Colloids and Surfaces A: Physicochemical and Engineering Aspects

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1 Colloids and Surfaces A: Physicochem. Eng. Aspects 4 (212) Contents lists available at SciVerse ScienceDirect Colloids and Surfaces A: Physicochemical and Engineering Aspects jo ur nal homep a ge: Ions near the air/water interface: I. Compatibility of zeta potential and surface tension experiments Marian Manciu a,, Eli Ruckenstein b a Physics Department, University of Texas at El Paso, TX, United States b Chemical and Biological Engineering Department, State University of New York at Buffalo, United States a r t i c l e i n f o Article history: Received 27 December 211 Received in revised form 18 February 212 Accepted 25 February 212 Available online 5 March 212 Keywords: Air/water interface Surface tension Ion adsorption Zeta potential a b s t r a c t A simple Structure Making/Structure Breaking (SM/SB) Modified Poisson Boltzmann approach is used to describe the distribution of ions in the vicinity of an air/water interface, which is assumed to be a layer possessing a thickness of a few Å. The interface is assumed to be depleted of SM ions, and the adsorption of SB ions on the interface is taken into account via Langmuir adsorption equations. Outside the interface, the ions are assumed to obey a modified Poisson Boltzmann distribution, which includes the screened image forces. The adsorption constants of SB ions, determined by fitting the existing zeta potential data, are further used to determine the surface excesses of salt ions and the dependence of the surface tension on added salt. The number of sites available for the adsorption of OH and H + ions, considered the water molecules of the interface, is (by more than two orders of magnitude) smaller than the available sites in an ice-like layer. This result suggests a (much) lower density of water at the hydrophobic air/water interface than in the bulk. The model can qualitatively explain the dependence of the surface tension upon addition of salt determined experimentally: a large decrease at low concentrations, due to the formation of a double layer, a large increase at intermediate concentrations, where the screened image forces (being less screened than the double layer forces) dominate, and a slower increase at large concentrations, where both double layer and image forces are screened and the ion hydration forces dominate. However, for large surface potentials, the accumulation of ions in the double layer (either as adsorbed on the interface or in the ion clouds in the vicinity of the interface) leads to large surface excesses of ions and consequently to a surface tension that decreases upon addition of salt up to large concentrations, in contrast to experiment. According to the present model, only the zeta potentials experiments that predict low surface potentials and small adsorption of salt anions on the surface are compatible with the surface tension experiments. 212 Elsevier B.V. All rights reserved. 1. Introduction It has been long emphasized that the concentrations of ions at the water/air interface are markedly different from those in bulk water. The presence of a dielectric discontinuity generates an image force on any approaching charge. Furthermore, the dielectric constant of the interfacial water is expected to be lower than that of bulk water, for two main reasons. Firstly, the rotation of the water molecules is somewhat obstructed at the interface, hence they are less likely to screen the electric field generated by surface charges. Secondly, and even more important, there is evidence [1,2] that the density of water at the hydrophobic air/water interface is much smaller than in the bulk, hence there are fewer permanent dipoles available to screen the electric field. Corresponding author. Tel.: ; fax: addresses: mmanciu@utep.edu (M. Manciu), feaeliru@buffalo.edu (E. Ruckenstein). Langmuir [3] even suggested that the increases in the surface tension of water upon addition of salts can be explained by assuming that the first water layer, with a thickness of about 4 Å, is completely depleted of ions. However, experimental data show that the surface tensions of acid solutions decrease with increasing acid concentration [4]. This indicates a positive net surface excess of ions, hence that at least H +, or the anion, or possibly even both are accumulating at the water/air interface. Furthermore, the observation of Jones and Ray [5], that there is a minimum surface tension around 1 mm for many salts, implies that surface excesses of at least one kind of ions are common at low electrolyte concentrations. Among the experiments most directly related to the general behavior of ions near an air/water interface are the determinations of the zeta potential and surface tension as functions of ph and salt concentration. The former experiments show whether the anions or cations are dominant at the interface (being either more adsorbed or less depleted than the ions of opposite charge), whereas the latter experiments indicate whether there is a net surface excess or a net surface depletion of all the ions added to /$ see front matter 212 Elsevier B.V. All rights reserved. doi:1.116/j.colsurfa

2 28 M. Manciu, E. Ruckenstein / Colloids and Surfaces A: Physicochem. Eng. Aspects 4 (212) the solution. Whereas such conclusions can be derived straightforwardly from experiment, the results are sometimes controversial. For example, it was assumed that the surface tension increases monotonically upon addition of salts [4], in agreement with the screened image forces theories of Wagner [6] and Onsager and Samaras [7]. However, the Jones and Ray experiments [5] exhibit a decrease in surface tension at low electrolyte concentrations, in a range where one should expect, because of reduced screening, stronger image forces than at high electrolyte concentrations. The dependence of the zeta potential on ph and salt concentration is also a topic of debate. Many experiments show that the zeta potential of water is negative, over almost the entire ph range (with the exception of very low phs possible less than 2 [8]). Recently, it was suggested that an isoelectric point might occur around ph = 4 [9]. Gray-Weale and Beattie [1] measured the zeta potential of a water/oil interface and obtained very low absolute values (albeit negative) at low phs. They suggested that an isoelectric point occurs when the absolute values of their experimentally determined zeta potentials are less than 3 mv (the experimental error), values obtained between 3 < ph < 4 [1]. These results are compatible with those of Ref. [9] for an air/water interface; however, the data of Ref. [8] provide in that ph range much larger absolute values for the zeta potential, around 1 mv, which cannot be attributed to experimental inaccuracies. Zeta potential experiments support the hypothesis that some kinds of ions are strongly adsorbed at the hydrophobic air/water interface. Let us assume that the (negative) surface charge of neat water is the result of the depletion of interfacial layer of H +, but not of OH. The corresponding surface charge density is in this case given by = coh q, where is the thickness of the depletion layer, q the electron charge and c OH the bulk concentration of OH. For neat water (c OH = 1 7 M) and a depletion layer = 4 Å, is C/m 2, and the corresponding surface potential (calculated in the linear approximation, S = /εε, with the Debye Huckel length, ε the dielectric constant of water and ε the vacuum permittivity) is only about V. However, experiments [8 1] indicate that the zeta potential of neat water is about 4 orders of magnitude larger, which in turn suggests a strong adsorption of OH on the hydrophobic interface. To explain these experimental results, the interfacial concentration of OH has to be by orders of magnitude larger than in the bulk. Similarly, the large (positive) zeta potential reported at ph = 3 in Ref. [9] cannot be explained by an interfacial depletion of OH ; the concentration of H + should be larger by at least an order of magnitude than in the bulk. Water cluster calculations [11] and molecular dynamics simulations for water slabs [12] indicated that some simple anions (Cl, Br, I ) have a preference for the interface, proportional to their polarizability [12]. Subsequent molecular dynamics calculations supported the idea that there is an excess of hydrogen and of simple anions (with the exception of F and OH ) on the interface [13]. This result, corroborated with the positive zeta potential values measured at very low ph values [9], stimulated the opinion that the surface of water is acidic [14]. This conclusion, mostly based on simulations, drew a lot of attention. It was immediately pointed out that many experimental results (such as the negative zeta potential of air bubbles or oil droplets in neat water, or the formation of hexadecane emulsions in neat water, which are stabilized via the adsorption of OH ), actually suggest that the neat water surface is basic [15]. Recent experiments further deepened the debate; whereas experiments on the zeta potential of water indicated a more basic interface than the bulk [8 1], other experiments (Second Harmonic Generation [16], Vibrational Sum-Frequency Spectroscopy [17], Phase Sensitive Sum-Frequency Vibrational Spectroscopy [18], Photoelectron Spectroscopy [19]) indicated the opposite, namely that the surface adsorption is dominated by H + in detriment of OH. Recent calculations did not resolve the issue: whereas some predicted a lower [12], other predicted a larger [2] concentration of OH at the interface than in bulk water. The goal of this paper is to investigate the compatibility of a very simple Structure Making/Structure Breaking (SM/SB) model [21] with the existing experiments on both the surface tension [5] and the zeta potential at various salt concentrations and ph values [8 1]. When the SM ions approach the interface at a distance of about 4 Å, they cannot be hydrated as well as in bulk and therefore their free energy changes. Whereas the dependence of ion hydration on the distance to the surface is not known, because the bulk hydration free energy is very large (1 2 kt), only a few percent change in ion hydration energy (which occurs over a very short distance), leads to a large change in their free energy [21]. Therefore, the air/water interface can be considered (up to the distance ) practically depleted of SM ions. Their distribution can be approximated by a modified Poisson Boltzmann model (that includes image forces) for distances larger than from the interface with a vanishing concentration at smaller distances. On the other hand, the SB ions are attracted by the interface via complex ion-hydration forces, which account not only for the free energy changes of the SB ions, but also for the free energy changes of the water molecules surrounding these ions. Such forces are difficult to estimate because they must involve the local changes in water density and dielectric constant, volume exclusion effects, ion dispersion forces, etc. For the sake of simplicity, it will be assumed that the adsorption of all SB ions on the interface of thickness follows the Langmuir isotherms. The parameters of the adsorption isotherms, which account for the forces that act close to the interface, will be evaluated by fitting the experimental data regarding the zeta potential. At distances larger than, it will be assumed that the ions follow modified Poisson Boltzmann distributions (which include image forces). At distances larger than, most interactions of the ions (except the mean field and the image forces) are short ranged and can be neglected. As an example of short-range forces, the energies associated with ion-dispersions interactions (which are of the form B/x 3, with the constant B depending on the nature of ion), are typically smaller than kt at x = 4 Å from the interface (between.4 and 1.17 kt, for B ranging from to Jm 3 [21]), hence their effect on the ion distributions outside the interfacial layer is negligible. The Langmuir adsorption model of the interface might constitute an oversimplification; however, it is difficult to build an accurate model of the air/water interface, since the structure of water in the first few Å from the interface is not well known. For example, it was suggested that the density of water in that region is much smaller than in the bulk [1,2], which is indeed supported by the results obtained in this paper. The adsorption constants will be obtained by fitting the zeta potential data; they will be used to calculate the dependence of surface tension on the electrolyte concentration. It will be shown that the zeta potentials obtained by three groups [8 1] are not entirely compatible with each other, and that some of them are not compatible with the experimental data of Jones and Ray regarding the surface tension [5] either. The main reason for the incompatibility is that large surface potentials generate large surface excesses of ions due to the double layer ion clouds in the vicinity of the surface. Such excesses lead to a decrease in surface tension with increasing electrolyte concentration up to large electrolyte concentrations, much larger than the values around 1 mm obtained experimentally [5]. Even more striking, if the surface charges would be generated by the adsorption of salt anions, their surface excess would become so large, that the surface tension would decrease even for large electrolyte concentrations, in contradiction with experiment, which shows that it should increase [4]. Therefore, the critical concentration at which the minimum surface tension is obtained in the Jones Ray effect provides some insight on the nature of ions that

3 M. Manciu, E. Ruckenstein / Colloids and Surfaces A: Physicochem. Eng. Aspects 4 (212) produce the negative charging of the surface of neat water observed experimentally [8 1]. For agreement with Jones Ray data, the surface potentials should be lower than typically reported [8,1] and the surface charge should be generated mostly by the adsorption of OH. However, the set of adsorption parameters obtained from fitting the data of Ref. [9] obey these conditions and provides good agreement with the Jones Ray data [5]. 2. The adsorption desorption model for SM/SB ions As in zeta potential experiments [8 1], the added salt is NaCl and the change in ph is achieved by using either HCl or NaOH. It will be assumed that the Structure Breaking (SB) anions, OH and Cl, as well as the small cation H +, are adsorbed on the interface, whereas the Structure Making (SM) cations (such as Na + ) prefer the bulk water. The ions adsorbed on the interface are in equilibrium with the ions (of the same kind) located at a distance from the interface, the concentration c i of which is related to their bulk concentration, c,i, by the Boltzmann factor: ( ) c i = c,i exp q i S + W i () (1) kt In Eq. (1), q i is the charge, S the surface potential, k the Boltzmann constant, T the absolute temperature and W i a free energy change due to additional interactions, not included in the mean field potential (such as the image forces [6,7]), calculated at a distance from the interface. Assuming that the added acid, base and salt are completely dissociated, the bulk concentrations of H + and OH are provided by the ph of the solution, whereas the amount of HCl (or NaOH) employed to change the ph affects the dissociation equilibrium of the water molecules: c,h c,oh = (c HCl c R H )(1 7 c R OH ) = 1 14 (2a) c,h c,oh = (c NaOH c R OH )(1 7 c R H ) = 1 14 (2b) where c,h and c,oh are the bulk concentrations of H + and OH ions, 1 7 is the concentration of H + and OH before adding the acid, c HCl is the concentration of H + due to the added acid, c NaOH is the concentration of OH due to the added base, and c R H = c R OH is the number of H + and OH ions, per unit volume, that recombines into water molecules. Consequently, the bulk concentrations of ions are provided by the expressions: c,h = 1 ph ; c,oh = 1 ph 14 ; c,cl = c HCl + c NaCl ; c,na = c NaOH + c NaCl (3) It will be assumed that the surface potential is equal to the zeta potential. The short range interactions (which are smaller than kt at distances larger than a few Å from the interface) will be neglected in Eq. (1), and only the long ranged image forces will be taken into account. In the Onsager Samaras model, they are provided by the equation [7]: ( ε ) ε exp(ai /) q 2 ( i W i (x) = ε + ε 1 + (a i /) 16ε εx exp 2x ), (x > ) (4) where x is the distance from the dielectric boundary, a i the radius of ion i, ε the vacuum permittivity, ε the dielectric constant of water, ε the dielectric constant of the other medium and = (εε kt/ c i q 2 i ) is the Debye Hückel length. Because i exp(a i /) = 1+ (a i /) + (1/2)(a i /) , the ion specificity effects are negligible until very large electrolyte concentrations ( 1 M), when becomes comparable with a i. The mean field potential is assumed to obey the modified Poisson Boltzmann equation for distances larger than : q i c,i exp( ((q i (x) + W i (x))/kt)) 2 (x) = i with the boundary conditions: ε ε (x) x = and = εε d dx x=, (x > ) where the surface charge density is provided by the number of ions adsorbed per unit area, N i : = q(n H N OH N Cl ) (7) q being the proton charge and i = H +, OH or Cl. We will consider that the water molecules at the interface provide the adsorption sites for H + and OH, which are competing for them, and that Cl is located in the free spaces between the water molecules. The H + and OH ions compete for N S sites (assumed to be the number of molecules of water per unit interfacial area), with the equilibrium constants K H and K OH, respectively, while Cl is adsorbed on (different) N A sites, with the equilibrium constant K Cl. The equilibrium equations have the form: K H H = c H (1 H OH ) (8a) K OH OH = c OH (1 H OH ) (8b) K Cl Cl = c Cl (1 Cl ) (8c) where i is the fraction of sites occupied by ions of kind i and c i their concentration near the interface (per unit volume). The number of ions adsorbed per unit area is therefore provided by: N H = N OH = N S 1 + (K H /c H ) + (K H /K OH )(c OH /c H ) N S 1 + (K OH /c OH ) + (K OH /K H )(c H /c OH ) (5) (6) (9a) (9b) N A N Cl = (9c) 1 + (K Cl /c Cl ) For a given set of parameters (N S, N A, K H, K OH, K Cl ), Eqs. (1 7) and (9) can be solved numerically, and the surface potential S = (x) x=, considered equal to the zeta potential, can be calculated. The set of parameters is then optimized to fit the experimental data for the zeta potential as follows: a penalty function, obtained as the sum of the square differences between the calculated and experimental zeta potentials is minimized using the Nelder Mead simplex direct search algorithm implemented in MATLAB. The dependence of the interfacial tension on the uni-univalent electrolyte concentration c E (which can be either an acid, base, or salt) can be calculated using the Gibbs adsorption equation: d = i d i (1) i=1,2 where i is the electrochemical potential and i is the surface excess of ion i: i (c E ) = (c i (x) c E )dx = (c i (x) c E )dx + (c i (x) c E )dx = c E + c i (x)dx + (c i (x) c E )dx (11) with the water/air interface located between x = (corresponding to air) and x =. The last integral corresponds to the surface adsorption of ions in the Poisson Boltzmann range (x > ), and, whereas

4 3 M. Manciu, E. Ruckenstein / Colloids and Surfaces A: Physicochem. Eng. Aspects 4 (212) the ion distribution c i (x) is not known between and, its integral is provided by the number of ions adsorbed per unit area on the interface, which can be obtained from Eq. (9). The electrochemical potential, which is independent of the distance from the interface, can be related to the bulk electrolyte concentration c E = c i ( ) via: d i = d(kt ln(c i ( )f i )) (12) where f i is the activity coefficient of the electrolyte in the bulk, which will be assumed to be unity. When salt is added to the system, but the ph remains constant, there is no change in the electrochemical potential for either H + and OH, hence their adsorption/desorption does not contribute to changes in surface tension upon addition of salt. Consequently, only the surface excesses of Cl (a SB ion, that can be adsorbed on the interface) and Na + (a SM ion, that cannot be adsorbed on the interface) have to be taken into account. The change in interfacial tension due to the addition of an electrolyte is given by: 1 = Na + Cl 2 (13) kt c E c E where the ratio = (( Na + Cl )/2c E ) has the dimension of a length, which can be interpreted as the thickness of an interfacial region, totally depleted of ions, that produces the same change in surface tension as the actual distribution of ions. A negative value of represents a surface excess of ions, which decreases the surface tension. The surface tension as a function of electrolyte concentration can be obtained by integrating Eq. (13): ce ce (c E ) () = c dc Na (c) + = kt Cl (c) dc c c= ce = 2kT dc (14) 3. Surface charge and surface tension In what follows, we will examine the zeta potentials determined by Li and Somasundaran [8], Takahashi [9] and Gray-Weale and Beattie [1] (see Fig. 1a). In all cases, NaCl was the added salt and the ph was changed either by adding HCl or NaOH. It should be noted that for phs lower than about 4, the bulk concentrations of H +, OH and Cl ions in Ref. [8] (salt concentration c S = 1 5 mol/l) and Ref. [9] (c S = ) are close; however the zeta potentials are sharply different. Furthermore, there are also sharp differences between the data reported in Refs. [8,1], which can be, however, attributed to the different kinds of interfaces involved in their experiments (air/water and oil/water, respectively). Therefore, the tentative fitting of all the data available (Fig. 1a) is not accurate. In Fig. 1b, the surface charge is plotted for the same data as a function of the concentration of OH in the vicinity of the interface (provided by the Boltzmann factor). In spite of the discrepancies between the reported data [8 1], the surface charge densities in all of them are low, indicating either a very weak adsorption of ions on a large number of sites, or a limited number of sites available for adsorption. The first hypothesis is not plausible, because it should predict a linear increase of the negative surface charge with increasing OH concentration (at least at very low salt concentrations c S and sufficiently high phs, for which Cl adsorption can be neglected). In contrast, Fig. 1b shows that the surface charge remains almost constant in a relatively large range of OH concentrations in the vicinity of the air/water interface. The data reported by Gray-Weale and Beattie [1] involving oil in water emulsions exhibit a stronger Fig. 1. (a) Zeta potentials vs. ph for various salt (NaCl) concentrations, reported by Li and Somasundran [8], Takahashi [9] and Gray-Weale and Beattie [1]. The lines represent an unsuccessful attempt to fit all the data together. (b) The surface charges corresponding to the zeta potentials in (a), as functions of ph, for various salt concentrations. dependence of the surface charge on the OH concentration in the vicinity of the interface, which suggests different adsorption equilibria for OH on the oil/water than on the air/water interface. A strong adsorption of OH in the former case is also supported by the increased stability of the oil in water emulsions with increasing ph [1]. The increase (in absolute value) of the negative surface charge density (Fig. 1b), with increasing Cl concentration (generated by adding either salt or acid) indicates that Cl is adsorbed on the water/air interface. The continuous lines in Fig. 1a and b represent results of calculations based on set 1 of parameters (Table 1) obtained by fitting all zeta potential data of Refs. [8 1]. In spite of the large number (5) of fitting parameters, the agreement between calculations and experimental data is quite poor, probably because of the incompatibility between the experimental results discussed above. Let now focus on the surface tension data. As well known, the addition of a salt at constant ph leads to an almost linear increase in surface tension at large electrolyte concentrations [4]. However, at very low electrolyte concentrations the surface tension first decreases and then increases [5], indicating that the total adsorption of salt ions is positive at low concentrations, but becomes negative at large salt concentrations. In Fig. 2, the derivative of the

5 M. Manciu, E. Ruckenstein / Colloids and Surfaces A: Physicochem. Eng. Aspects 4 (212) Table 1 Equilibrium adsorption parameters. N S (sites/m 2 ) N A (sites/m 2 ) K OH (M) K H (M) K Cl (M) Set 1 (Refs. [8 1]) Set 2 (Refs. [8]) Set 3 (Ref. [9]) Set 4 (Ref. [1]) Fig. 2. The depletion lengths for salt ions vs. salt concentration, calculated from the derivative of the experimental surface tension data, from Refs. [4,5]. The depletion lengths due to double layer, ion hydration and screened image forces alone, as well as all of them together are plotted. surface tension, which is proportional to the depletion length 2, is plotted against the electrolyte concentration. The data have been obtained via the numerical derivative of the surface tension experimental data from Refs. [4,5], which coincide for sufficiently large salt concentrations. At very low salt concentrations, the depletion length is large in absolute value and negative; at intermediate concentrations, it is large and positive; whereas at large concentrations it is positive and almost constant. This behavior can be attributed to the formation of a double layer at low salt concentrations, which being screened stronger becomes less important than the image forces [6,7] at intermediate salt concentrations. When the salt concentration becomes sufficiently large, both the double layer and the image forces are screened and the ion-hydration forces (which are not screened by ions [21]) become dominant. The depletion induced either by double layer forces alone, by image forces alone, or by SM forces alone, as well as the depletion induced by all three together are plotted in Fig. 2. To understand these results, let us examine the depletion length generated by the double layer alone. The total adsorption of ions can be obtained from Eq. (11): Na + Cl = (c Na (x) + c Cl (x) 2c S )dx + ( c S exp ( q (x) kt ( ) ) q (x) +c S exp 2c S dx (15) kt ) After expanding the exponential, the depletion length (Eq. (13)) becomes: = Na + Cl 1 c 2c S 2c Cl (x)dx S ( 1 2 ( q (x) kt ) 2 ( + 1 q (x) 24 kt ) 4 + ) dx (16) where it was assumed that Na + are SM ions, hence c Na (x) = for x < <. At very large electrolyte concentrations, when the double layer collapses, both integrals are vanishingly small and is a positive constant that provides a linear increase in surface tension with increasing electrolyte concentration. At low electrolyte concentrations, the integrals cannot be neglected, and they will be examined separately in what follows. The distribution of Cl between and is not known, but its integral provides the total number of Cl adsorbed per unit surface. The corresponding depletion length is: 1 c 2c Cl (x)dx = ϕ S (17a) S 2c S q where ϕ represents the fraction of the surface charge S generated by the adsorption of Cl ions, while (1 ϕ) S is due to the adsorption of OH and H +. The depletion length generated by the repulsive forces (screened image and ion-hydration forces), at c S = 1 mm, is about 2 3 Å (see Fig. 2). Assuming ϕ = 1 and a surface charge S of the order of 1 2 C/m 2, as suggested by Fig. 1b, the depletion length provided by Eq. (17a) is of the order of 1 3 Å. To obtain a vanishing depletion length at 1 mm, as obtained in the Jones Ray experiment [5], either the surface charge should be much smaller than those calculated from the zeta potentials determined experimentally [8 1], or the Cl adsorption should be very small (ϕ ); as mentioned above, H + and OH surface excesses do not contribute to the changes in surface tension upon addition of salt. Note that the zeta potential experiments from Ref. [9] were performed at c S =, hence the surface charge at c S = 1 mm cannot be inferred directly from these experiments. The second integral in Eq. (16) contains a series of only positive terms. Since the potential behaves in the bulk roughly as (x) Sexp( (x/)), at low electrolyte concentrations (hence large Debye Huckel lengths ), the integral is much larger than and is large in absolute value and negative. By assuming an exponential dependence of the potential (x), the second integral in Eq. (16) can be evaluated: ( ( ) 2 ( ) 4 1 q (x) + 1 q (x) + ) dx 2 kt 24 kt ( ( ) 2 ( ) 4 1 q () = + 1 q () + ) (17b) 4 kt 48 kt Since (q S/kT) is usually of the order of unity ( S = ()), the depletion length due to the ion clouds near the surface

6 32 M. Manciu, E. Ruckenstein / Colloids and Surfaces A: Physicochem. Eng. Aspects 4 (212) Fig. 3. The depletion length due to image forces, calculated by assuming that the image forces are not screened over a distance l from the interface, vs. l, at various salt concentrations. is of the order of the Debye Huckel length. At c S = 1 mm, 1 Å, much larger than the depletion length due to the Wagner Onsager Samaras image forces (See Fig. 2). Consequently, only for small surface potentials the total depletion length will vanish at c S = 1 mm, as obtained by Jones and Ray [5]. Can a large in absolute value and negative depletion length be compensated by additional repulsive forces acting between the salt ions and the interface (that have been neglected in the present model)? One possibility is that the ions in the vicinity of the interface are not completely free to move and hence the image force is not fully screened in the vicinity of the interface. The non-screened image forces provide divergently large depletion lengths [6]. However, the divergence is logarithmic and increases very slowly with the non-screening distance. To evaluate this effect, let assume that the image forces are provided by: W i (x) = q 2 i 16ε εx, < x < l (18a) W i (x) ( ε ) ε exp(ai /) q 2 ( i = ε + ε 1 + (a i /) 16ε εx exp 2(x ) l), l < x < (18b) where l represents the distance from the surface up to which the image force is not screened. The depletion length is plotted in Fig. 3 vs l for various c S and shows that even for unreasonably large l values, the depletion length is still smaller than 5 Å, therefore cannot compensate the (negative) depletion length generated at 1 mm by the double layer, for large S values. The volume exclusion effects increase slightly the depletion length, but for c S = 1 mm and surface charge S = 1 2 C/m 2 (see Fig. 1b), neither the concentration of Na + in the vicinity of the interface (x > ), which is less than 1 2 M, nor the concentration of Cl ion on the surface (less than 1 ion/1 3 Å 2 ) can provide a long-ranged volume-exclusion repulsion. The strongest ion-dispersion forces lead to a maximum depletion length of less than 1 Å [21], hence they cannot compensate a strong double layer, either. The surface potential compatible with Jones Ray data can be determined by calculating the critical salt concentration at which the minimum in surface tension occurs (when the depletion length vanishes). The calculation implies the existence of a double layer and accounts for the ion hydration and screened image forces, but Fig. 4. (a) The surface potentials vs. the critical salt concentration, calculated for the two extreme cases, ϕ = and ϕ = 1. (b) The surface charges vs. the critical salt concentration, calculated for the two extreme cases, ϕ = and ϕ = 1. is independent of the model for surface charging. Two extreme cases are considered, ϕ = 1 (the surface charge is completely generated by the adsorption of Cl ) and ϕ = (no Cl is adsorbed on the interface); these extremes provide a range of surface potentials compatible with the Jones Ray experiment. In Fig. 4a, the surface potentials are plotted vs. the critical salt concentrations for which a minimum in surface tension has been obtained. To obtain a minimum in surface tension at 1 mm, the surface potential (which is assumed equal to the zeta potential) should be located between 2 and 16 mv, corresponding to a surface charge generated by the adsorption of only Cl (ϕ = 1) and only OH (ϕ = ), respectively. The surface potentials required for the Jones Ray minimum at 1 mm are smaller than the experimental values usually reported in literature. It is possible that the surface charge is generated mostly by the adsorption of the salt anion, as suggested recently [22], but this will lead at even smaller zeta potentials than when the adsorption of OH generates most of the surface charge. The surface charge required for a minimum at 1 mm (Fig. 4b), which is between 1 4 and 1 3 C/m 2, is also much smaller than those corresponding to the zeta potentials determined experimentally (see Fig. 1b). It should be emphasized that the results of Eqs. (17a) and (17b) are general characteristics of the double layer and do not depend

7 M. Manciu, E. Ruckenstein / Colloids and Surfaces A: Physicochem. Eng. Aspects 4 (212) Fig. 6. (a) The surface tension vs. salt concentration, with the adsorption parameters determined by fitting the data of Refs. [8,1] are not compatible with Jones Ray data. (b) The surface tension vs. salt concentration, with the adsorption parameters determined by fitting the data of Ref. [9] is compatible with Jones Ray data. upon the model selected for the charging of the air/water interface (the Langmuir adsorption isotherm in this paper). A large zeta potential, hence a large surface potential, and a corresponding large surface charge generates large surface excesses of salt ions via two mechanisms: the contribution of the salt ions to the surface charge, and the net accumulation of ions in the ion cloud due to the double layer. While the former can be small if the fraction of the surface charge, ϕ, generated by the salt anions is sufficiently small, the second is small only when the surface potential is sufficiently small. 4. Compatibility between surface tension and zeta potential data Fig. 5. (a) Zeta potentials vs. ph for various salt (NaCl) concentrations, reported by Li and Somasundran [8]. The lines represent the prediction of the present model using fitted adsorption parameters. (b) Zeta potentials vs. ph, reported by Takahashi [9]. The line represents the prediction of the present model using fitted adsorption parameters. (c) Zeta potentials vs. ph, reported by Gray-Weale and Beattie [1]. The line represents the prediction of the present model using fitted adsorption parameters. Whereas the present model cannot describe accurately all the zeta potential data via only one set of parameters, let us try to apply the model to each individual data set. Firstly, the adsorption parameters have been adjusted to fit the zeta potential data reported by Li and Somasundaran [8] (see Table 1, set 2), which cover a large range of ph values for three salt concentrations. In Fig. 5a, the zeta potentials calculated based on these parameter values (continuous lines) are compared with the experimental data. The fitting procedure has been repeated for the data of Refs. [9] (set 3) and [1] (set 4). The zeta potentials calculated with these new sets of parameters (sets 3 and 4 in Table 1) are presented in Fig. 5b and c, respectively.

8 34 M. Manciu, E. Ruckenstein / Colloids and Surfaces A: Physicochem. Eng. Aspects 4 (212) for adsorption. At very low salt concentrations, the surface charge is generated mostly by the adsorption of OH, and for neat water, the interfacial OH concentration is about 4 orders of magnitude larger than in bulk. This corresponds to a free energy of OH at the interface by about ln(1 4 )kt = 1 kt lower than in bulk. However, at large ph values, the interfacial concentration of OH becomes lower than in the bulk. This surface charge saturation cannot be attributed to interactions between ions at large ph values; the volume excluded effects are very small, because the surface density of OH is less than 1 ion/1 3 Å 2 while the electrostatic energy is also much lower than 1 kt ( S being less than 4 kt, and smaller at large ph values). Therefore, the saturation of the OH adsorption is likely to be caused by the existence of a limited number of adsorption sites on the interface, perhaps individual water molecules. The large zeta potential for neat water predicted by the set 2 and 4 of adsorption parameters, as well as the large contribution of Cl to the surface charge (particularly for set 2), lead to large negative depletion lengths for all electrolyte concentrations, hence to a monotonous decrease of surface tension upon addition of salt (Fig. 6a), in contrast to experiment. It should be emphasized again that set 4 of the parameters has been derived from zeta potential data for an oil/water interface, while the Jones Ray experiment has been performed for the air/water interface. However, using set 3 of parameters (based on the data of Ref. [9]), good agreement has been obtained with the Jones Ray data (Fig. 6b). In this case, the compatibility between the zeta potential and surface tension experiments is a result of low surface potentials and small ϕ values (the fraction of the surface charge generated by the adsorption of Cl ), plotted in Fig. 7a and b, respectively. 5. Conclusions Fig. 7. (a) The zeta potentials vs. salt concentration for the three set of parameters, determined by fitting the experimental data from Refs. [8 1], respectively. (b) The ratio ϕ between the surface charge generated by the adsorption of Cl ions and the total surface charge, vs. salt concentration for the three set of parameters, determined by fitting the experimental data from Refs. [8 1], respectively. The most significant differences in the adsorption parameters resulted from the fitting of the different data sets are the number of adsorption sited for Cl, which is of the same order of magnitude as the number of adsorption sited for H + and OH for set 2, about 1 times smaller for set 4, and about 1 times smaller for set 3. The number of adsorption sites for H + and OH resulted from the fit is in all cases of the order of 1 16 /m 2, which is much smaller than the number of water molecules that would be present at the interface, when assuming that the interfacial water has the same density as the bulk water. Indeed, in bulk each water molecule occupies about 3 Å 3, hence in the first 4 Å from the interface there should be about water molecules/m 2. The number of adsorption sites determined via fitting is by more than two orders of magnitude smaller, and the number of adsorption sited for Cl is even smaller. The much lower density of adsorption sites in the interfacial water than in an ice-like interfacial layer points toward the existence of a region of low density of water near a hydrophobic interface, as demonstrated theoretically earlier [1,2]. The reason for the suggestion that the adsorption sites are interfacial water molecules is the observation that the surface charge does not change much when the ph increases by adding NaOH (see Fig. 1b), which indicate the existence of a saturation mechanism A simple SM/SB Poisson Boltzmann model has been employed to describe simultaneously the experimental data for both the zeta potential and the surface tension. The interface was defined as the volume between and = 4 Å; for distances larger than, a modified Poisson Boltzmann distribution (that accounts also for screened image forces) has been assumed. In addition, all structure breaking ions have been considered to obey Langmuir adsorption isotherms. The H + and OH ions are assumed to compete for the same kind of interfacial sites, provided by the water molecules of the interface. However, the Cl ions have a different kind of adsorption sites on the interface. The values of the adsorption constants have been obtained by fitting the zeta potential data reported by different groups [8 1]. The behavior of the surface tension upon addition of salt can be explained qualitatively very well in terms of positive surface excesses due to the formation of a double layer, and negative surface excesses due to the screened image forces and ion hydration forces (the latter preventing the SM ions to approach the interface). The double layer dominates at very low concentrations, where the depletion length is large in absolute value and negative, hence the surface tension decreases upon addition of salt. At large salt concentrations, both the double layer and the image forces are strongly screened, and the ion hydration forces generate a depletion length independent of electrolyte concentration, leading to a surface tension which increases linearly upon addition of salt. Being screened less than the double layer forces, the image forces dominate at intermediate salt concentrations, where they provide the largest depletion length. In this range, the surface tension as a function of salt concentration has the highest slope. The quantitative description of the behavior of the surface tension upon addition of salt constitutes a more difficult task. For large surface potentials, the accumulation of ions in the double layer is so large, that it cannot be compensated at 1 mm by screened image

9 M. Manciu, E. Ruckenstein / Colloids and Surfaces A: Physicochem. Eng. Aspects 4 (212) forces or ion hydration repulsions. The surface excesses of salt ions are even higher when Cl is strongly adsorbed on the interface. In this case, the surface tension decreases upon addition of salt up to very high concentrations, in contradiction with well accepted experimental data [4]. Whereas our model cannot fit well all the zeta potential data available using only one set of parameters, the data reported by each of the groups can be well described by a single set of parameters. The number of sites for the adsorption of H + and OH (considered as the number of water molecules on the interface) is about the same in all cases and by more than two orders of magnitude smaller than the number of water molecules available in an ice-like interfacial layer. This suggest that the density of water near the hydrophobic air/water interface is much smaller than in the bulk water, as already predicted theoretically [1,2]. The number of sites for Cl adsorption obtained by fitting differs strongly in each of the cases; in the cases when the interfacial adsorption of Cl is large, the surface tension decreases upon addition of salt up to large electrolyte concentrations (as expected from Eq. (16)) but in contrast to experiment. However, the fit of the zeta potential data of Ref. [9] leads to a set of parameters that correspond to small zeta potentials and low Cl adsorption, which are compatible with the surface tension data. References [1] J.H. Stillinger, Structure in aqueous solutions of nonpolar solutes from the standpoint of scaled-particle theory, J. Solution Chem. 2 (1973) [2] E. Ruckenstein, Y.S. Djikaev, Effect of hydrogen bonding between water molecules on their density distribution near a hydrophobic surface, Phys. Chem. Lett. 2 (211) [3] I. Langmuir, The role of attractive and repulsive forces in the formation of tactoids, thixotropic gels, protein crystals and coacervates, J. Chem. Phys. 6 (1938) [4] P.K. Weissenborn, R.J. Pugh, Surface tension of aqueous solution of electrolytes: relationship with ion hydration, oxygen solubility, and bubble coalescence, J. Colloid Interface Sci. 184 (1996) [5] G. Jones, W.A. Ray, 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. 59 (1937) [6] C. Wagner, Phys. Zeit. 25 (1924) 474. [7] L. Onsager, N.N.T. Samaras, The surface tension of Debye Hückel electrolytes, J. Chem. Phys. 2 (1934) [8] C. Li, P. Somasundaran, Reversal of bubble charge in multivalent inorganic salt solutions effect of magnesium, J. Colloid Interface Sci. 146 (1991) [9] M. Takahashi, Zeta potential of microbubbles in aqueous solutions: electrical properties of the gas water interface, J. Phys. Chem. B 19 (25) [1] A. Gray-Weale, J.K. Beattie, An explanation for the charge on water s surface, Phys. Chem. Chem. Phys. 11 (29) [11] L. Perera, M.L. Berkowitz, Many-body effects in molecular dynamics simulations of Na + (H 2O) n and Cl (H 2O) n clusters, J. Chem. Phys. 95 (1991) [12] P. Jungwirth, D.J. Tobias, Ions at the air/water interface, J. Phys. Chem. B 16 (22) [13] M. Mucha, T. Frigato, L.M. Levering, H.C. Allen, D.J. Tobias, L.X. Dang, P. Jungwirth, Unified molecular picture of the surfaces of aqueous, acid, base, and salt solutions, J. Phys. Chem. 19 (25) [14] V. Buch, A. Millet, R. Vacha, P. Jungwirth, J.P. Devlin, Water surface is acidic, Proc. Natl. Acad. Sci. 14 (27) [15] J.K. Beattie, A.M. Djerddjiev, G.G. Warr, The surface of neat water is basic, Faraday Disc. 141 (29) [16] P.B. Peterson, R.J. Saykally, Is the liquid water surface basic or acidic? Macroscopic vs. molecular-scale investigations, Chem. Phys. Lett. 458 (28) [17] T.L. Tarbuck, S.T. Ota, G.L. Richmond, Spectroscopic studies of solvated hydrogen and hydroxide ions at aqueous surfaces, J. Am. Chem. Soc. 128 (26) [18] C. Tian, N. Ji, G.A. Waychunas, Y.R. Shen, Interfacial structures of acidic and basic solutions, J. Am. Chem. Soc. 13 (28) [19] B. Winter, M. Faubel, R. Vacha, P. Jungwirth, Behaviour of hydroxide at the water/vapor interface, Chem. Phys. Lett. 474 (29) [2] C.J. Mundy, I.-F.W. Kuo, M.E. Tuckerman, H.S. Lee, D.J. Tobias, Hydroxide anion at the air water interface, Chem. Phys. Lett. 481 (29) 2 8. [21] M. Manciu, E. Ruckenstein, Specific ion effects via ion hydration: I. Surface tension, Adv. Colloid Interface Sci. 15 (23) [22] P.B. Peterson, R.J. Saykally, Adsorption of ions to the surface of dilute electrolyte solutions: the Jones Ray effect revisited, J. Am. Chem. Soc. 127 (25)