Langmuir 2005, 21, 2619-2623
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Hofmeister Effects in Surface Tension of Aqueous Electrolyte Solution M. Bostro¨m,*,† W. Kunz,‡ and B. W. Ninham‡,§ Department of Physics and Measurement Technology, Linko¨ ping University, SE-581 83 Linko¨ ping, Sweden, Institute of Physical and Theoretical Chemistry, University of Regensburg, D-93040 Regensburg, Germany, and Research School of Physical Sciences and Engineering, Australian National University, Canberra 0200, Australia Received October 18, 2004. In Final Form: January 3, 2005 The surface tension of electrolyte solutions shows marked specific ion effects. We here show an important role for both ionic solvation energies and ionic dispersion potentials in determining this ion specific surface tension of salt solutions. The ion self-free energy changes when an ion moves from bulk solution into the interfacial region, with its decreasing water density profile. We will show that the solvation energies of different ions correlate very well with the surface tension of salt solutions. Inclusion of this distancedependent self-free energy contribution brings qualitative agreement with experiments and the right Hofmeister series. This is so not only for surface tension changes but also for measured surface potentials. The inclusion of ionic dispersion interaction potentials further improves the agreement with experiments. We discuss how further progress in the theory of the surface tension of salts can be achieved.
Introduction The surface tension of electrolyte solutions shows marked specific ion effects that have remained unexplained for a long time. It has earlier been demonstrated that if dispersion forces acting between ions and the airwater interface are included in theory, then the right order of magnitude for the surface tension change with added salt follows. These forces have usually been ignored previously. Or when they have been considered and dismissed they were included incorrectly or not at the same level as the other forces. However, their proper inclusion gives the Hofmeister sequence in the wrong order.1-3 Jungwirth and Tobias4 performed simulations of the air electrolyte interface that for the first time included the effect of static polarizabilities of ions and water molecules in this system, but they neglected manybody ionic dispersion potentials. These simulations gave the right Hofmeister sequence but were roughly a factor of 2 too large in magnitude. Simulations also give an incorrect surface tension value and freezing point temperature for pure water.4 To be fair to this work it should be stressed that they were the first that made a prediction without any adjustable parameter and, second, the statistics of their simulation as well as the size of their simulation box made it impossible to get precise values. (Recall that the surface tension is an integral over the concentration profile from the surface up to infinity in the bulk, and this is not possible within a small simulation box. Therefore, we would expect their surface potentials also to be in numerical disagreement with experiment.) Hence, while important progress has been made, a lot still remains before the sources of ion specificity of surface tension of salts is put on solid ground. With some †
Linko¨ping University. ‡ University of Regensburg. § Australian National University. (1) Ninham, B. W.; Yaminsky, V. Langmuir 1997, 13, 2097. (2) Bostro¨m, M.; Williams, D.; Ninham, B. W. Langmuir 2001, 17, 4475. Bostro¨m, M.; Ninham, B. W. Langmuir 2004, 20, 7569. (3) Kunz, W.; Belloni, L.; Bernard, O.; Ninham, B. W. J. Phys. Chem. B 2004, 108, 2398. (4) Jungwirth, P.; Tobias, D. J. Phys. Chem. B 2001, 105, 10468.
simulation as benchmarks, there is also a need for a simpler predictive theory applicable to more complex situations. The original theory for the surface tension change with added salt was due to Onsager and Samaras.5 It invokes the repulsive electrostatic image force seen by an ion near an air-water interface. But this force is the same for all monovalent ions, and according to this theory all monovalent salts should give the same increment in surface tension. (The result usually quoted for the limiting law involves a weak logarithmic dependence on ion sizes. That is an artifact due to linearization of the ionic distribution function profile.) This is in marked contrast with experiment that reveals large ion specificity.6 Dissolved inorganic salts for the most part increase the surface tension of the air-water interface. At low concentrations the increase is proportional to the salt concentration, and unless the solution is extremely dilute, it depends strongly on both anions and cations (usually more strongly on the anions). There have been several attempts to improve the Onsager-Samaras theory1-3,7-9 to explain this ion specificity. But none has been really successful in the sense of predictability. One important effect that was neglected by us (Bostro¨m et al.2 and others) in several such attempts was change in the water density profile in the interfacial region. It changes over a distance of about two water molecules, roughly 4 Å10 to 6 Å,4 from zero to bulk values. We will here argue that a missing key point in understanding the observed ion specificity is that previous attempts to include ionic dispersion potentials and other forces due to ionic polarizabilities1-4 have to be complemented with a proper (5) Onsager, L.; Samaras, N. N. T. J. Chem. Phys. 1934, 2, 528. (6) Weissenborn, P. K.; Pugh, R. J. J. Colloid Interface Sci. 1996, 184, 550. Maheshwari, R.; Sreeram, K. J.; Dhathathreyan, A. Chem. Phys. Lett. 2003, 375, 157. Aveyard, R.; Saleem, S. M. J. Chem. Soc., Faraday Trans. 1976, 22, 1609. (7) Stairs, R. A. Can. J. Chem. 1995, 73, 781. (8) Bhuiyan, L. B.; Bratko, D.; Outhwaite, C. W. J. Phys. Chem. 1991, 95, 336. (9) Manciu, M.; Ruckenstein, E. Adv. Colloid Interface Sci. 2003, 105, 63. (10) Ashbaugh, H. S.; Pethica, B. A. Langmuir 2003, 19, 7638.
10.1021/la047437v CCC: $30.25 © 2005 American Chemical Society Published on Web 02/10/2005
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treatment of self-free energies of ions in this interfacial region. The effect of the water density profile was first included in the simulations performed by Jungwirth and Tobias. But its effect on self-free energies was not discussed (this is because in their nonprimitive model; this is simply not necessary). The self-free energy of ions in water contains contributions from both electrostatic Born selffree energy and electrodynamic dispersion self-free energies.11-14 We will here demonstrate that the role of these ionic solvation energies and ionic dispersion potentials is essential to understanding the surface tension of electrolytes. In the interfacial region, in going from bulk water to air there is a region, roughly (and at most) 6 Å wide, with decreasing density of water molecules. The ion selffree energy (or solvation energy) changes when the ion moves into this region with lower water density. To model the density profile of water, we use an approximate formula based on results from molecular simulations.4 We will demonstrate how one can estimate the increase in self-free energy of ions when they move into the interfacial region. There will also be an effect due to the anisotropic orientation of the water molecules near the interface. This anisotropy will have an effect on both selffree energies and the ionic dispersion interaction potentials. A further effect that we also ignore is that of adsorbed ions on the interfacial profile. However, the main effects should already be included in the present description. And if they are not, this will show up in the results. We will show that the solvation energies of different ions correlate very well with the surface tensions of the salt solutions. The solvation energies of the ions that we will consider run in the sequence F- > Cl- > Br- > I-. This corresponds to a repulsive force larger for chloride than for iodide. This gives exactly the right order of magnitude and order of the ionic sequence for the surface tension increment with added salt. Some attempts have been made in the past to correlate the Hofmeister series observed for surface tension with that observed, for example, for protein precipitation. But because there may be less dramatic changes in the water concentration near proteins, as compared to that near the air-water interface, this may not necessarily be a meaningful or illuminating approach. In this and many other cases there will be a much more dominating role for ionic dispersion potentials. From that point of view, the air-water interface is different. But it is clear that changes in water concentrations (such as the slight changes in water density near some proteins,15-17 near some active sites,18 near water-oil interfaces,19 and near micelles20) can lead to similar self-free energy shifts that can and should be accounted for to understand such phenomena. Recent experiments indicate that ions have no influence on rotational dynamics of water molecules outside the (11) Rashin, A. A.; Honig, B. J. Phys. Chem. 1985, 89, 5588. (12) Bostro¨m, M.; Ninham, B. W. J. Phys. Chem. B 2004, 108, 12593. (13) Tissandier, M. D.; Cowen, K. A.; Feng, W. Y.; Gundlach, E.; Cohen, M. H.; Earhart, A. D.; Coe, J. V. J. Phys. Chem. A 1998, 102, 7787. (14) Grossfield, A.; Ren, P., Ponder, J. W. J. Am. Chem. Soc. 2003, 125, 15671. (15) Scatena, L. F.; Richmond, G. L. J. Phys. Chem. B 2001, 105, 11240. (16) Dellerue, S.; Bellissent-Funel, M.-C. Chem. Phys. 2000, 258, 315. (17) Zanotti, J.-M.; Bellissent-Funel, M.-C.; Parello, J. Biophys. J. 1999, 76, 2390. (18) Bandyopadhyay, S.; Chakraborty, S. Balasubramanian, S. J. Phys. Chem. B 2004, 108, 12608. (19) Dang, L. X. J. Phys. Chem. B 2001, 105, 804. (20) Soldi, V.; Keiper, J.; Romsted, L. S.; Cuccovia, I. M.; Chaimovich, H. Langmuir 2000, 16, 59.
Bostro¨ m et al.
first solvation shells21 and that changes in interfacial water caused by ions (unlike, e.g., surface potentials and conformational changes of macromolecules) do not follow a Hofmeister sequence.22 This provides strong experimental evidence that the many different ion specific effects observed in biology and chemistry (including the surface tension of electrolytes) are not primarily due to ion specific water structure effects but due to interactions between ions and interfaces as discussed here. We first briefly rehearse the theory of surface tension increment with added salt and describe how to estimate the change in self-free energy near the air-water interface. We then demonstrate numerically that inclusion of this solvation energy contribution brings qualitative agreement with experiments and the right Hofmeister series. The inclusion of ionic dispersion potentials (that neglect anisotropy) then improves the agreement with experiments further. We will come back to the effect of anisotropy in a later publication. Here we use an extremely simple model to demonstrate how extension to include anisotropy may improve the agreement with theory even more. We also briefly discuss some other effects not accounted for here, which influence the surface tension at the air-water interface. We finally end with a brief summary and discuss how one also obtains the correct Hofmeister sequence for the surface potentials of electrolytes when the previously missing solvation energy changes are accounted for. Theory We briefly rehearse the theory of surface tension changes with added salt. The sole new aspect as compared to the earlier paper by Bostro¨m et al.2 is that at the end of this section we discuss how one can include the solvation energy effect. We consider an aqueous solution of monovalent anions (-) and cations (+), each with a bulk concentration c0 and charge e. Except for the effect on the solvation energy of ions in the interfacial region the water is considered to be a continuum. Each ion is acted upon by external interaction potentials. In the original Onsager-Samaras theory only electrostatic (φ) and image potentials [Uimage(x)] were considered. Here we will also take into account that ions experience ionic dispersion potentials [Udispersion(x)] and solvation energy potentials [Usolvation(x)]. Strictly speaking, in the original theory of dispersion (electrodynamic fluctuation) self-energies of Mahanty and Ninham, interaction energies are just the change in dispersion selfenergy due the presence of an interface23 (just as the image potential for an ion is the change in Born energy due to the interface). These potentials lead via the Gibbs adsorption excess
Γ((c) ) c
∫0∞ dx {exp[-(Uimage + Udispersion +
Usolvation ( eφ)/kT] - 1} (1)
to the surface tension increment with added salt
∆γ(c) ) -kT
∫0c
dc1 (Γ + Γ-) c1 +
(2)
In these expressions T is the temperature and k is Boltzmann’s constant. To estimate the position of the air(21) Omta, A. W.; Kropman, M. F.; Woutersen, S.; Bakker, H. J. Science 2003, 301, 347. (22) Gurau, M. C.; Lim, S.-M.; Castellana, E. T.; Albertorio, F.; Kataoka, S.; Cremer, P. S. J. Am. Chem. Soc. 2004, 126, 10522. (23) Mahanty, J.; Ninham B. W. Dispersion Forces; Academic Press: London, 1976.
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water interface we proceed as follows: Using Figure 1e from the paper by Jungwirth and Tobias,4 we find that the ions are more or less entirely in air at “z ) 18 Å” (in their notation) so we assume that an ion has increased its self-free energy by the entire solvation energy here (x ) 0). Going in the direction toward bulk water the amount of water is very low in the following 2 Å so we take (in a very crude way) the Gibbs dividing surface to be at x ) 2 Å. These details are not so important here because we are mainly interested in demonstrating the general principles. We will come back with a more refined theory that deals with this in a better way, besides considering a number of other points that will be discussed later. The image potential acting on an ion a distance x from an air-water interface is
Uimage(x) )
e2∆ exp(-2κDx) 16πw(0)0x
Usolvation(x) ≈ { ≈ 1 + FR/0} ≈ -z2e2 8π0rion
R/
0 dF ∫FF(x)(1 + FR/ )2 w
(4)
The dispersion coefficient (B) depends on the dielectric function of water and the excess polarizability of ions in water. In the proximity of the interface this expression is modified by inclusion of a finite ion size so that it approaches a constant value. We used the experimental dielectric function of water and the adjusted polarizabilites that Kunz et al. demonstrated could fit the osmotic coefficient for a large number of salts. In this way we obtained the following B values for the sodium, chloride, and iodide ions: 1.4 × 10-50, 13.6 × 10-50, and 15.1 × 10-50 J‚m3. Besides these contributions, one has to include the effect from solvation energy changes when the ion moves into the interfacial region. To be able to estimate this effect we need to know the solvation energy of individual ions. While the sum of solvation energies of ion pairs is quite wellknown the situation is less clear for individual ions and requires a theoretical calculation. We will here mainly use the values presented by Bostro¨m and Ninham12 (complemented with more data from Rashin and Honig11). But we will later also discuss how the result changes when the values derived by Grossfield et al.14 are used. For Na+, F-, Cl-, Br-, and I- we estimate that the solvation energies are 407.65, 502.67, 361.79, 334.26, and 209.49 kJ/mol. Solvation energies can in general comprise 5-30% from dispersion self-free energies, and the rest from electrostatic Born energies. In the calculation of the distance-dependent self-free energy (or solvation energy) we treat the entire contribution as if it originated from electrostatics. This introduces a small error, but in the light of the well-known uncertainty of radii and polarizabilities of ions in water, it is difficult to establish exactly how much comes from dispersion self-free energies and how much comes from Born energies. It is relatively straightforward to improve this approximation, along with the others made, which is
(5)
0
where p(x) ) F(x)/Fw is the local relative water concentration and R is water molecular polarizability. This expression can be rewritten in terms of the solvation energy (∆Gsolvation) of bringing an ion from water to air
{
Usolvation(x) ≈ ∆Gsolvation
}/
1 1 1 + p(x)[w(0) - 1] w(0)
(3)
where ∆ ) [w(0) - 1]/[w(0) + 1] ≈ 1, w(0) is the dielectric constant of water, and κD ) e[2c0/(kT0w(0)]1/2 is the inverse Debye length. The ionic dispersion potential has been the focus of a series of publications during the past few years.1-3,12 In the numerical examples presented in the next section we took ion size effects into account in the way described by Kunz et al.3 We will here only give the dispersion potential far from the interface, which is approximately
Udispersion(x) ) B/x3
something that will be done in a more detailed investigation. With a few approximations we then find that (cf. the discussion by Israelachvili on self-energy changes24)
[
1-
]
1 (6) w(0)
For the relative water density profile we used an approximate formula that was fitted to water simulations performed by Jungwirth and Tobias:4
p(x) ≈ 1 - 1.0302 exp(3.5 - x)/[1 + exp(3.5 - x)] (7) where the distance x to the interface should be given in angstroms. This function agrees with simulations at x ) 0 and at x ) infinity and follows the result of the simulation reasonably well in the transition region. (In a more detailed work the use of this function could be replaced with either the exact water density profile from simulations or the experimental data). Numerical Results To be able to compare with experiments we begin this section with a brief discussion on experimental results. Jungwith and Tobias4 quote the following values for the surface tension increment with added salt: 3.6 (mN/m)/ (mol/L) for NaF; 2.0 (mN/m)/(mol/L) for NaCl; 1.6 (mN/ m)/(mol/L) for NaBr; and 1.2 (mN/m)/(mol/L) for NaI. However, it is important to recall that it is extremely difficult to prepare “surface pure” electrolyte solutions. This can be seen, for example, in the large variation in experimental results. Weissenborn and Pugh6 reported the following results (that are very different compared to those quoted by Jungwirth and Tobias). For NaCl they found 2.08 (mN/m)/(mol/L), for NaI 1.23 (mN/m)/(mol/L), and for NaF 1.83 (mN/m)/(mol/L).6 Unpublished results by Craig are again different from both these examples. There is an important and previously neglected role for dissolved CO2 and other dissolved gases in the interfacial region. That might be one reason behind some of the difficulties in reproducing the results in different experiments, but other impurities are probably much more important. For fluoride salts it is also important to remember that fluoride reacts with water making this a more complicated example. There are many other results published by different authors that span almost a factor of 2 in magnitude. Nonetheless, the sequence seems not in dispute. We will in this numerical section see if we can understand the observed Hofmeister sequence. (24) Israelachvili, J. Intermolecular & Surface Forces, 2nd ed.; Academic Press: London, 1992.
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Figure 1. Charge distribution in a 1 M electrolyte for two different combinations of dispersion constants. The combinations for cations and anions are (in units of 10-50 J‚m3) 1.4, 13.57 (“NaCl”, dashed line) and 1.4, 15.13 (“NaI” solid line). These values were obtained from the ionic polarizabilities used by Kunz et al. to fit osmotic coefficients for a large number of salts.3 Table 1. Calculated Surface Tension Changes with Added Salt for 1 M NaCl and 1 M NaI Given for the Different Combinations of Interaction Potentials Acting between the Ion and the Air-Water Interfacea interaction potentials
d(∆γ)/dc for 1 M NaCl (mN/m)/(mol/L)
d(∆γ)/dc for 1 M NaI (mN/m)/(mol/L)
iso. disp. solv.12 solv.14 iso. disp. + solv.12 iso. disp. + solv.14 aniso. disp. aniso. disp. + solv.12 experimental6
0.77 1.64 1.62 1.43 1.40 0.51 1.47 1.55
0.82 1.58 1.61 1.31 1.36 0.42 1.29 1.21-1.45
a These model interaction potentials are isotropic ionic dispersion potential; anisotropic ionic dispersion potential; and solvation energy potential with solvation energies given by ref 12 or by ref 14. Details are given in the text.
To obtain the contribution from the self-consistent electrostatic potential we need to solve the nonlinear generalized Poisson-Boltzmann equation
d2φ ) -e(c+ - c-)/0w(0) dx2
(8)
where the concentrations are given by
c( ) c0 exp[-(Uimage + Udispersion + Usolvation ( eφ)/kT] (9) We found earlier that inclusion of ionic dispersion potentials gave rise to a double layer with more positively charged ions near the interface due to the larger repulsive dispersion potentials acting on the anions. In Figure 1 we show the numerically solved charge distribution when both ionic dispersion potentials and solvation energy contributions are included for “NaCl” and “NaI”. The large differences in the repulsive solvation energy contributions for sodium and iodide ions are in this example sufficiently large to reverse the charge of the double layer (more iodide than sodium ions near the interface). When we include only the dispersion potentials discussed in the previous section we find surface tension changes with added salt as follows: 0.82 (mN/m)/(mol/L) for 1 M NaI and 0.77 (mN/m)/(mol/L) for 1 M NaCl (see Table 1). When both ionic dispersion potentials and solvation energy contributions are included we find 1.58 (mN/m)/(mol/L) for 1 M NaI and 1.64 (mN/m)/(mol/L) for 1 M NaCl. This shows that one can obtain the right
Hofmeister series when both ionic dispersion potentials and ion solvation effects are included. It is interesting to see how sensitive these results are to the exact values of the individual solvation energies. Using values derived from the result of Grossfield et al.14 we find 1.61 (mN/m)/(mol/L) for 1 M NaI and 1.62 (mN/ m)/(mol/L) for 1 M NaCl when both solvation energies and dispersion potentials are included. When these solvation energies are included but ionic dispersion potentials are not we find 1.36 (mN/m)/(mol/L) for 1 M NaI and 1.40 (mN/m)/(mol/L) for 1 M NaCl. When the solvation energies from Bostro¨m et al. are included (but not the ionic dispersion potentials) we find 1.31 (mN/m)/(mol/L) for NaI; 1.41 (mN/m)/(mol/L) for NaBr; 1.43 (mN/m)/(mol/L) for NaCl; and 1.51 (mN/m)/ (mol/L) for NaF. It is evident that the fact that the solvation energy changes as an ion enters the interfacial region is the main contribution to ion specificity at the air-water interface. It gives the right Hofmeister sequence for the interfacial tensions. The dispersion potential then gives an important contribution that improves the agreement with experiments further. Parsegian and Weiss25 derived a model that dealt with dispersion forces acting across anisotropic structured media. Bostro¨m has recently (M. Bostro¨m and B. W. Ninham, unpublished) extended this model to consider dispersion potential acting on a pointlike polarizable particle in a structure consisting of air-anisotropic media-isotropic media. Preliminary calculations reveal that near an interface between two very similar media (one anisotropic and one isotropic) there can be a region with attractive dispersion potentials. In a 6 Å thin film one can have repulsive dispersion potentials near the airwater interface and an attractive dispersion potential near the interface between anisotropic and isotropic water. These calculations break down for the system considered for a number of reasons. First one needs to include finite ion size effects to avoid divergence at the interfaces, second one needs a refined model for the dielectric function of anisotropic water, and finally one needs to include the effect of a spatially varying dielectric function (rather than having a thin anisotropic film). All of these aspects have been considered separately (the effect of a continuously varying dielectric function has, for instance, recently been considered by V. A. Parsegian with other examples in mind that did not involve polarizable particles). But all need to now be considered together for our particular system. Another important fact that should also be taken into account is that there will be some dependence of the dielectric properties of the surface water from the presence of salt (both species and concentration).21-22 This leads to the conclusion that one could solve self-consistently for dielectric properties of the interfacial water, ion profiles, and ionic interaction potentials. Using simple model calculations with point ions we will use a correspondingly simplistic model to illuminate this issue. The result of this model should not be taken too seriously. But it might we hope stimulate further work along the lines discussed here. Having said this, we use the following simple model for the dispersion potential, namely,
Udispersion* )
B1 3
x +
rion3
+
B2 |x - dfilm|3 + rion3
(25) Parsegian, V. A.; Weiss, G. H. J. Adhesion 1972, 3, 259.
Hofmeister Effects in Surface Tension
Figure 2. Ion specific self-consistent relative concentration profile (c(/c0) as a function of distance to an air-water interface. Solid lines (dashed lines) are for NaI (NaCl) salt, and the anion profiles are marked with circles. Note that this figure is based on a simple model for the ionic dispersion potential near an air-water interface that may be more or less realistic. Its only purpose is to illustrate how inclusion of anisotropy in the dielectric function of surface water may change ionic profiles drastically.
Here rion is the ionic radius (here used as a simple way to avoid divergence at the interfaces), B1 is the dispersion coefficient described earlier (corresponding to dispersion interaction between water and air), and B2 is an additional dispersion contribution (corresponding in a crude way to the dispersion interaction near the interface between regions with anisotropic and isotropic water). The thickness of the film (dfilm) was taken to be 6 Å. Values for B2 that we use are, as is everything related to this example, only intended for demonstrational purposes: -0.06 × 10-50, -0.6 × 10-50, and -1 × 10-50 J‚m3 for sodium, chloride, and iodide. Even though these values are much smaller than the corresponding values for the air-water interface they are sufficient to give the “right” Hofmeister series by themselves: 0.42 (mN/m)/(mol/L) for 1 M NaI and 0.51 (mN/m)/(mol/L) for 1 M NaCl. When both solvation energies and ionic dispersion potentials are included we find in this case 1.29 (mN/m)/(mol/L) for 1 M NaI and 1.47 (mN/m)/(mol/L) for 1 M NaCl. These values are very similar to the literature values quoted by Weissenborn and Pugh (1.21-1.45 for NaI and 1.55 for NaCl). However, we stress again that this last calculation was only intended for demonstrational purposes. Its main purpose is to illustrate how inclusion of anisotropy in the dielectric function of surface water may give rise to regions with attractive dispersion potentials that may change the ionic profiles drastically. This has the potential to improve the agreement between theory and experiments further. As can be seen in Figure 2 the effects from anisotropy on the dispersion potential could also give rise to the enhanced concentration of polarizable ions such as iodide near the interface similar to what has already been observed in simulations. Summary The important work of Jungwirth and Tobias (and extensions) provides a benchmark that is useful and illuminating. But it is hard to extend such simulations to mixtures of electrolytes, oil-water or membrane-water systems, or proteins. The key feature of this manuscript is the following: the nonprimitive model is very timeconsuming and can also for the forseeable future only yield reference data. It is the task of the theoretician to grasp the main features of such simulation and to translate them
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Figure 3. Electrostatic potential near air-water interfaces in the presence of a monovalent 1 M model salt solution. The following curves are for the case when only solvation energy effects were included: triangles (NaF); open squares (NaCl); crosses (NaBr); and open circles (NaI). The dashed (dotted) line represents the case when solvation energy effects and isotropic dispersion potentials are included for 1 M NaI (NaCl). The filled circles (filled squares) represent the model calculation when solvation energy effects and the simple model dispersion potential (representing anisotropy) were used for NaI (NaCl).
into a primitive model in a way that admits easy application to a range of complicated real world situations. So far as we are aware, the attempt to do this in this paper is the first work that translates physically reasonable interactions into a full interaction potential. We have here a semiclassical continuum theory that captures the essence of the problem and at least predicts the correct magnitudes and trends. As can be seen in Figure 3 it also gives the right Hofmeister sequence for the surface potential of salt solutions. One should note that the magnitudes depend strongly on the difference of solvation energies of different ions (among other things) and that the surface potential of NaI is slightly smaller than the experimental result.26 But the essential observation is that the theoretical calculation for the surface potential gives exactly the right Hofmeister sequence and a fairly good result for a 1 M NaCl solution.26 In other words, we may now be on the right track. An unknown reviewer kindly suggested that we could also calculate the electrostatic potential for pure water within our formalism using the known dissociation equilibrium of water.27 As suggested by the reviewer the sign of this potential (which experimentally is known to be negative near the air-water interface27) would depend on the relative sizes of H3O+ (or H+) and OH-. Because hydronium ions have roughly twice as large a solvation energy as hydroxide ions (this can be deduced from refs 12 and 13) the potential that is due to the solvation energy change produces a negative surface potential near an airwater interface. We will return to this point and other things discussed here in a subsequent publication. Acknowledgment. M.B. thanks the Swedish Research Council for financial support. We also thank Dr. Pavel Jungwirth for interesting discussions during our visit to Prague. LA047437V (26) Jarvis, N. L.; Scheiman, M. A. J. Phys. Chem. 1968, 72, 75. (27) Scheechter, R. S.; Graciaa, A.; Lachaise, J. J. Colloid. Interface Sci. 1998, 204, 398.
