Charged Surface-Active Impurities at Nanomolar Concentration

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Letter Cite This: J. Phys. Chem. Lett. 2018, 9, 189−193

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Charged Surface-Active Impurities at Nanomolar Concentration Induce Jones−Ray Effect Yuki Uematsu,†,‡ Douwe Jan Bonthuis,‡ and Roland R. Netz*,‡ †

Department of Chemistry, Kyushu University, Fukuoka 819-0395, Japan Fachbereich Physik, Freie Universität Berlin, 14195 Berlin, Germany

‡

S Supporting Information *

ABSTRACT: The electrolyte surface tension exhibits a characteristic minimum around a salt concentration of 1 mM for all ion types, known as the Jones−Ray effect. We show that a consistent description of the experimental surface tension of salts, bases, and acids is possible by assuming charged impurities in the water with a surface affinity typical for surfactants. Comparison with experimental data yields an impurity concentration in the nanomolar range, well below the typical experimental detection limit. Our modeling reveals salt-screening enhanced impurity adsorption as the mechanism behind the Jones−Ray effect: for very low salt concentration added salt screens the electrostatic repulsion between impurities at the surface, which dramatically increases impurity adsorption and thereby reduces the surface tension.

S

concentrations,2,6 as discussed further below. There are four more scenarios, not explicitly discussed in literature: (iii) In contrast to hydroxide, the hydronium ion does adsorb to the surface, as indicated by the negative surface tension change of acidic solutions.2 However, the surface affinity extracted from experimental surface tensions of acids is too small to explain the Jones−Ray effect (as shown further below). (iv) Experiments are typically performed in the presence of atmospheric carbon dioxide, which in water forms bicarbonate ions. In fact, bicarbonate ions show significant interfacial activity, yet the bicarbonate surface affinity extracted from experimental data is not strong enough to quantitatively explain the Jones−Ray effect (as discussed further below). (v) As we show in this paper, the postulation of charged surface-active impurities in the aqueous phase leads to a Jones−Ray effect that is universal for all salts and quantitatively matches experimental surface tension data. For the impurity surface affinity, we assume a value that we derive from experimental interfacial tension data for solutions of typical charged surfactants such as anionic sodium dodecyl-sulfate (SDS) or cationic dodecyl-dimethylammonium chloride (DDAC). The impurity concentration we obtain by the fit to the Jones−Ray data is in the nanomolar range, and thus below the detection limit of many experimental techniques. (vi) Yet another possible scenario involves impurities in the added salt. As we show in the Supporting Information (SI), however, this scenario does not match the salt concentration dependence of the experimental surface tension data well, and is thus dismissed. Figure 1a shows the original Jones−Ray data, corresponding to the surface tension difference of monovalent electrolyte

urface tension measurements reveal the surface affinity of solutes. In fact, the Gibbs adsorption isotherm quantitatively relates the change of the surface tension as the solute concentration varies to the total surface excess of adsorbed solute. For almost all ion types, the surface tension increases with concentration, indicative of a net repulsion of ions from the surface. Onsager and Samaras quantitatively explained this by the screened dielectric ion-surface repulsion.1 Later, small differences between the surface tension increase for different monovalent ions were rationalized by additional nonelectrostatic surface-ion interactions, which reflect the Hofmeister series.2−9 However, for a long time it has been known that at dilute concentrations around 1 mM, electrolytes reduce the surface tension.10−18 The mechanism behind this so-called Jones−Ray effect, which is not captured by Onsager−Samaras theory, has been controversially debated ever since.16−23 Six scenarios address the Jones−Ray effect: (i) Surface adsorption of one of the added ions was argued to cause the surface tension minimum.24,25 This scenario received support from molecular dynamics simulations 26,27 and experiments28−30 that indeed showed large halides like iodide to exhibit some surface affinity. However, chloride and fluoride salts, which are known to be surface inactive, also exhibit the Jones−Ray effect,10−18 which clearly rules out this explanation. (ii) According to the second scenario, the interfacial adsorption of hydroxide ions, which are always present due to water dissociation, gives rise to the Jones−Ray effect. Quantitative models reproduced the Jones−Ray effect by assuming strong hydroxide surface adsorption.3,4 From the molecular modeling side, the situation is not clear, with some simulations supporting hydroxide adsorption31−33 and others not.34−37 However, the assumption of hydroxide adsorption is clearly ruled out by experiments, since the surface tension of alkali hydroxide solutions strongly increases at elevated © XXXX American Chemical Society

Received: November 7, 2017 Accepted: December 20, 2017 Published: December 20, 2017 189

DOI: 10.1021/acs.jpclett.7b02960 J. Phys. Chem. Lett. 2018, 9, 189−193

Letter

The Journal of Physical Chemistry Letters f (z ) = kBT

∑ ci(z)[ln(ci(z)) − 1 + Ui(z)] + i

εε0 (∇ψ (z))2 2kBT (1)

where kBT is the thermal energy, c i(z) is the local concentration of ion type i, Ui(z) is a nonelectrostatic interaction between ion and surface, εε0 is the solution dielectric constant, ψ(z) is the local electrostatic potential. We approximate the ion-surface interaction by a square well according to Ui(z) = αiθ(z* − z) where θ(z) is the Heaviside function, αi is the ion-specific surface affinity and z* the interaction range. This simple choice for the interaction potential allows for an analytic solution.39 The electrostatic boundary conditions are dψ/dz|z=0 = 0 at the interface, corresponding to a neutral interface, and ψ(z → ∞) = 0, meaning that the bulk is electroneutral. The free energy density eq 1 is minimized by the Boltzmann distribution ci(z) = cbi e−qieψ(z)/kBT−Ui(z), where cbi denotes the bulk concentration and qi = ± 1 the valency of ion type i. In combination with the Poisson equation, we obtain the Poisson−Boltzmann equation

Figure 1. (a) Difference of electrolyte and pure water surface tension Δγ as a function of bulk electrolyte concentration cbsalt. The points are experimental data11−13 for different salts. In the data extraction we use a pure water surface tension of γ0 = 72 mN/m.38 The solid lines present solutions of the mean-field model eq 2 with finite impurity concentrations cbimp = 1 nM, 2.8 nM, and 10 nM (blue, black, and red lines), while the dashed line is obtained in the absence of impurities. We use z* = 0.5 nm for the interfacial width and αNa = 1.16, αCl = 0.98, αimp = −15.1, and αcou = 1.07 for the surface affinities of Na+, Cl−, impurities, and impurity counterions. (b) Predicted impurity surface concentration csurf imp = cimp(z = 0) (black solid line, right axis) and surface potential (green solid line, left axis) for cbimp = 2.8 nM as a function of cbsalt; for cbsalt = 0 we predict csurf imp = 0.3 mM and ψ(0) = −106 mV.

εε0

d2ψ * = −e ∑ qicibe−qieψ / kBT − αiθ(z − z) dz 2 i

(2)

The analytic solution of eq 2 is given in the SI. The surface tension γ follows from the Gibbs isotherm as γ = −kBT ∑ i

∫0

cib

Γi cĩ

b

dcĩ b

(3)

and involves an integral over the surface excess Γi of all ions b defined by Γi = ∫ ∞ 0 (ci(z)−ci ) dz. The derivation of eq 3 is given in the SI. The temperature is T = 298 K and for the relative dielectric constant of water we use ε = 78.40 For the range of the ion− surface interaction we take z* = 0.5 nm, close to results from molecular dynamics simulation27 (see SI). By matching the single-ion surface excess of our box model with previous MD simulation results, we obtain for the ionic surface affinities αNa = 1.16 for Na+ and αCl = 0.98 for Cl− (see SI for this matching procedure). With these parameters and in the absence of impurities, we obtain from our model the solid black line in Figure 2a. The agreement with the experimental data for NaCl solutions41 (black circles) up to molar concentrations is perfect, showing that our model, combined with realistic ionsurface affinities αi, describes experimental high-concentration surface tension data quantitatively. However, comparing our model results for the two-component system with only Na+ and Cl− ions (black dashed line) with the experimental data in Figure 1a on a logarithmic scale including low concentrations reveals large deviations, thus showing that the surface affinities of the electrolyte ions do not cause the Jones−Ray effect. In Figure 2a we also show experimental surface tension data for NaOH, HCl, and NaHCO3 solutions,41,42 which differ drastically from NaCl. Using the analytic solution of our PB model, we extract the ion-surface parameters from the experimental data, which is possible in an unambiguous manner since in the fitting we fix αNa = 1.16 and αCl = 0.98. The resulting fits, shown as solid lines in Figure 2a, are perfect, and we obtain αH3O = −0.9, αOH = 1.6, and αHCO3 = −0.4. We see that H3O+ and HCO−3 are slightly surface active. To check for the consequence of this, we generalize our model in the next step to include, besides Na+ and Cl− ions, also H3O+ and

solutions compared to pure water, Δγ, as a function of salt concentration.11−13 We split the data into positive and negative values to allow for a double-logarithmic plot; different symbol colors denote different salt types. The black dashed line results from our mean-field model including surface−ion interactions representative of NaCl in the absence of impurities, which agrees closely with the Onsager−Samaras theory (as shown in the SI) and stays strictly positive, thus not explaining the Jones−Ray effect. The three solid lines follow from our model in the presence of charged surface-active impurities with bulk concentrations cbimp = 1 nM, 2.8 nM, 10 nM (blue, black, and red solid lines). For the impurity surface affinity, we use a value derived from experimental surfactant data, as explained below. The solid lines correctly show a minimum at millimolar salt concentration with a depth that depends on cbimp; the curve for cbimp = 2.8 nM matches the experimental data nicely. This impurity concentration is considerably lower than the concentration of autodissociated water ions, which is at least 100 nM. Data from different laboratories employing different measurement techniques15−18 show pronounced deviations among each other but can all be fitted by our model using varying impurity concentrations in the nanomolar range (see SI). We conclude that trace amounts of charged surface-active impurities give rise to the Jones−Ray effect. Before we discuss alternative scenarios for the Jones−Ray effect and supply further evidence for our impurity mechanism, we introduce our model: We consider a planar interface at z = 0 between the electrolyte solution at z > 0 and air at z < 0. The ionic distributions are assumed to be laterally homogeneous, so the mean-field free energy density is 190

DOI: 10.1021/acs.jpclett.7b02960 J. Phys. Chem. Lett. 2018, 9, 189−193

Letter

The Journal of Physical Chemistry Letters

tension data of two common ionic surfactants, SDS43 and DDAC,44 as circles. The comparison with our PB model for moderate concentrations (solid lines), using αNa = 1.16 and αCl = 0.98, yields αSDS = −15.6 and αDDAC = −14.5, which are quite similar and not much smaller than the transfer free energy of dodecane from water to hydrocarbon liquid, which is −22kBT.46 Obviously, surfactants are much more surface active than all other ions. In Figure 1a we show the calculated surface tension difference Δγ = γ(cbsalt, cbimp)−γ(cbsalt = 0,cbimp) for a fourcomponent system (model 1), consisting of charged impurities with surface affinity αimp = −15.1 (the mean of αSDS = −15.6 and αDDAC = −14.5) and counterion surface affinity αcou = 1.07 (the mean of αNa = 1.16 and αCl = 0.98) for a few different values of the impurity bulk concentration cbimp. The impurity model describes the experimental data nicely, with an almost perfect match for cbimp = 2.8 nM. We note that we obtain an equally good match of the experimental data for a wide range of impurity surface affinities αimp if the impurity concentration cbimp is adjusted accordingly (see SI), so our results do not imply that the impurities necessarily are SDS or DDAC. Figure 1b shows that the impurity surface concentration csurf imp ≡ cimp(z = 0) (black line) strongly increases with added salt. This increase is due to the screening of the impurity repulsive charge interactions at the surface, and in turn causes the dramatic decrease of the surface tension and thus is at the heart of the Jones−Ray effect. Although the impurity surface affinities are very large, the impurity surface concentration does not exceed 10 mM, as seen in Figure 1b, which shows that the surfactants are still quite dilute at the surface and our ideal mixing model remains valid. The surface tension reduction due to impurities without added electrolytes is only around 1 μN/m and difficult to detect experimentally (see SI). Thus, while the impurities by themselves give a negligible contribution to γ, their secondary contribution due to added salt is large. As a robustness check, in Figure 2d we show the more complicated scenarios where in addition to charged impurities and salt (model 1) we include H3O+ and OH− ions (model 2) and H3O+ and OH− as well as HCO−3 ions (model 3). We fix the impurity concentration at cbimp = 2.8 nM, which gives the best comparison with experimental data in Figure 1a, and use for the surface affinities of all ions the values obtained from experimental data in Figure 2a. The differences between the three models are most pronounced at low concentrations and even improve the comparison with experimental data (see SI). Our mean-field model also allows for asymptotic scaling analysis. For large impurity surface affinity, i.e., for αimp ≪ 0 we obtain

Figure 2. (a) Surface tension of NaCl, NaOH, HCl, NaHCO3 solutions. Circles are experimental data,41,42 and lines are solutions of eq 2 with z* = 0.5 nm, αNa = 1.16, αCl = 0.98, αH3O = −0.9, αOH = 1.6, and αHCO3 = −0.4. (b) Surface tension of SDS and DDAC solutions. Circles are experimental data,43,44 lines are solutions of eq 2 with αSDS = −15.6 and αDDAC = −14.5. (c) Comparison of results in the absence of impurities for only Na+ and Cl− (black dashed line), for Na+, Cl−, H3O+ and OH− (red dashed line), and for Na+, Cl−, H3O+, OH−, and HCO−3 (blue dotted line). The inset shows the surface potential ψ(0). (d) Comparison of results with impurities (αimp = −15.1, αcou = 1.07, cbimp = 2.8 nM) for only Na+ and Cl− (model 1), with additional H3O+ and OH− (model 2) and with additional HCO−3 (model 3). The red line depicts the asymptotic scaling for low salt concentration (eq 4), while the blue line shows the asymptotic scaling for large salt concentration (eq 5).

OH− ions. Fixing the bulk concentrations at cbH3O = 10−7 M and cbOH = 10−7 M, corresponding to pH = 7, we obtain the red broken line in Figure 2c, which coincides with the results for a pure NaCl solution (black broken line) and does not explain the Jones−Ray effect. Changing the H3O+ surface affinity αH3O leads to negative Δγ only for unrealistically negative αH3O values, which contradicts the pure acid data in Figure 2a (see SI). Most experiments are done in the presence of CO2 in air. Since CO2 readily dissolves in water45 and further dissociates into HCO−3 ions, which exhibit slight surface affinity (as shown in Figure 2a), it remains to be checked whether CO2 can explain the Jones−Ray effect. From the chemical equilibrium between the water ions in bulk cbH3OcbOH = 10−14 M2, the aqueous solubility of CO2 according to cbCO2/cair CO2 = 0.86, the b b b dissociation of carbonic acid cH3OcHCO3/cCO2 = 4.4 × 10−7 M, −5 and a typical CO2 concentration of cair M, we CO2 = 1.6 × 10 obtain a pH of pH = 5.6 (see SI for details). For Δγ we obtain the blue dotted line in Figure 2c, which is indistinguishable from the results in the absence of CO2 and does not yield the Jones−Ray effect. Only a minor effect due to CO2 is seen in the surface potential ψ(0) in the inset of Figure 2c. Next we explore the effects of surface-active impurity ions. As an example, we show in Figure 2b experimental surface

1/3

b b 1/3 b Δγ ≈ −2AkBT[(cimp + csalt ) − cimp

]

(4)

for low electrolyte concentration cbsalt and b Δγ ≈ 2BkBTcsalt

large cbsalt, where −(αNa+αCl)/2

(5)

(2εε0kBTz*cbimpe−αimp/e2)1/3

for A = and B = z*(1−e ) (see SI for the derivation). In Figure 2d we compare the scaling limits with the full solution for model 1 and find perfect asymptotic agreement. The same intermediate 1/3 power law has previously been derived in the context of charge regulation in carbon nanotubes.47 Summarizing, based on an exactly solvable mean-field model that accounts for ion-surface interactions, we simultaneously describe experimental data for the surface tension of salt, acid, 191

DOI: 10.1021/acs.jpclett.7b02960 J. Phys. Chem. Lett. 2018, 9, 189−193

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The Journal of Physical Chemistry Letters

(4) Manciu, M.; Ruckenstein, E. Specific ion effects via ion hydration: I. Surface tension. Adv. Colloid Interface Sci. 2003, 105, 63−101. (5) Petersen, P. B.; Saykally, R. J. Adsorption of Ions to the Surface of Dilute Electrolyte Solutions: The Jones−Ray Effect Revisited. J. Am. Chem. Soc. 2005, 127, 15446−15452. (6) Pegram, L. M.; Record, M. T. Hofmeister Salt Effects on Surface Tension Arise from Partitioning of Anions and Cations between Bulk Water and the Air-Water Interface. J. Phys. Chem. B 2007, 111, 5411− 5417. (7) Onuki, A. Surface tension of electrolytes: Hydrophilic and hydrophobic ions near an interface. J. Chem. Phys. 2008, 128, 224704. (8) Bier, M.; Zwanikken, J.; van Roij, R. Liquid-Liquid Interfacial Tension of Electrolyte Solutions. Phys. Rev. Lett. 2008, 101, 046104. (9) Beattie, J. K.; Djerdjev, A. M.; Gray-Weale, A.; Kallay, N.; Lützenkirchen, J.; Preočanin, T.; Selmani, A. pH and the surface tension of water. J. Colloid Interface Sci. 2014, 422, 54−57. (10) Jones, G.; Ray, W. A. The surface tension of solutions. J. Am. Chem. Soc. 1935, 57, 957−958. (11) Jones, G.; Ray, W. A. The Surface Tension of Solutions of Electrolytes as a Function of the Concentration. I. A Differential Method for Measuring Relative Surface Tension. J. Am. Chem. Soc. 1937, 59, 187−198. (12) Jones, G.; Ray, W. A. The Surface Tension of Solutions of Electrolytes as a Function of the Concentration II. J. Am. Chem. Soc. 1941, 63, 288−294. (13) Jones, G.; Ray, W. A. The Surface Tension of Solutions of Electrolytes as a Function of the Concentration III. Sodium Chloride. J. Am. Chem. Soc. 1941, 63, 3262−3263. (14) Jones, G.; Ray, W. A. The Surface Tension of Solutions of Electrolytes as a Function of the Concentration IV. Magnesium Sulfate. J. Am. Chem. Soc. 1942, 64, 2744−2745. (15) Dole, M.; Swartout, J. A. A Twin-Ring Surface Tensiometer. I. The Apparent Surface Tension of Potassium Chloride Solutions. J. Am. Chem. Soc. 1940, 62, 3039−3045. (16) Passoth, G. Uber den Jones−Ray-effekt und die Oberflächenspannung verdünnter elektrolytlosungen. Z. Phys. Chem. 1959, 211O, 129−147. (17) Randles, J. E. B.; Schiffrin, D. J. Surface tension of dilute acid solutions. Trans. Faraday Soc. 1966, 62, 2403−2408. (18) Chen, Y.; Okur, H. I.; Gomopoulos, N.; Macias-Romero, C.; Cremer, P. S.; Petersen, P. B.; Tocci, G.; Wilkins, D. M.; Liang, C.; Ceriotti, M.; et al. Electrolytes induce long-range orientational order and free energy changes in the H-bond network of bulk water. Sci. Adv. 2016, 2, e1501891. (19) Langmuir, I. Repulsive Forces Between Charged Surfaces in Water and the Cause of the Jones−Ray Effect. Science 1938, 88, 430− 432. (20) Langmuir, I. The Role of Attractive and Repulsive Forces in the Formation of Tactoids, Thixotropic Gels, Protein Crystals and Coacervates. J. Chem. Phys. 1938, 6, 873−896. (21) Long, F. A.; Nutting, G. C. The Relative Surface Tension of Potassium Chloride Solutions by a Differential Bubble Pressure Method. J. Am. Chem. Soc. 1942, 64, 2476−2482. (22) Venkateshwaran, V.; Vembanur, S.; Garde, S. Water-mediated ion-ion interactions are enhanced at the water vapor-liquid interface. Proc. Natl. Acad. Sci. U. S. A. 2014, 111, 8729−8734. (23) Okur, H. I.; Chen, Y.; Wilkins, D. M.; Roke, S. The Jones−Ray effect reinterpreted: Surface tension minima of low ionic strength electrolyte solutions are caused by electric field induced water-water correlations. Chem. Phys. Lett. 2017, 684, 433−442. (24) Dole, M. Surface Tension of Strong Electrolytes. Nature 1937, 140, 464−465. (25) Dole, M. A Theory of Surface Tension of Aqueous Solutions. J. Am. Chem. Soc. 1938, 60, 904−911. (26) Jungwirth, P.; Tobias, D. J. Molecular Structure of Salt Solutions: A New View of the Interface with Implications for Heterogeneous Atmospheric Chemistry. J. Phys. Chem. B 2001, 105, 10468−10472.

and base solutions. The negative tension differences at low salt concentrations, known as Jones−Ray effect, are reproduced by postulating trace amounts of surface-active charged impurities. The mechanism is independent of the added salt type, which explains the universality of the Jones−Ray effect. Purified water is inevitably contaminated with impurities and typically characterized by conductivity and total organic carbon content.48 The nanomolar impurity concentrations we show to be sufficient to explain the Jones−Ray effect are significantly below the detection limit of resistivity measurements, set by OH− and H3O+ ions. While only few works have addressed impurity effects on interfacial properties,49−51 ion-specific electrokinetic studies were recently performed at pico- to nanomolar electrolyte concentrations,52 indicating that experiments at superlow electrolyte concentrations are possible. A recent experimental study on bubble dynamics postulated the presence of impurity surfactants at the surface, very similar to our conclusions.53 We show that the presence of charged surface-active impurities at concentrations in the nanomolar range gives rise to the Jones−Ray effect, but alternative mechanisms cannot be excluded. As an independent confirmation of our impurity scenario we demonstrate that the surface potential in Figure 1b (green solid line) reaches about −100 mV for low salt concentration, similar to zeta potentials of gas and oil bubbles in water51,54 and to surface potentials of the air−water interface in thin wetting films.55 The impurity mechanism we propose could possibly be substantiated by detection of interfacial impurities using nonlinear optical techniques.5,56

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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.jpclett.7b02960. Theoretical details and supporting results (PDF)

■

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. ORCID

Yuki Uematsu: 0000-0002-4970-4696 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS Y.U. was supported by Grant-in-Aid for JSPS Fellows 16J00042. We thank the European Innovative Training Network (ITN) Transport of Soft Matter at the Nanoscale (NANOTRANS) for support.

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