1H NMR Diffusion Studies of Water Self-Diffusion in Supercooled

Article pubs.acs.org/JPCA

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H NMR Diffusion Studies of Water Self-Diffusion in Supercooled Aqueous Sodium Chloride Solutions

Piotr Garbacz†,‡ and William S. Price*,‡ †

Faculty of Chemistry, University of Warsaw, Pasteura 1, 02-093 Warsaw, Poland Nanoscale Organisation and Dynamics Group, University of Western Sydney, Penrith, NSW 2751, Australia

‡

ABSTRACT: The physical properties of aqueous sodium chloride solutions have been studied theoretically, but so far no experimental diffusion data have been obtained under supercooled conditions. Here the results of 1H NMR translational diffusion measurements of water in sodium chloride solutions in the temperature range 230 to 300 K and sodium chloride concentrations up to 4.2 mol/kg are presented. It was found that the diffusion data were well-described by the Vogel−Tamman−Fulcher relationship with concentration-dependent parameters D0, B, and T0. The results indicate that under supercooled conditions the influence of sodium chloride on water diffusion is much smaller than predicted by molecular dynamics simulations.

hydration shells, in pure liquid water.6 Other authors have emphasized the limitation of this approach and the applicability of the structure makers/breakers model for dilute salt-water solutions.7 Another area of importance is the possibility of exploring water behavior below the temperature of homogeneous nucleation of crystalline ice through studying supercooled aqueous salt solutions. Thus, in principle, one can estimate properties of deeply supercooled water by analyses of asymptotic properties of salt solutions, which are extrapolated to the zero-concentration limit. This is an alternative method to studies of confined water, for example, in porous silica materials; however, the latter method requires taking into account water wetting the pore surface, which can have different properties than bulk water.8 Studies of transport properties are valuable for examining the possible similarities between the influence of inorganic salts and pressure on water diffusion. The results of neutron diffraction experiments in aqueous sodium chloride solutions indicate that oxygen−oxygen radial distribution functions are strongly modified by the ions in a manner closely analogous to what happens in pure water under pressure.9 Molecular dynamics simulations of water microstructure in aqueous CaCl2 solutions demonstrate that it cannot be emulated as a pressure effect due to the local nature of such structure perturbations.10 There are several reports on the diffusion of pure water under supercooled conditions.11−14 However, water selfdiffusion in aqueous solutions of sodium chloride or other simple inorganic salts has only been studied for temperatures

I. INTRODUCTION Transport-related properties of water, such as the self-diffusion coefficient or viscosity, play important roles in many physical and chemical phenomena. Supercooled conditions attract much attention because of the presence of non-Arrhenius behavior of water due to hydrogen-bond interactions. The behavior of aqueous supercooled sodium chloride solutions is of particular contemporary interest due to the effects of climate change on sea ice. For instance, first-year Antarctic sea ice was studied by NMR diffusometry using the pulsed gradient spin−echo sequence to detect convective instabilities that could be deduced from the difference between transversal and longitudinal measurements of water diffusion coefficients.1,2 The influence of sodium chloride on water diffusion is also important in the context of salt-water ice imaging, which is performed typically in temperatures from 253 to 273 K.3 Studies of the influence of dissolved inorganic salts on water are also essential for understanding the structure of hydrogenbond networks in aqueous solutions. The structures of such networks are still far from clarified. For example, the effect of ions on the structure of water can be described by the concept of structure making ions (i.e., kosmotropes) or structure breaking ions (i.e., chaotropes) depending on the gain or loss of hydrogen bonding per water molecule due to the presence of ions. This description views aqueous salt solutions as homogeneous liquids with modified intermolecular interactions.4,5 Measurements of the reorientational correlation times of water molecules in aqueous Mg(ClO4)2 solutions by femtosecond pump−probe spectroscopy showed only a weak influence of the ions on the reorientational dynamics of water molecules outside the first solvation shell.6 It was suggested that it is more appropriate to describe this system as a colloidal suspension of inert particles, that is, ions and their first © 2014 American Chemical Society

Received: February 11, 2014 Revised: April 10, 2014 Published: April 11, 2014 3307

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above the melting point.15 Sodium chloride solutions have been frequently studied theoretically by molecular dynamics over extended temperature ranges.16−19 Unfortunately, direct comparisons between the results of experiment and simulations of water diffusion were not performed. The purpose of this paper is to fill this gap. The plan of the paper is as follows. Details of the experimental procedure including NMR measurements of the water self-diffusion coefficient in aqueous solutions of sodium chloride are presented in Section II. This section also includes the experimental data analysis based on the series expansion of the D0, B, and T0 parameters of the Vogel−Tamman−Fulcher (VTF) relationship in terms of the sodium chloride concentration. The measured influence of sodium chloride on water diffusion and molecular dynamics studies in the literature is compared in Section III. Finally, in Section IV, the main conclusions are summarized.

nonlinear least-squares regression of eq 2 onto the experimental spin−echo attenuation data using the Levenberg−Marquardt algorithm implemented in Origin 8.5 (OriginLab, Northampton, MA). Modeling the Diffusion Data. To allow comparison with previous studies of the temperature dependence of the diffusion coefficient of supercooled liquids, especially of water and heavy water,13,14 we investigated the ability of the empirical Vogel− Tamman−Fulcher relationship24−26 to model the present diffusion data. Here the Vogel−Tamman−Fulcher relationship was expressed as ⎛ B (C ) ⎞ D(C , T ) = D0(C) exp⎜ − ⎟ ⎝ T − T0(C) ⎠

where C is the sodium chloride concentration (in mol/kg) and D0, B, and T0 are concentration-dependent fitting parameters. The initial conditions for the nonlinear regression were chosen equal to corresponding parameters for pure water.13 Next, a polynomial was fitted to each of the VTF parameters to model their concentration dependence. This is equivalent to finding the series expansion of D0, B, and T0 in the sodium chloride concentration

II. EXPERIMENTAL SECTION Sample Preparation. Sodium chloride (Merck) was used without further purification. Reverse osmosis (Milli-Q) water was used in all samples. Aqueous solutions containing sodium chloride concentrations from 0 (i.e., pure water) to 4.2 mol/kg, which corresponds to molar concentrations of 0−5 mol/L, at 300 K. The chosen range of concentrations ranges up to the maximal concentration of sodium chloride in water under equilibrium conditions (i.e., 4.45 mol/kg).20 NMR Measurements of Water Diffusion. Each NMR sample was prepared by placing 0.2 μL of anhydrous methanol and 0.2 μL of an aqueous chloride solution, separately, into two glass capillaries (0.13 mm i.d., Nihon Rikagaku Kikai, Tokyo) and flame-sealed. The capillaries were then aligned and positioned by spacers in the center of a 5 mm o.d. NMR tube (528-PP-7, Wilmad). NMR measurements were carried out on a Bruker Avance 400 MHz spectrometer equipped with a BBO probe. Because of the need for highly accurate temperatures the temperaturedependent chemical shift of methanol was used as an internal thermometer21 T (K ) = 468.1 − 108.6 × Δδ

D0(C) = d0 + d1C + d 2C 2 + ...

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B(C) = b0 + b1C + b2C 2 + ...

(5)

T0(C) = t0 + t1C + t 2C 2 + ...

(6)

Analysis of the series expansions was started from the VTF equation for pure water to determine d0, b0, and t0. To obtain more reliable fits, we fixed the parameter d0 at the value reported in ref 13, that is, 4.00 × 10−8 m2 s−1. Values of b0 and t0 parameters were consistent within experimental error of those previously reported.13 Then, higher order terms of D0(C) were investigated. In the series expansion of D0, the nonlinear terms (i.e., d2 and higher) in the expansion for D0(C) were neglected. This assumption was chosen because the fitting of exponential functions of all three parameters (i.e., D0(C), B(C), T0(C)) was difficult due to presence of shallow local minima. Nonetheless, simulations indicate that a small d2 term did not have any observable influence on the degree of fit of eq 3. Other parameters (i.e., B(C) and T0(C)) show relatively small deviations from the linearity. For B(C), it was sufficient to determine the b0 and b1 terms, whereas for T0(C) three coefficients (i.e., t0, t1, and t2) were required to describe the dependence on the sodium chloride concentration.

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where Δδ is the difference in chemical shift of OH and CH3 group in ppm. For temperatures between 300 and 273 K, the temperature was changed in 8 K increments with a cooling rate of 2 K min−1. For temperatures below 273 K, increments of 4 K and a cooling rate of 0.2 K min−1 was used. Before each measurement, at last 10 min was allowed for temperature equilibration. All diffusion measurements were conducted with the pulsed gradient stimulated spin−echo sequence with square gradient pulses.22 Typical acquisition parameters were gradient pulse duration δ = 1 ms, time between gradient pulses Δ = 50 ms, with the gradient strength varied from 2.5 to 50 G cm−1 in 2.5 G cm−1 steps. The gradient was calibrated assuming that the diffusion coefficient of pure water at 298 K equals 2.30 × 10−9 m2 s−1.23 The spin−echo attenuation is related to the pulsesequence parameters and the diffusion coefficient, D, by22 ⎛ ⎛ δ ⎞⎞ E(g ) = exp⎜ −γ 2g 2Dδ 2⎜Δ − ⎟⎟ ⎝ ⎝ 3 ⎠⎠

(3)

III. RESULTS AND DISCUSSION The temperature dependence of the water diffusion coefficients in selected aqueous chloride solutions from 300 K to sample freezing is shown in Figure 1. Approximately half of the diffusion coefficients were measured under supercooled conditions. The expansion coefficients for the fitting parameters, D0, B, and T0, of the VTF equation are tabulated in Table 1, and using these parameters the simulations agree with the experimental data to within 10%. Taking into account experimental errors, the total error of the diffusion coefficient calculated from eq 3 was estimated to be T*) this energy cost is greater than for the water−water hydrogen bond stretching, and thus diffusion of a water molecule is decelerated by interaction with ions. This supports molecular dynamics simulations: ΔG(H2O) ≈ 0.6 kcal/mol, ΔG(Cl−) ≈ 1.0 kcal/mol.37 At low temperatures (T < T*), the hydrogen-bond network of bulk water decelerates the diffusion of water molecules more than the interactions with ions, and water molecules diffuse faster in the aqueous sodium chloride solution than in pure H2O. According to this explanation, the hydrogen-bond network of water is only slightly perturbed by ions at low concentrations of salt. Most probably, the reason for the slowdown of water diffusion at high sodium chloride concentration is the association of ions, that is, the increase in the number of ion pairs and other associated species. The slowdown of water diffusion with increasing salt concentration is also commonly observed in aqueous solutions of other salts.28 Association becomes important for NaCl solutions at concentrations above

Figure 3. Calculated dependencies of D0, B, and T0 on the sodium chloride concentration (green, red, and blue ●, respectively) and fitted second-order polynomials (solid lines). The literature values of the parameters for pure water (green, red, and blue ○, respectively) were taken from Price et al.13 Also shown are the molecular dynamic simulations of Longinotti et al.17 (green, red, and blue □, respectively).

simulations reported by Longinotti et al.17 All parameters exhibit systematic deviations from the experimental results: D0 and B are smaller by ∼15 × 10−9 m2 s−1 and 184 K, respectively, and T0 is 44 K greater than expected from the simulations, whereas the concentration dependence of these parameters agrees well with the experimental data with the curves corresponding to the experimental and simulated data being approximately parallel (i.e., offset) to each other. These differences are clearly visible in the concentration dependence of the water diffusion coefficient in the sodium chloride solutions relative to the diffusion coefficient of pure water shown in Figure 2. Both available molecular-dynamics simulations17,18 overestimate the effects of sodium chloride 3310

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comparable with the activation energies for diffusion in other liquids. For instance, taking literature data, one can estimate that diffusion activation energy of methanol at the freezing point (176 K) is 15 kJ/mol, and it increases to 25 kJ/mol if temperature is decreased by 15 K.41,42 For glycerol, this energy equals 120 kJ/mol at the freezing point (291 K), and it rises to 320 kJ/mol at 260 K.43

on the translational diffusion of water. The theoretical simulations agree with our data above 280 K (not shown). In contrast with the simulations, the amplitude of sodium chloride effect on water diffusion does not exceed 40% of the water diffusion coefficient in the studied range of concentrations and temperatures. One can presume that the primary source of the discrepancy between the results of these molecular dynamics simulations and the results reported here is the overestimation of the slowdown of the pure water diffusion below its freezing point. More specifically, the TIP5P model, which was used in both of the previously mentioned simulations, predicts a higher spontaneous freezing temperature for bulk water (250 K) than observed experimentally (235 K).40 This difference can be removed by appropriative linear rescaling of temperature, namely, using the parameter τ = (T − TW)/(Tm − TW), where TW is the temperature of water maximal heat capacity and Tm is the freezing point of water.40 Using this rescaled temperature in the TIP5P model and the present data, one can reproduce the observed temperature dependence of the self-diffusion coefficient for supercooled water. Thus, in principle, this method could reduce the constant offset between the results of molecular dynamic simulations and the NMR experiment shown in Figure 2; however, this procedure incorporates arbitrarily a new parameter and most probably requires further computational studies to find a clear explanation why τ reproduces better the experimental trends than temperature T. The water diffusion activation energy was estimated from EA (C , β) = −

∂ ln D(C , β) ∂β

IV. CONCLUSIONS The results show that the effect of sodium chloride concentration on water diffusion can be parametrized by a VTF-type relationship with concentration-dependent coefficients D0, B, and T0 expressed in polynomial form. The results obtained for temperatures from 300 K down to freezing are consistent with both previous studies and molecular dynamics simulations, but under supercooled conditions the molecular dynamics simulations underestimate the effects of sodium chloride on water diffusion. We found that there exists a temperature T* where the diffusion coefficient of water is the same for a neat liquid and a sodium chloride aqueous solution. This point could be used for the calibration of parameters used in molecular dynamics simulations. Moreover, one can hypothesize that the acceleration of water diffusion by salts for T < T* is not limited to only particular salts, such as CsI, but it is a common feature of aqueous salt solutions; however, for its observation, supercooled conditions are required.

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AUTHOR INFORMATION

Corresponding Author

*Tel: +61 2 4620 3336. Fax: +61 2 4620 3025. E-mail: w. [email protected].

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where β = (RT)−1 and the gas constant R = 8.3144621(75) J mol−1 K−1. The temperature dependence of the water diffusion activation energy is shown in Figure 4. The activation energy clearly decreases with increasing salt concentration, and the effect is larger at lower temperatures. The activation energy observed for water diffusion in the 1 mol/kg NaCl solution is very similar to that observed for 2H2O in ref 14. The activation energies for water diffusion in sodium chloride solutions are

Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This project was co-operated within the Foundation for Polish Science MPD Programme cofinanced by the EU European Regional Development Fund.

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REFERENCES

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Figure 4. Sodium chloride concentration dependence of activation energy for diffusion estimated from the temperature dependence of the water diffusion coefficient. The inset shows the decrease in diffusion activation energy with the sodium chloride concentration. This energy is reported relative to activation energy for the diffusion of water measured at 300 K. 3311

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