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J. Phys. Chem. 1996, 100, 5004-5010
Transitional Behavior in Adsorbed Layers of n-Decanoic Acid at the Air/Water Interface† J. C. Earnshaw* and C. P. Nugent The Department of Pure and Applied Physics, The Queen’s UniVersity of Belfast, Belfast BT7 1NN, Northern Ireland
K. Lunkenheimer Max-Planck Institut fu¨ r Kolloid- und Grenzfla¨ chenforschung, Rudower Chausee 5, D-12489 Berlin-Adlerhof, Germany
R. Hirte Technische Fachhochschule Wildau, D-15745 Wildau, Germany ReceiVed: September 5, 1995; In Final Form: January 2, 1996X
The surface viscoelasticity of aqueous solutions of surface chemically pure n-decanoic acid has been studied by light scattering from thermally excited capillary waves of frequency between 5 × 104 and 9 × 105 s-1. The surface dilatational elastic modulus measured by light scattering, corresponding to such frequencies, agrees with the equilibrium value derived from the π-ln(c) variation for concentrations below 8 × 10-6 M and above 6 × 10-5 M, but systematically exceeds the equilibrium variation between these concentrations. This intermediate concentration range has been described as one of transition between two different states of adsorption (Lunkenheimer and Hirte, J. Phys. Chem. 1992, 96, 8683). The behavior of the elastic modulus can be explained by relaxation involving molecular reorientation within the adsorbed layer, with a relaxation time . 4 µs. Such reorientation would be entirely consistent with a change of adsorption state, such as has been suggested for this system. Other aspects of the surface viscoelasticity are briefly discussed.
1. Introduction Adsorption properties of n-alkanoic acids have been investigated since the advent of surface chemistry. Novel achievements in surface tension measurement1 and purity of surfactant solutions2,3 prompted an investigation4 of the adsorption properties of soluble n-alkanoic acids at the air/water interface. Their equilibrium surface tension-concentration (γe-c) isotherm could not be described satisfactorily by Frumkin’s surface equation of state over the whole concentration range. This led to a new approach to the surface equation of state for soluble amphiphiles.4 The basic idea is to consider the adsorption as occurring via two thermodynamically discriminable states, characterized by different surface areas for the adsorbed molecules. In this framework there is a certain range of intermediate bulk concentrations, the transition region, where the adsorption can be thought of as involving a mixture of the two different configurations of the amphiphiles. Below and above this range only one configuration is present in the adsorbed layer, and the adsorption isotherms can be well fitted by a single equation of state. This novel approach not only yielded a considerably improved fit to the γe-c isotherms but also revealed novel features of adsorption. To seek additional support for this idea we have measured the surface dilatational elastic modulus of aqueous n-decanoic acid solutions using surface light scattering.5 The surface elastic modulus should sensitively indicate changes in the state of adsorption provided that it can be determined accurately and that diffusional exchange with the bulk can be neglected during the deformation of the adsorption layer, as is the case for surface light scattering. Advantageously, can be determined most accurately when it is relatively small compared to the tension:6 † X
Dedicated to the memory of A. Scheludko. Abstract published in AdVance ACS Abstracts, February 15, 1996.
0022-3654/96/20100-5004$12.00/0
this occurs at relatively low surfactant concentrations, where the transition between the two molecular states is thought to be centered.4 2. Background 2.1. Surface Chemistry. 2.1.1. Surface Chemical Purity. Generally, materials produced by chemical synthesis contain at least traces of their parent compounds. In the case of amphiphiles, if the concentration of the parent is less than 1 or 0.1 mol %, the amphiphile can be considered as adequately pure as regards its bulk properties. However, when dealing with interfacial properties, such grades of purity may be quite inadequate, as the surface activity of the hydrophobic parent compound can be much greater than that of the amphiphile itself. The parent will then be preferentially enriched at the interface. It can thus be difficult to obtain reliable results on surface or interfacial properties if amphiphiles are used “as received”, as the adsorption layer will usually comprise a mixture of the main component and the hydrophobic parent compound. A standard for the state of purity of the adsorbed surface layer, called “surface chemically pure”, has been introduced to avoid this problem. This guarantees the necessary and sufficient conditions to enable reliable investigations of the amphiphile’s adsorption behavior. Methods for the production of such surface chemically pure surfactant solutions3 as well as reliable criteria for judging them2,7 have been published. 2.1.2. Surface States. Various workers have introduced the idea that adsorbed monolayers could exist in two different surface states.8-10 However, this was based on claims of a discontinuity or “break-point” in the variation of the equilibrium tension (γe) with concentration, attributed to a surface phase transition (cf. ref 11). Such break-points have never been observed when surface chemically pure materials were used, so the significance of these observations is open to some © 1996 American Chemical Society
Transitional Behavior of n-Decanoic Acid question. In fact, surface thermodynamics suggests that a firstorder phase transition should be characterized by a discontinuity in the surface pressure (π) versus surface area (A) dependence, rather than in the π-c (bulk concentration) variation,12 so that claims of a phase transition would have to be substantiated by determination of the surface excess adsorption Γs from the Gibb’s adsorption equation. However, even from the smooth variation of π with c, with continuously increasing curvature, it is clear that first-order phase transitions should not be expected for soluble surfactants. Moreover, in the present case of n-decanoic acid, the principle of corresponding states, which shows that the π-A variations of a homologous series of amphiphiles can be brought into agreement by increasing the temperature by about 10 °C for every reduction of two -CH2- groups in the acyl moiety,13 suggests that the temperature dependence of the π-A isotherms for myristic acid on 0.01 M HCl14 can be interpreted as indicating that no phase transition should be expected for n-decanoic acid monolayers at room temperature: films of n-decanoic acid at about 20 °C should display behavior resembling that of myristic acid above 40 °C. Such considerations led4 to the suggestion that the adsorption of soluble surfactants could be described as occurring via a surface mixture continuously passing over from one surface configuration to another. The equilibrium tension γe-c isotherm is fitted by a sum of two established isotherms, Traube’s law at low c and Frumkin’s equation at high c, weighted in accord with a transition function which tends to 1 for c f 0 and to 0 for c f cmax.4 This idea is quite successful. Generally, the transition interval covers only a certain, rather narrow concentration range, the width of which is determined by the molecular geometry and interactions of the amphiphiles. Thermodynamic considerations provide further evidence for the existence of two different surface configurations which lead to transitional behavior. The two surface configurations can thus be discriminated by physically reasonable differences in the corresponding thermodynamic standard states.4 Mathematically, there are various ways to describe the transitional behavior. A Heaviside step function is generally used to describe a sharp transition, and a symmetrically smeared step function of variable width (e.g., the tanh function or polynomials) is convenient for a real, macroscopic transition of as yet unknown physical character. While such a transition function is mathematically convenient, involving as it does only two parameters, it does not, of course, reveal anything about the underlying physical mechanism of the transition. However, we have succeeded in describing the transition function simply by the surface concentration ratio of the two different surface configurations within the transition interval.15 In this way additional support for the molecular mechanism driving the transition is provided. The molecular mechanism of the transition will affect various available experimental probes in different ways. If, as has been suggested,4 the transitional behavior arises from reorientational processes in the adsorbed layer, then on short enough time scales it should be reflected in the surface elastic modulus, as suggested by Scheludko.16 Surface light scattering probes the elasticity on such time scales. 2.2. Surface Light Scattering. The surface of a liquid supporting a molecular film sustains various modes of fluctuation,17 which are excited by thermal excitation. Two are of present concern: capillary waves and dilatational waves. The capillary waves are primarily governed by the surface tension γ, while the dilatational waves are subject to the surface dilatational elastic modulus . In principle, is equivalent to
J. Phys. Chem., Vol. 100, No. 12, 1996 5005 the Gibb’s modulus. However, the surface waves are sensitive to surface properties appropriate to the frequencies of the capillary fluctuation, which may differ from their equilibrium values due to relaxation processes. This is discussed in more detail below. It is useful to note that where the surface waves propagate as damped oscillations, the complex wave frequencies (ω) of the capillary mode of wavenumber q can be approximated:18,19
ω≈
x
γq3 2ηq2 +i F F
(1)
where γ, η, and F are respectively the surface tension, viscosity, and density of the liquid. This formula is a useful indicator of the dependence of ω upon q and the system properties for the capillary waves. Dissipative effects within the film can be incorporated into the formalism by expanding the relevant surface moduli as positive definite response functions:20
γ(ω) ) γ0(ω) + iωγ′(ω)
(2)
(ω) ) 0(ω) + iω′(ω)
(3)
where γ′ acts primarily to increase the damping of the capillary waves and ′ that of the dilatational waves. Neither of these surface viscosities is that normally studied, which relates to shear within the surface plane. γ′ relates to shear normal to that plane, and ′ to dilatation within it. However, it should be noted that the capillary waves exert a uniaxial stress upon the surface film, so that the relevant dilatational modulus is the sum of the moduli governing pure (hydrostatic) dilatation and shear, respectively. It should be noted that all the surface properties of eqs 2 and 3 may be frequency dependent if the surface film displays viscoelasticity. We will restrict the notation γ0(ω) and 0(ω) to the light-scattering values of the tension and dilatational elastic modulus to emphasize this point. The tension is always the thermodynamic quantity determined by equilibrium methods. However, as Goodrich20 showed, a surface viscoelastic modulus governing shear normal to the surface is additive to the tension. The elastic part of this modulus is subsumed into γ0(ω) of eq 2. The thermally excited capillary waves on a liquid surface can be studied by quasi-elastic light scattering.21 They are also coupled to the dilatational waves,22 and therefore the surface light scattering is sensitive to dilatational surface properties. The main observable consequence of the mode coupling is a resonance between the surface modes at which the capillary wave damping is considerably increased above the value for pure water.22 This occurs at about 0 ∼ 0.16γ0. Far above the resonance the effects of upon the capillary waves is much reduced,23 and so its precise determination becomes difficult. This does not affect the main results of present interest. 3. Experimental Section We have studied adsorption layers of surface chemically pure n-decanoic acid dissolved in various concentrations in aqueous 5 × 10-3 M HCl to suppress dissociation. The surface tensions were determined at 23 °C using a Lauda ring tensiometer, taking into account the modifications necessary when this method is applied to surfactant solutions.1 Before starting tension measurements the surface was aspirated to provide reliable initial conditions; measurements were continued until the constant equilibrium surface tension γe was established. Figure 1 shows the fit to the measured concentration dependence of γe as well
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Earnshaw et al.
Figure 1. Variation of the equilibrium tension with concentration for n-decanoic acid (solid line), together with the Traube and Frumkin isotherms used in the fitting (dashed lines). The concentration dependence of the transitional function is also shown.
as the contributions to the fit from each of the two isotherms. The transition function is also shown. It reaches 0.5 at c ) 1.25 × 10-5 M and extends from 3.5 × 10-6 to 5 × 10-5 M. The same solutions were used in the light-scattering experiments, also carried out at 23 °C. All solutions were equilibrated over at least 3 h before commencement of light-scattering observations. 3.1. Surface Light Scattering. Our surface scattering setup has been described in detail elsewhere.5 In brief, light from an Ar+ laser (λ ) 488 nm) was incident upon the liquid surface, where it was scattered by thermally excited capillary waves. Capillary waves of given wavenumber (q) scatter light at a particular angle from the specular reflection. Photon correlation was used to determine the temporal evolution of the scattered light, rapid data acquisition methods24 yielding data of low noise (typically e. Scheludko points out that dyn > st because for t , τr the free area available must be smaller than for t . τr:16 if the molecules do not have time to reorientate, compressing the film by a given ∆Γs will not lead to a corresponding change ∆A. Without further theoretical work, the more detailed frequency dependence of 0 due to such molecular relaxation remains essentially unknown.
Transitional Behavior of n-Decanoic Acid
Figure 7. Variation of the diffusive time scale τd with concentration. See text for discussion.
st (i.e., e) characterizes the state of the adsorption layer when there is no exchange of matter with the bulk solution but when the structural equilibrium within the adsorbed layer is fully established, and it can be computed from the surface equation of state describing the γe-c isotherm. The e-c variation carries no more information on the structure of the adsorbed layer than that provided by this isotherm. However, dyn corresponds to the state of the adsorption layer on time scales such that orientational relaxation of the adsorbed amphiphiles cannot have occurred, so that structural equilibration is impossible. Thus, dyn reflects the instantaneous state of the adsorbed layer. How do the present data fit into the scenario just outlined, involving two relaxation times τd and τr? Of the two processes involved, the diffusional exchange is susceptible to detailed analysis. τd can be computed from eq 7, taking dΓs/dc from the γe-c isotherm (Figure 1) and assuming D ) 10-5 cm2/s. Figure 7 shows τd as a function of c. Now the frequency of the perturbations of Γs is just that of the capillary waves driving the dilatational fluctuations (ω0, see Figure 2). Combining the variations shown in Figures 2 and 7, we see that even for the lowest frequencies studied (at q ) 403 cm-1) ω0τd . 1. The adsorbed layer of n-decanoic acid is therefore essentially insoluble at all frequencies studied in the present experiments, which probe the film’s dynamic response. The effectively insoluble nature of the present surface layer may lead to differences from expectation based on equilibrium studies. In particular, the general view that adsorbed molecular films do not exhibit phase transitions such as those characteristic of spread monolayers is based on the equilibrium behavior of the films. It would not be surprising if the conventional wisdom were inappropriate to the present experiments. With respect to the dynamic surface elastic modulus the behavior of the n-decanoic acid films strongly resembles that of various spread monolayers,26,33 in which transitions between condensed and vapor phases occur. Now, for frequencies from 5 to 150 Hz, 0 found using the oscillating bubble method37 for adsorbed layers of n-decanoic acid does agree exactly with the variation predicted by the diffusional exchange, e being taken from the γe-c isotherm using the surface equation of state. However, the light-scattering probe of surface viscoelasticity involves much higher frequency
J. Phys. Chem., Vol. 100, No. 12, 1996 5009 deformations of the surface, and as just outlined, one would expect that the surface layer would appear to be effectively insoluble. From Lucassen and van den Tempel’s formulation for the effects of diffusive exchange upon 27 the value of 0 expected at capillary wave frequencies should exceed 0.94e at all concentrations studied. Thus, if diffusional exchange were the only relaxation process involved, 0(ω) should be virtually indistinguishable from e at all c. Figure 5 confirms that, averaged over all q (i.e. ω0), 0(ω) never falls significantly below e at any concentration. The comparison is not very reliable at large c, where the precision of determination of the rather large values of the light-scattering 0(ω) is relatively poor. Diffusional exchange is thus far slower than the perturbations of the film due to the capillary waves, which occur on time scales of the order of 1/ω0 (j10-5 s, cf. Figure 2). However, this appears not to be the case for intrafilm relaxation. An adsorbed molecular layer in equilibrium with respect to diffusional exchange with the bulk phase, but not with respect to structural relaxation, will display a dynamic surface elastic modulus exceeding e. This is exactly what we observe in the transitional region, for concentrations of n-decanoic acid between 8 × 10-6 and 5 × 10-5 M. We infer that in this transitional region (cf. Figure 1) some relaxation processes other than diffusive exchange must occur, with relaxation time less that 1/ω0 (cf. Table 1). The frequency of capillary waves of given q remains roughly constant as c is increased through 8 × 10-6 M (Figure 2), so the time scale characterizing the relaxation must increase substantially at this point. We infer that τr, the time scale for molecular reorientation, here becomes significantly greater than ω-1 0 (i.e. ω0τr . at lower concentrations 1), having been much less than ω-1 0 (i.e. ω0τr , 1). At no concentration is there any evidence of any q dependence of the light-scattering values of 0(ω). Thus, between 8 × 10-6 and 5 × 10-5 M, τr . 14 µs (i.e. the reciprocal of the lowest capillary wave frequency observed). For c < 8 × 10-6 M or > 5 × 10-5 M, either τr must be much less than the reciprocal of the highest ω0 seen (i.e. τr , µs) or the faster relaxation must be negligible. The higher values of dyn are only found within the transition region, within which there is “a gradually proceeding alteration from a flat to an upright position within the adsorption layer”.4 Indeed this suggestion can be substantiated on molecular area grounds. The discontinuous jump in 0(ω) relative to e occurs for c between 7.5 × 10-6 and 8 × 10-6 M (Figure 4), corresponding to an area per molecule in the adsorbed film between 461 and 513 Å2. We thus consider the transition as occurring at the middle of this range, at 487 ( 26 Å2. This area is rather large: can we correlate it with any characteristic size of the n-decanoic acid molecules? Using known van der Waals radii and bond angles, we may estimate the effective length of the molecule as between 11.9 and 12.9 Å (depending on whether the -OOH group is included or not). Thus, the area swept out by an n-decanoic acid molecule rotating in the surface about the head group would be between 445 and 520 Å2, in quite good accord with the value just cited. We recall that the basic concept underlying the present investigation is that the n-decanoic acid molecules in the surface film exist in two different states. At large areas per molecule they are widely separated on the surface and presumably essentially independent, whereas at small areas they must be rather close packed and interact relatively strongly. It is apparent that at about 8 ×10-6 M, where the jump in 0(ω) for n-decanoic acid occurs, the area per molecule is such that the molecules in the film just begin to influence each other. We
5010 J. Phys. Chem., Vol. 100, No. 12, 1996 may associate this with the first appearance of molecular reorientation in the film, as the molecules change from being recumbent to a more erect state. In such a situation molecular relaxation processes might well change their character or relaxation times. At very low c the molecules probably never leave the flat state, so that effects due to reorientation are likely negligible, whereas at the upper end of the transitional region the molecules will essentially all be in the more erect state and any reorientation is probably rather fast. In the latter case, if Scheludko’s reorientational mechanism is indeed relevant, the dynamic surface behavior characterized by dyn > e should vanish. This is observed for c > 5 × 10-5 M, exactly as expected. Furthermore, as the differences between 0(ω) and e in the transition region are attributable solely to reorientation in the adsorption layer, it would be expected that there should be a more or less pronounced maximum in the difference 0(ω) e roughly in the middle of the transition region or, in terms of the two-state adsorption model, at the transition concentration ctr.4 This suggestion again accords with observation (Figure 5). This discussion has been based on Scheludko’s arguments regarding molecular reorientation. These appear to parallel arguments concerning mixed monolayers recently advanced by Serrien et al.38 In the present context the mixture comprises the two adsorption states of the amphiphile. The present conclusions regarding the time scale for reorientation of molecules could equally well be couched in terms of the rate of transition between the two adsorption states. 6. Conclusions We have shown that light scattering from thermally excited capillary waves on the surfaces of aqueous solutions of n-decanoic acid yields values of the dynamic surface elastic modulus which exceed the equilibrium value over a significant range of concentration. The deviations occur just within a region which has been described as one of transition between two different states of adsorption4 and may be regarded as supporting that description. Secondly, the deviations of 0 from the equilibrium e are exactly as expected if relaxation, such as molecular reorientation, occurred within the adsorbed layer with a time constant less than the inverse of the capillary wave frequency.16 It should thus be possible to experimentally explore such relaxation times in adsorbed layers of surfactant. The equilibrium properties of the n-decanoic acid adsorbed layers originally led to the suggestion that the layers underwent a change of state. This effect was rather subtle and could not really be characterized as a phase transition, in accord with the accepted belief4 that adsorbed layers do not exhibit phase transitions in the same way as spread monolayers. However, the dynamic surface dilatational elastic modulus displays behavior exactly as that found for spread monolayers showing a condensed to vapor phase transition.26,33 It therefore seems apparent that, when probed on time scales less than about 20 µs, under conditions in which the n-decanoic acid surface layer is effectively insoluble, the adsorbed layer does undergo a change in state similar to that which is observed of insoluble monolayers during the phase transition. The quasi-static adsorption isotherm provides a good description of the dynamic behavior of an adsorbed film provided the perturbations involved are of rather low frequency (
