Salt Solutions in Carbon Nanotubes: The Role of Cation−π

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Salt Solutions in Carbon Nanotubes: The Role of Cation−π Interactions Tuan Anh Pham,*,† S. M. Golam Mortuza,‡ Brandon C. Wood,† Edmond Y. Lau,† Tadashi Ogitsu,† Steven F. Buchsbaum,§ Zuzanna S. Siwy,§ Francesco Fornasiero,† and Eric Schwegler† †

Lawrence Livermore National Laboratory, Livermore, California 94551, United States School of Mechanical and Materials Engineering, Washington State University, Pullman, Washington 99164, United States § Department of Physics and Astronomy, University of California, 4129H Frederick Reines Hall Irvine, Irvine, California 92697-4575, United States ‡

S Supporting Information *

ABSTRACT: Understanding the structure of aqueous electrolytes at interfaces is essential for predicting and optimizing device performance for a wide variety of emerging energy and environmental technologies. In this work, we investigate the structure of two common salt solutions, NaCl and KCl, at a hydrophobic interface within narrow carbon nanotubes (CNTs). Using a combination of first-principles and classical molecular dynamics simulations in conjunction with molecular orbital analysis, we find that the solvation structure of the cations in the CNTs can deviate substantially from the conventional weakly interacting hydrophobic picture. Instead, interactions between solvated ions and π orbitals of the CNTs are found to play a critically important role. Specifically, the ion solvation structure is ultimately determined by a complex interplay between cation−π interactions and the intrinsic flexibility of the solvation shell. In the case of K+, these effects result in an unusually strong propensity to partially desolvate and reside closer to the carbon wall than both Na+ and Cl−, in sharp contrast with the known ion ordering at the water−vapor interface.

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INTRODUCTION Aqueous solutions at graphitic interfaces are essential components in a wide variety of energy and environmental technologies, including ion-selective membranes,1,2 drug delivery and biosensing,3,4 and supercapacitors.5,6 Within these devices, detailed information on the interfacial structure of aqueous solutions is often lacking, yet it is crucial for predicting and optimizing performance. For example, desolvation of ions in subnanometer pores of carbon electrodes leads to high capacitance in supercapacitors and opens up opportunities for designing high-energy density storage devices.7−9 In addition, tuning interactions governing fast transport and high ion selectivity in narrow carbon nanotube (CNT) pores have great potential for water desalination technologies10−12 and lab-on-chip applications.13 It is commonly held that the interaction of water with graphitic carbon is dictated by hydrophobicity;14 however, much less is known about the properties of interfaces between carbon and aqueous salt solutions. To this end, molecular dynamics (MD) simulations with classical force fields have been extensively employed to probe the interactions of aqueous salt solutions within CNTs15−23 and membranes24−26 as well as carbon-slit pore electrodes;27,28 however, the interatomic potentials utilized in classical MD simulations are often parametrized to reproduce the properties of specific model © XXXX American Chemical Society

systems, and the transferability of the potentials to more complicated systems, such as a liquid−solid interface, can be questionable. An unbiased microscopic description of the interfacial interactions and their physiochemical origin is highly desirable for improving simulation accuracy and fidelity. In this regard, first-principles simulations, which do not require any a priori assumptions, are particularly valuable. For example, it has been demonstrated for NaCl solutions in CNTs that the ion solvation structure obtained from commonly used empirical force fields and first-principles simulations can be significantly different.29 A number of previous studies have investigated the physical origins of anion desolvation and stabilization, particularly at the water−vapor interface.30−36 We show that solvated cations can be analogously affected by interfacial interactions when graphitic carbon substrates are present. In this case, the primary physical origin lies in the interaction between cations and the diffuse π orbitals of sp2 carbon. To demonstrate this, we compare the interfacial properties of two common salt solutions, NaCl and KCl, in narrow, single-walled CNTs using a combination of first-principles simulations based on density Received: December 14, 2015 Revised: February 2, 2016

A

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T = 300 K (Supplementary Figures S1 and S2).42,43 Statistics were collected over 45 ps microcanonical simulations for the bulk solutions, while a shorter 20 ps simulation length was used for the CNT-confined KCl solution because of its higher computational cost. Classical MD simulations were carried out using the CHARMM package.44 For the simulations without cation−π interactions, we employed the SWM4-NDP water model,45 and we used polarizable force fields for both ions and CNTs.46 When cation−π interactions were included, simulations were performed using the polarizable force fields developed in ref 47 for K+ and Na+. Specifically, the polarizability was modeled as a classical Drude oscillator by attaching a fictitious (Drude) particle with a charge qD to all non-hydrogen atoms using a harmonic spring with a force constant kD. The Drude particle is able to move away from the atom center in response to the surrounding environment and has a partial charge contribution determined by the atomic polarizability α = q2D/kD. The overall partial charge of the polarizable atom is given by q = qC + qD, which is distributed between the Drude particle and the atom center having a charge of qC. The cation−π interaction was modeled with optimized Lennard-Jones parameters between specific atom pairs that override the default Lennard-Jones values and was parametrized based on potential energy surfaces of the cation−benzene complexes computed at the Møller− Plesset MP2/6-311++G(d,p) level using Gaussian 09,48 as presented in ref 47. Our classical simulations were carried out at 300 K, and statistics were collected over 2 ns NVT simulations.

functional theory (DFT) and classical MD simulations. The first-principles simulations reveal the importance of the aforementioned cation−π interactions and indicate a complex interplay with the structure and dynamics of the ion solvation shell. Interestingly, in the case of K+, these factors act synergistically, causing the cation to approach the carbon wall much closer than both Na+ and Cl−. Using classical MD simulations with specially designed empirical force fields, we are able to systematically decompose the effects of specific interactions and demonstrate that cation−π interactions are critical to properly describe the interfacial solvation structure of the cations.

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COMPUTATIONAL METHODS The confined salt solutions were represented by a tetragonal supercell constructed from four repeat units of the (19,0) CNT primitive cell, with dimensions of a = b = 21.17 Å, c = 17.06 Å. The supercell contained 1 cation−anion pair and 52 water molecules within the CNT (diameter ≈ 14.0 Å), yielding a 1.0 M salt solution with density matching that of bulk water at ambient conditions (1.0 g/cm3). The simulation setup we adopted for the confined KCl solution is identical to that of a previous study for a NaCl solution,29 thus allowing for a direct comparison between structural properties of the two solutions within the CNT. For comparison, bulk salt solutions were also considered, modeled by periodic cubic cells consisting of one cation−anion pair and 62 water molecules. In addition, to investigate the effect of invidual ions on the dynamical properties of water, we considered models consisting of 63 water molecules and a single solvated ion, with the excess charge in these models compensated by a uniform background charge rather than explicit inclusion of a counterion. The size of the cells was chosen to yield the experimental density of liquid water under ambient conditions for all bulk models. The first-principles simulations were carried out using Born− Oppenheimer molecular dynamics with the Qbox code,37 in which the electronic ground-state wave functions were optimized at each ionic step. The interatomic force in the simulations was derived from density functional theory (DFT) and the Perdew, Burke, and Ernzerhof (PBE) approximation for the exchange-correlation energy functional.38 The interaction between valence electrons and ionic cores was represented by norm-conserving pseudopotentials,39 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 au. We note that simulations with more sophisticated approximations for the exchangecorrelation functional, such as the PBE0 hybrid density functional,40 are prohibited for the system size considered in this work due to their high computational cost. In addition, the choice of the PBE0 hybrid functional is expected to lead to negligible effects on the solvation structure of the cations, as demonstrated in ref 41. For the first-principles molecular dynamics simulations, we equilibrated the bulk and confined solutions at a constant temperature of T = 400 K for 15 and 5 ps, respectively. An elevated temperature was chosen as the employment of the PBE approximation is known to yield an overstructured liquid water under ambient conditions, and the use of a simulation temperature around 400 K was shown to recover the experimental liquid structure and water diffusion coefficient at

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RESULTS Ion Solvation in Bulk Water. To establish a baseline for the discussion of salt solutions at the interface with CNTs, we first summarize the first-principles results for the solvation structure of Na+, K+, and Cl− in bulk water. In Figure 1, we

Figure 1. Ion−oxygen radial distribution functions gXO(r) for solvated ions in bulk water obtained from first-principles simulations. Blue, magenta, and green lines indicate results for Na+, K+, and Cl−, respectively.

report the ion−oxygen radial distribution function (gXO(r)) describing the solvation structure of the three ions. For each ion, we also summarize the position of the first maximum in gXO(r) and the corresponding first-shell coordination numbers NXO in Table 1. Note that our results for the gXO(r) peak positions are in good agreement with previous first-principles simulations41,49,51 and experimental measurements.50,52,53 The oxygen coordination numbers of 5.3, 6.2, and 6.1 for Na+, K+, and Cl−, respectively, are also consistent with experimental data.50,52,53 B

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The Journal of Physical Chemistry C Table 1. Solvation Characteristics of K+, Cl−, and Na+ Ions in Bulk Solutions rmax KO (Å) rmax ClO (Å) rmax NaO (Å) NKO NClO NNaO

present

other theory

expt.

2.77 3.12 2.41 6.2 6.1 5.3

2.7749 3.11−3.1241,51 2.4241 6.149 5.9−6.141,51 5.341

2.7350 3.1152 2.4353 6.1 ± 1.050 6.4 ± 1.052 5.4 ± 0.153

our results indicate that K+ has a stronger propensity to reside near the CNT wall than both Cl− and Na+. This is in contrast with the known ion ordering at the water−vapor interface, where Cl− was found to have the strongest surface propensity as previously mentioned.30−36,56,57 Finally, it is worth mentioning that although K+ shows a strong propensity to reside near the carbon, our simulations show that it is not statically bound but rather diffuses along the CNT wall (Supplementary Figure S4).

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DISCUSSION OF PHYSICAL ORIGINS Flexibility of Solvation Shell. To understand the origin of the ion structure and ordering near the carbon wall, it is instructive to independently investigate both the relative solvation strength and the specific interactions with the carbon sidewall. First, we focus on the solvation strength by examining the bulk solvation behavior of the cation−anion pairs. We computed the histogram of the oxygen coordination number in the first solvation shell of each ion averaged over the dynamics trajectories (Supplementary Figure S5). We find that the standard deviations in the first-shell coordination number for Cl− and K+ are σ = 1.07 and 0.97, respectively, considerably larger than the corresponding value of σ = 0.78 for Na+. This analysis indicates that the solvation shell of K+ is more flexible than Na+ with faster water exchange, while Cl− has the most flexible solvation shell. This observation is consistent with experiments58 as well as other first-principles MD studies.49,59,60 Furthermore, it suggests that Cl− and K+ are likely to have a stronger tendency to be desolvated than Na+ at a hydrophobic interface. The above analysis does not reflect the instantaneous collective motion of the water molecules in the solvation shell because each water molecule is averaged independently. Accordingly, we introduce a second metric P = ⟨|Rion − Rsolv COM|⟩, where Rion and Rsolv COM are the instantaneous coordinates of the ion and center of mass of the first water solvation shell, respectively.61 Here the angle brackets indicate an average over all configurations. Physically, this quantity describes the “rattling” of an ion within its solvation shell and evokes the distortion response of the solvation shell to an external perturbation (in our case, the presence of an interface). Consistent with the analysis of the first-shell coordination numbers, we found that P computed for bulk solutions follows the order Cl− (0.61 Å) > K+ (0.52 Å) > Na+ (0.39 Å), which indicates that the first water solvation shell of Cl− is more distorted than K+ and Na+. In addition to the analysis of the ion pair solvation structure, we further investigated the dynamical properties of water in the presence of each of the ions. To deconvolve possible combined effects of cation−anion pairs and focus exclusively on an individual ion’s impact on water dynamics, these simulations were carried out without an explicit counterion. The water diffusion coefficients computed from the oxygen mean-square displacement show that Cl− enhances the diffusivity of water, whereas Na+ slightly suppresses this motion at the considered salt concentration, with K+ in between the two. In particular, we found that water diffusion coefficients computed for the solution models follow the order Cl− (2.45 × 10−5 cm2/s) > K+ (2.27 × 10−5 cm2/s) > Na+ (2.15 × 10−5 cm2/s), compared with a value of 2.29 × 10−5 cm2/s obtained for liquid water (Supplementary Figure S6). Note that this ordering is related to the dynamical flexibility of the ion solvation environment.

Ion Solvation in CNTs. We now discuss the first-principles results for the KCl and NaCl solutions within the CNT, focusing on the structure of the solution−CNT interface. Note that there has been speculation that the water−vapor interface may serve as a minimal model system for other complex hydrophobic interfaces.54,55 Consequently, we also compare our results against the solution−vapor interface, for which MD simulations30−36 and experiments56,57 have consistently shown that the ion surface propensity follows the order Cl− > K+ > Na+. The KCl data presented in this study are compared with results for NaCl from ref 29, which was based on an identical system setup. The radial atomic density distribution function of the KCl solution in the CNT (Figure 2) shows the propensity

Figure 2. Radial atomic density distribution functions of oxygen (red), chloride (green), sodium (blue), and potassium (magenta) in a (19,0) CNT, as obtained with first-principles simulations. The carbon wall is indicated by the dashed-dotted line, and the origin is the center of the CNT. The results for Na+ are from ref 29.

of Cl− to reside near the interface, which is consistent with the results obtained for the confined NaCl solution.29 We found that K+ exhibits a narrow distribution with the peak position noticeably closer to the CNT wall than Cl− or O (i.e., water). We also carried out an additional short simulation with the initial position of K+ chosen to be near the center of the CNT, and we found that the ion migrates to the interface within 1 ps (Supplementary Figure S3). These observations indicate a strong interaction between K+ and the CNT wall and a tendency of the cation to be partially desolvated. The desolvation of K+ can be qualitatively described using a comparison of the oxygen coordination number between the bulk and interfacial environments. Specifically, we find that the oxygen coordination around K+ decreases from a value of 6.2 in the bulk to 4.9 in the CNT, which is a significantly larger reduction than for Cl− (6.1 to 5.7). In addition, our simulations show that the behavior of K+ at the CNT interface contrasts with that of Na+, which is located farther from the interface than Cl−, retaining its first solvation shell.29 As a consequence, C

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The Journal of Physical Chemistry C Collectively, the trends in structural and dynamical properties from the bulk solvation studies consistently indicate that the overall flexibility of the K+ solvation shell lies somewhere between Cl− and Na+. Given these trends, one might expect that when the ions are solvated within a CNT it would be easiest for Cl− to become partially desolvated and approach the wall, followed by K+ and finally Na+; however, this is in clear disagreement with the results in Figure 2. We therefore conclude that bulk solvation properties alone are not sufficient to fully explain the desolvation of K+ and the relative ionic ordering at the solution−CNT interface. Cation−π Interactions. For more detailed understanding, we must consider additional contributions that arise from the specific interaction of the ion with the CNT. We therefore return to our simulations and examine how the electronic density rearranges upon introduction of the CNT interface. The electronic charge density difference Δρe is defined as Δρe = ρe(tot) − ρe(CNT) − ρe(sol), where ρe(tot) is associated with the composite CNT+solution system and ρe(CNT) and ρe(sol) represent the isolated CNT and solution components, respectively. The computed Δρe for single snapshots of KCl (this work) and NaCl (simulation data from ref 29) in Figure 3

ECb6H6(N )= E hyd. − C6H6(N ) − EC6H6 E Hb 2O(N )=

(2)

In eq 2, Ehyd.−C6H6(N) and Ehyd.−H2O(N) are the total energies of the complex consisting of hydrated cation with N water molecules and C6H6 and H2O, respectively; EC6H6 and EH2O are the total energies of isolated C6H6 and H2O molecules. Schematic diagram representing the calculation of EbC6H6(N) and EHb 2O(N) is also shown in Figure 4b.

Figure 3. Electron density analysis of the KCl (left) and NaCl (right) solutions in (19,0) CNTs. Red, green, blue, magenta, and black spheres correspond to O, Cl−, Na+, K+, and C atoms, respectively. Negative and positive polarization charges appearing in the nanotube are represented by the yellow and cyan surfaces, respectively. Negative charge on the CNT stabilizes the interaction with the K+ ion.

Figure 4. Top panel: The energy difference ΔE(N) = EbC6H6(N) − EHb 2O(N) computed with DFT and the PBE approximation, where EbC6H6(N) and EHb 2O(N) are the binding energies of benzene and water to a hydrated cation with N water molecules (see eq 2). Blue and magenta lines indicate results obtained for Na+ and K+, respectively. Lower panel: Schematic diagram representing the calculation procedure for EbC6H6(N) and EHb 2O(N).

reveals qualitative differences. In particular, negative electronic charge is enhanced in carbon atoms in the proximity of K+ and stabilizes the cation near the CNT; this same behavior is absent in NaCl, for which Na+ remains solvated. Indeed, specific interactions between cations and diffuse π electrons are known to be important factors in gas-phase binding of cations to aromatic carbon.62,63 We make an initial assessment of the relevance of cation−π effects in the presence of a solvent using models of benzene and hydrated K + and Na + . Specifically, we considered M+(H2O)m=0−5(C6H6)n=0−1 complexes, where M+ is K+ or Na+. The geometries of the complexes were optimized using DFT with the PBE approximation for the exchange-correlation function. We then evaluated the energy difference ΔE(N ) = ECb6H6(N ) − E Hb 2O(N )

E hyd. − H2O(N ) − E H2O

If ΔE (N) is negative, an N-hydrated cation has a propensity to bind to benzene over water, implying the corresponding cation−π interaction strength exceeds the tendency for further solvation. The results in Figure 4 indicate that when solvation is neglected (N = 0) the binding of both ions to benzene is stronger than that to water and is slightly larger for Na+ than for K+. Note that this appears to conflict with the qualitative ordering in Figure 2, where K+ was found to approach the CNT interface closer than Na+; however, as we populate the first solvation shell with water, the relative interaction strengths of the cations with benzene change at different rates. Ultimately, any preference of hydrated Na+ to bind to benzene is significantly decreased in favor of further hydration (positive ΔE(N)), whereas K+ retains a strong propensity toward benzene (negative ΔE(N)). In other words, the relative strength and ordering of the cation−π interactions becomes qualitatively different once solvation is considered. This conclusion remains valid when a larger aromatic hydrocarbon such as coronene (C24H12) is considered (Supplementary Section IV). Therefore, our analysis highlights the crucial role

(1)

where EbC6H6(N) and EHb 2O(N) are the binding energies of benzene and water, respectively, to a hydrated cation with N water molecules D

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water, ions, and CNT but with cation−π interactions excluded, and second, an otherwise identical simulation including cation−π interactions. The inclusion of polarizability was motivated by prior investigations, suggesting its necessary role in reproducing anion behavior.29−36 Figure 6 compares the radial atomic distribution functions obtained using the two different classical simulation scenarios.

of the water environment and hints at the complexity of the interplay between solvation and interface propensity. The effect of solvation on the cation−π interaction is also reflected in the variation of the molecular orbitals of the hydrated cation−benzene complexes. When solvation is not taken into account, analyses of the highest occupied molecular orbitals (HOMOs) of both Na+(C6H6) and K+(C6H6) show hybridization between the benzene π orbitals and cation states (Figure 5a,b); however, the observed hybridization for

Figure 6. Radial atomic density distribution functions of oxygen (red), chloride (green), potassium (magenta), and sodium (blue) confined in a (19,0) CNT, as obtained from classical simulations using polarizable force fields without (dashed lines) and with cation−π interactions (solid lines). The carbon wall is indicated by the dashed-dotted line, and the origin is the center of the CNT.

When cation−π interactions are absent, K+ and Na+ remain fully solvated in the center of the CNT; however, their inclusion drives both cations toward the interface, with K+ approaching closer and showing a clear tendency to be desolvated. The resulting ion ordering is in full concordance with the first-principles results in Figure 2. Thus, we have evidence that the solvation properties of the ions can be strongly controlled by cation−π interactions and that polarizability alone is not sufficient for a proper description. We note that classical MD simulations have typically neglected these interactions when describing salt solutions in CNTs;15−23 here our study shows that including such interactions in polarizable force fields is in fact critical for obtaining results in qualitative and quantitative agreement with first-principles simulations.

Figure 5. Isosurface representation of the highest occupied molecular orbitals (HOMO) of M+(C6H6) and M+(H2O)4 (C6H6) complexes, where M+ is K+ or Na+. Magenta and blue spheres represent K+ and Na+, respectively. An isosurface value of 0.0002 au was used.

Na+(H2O)4(C6H6) becomes significantly weaker than for K+(H2O)4(C6H6) once water is added (Figure 5c,d). This implies a weakening of the cation−π interaction for Na+ relative to K+ once the solvation effect is taken into account. The conclusion of a weaker Na+−benzene interaction relative to K+ in aqueous solution is consistent with several previous studies. For instance, ref 62 similarly showed that interaction energies of the alkali cations with benzene follow the order Na+ > K+ in the gas phase, while the reverse order K+ > Na+ was found using an implicit solvation model. Similar conclusions concerning the preference for solvated K+−benzene complexes have also been drawn in classical MD calculations.47 In addition, our conclusion is also supported by experimental evidence, where hydrated K+ exhibited ligand exchange with benzene due to preferential cation−π binding, whereas Na+ did not.64,65 Our analysis of the effects of bulk solvation and cation−π interactions in solution suggests that desolvation of K+ at the CNT interface has its origin in the interaction of the ion with diffuse π orbitals of carbon, combined with the flexibility of its solvation shell. Similar complex interplay has also been discussed in the context of anions at the water−vapor interface, where the surface propensity derives from a combination of polarization effects and solvation shell flexibility.66 To further probe our interpretation and directly assess the relevance of cation−π interactions, we leverage classical MD simulations, which afford an advantage over first-principles approaches in their ability to include or exclude various physiochemical interactions at will. We performed two different simulations with different sets of ingredients in the interaction potential: first, a reference simulation with fully polarizable

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CONCLUSIONS A series of first-principles MD simulations were carried out to investigate structural properties of salt solutions in CNTs. By combining the results with model cluster calculations and classical MD simulations intended to probe different physical effects, we show that the solvation structure of the ions is controlled by both ion−solvent and ion−carbon interactions, the latter of which is chiefly dictated by the diffuse π orbitals of the CNT. These factors act synergistically for K+, which unlike Na+ exhibits a significant propensity to reside near the CNT wall and be desolvated. As a result, the behavior of salt solutions at carbon interfaces does not necessarily follow conventional hydrophobic descriptions. It may also differ significantly from the water−vapor interface, for which the attractive cation−π interaction is absent.30−36,56,57 Highlighting the importance of these interactions on the solvation structure of salt solutions in carbon-based materials may provide additional valuable insight for applications from nanofluidic transport13,67 to drug delivery and biosensing68 as well energy storage in aqueous supercapacitors.6 Finally, the present study considered CNTs with the same diameters and chiralities; effects of the radius and E

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curvature on the cation−π interaction will be addressed in our future work.

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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/acs.jpcc.5b12245. Optimized cluster geometries. (ZIP) Figure S1: Oxygen−oxygen radial distribution function of liquid water obtained from first-principles simulations. Figure S2: Mean square displacement of oxygen in liquid water, as obtained from first-principles simulations. Figure S3: Evolution of the ion positions along the CNT radial axis in the initial stage of the simulations. Figure S4: Evolution of the ion positions along the CNT axial axis in the course of the simulations. Figure S5: Histogram of oxygen coordination numbers for the first solvation shell around the Na+, and K+, and Cl− ions in bulk solutions. Figure S6: Mean square dispacement of oxygen computed for solution models consisting of 63 water molecules and a solvated ion: Na+, K+, and Cl−. (PDF)

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS Part of this work was performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under Contract DE-AC52-07NA27344 and funded by the Laboratory Directed Research and Development Program at LLNL under project tracking code 13-ERD-030. T.A.P. acknowledges support from the Lawrence Fellowship; F.F., S.B. and Z.S.S. acknowledge support from the UC Lab Fees Research Program (UCOP Grant ID # 236772). Computational support was from the LLNL Grand Challenge Program.

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