J. Phys. Chem. B 2000, 104, 9179-9185
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Capillary Wave Phenomena at the Air Interface of Aqueous Dispersions of a Linear Polystyrene-Poly(ethylene oxide) Diblock Copolymer Marcella Alexander† and Randal W. Richards* Interdisciplinary Research Centre in Polymer Science, and Technology UniVersity of Durham, Durham DH1 3LE, U.K. ReceiVed: February 9, 2000; In Final Form: July 11, 2000
Aqueous dispersions of a linear diblock copolymer of polystyrene and poly(ethylene oxide) that forms welldefined micelles have been investigated by surface light scattering. The concentrations examined range from below the critical micelle concentration (3 × 10-5 g mL-1) to well above it (1 × 10-4 g mL-1). Correlation functions of the scattered light have been analyzed to provide capillary wave frequency and damping, surface tension, dilational modulus, and dilational viscosity. The surface tension gradually decreases with time for all dispersion concentrations, but after 24 h all have the same surface tension. This is interpreted to mean that the surface concentrations of each dispersion are identical. The equilibrium dilational moduli increase as the bulk concentration increases, and this is attributed to differences in the subsurface stratified layer structure. From the frequency dependence of real and imaginary dilational moduli, the mechanism suggested for the approach to equilibrium is the breakdown of micelles followed by the adsorption of individual copolymer molecules at the surface after diffusing through the brushlike layer of poly(ethylene oxide) at the surface and then the re-formation of aggregated structures on the surface.
Introduction Amphiphilic linear diblock copolymers of sufficiently low molecular weight and compositional asymmetry form micelles when dispersed in a selective solvent.1 The critical micelle concentration (cmc) for such diblock copolymers can be extremely small when the repulsive potential between dispersion medium and one of the blocks is strong, a situation that occurs when a linear diblock copolymer of polystyrene (PS) and poly(ethylene oxide) (PEO) is dispersed in water. The majority of the work reported on block copolymer micelles is focused on the structure, organization, and thermodynamics of the dispersions, and little has been published on their interfacial behavior, although many clearly have surfactant ability. We discussed the organization of a PS-PEO linear diblock copolymer at the air-aqueous dispersion interface in an earlier publication.2 Diblock copolymer micelles were found to be present at all times at the air-dispersion interface, even when the bulk concentration was below the cmc. For high concentrations (i.e., above the cmc), a somewhat disordered layer structure was evident, suggesting a second stratum of micelles below the interfacial layer. Fluid interfaces are subjected to continual thermally driven stochastic fluctuations collectively named capillary waves.3 A surface excess layer or a spread film increases the damping of the capillary waves due to the cohesive resistance to changes in the area of the interface wrought by the capillary waves. The height fluctuations of the interface induce longitudinal fluctuations of the concentration of the surface excess layer or spread film, and these dilational waves are opposed by the dilational elasticity of the surface excess layer or spread film.4 The capillary and dilational waves are orthogonal to each other but are coupled, and observation of
the capillary wave phenomena gives access to dilational moduli (vide infra).5 Here we report the surface viscoelastic moduli for aqueous dispersions of a PS-PEO diblock copolymer determined by surface quasi-elastic light scattering (SQELS) on dispersions with bulk concentrations from just below the cmc to considerably above the cmc. For one selected dispersion concentration (above the cmc), the dependence of the surface viscoelastic parameters on capillary wave frequency has been examined. The major feature was the extremely long times needed for the surface viscoelastic moduli to reach their equilibrium values. Times longer than 8 h were required for all dispersion concentrations. The paper is organized in the following way: The basis of capillary wave dispersion and SQELS are described as well as the manner by which physical parameters are extracted from the data. The molecular features of the block copolymer used and experiments performed are described. Major features of the results obtained are commented on in the Results, and these are also discussed in relation to the known surface organization and current theories of surface moduli. Surface Quasi-elastic Light Scattering. The stochastic fluctuations of a free liquid surface can be Fourier decomposed to a set of surface waves with wavenumbers represented by q and each wave having a complex propagation frequency ω ) ωo + iΓ, where ωo is the real frequency and Γ the wave damping.5-8 The complex frequency is related to the wavenumber via the dispersion equation, D(ω). The parameters of the liquid and its surface combine to ensure that D(ω) ) 0, and in the presence of a surface film the dispersion equation is given by9
D(ω) ) * To whom correspondence should be addressed. E-mail: R.W.Richards@ Durham.AC.UK. Fax: 44-191-374 3153. † Present address: Physique Experimental, Universite ´ de Fribourg, Chemin du Musee, CH-1700 Fribourg, Switzerland.
[
][
q2 γq2 gF ωF + + iη(q + m) + ωo ωo ω q
]
iη(q + m) + [η(q - m)]2 (1)
10.1021/jp000514k CCC: $19.00 © 2000 American Chemical Society Published on Web 09/09/2000
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where η and F are the viscosity and density of the fluid and m ) q[1 + iωF/(ηq2)]1/2 for Re(m) > 0. In eq 1, γ is the surface tension and is the dilational modulus, and the latter is a complex term including a dilational viscosity, ′, as an additional energy dissipation mode in the film:
) o + iωo′ When a surface film or surface excess layer is present, the dispersion equation has two roots, one corresponding to the capillary wave, and the other corresponding to the dilational wave. Although the capillary waves have only a small amplitude (∼2 Å), they are efficient scatterers of light, and the power spectrum of this scattered light is demonstrated by the following: 5,8,9
P(ω) )
[
]
kBT iωoη(m + q) + q2 Im πω D(ω)
Figure 1. Heterodyne correlation function obtained for a copolymer dispersion concentration of 5 × 10-5 g mL for q ) 339 cm-1 at 298 K.
(2)
The Fourier transform of this power spectrum is the correlation function of the scattered light. Unbiased estimates of γo, o, and ′ can be obtained by using these as adjustable parameters to fit the theoretical form of the correlation function to experimental data.7,10 The parameters that are directly observable in SQELS are the capillary wave frequency, ωo, and damping, Γ. These can be obtained from the experimental data by fitting an exponentially damped cosine function to the experimental data. More extensive details regarding the power spectrum of light scattered by capillary waves and the analysis of the signal to provide surface viscoelastic parameters have been frequently provided elsewhere.5-7,11 Experimental Section Linear Diblock Copolymer. The linear diblock copolymer of PS and PEO was used in the earlier2 neutron reflectometry investigation of the surface organization in aqueous dispersions of the copolymer. The number-average molecular weight was 8490 g mol-1 and M h w/M h n ) 1.03 as determined by size exclusion chromatography using poly(ethylene oxide) standards and chloroform as the solvent. The molar composition determined from 1H NMR was 1:12 styrene to ethylene oxide. This corresponds to a PS block degree of polymerization of ∼13 and a PEO block of 160 EO units. Aqueous dispersions were made using ultrapure water (Elgastat UHQ), the initial dispersion concentration being 2.5 × 10-3 g mL-1. Lower concentrations were made by taking aliquots and diluting, the concentration range covered being from 3 × 10-5 to 1 × 10-4 g mL-1 of PS-PEO diblock copolymer dispersed in water. All dispersions were made up at least 24 h before they were examined by surface quasi-elastic light scattering. Surface Quasi-elastic Light Scattering. The equipment used to obtain heterodyne correlation functions for light scattered by the capillary wave fluctuations of the dispersion surface has been described elsewhere.12 The light source was a solid-state frequency doubled laser with a wavelength (in vacuo) of 532 nm and a power of 95 mW. Scattered light (mixed with reference light) was focused onto the photocathode of a photomultiplier tube connected to a Brookhaven Instruments correlator. For the first series of experiments, the scattering vector, q, was constant at 339 cm-1. Each dispersion of different concentration was placed in a PTFE trough, and the transmission
grating was imaged on the liquid surface. Correlation functions were then collected at hourly intervals for up to 8 h. The dispersion was allowed to stand overnight, and further correlation functions were collected for times corresponding to 23 and 24 h after the formation of the liquid surface. In a second series of experiments, the q dependence of the capillary wave properties was examined for a dispersion with a PS-PEO diblock copolymer concentration of 7.5 × 10-5 g mL-1. After placement of the dispersion in the trough, correlation functions over the whole q range accessible (∼300-1200 cm-1) were immediately collected. Further correlation functions for each q were collected at intervals over the succeeding 24 h. Data Analysis. Each correlation function was analyzed in two ways. First, the real frequency (ωo) and damping (Γ) of the capillary waves were obtained from the fit of a phase-shifted cosine function (plus instrumental factors) to the normalized correlation function. Second, the direct spectral analysis outlined earlier and developed by Earnshaw7 was applied to extract the values of the surface viscoelastic moduli. The transverse shear viscosity that has often been included in such analyses was fixed at zero in compliance with the theoretical analysis of Buzza et al.13 for polymers at fluid interfaces. Results A. Concentration Dependence of Capillary Wave Properties and Surface Viscoelastic Moduli. A typical heterodyne correlation function obtained by SQELS is shown in Figure 1, the line being a fit to the data obtained by the direct spectral analysis outlined earlier. Over an 8 h period, the capillary wave frequency decreases continuously; this decrease is more marked for the higher concentration dispersions (Figure 2). Since the capillary wave frequency for the freshly formed surface (time ) 0) is lower than that of clean water at this wavenumber (5.4 × 104 s-1), it is evident that the freshly formed air-dispersion interface is already populated with some copolymer. Equilibrium values of the wave frequency were obtained within 24 h after formation of the surface. Damping increases over 8 h for the most dilute dispersions (3 × 10-5 to 7.5 × 10-5 g mL-1), again reaching equilibrium values within 24 h after the formation of the surface (Figure 3). The two most concentrated dispersions show negligible change in the damping with age of the dispersion surface after an initial sharp increase over the first hour. For all dispersions, the capillary wave damping 24 h after creation of the surface is ca. twice that for clean water at the same wavenumber.
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Figure 2. Capillary wave frequency variation as a function of time for all block copolymer dispersions. The concentrations (in g mL-1) are as indicated. The lines are smoothed approximations to the data as “guides to the eye”.
Figure 3. Capillary wave damping dependence on surface age for block copolymer dispersions with concentrations (g mL-1) as marked.
The dependence of the three surface moduli on the age of the surface is shown in Figure 4. The surface tension (Figure 4a) of each dispersion falls continuously for 8 h, but all have approximately the same surface tension 24 h after surface formation. The dispersion concentration of 7.5 × 10-5 g mL-1 has a lower surface tension after 8 h than it does after 24 h. Over the initial 8 h aging period, the dilational modulus increases for all dispersion concentrations (Figure 4b) and each dispersion (except the two highest concentrations) has a different dilational modulus 24 h after formation of the fresh surface. Dilational viscosities (Figure 4c) initially have positive values that decrease with increasing surface age and after 24 h are either zero (two lowest concentrations) or negative (all higher concentrations). The equilibrium values (i.e., 24 h after formation of the surface) of each of these moduli are plotted as a function of dispersion bulk concentration in Figure 5. Although surface tensions are all essentially identical at 60 ( 1 mN m-1, the error on the individual data points means that a linear least-squares line drawn through the data may be pertinent. This is the solid line in Figure 5a, and, assuming the Gibbs adsorption equation applies, the surface concentration of PS-PEO diblock copolymer varies from (2 ( 1) × 10-7 mol m-2 to (8 ( 4) × 10-7 mol m-2. The dilational modulus increases with increased dispersion concentration up to a concentration of 9 × 10-5 g mL-1 that has the same dilational modulus as the dispersion with 1 × 10-4 g mL-1 of PS-PEO diblock copolymer. Dilational viscosities generally become increasingly negative as the concentration of the block copolymer dispersion increases. B. Wave Number Dependence of Frequency, Damping, and Surface Viscoelastic Moduli. For a PS-PEO diblock
Figure 4. Dependence of surface viscoelastic moduli on the age of the aqueous block copolymer dispersions with concentrations (g mL-1) indicated: (a) surface tension, the lines through the data for the lowest and highest bulk concentrations are guides to the eye indicating the general behavior for all dispersion concentrations; (b) dilational modulus; (c) dilational viscosity.
copolymer dispersion concentration of 7.5 × 10-5 g mL-1, SQELS data were collected for each accessible wavenumber, and the dependence on the age of the dispersion surface at each q value was obtained. Figure 6 shows the dependence of the capillary wave frequency and damping on q. As anticipated, the frequencies are less than that of clean water because of the relation between capillary wave frequency and surface tension:
ωo =
x
γq3 F
Damping is always greater than that of water over the whole q range and appears to have a stronger dependence on q for values greater than 900 cm-1. A maximum in surface tension at q = 600 cm-1 is evident for all times after creation of the fresh surface (Figure 7a), whereas the dilational modulus initially
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Figure 6. Wavenumber dependence of capillary wave frequency and damping for various times after formation of the surface of a PSPEO block copolymer aqueous dispersion with a concentration of 7.5 × 10-5 g mL-1.
Figure 5. Concentration dependence of equilibrium values of surface viscoelastic moduli of the block copolymer dispersions: (a) surface tension, solid line is a least-squares fit to the data; (b) dilational modulus; (c) dilational viscosity.
exhibits a minimum at q = 600 cm-1 that becomes shallower as the age of the surface increases, and after 24 h a maximum in the dilational modulus is evident (Figure 7b). At low q and for short aging times, the dilational viscosity is negative. A positive maximum at q ∼ 600 is evident for these short times, but at higher q values the dilational viscosities all collapse to essentially the same small negative values. The equilibrium values, i.e., after the surface has aged 24 h, are collected in Figure 8 and plotted as a function of the capillary wave frequency. Surface tension and dilational modulus both have maximum values at a capillary wave frequency of 1.5 × 105 cm-1, whereas the dilational viscosity decreases continuously from positive values at low frequency to negative values at high capillary wave frequencies. Discussion Before discussion of the surface viscoelastic properties of these dispersions, it is pertinent to summarize the structural
Figure 7. Wavenumber dependence of parameters: (a) surface tension and (b) dilational modulus for a block copolymer dispersion of concentration 7.5 × 10-5 g mL-1 for increasing times after surface creation.
information that is known for the air-dispersion interface and the micelle in the bulk of the dispersion. The cmc of the PS-PEO linear diblock copolymer in water is 3.5 × 10-5 g mL-1, and small angle neutron scattering on these dispersions shows they have a core-shell structure with a polystyrene core radius of 43 Å. The poly(ethylene oxide) shell thickness is approximately 140 Å, and each micelle contains some 220 diblock copolymer molecules.14 For the concentrations used here, there is no long range ordering of the micelles in the dispersion. Because the radius of gyration of PEO of the same molecular weight as the PEO block in the copolymer would be expected to be ∼40 Å, the PEO corona of the micelle is stretched. From the areal density of PEO blocks attached to the PS core, the PEO blocks are in the stretched
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Figure 9. Sketch of the surface organization in the block copolymer dispersions deduced from neutron reflectometry data. The bulk concentration of the dispersion increases from (a) to (c).
of the dispersion for all dispersion concentrations including those below the cmc. Time Dependence of Surface Tension. A change of surface tension over 24 h is observable using classical tensiometry on the dispersions, and the final, essentially zero frequency surface tension values are marginally higher than the values obtained by SQELS after the surface has aged 24 h. The major aspect of the SQELS data is that a dynamic surface tension and dilational modulus are observed for all the dispersion concentrations. Unlike many other examples where dynamic surface tension behavior is observed, for the PS-PEO dispersions over a 3-fold bulk concentration range the final surface tension values of all dispersions are very similar to each other and the final surface concentration are also within a narrow range. The time dependence of surface concentration, i.e., the kinetics of adsorption to the air interface, is frequently based on forms of the expression first given by Ward and Tordai,15
Γ ) 2cb(Dt/π)1/2
Figure 8. Capillary wave frequency dependence of the equilibrium values of the surface viscoelastic moduli for a block copolymer dispersion with a concentration of 7.5 × 10-5 g mL-1: (a) surface tension; (b) dilational modulus; (c) dilational viscosity.
wet brush regime; i.e., the corona of the micelle is a brushlike layer of PEO, the molecules of which are strongly stretched. Neutron reflectometry data2 suggested that at the airdispersion interface this core-shell structure was retained as “half micelles”. As the concentration of the bulk dispersion increased, the PEO corona stretches deeper into the aqueous dispersion. The interfacial structure is summarized in the schematic sketch of Figure 9, and it is noteworthy that for the dispersion with a bulk concentration of 10-4 g mL-1 the PEO layer thickness was 140 Å, i.e., almost identical with the corona thickness of micelles in the bulk dispersion. The surface organization deduced from the reflectometry data is essentially the equilibrium structure because of the length of time needed to collect reflectometry data with acceptable statistics. Perhaps the most pertinent fact for the experiments discussed here from these reflectometry data is the observation of micelles at the surface
where Γ is the surface concentration when the bulk concentration is cb and the species have a diffusion coefficient D. Since the surface tension is directly proportional to the surface concentration, the slopes of surface tension plotted as a function of (time)1/2 for each dispersion should scale with each other in the same ratio as the bulk concentrations. This is not the case for our values of surface tension; all the slopes were identical at approximately -0.018 mN m-1 s-1/2 except for the dispersion with a concentration of 7.5 × 10-5 g mL-1, which had a slope of approximately -0.04 mN m-1 s-1/2. Evidently, the diffusionlimited process of Ward and Tordai does not prevail here and moreover the observation of the same slope for all concentrations (bar one) suggests that the same mechanism is at work in each dispersion. An empirical expression16 has been used to describe the variation of surface tension with time:
γ(t) ) γe + (γo - γe)/(1 +(t/τ)n) where γe is the equilibrium surface tension for the dispersion for which the freshly made surface tension is γo and τ is a “relaxation” time for the surface pressure to reach a value of (γo - γe)/2. Applying this equation to our surface tension data gave the same γe value for all dispersions of 59.2 ( 0.7 mN m-1. The relaxation time decreased from ∼2.3 × 105 s for the
9184 J. Phys. Chem. B, Vol. 104, No. 39, 2000 most dilute dispersion to ∼1 × 104 s for the most concentrated. No trend could be discerned in the values of the exponent, n, the value being between 1 and 3 except for the dispersion with a concentration of 7.5 × 10-5 g mL-1 where n ) 5 was obtained. Perhaps the widest ranging consideration of dynamic surface phenomena has been that of van den Tempel and LucassenReynders.17 Four possibilities of relaxation were discussed: (1) diffusional exchange between the surface and the bulk, (2) micellar breakdown, (3) exchange with multilayer particles, and (4) adsorption-barrier processes. Of particular relevance to the dispersions under consideration here is the researchers’ conclusion that slow equilibration of the surface is most probably due to structure formation in the surface. Of the four mechanisms cited by van den Tempel and Lucassen-Reynders, we can dismiss mechanisms 1 and 4 above. The brief consideration given earlier to the Ward and Tordai equation does not support diffusion control, and the absence of multilayer micelles (vesicles or lamellar sheets) means that mechanism 4 is not relevant. Because we have micelles in the dispersion, consideration of mechanism 2 is clearly pertinent. The adsorption-barrier process is also relevant because it has been cited as a possible source for the observation of negative dilational viscosities.18 These two mechanisms can be discriminated from each other, in principle, by the frequency dependence of the ratio of the imaginary dilational modulus (≡ωo′) to the real part of the dilational modulus (o). Before turning attention to this aspect, we need to consider other aspects that will be important to the understanding of the relaxation process. Resonance and Negative Surface Viscosities. We noted earlier that the capillary and dilational modes are orthogonal to each other and this can lead to resonance, i.e., a coincidence of the real frequencies of each mode. This produces a maximum in the damping and the condition for resonance is o/γo = 0.16. At the resonance condition, the coupling between the modes is a maximum and SQELS data are most sensitive to the dilational moduli. From the values of o and γo obtained, all dispersions with PS-PEO concentrations equal to or greater than 7.5 × 10-5 g mL-1 pass through the resonance condition and it appears that the dispersion with a concentration of 7.5 × 10-5 g mL-1 is closest to resonance when the surface is at equilibrium. The resonance condition provides the greatest opportunity for transfer of energy between the two modes, and this possibility is relevant to the observation of negative dilational viscosities. The dilational viscosities are systematically negative for the dispersions with concentrations of 5 × 10-5 g mL-1 or greater after the surface has aged for 24 h. Furthermore, the dilational viscosity becomes increasingly negative as the capillary wave frequency increases. The dilational viscosity is a measure of the energy dissipation in the surface film that increases the dilational wave damping. Consequently, a negative dilational viscosity suggests a reduction in the damping relative to the situation when ′ ) 0; i.e., the dilational waves are becoming destabilized. Negative dilational viscosities have been observed in other systems that have considerably different features from those that pertain here,12,19 and the consequences and characteristics of the surface waves associated with such values have been discussed by Earnshaw and McLaughlin.20,21 In some cases, the variation of dilational viscosity with concentration can be quite distinctive. It was the observation of such values that prompted a re-examination of capillary and dilational wave theory which introduced some additional factors. However, the dimensional requirements that need to be satisfied to make these additional factors important are far in excess of those that apply
Alexander and Richards for block copolymer micelles, and their incorporation into the dispersion equation is not justified. The form of the dispersion equation used was developed for spread monolayers and seems to account accurately for all the processes that take place when such a thin film is perturbed by capillary waves. For the surface layer of these block copolymer dispersions, the existence of a stratified organization of micelles may introduce other factors that are not incorporated into the dispersion equation. Consequently, the negative dilational viscosities may result from the fitting of an inappropriate equation to data which do not include all the processes influencing dilational wave damping. Under these circumstances, the dilational viscosities can only be regarded as effectiVe values. Essentially, negative dilational viscosities are symptomatic of a destabilization of the dilational waves. One possible mechanism that may be a source of this destabilization is a Marangoni effect due to the presence of a potential barrier between the air-liquid interface and the adsorption of the copolymer from the bulk.18,19 The Marangoni effect has negligible effect on the transverse capillary waves and, depending on the frequency, can be a stabilizing or destabilizing influence on the dilational waves. Consequently, to progress further, we need to consider the capillary wave frequency dependence of the surface viscoelastic properties. Frequency Dependence of Surface Viscoelastic Parameters. Before any detailed consideration of frequency dependence of the dilational moduli, we recall that small angle scattering data suggest a stretched brushlike layer as a good description of the PEO corona of the micelles. This brush layer organization of the PEO is retained at the air-water interface, and we note that micellar structures are always present in the surface layer. Consequently, as a micelle from the bulk approaches the surface that is already partially covered with a brush PEO layer, there will be a considerable repulsive potential generated due to excluded volume interactions between the two stretched PEO layers. This will resist the adsorption of the micelle at the air-dispersion interface, and we can speculate on two possibilities. First, the sublayer micelles could break up and individual copolymer molecules will be adsorbed at the interface more easily where they slowly reorganize into the “half micelle” structures suggested by the neutron reflectometry data. Second, the repulsive potential could play the role of an adsorption barrier as described by van den Tempel17 and elaborated on by Hennenberg et al.18 Discrimination between the various relaxation mechanisms is made possible by comparing the behavior of i/r as a function of capillary wave frequency, where i is the imaginary dilational modulus (≡ωo′) and r is the real part of the dilational modulus. Unfortunately, for the two mechanisms that would appear to be relevant here, both should have a clear maximum in i/r, although that for the micellar breakup process should be a narrower maximum relative to that for the potential barrier. Figure 10 shows i/r as a function of capillary wave frequency after the surface has aged 1 h. A maximum at a frequency of ∼1 × 105 s-1 appears to be evident (we note that this is based on only one data point), and the shape of this curve is retained as the dispersion surface continues to age (but with negative dilational viscosities being obtained), the frequency of the maximum increasing slightly to ca. 1.5 × 105 s-1. The similarity of this characteristic frequency as the bulk dispersion concentration increases suggests that the same mechanism is at work for all. The comment by van den Tempel and Lucassen17 that time dependence of surface properties is most likely to be associated with structure formation is pertinent here. Spread films of PSPEO diblock copolymers have been shown to form well-defined
Capillary Wave Phenomena
J. Phys. Chem. B, Vol. 104, No. 39, 2000 9185 increase as the bulk dispersion concentration increases, and this has been attributed to changes in the lateral organization in the subsurface stratified micellar layers. Negative dilational viscosities have been observed, and although these may be due to an effective adsorption barrier to adsorption from subsurface layers, it is believed that they are more likely to be due to the dispersion equation not accounting for all the dynamic processes in the complex surface layer structure of these copolymer micellar systems. A dispersion equation that accounts for all possible hydrodynamic interactions has yet to be derived. References and Notes
Figure 10. Ratio of imaginary dilational modulus to real dilational modulus for the copolymer dispersion with a bulk concentration of 7.5 × 10-5 g mL-1 1 h after surface formation.
aggregates at the air-water interface, and the neutron reflectometry data support the retention of a micellar structure at the interface. The adsorption of whole micelles from the bulk to the surface would be resisted by the interfacial brushlike layer; however, individual copolymer molecules can diffuse through this brushlike layer much more easily, and once adsorbed at the interface, they slowly aggregate to form the surface micellarlike structures observed by reflectometry. Although the surface concentration of the dispersions is identical, the subsurface organization plays a role in determining the surface viscoelastic parameters and the difference in the dilational modulus is most probably associated with lateral organization differences in the stratified layer organization below the surface. Conclusions Surface quasi-elastic light scattering shows that the surface of aqueous dispersions of a polystyrene-poly(ethylene oxide) linear diblock copolymer evolves over times in excess of 8 h. Equilibrium surface viscoelastic moduli are obtained within 24 h, and over a 3-fold range of bulk concentration very similar surface tensions were observed with resultant surface concentrations (assuming application of the Gibbs adsorption equation) also being in close proximity. Dilational moduli, however,
(1) Hamley, I. W. The Physics of Block Copolymers; Oxford University Press: Oxford, 1998. (2) Dewhurst, P. F.; Lovell, M. R.; Jones, J. L.; Richards, R. W.; Webster, J. R. P. Macromolecules 1998, 31, 7851. (3) Lucassen-Reynders, E. H.; Lucassen, J. AdV. Colloid Interface Sci. 1969, 2, 347-395. (4) Lucassen, J. Trans. Faraday Soc. 1968, 64, 2221-2229. (5) Langevin, D. Light Scattering by Liquid Surfaces and Complementary Techniques; Marcel Dekker: New York, 1992; Vol. 41. (6) Earnshaw, J. C. Thin Solid Films 1983, 99, 189-195. (7) Earnshaw, J. C.; McGivern, R. C.; McLaughlin, A. C.; Winch, P. J. Langmuir 1990, 6, 649-660. (8) Fan, C. J. Colloid Interface Sci. 1973, 44, 369. (9) Bouchiat, M. A.; Langevin, D. J. Colloid. Interface Sci. 1978, 63, 193. (10) Earnshaw, J. C.; McGivern, R. C. J. Colloid Interface Sci. 1988, 123, 36-42. (11) Jones, R. A. L.; Richards, R. W. Polymer Surfaces and Interfaces; Cambridge University Press: Cambridge, 1999. (12) Peace, S. K.; Richards, R. W.; Williams, N. Langmuir 1998, 14, 667. (13) Buzza, D. M. A.; Jones, J. L.; McLeish, T. C. B.; Richards, R. W. J. Chem. Phys. 1998, 109, 5008. (14) Bown, G. J. Ph.D. Thesis, University of Durham, Durham, U.K., 1999. (15) Ward, A. F. H.; Tordai, L. J. Chem. Phys. 1946, 14, 453. (16) Hua, X. Y.; Rosen, M. J. J. Colloid Interface Sci. 1988, 124, 652. (17) van den Tempel, M.; Lucassen-Reynders, E. H. AdV. Colloid Interface Sci. 1983, 18, 281. (18) Hennenberg, M.; Chu, X.-L.; Sanfeld, A.; Velarde, M. G. J.Colloid Interface Sci. 1992, 150, 7. (19) Earnshaw, J. C.; McCoo, E. Langmuir 1995, 11, 1087-1100. (20) Earnshaw, J. C.; McLaughlin, A. C. Proc. R. Soc. London, Ser. A 1991, 433, 663-678. (21) Earnshaw, J. C.; McLaughlin, A. C. Proc. R. Soc. London, Ser. A 1993, 440, 519-536.
