Individual Ionic Surface Tension Increments in Aqueous Solutions

Article pubs.acs.org/Langmuir

Individual Ionic Surface Tension Increments in Aqueous Solutions Yizhak Marcus Institute of Chemistry, The Hebrew University of Jerusalem, 91904 Israel ABSTRACT: Surface tension increments by aqueous electrolytes, kE = [γ(cE) − γ(W)]/cE, can be split into the ionic values, ki (kE = Σνiki), on an arbitrary but plausible manner, notwithstanding the effects of counterions on the behavior of specific ions. Values for 41 ions, mono- and polyatomic and uni- and multivalent, are presented in conjunction with some other ionic properties. The surface potential increments of electrolytes, ΔΔχ = ΔχE (at cE = 1 M) − ΔχW, depend linearly on the kE values for four anion series with common cations and on the differences between cation and anion ki values. The ki (normalized to unit charge number) are correlated linearly with the ionic radii ri, the excess ionic molar refractivity over that of water, RDi − RDW, the ionic softness parameters (modified by adding +0.5 to anion and −0.5 to cation values), σ±0.5, and to the geometrical factor of water structure making/breaking, ΔHBG. No correlation takes place with the ionic polarization corrected for that of water, αi* = αi − αW(ri/rW)3, nor with the molar Gibbs energy or enthalpy of hydration. The latter fact implies that ion dehydration does not play a major role in the sorption/desorption of ions at the surface. The correlations that were found are discussed in a qualitative manner and compared with theoretical arguments in the literature.

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of HCl,3 HI,4 NaCl,5 and NaI,4,5 albeit at moderately large concentrations, are good illustrative examples. For these, kE = −0.27, −1.02 (estimated from ionic additivity6), 2.08, and 1.23, respectively. Iodide ions are attracted to the surface, but their increase is by 55% larger when the electrolyte is HI than when it is NaI (both at 4 M).4 Whereas in 1.2 M HCl chloride ions are attracted to the surface at about the same amount as the hydrogen ions, in 1.2 M NaCl the sodium ions that are repelled from the surface drag the chloride ions somewhat away from it.3 An analysis of the molar STIs in terms of the partition equilibrium constants of the ions between the surface layer and the bulk, Kp±, by Pegram and Record7 included the premise that these constants are independent and additive for individual cations and anions. The Kp− value of a given anion (e.g., chloride) indicated that the cations and anions partition independently, contrary to the above MD and SHG findings. Indeed, the molar STIs of dilute electrolytes do show ionic additivity. This was first suggested by Lorenz,8 but the Δγ data available to him were quite sparse. The comprehensive and recent critical compilation of Δγ data by the present author6 permitted a more severe test of the kE = Σνiki premise. This was tested for the couples Na+−Li+, Na+−K+, Cl−−Br−, and Cl−− NO3−, for which sufficient data were found. It was shown that the accuracy of the Δγ data available from several authors using a variety of methods (mostly maximum bubble pressure, drop volume, capillary rise, ring pulling force, and plate detachment) is no better than ca. ±0.2 mN m−1 M−1 and so is that of the ki additivity within the range 0.1 ≤ cE/M ≤ 1.0.

INTRODUCTION Most electrolytes in aqueous solutions at ambient conditions raise the surface tension of the solution in a manner proportional to their concentration. The surface tension increment (STI) is Δγ = γ(c E) − γ(W) = kEc E

(1)

where γ(cE) is the surface tension in the presence of cE M (mol L−1) of electrolyte E, γ(W) is the surface tension of water, and kE = (∂Δγ/∂cE)T is the molar STI, an electrolyte-specific constant, that depends only slightly on the temperature near ambient. Equation 1 holds for cE between ca. 0.05 and 1.0 M, and in some cases to higher concentrations too. There are few experimental studies at cE < 0.05 M due to inherent difficulties to measure Δγ accurately; a notable exception is the work of Jones and Ray1 of some 70 years ago, using capillary rise at concentrations as low as 0.0001 M. They found that up to cE ≈ 0.005 M kE < 0 for salts such as LiF, CsI, BaCl2, and LaCl3 but becomes >0 and reaches constant positive values at higher concentrations. The kE < 0 results were subsequently attributed to an artifact due to sorption on the capillary walls,2 and in fact eq 1 for 0.05 ≤ cE/M ≤ 1.0 extrapolates linearly quite accurately to zero. It may, therefore, appear attractive to consider the values of the STI, and specifically of kE, to be established also at infinite dilution, where the individual ionic contributions, ki, should be additive, kE = Σνiki over all ionic species i with the stoichiometric coefficients νi. However, the real situation is not so simple, because, although individual ions do show characteristic behaviors at the water/air (or dilute vapor) interface, these are influenced by the nature of the counterions. This is demonstrated by molecular dynamics (MD) simulations and second harmonic generation (SHG) spectroscopic studies. The results for aqueous solutions © 2013 American Chemical Society

Received: October 21, 2012 Revised: December 18, 2012 Published: February 6, 2013 2881

dx.doi.org/10.1021/la3041659 | Langmuir 2013, 29, 2881−2888

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Table 1. Ionic Surface Tension Increments, ki = dγ/dci/(mN m−1 M−1), of Aqueous Ions at Ambient Conditions, Rounded to 0.05 Units with an Uncertainty of ±0.2 Units6 (Adjusted As Described in the Text) and Other Ionic Propertiesa ion

ki

H Li+ Na+ K+ Rb+ Cs+ Ag+ Tl+ NH4+ (CH3)4N+ C(NH2)3+b Mg2+ Ca2+ Sr2+ Ba2+ Mn2+ Co2+ Ni2+ Pb2+ Al3+ La3+ OH− F− Cl− Br− I− SCN− NO3− ClO3− BrO3− IO3− ClO4− HCO2− CH3CO2− H2PO4− CO32− SO42− CrO42− HPO42− S2O32− PO43−

−1.05 0.95 1.20 1.10 0.95 0.80 0.70 0.60 0.70 −0.10 0.04 2.25 2.10 1.80 1.10 1.35 1.65 1.70 2.40 2.65 3.20 1.05 0.80 0.90 0.55c −0.05c −0.65d 0.15 0.00e 0.35e 0.70e −0.70c 0.20c −0.25 0.95 0.30 0.55 0.85 0.70 0.65d 1.10

+

ri 0.069 0.102 0.138 0.149 0.170 0.115 0.150 0.148 0.280 0.210 0.072 0.100 0.113 0.136 0.082 0.075 0.069 0.118 0.053 0.105 0.133 0.133 0.181 0.196 0.220 0.213 0.200 0.200 0.191 0.181 0.240 0.204 0.232 0.200 0.178 0.230 0.240 0.200 0.250 0.238

σi±0.5

ΔHBG

−0.50 −1.52 −1.10 −1.08 −1.03 −1.04 −0.32 −0.30 −1.10 0.31

0.28 −0.03 −0.52 −0.56 −0.69 −0.02 −0.52 −0.18 −0.47

−0.91 −1.16 −1.14 −1.16 −0.65 −0.61 −0.61 −0.09 −0.81 −1.25 0.50 −0.16 0.41 0.67 1.00 1.35 0.53 0.53

0.78 0.34 0.29 0.01 0.57 0.86 0.90 0.03 0.17 0.78 0.28 0.08 −0.61 −0.80 −1.09 −0.82 −0.68 −0.65 −0.49 0.11 −1.01 −0.33 0.12 −0.10 0.28 −0.21 −0.34 0.33 −0.43 0.93

0.20 0.17 0.28 0.00 0.12

−0.28

(RDi − RDW)

−ΔhydGi°/zi2

−ΔelstrVi

−3.81 −3.63 −3.06 −1.00 0.39 3.18 1.39 7.79 0.99 19.19 7.50 −4.41 −2.12 −1.06 1.46 −1.61 −1.66 −2.11 8.19 −4.89 −0.97 0.94 −1.50 4.92 8.53 15.24 13.29 6.72 8.39 11.49 15.14 9.06 5.72 10.16 10.89 7.74 10.08 11.50

1056 481 375 304 281 258 440 310 292

7.5 12.9 8.6 5.9 5.3 4.4 13.2 8.5 4.5 10.7 0.6 52.5 38.5 33.9 27.5 30.7 38.5 41.8 35.6 59.3 60.3 5.7 6.2 4.0 3.5 2.8 2.4 2.7

19.49 11.39

583 460 379 347 315 443 481 498 359 503 351 439 472 347 321 28. 287 306 287 340 408 214 403 373 473 120 273 240

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2.4 12.2 13.4 4.6 25.2 13.8 34.0 25.6 33.4 72.3

Radius,19 ri/nm, softness parameters,19 modified as in the text, σi±0.5, water structure making/breaking,24 ΔHBG, excess molar refractivity,19 (RDi − RDW)/ cm3 mol−1, the negative of the standard molar Gibbs energy of hydration19 normalized by division by the square of the ionic charge number, −ΔhydGi°/zi2/ (kJ mol−1), and the standard molar electrostriction volume, −ΔelstrVi/(cm3 mol−1) (see the text). bGuanidinium cation, data from ref 41. cRevised value after reweighting the entries in ref 6. dRevised values from ref 6 and additional values from Adamzon and Gaukberg (cited in ref 4 there) not previously considered. eFrom ref 18. a

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INDIVIDUAL IONIC SURFACE TENSION INCREMENTS

anions should be between the values for these ions. A listing of the improved ki values, rounded to 0.05 mN m−1 M−1 with uncertainties of ±0.2 of these units, is shown in Table 1 and includes a few revised values and some that were not included in the previous compilation.6 The revisions were made in view of the recent suggestion11 that the larger reported kE values for a given electrolyte are probably more accurate than the smaller ones, because impurities are generally surface active and diminish the surface tension. The sequence of the ki of ions within a given charge sign, i.e., cations (or anions) among themselves, is independent of the arbitrary splitting of the electrolyte values.

The problem of deciding on an individual ionic scale for ki remains, however, since the splitting of the experimental kE into the ionic contributions is arbitrary. The choice ki(Cl−) = 1.20 mN m−1 M−1 (leading to ki(Na+) = 0.90 mN m−1 M−1) was arbitrarily made,6 but a better value, ki(Cl−) = 0.90 mN m−1 M−1, was later suggested by the author.9 The basis for this change was the realization that the previously suggested anion values were somewhat too large and that, whereas formate ions are repelled from the surface together with the sodium ions, acetate ions are attracted to it,10 so that the zero value for the 2882


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Figure 1. Surface potential increment of aqueous 1:1 electrolyte solutions at 1 M over that of pure water, ΔΔχ. Left hand panel: plotted against their molar surface tension increments, kE; right-hand panel: plotted against the difference between the cation and anion molar surface tension increments, k+ − k−. Squares are for acids HX, circles are for NaX, upright triangles are for KX, and downward triangles are for NH4X, with X being the anion.

The values of the Pegram and Record7 electrolyte partition constant KpE − 1 (determined on the molal scale) are essentially proportional to the molar STIs (kE values) at the limit of low concentrations where the solutions approach ideality and the molality approaches the molarity. Hence, the approach of these authors is the same as that taken here, but they chose the arbitrary values of zero for the Kp± of Na+ and SO42− without fully explaining this choice. Many authors tried to explain the specific ionic STIs by means of theoretical calculations (see below) but generally confined their arguments and comparison with experimental values (often chosen arbitrarily from the many published values) for the monatomic univalent alkali metal and halide ions. In this paper the entire set of 41 ions for which reasonably accurate STIs have been established (Table 1) is dealt with, including polyatomic and multivalent ions.

ΔΔχ /mV = (55 ± 2) − (29 ± 1)(kE/mN m−1 M−1) (3a)

The correlation coefficient with 25 data points is 0.973 and the standard error of the fit is ±8 mV, the outliers sodium acetate and sulfuric acid having been excluded. In spite of the scatter a clear dependence is observed, the ΔΔχ values being governed by the anions. The right-hand panel of Figure 1 shows the plot of the ΔΔχ values against the difference between the individual ionic STIs, that of the cation minus that of the anion, for the 1:1 electrolytes included in the plot on the left-hand side. In this case the linear plot passes essentially through the origin for the KX salts and does so for the other salts when −80, +20, and −15 mV are added to the HX, NaX, and NH4X electrolyte data ΔΔχ /mV = ( −3 ± 2) + (30 ± 2)[(k+ − k −)

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/(mN m−1 M−1)]

CORRELATION OF THE ki VALUES WITH OTHER QUANTITIES The surface concentration of an electrolyte having a bulk activity of aE is given by the Gibbs adsorption law ΓE = −(aE /RT )(∂γ /∂aE)T , P

(3b)

The correlation coefficient with 25 data points is 0.958, and the standard error of the fit is ±9 mV. This means (at least in the case of the KX salts, where no adjustment is made) that the surface potential is dominated by the ion sorption/desorption at the surface and shows the practical value of the splitting of the electrolyte molar STIs into the individual ionic values. The sizes of the ions are a point to be considered. This was initially suggested by Schmutzer15 and taken up by Aveyard and Saleem,16 Markin and Volkov,17 dos Santos et al.,18 and Slavchov and Novev,11 among others. The plot in Figure 2 of ki normalized with respect to the absolute ionic charge numbers, zi, against the (bare) ionic radius, ri,19 shows distinct dependencies of the cations and anions, but an overall roughly linear trend of diminishing STIs with increasing sizes

(2)

and at the reference state and unit concentration it is proportional to kE. Hence, cations with ki > 0 are repelled from the surface (ΓE < 0), and if k+ > k− they are repelled more than the anions. This causes a charge imbalance in the surface layer leading to the establishment of an electric double layer. The surface potential of electrolyte solutions over that of pure water (with respect to vacuum/air/dilute water vapor), ΔΔχ, was measured by Frumkin,12 Randles,13 and Jarvis and Scheiman14 as a function of the electrolyte concentration. It is noted that the resulting dependencies are not linear, so that comparison of the ΔΔχ results with ki values is not simple. Still, for M = H+, Na+, K+, and NH4+ with a variety of anions X−, the available ΔΔχ values at 1 M MX can be compared. The results are shown in Figure 1, left-hand panel, where 30 mV have been added to the ΔΔχ values for HX. The adjustment in the case of the acids is due to the hydrogen ions being attracted to the surface rather than repelled from it as are the other cations considered. The scatter in the plot of ΔΔχ vs kE is appreciable, but the plot is linear

(k i /z i)/(mN m−1 M−1) = (1.51 ± 0.12) − (5.8 ± 0.7)(ri /nm)

(4)

Equation 4 holds for 37 ions of both signs, uni- as well as multivalent, and monatomic as well as polyatomic ones, with a correlation coefficient of 0.806 and a standard deviation of the fit of ±0.24, not much larger than the uncertainty of the ki values. Four ions are outliers, see Figure 2. Several authors, including Kunz et al.20 and Boström et al.,21 discussed the importance of the role played by dispersion forces 2883


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seldom considered in theoretical treatments of the surface tension increments. A quantity that resembles in a way the polarizability of the ions is their softness or hardness.19,22 These are defined as the difference in the energetics involved in the gain or loss of electrons from neutral atoms to produce the ions in the ideal gas phase on the one hand and in transfer of the ions from there to an aqueous solution to produce the standard aqueous ions on the other. The published softness parameters σi are based on the arbitrary assignment of zero to the hydrogen ion for cations and to the hydroxide ion for anions, but a common scale is produced when 0.5 units are subtracted from the cation values and 0.5 is added to the anion values. A plot of the STIs normalized to unit charge, ki/zi, against these modified softness Figure 2. Molar ionic surface tension increments of ions normalized to unit charge, ki/zi, plotted against their ionic radii ri. Triangles denote cations, circles denote anions. The dashed lines denote 2 standard deviations of the fit of eq 4 (solid line).

in the determination of the surface concentration of an electrolyte. The dependence of the ionic molar STIs on the polarizabilities and/or softness of the ions is therefore worthy of exploration. Indeed, there is a fairly good correlation of the ionic molar STIs with the ionic molar refractions19 (or their excess over that of water, RDW = 3.67 cm3 mol−1) (k i /z i)/mN m−1 M−1 = (0.82 ± 0.04) − (0.052 ± 0.006)[(RDi − RDW ) /cm 3 mol−1]

(5)

for 33 ions, with a correlation coefficient of 0.871 and a standard error of the fit of ±0.19 mN m−1 M−1, see Figure 3. The accuracy of the fit is less than desirable and there are important outliers: H+, Pb2+, IO3−, ClO4, CH3CO2−, HPO4−, and S2O32−. However, it should be noted that the correlation covers both univalent and multivalent ions, the latter being

Figure 4. Molar ionic surface tension increments normalized to unit charge, ki/zi, plotted against the modified ionic softness parameters σ±0.5. Circles denote cations, triangles denote anions, and squares are outliers (see text). The dashed lines denote 2 standard deviations of the fit of eq 6 (solid line).

parameters σi±0.5 is shown in Figure 4. For 29 ions for which the data are available the linear fit is (k i /z i)/mN m−1 M−1 = (0.35 ± 0.05) − (0.55 ± 0.05)σi ± 0.5

(6)

with correlation coefficient of 0.889 and a standard error of the fit of ±0.22 mN m−1 M−1. Notable outliers are the hard H+ and the very soft Pb2+ among the cations and the OH− and ClO4− among the anions but surprisingly also the neither soft nor hard Cl− anion. A further correlation that is noteworthy is between the STIs and the effects of the ions on the structure of the water in their vicinity,23 suggested by Manciu and Ruckenstein.24 The quantity describing these effects, pertaining to the ions in the bulk of the solution, is perhaps best expressed in terms of the ionic effect on the geometric factor governing the hydrogen bonding of the water, ΔHBG, as derived from the structural entropy of the water in the electrolyte solutions or the viscosity B coefficients with which they are linearly related.25 Positive values of ΔHBG denote structure-making ions and negative ones denote structure-breaking ones. The correlation is shown in Figure 5, where, despite the scatter, a linear dependence

Figure 3. Molar ionic surface tension increments of ions normalized to unit charge, ki/zi, plotted against their excess molar refractivities over that of water RDi − RDW. Triangles denote cations, circles denote anions, and squares denote outliers (see the text). The dashed lines denote 2 standard deviations of the fit of eq 5 (solid line). 2884


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k i /mN m−1 M−1 = (0.96 ± 0.08) + (1.03 ± 0.14)ΔHBG

too low experimental value) and too large for NaI (the calculated value agrees better when also a dispersion term is included). It turns out that when all of the ions for which ki values are listed in Table 1, for which also ΔhydGi° values are known,19 that is 21 cations and 18 anions, are considered, hardly any correlation exists as show in Figure 6 (similar results are

(7)

Figure 5. Ionic surface tension increments, ki, plotted against the effects of the ions on the bulk water structure, measured by the hydrogen bonding geometrical factor ΔHBG. Triangles denote cations, circles denote anions, and squares are outliers (see text). The dashed lines denote 2 standard deviations of the fit of eq 7 (solid line).

Figure 6. Plot of the molar STIs of ions against their molar hydration Gibbs energies: circles for cations, triangles for anions, filled symbols for univalent ions, and empty ones for multivalent ions.

is seen for 35 ions, with a correlation coefficient of 0.785 and a standard error of the fit of ±0.4 mN m−1 M−1. The outliers in this case are the cations Pb2+, Al3+, and La3+ and the anions CH3CO2−, CO32−, and PO43−, and the uncertainties for the entries on both axes are ±0.2 units. Thus, water structure breaking ions with ΔHBG < 0 have small or even negative molar STIs and structure-making ions with ΔHBG > 0 are desorbed from the water surface with positive molar STIs. It has been suggested by Kunz et al.20 among others that aqueous ions approaching the surface lose some of their hydration shell, because of the nonisotropic environment they encounter. The tendency of the ions to be displaced from the surface should then be related to the energetic cost of partial dehydration and therefore to their molar enthalpies ΔhydH° or Gibbs energies ΔhydG° of hydration. Weissenborn and Pugh26 stated that the “negative adsorption of strongly hydrated cations (and anions) from the interface can thus be explained by the hydration Gibbs energy (the correlation between hydration Gibbs energy and dΔγ/dc is 0.98)” but failed to show this correlation. They did show plots for 9 cations and properties of them other than ΔhydG°, e.g., the hydration entropies that are closely related to the ΔHBG values discussed above. A linear correlation with the molar enthalpies of hydration was reported explicitly by Hey et al.,27 who showed a plot of kE for nine electrolytes against their ΔhydH° values. They obtained a “reasonable linear correlation” but with considerable scatter. Pegram and Record7 ascribed to Colussi et al.28 the notion that dehydration was “a major source of specificity for partitioning of anions between the bulk and the air-water surface”. Boström et al.29 included a solvation energy term that is a function of ΔhydG° in their expression for the calculation of the molar STI of sodium chloride and iodide. This term ranged from ∼30% of ΔhydG° right at the surface to ∼1% of it at the bottom of the surface layer, 0.35 nm down (cf. also Edwards and Willams30). However, the calculated values, disagree with the experimental values, being too low for NaCl (they29 quote a

obtained in plots against ΔhydHi°). Thus, ion dehydration appears not to play a major role in the desorption of ions from the surface layer. A similar view was expressed many years ago by Bhuiyan et al.,31 who allowed ions to approach the interface up to their hydrated radius distance and assumed that “no dehydration of the ions in the interfacial layer takes place”. Nevertheless, when a multivariate linear regression of the ki/ zi values against the independent variables in Table 1 is done, it turns out that for the cations alone (19, excluding hydrogen) the best regression requires three of the variables, including the Gibbs energy of hydration (k i /z i)/(mN m−1 M−1) = (3.8 ± 0.8) − (11.7 ± 3.3)ri /nm + (0.53 ± 0.17) × 10−3[(RDi − RDW )/cm 3 mol−1] − (4.3 ± 1.3) × 10−3[( −Δhyd G°/z 2)/kJ mol−1)

(8)

The correlation coefficient is 0.847 and the standard error of the fit is ±0.17 mN m−1 M−1, commensurate with the uncertainties of the data. The anions do not yield multivariate regressions that are better than those against single variables. When all the ions for which all the independent variables are known are submitted to the multivariate regression (19 cations and 16 anions) the resulting best regression is (k i /z i)/mN m−1 M−1 = (1.0 ± 0.2) − (3.0 ± 1.3)ri /nm + (0.28 ± 0.12)ΔHBG − (0.17 ± 0.10)σ±0.5

(9)

The correlation coefficient is 0.794 and the standard error of the fit is ±0.31 mN m−1 M−1, worse than the uncertainties of the data. Except for hydroxide and fluoride, the anions are large, with radii 0.178 ≤ ri/nm ≤0.250, so that this variable has a lower weight than for the cations alone. In the case where all 2885


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the ions are considered, ΔhydG°/z2 is no longer a required variable, following the scatter shown in Figure 6. The combination of the ion softness and its effect on the water structure, when all the ions are considered, play the role of the excess refractivity when only the cations are dealt with.

treatments. Kunz et al.20 attempted to fit the osmotic coefficients of 16 aqueous electrolytes up to 1 M by means of adjusted ionic radii and adjusted excess polarizabilities, αi* = αi − αWVi/VW. In their calculation of αi* (before the subsequent adjustment) the ionic molar volume referred to the bare ion, Vi = (4πNA/3)ri3, but the molar volume of water, VW, was that of the liquid that included void spaces between the molecules; this discrepancy resulted in incorrect values. They then applied these adjusted parameters to fit the surface tension increments (STIs), but conceded that the agreement with experiment was poor. Earlier Boström et al.21 applied the potential of dispersion forces in the form Udispersion(x) = Bix−3, where x is the distance of the position of the ion from the interface, together with other interaction potentials to the calculation of ΓE, hence of the molar STIs via eq 2. Here Bi ≈ [ℏω(nW2−nair2)/8]αi*, the coefficient in the square bracket being ∼1 × 10−50 J m−3. They21 then arbitrarily assigned the following values (in 10−50 J m−3) to Bi: Na+ −1, K+ −3, Li+ −5, Cl− 31, Br− 21, I− 7, and CH3CO2− 5 to fit quite well the experimental molar STIs of 10 electrolytes involving these ions. However, these assigned Bi values bear little resemblance to those derived from the ionic excess polarizabilities, αi*, neither to the Kunz et al.20 values nor when VW is calculated on the same basis as Vi, namely as (4πNA/3)rW3, with rW = 0.138 nm. The latter Bi are Na+, −0.4; K+, −0.5; Li+, −0.2; Cl−, 0.1; Br−, 0.6; I−, 1.5; and CH3CO2−, −1.5. In particular, the decreasing order of the Bi values for the halides assigned by Boström et al.21 is improbable. In the plot (Figure 7) of ki values against the correctly evaluated excess polarizabilities, αi*, however, they are very scattered and do not show discernible trends.

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DISCUSSION There exists a plethora of theoretical approaches for the calculation of the molar STIs of aqueous electrolytes at concentrations up to ∼1 M. The electrostatic image contribution to the STI according to Wagner32 and Onsager and Samaras33 is, however, negligible as is generally conceded except at the lowest concentrations (≤0.1 M for 1:1 electrolytes), due to Debye screening of the electrostatic forces.24,30 Although an explanation was provided by Manciu and Ruckenstein24 for the reality of the Jones-Ray effect,1 it is still generally considered to be an artifact due to the zeta potential in very dilute solutions that causes a wetting layer in the very fine quartz capillaries used by Jones and Ray, as pointed out by Langmuir (see ref 2). Furthermore, it is also conceded that the displacement of the Gibbs dividing surface (of zero excess water) from the actual surface is negligible,11,17 except at very high electrolyte concentrations. Since in this paper concentrations in the medium range are treated, these two effects may be dismissed in the following. A point that ought to be considered with respect to correlations of the ki values with quantities that vary in a monotonic manner with the ionic sizes (such as the radius, polarizability, enthalpy or Gibbs energy of hydration, etc.) is the following. A reversal occurs in the triades Li+, Na+, and K+ and F−, Cl−, and Br−, the value for the smallest ion in the series being between those for the other two. Although the absolute accuracy claimed for the ki values is no better than ±0.20 mN m−1 M−1, the internal consistency of the values for univalent ions of the same charge sign in the various reports of experimental values is considerably better, so the inversion should be real. There are, however, precedents for such inversions in the case of the alkali metal ions, for example in the standard partial molar ionic volumes19 and the Setchenow constants for the salting out of gases34 or of benzene.35 Such an inversion can take place if two forces, one promoting sorption at the interface and the other opposing it, operate to yield the resulting behavior of the ions. It is conceded that linear correlations of the STIs with individual ionic properties or a superposition of linear relationships in a multivariate correlation is an oversimplification of the complicated situation in aqueous electrolyte solutions. Still, the qualitative trends shown by the correlations (4) to (9) need to be considered in any theoretical treatment of STIs, and some of them, in fact, are so considered. The smaller the ion, the higher is the charge density at its own surface, and the more it is repelled from the water surface with ki values up to 1.5zi, eq 4. For ions with radii larger than 0.21zi nm (compatible with eq 4 when the uncertainties are included) ki becomes negative, and the ions are attracted to the surface. This is in line with correlation (7), the water structure breaking effects of ions being well correlated with their sizes, and these effects appear to be responsible, at least in part, for their sorption/desorption at the surface of the aqueous solutions.24 The polarizability/refractivity/softness of the ions, correlations (5) and (6), showing that the larger these ionic attributes are the smaller the molar STI, even turning negative, are another aspect that has been considered in theoretical

Figure 7. Plot of the molar STIs of ions against their polarizabilities corrected for that of water, α*: circles for cations, triangles for anions,.

Slavchov and Novev11 were interested in the STIs at higher concentrations that those treated here and correctly pointed out that the nonideality of the solutions needed then to be taken into account. This can be done, for instance by using the mean activity of the electrolytes as in eq 2 for the Gibbs adsorption, and as done by Pegram and Record7 using osmolalities for calculation of the molal surface tension increments. However, Slavchov and Novev11 insisted on a measure of the nearest approach of an ion to the surface as its effective ionic radius rieff = ri + rW, the sum of its crystal ionic 2886


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the cations there exists a good correlation between ki and ΔelstrVi

radius ri plus that of a water molecule, rW (but why not the water molecular diameter 2rW, to make rieff express the hydrated ion radius?). A consequence of this adherence to such rieff values is that anions that are generally larger than cations are displaced from the surface farther away. This should cause surface potentials of the opposite sign to those observed experimentally,12,14 unless the redistribution of the dipole moments of the water molecules near the surface in the presence of the ions negates this effect. Still, if the difference between the cation and anion STIs is large, so is the surface potential (right-hand panel of Figure 1), hence the ion sorption/desorption at the surface dominates the potential and repulsion of anions from the surface should be reflected in the surface potentials, which is not the case. Therefore, the approach of Slavchov and Novev11 may not be correct. The sizes of the ions come in, in an implicit manner, in their polarizabilities or, equivalently, in their molar refractivities, or the excess of the latter over that of water. Despite the correlation in Figure 3, the outliers are noteworthy: perchlorate is a hard ion with relatively low (RDi − RDW)/cm3 mol−1 = 9.06, in contrast with the soft thiocyanate, for which the value is 13.29, but they have nearly the same ki/mN m−1 M−1 values −0.70 and −0.65, respectively. Thus, the larger size of the perchlorate anion, with ri = 0.240 nm, compared with that of thiocyanate, 0.213 nm, causes it to be pushed more strongly from the bulk toward the surface. This is due to its larger bulk water structure breaking effect, ΔHBG = −1.01 than that of thiocyanate, −0.82, in spite of its lower polarizability. For the three halate anions, the polarizability αi increases from chlorate through bromate to iodate, so do the ki values, contrary to the trend in Figure 3, but the water structure breaking abilities ΔHBG diminish (iodate is even mildly structure-making), leading to ki values in line with the trends in Figure 5. A further point that has not been discussed in the literature with respect to the surface tension increments of ions is the electrostriction caused by them and the diminished permittivity of the water, down to saturation, in their immediate vicinity. These quantities have been established for many ions in bulk solutions,36,37 but are not well-known (or not al all) for ions near the surface. Authors tend to employ implicitly or explicitly the bulk permittivity of pure water, εW, for the electrostatic calculations of the image potential energy,21,29,33 the solvation potential energy,17,18,24,29,38,39 and the dispersion potential.20,30,40 Slavchov and Novev11 did introduce a variable permittivity, taking into account the dielectric decrement associated with increasing electrolyte concentrations in the bulk of the solution. However, they did not reckon with conditions at the surface and in the near vicinity of the ions at the surface in their calculations. The author has calculated36,37 the standard molar ionic volume decrement due to electrostriction, −ΔelstrVi/cm3 mol−1, for the monatomic alkali metal, alkaline earth metal and halide ions and a few polyatomic ones (NH4+, NO3−, ClO4−, and SO42−) at 298.15 K and these are shown in Table 1. For other ions the electrostriction volume is calculated as Δelstr Vi = Vi ∞ − Vi intr = Vi ∞ − (4πNA /3)ri mod 3

k i /mN m−1 M−1 = (0.56 ± 0.13) − (0.036 ± 0.004)Δelstr Vi /cm 3 mol−1

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for 18 ions, with a correlation coefficient of 0.916 and a standard error of the fit of ±0.3 mN m−1 M−1. The more negative the electrostrictive volume decrement is, the larger is the molar STI. Outliers are the hydrogen, tetramethylammonium, and guanidinium ions, that can be accounted for by the special positions of protons on surface water molecules, by the large hydrophobic volume of Me4N+ and a probably overestimation of its electrostriction (it may well not take place at all) and still not sufficiently well-known properties40 of C(NH2)3+. For the anions, however, no reasonable correlation could be found between ki and ΔelstrVi. For the univalent anions ki does increase with increasingly negative ΔelstrVi values, but the spread of the latter is too narrow (between −2.4 and −6.2 cm3 mol−1, except for formate and acetate) to permit a useful correlation, but for the multivalent anions, the same trend prevails, but with only one-half the slope as for the cations. Of course, the effects of the compression of the water and the orientational immobilization of the water, leading to diminished permittivity, due to the large electrostatic field of the ion in its near vicinity, are already implicit in the variables with which the molar STIs are correlated. In fact, ΔelstrVi is the one variable among those shown in Table 1 that the multivariate regression rejects on statistical grounds. However, a theory for the prediction of the surface tension increments of electrolytes yielding numerical values to be compared with experimental data ought to take these effects into account. This is a challenge for theoreticians dealing with surface tensions of aqueous electrolytes.

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AUTHOR INFORMATION

Notes

The authors declare no competing financial interest.

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REFERENCES

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where Vi∞ is the standard molar partial ionic volume, Vi intr is the ionic intrinsic volume, and ri mod is the ionic radius modified from the bare radius, ri by either multiplying it by 1.213 according to Mukerjee for monatomic ions or by adding to it 0.055 nm according to Glueckauf for polyatomic ones.36,42 For 2887


Langmuir

Article

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Individual Ionic Surface Tension Increments in Aqueous Solutions

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