Organic Solvents

Article Cite This: J. Phys. Chem. B XXXX, XXX, XXX−XXX

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Ion Polarizabilities in Binary Liquid Mixtures of Water/Organic Solvents Minglun Li,†,‡ Yuyuan Lu,*,† and Lijia An† †

State Key Laboratory of Polymer Physics and Chemistry, Changchun Institute of Applied Chemistry, Chinese Academy of Sciences, Changchun 130022, People’s Republic of China ‡ University of Chinese Academy of Sciences, Beijing 100049, People’s Republic of China

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S Supporting Information *

ABSTRACT: Using our recently proposed method to obtain salt and ion polarizabilities in aqueous solutions, we determine the polarizabilities of five salts (LiCl, NaCl, NaBr, KBr, and MgSO4) in water−acetonitrile, water− ethanol, and water−acetone solutions at eight different water−organic solvent compositions at the D-line of sodium (589.3 ± 0.1 nm). Setting Li+ as the reference ion, we determine the ion polarizabilities of Na+, Cl−, and Br− in binary liquid mixtures. Our results show that cation polarizability is nearly unaffected by solvent composition, but anion polarizability exhibits a nonmonotonic behavior with increasing mole fraction of the organic component in the liquid mixture. This suggests that ion polarizability in a solution is affected by the solvent. The results of salt and ion polarizabilities can be used as important reference data for physical chemistry, atmospheric science, and biophysics.

I. INTRODUCTION Salt and ion polarizabilities in solution are fundamental to a wide range of biophysical,1−5 atmospheric,6−8 and chemical and interfacial sciences.9−18 For example, solution-phase ion polarizability is a key physical parameter for calculating the self-energy,11 interfacial tension,12−14 viscosity,15,16 chargetransfer kinetics,17 and charge distribution near an interface.18 In fact, the ion polarizability has been demonstrated to be the basis of numerous complex physicochemical phenomena, including ion-induced nucleation of water19 and specific ion effects5,20−25 (manifested in the Hofmeister series that is of growing interest3−5). The interest in solution-phase ion polarizabilities does not lie only in water-based systems;26−33 binary electrolyte liquid mixtures of water/organic solvent are of much current technological interest as an excellent extractant system.34−40 As such, accurate reference data for salt and ion polarizabilities in water/organic solvents are required for us to better understand, evaluate, and make use of ion-polarizability effects in a quantitative and systematic manner. Direct determination of ion polarizability in liquid mixtures remains a challenge. In the past few decades, Marcus and coworkers extensively measured several ionic properties in nonaqueous solvents, including ionic partial molar heat capacities,29 ionic partial molar volumes,30 solvation numbers of divalent metal ions,31 and standard molar Gibbs free energies/enthalpies transfer of ions.32,33 However, measurements of ion polarizability in liquid mixtures are not included. More recently, Mazzini and Craig systematically investigated the specific ion effects in both water and nonaqueous solvents © XXXX American Chemical Society

and their correlations with standard partial molar volumes and electrostrictive volumes of electrolytes.41−44 They found that specific ion effects may reverse its trend in certain nonaqueous solvents, and interpreted their observation based on solvent polarizabilities and the ion-solvent and the ion-surface interactions.44 One may naturally expect that ion polarizabilities play a crucial role, too, because ion polarizabilities are central to specific ion effects, as reviewed by Parsons et al.45 To investigate the role of ion polarizabilities, one would have to first quantify the solution-phase ion polarizabilities in an extensive set of liquid mixtures. Recently, there have been computational efforts for determining solution-phase ion polarizabilities in aqueous solution using density functional theory.46,47 Specifically, Molina et al. calculated the polarizabilities of a series of monoatomic cations and anions with maximally localized Wannier functions in an applied external field,46 and Masia measured the polarizability of Cl− in aqueous solution by accounting for the spatial extent of the electronic density.47 However, it is difficult to extend these calculations in aqueous solution to liquid mixtures of water/organic solvents, because ion polarizabilities are strongly affected by the solvent shell structure surrounding the ion,9,12,48,49 such that solution-phase ions behave differently from those in the gas or crystalline phases.50,51 In addition, numerical accuracy of the calculation is uncertain, as calculated ion polarizabilities have a nonReceived: July 30, 2018 Revised: September 24, 2018 Published: October 11, 2018 A

DOI: 10.1021/acs.jpcb.8b07327 J. Phys. Chem. B XXXX, XXX, XXX−XXX

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The Journal of Physical Chemistry B

different salts yield different values of η,55 so we treat η as a parameter for the nonlinear fitting of Vss/Vs. Finally, the mole fraction of salt xsalt is given by

negligible dependence on system sizes as pointed out by Masia.47 To accurately determine the polarizabilities of salts and ions in solutions, we recently proposed a novel method52,53 based on a modified Clausius−Mossotti equation combined with the Debye−Hückel limiting law.54,55 While our earlier work focused on ion polarizability in aqueous solution, in this work, we generalize this method to binary liquid mixtures. We systematically determine the polarizabilities of five salts (LiCl, NaCl, NaBr, KBr, and MgSO4) in three different water/organic solvents (water−acetonitrile (ACN), water−ethanol (EA), and water−acetone (CP)) at eight volume ratios of water/organic solvent mixtures (9.5:0.5, 9:1, 8.5:1.5, 8:2, 7.5:2.5, 7:3, 6.5:3.5, and 6:4). Setting Li+ as the standard ion, we determine the polarizabilities of single ions (Na+, Cl−, and Br−) in these water/organic solvents. Our results suggest that ion polarizabilities significantly depend on the solvent type and mixing ratio of the binary mixture; an accurate theoretical description of the salt effect in binary liquid mixtures requires the incorporation of these effects in modeling. The rest of this paper is organized as follows. In Section II, we present the key theoretical formula for salt polarizability from our previous work.52,53 In Section III, we describe the materials and experimental methods. In Section IV, we present our experimental results on the polarizabilities of salts and ions in binary liquid mixtures and compared the calculated refractive indices based on different salt polarizabilities. We conclude in Section V.

xsalt = Nsalt /(Nsalt + Nos + Nwater)

where Nsalt, Nwater, and Nos are the particle numbers of the salt, water, and the organic solvent in a mixture of the volume Vss, respectively. The subscript “os” represents acetonitrile (ACN), ethanol (EA), or acetone (CP). Expanding eq 1 to the first order in xsalt, we obtain the following simplified expression of refractive indices for low salt concentrations52,53 n = ns + Kxsalt

which can be re-expressed as ÄÅ ÉÑ ÑÑ 3Vs 6ns 1 ÅÅÅÅ 2 ÑÑ K + ( n − 1) γ αsalt = Å ÑÑ s ÑÑÑ 4πNA ns2 + 2 ÅÅÅÅÇ ns2 + 2 Ö

ns2 + 2

=

∑ j ∈ solvents

(1)

(2)

where nj and ρ(0) are the refractive index and the number j density in the pure liquid of the jth component of the solvent (water or the organic solvent); ρj is the number density for the jth component in the mixture. In eq 1, Vs is the molar volume of a salt-free solvent mixture (water/organic solvent) and Vss is the actual volume of the system, when salt is added to 1 mol of water/organic solvent. Following the Debye−Hückel limiting law, Vss is related to Vs via54,55 3/2 Vss = Vs[1 + γxsalt + ηxsalt ]

(7)

III. EXPERIMENTAL METHODS III.I. Chemicals. Deionized and doubly distilled water, acetonitrile (Aladdin, anhydrous, H2O: 20−30 ppm), ethanol (Aladdin, 99.8%, spectroscopically pure), and acetone (Beijing, A. R.) were used in the experiments. The salts were dried in a vacuum oven (80 °C, 133Pa) for 2 h prior to use. We studied the following salts: lithium chloride (LiCl, Vetec, reagent grade), sodium chloride (NaCl, Vetec, 99%, reagent grade), sodium bromide (NaBr, Vetec, 98%, reagent grade), potassium bromide (KBr, Vetec, 99%, reagent grade), and magnesium sulfate (MgSO4, Sigma-Aldrich, 99.5%, anhydrous). III.II. Measurements. The samples were kept in Thermo HAAKE SC150-A5B circulating water bath (Newington) with a digital temperature-control unit to maintain the required temperature (25 °C) within ±0.1 °C for 1 h to reach thermostatic equilibrium before being removed for density and refractive index measurements. All mixtures were prepared by weighing the masses with an uncertainty of ±0.0001 g due to evaporation. The volumes of the solutions were calculated via density data with known masses of solutions (mass divided by density). The masses were then measured with a balance (Sartorius, BT 125D, Beijing, China) with a precision of

ρj nj2 − 1 2 ρj(0) nj + 2

(6)

Because γ and K can be obtained from experiment through the variation of volume and refractive index with salt concentration, eq 7 provides a valuable method for determining the polarizabilities of a salt in binary liquid mixtures. Generally speaking, the refractive index and volume depend on the temperature, thus the polarizability is also dependent on the temperature. Our previous work,53 however, showed that the temperature dependence of salt polarizability is generally quite weak; we thus focus on the polarizability at a fixed temperature in this work. Furthermore, in this work, we focus on the dependence of αsalt on the molar fraction of organic compounds in binary liquid mixtures of water/organic solvents. Hereafter, we adopt cos = Nos/Vs to denote the molar concentration of the organic solvent in the binary liquid mixture without salt.

where NA is Avogadro’s constant and αsalt denotes the salt polarizability in cgs units. ns is the refractive index of the saltfree binary liquid mixture satisfying the Clausius−Mossotti equation56 ns2 − 1

(5)

Here, the slope K is ÅÄ ÑÉÑ n 2 + 2 ÅÅÅ 4πNA 2 ÑÑ 2 ÅÅ ÑÑ K= s ( n + 2) α − ( n − 1) γ s salt s ÑÑ 6ns ÅÅÅÇ 3Vs ÑÖ

II. THEORETICAL BACKGROUND Based on our previous work,52,53 the refractive index n of binary liquid mixtures containing salts is given by Vs ijj xsalt 4πNA ns2 − 1 yzz n2 − 1 j zz = α + j salt Vss jk 1 − xsalt 3Vs n2 + 2 ns2 + 2 z{

(4)

(3)

where γ and η are the parameters that can be extracted from experimental measurements. Physically, the first order coefficient γ indicates the changing degree of the volume ratio of the salt solution to the solvent with salt concentration (xsalt). γVs corresponds to the infinite dilution limit of the partial molar volume of the salt defined as V̅ salt = limxsalt→0 [(Vs −V(0) water)/xsalt]. The constant η only depends on the solvent and the valency of the ions, but experimentally, it was shown that B


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Figure 1. Rate of change in the refractive index with mole fraction of salt, K, vs the organic-solvent concentration, cos, in binary liquid mixtures (water−ACN, water−EA, and water−CP) for (a) NaCl, (b) KBr, and (c) MgSO4; and the rate of change in the mixture volume with the mole fraction of salt, γ vs the organic-solvent concentration, cos, in binary liquid mixtures (water−ACN, water−EA, and water−CP) for (d) NaCl, (e) KBr, and (f) MgSO4. When cos = 0, the K and γ values are imported from our previous work.53

±0.00001 g. The densities of the solutions were measured with a precision of 0.0001 g/cm3 using an Anton Paar DMA 4100M digital temperature-control densitometer (Graz, Austria). The densitometer has a self-temperature-control function (Thermo Balance) that sets the temperature to 25 ± 0.01 °C. The refractive indices were measured at 25 °C using an Anton Paar Abbemat HP thermostatic digital refractometer (±0.002 °C) at the D-line of sodium (589.3 ± 0.1 nm). The precision of the refractive index measurement is estimated to be 0.00002. All of the measurements were performed at ambient pressure. The following protocol was used for a given salt solution and a given temperature: first, we plotted the refractive index n vs xsalt in the low concentration range and obtained the slope K according to eq 5 Next, we plotted Vss/Vs vs xsalt in the same low concentration range to obtain γ according to eq 3. Finally, we used eq 7 to determine salt polarizability αsalt. Experimental volume ratios of water−organic solvent mixtures are 9.5:0.5, 9:1, 8.5:1.5, 8:2, 7.5:2.5, 7:3, 6.5:3.5, and 6:4. The values of cos are cACN = 0.952, 1.910, 2.875, 3.850, 4.821, 5.789, 6.766, and 7.734 mol/L; cEA = 0.859, 1.719, 2.591, 3.473, 4.361, 5.256, 6.151, and 7.050 mol/L; cCP = 0.679, 1.367, 2.061, 2.763, 3.470, 4.180, 4.895, and 5.614 mol/ L, respectively.

xsalt in the dilute-salt limit (based on eqs 3 and 5). In Figure 1, we show K and γ as a function cos of NaCl, KBr, and MgSO4 (see Figure S1 in the Supporting Information for NaBr and LiCl). We find that K decreases with cos for all three salts, while γ decreases with cos for the first two salts but increases approximately linearly for MgSO4. The trends in K can be rationalized by considering the molar volume of the liquid mixtures. For one mole of a liquid mixture, the molar volume increases with the mole fraction of the organic solvent (since ACN, EA, and CP all have a larger molar volume than water). When a given amount of salt is added to a larger volume of solvent, the effect of salt diminishes. Therefore, K decreases with increasing cos. For a given solvent composition cos, we note that the relation KACN > KEA > KCP holds true for all salts. This observed trend is due to the fact that among the three organic solvents, the molar volume is the smallest for ACN and the largest for CP. The smaller molar volume of the water−ACN mixture and the larger molar volume of the water−CP mixture result in the observed trend. The trends in γ, on the other hand, are not so simple. We observe that γ decreases with cos for NaCl and KBr, but increases for MgSO4. We speculate that as the molar volume of the liquid mixtures increases with cos, addition of a fixed amount of salt leads to a smaller percentage change in the volume, and this is the trend observed for NaCl and KBr. However, besides the molar volume of the solvents, the specific ion-solvent association also significantly affects γ. In general, when the ion-solvent association is strong, it leads to a more compact molecular arrangement and thus a smaller volume in the salt−solvent mixture. In the case of MgSO4 solutions, the association between MgSO4 and water is much stronger than

IV. RESULTS AND DISCUSSION IV.I. Effect of Solvent Composition on Solution Properties upon Salt Addition. To obtain salt polarizability in binary liquid mixtures using eq 7, we first measure the refractive indices (n) and volumes (Vss) of the water−ACN, water−EA, and water−CP mixtures upon addition of salts, and determine the rate of change K in the refractive index and the rate of change γ in the volume with the mole fraction of salt C


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The Journal of Physical Chemistry B that between MgSO4 and the organic solvents (note that γMgSO4 is negative when cos is small), because the first solvation shell of Mg2+ is fully ordered57−59 and this order may weaken in the presence of organic solvent. As a result, γ increases with cos due to the decreasing water fraction in the mixture and despite the increasing molar volume. For a given cos, we do not observe an obvious trend of γ varying with the identity of the organic solvent; this is again because of the specific interactions between the ions and the organic solvents. IV.II. Effect of Solvent Composition on Salt Polarizability. Using K and γ determined from experimental measurements, we compute the polarizabilities of five salts αsalt (NaCl, KBr, MgSO4, NaBr, and LiCl) in binary liquid mixtures (water−ACN, water−EA, and water−CP) through eq 7. Figure 2 shows the dependence of αsalt of NaCl, KBr, and

Figure 3. Refractive indices ns vs the organic-solvent concentration cos in binary liquid mixtures.

effect on αsalt is not directly related to the dielectric constant, the dipole moment, or the refractive indices of the added organic solvents. To uncover the factors contributing to the variation of αsalt with cos, we first differentiate eq 7 by cos, and the result is ÄÅ ÉÑ ÅÅ 6n 6Vs(2 − 3ns2) ∂ns ÑÑÑ ∂Vs 4πNA ∂αsalt s Å Å ÑÑK = ÅÅ 2 + 2 3 ÑÑ ÅÅÅ (ns + 2)2 ∂cos 3 ∂cos ∂ c ( 2) n + ÑÑÖ os s Ç ÄÅ 2 ÉÑ ÅÅ n − 1 ∂V 6V n ∂n ÑÑ s + ÅÅÅÅ s2 + 2 s s 2 s ÑÑÑÑγ ÅÅÅ ns + 2 ∂cos (ns + 2) ∂cos ÑÖÑÑ Ç 6V n n 2 − 1 ∂γ ∂K + 2 s s 2 + Vs s2 (ns + 2) ∂cos ns + 2 ∂cos (8) Equation 8 suggests that numerous factors influence the value of ∂αsalt . Specifically, we notice that the second term on the ∂cos

right-hand side of eq 8 is always greater than 0 (see Table S1 and Figure S3 in the Supporting Information for ∂ns and ∂Vs ∂cos

∂cos

being always greater than 0, besides K and γ > 0) and the last ∂K two items are generally negative (see Table S2 as ∂c < 0 and os

∂γ ∂cos

< 0 for most salts). The first term on the right-hand side of

eq 8 can be either positive or negative, but we found the term to be mostly positive from our measurements. The competition among these four terms results in a complex nonlinear relationship between αsalt and cos. In addition, we determine the fractional contribution of each of the terms towards ∂αsalt (see Table S3), and the numerical results suggest

Figure 2. Salt polarizabilities αsalt vs organic-solvent concentrations cos in binary liquid mixtures (water−ACN, water−EA, and water−CP) for (a) NaCl, (b) KBr, and (c) MgSO4. When cos = 0, the αsalt values are imported from our previous work.53

∂cos

that none of the terms makes a decisive contribution. This reaffirms that the value of αsalt in a binary water/organic solvent mixture is affected by a myriad of factors. IV.III. Effect of Solvent Composition on Ion Polarizability. The single-ion polarizability in solution can be determined from salt polarizability once we select a reference ion. The strategy of ion polarizability computation is described in ref 53. With the polarizability of the reference ion, the polarizabilities of another ion can be determined through the polarizability of the salt (αsalt) made up of these two ions. Earlier work suggests that the polarizabilities of ions with a more stable first solvation shell are largely unaffected by the organic solvent in binary liquid mixtures.61,62 In addition, the smaller value of polarizability for smaller cations makes them appropriate choices as references because it minimizes the errorsthe errors are bounded by the value of the polarizability of the reference ion. In view of these considerations, Li+ is the best choice as the reference because it is the smallest

MgSO4 (see Figure S2 for NaBr and LiCl) on the solvent composition cos. For convenience, the numerical results of αsalt are listed in Table S1. Generally, the relationship of αsalt with cos is very nonlinear. This is somewhat surprising because a Clausius−Mossotti type of relationship between the refractive index and the polarizability yields a rather linear relationship (as shown in Figure 3). At a given cos, αCP > αACN > αEA holds true for all salts considered, i.e., acetone increases αsalt most significantly, while ethanol the least. This order is not consistent with the order of dielectric constants (εACN (36.64) > εEA (25.3) > εCP (21.01))60 or the order of the dipole moments (μACN (3.93 D) > μCP (2.88 D) > μEA (1.69 D))60 or the order of refractive indices of pure organic solvents (nEA (1.3611) > nCP (1.3588) > nACN (1.3442)).60 This suggests that the organic-solvent D


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Table 1. αNa+, αCl−, and αBr− in Different Water−Organic Solvent Compositions, cos (with the Standard Error after ±) Vwater/VACN cACN (mol/L) Na+ (Å3) Cl− (Å3) Br− (Å3)

9.5:0.5 0.952 0.268 ± 0.011 3.287 ± 0.034 4.703 ± 0.032

9:1 1.910 0.263 ± 0.021 3.319 ± 0.049 4.739 ± 0.023

8.5:1.5 2.875 0.260 ± 0.008 3.335 ± 0.029 4.786 ± 0.025

8:2 3.850 0.260 ± 0.009 3.346 ± 0.027 4.821 ± 0.038

Vwater/VEA cEA (mol/L) Na+ (Å3) Cl− (Å3) Br− (Å3)

9.5:0.5 0.859 0.274 ± 0.007 3.254 ± 0.024 4.683 ± 0.017

9:1 1.719 0.268 ± 0.003 3.263 ± 0.025 4.691 ± 0.050

8.5:1.5 2.591 0.263 ± 0.017 3.270 ± 0.041 4.714 ± 0.017

8:2 3.473 0.270 ± 0.007 3.265 ± 0.020 4.708 ± 0.024

Vwater/VCP cCP (mol/L) Na+ (Å3) Cl− (Å3) Br− (Å3)

9.5:0.5 0.679 0.280 ± 0.012 3.284 ± 0.020 4.709 ± 0.063

9:1 1.367 0.270 ± 0.006 3.317 ± 0.033 4.761 ± 0.053

8.5:1.5 2.061 0.287 ± 0.010 3.327 ± 0.033 4.800 ± 0.071

8:2 2.763 0.271 ± 0.004 3.350 ± 0.046 4.845 ± 0.055

Vwater/VACN cACN (mol/L) Na+ (Å3) Cl− (Å3) Br− (Å3)

7.5:2.5 4.821 0.259 ± 0.005 3.342 ± 0.033 4.833 ± 0.027

7:3 5.789 0.266 ± 0.018 3.336 ± 0.024 4.840 ± 0.031

6.5:3.5 6.766 0.261 ± 0.005 3.329 ± 0.066 4.842 ± 0.045

6:4 7.734 0.267 ± 0.009 3.278 ± 0.065 4.848 ± 0.050

Vwater/VEA cEA (mol/L) Na+ (Å3) Cl−(Å3) Br− (Å3)

7.5:2.5 4.361 0.281 ± 0.014 3.252 ± 0.017 4.689 ± 0.022

7:3 5.256 0.283 ± 0.009 3.248 ± 0.032 4.667 ± 0.047

6.5:3.5 6.151 0.297 ± 0.022 3.227 ± 0.027 4.633 ± 0.061

6:4 7.050 0.297 ± 0.003 3.219 ± 0.030 4.617 ± 0.057

Vwater/VCP cCP (mol/L) Na+ (Å3) Cl− (Å3) Br− (Å3)

7.5:2.5 3.470 0.270 ± 0.012 3.368 ± 0.058 4.903 ± 0.026

7:3 4.180 0.265 ± 0.013 3.371 ± 0.054 4.937 ± 0.039

6.5:3.5 4.895 0.262 ± 0.002 3.373 ± 0.067 4.967 ± 0.040

6:4 5.614 0.243 ± 0.023 3.370 ± 0.073 4.989 ± 0.068

Instead, it experiences a modified electric field formed by the original external electric field plus a “depolarization field” due to the polarized medium. This depolarization field leads to excess polarizability, which is the difference between the polarizabilities of a solution-phase ion and an isolated ion. The excess polarizability is solvent specific, and for binary liquid mixtures. Excess polarizability is also specific for different water−organic solvent ratios (cos). Our results show that the excess polarizability of the cation is weaker than that of the anion. The variation of excess polarizability with respect to solvent composition is mostly due to the solvent structure in the vicinity of the ions. To explain this variation, we need to carefully consider how water and organic solvent molecules affect the first solvation layer of a single ion. For most cations, the first solvation shell is relatively stable;57,59,61,64 in a liquid mixture, the first solvation shell is preferentially occupied by water.65 Thus, the cation polarizabilities in binary liquid mixtures are nearly the same as those in aqueous solutions. In contrast, for anions, the first solvation shell is less stable due to the larger size of the ions,58 and hence the anionic excess polarizability is subjected to larger variations. Addtionally, we note that the anion-solvent interaction is stabilized by the presence of a proton in the solvent molecule. While a proton is available in ethanol, it is not available in acetonitrile or acetone.

ion in our measurements. Previous density functional theory calculation suggests that the polarizability of Li+ is 0.029 Å3 (solution phase),46 and we thus choose this value as our reference polarizability. All values of αion can be deduced once the reference ion is selected. Assuming the chemical formula of the inorganic salt as CxAy, the polarizability of the salt αsalt and the polarizabilities of its cations and anions (α+ and α−) satisfy the following relation: αsalt = xα+ + yα−. First, α− in a salt containing Li+ is determined by α− = (αsalt − xαLi+)/y. Next, the polarizabilities of other metal ions are determined by subtracting the above polarizabilities of anions. Here, the ions are assumed to be mutually independent; this assumption is good in the case of dilute salt concentration, which is the concentration regime considered in this work. Our results for the ion polarizabilities of Na+, Cl−, and Br− at different molar ratios of organic solvents are tabulated in Table 1 and graphically presented in Figure 4. In addition, the polarizabilities of the cation (Na+) are hardly affected by the presence of organic solvents, but the polarizabilities of the anions (Cl− and Br−) significantly depend on cos. In most cases, the anion polarizabilities first increase with cos and then decrease upon further addition of the organic solvent. This result is certainly intriguing. According to the work of Parsons and Ninham,63 an ion in solution does not simply experience the full external field. E


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organic solvent content. Our results suggest that the solvent effects on ion/salt polarizability are non-negligible. Our work presents a promising strategy for determining ion polarizabilities of water−organic binary liquid mixtures. A more extensive application of the strategy to a wider range of salts, ions, and solvents is reserved for forthcoming work. The solution-phase salt and ion polarizabilities can be directly employed in simulations and modeling of electrolytic systems involving liquid mixtures. This work also prompts the development of new theories that can better explain the variation of ion polarizability in liquid mixtures. We hope that our results not only provide reference data for salt effects in binary liquid mixtures, but also provide inspirations for solving outstanding electrochemical problems such as specific ion effects.

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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.jpcb.8b07327. K, γ, and salt polarizabilities vs cos in binary liquid mixtures (water−ACN, water−EA, and water−CP) for NaBr and LiCl; ns and Vs vs cos in binary liquid mixtures (water−ACN, water−EA, and water−CP); numerical 4πN ∂α values for salt polarizabilities, parameters for 3 A ∂csalt , os

Figure 4. Ion polarizabilities vs the organic-solvent concentration cos in binary liquid mixtures (water−ACN, water−EA, and water−CP) for (a) Na+, (b) Cl−, and (c) Br−. When cos = 0, the αion values are imported from our previous work.53

and the fractional contribution of each of the terms towards ∂αsalt (PDF)

■

∂cos

AUTHOR INFORMATION

Corresponding Author

As such, anions in acetonitrile or acetone have larger excess polarizability than those in ethanol, as shown in Figure 4. The nonmonotonicity in the variation of excess polarizability suggests competing factors at work. Recently, Fiedler et al.66 examined how the size of molecular cavity67 determines the effective polarizability of small, nonionic species. This corroborates with our understanding that ion polarizability is strongly influenced by the arrangement of solvent molecules in the immediate vicinity, which determines the effective cavity size of the solvated ion. It is certainly interesting and useful to compute the effective ion sizes with our experimentally-determined ion polarizabilities. We reserve this effort for future work.

*E-mail: [email protected]. Phone: +86-431-85262150. ORCID

Minglun Li: 0000-0002-1286-6915 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The authors thank Prof. Zhen-Gang Wang, Dr. Pengfei Zhang, and Dr. Bilin Zhuang for many useful discussions. This work was supported by the Science Challenge Project (Grant No. TZ2018004), the National Natural Science Foundation of China (Grant No. 21674113), the Key Research Program of Frontier Sciences, CAS (Grant No. QYZDY-SSW-SLH027), and the Jilin Scientific and Technological Development Program (Grant No. 20180519001JH). Additional support for Y.L. was provided by the Young Elite Scientist Sponsorship Program by CAST (Grant No. YESS20160032). We thank the anonymous reviewers, whose comments have helped in improving the presentation of our work.

V. CONCLUSIONS AND OVERLOOK In this work, we have determined the polarizabilities of salts (LiCl, NaCl, NaBr, KBr, and MgSO4) and ions (Na+, Cl−, and Br−) in water−acetonitrile, water−ethanol, and water−acetone solutions. We have computed polarizabilities from experimental measurements of refractive indices of salt solutions in binary liquid mixtures, using a theory that combines the Clausius− Mossotti equation and the Debye−Hü ckel limiting law developed by us in an earlier work.54,55 When a given amount of salt is added to one mole of solvent mixtures, our results show that both the refractive index and the volume change decrease with increasing organic solvent content for all salts except MgSO4. Salt polarizability depends on the molar fraction of the organic component in the binary liquid mixtures in a nonlinear manner; this is primarily because cation polarizability is barely affected by organic solvents, but anion polarizability is mostly nonmonotonically affected by the

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REFERENCES

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