
Raju
,
A.
Van Duin
, and
M.
Ihme
, “
Phase transitions of ordered ice in graphene nanocapillaries and carbon nanotubes
,”
Sci. Rep.
8
,
3851
(
2018
).
23.
K. V.
Agrawal
,
S.
Shimizu
,
L. W.
Drahushuk
,
D.
Kilcoyne
, and
M. S.
Strano
, “
Observation of extreme phase transition temperatures of water confined inside isolated carbon nanotubes
,”
Nat. Nanotechnol.
12
,
267
(
2017
).
24.
H.
Zhu
,
A.
Ghoufi
,
A.
Szymczyk
,
B.
Balannec
, and
D.
Morineau
, “
Anomalous dielectric behavior of nanoconfined electrolytic solutions
,”
Phys. Rev. Lett.
109
,
107801
(
2012
).
25.
C.
Zhang
,
F.
Gygi
, and
G.
Galli
, “
Strongly anisotropic dielectric relaxation of water at the nanoscale
,”
J. Phys. Chem. Lett.
4
,
2477
2481
(
2013
).
26.
W.
Qi
and
H.
Zhao
, “
Hydrogen bond network in the hydration layer of the water confined in nanotubes increasing the dielectric constant parallel along the nanotube axis
,”
J. Chem. Phys.
143
,
114708
(
2015
).
27.
R.
Renou
,
A.
Szymczyk
, and
A.
Ghoufi
, “
Tunable dielectric constant of water at the nanoscale
,”
Phys. Rev. E
91
,
032411
(
2015
).
28.
C.
Schaaf
and
S.
Gekle
, “
Spatially resolved dielectric constant of confined water and its connection to the non-local nature of bulk water
,”
J. Chem. Phys.
145
,
084901
(
2016
).
29.
L.
Fumagalli
,
A.
Esfandiar
,
R.
Fabregas
,
S.
Hu
,
P.
Ares
,
A.
Janardanan
,
Q.
Yang
,
B.
Radha
,
T.
Taniguchi
,
K.
Watanabe
 et al, “
Anomalously low dielectric constant of confined water
,”
Science
360
,
1339
1342
(
2018
).
30.
S.
Mondal
and
B.
Bagchi
, “
Water in carbon nanotubes: Pronounced anisotropy in dielectric dispersion and its microscopic origin
,”
J. Phys. Chem. Lett.
10
,
6287
6292
(
2019
).
31.
A.
Striolo
,
A.
Michaelides
, and
L.
Joly
, “
The carbon-water interface: Modeling challenges and opportunities for the water-energy nexus
,”
Annu. Rev. Chem. Biomol. Eng.
7
,
533
556
(
2016
).
32.
S.
Chakraborty
,
H.
Kumar
,
C.
Dasgupta
, and
P. K.
Maiti
, “
Confined water: Structure, dynamics, and thermodynamics
,”
Acc. Chem. Res.
50
,
2139
2146
(
2017
).
33.
W.
Qi
,
J.
Chen
,
J.
Yang
,
X.
Lei
,
B.
Song
, and
H.
Fang
, “
Anisotropic dielectric relaxation of the water confined in nanotubes for terahertz spectroscopy studied by molecular dynamics simulations
,”
J. Phys. Chem. B
117
,
7967
7971
(
2013
).
34.
Z.
He
,
J.
Zhou
,
X.
Lu
, and
B.
Corry
, “
Ice-like water structure in carbon nanotube (8, 8) induces cationic hydration enhancement
,”
J. Phys. Chem. C
117
,
11412
11420
(
2013
).
35.
G.
Cicero
,
J. C.
Grossman
,
E.
Schwegler
,
F.
Gygi
, and
G.
Galli
, “
Water confined in nanotubes and between graphene sheets: A first principle study
,”
J. Am. Chem. Soc.
130
,
1871
1878
(
2008
).
36.
H. J.
Kulik
,
E.
Schwegler
, and
G.
Galli
, “
Probing the structure of salt water under confinement with first-principles molecular dynamics and theoretical x-ray absorption spectroscopy
,”
J. Phys. Chem. Lett.
3
,
2653
2658
(
2012
).
37.
F.
Shayeganfar
,
J.
Beheshtian
, and
R.
Shahsavari
, “
First-principles study of water nanotubes captured inside carbon/boron nitride nanotubes
,”
Langmuir
34
,
11176
11187
(
2018
).
38.
C. D.
Wick
,
I.-F. W.
Kuo
,
C. J.
Mundy
, and
L. X.
Dang
, “
The effect of polarizability for understanding the molecular structure of aqueous interfaces
,”
J. Chem. Theory Comput.
3
,
2002
2010
(
2007
).
39.
M. F.
Calegari Andrade
,
H.-Y.
Ko
,
R.
Car
, and
A.
Selloni
, “
Structure, polarization, and sum frequency generation spectrum of interfacial water on anatase TiO2
,”
J. Phys. Chem. Lett.
9
,
6716
6721
(
2018
).
40.
M. H.
Köhler
,
J. R.
Bordin
,
C. F.
de Matos
, and
M. C.
Barbosa
, “
Water in nanotubes: The surface effect
,”
Chem. Eng. Sci.
203
,
54
(
2019
).
41.
F.
Moučka
,
S.
Zamfir
,
D.
Bratko
, and
A.
Luzar
, “
Molecular polarizability in open ensemble simulations of aqueous nanoconfinements under electric field
,”
J. Chem. Phys.
150
,
164702
(
2019
).
42.
J.
Perdew
,
K.
Burke
, and
M.
Ernzerhof
, “
Generalized gradient approximation made simple
,”
Phys. Rev. Lett.
77
,
3865
(
1996
).
43.
E.
Schwegler
,
J. C.
Grossman
,
F.
Gygi
, and
G.
Galli
, “
Towards an assessment of the accuracy of density functional theory for first principles simulations of water. II
,”
J. Chem. Phys.
121
,
5400
5409
(
2004
).
44.
W.
Dawson
and
F.
Gygi
, “
Equilibration and analysis of first-principles molecular dynamics simulations of water
,”
J. Chem. Phys.
148
,
124501
(
2018
).
45.
M. D.
LaCount
and
F.
Gygi
, “
Ensemble first-principles molecular dynamics simulations of water using the SCAN meta-GGA density functional
,”
J. Chem. Phys.
151
,
164101
(
2019
).
46.
F.
Gygi
, “
Architecture of Qbox: A scalable first-principles molecular dynamics code
,”
IBM J. Res. Dev.
52
,
137
144
(
2008
).
47.
See http://www.qboxcode.org for Qbox code.
48.
D.
Hamann
,
M.
Schluter
, and
C.
Chiang
, “
Norm-conserving pseudopotentials
,”
Phys. Rev. Lett.
43
,
1494
(
1979
).
49.
T. A.
Pham
,
S. G.
Mortuza
,
B. C.
Wood
,
E. Y.
Lau
,
T.
Ogitsu
,
S. F.
Buchsbaum
,
Z. S.
Siwy
,
F.
Fornasiero
, and
E.
Schwegler
, “
Salt solutions in carbon nanotubes: The role of cation-π interactions
,”
J. Phys. Chem. C
120
,
7332
7338
(
2016
).
50.
A. P.
Gaiduk
,
C.
Zhang
,
F.
Gygi
, and
G.
Galli
, “
Structural and electronic properties of aqueous NaCl solutions from ab initio molecular dynamics simulations with hybrid density functionals
,”
Chem. Phys. Lett.
604
,
89
96
(
2014
).
51.
A.
Bankura
,
V.
Carnevale
, and
M. L.
Klein
, “
Hydration structure of salt solutions from ab initio molecular dynamics
,”
J. Chem. Phys.
138
,
014501
(
2013
).
52.
C.
Zhang
,
T. A.
Pham
,
F.
Gygi
, and
G.
Galli
, “
Communication: Electronic structure of the solvated chloride anion from first principles molecular dynamics
,”
J. Chem. Phys.
138
,
181102
(
2013
).
53.
V.-A.
Glezakou
,
Y.
Chen
,
J. L.
Fulton
,
G. K.
Schenter
, and
L. X.
Dang
, “
Electronic structure, statistical mechanical simulations, and EXAFS spectroscopy of aqueous potassium
,”
Theor. Chem. Acc.
115
,
86
99
(
2006
).
54.
L. X.
Dang
,
G. K.
Schenter
,
V.-A.
Glezakou
, and
J. L.
Fulton
, “
Molecular simulation analysis and x-ray absorption measurement of Ca2+, K+ and Cl ions in solution
,”
J. Phys. Chem. B
110
,
23644
(
2006
).
55.
A.
Luzar
and
D.
Chandler
, “
Effect of environment on hydrogen bond dynamics in liquid water
,”
Phys. Rev. Lett.
76
,
928
(
1996
).
56.
G. H.
Wannier
, “
The structure of electronic excitation levels in insulating crystals
,”
Phys. Rev.
52
,
191
197
(
1937
).
57.
N.
Marzari
and
D.
Vanderbilt
, “
Maximally localized generalized Wannier functions for composite energy bands
,”
Phys. Rev. B
56
,
12847
12865
(
1997
).
58.
F.
Gygi
,
J.-L.
Fattebert
, and
E.
Schwegler
, “
Computation of maximally localized Wannier functions using a simultaneous diagonalization algorithm
,”
Comput. Phys. Commun.
155
,
1
6
(
2003
).
59.
D.
Pan
,
M.
Govoni
, and
G.
Galli
, “
Communication: Dielectric properties of condensed systems composed of fragments
,”
J. Chem. Phys.
149
,
051101
(
2018
).
60.
M.
Thomas
and
B.
Corry
, “
A computational assessment of the permeability and salt rejection of carbon nanotube membranes and their application to water desalination
,”
Philos. Trans. R. Soc., A
374
,
20150020
(
2016
).
61.
A. P.
Gaiduk
,
T. A.
Pham
,
M.
Govoni
,
F.
Paesani
, and
G.
Galli
, “
Electron affinity of liquid water
,”
Nat. Commun.
9
,
247
(
2018
).
62.
T. A.
Pham
,
C.
Zhang
,
E.
Schwegler
, and
G.
Galli
, “
Probing the electronic structure of liquid water with many-body perturbation theory
,”
Phys. Rev. B
89
,
060202
(
2014
).
63.
V.
Garbuio
,
M.
Cascella
,
L.
Reining
,
R.
Del Sole
, and
O.
Pulci
, “
Ab initio calculation of optical spectra of liquids: Many-body effects in the electronic excitations of water
,”
Phys. Rev. Lett.
97
,
137402
(
2006
).
64.
T.
Ohba
,
K.
Hata
, and
H.
Kanoh
, “
Significant hydration shell formation instead of hydrogen bonds in nanoconfined aqueous electrolyte solutions
,”
J. Am. Chem. Soc.
134
,
17850
17853
(
2012
).
65.
S. M.
Khan
,
S.
Faraezi
,
Y.
Oya
,
K.
Hata
, and
T.
Ohba
, “
Anomalous changes of intermolecular distance in aqueous electrolytes in narrow pores of carbon nanotubes
,”
Adsorption
25
,
1067
1074
(
2019
).

Supplementary Material