ReaxFF molecular dynamics simulations on the structure and dynamics of electrolyte water systems at ambient temperature

Computational Materials Science xxx (xxxx) xxxx

Contents lists available at ScienceDirect

Computational Materials Science journal homepage: www.elsevier.com/locate/commatsci

ReaxFF molecular dynamics simulations on the structure and dynamics of electrolyte water systems at ambient temperature Nabankur Dasguptaa, Yun Kyung Shinb, Mark V. Fedkinb, Adri C.T. van Duinb, a b

⁎

Department of Engineering Science and Mechanics, Pennsylvania State University, University Park, PA 16802, United States Department of Mechanical Engineering, Pennsylvania State University, University Park, PA 16802, United States

A R T I C LE I N FO

A B S T R A C T

Keywords: ReaxFF Ions Molecular dynamics Diffusion Hydrogen bonds Residence time

ReaxFF molecular dynamics simulations have been performed to study the effect of cations Li+, Na+ and K+ and anion Cl− on the structural and dynamical properties of water, using the force field recently developed by Fedkin and co-workers. The structural relationship of ion and water has been analyzed from the radial distribution function and angular distribution. Comparisons of ReaxFF angle variation of ions and water within the first solvation shell were made and found to be in good agreement with literature. The disruption of hydrogen bond network of water by ions is elucidated by ion-water residence times, water-water hydrogen bond dynamics and reorientational dynamics. ReaxFF diffusion coefficient and residence times of electrolyte water system were compared with ab initio and non-reactive potentials to analyze the difference in dynamics. We gained insight into the ion interaction with water and how it can accelerate or decelerate water dynamics. ReaxFF outlines the formation and dissolution of metal hydroxides and metal chlorides over the course of simulation to explain the diffusion dynamics of water in salt solutions, allowing us to elucidate the impact of concentration on the selfdiffusivity of water and ions in solutions, and to reveal that this effect always decreases the mobility and is not at all ion-specific. The obtained results have opened new opportunities to extend the ReaxFF methodology towards systems involving electrolytes.

1. Introduction Water, a ubiquitous solvent, has unique properties crucial to biological, atmospheric and geological roles. Aqueous salt solutions have been of both theoretical and experimental interest over the years [1–16]. Ions present in water participate in a range of processes, from corrosion [17], cellular activity [18–21], and rechargeable batteries [22], to atmospheric aerosol reactivity [23,24]. The impact of ions on the structure and dynamics of water is explained by translational, rotational and reorientational time correlation function of water molecules [25–28]. The concept of “structure making” or “structure breaking” ions has been introduced in order to systematize the way ions affect the hydrogen bond network of water [29]. Understanding the mechanism of ion-water interactions at the atomistic level is important for processes such as adsorption, ion exchange, biodegradation and material synthesis. Molecular dynamics (MD) simulations provide an approach to understand the mechanism of ion-water interaction. Modelling processes such as ion hydration or salt formation where bonds form or break are possible by quantum mechanical (QM) approaches like density

⁎

functional theory (DFT) [30–38]. Non-reactive force fields have also been successfully applied to water [39–44] and ion-water [45–49] systems to study their structural and dynamical properties. They are faster than QM models and can simulate larger systems (> 1000 atoms). QM methods are usually limited to a few hundred atoms as they are computationally expensive compared to MD methods when scaling up of larger system is required. Non-reactive force fields provide bond stretching and twisting interactions with other atoms in the vicinity, but not bond breaking. Reactive force fields have additional bond order terms which modify pair potential depending on the environment. This allows molecular bonds to be broken and reformed without using QM methods. ReaxFF [50] force fields are parameterized according to DFT data and are capable of accurately defining bond formation and bond breaking in large systems (above 106 atoms). Here, we compare the reliability of ReaxFF force field with DFT and experimental results. ReaxFF MD has been successfully applied to modeling of complex chemical transformations involving high-energy materials [51], silicon/ silicon oxides [52], polymer decompositions [53] in the gas and solid

Corresponding author. E-mail address: [email protected] (A.C.T. van Duin).

https://doi.org/10.1016/j.commatsci.2019.109349 Received 25 July 2019; Received in revised form 10 October 2019; Accepted 12 October 2019 0927-0256/ © 2019 Elsevier B.V. All rights reserved.

Please cite this article as: Nabankur Dasgupta, et al., Computational Materials Science, https://doi.org/10.1016/j.commatsci.2019.109349

Computational Materials Science xxx (xxxx) xxxx

N. Dasgupta, et al.

phase and at the metal liquid interface [54], as well as the structural migration of OH– and H3O+ ions [55]. The reactive force fields for the ReaxFF method have been developed for a number of aqueous systems including metal ions or solids in contact with water [56–60]. This paper further explores the recently developed ReaxFF force field for metal/ halide ions solvation in water developed by Fedkin and co-workers [61]. Although ion solvation in ambient water involves no chemical reactions, the fact that ReaxFF includes covalent bond terms can address the degree of bond formation and dissociation of ions in terms of solvation. Also, at high temperature and high ion concentration, ion aggregation and different chemical species formation can be better understood by ab-initio and reactive force fields. Therefore, it is necessary for us to study the current system using ReaxFF MD. The aim of this paper is to address the change in structure and dynamics of the system for different electrolytes and concentration at ambient temperature. The main goal of this paper is to elucidate the diffusion mechanism of water through salt solutions, and we have organized it as follows. First, we list the details of the simulation procedure we implement. Next, we enunciate the structural relationship between water and ions from radial distribution and angular distribution functions. Then, we compare the diffusion coefficient of ions and water for different systems. Thereafter, we investigate the water-water and ion-water interaction in the form of correlation functions for different systems. Finally, we investigate the effect of concentration on ion mobility through water.

Fig. 1. Initial system configuration of a salt solution for ReaxFF MD simulation at 300 K. The alkali metal (Li, Na or K) and Cl are colored by blue and cyan, respectively.

3. Results and discussions 2. Computational details

3.1. Radial distribution function

In order to understand the dynamics of different salt solutions, MD simulations were performed with three different concentrations of LiCl, NaCl, and KCl (1 M, 3 M and 5 M). In addition, MD simulation of pure water was also performed to elucidate the transition of diffusion phenomenon of various ions in water. A periodic simulation box was created with 1000 water molecules for pure water case, and 700 water molecules for the electrolyte water solution. The volume of the box was adjusted accordingly with van der Waal’s radii of ions (Li+ = 0.76 Å, Na+ = 1.02 Å, K+ = 1.38 Å and Cl− = 1.81 Å) and number of mols water. Table 1 reports the box dimension and the number of molecules of salts of each salt solution. The initial system was created at a very low density, and then minimized and compressed to the desired box size. A ReaxFF simulation setup of salt ions in water is shown in Fig. 1. The temperature of the system was gradually increased to 300 K. Periodic boundary condition was maintained to avoid boundary effects caused by finite size and considering the system as an infinite one. We equilibrated the system at this temperature for 100 ps and conducted MD simulations for 0.5 ns. The last 200 ps were considered for the statistical analysis of the dynamical properties. In our simulation, the time step was set to 0.25 fs to integrate Newton’s equation of motion by velocity-verlet algorithm. A Berendsen thermostat with a 100 fs damping constant was used to control the temperature of the entire system. All of the ReaxFF MD simulations were performed by Amsterdam Density Functional [62] (ADF) package. We used the recent ReaxFF force field developed by Fedkin et al. [61] to study electrolyte water system.

The oxygen–oxygen Radial Distribution Function (RDF) of different electrolyte water systems are computed and illustrated in Fig. 2a. Noticeable oscillations between 3 Å and 6 Å allude to the presence of second hydration shell in pure water, aqueous NaCl and aqueous KCl. The oxygen–oxygen RDF of aqueous LiCl system is more flattened, leading to structure breaking of water molecules and possibility of Li+ hydration. The dynamics of water will be more pronounced when we make comparison of diffusion coefficients of ions and water in Section 3.3. Comparing ion-oxygen RDF in Fig. 2b, we gain further insights into the perturbation of hydrogen bond (HB) dynamics of the different systems. Due to larger van der Waal’s radii of Na+ and K+ compared to Li+, they have a larger first solvation shell radius. Li+ has a very prominent second solvation shell, unlike Na+ and K+, indicating higher structural orders of water molecules. For K+ ions, we find immediate flattening of RDF due to the larger ion size. This feature also adds to the enhancement of water diffusion through salt solution. The chlorineoxygen RDF, shown in Fig. 2c, remains similar in the three different ion water systems. However, there might be some formation of HCl which justifies the slight flattening of RDF between 5 Å and 7 Å which implies structure breaking effect of water in the solvation shell. The ion-Cl RDF shows two distinct peaks for LiCl and NaCl water system but not in aqueous KCl solutions. We can see the presence of Cl− ions in the second solvation shell of K+ ions and no interaction between the ions. However, at high concentrations there might be clustering effect of salts in the higher solvation shells leading to hindered diffusion of ions

Table 1 Electrolyte systems modelled for ReaxFF MD simulations at 300 K. Salt

LiCl NaCl KCl

Box Size in Å3 (no of molecules of solute) 1M

3M

5M

27.65 × 27.65 × 27.65 (13) 27.67 × 27.67 × 27.67 (13) 27.70 × 27.70 × 27.70 (13)

27.80 × 27.80 × 27.80 (40) 27.82 × 27.82 × 27.82 (40) 27.86 × 27.86 × 27.86 (40)

27.94 × 27.94 × 27.94 (66) 27.96 × 27.96 × 27.96 (66) 28.00 × 28.00 × 28.00 (66)

2

Computational Materials Science xxx (xxxx) xxxx

N. Dasgupta, et al.

Fig. 2. Radial distribution function for (a) Oxygen-Oxygen (b) Ion-Oxygen (c) Chlorine-Oxygen and (d) Ion-Chlorine in salt solution (3 M) at 300 K. n(r) denotes the no of atoms within the coordination shell.

orientational preferences of atoms in the first solvation shell. The orientational distribution represents the angle between ion-oxygen vector, IOA and dipole vector of water molecule H2OA in its coordination shell. Fig. 3a represents Metal-O–H bisector angular distribution where we find that majority of water molecules are aligned within θ value of 140° and 180°. Due to the smaller van der Waal’s radius of Li+ and its higher binding affinity with water, the molecules can align themselves up to an angle of 90°. On the other hand, the orientational angular preference of water molecules around Na+ and K+ ions is very close to 180°. The cations seem to act as hydrogen donor since the peak of their angular distribution is very close to 180°. The Cl-O–H bisector angular distribution for different electrolyte water systems is shown in Fig. 3b. Cl− acts as a hydrogen acceptor in all electrolyte water systems and aligns with a dipole vector of water molecules between 0° to 30°. The O-O–H bisector orientation distribution shown in Fig. 3c consists of two peaks which all indicate that water molecules can act both as hydrogen donor and acceptor. Similar behavior is shown by water molecules in all electrolyte systems due to very low concentration of ions to disrupt the HB dynamics. The ions successfully take the role of water to maintain the overall HB network. The oxygen-ion-oxygen, oxygen-chlorine-oxygen and oxygen–oxygen–oxygen angle distributions are represented in Fig. 3d, 3e and 3f, respectively, demonstrating the water molecule distribution in the first solvation radius of ions and water. Fig. 3d shows maxima at θ = 180° and θ = 90° for Li+ and Na+, which means that they have a high probability of a six-fold coordinated structure at 300 K. This also means that they arrange themselves in an octahedral structure. K+ shows its maxima nearly at θ ≈ 160° and 80° which is also consistent with the fact that its hydration number is at least 7. Fig. 3e presents oxygenchlorine-oxygen angle distribution for the three different electrolyte water systems showing multiple peaks, with a highest probability around θ ≈ 75°. This means that the Cl ion does not possess a six-fold

through water. Table 2 lists the solvation shell radius and hydration number of the ions and water. The hydration number Nh in the primary shell was calculated from the ion-oxygen or oxygen–oxygen distribution functions gio (r ) using eq. 1. R1

Nh = ∫ gio (r )4πr 2dr

(1)

0

where R1 is the radius of the first hydration sphere which corresponds to the first minimum in the ion-oxygen or oxygen–oxygen RDF curve. 3.2. Angular distribution Although RDFs provide information about the position of different atoms, structural differences can also be interpreted by the Table 2 Magnitude of maxima and minima of ion-oxygen and oxygen–oxygen RDF and hydration number at 300 K. Radius (in Å) ion

1st max

1st min

2nd max

Nh

Li Na K Cl

2.35 2.54 2.75 3.03 Radius (in Å) 1st max 2.75 2.73 2.73 2.71

3.06 3.38 3.67 3.34

4.05 4.67 5.23 4.44

5.38 5.51 6.09 4.81

1st min 3.35 3.62 3.33 3.31

2nd max 4.32 4.57 4.21 4.12

Nh 6.02 4.51 4.43 4.72

O-O water LiCl NaCl KCl

3

Computational Materials Science xxx (xxxx) xxxx

N. Dasgupta, et al.

Fig. 3. Angle distribution function for (a) Ion-O–H bisector (b) Cl-O–H bisector (c) O-O–H bisector (d) O-ion-O (e) O-Cl-O and (f) O-O-O in the first coordination shell of ions and water at 300 K and the salt concentration of 3 M.

Diffusion of particles in polar solvent depends on hydrodynamic and microscopic friction [66,67]. Microscopic friction is comprised of local number density, polarization fluctuation and collision between particles at molecular level. Polarization fluctuations involve long-range anisotropic interactions, whereas local number density fluctuations, along with particle collisions, involve short-range fluctuations. Hydrodynamic friction originates from solvent polarization current. Ion diffusion in solvents therefore depends on multiple factors like ion size, ion charge, ion concentration and nature of solvent. For ion diffusion in water, microscopic friction predominates over hydrodynamic friction. Dielectric friction decreases with increasing ion size, and local number density fluctuation, along with collision, increases with increasing ion size. The rate of change of dielectric friction is higher than the rate of change of the latter two terms. Therefore, dielectric friction results in higher Di of K+ compared to Li+. Fig. 6a, 6b and 6c represent the occupancy of atoms till the second coordination shell of Li+, Na+ and K+ ion, respectively. The local number density is approximately equal in all the three ions. However, due to small ion size and large polarization effect of Li+, the microscopic friction is generally high. On the other hand, K+ ion, which has a larger size and lower polarization effect, can diffuse faster through bulk water. The microscopic friction in a salt solution is largely dependent on the shear viscosity of the solution. The shear viscosity of the solution is calculated using the Green-Kubo autocorrelation of the off-diagonal components of the stress tensor given by Eq. (3).

coordinated structure and has lower number of oxygen atoms in the solvation shell compared to metal ions. Finally, the oxygen–oxygen–oxygen angle distribution in Fig. 3f shows both the proton donor and acceptor responsibility of water in each system. Rowley and Roux [36] had previously performed MD simulations of Na+ and K+ hydration based on a novel method designed for the challenges of QM/MM simulations of solvent molecules in the liquid phase. They introduced a Flexible Inner Region Ensemble Separator (FIRES) for the ion and a fixed number of nearest water molecules forming a dynamical and flexible inner region represented with high level ab initio QM methods, while bulk water molecules forming the outer region were represented by a polarizable MM Drude potential. We have performed ReaxFF MD simulations of exactly the same number of atoms and volume of box as that of Rowley and Roux [36] to compare the angular distribution of water molecules around metal ions. The comparison is shown in Fig. 4 and the trend of angular distribution is in good agreement. 3.3. Self-Diffusion coefficients of ions We have calculated the diffusion coefficients (Di) of ions for each system. The diffusion coefficient is calculated from the mean square displacement (MSD) by eq 2 [63]. We have obtained Di by making the least square fit of MSD from very long simulations (∼200 ps).

Di = lim

t →∞

[r (t ) − r (0)]i2 6t

2

(2)

η = lim t →∞

Di is calculated from the slope of MSD plots (Fig. 5a and 5b) which are fitted to linear plots. Di for water and metal ions are listed in Table 3 and are consistent with previous experimental [7,64,65] and simulation [9] results. Water molecules in salt solutions have Di smaller than pure water while metal ions follow an increasing trend with increase in size. Diffusion is inversely related to the water retaining ability of ions in solutions.

1 V ⎛ t ∫ Pαβ (t ′) dt ′⎞ 2t kB T ⎝0 ⎠ ⎜

⎟

(3)

where V is the volume of the system, kB the Boltzmann constant and Pαβ the three off-diagonal components of stress-tensor. The simulation details are provided in the Supporting Information (Table S1). The viscosity of the solution increases with the concentration of salts and is inversely proportional to the diffusivity of ions through the solution. We compare the diffusion constants of aqueous NaCl solutions at 4

Computational Materials Science xxx (xxxx) xxxx

N. Dasgupta, et al.

Fig. 4. Comparisons of ion-O–H bisector (top) and O-ion-O angular distribution (bottom) with Rowley and Roux [36]. MM stands for molecular mechanics and CPMD stands for Car-Parinello molecular dynamics.

ability of ions to retain water molecules in their primary shell is represented by the residence time correlation function. The residence time is calculated from the time correlation function [49] given as follows.

different concentrations with Zhang and Han [68]. The diffusion constants are not in well agreement with experiments at high concentrations of salt which can be attributed to the bonding interaction terms developed within ReaxFF force field originating from large number of ions in the system.

R (t ) = 3.4. Residence times

1 Nh

Nh

∑ [θi (0) θi (t )] i=1

(4)

Here θi(t) is the Heaviside unit step function equal to 1 if water molecule is within the primary shell of the ion at time t and 0 otherwise, Nh is the hydration number of the ion or the integral of radial distribution function till the first solvation shell radius. Following Impey et al. [69] and Koneshan et al. [49] we have considered a delay of 2 ps while calculating our residence times of hydration shells. This means

Residence time of water in solvation shell of ions gives us information about the dynamics and lifetime of solvent molecules. It is directly related to the diffusion coefficient, charge and size of ions. In a dynamic system, in order to maintain the hydration number, water molecules are exchanged between the solvation shells of ions. The

Fig. 5. Mean-squared displacement of (a) Ions and (b) Oxygen atoms in different electrolyte systems (3 M) at 300 K. 5

Computational Materials Science xxx (xxxx) xxxx

N. Dasgupta, et al.

Table 3 Diffusion coefficient of water and ions for different systems at 3 M. Do is for pure water. D (water)/Do

Present Ding et al. [9] Kim et al. [7] Muller & Hertz [64]

Present Braun et al. [65]

KCl

NaCl

0.64 ± 0.0161

0.612 ± 0.0198 0.923 0.7 0.809

0.76 1.02 D (ion), 10−9 (m2/s) LiCl 0.611 ± 0.0158 0.761

NaCl 0.787 ± 0.0213 1.051

Fig. 7. Residence time distribution of water in the first coordination shell of ions at 300 K.

that we count a water molecule within primary shell if it is only absent for t ≤ 2 ps. For cations this does not necessarily change the residence time noticeably for the primary shell. It might, however, change the residence time of secondary shell and henceforth, due to frequent exchange of water molecules from the bulk. Fig. 7 shows the residence time of water around ions for different salt water systems. The residence time τ, is calculated by eq 4 and fitted exponentially.

Table 4 Comparisons of residence times of different salt solutions with Koneshan et al [49]. Present

∞

τ = ∫ 〈R (t ) 〉 dt

(5)

0

Koneshan et al. [49] have studied the mobility of different metal ions and halide ions in water at 25 °C using the SPC/E force field model. The structure and dynamics of solvation shells of different ions were understood by various analysis data like RDF, diffusion coefficients, residence times and hydrogen bond dynamics. We have created the electrolyte water system similar to Koneshan et al. [49] to study the dynamics of ions in water using ReaxFF MD. Residence time distribution for different metal ions using SPC/E force field by Koneshan et al. [49] was compared with our present results using ReaxFF MD and reported in Table 4. They are in decent agreement. Introduction of ions in pure water leads to decrease in diffusion of water. Ions which act as “structure makers” have higher numbers of bounded water molecules compared to pure water. Water residence time in cation solvation shell is longer as seen in Fig. 7. Due to smaller size of Li+ ion compared to Na+ and K+ ions, it has higher charge density and more hydration energy. This leads to retention of water around Li+ and lowers the diffusion of Li+.

ion

numerical

exponential

numerical

exponential

Li+ Na+ K+

46.82 15.56 13.31

49.27 13.88 11.61

54.4 19.6 8.7

54.5 19.8 9.4

breaking. Contrary to residence time correlation function, which showed dynamics of water around ions and itself can be characterized by an exponential function, the hydrogen bond dynamics are non-exponential in nature. There cannot be any single time constant which can describe the long-term relaxation time of hydrogen bonds. The kinetics of electrolyte-water system are based on the interplay between diffusion and hydrogen bond dynamics. The correlation that defines the hydrogen bond dynamics [70] is defined by eq 5.

C (t ) =

〈h (0) h (t ) 〉 〈h〉

(5)

C(t) depends on three criteria [9,71]: O-O distance is less than 3.5 Å, O–H distance is less than 2.5 Å and ∠OOH angle is less than or equal to 30°. A configurational criterion for whether a particular pair of water molecules is bonded allows the construction of a hydrogen bond population operator [72], h(t), where t stands for time. It is unity when the particular tagged pair of molecules is hydrogen bonded. < h > denotes the time average of the hydrogen bond function. Fig. 8a

3.5. Hydrogen bonding kinetics The hydrogen bond plays a very important role in the behavior of water as it explains the dynamics of hydrogen bond making and

(a)

Koneshan et al. [49]

(b)

(c)

Cl Li

K

Na

Cl

Fig. 6. Typical hydration shell of (a) Li+ (b) Na+ and (c) K+ ion in 3 M aqueous solution of salt at 300 K. The Cl- ions are represented in blue. The water molecules denoted by red oxygen atoms are within the first coordination shell and the ones denoted by blue oxygen atoms are in the second coordination shell. 6

Computational Materials Science xxx (xxxx) xxxx

N. Dasgupta, et al.

Fig. 8. Correlation function for (a) Hydrogen bond dynamics and (b) Reorientational dynamics of water in different electrolyte systems (3 M) at 300 K.

oxygen atom from a nearby HB network due to high charge density and build a new stronger and structured network of water molecules around itself. Li+ is an example of structure maker and its effect is prominent until its second and third solvation shell. Also, the reorientation time of water molecules around ions displayed in Fig. 8b reinforces the fact that Li+ has stronger electrostatic attractions for water than Na+ and K+. The water molecules present in the vicinity of Li+ are more attracted to it compared to the water molecules in bulk water. Ions which act as structure breakers tend to have shorter reorientation time and residence time, do not have enough charge density to electrostatically attract water molecules and independently rebuild a network. However, we do not see any structure breaking effect among the three different ions in water. The existence of the second hydration shell and bigger radius enable the “structure breaking” ions to influence a larger amount of space in the solution, especially for water molecules in the bulk. The HB kinetics is also described based on the jump statistics. Section S3 of the supplementary information explains the extended jump model which describes the ion diffusion based on the jump rotation of water molecules throughout the simulation time. Fig. 9 provides the average jump distribution time of water molecules in different salt solutions. Figure S1 reports the probability of jump length and jump directionality of water molecules through the vast HB network of different systems. The time required for a water molecule to jump in a pure water system is largest owing to a well-established network of hydrogen bonds. However, introduction of ions strongly changes the HB dynamics within the system thereby changing the diffusion. The water molecules present within the solvation shell of the ion take longer time to jump compared to the ones present within the bulk. Li+ being a “structure maker” reinforces the hydrogen bonding and delays water jump time compared to K+ ion. The probability of jump length and jump angle is also higher for KCl solutions compared to LiCl solutions due to the same reason.

time (ps)

Jump time distribution 0.5 0.4 0.3 0.2 0.1 0 pure water

LiCl

NaCl

KCl

Solution Fig. 9. Jump time distribution of water molecules in different systems at 300 K.

compares the hydrogen bond correlation function for different electrolyte water systems. Introduction of ions in water reduces the selfdiffusion of water. The dynamics of water become slower, with Li+ showing the longest relaxation time, followed by Na+ and K+. This agrees well with the diffusion coefficient of cations in the previous section. We have calculated the reorientation time of water molecules in the primary shell of ions and pure water using the time correlation function (TCF). The rotational motion of water is either deteriorated or accentuated by the presence of ions in water. This is due to the electrostatic attraction of charge density of ions in water. TCF, which investigates the rotational dynamics of water is given by eq 6.

→ → C2 (t ) = P2 [u (0). u (t )]

(6)

Experimental measurements, which include ultrafast infrared anisotropy decays [4,73] and NMR orientational time relaxations [74,75], have shown that anions affect the OH– dynamics of water while cations affect the water dipole movement. For our present study, we therefore find it necessary only to study the dynamics of water dipole reorientation over time for various cations. We have considered the bisector of a water molecule, which is very much aligned to the direction of water dipole moment, as our vector of interest. Due to the inertial effects [66] at the onset of the simulation, C2 (t ) decay is non-exponential in nature and gradually as diffusion prevails, this trend approaches exponential nature. TCF displayed in Fig. 8b quantifies the dynamics wherein water reorientation around Li+ is the slowest, whereas K+ induces nearly similar dynamics as pure water. The results reinforce the fact that Li+ acts as a strong “structure maker”. Ionic concentration might play an important role in the dynamics of water, as they can either increase or decrease the self-diffusion coefficient of water. Ions which act as a structure maker like Li+ and Na+ can remove an

3.6. Effect of concentration on self-diffusion of water We studied the effect of salt concentration on the self-diffusion of water using MD simulations for each system. We studied aqueous solution of salts LiCl, NaCl and KCl using ReaxFF MD simulations at higher concentration. Increase in concentration of electrolyte solutions can have two disrupting effects on the water dynamics. First, it can interrupt the hydrogen bonding network of the water, and second, the electrolyte ions can interact with water molecules and form its own network. Since one of the characteristics of ReaxFF is to describe implicit chemical bonding, we analyzed the species distribution over time. Fig. 10 illustrates the formation and disintegration of ion-water cluster along with hydroxide formation with time. Fig. 10a and 10b compare the number of lithium water clusters in 3 M and 5 M solution, respectively, and show that with increase in concentration, the hydrogen 7

Computational Materials Science xxx (xxxx) xxxx

N. Dasgupta, et al.

Fig. 10. Species formation over time (a) Lithium-water cluster in 3 M (b) Lithium-water cluster in 5 M (c) Metal-hydroxide in 3 M and (d) Metal-hydroxide in 5 M solution at 300 K.

Fig. 11. Overlapping of coordination shells of metal ions in 5 M solutions (left) Li+, (right) K+. The circles denote the shell enclosure of metal and non-metal ions. The blue oxygen atoms belong to the overlapped water molecules in the solvation shells of ions.

bonding network around Li+ ions increase, resulting in overlapping of lithium solvation shells. Fig. 11a provides a picture of Li+ solvation shells in 5 M solution which emphasizes overlapping of hydration shells. Fig. 10c and d compare the metal hydroxide distribution over time for 3 M and 5 M solution, respectively. KOH formation decreases with increase in concentration due to the presence of K+ and Cl− ion in its solvation shell. Due to higher affinity for water, the formation and dissolution of LiOH is expected to be larger than KOH. But as we increase the concentration of ions in water, solvation shells of Li+ ions tend to overlap with Cl− ions disrupting the HB network. This leads to clustering effect and slows down ion mobility through solution. A snapshot of K+ solvation shells along with Cl− solvation shells in Fig. 11b indicates such behavior. Disruption of hydrogen bonding slows down the dynamics of water in concentrated solutions as well. Concentrated solutions are viscous in nature due to reduced mobility of ions in such systems. As indicated by the Stokes-Einstein equation, D = kB T /6πRη, viscosity is inversely related to the diffusion coefficient and at a constant temperature, diffusion reduces at high salt concentrations. In all cases, we see a decrease in self-diffusion coefficient of water as seen in Fig. 12a and 12b. Kim et al. [7] has studied the effect of salt on the dynamics of water molecules using pulse field gradient NMR experiments and MD simulations using polarizable and non-polarizable models. The study concluded that the polarizable and non-polarizable

models at room temperature could not reproduce the experimental trend of concentration dependence for structure-breaking salts upon temperature. The diffusion dependence on concentration of salt solution behaves in a similar way for ReaxFF MD simulations. ReaxFF and other simulation models predict that diffusion decreases with increasing salt concentration for both structure-breaking and structuremaking salts. We have compared our present ReaxFF results with Kim et al. [7] in Fig. 13 and the qualitative trend of ReaxFF agrees well with the simulation models. The quantitative trend of the diffusivity does not match well with experiments with increase in concentration. We attribute the origin of discrepancy to the additional covalent bond parameters within the ReaxFF potential. The empirical covalent potentials within the ReaxFF framework might overestimate the ion-water dynamics in the solvation shell and deduce a slightly different diffusion phenomenon. This might lead to different dynamical properties of different salt solution systems. 4. Conclusions In this work we have studied the effect of electrolyte ions – in particular Li, Na and K cations and Cl anions, on the structure and the dynamics of water at 300 K. The ability of ReaxFF to simulate faster, bigger systems compared to DFT methods has made it a promising tool. While there are differences in static and dynamic properties of water 8

Computational Materials Science xxx (xxxx) xxxx

N. Dasgupta, et al.

Fig. 12. Variation in diffusion coefficient at different concentrations for (a) water and (b) metal ions at 300 K.

CRediT authorship contribution statement Nabankur Dasgupta: Data curation, Software, Investigation, Writing - original draft. Yun Kyung Shin: Formal analysis, Supervision, Writing - review & editing. Mark V. Fedkin: Formal analysis, Supervision. Adri van Duin: Conceptualization, Methodology, Funding acquisition. Declaration of Competing Interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. Acknowledgements We acknowledge funding support from the Multi-Scale Fluid-Solid Interactions in Architected and Natural Materials (MUSE) Center, an Energy Frontier Research Center funded by the U.S. Department of Energy (DOE), Office of Science, Basic Energy Sciences and from the Laboratory Directed Research and Development (LDRD) program of Sandia National Laboratories.

Fig. 13. Comparisons of variation of self-diffusion of water with NaCl concentration with Kim et al. [7].

Appendix A. Supplementary data using ReaxFF and ab initio methods, such as hydrogen bond and reorientational dynamics of water around ions, our results have successfully described the inherent chemical reactions along with diffusional behaviour for these systems. One of the key advantages of using ReaxFF is the ability to relate the qualitative trend of hydrogen bond kinetics with species distribution for different systems. We have computed some of the relevant properties of water at ambient temperature in the presence of ions and compared our results with experimental and ab initio methods. Overall, we can conclude that the structure and dynamics of water at ambient temperature in presence of ions as established by ReaxFF have been satisfactory. RDF indicates that K+ has the largest coordination shell and the coordination number out of all the three ions. Our comparison shows that structural properties of the electrolytewater system like the angular distribution are in decent agreement with dynamic properties such as residence time distribution. HB dynamics and reorientational dynamics correlation function indicate an inverse relation with ion size. The diffusion of ions through water is largely affected by the ion size and the polarization effect as obtained from the self-diffusion constants. We argue that ReaxFF has been able to include additional covalent interaction potentials going beyond Lennard-Jones interactions, and has successfully described phenomena like overlapping of hydration shells of ions. The diffusion of ions through water using ReaxFF MD, can be extended to other electrolyte-water systems and thermodynamic states in the future.

Supplementary data to this article can be found online at https:// doi.org/10.1016/j.commatsci.2019.109349. References [1] H.J. Bakker, Structural Dynamics of Aqueous Salt Solutions, Chem. Rev. 108 (2008) 1456–1473, https://doi.org/10.1021/cr0206622. [2] C.D. Cappa, J.D. Smith, K.R. Wilson, B.M. Messer, M.K. Gilles, R.C. Cohen, R.J. Saykally, Effects of Alkali Metal Halide Salts on the Hydrogen Bond Network of Liquid Water, J. Phys. Chem. B. 109 (2005) 7046–7052, https://doi.org/10.1021/ jp0445324. [3] J.D. Smith, R.J. Saykally, P.L. Geissler, The Effects of Dissolved Halide Anions on Hydrogen Bonding in Liquid Water, J. Am. Chem. Soc. 129 (2007) 13847–13856, https://doi.org/10.1021/ja071933z. [4] K.J. Tielrooij, N. Garcia-Araez, M. Bonn, H.J. Bakker, Cooperativity in Ion Hydration, Science 328 (5981) (2010) 1006–1009, https://doi.org/10.1126/ science:1183512. [5] D.J. Tobias, J.C. Hemminger, Getting Specific About Specific Ion Effects, Science (80-.). 319 (2008) 1197 LP – 1198. doi:10.1126/science.1152799. [6] G. Stirnemann, E. Wernersson, P. Jungwirth, D. Laage, Mechanisms of Acceleration and Retardation of Water Dynamics by Ions, J. Am. Chem. Soc. 135 (2013) 11824–11831, https://doi.org/10.1021/ja405201s. [7] J.S. Kim, Z. Wu, A.R. Morrow, A. Yethiraj, A. Yethiraj, Self-Diffusion and Viscosity in Electrolyte Solutions, J. Phys. Chem. B. 116 (2012) 12007–12013, https://doi. org/10.1021/jp306847t. [8] J. Mähler, I. Persson, A Study of the Hydration of the Alkali Metal Ions in Aqueous Solution, Inorg. Chem. 51 (2012) 425–438, https://doi.org/10.1021/ic2018693. [9] Yun Ding, Ali A. Hassanali, Michele Parrinello, Anomalous water diffusion in salt

9

Computational Materials Science xxx (xxxx) xxxx

N. Dasgupta, et al.

[10] [11]

[12]

[13] [14]

[15]

[16]

[17] [18] [19] [20] [21]

[22]

[23]

[24]

[25]

[26]

[27] [28] [29] [30]

[31]

[32]

[33]

[34]

[35]

[36]

[37]

[38]

solutions, Proc Natl Acad Sci USA 111 (9) (2014) 3310–3315, https://doi.org/10. 1073/pnas.1400675111. M.D. Fayer, Dynamics of Water Interacting with Interfaces, Molecules, and Ions, Acc. Chem. Res. 45 (2012) 3–14, https://doi.org/10.1021/ar2000088. J.L. Fulton, G.K. Schenter, M.D. Baer, C.J. Mundy, L.X. Dang, M. Balasubramanian, Probing the Hydration Structure of Polarizable Halides: A Multiedge XAFS and Molecular Dynamics Study of the Iodide Anion, J. Phys. Chem. B. 114 (2010) 12926–12937, https://doi.org/10.1021/jp106378p. S. Funkner, G. Niehues, D.A. Schmidt, M. Heyden, G. Schwaab, K.M. Callahan, D.J. Tobias, M. Havenith, Watching the Low-Frequency Motions in Aqueous Salt Solutions: The Terahertz Vibrational Signatures of Hydrated Ions, J. Am. Chem. Soc. 134 (2012) 1030–1035, https://doi.org/10.1021/ja207929u. M.F. Kropman, H.J. Bakker, Dynamics of Water Molecules in Aqueous Solvation Shells, Science (80-.). 291 (2001) 2118 LP – 2120. doi:10.1126/science.1058190. H.J. Kulik, E. Schwegler, 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 (2012) 2653–2658, https://doi. org/10.1021/jz300932p. D.E. Moilanen, D. Wong, D.E. Rosenfeld, E.E. Fenn, M.D. Fayer, Ion-water hydrogen-bond switching observed with 2D IR vibrational echo chemical exchange spectroscopy, Proc. Natl. Acad. Sci. USA 106 (2009) 375–380, https://doi.org/10. 1073/pnas.0811489106. C.J. Mundy, I.-F.W. Kuo, First-Principles Approaches to the Structure and Reactivity of Atmospherically Relevant Aqueous Interfaces, Chem. Rev. 106 (2006) 1282–1304, https://doi.org/10.1021/cr040375t. Z.Y. Ding, M.A. Frisch, L. Li, E.F. Gloyna, Catalytic Oxidation in Supercritical Water, Ind. Eng. Chem. Res. 35 (1996) 3257–3279, https://doi.org/10.1021/ie960022n. K.A. Dill, Dominant forces in protein folding, Biochemistry. 29 (1990) 7133–7155, https://doi.org/10.1021/bi00483a001. R.L. Baldwin, How Hofmeister ion interactions affect protein stability, Biophys. J. 71 (1996) 2056–2063, https://doi.org/10.1016/S0006-3495(96)79404-3. P. Ball, Water as an Active Constituent in Cell Biology, Chem. Rev. 108 (2008) 74–108, https://doi.org/10.1021/cr068037a. Y. Zhang, P.S. Cremer, Interactions between macromolecules and ions: the Hofmeister series, Curr. Opin. Chem. Biol. 10 (2006) 658–663, https://doi.org/10. 1016/j.cbpa.2006.09.020. P. Vassilev, R.A. van Santen, M.T.M. Koper, Ab initio studies of a water layer at transition metal surfaces, J. Chem. Phys. 122 (2005) 54701, https://doi.org/10. 1063/1.1834489. E.M. Knipping, M.J. Lakin, K.L. Foster, P. Jungwirth, D.J. Tobias, R.B. Gerber, D. Dabdub, B.J. Finlayson-Pitts, Experiments and Simulations of Ion-Enhanced Interfacial Chemistry on Aqueous NaCl Aerosols, Science (80-.). 288 (2000) 301 LP – 306. doi:10.1126/science.288.5464.301. E.C. Brown, M. Mucha, P. Jungwirth, D.J. Tobias, Structure and Vibrational Spectroscopy of Salt Water/Air Interfaces: Predictions from Classical Molecular Dynamics Simulations, J. Phys. Chem. B. 109 (2005) 7934–7940, https://doi.org/ 10.1021/jp0450336. R.G. Linck, A Review of: “Metal Ions in Solution, John Burgess, Ellis Horwood Limited, Chichester, Sussex, England, 1978. 481 pages, $60.00.”, Synthesis and Reactivity in Inorganic and Metal-Organic Chemistry 9 (3) (1979) 295–296, https://doi.org/10.1080/00945717908057467. J. Heinze, Principles of Electrochemistry. Von J. Koryta, J. Dvorák und L. Kavan. Wiley, Chichester, 1993. 486 S., Broschur 24.95 £. – ISBN 0-471-93838-6, Angew. Chemie. 106 (1994) 2441–2442. doi:10.1002/ange.19941062239. H.D.B. Jenkins, Y. Marcus, Viscosity B-Coefficients of Ions in Solution, Chem. Rev. 95 (1995) 2695–2724, https://doi.org/10.1021/cr00040a004. H. Ohtaki, T. Radnai, Structure and dynamics of hydrated ions, Chem. Rev. 93 (1993) 1157–1204, https://doi.org/10.1021/cr00019a014. F.H. MacDougall, Ions in Solution. By R, W. Gurney, J. Phys. Chem. 41 766 (1937), https://doi.org/10.1021/j150383a018. A. Bankura, V. Carnevale, M.L. Klein, Hydration structure of salt solutions from ab initio molecular dynamics, J. Chem. Phys. 138 (2013) 14501, https://doi.org/10. 1063/1.4772761. S.B. Rempe, L.R. Pratt, G. Hummer, J.D. Kress, R.L. Martin, A. Redondo, The Hydration Number of Li+ in Liquid Water, J. Am. Chem. Soc. 122 (2000) 966–967, https://doi.org/10.1021/ja9924750. M. Cavallari, C. Cavazzoni, M. Ferrario, Structure of NaCl and KCl concentrated aqueous solutions by ab initio molecular dynamics, Mol. Phys. 102 (2004) 959–966, https://doi.org/10.1080/00268970410001711904. J.A. White, E. Schwegler, G. Galli, F. Gygi, The solvation of Na+ in water: Firstprinciples simulations, J. Chem. Phys. 113 (2000) 4668–4673, https://doi.org/10. 1063/1.1288688. T. Ikeda, M. Boero, Communication: Hydration structure and polarization of heavy alkali ions: A first principles molecular dynamics study of Rb+ and Cs+, J. Chem. Phys. 137 (2012) 41101, https://doi.org/10.1063/1.4742151. D. Bucher, L. Guidoni, P. Carloni, U. Rothlisberger, Coordination Numbers of K+ and Na+ Ions Inside the Selectivity Filter of the KcsA Potassium Channel: Insights from First Principles Molecular Dynamics, Biophys. J. 98 (2010) L47–L49, https:// doi.org/10.1016/j.bpj.2010.01.064. C.N. Rowley, B. Roux, The Solvation Structure of Na+ and K+ in Liquid Water Determined from High Level ab Initio Molecular Dynamics Simulations, J. Chem. Theory Comput. 8 (2012) 3526–3535, https://doi.org/10.1021/ct300091w. L.M. Ramaniah, M. Bernasconi, M. Parrinello, Ab initio molecular-dynamics simulation of K+ solvation in water, J. Chem. Phys. 111 (1999) 1587–1591, https://doi. org/10.1063/1.479418. A. Bankura, A. Karmakar, V. Carnevale, A. Chandra, M.L. Klein, Structure,

[39]

[40]

[41]

[42]

[43]

[44]

[45]

[46]

[47]

[48]

[49]

[50]

[51]

[52]

[53]

[54]

[55]

[56]

[57]

[58]

[59]

[60]

[61]

[62]

[63] [64]

10

Dynamics, and Spectral Diffusion of Water from First-Principles Molecular Dynamics, J. Phys. Chem. C. 118 (2014) 29401–29411, https://doi.org/10.1021/ jp506120t. F. Sedlmeier, D. Horinek, R.R. Netz, Spatial Correlations of Density and Structural Fluctuations in Liquid Water: A Comparative Simulation Study, J. Am. Chem. Soc. 133 (2011) 1391–1398, https://doi.org/10.1021/ja1064137. W.L. Jorgensen, J. Chandrasekhar, J.D. Madura, R.W. Impey, M.L. Klein, Comparison of simple potential functions for simulating liquid water, J. Chem. Phys. 79 (1983) 926–935, https://doi.org/10.1063/1.445869. C. Vega, J.L.F. Abascal, Simulating water with rigid non-polarizable models: a general perspective, Phys. Chem. Chem. Phys. 13 (2011) 19663–19688, https://doi. org/10.1039/C1CP22168J. J.L.F. Abascal, C. Vega, Dipole-Quadrupole Force Ratios Determine the Ability of Potential Models to Describe the Phase Diagram of Water, Phys. Rev. Lett. 98 (2007) 237801, , https://doi.org/10.1103/PhysRevLett. 98.237801. H.J.C. Berendsen, J.R. Grigera, T.P. Straatsma, The missing term in effective pair potentials, J. Phys. Chem. 91 (1987) 6269–6271, https://doi.org/10.1021/ j100308a038. B.S. Mallik, A. Chandra, An ab initio molecular dynamics study of the frequency dependence of rotational motion in liquid water, J. Mol. Liq. 143 (2008) 31–34, https://doi.org/10.1016/j.molliq.2008.04.015. M. Fyta, R.R. Netz, Ionic force field optimization based on single-ion and ion-pair solvation properties: Going beyond standard mixing rules, J. Chem. Phys. 136 (2012) 124103, , https://doi.org/10.1063/1.3693330. S. Tazi, J.J. Molina, B. Rotenberg, P. Turq, R. Vuilleumier, M. Salanne, A transferable ab initio based force field for aqueous ions, J. Chem. Phys. 136 (2012) 114507, , https://doi.org/10.1063/1.3692965. Z.R. Kann, J.L. Skinner, A scaled-ionic-charge simulation model that reproduces enhanced and suppressed water diffusion in aqueous salt solutions, J. Chem. Phys. 141 (2014) 104507, , https://doi.org/10.1063/1.4894500. S. Chowdhuri, A. Chandra, Hydration structure and diffusion of ions in supercooled water: Ion size effects, J. Chem. Phys. 118 (2003) 9719–9725, https://doi.org/10. 1063/1.1570405. S. Koneshan, J.C. Rasaiah, R.M. Lynden-Bell, S.H. Lee, Solvent Structure, Dynamics, and Ion Mobility in Aqueous Solutions at 25 °C, J. Phys. Chem. B. 102 (1998) 4193–4204, https://doi.org/10.1021/jp980642x. A.C.T. van Duin, S. Dasgupta, F. Lorant, W.A. Goddard, ReaxFF: A Reactive Force Field for Hydrocarbons, J. Phys. Chem. A. 105 (2001) 9396–9409, https://doi.org/ 10.1021/jp004368u. A. Strachan, A.C.T. van Duin, D. Chakraborty, S. Dasgupta, W.A. Goddard, Shock Waves in High-Energy Materials: The Initial Chemical Events in Nitramine RDX, Phys. Rev. Lett. 91 (2003) 98301, https://doi.org/10.1103/PhysRevLett. 91. 098301. A.C.T. van Duin, A. Strachan, S. Stewman, Q. Zhang, X. Xu, W.A. Goddard, ReaxFFSiO Reactive Force Field for Silicon and Silicon Oxide Systems, J. Phys. Chem. A. 107 (2003) 3803–3811, https://doi.org/10.1021/jp0276303. K. Chenoweth, S. Cheung, A.C.T. van Duin, W.A. Goddard, E.M. Kober, Simulations on the Thermal Decomposition of a Poly(dimethylsiloxane) Polymer Using the ReaxFF Reactive Force Field, J. Am. Chem. Soc. 127 (2005) 7192–7202, https:// doi.org/10.1021/ja050980t. M.F. Russo, R. Li, M. Mench, A.C.T. van Duin, Molecular dynamic simulation of aluminum–water reactions using the ReaxFF reactive force field, Int. J. Hydrogen Energy. 36 (2011) 5828–5835, https://doi.org/10.1016/j.ijhydene.2011.02.035. W. Zhang, A.C.T. van Duin, ReaxFF Reactive Molecular Dynamics Simulation of Functionalized Poly(phenylene oxide) Anion Exchange Membrane, J. Phys. Chem. C 119 (2015) 27727–27736, https://doi.org/10.1021/acs.jpcc.5b07271. H. Manzano, R.J.M. Pellenq, F.-J. Ulm, M.J. Buehler, A.C.T. van Duin, Hydration of Calcium Oxide Surface Predicted by Reactive Force Field Molecular Dynamics, Langmuir. 28 (2012) 4187–4197, https://doi.org/10.1021/la204338m. B. Jeon, S.K.R.S. Sankaranarayanan, A.C.T. van Duin, S. Ramanathan, Reactive Molecular Dynamics Study of Chloride Ion Interaction with Copper Oxide Surfaces in Aqueous Media, ACS Appl. Mater. Interfaces. 4 (2012) 1225–1232, https://doi. org/10.1021/am201345v. J.D. Gale, P. Raiteri, A.C.T. van Duin, A reactive force field for aqueous-calcium carbonate systems, Phys. Chem. Chem. Phys. 13 (2011) 16666–16679, https://doi. org/10.1039/C1CP21034C. A.C.T. van Duin, V.S. Bryantsev, M.S. Diallo, W.A. Goddard, O. Rahaman, D.J. Doren, D. Raymand, K. Hermansson, Development and Validation of a ReaxFF Reactive Force Field for Cu Cation/Water Interactions and Copper Metal/Metal Oxide/Metal Hydroxide Condensed Phases, J. Phys. Chem. A. 114 (2010) 9507–9514, https://doi.org/10.1021/jp102272z. O. Rahaman, A.C.T. van Duin, V.S. Bryantsev, J.E. Mueller, S.D. Solares, W.A. Goddard, D.J. Doren, Development of a ReaxFF Reactive Force Field for Aqueous Chloride and Copper Chloride, J. Phys. Chem. A. 114 (2010) 3556–3568, https://doi.org/10.1021/jp9090415. M.V. Fedkin, Y.K. Shin, N. Dasgupta, J. Yeon, W. Zhang, D. Van Duin, A.C.T. Van Duin, K. Mori, A. Fujiwara, M. Machida, H. Nakamura, M. Okumura, Development of the ReaxFF Methodology for Electrolyte-Water Systems, J. Phys. Chem. A. 123 (2019), https://doi.org/10.1021/acs.jpca.8b10453. G. te Velde, F.M. Bickelhaupt, E.J. Baerends, C. Fonseca Guerra, S.J.A. van Gisbergen, J.G. Snijders, T. Ziegler, Chemistry with ADF, J. Comput. Chem. 22 (2001) 931–967, https://doi.org/10.1002/jcc.1056. A. Einstein, Investigations on the Theory of the Brownian Movement, Dover Publications, 1956 https://books.google.com/books?id=AOIVupH_hboC. K.J. Müller, H.G. Hertz, A Parameter as an Indicator for Water−Water Association in Solutions of Strong Electrolytes, J. Phys. Chem. 100 (1996) 1256–1265, https://

Computational Materials Science xxx (xxxx) xxxx

N. Dasgupta, et al.

[71] S. Chowdhuri, A. Chandra, Molecular dynamics simulations of aqueous NaCl and KCl solutions: Effects of ion concentration on the single-particle, pair, and collective dynamical properties of ions and water molecules, J. Chem. Phys. 115 (2001) 3732–3741, https://doi.org/10.1063/1.1387447. [72] A. Luzar, D. Chandler, Effect of Environment on Hydrogen Bond Dynamics in Liquid Water, Phys. Rev. Lett. 76 (1996) 928–931, https://doi.org/10.1103/PhysRevLett. 76.928. [73] S. Park, M. Odelius, K.J. Gaffney, Ultrafast Dynamics of Hydrogen Bond Exchange in Aqueous Ionic Solutions, J. Phys. Chem. B. 113 (2009) 7825–7835, https://doi. org/10.1021/jp9016739. [74] G. Engel, H.G. Hertz, On the Negative Hydration. A Nuclear Magnetic Relaxation Study, Berichte Der Bunsengesellschaft, Für Phys. Chemie. 72 (1968) 808–834, https://doi.org/10.1002/bbpc.19680720713. [75] L. Endom, H.G. Hertz, B. Thül, M.D. Zeidler, A Microdynamic Model of Electrolyte Solutions as Derived from Nuclear Magnetic Relaxation and Self-Diffusion Data, Berichte Der Bunsengesellschaft Für Phys. Chemie. 71 (1967) 1008–1031, https:// doi.org/10.1002/bbpc.19670710907.

doi.org/10.1021/jp951303w. [65] B.M. Braun, H. Weingaertner, Accurate self-diffusion coefficients of lithium(1+), sodium(1+), and cesium(1+) ions in aqueous alkali metal halide solutions from NMR spin-echo experiments, J. Phys. Chem. 92 (1988) 1342–1346, https://doi.org/ 10.1021/j100316a065. [66] S. Ravichandran, B. Bagchi, Non-exponential orientational relaxation in dipolar solids: The role of dipolar interactions and dielectric friction, J. Mol. Struct. 327 (1994) 247–254, https://doi.org/10.1016/S0022-2860(94)85012-7. [67] B. Bagchi, Microscopic derivation of the Hubbard–Onsager–Zwanzig expression of limiting ionic conductivity, J. Chem. Phys. 109 (1998) 3989–3993, https://doi.org/ 10.1063/1.476998. [68] Han Zhang, Viscosity and Density of Water + Sodium Chloride + Potassium Chloride Solutions at 298.15 K, J. Chem. Eng. Data. 41 (1996) 516–520, https:// doi.org/10.1021/je9501402. [69] R.W. Impey, P.A. Madden, I.R. McDonald, Hydration and mobility of ions in solution, J. Phys. Chem. 87 (1983) 5071–5083, https://doi.org/10.1021/j150643a008. [70] A. Luzar, D. Chandler, Hydrogen-bond kinetics in liquid water, Nature. 379 (1996) 55, https://doi.org/10.1038/379055a0.

11