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Surface Tension of Aqueous Electrolyte Solutions. Thermodynamics Jan Drzymala† and Johannes Lyklema*,‡ †
Laboratory of Mineral Processing, Institute of Mining Engineering, Wroclaw University of Technology, Wybrzeze Wyspianskiego 27, 50-370 Wroclaw, Poland ‡ Laboratory of Physical Chemistry and Colloid Science, Wageningen University, Dreijenplein 6, 6703 HB Wageningen, Netherlands ABSTRACT:
A thermodynamic theory is developed for obtaining the enthalpic and entropic contributions to the surface excess Gibbs energy of electrolyte solutions from the dependence of the surface tension on concentration and temperature. For elaboration, accurate activity coefficients in solution as functions of concentration and temperature are required. The theory is elaborated for (11) electrolytes and applied to HClO4, HNO3, NaCl, NaBr, and LiCl, of which the first two adsorb positively and the other three negatively. One of the conspicuous outcomes is that in all cases, the surface excess entropies slightly decrease with electrolyte activity but remain close to that of pure water, whereas the enthalpy is different from that. The implication is that the driving force for positive or negative adsorption must have an enthalpic origin. This finding can be useful in developing and evaluating theoretical models for the interpretation of surface tensions of electrolyte solutions.
1. INTRODUCTION The surfaces of electrolyte solutions remain in many aspects enigmatic. Although the phase with which the solution is at equilibrium (air) does neither attract nor repel electrolytes, it is observed that these solutes adsorb either positively or negatively, depending on their nature. This begs the question of the driving force for salt accumulation or depletion; is it of an entropic or enthalpic nature? Although many model studies have been carried out on the structure of these surfaces, this basic question has not yet been systematically addressed. Insight into the surface thermodynamics of electrolyte solutions is helpful in understanding speciation for these systems, but also, it helps to discriminate between various model interpretations. Most of these assume a spontaneous polarization in the surface region, resulting from some separation between cations and anions in the surface layer, with the ensuing creation of an electric double layer. Such analyses involve many uncertainties. Little is known about the density distribution of water across the interface and about the orientation of water molecules in the surface layers. As a result, it is not easy to rigorously predict the surface potential (the so-called χ potential) for pure water, let alone the influence of ions on it. The meaning and value of the dielectric permittivity on a molecular scale in the water r 2011 American Chemical Society
surface is a related problem. This quantity plays, of course, a crucial role in assessing the electric interactions between ions, dipoles, and higher poles in the surface layer. Anyway, the distribution of individual ionic species and the assessment of local potentials remain topics of dispute. Even the driving force for the spontaneous charge separation is not yet unambiguously established. Mostly, it is necessary to make model assumptions. Such assumptions are also needed when solutions are sought on a molecular scale by molecular dynamics (MD) or Monte Carlo simulations. Obviously, the quality of the results is as good as the assumptions made. In the present contribution, we propose a thermodynamic, that is, phenomenological, approach. The idea is to analyze the temperature dependence of the surface tension, aiming at establishing the surface excess enthalpy and entropy for a selection of positively and negatively adsorbing electrolytes. By its very nature, our phenomenological approach means that no a priori Special Issue: Herman P. van Leeuwen Festschrift Received: November 16, 2011 Revised: December 22, 2011 Published: December 23, 2011 6465
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The Journal of Physical Chemistry A assumptions about adsorption or depletion of specific ionic species have to be made. Typically, electrolytes are treated as electroneutral entities, and so is the surface layer as a whole. Single ions are thermodynamically inoperable. The advantage of this type of approach is of course that for each electrolyte studied experimentally, valid results are obtained that do not depend on model assumptions. The information to be obtained may assist in the development of model interpretations. However, we are unable to produce molecular information without making additional assumptions. Our method works both for positively and negatively adsorbing electrolytes. By way of introduction, we summarize some experimental information as described in a recent textbook.1 For pure water, the temperature dependence γ(T) is fairly well-known (see below, Figure 1). There is agreement between different authors, using different experimental techniques. Between 0 and 30°, the decay is more or less linear, implying a value of the surface excess entropy Sσa of +0.141 ( 0.0087 mN m1 K1 at 0 °C. At higher temperatures, this entropy increases somewhat. We return to this in section 4.1. From other sources, the χ potential is concluded to be positive, meaning that at the surface, the water molecules are, on average, oriented with their negative parts out and/or with OH ions preferentially enriching the outer side of the waterair interface. The absolute value is about 1020 mV, meaning that surface polarization is not a pronounced phenomenon. This result goes back to Frumkin et al.2 and was later independently confirmed by Randles and Schiffrin,3,4 Trasatti,5 and Borazio et al.6 using various techniques. For details, see ref 7. So far, MD simulations have not (yet) confirmed this well-established fact.8 With respect to the influence of electrolytes on the surface tension, the intuitive trend that bigger, that is, more hydrophobic, groups tend to enrich the outer part of the surface is mostly confirmed. For instance, in the series of alkyl ammonium chlorides, the surface excess increases with the length of the hydrocarbon chain, with the “zero term” NH4Cl adsorbing slightly negatively.9 For simple electrolytes, not containing hydrocarbon groups, the same trend applies; KF adsorbs more strongly negatively than KI. Acids tend to adsorb positively,10,11 probably because the protons are attracted to the negative outside of the pristine water surface. All of this is experimentally well-documented, but that does not mean that unexplained phenomena involving the salt effect on the surface tension do not remain. We mention the Jones-Ray effect12 (is it real or an artifact?), some irregularities in the salt effect on flotation,13 and the esoteric influence of electrolytes on air bubble coalescence.14 Not many papers have been published on the temperature dependence of the surface tension of electrolytes solutions, with the option of discriminating between the enthalpic/energetic and entropic components of the surface excess Gibbs/Helmholtz energy. We mention a contribution by Matubayashi et al.,15 who found the surface excess entropy to be a decreasing function of the concentration of NaCl, MgCl2, and LaCl3, with little difference between these electrolytes. This observation could suggest that the entropy is mainly determined by the water structure. However, the elaboration was a bit sloppy because the temperature effect of the activity coefficients was ignored. In the present paper, we present a more rigorous derivation. As this is rather laborious and we want to emphasize the basic principles, we shall restrict ourselves to (11) electrolytes. In a later contribution, further elaborations and extensions can be considered.
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Figure 1. Surface tension of pure water from 0 to 100 °C. Data by Gittens, Kayser, Moser, Teitelbaum, and NBS; adapted from ref 18, where details and further references can be found.
2. THEORY The surface tension of a liquid is identical to the surface excess Gibbs or Helmholtz energy between which we will not distinguish because we ignore the pressure dependence. This excess consists of an enthalpic and an entropic part γ ¼ Gσa ¼ Haσ TSσa
ð1Þ
Here, the symbols G, H, T, and S refer to the Gibbs energy, enthalpy, absolute temperature, and entropy, respectively. The superscript σ refers to the surface excess with respect to the solvent (water) and the subscript a indicates “per unit area”. In the present contribution, we consider changes of the surface tension with temperature and composition of the solution. For this, we have the Gibbs adsorption equation dγ ¼ Sσa dT
∑i Γi dμi
ð2Þ
where the sum over i covers all electroneutral solutes in the system except water because the surface excess entropy and all surface concentrations are referred to this solvent. This is consistent with the Gibbs convention for defining interfacial excesses. For low solute mole fractions, to which we shall restrict ourselves, all surface excesses are identical to those measured analytically so that Γi refers to the surface concentration of component i.16 In the present case, we consider only one electroneutral electrolyte as the solute, which, where needed, we shall denote by the subscript s dγ ¼ Sσa dT Γs dμs
ð3Þ
From this, two thermodynamic quantities can be obtained. At a given temperature, the surface concentration of s follows as ! ∂γ Γs ¼ ð4Þ ∂μs T
and the surface excess entropy follows as ∂γ Sσa ¼ ∂T μs
ð5Þ
Equation 4 is the common Gibbs adsorption equation. In the present thermodynamic approach, Γs refers to the excess of electroneutral electrolyte, not to that of individual ionic species. 6466
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Note that the interfacial layer as a whole is electroneutral; therefore, thermodynamically, its properties can only be described in terms of adsorption/desorption of electroneutral amounts of electrolytes. In principle Sσa can be found from eq 5 so that, after substitution in eq 1, also Hσa becomes available. However, before doing that, transformations are needed because experimentally, the derivative of the surface tension with respect to the temperature is never reported at constant chemical potential of the electrolyte but at fixed mole fraction or concentration. Conversion can be carried out using Jacobians,17 which in our case leads to ! ∂γ ∂γ ∂μs Sσa ¼ þ ð6Þ ∂T xs ∂μs ∂T xs T
The first term on the right-hand side of eq 6 is mostly leading and experimentally available, though not always in as much detail and with as much precision as wanted. As μs ¼ μ°s þ 2RT ln fs xs
ð7Þ
with the factor 2 stemming from the fact that our (11) electrolytes are fully dissociated, and as μ°s is only a function of T and (d μs)T = 2RT d ln fsxs, we get for the last derivative in eq 6 ∂μs ¼ ∂T xs
∂μ°s ∂T
!
∂ ln fs þ 2R ln fs xs þ 2RT ∂T
xs
ð8Þ with dμ°s =dT ¼ S°s
ð9Þ
which is the standard molar entropy of the electrolyte in solution, also known as the standard molar entropy of hydration. Note that fs refers to the activity coefficient of the electroneutral electrolyte. With all of this, the final expression for the surface excess entropy becomes
∂γ Sσa ¼ ∂T xs ! 1 ∂γ ∂ ln fs ° þ Ss þ 2R ln fs xs þ 2RT 2RT ∂ ln fs xs T ∂T xs
ð10Þ This equation contains two entropies S. The one on the left-hand side is the entropy excess in the surface, determined by the water and the electrolyte; it is counted per unit area. The entropy on the right-hand side is the partial bulk entropy per mole of electrolyte under standard conditions, reflecting the interaction between ions and water.
3. DATA ACQUISITION AND ELABORATION 3.1. General. Finding suitable literature data is not a routine matter. First, accurate data for γ(T,xs) and fs(T,xs) must be found for the same electrolyte over a suitable range of concentrations and temperatures. Often, conversion of concentration units is mandatory. The upper boundary of concentrations is limited by the validity of eq 7, requiring a mole fraction of xs , 1. Only under this condition may the Gibbs surface excess be identified
with the analytical surface concentration. Mostly, we restricted ourselves to values below xs = 0.1. For many systems, available data cover too short of a range; some have too few measuring points, or they must be discarded because there are other reasons for mistrusting the data, for instance, because of irrational breaks in the dependencies. Other criteria for the quality of data are that γ and (dγ/dT) must extrapolate within experimental error to their values at xs f 0, which are well-established for pure water.18 By way of illustration, surface excess entropies computed on the basis of surface tension data for NaBr from Gruzdev and Kiselev19 exceeded those based on data by Rusanov and Faktor,20 but the former had to be rejected because the limiting value for zero concentration was almost 20% too high. Values for S°s , needed in eq 10, can, for room temperature, be obtained from ref 21. Their variation with temperature, which is a correction to a correction, was found to be negligible using partial specific heat capacities from ref 22. After scrutinizing the literature, we eventually decided that so far, sufficiently reliable and complete surface tension and activity data are available to allow elaboration for the electrolytes LiCl, NaCl, NaBr, HNO3, and HClO4. The three halides adsorb negatively, whereas the acids adsorb positively. Therefore, we can differentiate between ions of the same valence (the usual systems considered in speciation studies) and between positively and negatively adsorbing electrolytes (an additional phenomenon). We note that the acids are miscible with water in all proportions, but for the reasons expounded above, we shall consider only the low concentration part, where the Gibbs equation is valid. 3.2. Activity Coefficients. The activity coefficients as functions of concentration and temperature for NaCl, NaBr, and LiCl were taken from Zaytsev and Aseyev;23 those for HClO4 are from Haase et al.,24 and those for HNO3 are from Clegg and Brimblecombe.25 For the three salts, the given activity coefficients had to be converted from the molality to the mole fraction scale. Where needed, interpolations were carried out using polynomial expressions.
4. RESULTS AND DISCUSSION 4.1. Pure Water as the Reference. By way of introduction, we present in Figure 1 the surface tension of pure water as a function of temperature. This graph is an essential reference because all curves in the presence of electrolytes must for zero concentration reduce to these values. The graph indicates the experimental uncertainty between different authors and different measuring methods. Between 0 and 30 °C, the decay is almost linear. At higher temperatures, the surface tension drops more strongly. As a first step, the data of this figure can be subjected to a thermodynamic analysis. At any T, the slope dγ/dT gives immediately the surface excess entropy Sσa . Thus, using eq 1, the corresponding excess enthalpy is also obtained. Results are plotted in Figure 2. This behavior is as expected; the higher the temperature, the larger the entropic contribution. The trend for TSσa is more strongly curved than that of γ because Sσa also increases with T. 4.2. Electrolyte Solutions. In Figure 3, surface tensions as functions of concentration (on a mole fraction activity scale) are given for the electrolytes studied. The data stem from works by Rusanov and Faktor for NaBr,20 by Faktor and Rusanov for NaCl26 and LiCl,27 by Neros and Eversole28 for HClO4, and by Granzhan and Laktionova29 for HNO3. 6467
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Figure 5. As in Figure 4, but now semilogarithmically.
Figure 2. The entropic and enthalpic contributions to the surface tension of pure water as a function of temperature. Surface tension data are based on ref 22).
Figure 6. Adsorption isotherms at room temperature (indicated) for five different electrolytes at the airwater interface. The data points are interpolations obtained using third-order polynomials.
Figure 3. Surface tension as a function of activity for five electrolytes at 25 °C.
Figure 4. Surface tension as a function of activity at different temperatures for LiCl (left) and HClO4 (right). Linear scale.
All five curves include a value for pure water. This value coincides within experimental error and agrees with those of Figure 1 at 25 °C. As expected, the curves fall into two categories, ascending branches for the salts and descending ones for the acids. Inside of these groups, there are small but significant mutual differences. The trend is that at low xs, the ascent of the negatively adsorbing solutes is slightly stronger than the descent of the positively adsorbing ones. We do not have corresponding data available for electrolytes for which γ(xs) is about horizontal. CH3NH4Cl is close to that.9 In Figures 4 and 5, the temperature effects are given as linear and semilogarithmic plots, respectively, taking LiCl and HClO4 as the paradigms. In Figure 4, the surface tensions for pure water
are again indistinguishable from those in Figure 1. This also is the case for the other electrolytes (not shown). In the semilogarithmic plots of Figure 5, the main effect of temperature is the vertical displacement of the curves. For HClO4, the curves approach each other slightly with increasing mole fraction. In a later stage, semilog plots will be needed to obtain surface excesses using Gibbs law. 4.3. Adsorption Isotherms at Room Temperature. The obvious first step is using the Gibbs adsorption eq 4 to obtain adsorption isotherms for all electrolytes investigated. Figure 6 represents the results. This figure quantifies the extent to which the two acids adsorb positively and the salts adsorb negatively. Although our phenomenological approach does not allow us to obtain properties of individual species, it is logical to infer that the positive adsorption of the acids finds its origin in attraction of the protons or hydronium ions H3O+ to the outer side of the surface. If the enrichment of the surface layer by protons is combined with the information that the outer water molecules have the negative sides of their dipole moments out (see section 1), one may infer that incorporation of hydronium ions into the outer layer of water molecules may be the driving force for their enrichment. In this sense, these ions behave as “charge-determining ions”. The potential that they create comes on top of the χ potential caused by the spontaneous polarization of the pure water itself. The negative adsorption of the other three electrolytes is the type of speciation that is usually considered in speciation studies. None of the ions involved have strong attraction with just one water molecule. In double-layer terminology, they should be classified as “indifferent”. Rather, their hydration with more water molecules keeps them out of the surface region. The observed ion specificities are relatively minor and do not exhibit a clear ionic trend. According to general expectation, bigger ions would 6468
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Figure 7. Square root dependence of the negative adsorption of electrolytes at the surface of water. Temperature = 20 °C.
dehydrate more easily than the smaller ones and hence be more inclined to enrich the surface. The difference between NaBr and NaCl is in line with that, but that between LiCl and NaCl is not. In fact, we must realize that the data refer to electroneutral salts and not to sums of combinations of individual ions. It is noted that the maximum in the adsorption of HClO4 is the onset of an inversion toward negative adsorption at more elevated activities, far beyond the range where the low activity case of the Gibbs equation applies. The two acids and water are miscible in all proportions; from a dilute solution of water in the pure acids, water is positively adsorbed. Quantitatively, the amounts of acids adsorbed are much lower than what is usually observed for surfactants. These amounts do not exceed those of the negative adsorption of salts; they may even be smaller. This behavior is opposite to that of electric double layers on charged solid surfaces. For such systems, the fraction of the charge compensated for by positive adsorption of counterions is mostly much higher than that by negative adsorption of co-ions. Only in the limiting case of very low potentials are these two contributions equal. For electric double layers on charged particles and polyelectrolytes, the expulsion of co-ions leads to the expulsion of indifferent electrolyte and hence to an increase of its concentration in the bulk. Phenomenologically, this is the Donnan effect. Comparing double layers on solids with those on air begs the question whether the two salt exclusions obey similar laws. For double layers on solids, salt exclusion can be computed by diffuse layer theory. Negatively adsorbing ions being absent in the inner part of the double layer, there is no need to account for specific adsorption, in particular, not when the potentials are not too low. According to this theory7 zFΓs ¼ ð2εεo cs RTÞ0:5 ½expðzyd =2Þ 1
ð11Þ
where ε is the relative dielectric constant of the medium and εo is the permittivity of free space, amounting to 8.84 1012 F m1 or C2 N1 m2. The other parameters have their usual meanings, and yd is the absolute value of the dimensionless potential of the diffuse double layer. For sufficiently high potentials, the exponential in eq 11 vanishes, and this equation reduces to zFΓs ¼ ð2εεo cs RTÞ0:5
ð12Þ
which makes the negative adsorption independent of the potential and proportional to the square root of the concentration. With this in mind, Figure 6 was replotted to yield Figure 7.
Figure 8. Interpolated experimental data on the temperature decay of the surface tension with temperature. The straight lines are drawn to guide the eye.
√ The linearity with cs is striking, but the figure also invites questions. The first is that for the vanishing of the exponential term in eq 11, a relatively high potential is needed; for example, for a diffuse double-layer potential of 100 mV, the exponential is still about 10% from unity. This is of the same order but higher than the spontaneous potential of pure water. Therefore, the first question is where does this potential come from? Second, why is there so much specificity? For a typical diffuse layer property, there should be no specificity at all. It may be added that any specificity of the activity coefficients in the bulk has already been incorporated. Third, there is a problem with the absolute value of the slopes. They range from 0.89 to 12.63 106 mole0.5 m0.5 According to eq 12, this should correspond to ε0.5(2εoRT)0.5/ F = 0.22 109ε0.5 at 300 K, which is much lower than the experimental slope. The only adjustable parameter is ε, but for a fit, this parameter should be about 40 times as high as that for bulk water. There is no independent information about this; one rather would expect a lower value. In summary, the square root scaling of Figure 7 is too convincing to ignore, but we have no quantitative explanation for it. 4.4. Surface Excess Entropies. For the evaluation of Sσa , we have eq 10, where the first term on the right-hand side is leading. However, the second term cannot be ignored. In fact, it represents the nonideal part of the variation of the entropy of the bulk, which is the reference for the surface excess. As a first step, we present in Figure 8 typical γ(T) at given activity curves, obtained by replotting data of the type of Figure 4. These figures are characteristic for the leading term on the right-hand side of eq 10. Within experimental error, all dependencies are linear. This means that at a given salt concentration, the temperature dependence of the slope is negligible. 6469
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Figure 9. Surface excess entropies for four electrolytes as functions of the bulk activities. The parameter d is the vertical shift applied to let all curves pass through the same origin.
Figure 10. The surface excess entropy as a function of the log of the surface concentration. Temperature = 25 °C, except where otherwise indicated.
For negatively adsorbing electrolytes, like NaCl, the surface tension increases with concentration; for positively adsorbing electrolytes, like HClO4, it decreases (see Figure 3). However, for both, the slope decreases with increasing concentration, implying that the leading term in the surface excess entropy (see eq 10) decreases with increasing electrolyte concentration, irrespective of whether the electrolyte is positively or negatively adsorbing. To the eye, the lowest curve in Figure 8 (top) and the top curve in Figure 8 (bottom) are identical. This should be the case because both refer to pure water. Upon closer inspection, there are small differences between them. These reflect minor but real differences between different authors (surface tensions from refs 28 and 30 activities from refs 23 and 24) to which we shall return in the discussion of the next figure. The data for the four curves in Figure 9 stem from different authors, resulting to minor differences in the absolute values. As we are now interested in the absolute values, we moved all curves to the common origin of 0.161 mN K1 m1, which is higher than the value of 0.141 at 0 °C, reported in section 1. The parameter d in the inset indicates the shift for each electrolyte. The result displayed in the figure is surprising. Three features emerge. (1) For all electrolytes, the surface excess entropy is lower than that for pure water. (2) Within experimental error, the surface excess entropy is the same for all electrolytes, irrespective of whether they adsorb positively or negatively. (3) Specific ionic effects show up between the three salts, but these are relatively small and hardly beyond experimental error. For pure water, the surface excess entropy is positive. The TSσa term in eq 1 causes the surface tension to be lower than the surface excess enthalpy. We already stated that the surface excess entropy is mainly determined by the water. Its positive sign can be rationalized as caused by the increased randomness of the interface as compared with that of the bulk. Hence, observations (1) and (2) may be rephrased by stating that for all electrolytes studied, the interfacial water becomes more organized with increasing activity. While it is obvious that electrolytes do influence the structure of the solvent water, it is surprising that adding electrolyte or withdrawing it has about the same effect. Otherwise stated, it is a generic phenomenon. One option that might be considered is looking at this entropy in terms of entropies of mixing. For bulk mixtures, this quantity is
generic; it only depends on the mole fraction but not on the nature of the admixture. Moreover, it is symmetrical between mole fractions x and 1 x. This option begs two questions, one about the sign and the other about the dependence on composition. As to the former, entropies of mixing are always positive, but here, we are discussing excesses, and these can be negative when the mixing entropy in the interface is lower that that in the bulk. Regarding the dependence on composition, entropies of mixing lead to the limiting logarithmic dependency of chemical potentials on x for both components of a mixture. Translated into our situation, it could be tried whether a plot of the surface excess entropy as a function of the surface mole fraction xσ approaches linearity for low xσ. Surface mole fractions are hardly accessible because it makes no sense to consider molten electrolytes as the reference. Nevertheless, it does make sense to replot Sσa semilogarithmically as a function of the absolute value of Γs. Results are presented in Figure 10. Before discussing these curves, it is necessary to keep in mind that this is the very limit of data analysis that we can do; both the ordinate and abscissa axes are derived quantities into which all experimental and methodical errors are compounded. A relatively large range has to be covered between the lowest measuring points and the extrapolated limiting value. See the dashed part. Extremely accurate data are needed to make this extrapolation more precise. As far as we are aware, such data are not available. In passing, we may recall that a lack of such data is also at the root of establishing the Jones-Ray effect.12 However, it is not unlikely that for LiCl and NaCl, extrapolation according to the dashed line is acceptable. For NaBr, the curve Sσa is slightly higher because these measurements are taken at a higher temperature, but linearity in the extrapolated part is again likely. Anyway, the overall trend is that this part is generic and does not discriminate between positive and negative adsorption. On the other hand, ideal mixing breaks down for the (absolute values of the) surface concentrations above about 0.03 μmol/m2, where the data become clearly specific. In contradistinction to the plots in Figure 9, a specific ionic effect shows up; at a given surface concentration, the trend is that the surface excess entropy increases with the size of the ion, NaBr > NaCl and NaCl > LiCl. Although this is in line with the general experience that the bigger an ion, the stronger it enriches the interface, it is nevertheless a problem because the electrolytes are negatively adsorbed. A similar conclusion was drawn in connection with Figure 7. 4.5. Surface Excess Enthalpies. Having concluded that electrolyte specificity is not entropically determined and that 6470
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Figure 11. Surface excess enthalpies with respect to the enthalpies of pure water.
the surface tension is definitely specific, it must follow that the origin is an enthalpic specificity. In principle, we have the required information available; we simply use eq 1 where γ and Sσa are known; see sections 4.2 and 4.5, respectively. In Figure 11, we immediately present the excess enthalpies as functions of the (absolute values of the) adsorbed amounts. For pure water, Hσa is positive, amounting to about 120 mN m1, depending on the temperature. See Figure 2. In Figure 11, this value for pure water is subtracted. Before discussing Figure 11, it must be repeated that this diagram approaches the limit of our information because of the many steps that had to be taken to obtain these data. In particular, the very steep slopes for the two acids result from the fact that in Figure 6, the adsorbed amounts do not continue to grow, but that trend is based on only one or two measuring points. Accepting that reservation, let us consider the main trends. Most striking is the observation that the excess enthalpies are significantly larger for the acids than for those the salts. Above, we attributed the negative contribution of the acids to the surface excess enthalpy as caused by the binding of protons to the outer negative part of the water surface. From Figure 11, adsorption energies of a few kT per molecule can be derived, which is of the right order of magnitude for this. One would expect linearity between Hσa and Γs in the initial parts of the isotherms for the acids, but more accurate data are needed to confirm that. The absolute values for the negatively and positively adsorbing salts are definitely different. For the salts, the contributions to Hσa are much smaller and even tend to decrease at higher salt expulsion. It is found for all of the salts, but it is difficult to rationalize. Perhaps it is related to hydrogen binding. By thermodynamic arguments, nothing more can be said about it.
5. CONCLUSIONS The present paper offers a thermodynamic analysis of the surface tension of electrolyte solutions. The primary aims are obtaining insight into the driving force for salt uptake or expulsion of basic interfacial and other phenomena and discriminating between generic and specific trends. Starting points are surface tensions as functions of electrolyte concentration and temperature. Generally valid equations have been derived, allowing computation of the entropic and enthalpic components of the surface tension. Thermodynamics are phenomenological, meaning that generally valid results are obtained regarding electroneutral combinations
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of ions, that is, salts and/or acids. In this way, it is not possible to say something about individual ionic species nor on the spontaneous polarization of electrolyte surfaces, which is at the root of most model interpretations. We can only discuss adsorption and/or desorption of electroneutral entities. Nevertheless, models that so far have been developed for the structure of the surface layers must obey our thermodynamic conclusions. In particular, the driving forces for spontaneous charge separation, as put forward in such theories, must be in harmony with the presented entropyenthalpy balance. We see invoking of these thermodynamic laws as a touchstone for a later systematic analysis of existing surface layer models. Relatively, the weakest point in our analysis is the requirement of very precise data over sufficiently long ranges of concentrations and temperatures, both for the surface tensions and activities. This demand stems partly from the many partial derivatives that enter this work and partly from the fact that we address excess quantities, implying the need for subtracting the bulk parts. Our presentation would vastly benefit if more and better data became available. Accepting the above, some surprising results may be mentioned. In the first place, it was established that the entropic contribution to the surface tension always decreases with increasing electrolyte concentration, irrespective of whether the electrolyte adsorbs positively or negatively. The fact that the surface tension decreases for positive adsorption but increases for negative adsorption is accounted for by enthalpic factors. The expulsion of salts scales as the square root of the salt concentration, which qualitatively resembles Donnan exclusion, but quantitatively, it is too strong. Most likely, the accumulation of acids is triggered by adsorption of the protons of the acids, whereas the excess entropy is essentially determined by the degrees of freedom of the water in the surface. The data on which our analysis is based are relatively old, but to our knowledge, they have never been improved. On the other hand, our conclusions can be useful as checks for modern developments. One category is that of simulations,8,31 a technique by which it is sometimes difficult to obtain excess entropies with sufficient accuracy. Marcus32 reviewed the additivity of surface tension increments or decrements for individual ionic species. Although this approach is beyond thermodynamics, we may perhaps expect that the specificity of the ionic components will have an enthalpic origin. Song and Kim33 coupled the surface tension to excess charge characteristics. We note that for such types of studies, a model assumption is required because as a whole, the surface layer is uncharged. At any rate, these examples indicate that the subject matter remains topical. Finally, this work also invites new experiments. In addition to the general need for more precise data, it would be interesting to study systematically the γ(xs,T) behavior of the first three terms of the alkylammonium chlorides because the first one (NH4Cl) adsorbs negatively, the third (C2H5NH3Cl) adsorbs positively, whereas the second (CH3NH3Cl) is almost independent of xs, probably because of a subtle entropyenthalpy compensation.
’ REFERENCES (1) Lyklema, J. Fundamentals of Interface and Colloid Science; Academic Press: New York, 2000; Vol. III, section 4.4. (2) Frumkin, A. N.; Iofa, Z. A.; Gerovich, M. A. Zhur. Fiz. Khim. 1956, 30, 1455. (3) Randles, J. E. B.; Shiffrin, D. J. J. Electroanal. Chem. 1965, 10, 480. (4) Randles, J. E. B. Phys. Chem. Liq. 1977, 7, 107. 6471
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