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Proc Natl Acad Sci U S A. 2006 September 26; 103(39): 14278–14281. Published online 2006 September 15. doi: 10.1073/pnas.0606256103. | PMCID: PMC1599954 |
Copyright © 2006 by The National Academy of Sciences of the USA Chemistry Partitioning of atmospherically relevant ions between bulk water and the water/vapor interface Laurel M. Pegram* and M. Thomas Record, Jr.*†‡ Departments of *Chemistry and †Biochemistry, University of Wisconsin, 433 Babcock Drive, Madison, WI 53706 Received June 6, 2006. Recently, surface-sensitive spectroscopy data and molecular dynamics simulations have generated intense interest in the distribution of electrolyte ions between bulk water and the air/water interface. A partitioning model for cations and anions developed for biopolymer surface is extended here to interpret the effects of selected acids, bases, and salts on the surface tension of water. Data for electrolytes were analyzed by using a lower-bound value for the number of water molecules in the surface region [0.2 H2O Å−2 (approximately two layers of water)], obtained by assuming that both Na+ and SO42− (i.e., Na2SO4) are fully excluded from this region. Surface–bulk partition coefficients of atmospherically relevant anions and the proton are determined. Notably, we find that H+ is most strongly surface-accumulated, I− is modestly accumulated, NO3− is evenly distributed, and OH− is weakly excluded. Keywords: surface tension, surface–bulk partition coefficients, inorganic salt ions The distribution of ions between bulk water and water located at a surface has major implications for processes in biochemistry, atmospheric chemistry, and technology. As early as 1957, the observation of negative surface potentials for aqueous solutions of alkali metal salts of I −, ClO 4−, SCN −, and PF 6− led to the proposal that these anions (but not the cations) were present in the interfacial region of aqueous salt solutions ( 1, 2). However, the traditional proposal of an ion-free water layer on the surface of salt solutions, based on their positive surface tension increments ( dγ/ dm2 > 0), went relatively unchallenged until a decade ago, when Hu and coworkers observed that the kinetics of halogen uptake by NaBr and NaI solutions were too rapid to be explained by a simple bulk-phase reaction mechanism ( 3). The authors concluded that significant concentrations of bromide and iodide must be present in the surface layer, even at low bulk salt concentrations. Since then, considerable attention has been focused on this topic because of its implications for atmospheric chemistry ( 4, 5). Surface-sensitive spectroscopic experiments ( 6– 9), molecular dynamics simulations ( 10– 12), and various theoretical/experimental collaborations ( 13– 15) provide evidence, recently reviewed ( 16), that, although “hard” and multiply charged ions are excluded from the surface, large polarizable anions (e.g., SCN − and I −) and the proton accumulate there, in some cases at concentrations greater than in the bulk solution. Only when both ions are hard and/or multiply charged (e.g., NaF and Na 2SO 4) do the simulations show both ions excluded from the surface, in agreement with the classical picture of a salt-free layer. In other cases, almost complete cationic exclusion and various degrees of anionic accumulation at the surface result in a range of net ion depletion at the surface ( 13); for these cases, a correspondingly wide range of positive surface tension increments have been reported ( 17). We apply a recently developed two-state, single-ion partitioning model (L.M.P. and M.T.R., unpublished data) to interpret effects of selected salts, acids, and bases on the surface tension of water. For atmospherically relevant ions, we obtain single-ion partition coefficients that quantify (relative to a reference salt) the accumulation at, or exclusion from, the local (surface) region of water. Significantly, we find that these single-ion partition coefficients are additive and independent of the nature of the other ion of the salt and of salt concentration. Thermodynamic Background and Analysis. The Guggenheim thermodynamic analysis of surface tension considers the surface region as a microphase of small but finite thickness at equilibrium with the bulk phase ( 18). Equations for the effects of both nonelectrolyte and electrolyte solutes on surface tension have been formulated in the context of the Guggenheim model ( 19). For electrolytes, the formal analysis based on the chemical potential of the electroneutral solute component is not subject to direct molecular interpretation because it does not explicitly incorporate the consequences of dissociation into individual ions, specifically the possibility of independent distribution of these ions between surface and bulk water. Our laboratory has analyzed the thermodynamic consequences of the distributions of individual electrolyte ions between the surfaces of nucleic acids and proteins and the bulk solution as a way to interpret salt–biopolymer preferential interaction coefficients and the effects of salt concentration on the thermodynamics of biopolymer processes ( 20, 21). An analogous interpretation of the effects of electrolyte concentration ( m2) on the surface tension (γ) of water (see ) provides quantitative information about the partitioning of cations and anions between surface and bulk water. By analogy with the nonelectrolyte analysis of Guggenheim ( 18), for the local surface region (denoted by σ) of a two-component solution of any binary electrolyte ( Mν+Xν−), at constant temperature and pressure, the Gibbs–Duhem equation is written in terms of electrochemical potentials § of the ions of the electrolyte component: where water is component 1, and the electrochemical potential for the ionic species i (i = +,−) is defined as In Eq. 2, F is the Faraday constant, ![[var phi]](/corehtml/pmc/pmcents/x03C6.gif) is the electrical potential of the region (surface or bulk), and zi is the valence of species i, with ionic activity ai = fimi in that region, where fi is the activity coefficient, and mi is the surface or bulk molality of the ion ¶. The differentials in Eq. 1 are related by the bulk-phase (superscript b) Gibbs–Duhem equation at constant temperature and pressure: From Eqs. 1 and 3, one obtains an expression for the surface tension increment dγ/ dm2: where the ratios of mole numbers ni/ n1 in the local surface region (σ) and in the bulk have been replaced by the equivalent ratios of molal concentrations, mi/ m1·, and m1· is the solvent molality (55.5 mol/kg for H 2O). In Eq. 4, the local molalities of cations and anions in the surface region ( m+σ, m−σ) are in general not equal to one another nor to the corresponding bulk molalities ( m+b, m−b). [The inequality of the local (surface) concentrations m+σ and m−σ does not violate the requirement for equality of Gibbs' surface excesses of the cation and anion because they are defined as integrals over the entire solution ( 16).] From Eq. 2, the derivative of the electrochemical potential of the ions in the bulk region with respect to bulk electrolyte concentration is where both bulk single-ion activity coefficients, fib, are approximated by the bulk mean ionic activity coefficient, f±b, and the nonideality correction term, ε ±b, is defined as ε ±b ![[equivalent]](/corehtml/pmc/pmcents/equiv.gif) dln f±b/ dln m2 (Table 3, which is published as supporting information on the PNAS web site). Neglect of any salt concentration dependence of the bulk electrical potential in Eq. 5 is a necessary approximation that appears justified by the results, at least at low electrolyte concentration ( ![[less, similar]](/corehtml/pmc/pmcents/lsim.gif) 1.0 m), where surface tension increments are generally independent of electrolyte concentration ( 17). From Eqs. 4 and 5, for solutions at sufficiently low electrolyte concentrations, the surface tension increment is where the superscript naught indicates the low-concentration regime (implied hereafter). In Eq. 6, the partition coefficients Kp,i are apparent equilibrium constants for partitioning of each ion between surface and bulk and are defined as the surface/bulk molal concentration ratio: Kp, i miσ/ mib ![[similar, equals]](/corehtml/pmc/pmcents/sime.gif) miσ/ν im2. Also in Eq. 6, b1σ n1σ/ A is the number of water molecules per unit surface area in the surface phase and ν ν + + ν − is the number of ions per formula unit of the salt. The ion partition coefficients ( Kp,+, Kp,−) are related to that which would be obtained if the electrolyte were treated as an electroneutral component ( Kp,2): Most inorganic acids reduce surface tension, (i.e., dγ/ dm2 < 0); therefore, values of Kp,2 for these acids must exceed unity. For inorganic salts, dγ/ dm2 > 0; thus, values of Kp,2 are less than unity. The traditional interpretation of this net exclusion (i.e., that the surfaces of salt solutions are devoid of ions) is too restrictive because it ignores the possibility of independent partitioning of ions resulting in a spectrum of degrees of accumulation at, or exclusion from, the surface. Although experimental and computational evidence exists for surface/bulk concentration ratios that differ widely for various ions ( 2, 8, 10), the above partitioning analysis has not previously been used to predict or interpret the effects of unequal distributions of cations and anions (or the effects of uncharged solutes) on surface tension. In what follows, we analyze the literature surface tension data for atmospherically relevant salts and acids, and we determine Kp,i for the individual cations and anions (relative to a reference salt). Application to Surface Tension Increments. Shown in Table 1 are the averages and standard deviations for the surface tension increment dγ/ dm2 for relevant alkali metal salts and the corresponding acids (e.g., NaCl, KCl, LiCl, and HCl) ( 17, 22– 27). Selected literature data ( 27) are also shown in . For these series, the salts and bases increase the surface tension, whereas the acids have the opposite effect. Eq. 6 predicts that, at low electrolyte concentration, the nonideality-corrected surface tension increment, ( dγ/ dm2)/(1 + ε ±b), is determined only by b1σ (related to the thickness of the surface region) and by the sum of the stoichiometrically weighted partitioning terms, ν i( Kp,i −1), for the individual ions of the electrolyte component. To obtain single-ion partition coefficients, we assume that the thickness of the surface region is independent of the concentration and nature of the electrolyte and assume that the salt with the largest surface tension increment [Na 2SO 4; dγ/ dm2 = 2.77 ± 0.09 ( Table 1)] is completely excluded from the surface region. The assumption that Kp,Na+ = Kp,SO42− = 0, which is qualitatively consistent with the conclusions of previous experiments and calculations ( 28, 29), yields a lower-bound value of b1σ from Eq. 6: b1σ = 0.194 molecules per squared angstrom. If a more surface-excluded electrolyte than Na 2SO 4 is subsequently characterized, b1σ will increase and all Kp,i values reported here will shift, but the relative order of cations and anions established by the following analysis will not be affected. ‖ If the average density of water in the surface region is comparable to the bulk, then this b1σ corresponds to a surface region depth of ≈6 Å, or approximately two layers of water. (If the average density is less, the region will be somewhat thicker.) Molecular dynamics simulations of aqueous salt solutions indicate that the thickness of the surface region is in the range of 4–7 Å ( 10, 14, 29). | Table 1.Average dγ/dm2 values at low electrolyte concentrations (≤1.5 M) (17, 22–27) |
By using Eq. 6 and the above assumption that Kp,Na+ = K p,SO 42− = 0, the NaCl, KCl, LiCl, and HCl data were iteratively analyzed to obtain Kp,Cl− = 0.70, Kp,K+ = 0.05, Kp,Li+ = 0.14, and Kp,H+ = 1.53. Thus, K + and Li + are almost completely excluded from the surface layer, Cl − is moderately excluded, and H + is moderately surface-accumulated. The cation partition coefficients were then used to obtain coefficients for the atmospherically relevant anions HO −, Br −, NO 3−, and I − ( Table 2). Notably, use of the above partition coefficients for Na +, K +, Li +, and H + yields Kp,− values for the anions that are independent of the electrolyte, within uncertainty, which supports the prediction of Eq. 6 that cation and anion effects at low m2 are additive. The most surface-excluded of these anions is OH − ( Kp 0.6), Cl − is slightly less excluded ( Kp 0.7), and Br − is weakly excluded ( Kp 0.9). The surface concentration of NO 3− ( Kp 1.0) is predicted by this analysis to be equal to its bulk concentration, and I − is weakly surface-accumulated ( Kp 1.2). | Table 2.Limiting partition coefficients calculated for cations and anions |
Heterogeneous reactions at the surfaces of seawater aerosols are now recognized as an important component of the understanding of atmospheric chemistry. For the formation of molecular chlorine and bromine from aqueous halide aerosols, Finlayson-Pitts and coworkers ( 4, 30) have shown that the kinetics model predictions cannot be reconciled with the experimental results unless interfacial reactions are included. Specifically, the amount of molecular bromine formed upon reaction of ozone with the bromide ion in deliquesced sodium bromide aerosols is ≈10-fold larger than that predicted by known gas phase and bulk aqueous phase chemistry ( 30). When an interface reaction was included in the kinetics modeling, the amount of Br 2 formed was reasonably reproduced. Although the presence of ions at the surface is presumably not the only factor accelerating the kinetics, incorporation of the surface/bulk proportionality of the Cl − or Br − concentration into the modeling should yield a better understanding of the reactions occurring in this region. Molecular dynamics simulations performed on a single nitrate ion in small water clusters and a water slab predict that this atmospherically ubiquitous ion has a significant surface propensity ( 31). Our analysis of the surface tension increment indicates that the nitrate anion is uniformly distributed between the surface and bulk regions. Molecular dynamics simulations performed by Jungwirth and Tobias ( 10) on infinite slabs of 1.2 M sodium halide solutions predict significant surface concentrations of the more polarizable halide ions; at a constant bulk concentration, the surface halide concentration increases with increasing ionic polarizability, whereas the sodium cation is mostly excluded. Our results are in agreement with the molecular dynamics-predicted exclusion of Na + and with the order of surface propensities of the halides ( Kp,I− > Kp,Br− > Kp,Cl−), although the simulations predict larger surface/bulk concentration ratios for these ions than those reported in Table 2. At a qualitative level, the decrease in surface tension caused by the addition of most inorganic acids to water indicates a net surface accumulation of the acid component, as has long been recognized ( 2, 17). At the level of individual ions, our finding that the proton has an enhanced surface concentration relative to the bulk ( Kp 1.5) is consistent with the results of a recent molecular dynamics simulation in which a single hydronium ion (with a chloride counterion) was allowed to migrate through a water slab in a manner consistent with the Grotthuss mechanism of proton transfer ( 32). The authors observed preferential distribution of the solvated proton at the air/water interface, which they attributed to the asymmetric hydrogen bonding of the ion. Other simulations of more concentrated acidic solutions also indicate that the proton is moderately accumulated at the surface ( 13). Experimentally, Petersen and Saykally ( 7) have obtained indirect evidence for accumulation of protons at the surface of an HI solution from surface-sensitive second harmonic generation spectroscopy. Because many atmospheric reactions are pH-dependent and/or acid-catalyzed ( 33), knowledge of the extent of proton accumulation at (and hydroxide exclusion from) the surface is important in understanding atmospheric processes. Results of analysis of surface tension increments provide a quantitative description of ion partitioning that is largely consistent with the results of recent surface-sensitive spectroscopy experiments and molecular dynamics simulations. Molecular dynamics simulations provide quantitative predictions of ion concentrations at the surface and of the distributions of ions with depth, although the results depend on the interaction potentials used ( 11, 34). Surface spectroscopy measurements provide important experimental validation of inorganic ion partitioning but have not yielded surface concentrations because it is not feasible to determine the depth being probed ( 6, 8, 9, 14). By applying a solute-partitioning model to literature surface tension data, we have determined a minimum estimate for the thickness of the surface region and deduced that concentrations of ions in this region are proportional to their bulk concentrations with proportionality constants (partition coefficients) that are ion-specific and relatively concentration-independent. 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