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Electric Field Effects on Air/Solution Interfaces B. A. Pethica Langmuir Center for Colloids and Interfaces, Columbia University, 911 S.W. Mudd Building, 119th Street, New York, New York 10027 Received October 20, 1997. In Final Form: March 18, 1998 Experiments to measure the effect of applied electric fields on the surface tension of aqueous solutions are difficult and have so far proved inconclusive. The effect of fields on both the surface pressure and surface excess of adsorbed solutes can be calculated from the simpler measurements of surface potential, using Maxwell relations from a thermodynamic analysis of the Volta effect. Examples for the air/water interface of NaCl and sodium dodecyl sulfate solutions are given. The results are compared with data for insoluble spread monolayers and contrasted with electrocapillarity. The effect of electric fields on the surface tension of water itself remains obscure.
The effect of electric fields on monolayers has become of interest recently as a factor modifying monolayer properties, for example packing1 and domain size.2 The measurement of changes in the surface tension and surface density of electrically polarized monolayers is basic to understanding field effects. Measurements on the polarization of spread insoluble monolayers have been reported, showing small but definite changes in density or surface pressure in single-phase films and large changes in local surface density in phase transition regions.3 Reports of field effects on liquid interfaces or monolayers adsorbed from solution are contradictory. Hayes4 was unable to detect changes in the surface tension of water and NaCl solutions with fields up to 106 V m-1. Jiang et al.5 report no change in the surface tension of solutions of NaCl or sodium dodecyl sulfate (SDS) in water, using a capillary wave technique sensitive to 0.1 mN m-1. Schmid et al.6 report substantial changes with NaCl solutions. The direct measurement of electric field effects at liquid surfaces is difficult, and it is one purpose of this communication to point out that, for solutions, the fieldinduced changes in surface pressure and surface excess adsorption of the solute may be obtained from relatively simple measurements of surface potential and surface tension as a function of the chemical potential of the solute, using Maxwell relations obtained by classical thermodynamic arguments.7 In a typical experiment, a plane metal plate is placed in a nonconducting phase (air, paraffin oil, etc.) parallel to the interface of a conducting solution such as an aqueous electrolyte. A potential (E) is applied between the plate and a suitable electrode in the conducting phase by means of an external potentiometer. The potential drop in the nonconducting gap at zero applied potential is the contact (Volta) potential. The applied potential required to obtain zero potential drop in the gap is the compensation potential (E0). The “surface potential” (∆V) of an adsorbed monolayer is the difference in E0 for the solvent and the solution under study. The adsorption (positive or negative) of a solute at the solution interface is a function of the surface tension σ of the solution, a negative change with respect (1) Arisawa, S.; Yamamoto, R. Langmuir 1993, 9, 1028. (2) Grunfelt, F.; Pitt, C. W. Thin Solid Films 1983, 99, 249. (3) Middleton, S. R.; Pethica, B. A. J. Chem. Soc., Faraday Symp. 1981, 16, 109. (4) Hayes, C. F. J. Phys. Chem. 1975, 79, 1689. (5) Jiang, Q.; Yew, Y. C.; Valentini, J. E. Colloids Surf., A 1994, 83, 161. (6) Schmid, G. M.; Hurd, R. M.; Snavely, E. S., Jr. J. Electrochem Soc. 1962, 109, 852. (7) Hall, D. G.; Pethica, B. A. Proc. R. Soc. London, A 1977, 354, 425.
to the solvent tension σ0 being denoted the positive surface pressure Π. Both ∆V and Π are functions of the chemical potentials µ of solutes in solution. From the variation of Π with µ for a chosen solute, the surface excess adsorption Γ of the solute (with respect to the solvent) is obtained from the Gibbs adsorption isotherm. These quantities are connected by the following Maxwell relations3,7 at constant temperature and pressure
( ) ( ) ∂∆V ∂Γi
∂∆V ∂µi
)
µj,q)0
( ) ( )
1 ∂Π Γi ∂q
)-
µj*i,q)0
(1)
µj,Γi
∂Γi ∂q
(2)
µj
where i and j refer to solutes and q is the surface charge density on the metal plate. The left-hand terms in eqs 1 and 2 refer to compensation states (q ) 0). Since µi for a solute in a conducting medium is not a function of the applied field, Π changes with q to maintain equilibrium for i between the charged film and the bulk solution, corresponding to an adjustment in the chemical potential of i in the surface equivalent to dΠ/Γi. The relatively simple measurement of ∆V as a function of µi leads directly (eq 2) to the effect of applied field on Γi for small induced surface charges. In principle, eqs 1 and 2 can be rewritten for q * 0, redefining ∆V as the difference in E required to achieve a chosen q for the solvent and solution, but these experiments will be more difficult. For the present purposes, it will be a physically reasonable approximation to take the coefficients on the right in eqs 1 and 2 as having their values at the compensation state over the range of practically accessible fields (up to 106 V m-1 across an air gap), corresponding to small surface charge densities up to the equivalent of one proton charge in 2 × 104 nm2 with the very low capacities at the nonconducting gap. Results Equations 1 and 2 are now applied for the air/solution interface of aqueous solutions of NaCl and of sodium dodecyl sulfate (SDS), using ∆V-µ and Π-Γ data available in the literature.8,9 To a sufficient precision, activity coefficients are neglected and dµ for these binary electrolyte solutes is taken as 2kT d ln c, where c is the concentration. This choice correspondingly ignores possible field-de(8) Jarvis, N. L.; Schieman, M. A. J. Phys. Chem 1968, 72, 76. (9) Pethica, B. A.; Few, A. V. Discuss. Faraday Soc. 1954, 18, 258.
S0743-7463(97)01142-6 CCC: $15.00 © 1998 American Chemical Society Published on Web 05/05/1998
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Figure 1. Change in surface pressure (π) and surface excess (Γ) induced by a field of 106 V m-1 at the air interface of aqueous sodium dodecyl sulfate solutions at 20 °C.
pendent ion-exchange (e.g. H3O+ for Na+) at the surface.10 Ion exchange can be addressed by measurements of E0 as a function of solute composition, for example by adding dilute HCl or NaOH to NaCl or SDS solutions. For NaCl solutions, only high concentrations are considered, for which the change in surface pressure with field is largest. For a field of 106 V m-1 with 5 M NaCl solutions it is readily calculated from the available ∆V, c, and Π data8 at 20-25 °C that the change in surface pressure (∆Π) is -0.3 µN m -1 when the plate is positive. We may note that a favorable case for measuring the change in surface tension with electric field for aqueous solutions of inorganic electrolytes is with concentrated NaSCN, for which both ∆V and Π at the air/solution interface are large and negative.8 At 9 M with an applied field of 106 V m-1, the surface pressure change will be 15 µN m-1. Sodium dodecyl sulfate is surface active. Data for ∆V and Π are available as a function of SDS concentration in water at 20 °C.9 Both Π and Γ increase monotonically with c, but ∆V goes through a minimum at 1 mM SDS, at which concentration both Γ and Π will be unaffected by an applied field. From about 2 to 6 mM, d∆V/d log c is rather constant (70 mV), so that ∆Γ (the change in Γ with field) is approximately constant at -3.4 × 1012 molecules m-2 for a (plate positive) field of 106 V m-1 over this concentration range. From the Π-c data, Γ is known and ∆Γ/Γ at 4 mM SDS is 2 × 10-5 at the same polarization. The change in Π with this field is 2 µN m-1 at 4 mM SDS, rising to about 4 µN m-1 closer to the critical micelle concentration. Below 1 mM SDS the sign of d∆V/d log c is negative, and both ∆Π and ∆Γ reverse sign, as shown in Figure 1. Addition of NaCl to SDS solutions reduces d∆V/d log c substantially, with corresponding reductions in ∆Π and ∆Γ as compared to the values for salt-free solutions. Discussion To compare the effect of field on the surface pressure of solutes (as calculated from the dependence of ∆V and Π on the chemical potential of the solute) with direct (10) Pethica, B. A. Trans. Faraday Soc. 1954, 50, 413.
Pethica
measurements of the change in surface tension of solutions with applied field, the effect of field on the surface tension of the pure solvent is required. No direct measurements appear to be available, nor has any purely thermodynamic procedure for calculating the change from alternative measurements been proposed. Rusanov and Kuz’min11 gave an electrostatic argument assuming that the hypothetical potential drop across the surface layer (χ) results from the net nonrandom orientation of the solvent molecules at the interface. At 106 V m-1 for a dipole potential drop of 0.1 V, the change in surface tension is calculated to be 1 µN m-1, comparable with the changes in surface pressure calculated above for NaCl and SDS solutions. Hayes4 also estimated the change in surface tension for water by a quasi-thermodynamic argument using a model for the electric state of the interface, including a contribution to χ from the ionic double layer formed by the intrinsic ions from the dissociation of the water. This model predicts an increase in σ0 of 3 × 10-1 µN m-1 at 106 V m-1, independent of the sign of the field, unlike the Rusanov and Kuz’min model. Thermodynamic analysis without introducing a model requires that changes in σ0 near the compensation state depend on q2 and are consequently independent of the sign of the polarization. Whether σ0 rises or falls with polarization depends on the sign of dχ/dq.27 It is usually accepted that there is no strictly thermodynamic method of measuring the χ potential, since this would be equivalent to measuring the Galvani potential between two regions of different chemical composition, a possibility forbidden by the arguments of Guggenheim.12,13 Attempts to estimate χ have been made by nonthermodynamic methods and by simulation models. The interest lies in the possibility of estimating single ion activities,14,15 but the problem is of significance in physics for the definition of electrostatic potentials in terms of the more fundamental thermodynamic variables.26 Guggenheim’s arguments have survived attack for half a century, but it is noteworthy that they are in effect arguments from a “gedanke” experiment. In contrast, the strictly thermodynamic analysis of the experimental variables for an electrical condenser, explicitly introducing the properties of the interfaces between the metal plates and the dielectric fluid, has led to the specification of an experimental procedure to measure the Galvani potential differences between two coexisting dielectric phases.26 This procedure, which involves difficult experiments, remains untested. There is long-standing discussion16 over both the sign and magnitude of χ for water as estimated from a variety of nonthermodynamic methods.28 Correspondingly it is uncertain whether estimates of the effect of the field on (11) Rusanov, A. I.; Kuz’min,V. L.; Kolloidn Zh. 1977, 39, 388. (12) Guggenheim, E. A. J. Phys. Chem. 1929, 33, 842. (13) Guggenheim, E. A.; J. Phys. Chem. 1930, 34, 1758. (14) Rybkin, Y. F. Russ. Chem. Rev. (Uspekhi Khim) 1975, 44, 1345. (15) Hall, D. G. J. Chem. Soc., Faraday Trans. 2 1978, 74, 405. (16) Mingins, J.; Pethica, B. A. J. Chem. Soc., Faraday Trans. 1 1973, 69, 500. (17) Damm, E. P. J. Electrochem. Soc. 1963, 110, 590. (18) Pallas, N. R.; Pethica, B. A. Langmuir 1985, 1, 509. (19) Kim, M. W.; Cannell, D. S. Phys. Rev. A 1976, 14, 1299. (20) Adam, N. K.; Harding, J. B. Proc. R. Soc. London, A 1932, 138, 419. (21) Pethica, B. A. Colloids Surf. A 1994, 88, 147. (22) Pallas, N. R.; Pethica, B. A. Langmuir 1993, 9, 361. (23) Klingler, J. F.; McConnell, H. M. J. Phys Chem. 1993, 97, 2962. (24) Dean, R. B.; Gatty, O.; Rideal, E. K. Trans. Faraday Soc. 1940, 36, 161. (25) Mingins, J.; Zobel, F. G. R.; Pethica, B. A.; Smart, C. Proc. R. Soc. London, A 1971, 324, 99. (26) Hall, D. G.; Pethica, B. A. Proc. R. Soc. London, A 1978, 364, 457. (27) Pethica, B. A.; Hall, D. G. J. Colloid Interface Sci. 1982, 85, 41.
Electric Field Effects on Air/Solution Interfaces
the surface tension of the solvent should be added to or subtracted from the calculated ∆Π to obtain the whole change in surface tension of a solution. However, it is clear that, with either sign of the change of the tension of pure solvent, the measurements of Jiang et al.5 would be unable to detect the changes in surface tension with applied field, since the experimental sensitivity (0.1 mN m-1) was insufficient by 2 orders of magnitude. Hayes4 also concluded that his experimental sensitivity was inadequate to detect the probable changes in surface tension. The data of Jiang et al. indicate a cmc of 6.2 mM for SDS, significantly lower than the accepted value. This discrepancy, probably due to impurities, will certainly affect the anticipated ∆Π and ∆Γ but is unlikely to affect the conclusions from this discussion unless unexpectedly large ∆V effects are observed with the experimental sample. The measurements of Schmid et al.6 have been criticized on experimental grounds17 and may certainly be discounted on the basis of the thermodynamic calculations given here. In general, the effects of applied field on the surface tension of water and aqueous solutions will be small and difficult to measure directly. The direct measurements made on insoluble spread monolayers3 were by micromanometry to a sensitivity of 25 nN m-1 but to a practical limit of about 50 nN m-1 due to other factors such as control of impurities. Changes in surface pressure up to 0.7 µN m-1 were measured with octadecyl sulfate and pentadecanoic acid monolayers at fields of 3 × 105 V m-1 in reasonable agreement with calculation from ∆V, Π, and Γ data in the compensation state. This agreement does not so much confirm eqs 1 and 2, which are necessary thermodynamic relations, but rather indicates that the experiments were adequately carried out at the current limits of micromanometric methods for insoluble monolayers. The Maxwell relations (eqs 1 and 2) predict that at a first-order phase transition in a monolayer (constant µ) electric fields applied to part of the monolayer will give very large changes in local Γ on the condition that ∆V for the whole monolayer (as measured with a large electrode covering the entire surface) varies with the average density of the monolayer in the phase transition region. Such changes have been observed.3 First-order transitions in one-component monolayers are characterized by constant surface pressure as Γ is varied, corresponding to the (28) From an analysis of the effect of temperature on ∆V for octadecyl sulfate monolayers at the A/W interface over a range of NaCl concentrations it was concluded (but not proven) that χ for dilute aqueous salt solutions is negative. Any further deduction that the water molecules have a net orientation with oxygen atoms toward the air is unsound, since χ includes the double-layer potential arising from the distribution of ions from the dissolved salt, the self-ionization of water, and the usually present CO2 in the surface ionic double layer. Electrophoresis of air bubbles shows negative potentials for NaCl solutions, with magnitude increasing at lower concentrations (80 mV at 10-5 M NaCl, pH 7.0),29 suggesting a negative χ for pure water. Further measurements on thoroughly pure CO2-free water are desirable. Recently, the wellknown asymmetric arrangement of surfactant molecules at liquid interfaces has been studied by second-harmonic measurements30 and, with more structural detail, by sum-difference frequency methods.31,32 Structural changes in monolayers and the local water are welldemonstrated by the sum-difference frequency method, but the direction of orientation of the water molecules is inferred from the anticipated double-layer fields and not obtained directly from the spectra. The evidence grows that χ for water is negative and probably large, but thermodynamic proof remains elusive. (29) Li, C.; Somasundaran, P. J. Colloid Interface Sci. 1992, 148, 587. (30) Ong, S.; Zhao, X.; Eisenthal, K. B. Chem. Phys. Lett. 1992, 191, 327. (31) Cragson, D. E.; Richmond, G. L. J. Am. Chem. Soc. 1998, 120, 366. (32) Cragson, D. E.; Richmond, G. L. Langmuir 1997, 13, 4804.
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coexistence of macroscopic areas of different molecular densities. These regions can be observed with a probe electrode a few millimeters in diameter, which will show fluctuations in apparent ∆V with position as the electrode passes over the large discrete patches of the two phases.3,18-22 Second-order transitions show a small increase in surface pressure as the monolayer density is increased, associated with the presence of micropatches or micellar clusters.3,19,20,22 The micropatches frequently observed by fluorescent or Brewster angle microscopy are in many instances the result of the presence of additional components or other experimental factors.21,22 Such monolayers will also undergo segregation if part of the monolayer is polarized, on the condition that ∆V for the whole monolayer varies with the average density of the monolayer in the phase transition region. This predicted field-induced segregation has been observed in monolayers showing microscopic patches.23 These observations on phase transition regions for which ∆V varies with the average density have the interesting consequence that in the compensation state with a plate covering the entire surface the condition of zero net charge requires that the aqueous surface is a patchwork of positive and negative charge regions. A further consequence of eqs 1 and 2 is that differences in local monolayer composition will occur when part of the surface is polarized in spread mixed films for which ∆V depends on the composition. This predicted effect has also been observed experimentally.3 Similarly, the composition of a mixed monolayer adsorbed from a multicomponent solution will be a function of applied field when the surface potential depends on the solution composition. Comparison of field polarization effects at air/water (or nonconducting oil/water) interfaces with electrocapillarity at the polarizable Hg/solution interface is useful. Fields of 106 V m-1 at the air/water interface are equivalent to changing the applied potential by about 50 µV near the electrocapillarity maximum, due to the large difference in capacity of the two experimental arrangements. The corresponding interfacial tension changes at the Hg/ solution interface would be beyond the sensitivity of typical electrocapillary instruments. Unlike the mercury electrocapillary case, polarization at the air/aqueous solution interface may not reduce the surface tension on either side of the zero charge state (electrocapillarity maximum; compensation state), since the surface pressure at the air/ solution interface can increase or decrease depending on the sign both of the polarization and of d∆V/dΓ (eq 1).7 Equations 1 and 2 are not applicable for interfaces between two conducting liquid phases which contain one or more ionic species in common. In this case, ∆V has no thermodynamic status.24,25 The apparent ∆V values observed with spread monolayers at such interfaces are nonequilibrium transients dependent on the specifics of the methods of measurement.25 In conclusion, the application of thermodynamic methods to relatively easy experiments on surface potential and surface tension as a function of solution composition allows quantitative estimates of the effect of applied fields on the surface pressure and density of adsorbed and insoluble monolayers, with potential utility in describing a variety of field-induced changes, particularly at phase transitions. The study of field-induced changes in surfaces will also be instructive for polarization effects in biological membranes.27 Acknowledgment. It is a pleasure to record the valued comments of Professor D. G. Hall. LA971142I
