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Langmuir 1997, 13, 1592-1601
Capillary Wave Studies of Polystyrene-b-poly(methacrylic acid) Diblock Copolymer Films at the Air-Water Interface J. V. Gandhi and J. V. Maher* Department of Physics and Astronomy, University of Pittsburgh, Pittsburgh, Pennsylvania 15260
K. A. Shaffer and T. M. Chapman Department of Chemistry, University of Pittsburgh, Pittsburgh, Pennsylvania 15260 Received August 22, 1996X We have used mechanically generated capillary wave and ellipsometric techniques to investigate interfacial viscoelastic properties of adsorbed monolayers of polystyrene-b-poly(methacrylic acid) diblock copolymer at an air-water interface, as a function of both the overall molecular weight, Mw, and the nominal interfacial number density of the copolymer. This experiment is a follow-up of our earlier experiment, in which we studied adsorbed monolayers of the same diblock copolymer at the toluene-water interface (Macromolecules 1993, 26, 6595). Now we have changed the environment of the polystyrene block from toluene to air and have studied the effect of such a change. The most prominent effect of this change is that it is more difficult to attain equilibrium at the air-water interface. Unlike the toluene-water case, no clear saturation of surface pressure is observed at the air-water interface. The maximum surface pressure values measured at the air-water interface are smaller than the saturation surface pressure values in the toluene-water case for all the three molecular weights we have investigated. Ellipsometric study shows that only a very small fraction of the copolymer molecules added to the system is adsorbed at the air-water interface. However, substantial changes in the longitudinal elasticity and longitudinal viscosity are observed.
I. Introduction Copolymer films dissolved at a fluid-fluid interface are interesting for their intriguing surface properties.1-11 Surface pressure vs molecular area isotherms of copolymer monolayers at an air-water (A/W) interface have shown a variety of interesting properties.2,6,12-16,36 Interesting behaviors like novel surface micelle formation by diblock copolymers have also been observed recently.8,10 However, the only experiment available where the quality of one of the solvents forming the interface has been changed and the corresponding effect on the interfacial viscoelastic properties has been measured has been performed with very low molecular weight poly(ethylene oxide)-polystyrene block copolymer at the A/W and oil-water interfaces by Sauer et al.17 X Abstract published in Advance ACS Abstracts, January 15, 1997.
(1) May-Colaianni, S. E.; Gandhi, J. V.; Ma˚løy, K. J.; Maher, J. V.; Kuhar, K. A.; Chapman, T. M. Macromolecules 1993, 26, 6595. (2) Gaines, G. L., Jr. Langmuir 1991, 7, 834. (3) Conner, M.; Kudelka, I.; Regen, S. L. Langmuir 1991, 7, 982. (4) Schlossman, M. L.; Schwartz, D. K.; Kawamoto, E. H.; Kellogg, G. J.; Pershan, P. S.; Kim, M. W.; Chung, T. C. J. Phys. Chem. 1991, 95, 6628. (5) Gentle, I. R.; Saville, P. M.; White, J. W.; Penfold, J. Langmuir 1993, 9, 646. (6) Bringuier, E.; Vilanove, R.; Gallot, Y.; Selb, J.; Rondelez, F. J. Colloid Interface Sci. 1985, 104, 95. (7) Sauer, B. B.; Yu, H.; Kim, M. W. Langmuir 1989, 5, 278. (8) Zhu, J.; Eisenberg, A.; Lennox, R. B. J. Am. Chem. Soc. 1991, 113, 5583. (9) Zhu, J.; Lennox, R. B.; Eisenberg, A. Langmuir 1991, 7, 1579. (10) Li, S.; Hanley, S.; Khan, I.; Varshney, S. K.; Eisenberg, A.; Lennox, R. B. Langmuir 1993, 9, 2243. (11) Shull, K. R. Macromolecules 1993, 26, 2346. (12) Gaines, G. L., Jr. Insoluble monolayers at liquid-gas interface; Wiley: New York, 1966. (13) Gaines, G. L., Jr. Adv. Chem. Ceram. 1975, 144, 338. (14) Zatz, J. L.; Knowles, B. J. Pharm. Sci. 1971, 60, 1731. (15) Ikada, Y.; Iwata, H.; Nagaoka, S.; Horii, F. J. Macromol. Sci., Phys. 1980, B17 (2), 191. (16) Lin, B.; Rice, S. A. J. Chem. Phys. 1993, 99, 8308. (17) Sauer, B. B.; Yu, H.; Tien, C.; Hager, D. F. Macromolecules 1987, 20, 393.
S0743-7463(96)00832-3 CCC: $14.00
In our previous work,1 we measured capillary wave dispersion relations and extracted viscoelastic moduli for adsorbed monolayers of polystyrene-b-poly(methacrylic acid) (PS-PMAA) diblock copolymer at the toluene-water (T/W) interface, as a function of copolymer molecular weight and copolymer number density. In this paper, we report measurements of the capillary wave dispersion relation and the extracted viscoelastic moduli of the adsorbed monolayers of the same diblock copolymer (PSPMAA) over the same range of copolymer molecular weight and nominal number density at an A/W interface. Since water is a good solvent for poly(methacrylic acid) (PMAA) and toluene is a good solvent for polystyrene (PS), our earlier experiment had both copolymer blocks in their respective good solvents. In our present work, our primary intention was to identify effects of changes in the PS block between the case where it was in good solvent (toluene) and the present case, where it is expected to be collapsed in the very poor solvent represented by air. Contrary to our intent, the most dramatic differences arising from this change in solvent quality involve (1) a dramatic increase in the difficulty of achieving thermodynamic equilibrium and (2) enhanced micelle formation in the bulk. We did, however, develop procedures to reproducibly reach an apparent equilibrium at the A/W interface, allowing us to measure the capillary wave dispersion relation and thus to observe significant differences in the interfacial mechanical moduli. To measure the amount of copolymer adsorbed at the interface, we used ellipsometry. In our capillary wave measurements, we have measured the complex wave number of mechanically generated capillary waves18 on an A/W interface covered with a copolymer film as a function of driving frequency, over a frequency range from 500 to 2900 Hz. These measurements allowed us to determine the viscoelastic mechanical moduli for both transverse and longitudinal interfacial (18) Ma˚løy, K. J.; Feder, J.; Jøssang, T. Rev. Sci. Instrum. 1989, 60, 481.
© 1997 American Chemical Society
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Table 1. Molecular Weight Data for PS-PMMA Copolymers sample
Mpa
Mw/Mna
Mwb
Mw/Mnb
14K.603 38K.395 283K.415
14 000 37 600 283 400
1.09 1.10 1.09
14 500 38 600 273 000
1.10 1.13 1.09
a From Polymer Laboratories. b Determined by GPC versus calibration with polystyrene standards.
Table 2. Results from Hydrolysis of PS-PMMA Copolymers with KOH in 1,4-Dioxane/Methanol sample
labela
PS/PMMAb
PS/PMAAb
yield of hydrolysis,c %
14K.603 38K.395 283K.415
50:50 47.0:53.0 42.5:57.5
42:58 47:53d 42:58
42:52 47:48 43:57
95.4 96.6 89.8
a PS/PMMA from Polymer Laboratories. b From 1H NMR in DMSO-d6 at 363 K. Determined from integration of the aromatic protons of PS and the R-methyl protons of PMMA or PMAA. c Determined from integration of the methyl protons of any remaining ester (unreacted MMA) and the R-methyl protons of PMAA. d From 1H NMR in CDCl3.
excitations as a function of the copolymer molecular weight and the nominal interfacial number density. We used the phase modulated ellipsometric technique19 to measure the change in the phase angle of the light reflected from the monolayer-covered interface. Microscopic models7,20,21 for the interface were then used to calculate the fraction of the copolymer molecules adsorbed at the A/W interface. This paper is organized in the following manner: Section II contains a description of the copolymer, solvent, and interface preparation along with a brief discussion of both the mechanically generated capillary wave method and the ellipsometry method. Section II also contains a discussion of metastable effects along with a description of the procedures which allowed the acquisition of reproducible data. Section III contains a discussion of the analysis of mechanically driven capillary wave and ellipsometric data. In section IV, we first present the analyzed ellipsometric results and then the extracted interfacial viscoelastic parameters for copolymer films at the A/W interface. We present these results in comparison with the results for the T/W case and point out important similarities and differences. II. Experimental Section A. Materials. Dimethyl sulfoxide (Fisher) was distilled before use. Water that had been doubly distilled was used during the entire experiment, including cleaning of the apparatus. The preparation of the polystyrene-b-poly(methacrylic acid) (PSPMAA) diblock copolymers used in this experiment has been described elsewhere.1 Table 1 summarizes the molecular weight data for these copolymers. The degree of hydrolysis and the relative monomer composition of the PS-PMAA copolymers were determined by 1H NMR in DMSO-d6 at 363 K using a Bruker 300 MHz spectrometer. These results are summarized in Table 2. As can be seen from column 4 of Table 2, the three block copolymers studied all have very similar relative monomer compositions. B. Measurement Methods. The mechanically generated capillary wave (MGCW) technique has been described in detail in our earlier experiment.1 We have modified the measurement procedure of our earlier experiment only slightly to facilitate the measurement of capillary waves on an A/W interface. Figure 1 shows the arrangement used in the present experiment. The sample cell was made of optical quality Pyrex glass.22 The beam from a 632.8 nm wavelength He-Ne laser, LB, was focused on (19) Azzam, R. M.; Bashara, N. M. Ellipsometry and Polarized Light; North Holland: New York, 1977. (20) Strachan, C. S. Cambridge Philos. Sco. 1933, 29, 116. (21) Bootsma, G. A.; Meyer, F. Surf. Sci. 1969, 14, 52. (22) G. Finkenbeiner Co., Waltham, MA 01002.
Figure 1. Experimental arrangement for mechanically generated capillary wave (MCGW) measurements. the A/W interface by lens L1 and was reflected from the interface. A 50 µm diameter Pt wire, W, was placed in the magnetic field of a horseshoe-shaped magnet, M, parallel to both the interface and the laser beam and less than ∼1 mm below the interface. An alternating current of frequency f was passed through the wire, producing mechanical oscillations in the wire which were transmitted to the nearby interface. A vertical knife edge, E, was positioned such that, with the wire at rest, half of the exiting reflected beam passed by the knife edge, and this light was focused by lens L2 onto a photodiode, PD. The photodiode signal was amplified and sent to a lock-in amplifier, with the ac signal driving the oscillating wire also serving as the reference signal for the lock-in amplifier. Stepper motor SM was used to move the sample cell in a direction, x, perpendicular to the plane of incidence/ reflection of the laser beam, resulting in the measurement of the photodiode signal as a function of x. As is discussed in refs 18 and 23, the lock-in amplifier extracts the part of the signal which correlates with the driving/reference signal to yield a spatial wave form
V(x) ) Ae-βx cos(qx + φ)
(1)
where A is a constant determined by the amplitude and frequency of the driven interfacial wave, q is the wavenumber, and β is the damping constant of the capillary wave. Using this technique to measure V(x), we have extracted values of q and β for frequencies typically in the range 500-2900 Hz. All the glassware used in the experiment was treated thoroughly with Chromerge24 and then rinsed thoroughly with double-distilled water. The temperature of the experimental setup was kept at all times in the range 25 ( 1 °C, although the temperature stability during any one measurement was generally much better than 1 °C. Our design of the ellipsometer was based on the phasemodulation principle.19 All the measurements were done at a fixed angle of incidence of 64 ( 0.25°. The phase modulation was induced by a photoelastic modulator.25 The modulator was kept at constant temperature and dry N2 gas was used to minimize condensation on the modulator crystal. The modulator induces a periodic relative phase shift between the two orthogonal components of the electric field of the light beam at a frequency of 50 kHz. Reflection from the monolayer-covered interface causes an additional phase shift δ∆, which was measured by locking into the 50 and 100 kHz frequencies. This change in ellipsometric phase angle, δ∆, was measured as a function of the nominal number density of molecules added to the system. To calibrate the ellipsometer, we reproduced the measurements of the change in the phase angle δ∆ for poly(vinyl acetate) monolayers at the A/W interface performed by Sauer et al.26 C. Sample Preparation. In the previous experiment,1 samples of a given number density were prepared by adding the appropriate amount of stock solution of the copolymer in the common solvent dimethyl sulfoxide (DMSO) to the surface of water and then adding toluene to the top. DMSO drops, being (23) May, S. E. Ph.D. thesis, University of Pittsburgh, 1992 (unpublished). (24) Mixture of chromic acid and sulfuric acid. (25) HINDS International, Portland, OR, PEM-80, Series I Head. (26) Sauer, B. B.; Yu, H.; Yazdanian, M.; Zografi, G.; Kim, M. W. Macromolecules 1989, 22, 2332.
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Figure 2. Roll-like patterns observed in the bulk liquid as samples containing the 283K molecular weight diblock copolymer evolve toward equilibrium. denser than water, sank into the bulk water phase as they dissolved. The copolymer molecules were then adsorbed at the T/W interface from the bulk water. It was found that the T/Wcopolymer system could be brought to equilibrium within approximately 1 h as long as reasonable care was taken to avoid attaching the copolymer to the glass sides or bottom of the sample container and as long as the copolymer was not introduced in a very concentrated region on the interface. The attainable states had the following properties: (1) no spatial inhomogeneity was observable in the capillary wave measurements; (2) except at the very largest copolymer concentrations (far above the concentrations at which the surface pressure reached its saturation value), light scattering and visual inspection showed no evidence of polymeric structures in either bulk liquid phase; and (3) the systems showed no evidence of change over hundreds of hours after coming to equilibrium in the first hour. Property 3 suggests that the reproducible results were indeed equilibrium results. Property 1 argues against both metastable structures and coexisting interfacial phases. And property 2 suggests that most, if not all, of the copolymer resides on the interface, allowing a plausible discussion of the interfacial energetics in terms of measured mechanical moduli and the global copolymer concentration of the sample. In the present experiment with an A/W interface, the attainability and properties of equilibrium are much less simply described. In general, a much longer time was required to attain a state whose properties were reproducible, although the method of preparation of the samples was similar to that for the T/W case as described above. Samples of a given number density were prepared by adding the appropriate amount of stock solution of the copolymer in the common solvent DMSO to the A/W interface. Drops of the stock solution were added at several different places on the interface, and the results were not sensitive to the exact positions and numbers of such drops. This care of not adding all the drops of the stock solution to just one position is necessary because it is known that successive additions of drops to just one position may trap long-lived entanglements between copolymer chains which do not relax easily.6 As in the previous experiment, DMSO again sank into the water, and the bulk water phase became cloudy after some time. This cloudiness decreased with time as an apparent equilibrium approached, leaving the bulk liquid relatively clear. The highest molecular weight copolymer (Mw ) 283K) took a much longer time (48-96 h) to come to such an equilibrium, as compared to the two lower molecular weights of 14K and 38K, which took only 5-10 h to come to an apparent equilibrium. Figure 2 shows a time-averaged photograph of light scattered from the water as a sample of the 283K molecular weight copolymer evolved toward the apparent equilibrium. Interesting roll-like convection patterns are clearly present. These patterns took about 48-96 h to dissipate, after which reproducible data could be taken. However, for the 283K molecular weight copolymer, beyond a certain nominal copolymer concentration, the bulk phase always exhibited some light scattering (which increased with further increase in the copolymer concentration) at equilibrium, suggesting that coexisting micelles contain some significant fraction of the available polymer. This also raises the related question of how much copolymer is actually adsorbed at the interface. Accordingly, we have used ellipsometry to measure the amount of copolymer adsorbed at the A/W interface. In a well defined range near the lowest values of nominal number density we have explored in the experiment (and especially with the 283K molecular weight copolymer) our capillary wave measurements showed spatial inhomogeneities in a monolayer which was allowed to come to equilibrium for a few days. These spatial inhomogeneities could be inferred from
Figure 3. Capillary wave profile I(x) vs distance x between the wire and the point of laser reflection. Top: on an interface which exhibits spatial inhomogeneity. Bottom: on a homogeneous interface. The lines are inserted to guide the eye. the measured capillary wave forms having a nonuniform exponential envelope (i.e. multiple damping constants, β) and/or a nonuniform sinusoidal wave (i.e. multiple wavelengths). Figure 3 shows two measured wave forms, one from a homogeneous interface and one which exhibits spatial inhomogeneity. As one seeks to understand these inhomogeneous layers at very low molecular density, there are two obvious candidates to provide an explanation: (1) The highest molecular weight copolymer (Mw ) 283K) might have more probability of being trapped in a long-lived metastable state,6 which would affect the capillary waves in a nontrivial way. This metastable state would then be unlikely to be reproducible. The weaker but similar effects in the samples of the lower molecular weight copolymer might then arise from a less dramatic form of the same phenomenon. Or, (2) it is also possible that the monolayer could exist at equilibrium in a two-dimensional liquid-gas coexistence phase, as observed by Miyano and Tamada27 when they performed fluorescence microscopy studies of their monolayers for which the capillary wave measurements showed spatial inhomogeneities. Since the inhomogeneities in our experiments appeared in carefully prepared samples in only restricted concentration ranges, always at very low concentrations, we lean toward the explanation that they arise from the interfacial two-phase equilibrium. If that is the case, then under the conditions of spatial inhomogeneity, our capillary wave measurements would be looking at regions which have different proportions of the liquid and gas phases. In a gas-phase dominant area, the capillary waves should be damped less than in a liquid-phase dominant area, and the wavelength of the waves should be different as well. The data shown in the next sections are all taken at higher number densities where the monolayers were uniform and the capillary wave spectra were also uniform. The regions of spatial inhomogeneity are all at such low copolymer concentrations as to be of rather little importance for the discussions below. Care was also taken not to disturb the sample container mechanically because it was found that tipping the sample back and forth could change the capillary wave spectra (always in the direction of spectra seen for an undisturbed sample with less polymer), indicating that polymer could adhere to the glass walls of the sample container if the liquid interface was moved along the container wall. All measurements discussed below were reproducible as long as samples were prepared according to the prescription described in the previous paragraphs, care was taken not to agitate the interface, the samples were allowed to come to an apparent equilibrium, and the samples were aged by up to several days before taking the measurements. It was unfortunately not practicable to follow the procedure of the earlier experiment in waiting hundreds of equilibrium times before making measure(27) Miyano, K.; Tamada, K. Langmuir 1992, 8, 160.
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Langmuir, Vol. 13, No. 6, 1997 1595
Figure 4. Measured capillary wave profile I(x) vs distance x between the oscillating wire and the point of laser reflection, for capillary wave frequency 1300 Hz, with wavenumber q ) 100.4 cm-1 and damping constant β ) 3.11 cm-1, at 12 × 1012 molecules/cm2 of 283K Mw PS-PMAA diblock copolymer. ments. In the discussion below, we will treat the observed reproducible effects as equilibrium effects.
III. Data Analysis A. Mechanically Generated Capillary Wave Technique. Each measured capillary wave profile obtained using the MGCW technique was fitted, using a leastsquares method, to the form given by eq 1. A measured capillary wave profile and its least-square fit are shown in Figure 4. The least-square fits for q and β for a single measured waveform exhibited very small uncertainties, but by repeating measurements we found that q and β are reproducible for any one sample to 0.25% and 7%, respectively. A possible source of systematic error in the damping coefficient is evaporation of water during a single scan (lowering the interface and changing the point of reflection). This would cause β to be underestimated for scans away from the wire and overestimated for scans toward the wire. We reversed the direction of scanning for each new frequency scan, and when the whole dispersion relation was fitted, this systematic error was thus limited. Figure 5 shows measured values of q and β as a function of the nominal interfacial number density of the 283K molecular weight diblock copolymer on the A/W interface for two different frequencies. The figure shows an interesting trend in q and β which is significantly different from the trend for the T/W-copolymer system. At very low nominal copolymer number density, neither β nor q shows a substantial change of value as copolymer density is increased. Then, as still more copolymer is added, first β shows an increase and then q also starts increasing. While q continues to increase (now with a smaller slope) with further increase in the copolymer number density, β goes through a maximum and then decreases before coming to a plateau value. In the T/W case, both β and q showed a steady and simultaneous increase with increasing copolymer number density, starting at the very smallest copolymer number densities until reaching saturation values which also happened to be their maximum values. These differences in capillary wave propagation on the diblock copolymer films at the two interfaces result in significant differences in the extracted values of their interfacial viscoelastic parameters, as will be discussed below. B. Dispersion Relation. The capillary wave dispersion relation for a thin viscoelastic interface between two simple fluids has been reported by Lucassen-Reynders and Lucassen.28 Since there is not enough polymer in any of our samples to produce an appreciable change in the viscosity of water if the polymer were dispersed in the (28) Lucassen-Reynders, E. H.; Lucassen, J. Adv. Colloid Interface Sci. 1969, 2, 347.
Figure 5. Wavenumber q and spatial damping constant β as a function of nominal polymer number density at two values of frequency for the 283K molecular weight PS-PMAA diblock copolymer at the A/W interface. The error bars for q in each case are smaller than the data symbol. Uncertainties for β are as shown.
bulk water phase and since the shortest wavelength we measure is very long in comparison with the thickness of any interfacial zone which our polymer could form (During the time scale of our measurements, the polymer molecules would only diffuse through a distance which would be very small compared to the shortest wavelength we measure.), this dispersion relation is appropriate for the present experiment, and we need not consider the more complicated relations which might otherwise be applicable.29,30 If we let F and η be the density and viscosity of water (the lower fluid), take the density and viscosity of air (the upper fluid) each to be zero, and define m ) [q*2 + i(ωF/η)]1/2 for water with q* ) q - iβ, the complex wavenumber, and angular frequency ω ) 2πf, we can construct functions
*q*2 + i[η(q* + m)] ω
(2)
gF ωF σ*q*2 + i[η(q* + m)] + ω ω q*
(3)
E) S)
where * ) + iωκ is the complex dilational elastic modulus associated with longitudinal interfacial modes and σ* ) σ + iωµ is the complex surface tension associated with transverse modes of the surface. The capillary wave dispersion relation can then be written as
D ) [η(q* - m)]2 + E‚S ) 0
(4)
To determine viscoelastic parameters for the interface, it is necessary to insert our measured q(f) and β(f) into D(q*,ω,σ*,*) and adjust σ* and * to satisfy D ) 0. To accomplish this, we defined a χ2, a weighted square fluctuation of D from its expected value of 0, as (29) Harden, J. L.; Pleiner, H.; Pincus, P. A. Langmuir 1989, 5, 1436. (30) Harden, J. L.; Pleiner, H.; Pincus, P. A. J. Chem. Phys. 1991, 94, 5208.
1596 Langmuir, Vol. 13, No. 6, 1997 N
2
χ )
∑ i)1
Gandhi et al.
|Di(q*i,ωi,σ*,*)|2
(5)
2 δ|D i|
where Di is the left-hand side of eq 4 evaluated for the ith 2 data point q*(ωi) and δ|D is an expected uncertainty in Di i| based on the measured uncertainties in q*i and ωi. We arbitrarily chose to treat the uncertainties in qi and βi as independent, and since the uncertainty in ωi is negligible compared to qi and βi, we write 2 ) δ|D i|
(∂D ∂q |
qi,βi,fi,σ*,*
) (∂D ∂β | 2
δqi +
qi,βi,fi,σ*,*
δβi
2
)
(6)
We minimized χ2 using the Marquardt-Levenberg algorithm.31 Unlike the water-toluene case, the density and viscosity contrast between air and water is sufficiently large that there is significant coupling between the transverse and longitudinal modes at the A/W interface. The division of energy between transverse and longitudinal modes through strong mode coupling is exhibited (in the present case where the apparatus drives transverse modes) mostly in the damping of the transverse modes. Thus the waves damp out faster than they would if there was no coupling between the two modes. The dispersion relation dictates that the effect of longitudinal elasticity, , on the damping constant, β, is much larger than that on the wavenumber, q. Figure 6 shows the theoretical calculations of q and β, as a function of at various values of longitudinal viscosity, κ, for a 50 dyn/cm surface tension and zero transverse viscosity at a frequency of 500 Hz, using eq 4. The most important feature of the graph is that β goes through a maximum at rather small values of (in this case ∼7 dyn/cm). This maximum damping occurs when resonance conditions are fulfilled between the transverse and longitudinal modes.28 After going through a maximum, it then relaxes to a plateau at higher values of . The wavenumber q goes through a minimum at a rather small value of before rising to a plateau at large values of . The most prominent effect of κ is to flatten the maximum/ minimum in β/q. At large values of longitudinal moduli and κ, both the transverse wave parameters q and β become insensitive to changes in and κ. Calculation of such large values of longitudinal moduli and κ from the measurement of transverse mode wave forms then becomes quite imprecise. (As will be noted in the next section, this is the reason to include large uncertainties once our determinations of and κ exceed values of ∼10 dyn/cm and 10-3 dyn‚s/cm, respectively.) Since both β and q are nonmonotonic functions of , we cannot deduce unique values of the four parameters from the measurement of just two parameters q and β. (Both β and q are reasonably monotonic functions of σ, µ, and κ.) Our measurements of q and β over a range of frequencies unambiguously reduced to no more than two the number of candidate solutions for the viscoelastic parameters of the system. At very low values of the polymer number density, there was only one best fit solution of the dispersion relation. Above a certain number density (depending upon the molecular weight of the polymer) we typically found two solutions. One solution (refer to it as solution 1) has a value of in the range 3-4 dyn/cm and a lower surface tension than the other solution, while the other (solution 2) has a much higher value of and a higher surface tension. To analyze the situation further, let us denote the surface tension obtained by (31) Press, W. H.; Flannery, B. P.; Teukolsky, S. A.; Vetterling, W. T. Numerical RecipessThe Art of Scientific Computing; Cambridge University Press: New York, 1985.
Figure 6. Theoretical calculations of q and β as a function of longitudinal elasticity for different values of longitudinal viscosity κ (with σ ) 50 dyn/cm, µ ) 0 dyn‚s/cm, f ) 500 Hz).
solving eq 3 (i.e. S ) 0) the apparent surface tension σapp.32 This would be the solution of the measured dispersion relation if there was no coupling between the transverse and longitudinal waves. In that case, all the energy reduction (in terms of the surface tension reduction or surface pressure) could be attributed to the transverse waves. In the case where coupling between the transverse waves and the longitudinal waves is present (as in our case), the solution of the measured dispersion relation should have a smaller energy reduction for the transverse waves, since some of the energy is diverted to longitudinal waves, thereby resulting in a lower surface tension reduction or higher surface tension. That is, the correct solution of the measured dispersion relation should include a surface tension which is higher than the apparent surface tension σapp. Of the two solutions mentioned above, only solution 2 had a calculated surface tension larger than σapp. While this argument favors solution 2, an independent measure of surface tension of the film-covered interface is needed to unambiguously determine the viscoelastic moduli. Even though the Wilhelmy plate method is not expected to be either easy or very accurate for surface tension measurements of stiff or viscous films,27 we did succeed in performing such measurements reproducibly for each of the three molecular weight copolymers at the A/W interface: new samples were prepared by the same procedures as described above, and after allowing adequate time for these samples to come to equilibrium, measurements of the surface pressure were performed using a platinum Wilhelmy plate. These measurements were performed at several copolymer number densities, and despite their large uncertainties, they always strongly and unambiguously favored solution 2. Accordingly, solution 2 is the result presented consistently throughout the remainder of this paper. Figure 7 compares the measured values for the wavenumber q and the damping constant β as a function of frequency with a line calculated using eq 4 and the best-fit parameters σ, µ, κ, and at a nominal number density of 12 × 1012 molecules/cm2 of 283K Mw PS-PMAA diblock copolymer. To deduce the number of copolymer molecules adsorbed at the interface from the ellipsometric measurements, we have followed the procedure used by Sauer et al.7 In their study of polystyrene-poly(ethylene oxide) diblock copoly(32) Lemaire, C.; Langevin, D. Colloids Surf. 1992, 65, 101.
Polystyrene-b-poly(methacrylic acid) Films
Figure 7. Measured values (filled circles) and best-fit curve for the wavenumber q and damping constant β for a film of 12 × 1012 molecules/cm2 of 283K Mw PS-PMAA diblock copolymer as a function of frequency. Measurement uncertainties are indicated wherever they exceed the size of the data symbol.
mer at the air-water interface, they were able to show that the ellipsometric phase angle difference δ∆ was directly proportional to the surface number density of molecules, in agreement with microscopic theory based on independent molecular polarizability.20,21 This theory considers the monolayer to be a distribution of scattering centers in two dimensions. Following Sauer et al.,7 we have assumed that the primary contribution to the phase angle comes from the polystyrene layer on the top of the air-water interface. The contribution of MAA monomers, if at all present above the bulk water phase, is expected to be small because of their small polarizability. Then the calculated number density of scattering centers should yield the number density of styrene monomers adsorbed at the A/W interface. IV. Results and Discussion We will first present the results of our analysis of the ellipsometric data, since they provide the crucial information about the amount of copolymer molecules adsorbed at the A/W interface. We will then present the results of our capillary wave study of the A/W interface independently as well as in comparison with the results of our previous study of the T/W interface. A. Ellipsometric Results. In the discussions in this section, the total number of copolymer molecules in each sample is presented as a nominal areal number density in units of molecules/cm2. Figure 8 shows the measured change in ellipsometric phase angle, δ∆, as a function of the nominal polymer number density of molecules added to the system for copolymer molecular weights of 14K and 283K. (Unfortunately, we could not perform similar measurements on the 38K molecular weight copolymer due to a limited supply of this copolymer.) For both molecular weights, δ∆ first increases linearly with the polymer number density. In this linear regime, the calculation of the actual number of molecules adsorbed at the interface shows that only about 10% of the 14K molecular weight copolymer and only about 5% of the 283K molecular weight copolymer added to the system are
Langmuir, Vol. 13, No. 6, 1997 1597
Figure 8. Change in ellipsometric phase angle, δ∆, as a function of the nominal number density N added to the system for the 14K and 283K molecular weight copolymers. The arrows indicate the nominal number density N1 at which the ellipsometric phase angle δ∆ saturates (also refer to Table 3).
adsorbed at the A/W interface. After a certain nominal number density of molecules, N1, δ∆ deviates from its linearly increasing behavior and reaches a saturation value δ∆sat, beyond which δ∆ shows no substantial change with further increase in the nominal number density. The picture that emerges from these measurements is that only a very small fraction of the polymer molecules added to the system is adsorbed at the A/W interface, suggesting that the rest may be forming micelles in the bulk or may be attached to the container walls. As mentioned before, we have followed the procedure used by Sauer et al.7 to measure and analyze our data. Their results showed that the ellipsometry can be used successfully to deduce the population of copolymer molecules at the interface. In that case, the saturation of δ∆ after a certain nominal number density N1 may plausibly indicate a saturation in the number of polymer molecules adsorbed at the interface. In this saturation regime, additional molecules adsorbed at the A/W interface are either negligible or too few to be detected accurately by ellipsometric measurements. This may also suggest that the copolymer molecules prefer to form micelles in the bulk rather than form dense structures at the A/W interface. These ellipsometric results immediately raise the question of what repulsive interactions at the A/W interface prevent the copolymer molecules from adsorbing at the interface after the interface has reached saturation. Table 3 shows the nominal number density of molecules at saturation, N1, along with the corresponding measured δ∆sat in columns 2 and 3 for both molecular weights. It is interesting to note that these δ∆sat values are almost the same for the two molecular weight copolymers. Column 4 shows the actual number density of copolymer molecules, N2, adsorbed at the interface as calculated by using the ellipsometric measurements. Columns 5 and 6 report the corresponding number densities of styrene and MAA monomers adsorbed at the A/W interface. These monomer
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Table 3. Nominal Number Density of Molecules Added to the System (N1), Maximum Measured Change in Ellipsometric Phase Angle ((δ∆)sat), Number Density of Molecules Actually Adsorbed at the Interface (N2), and Corresponding Number Densities of Styrene and MAA Monomers at the (δ∆)sat as a Function of the Molecular Weight (Mw) of the Diblock Copolymer at the A/W Interface Mw
10-12N1, #/cm2
(δ∆)sat, deg
10-12N2,a #/cm2
10-14N′2,b #/cm2
10-14N′2,c #/cm2
14K 283K
126 12.2
1.16 ( 0.06 1.2 ( 0.1
10.6 0.59
7.4 7.7
9.2 10.0
a Calculated from (δ∆) . b Monomer number density of styrene sat monomers corresponding to polymer number density N2. c Monomer number density of MAA monomers corresponding to polymer number density N2.
Table 4. Properties of Molecules in an Assumed Homogeneous Monolayer at the Density Indicated by (δ∆)sat
Mw 14K 283K
A2,a A3,b Å2/molecule Å2/molecule 940 17000
616 4300
% of area covered A4,c overlap (A3/A2) Å2/molecule (A4/A2) 66 25
2640 52300
2.8 3.1
a A is the available surface area per molecule. b A the area of 2 3 a dense sphere formed by the PS block as discussed in the text. c A4 the projected area of a very unlikely self-avoiding random configuration for the PMAA block as discussed in the text. b Assuming spherical shape for PS chains and the mass density of solid polystyrene. c Reference 33.
number densities are almost the same for both molecular weights because the corresponding δ∆sat values are almost equal. In Table 4, column 2 shows the area A2 occupied by each copolymer molecule at δ∆sat if they are assumed to form a uniform monolayer for both molecular weight copolymers. In its bad solvent air, a PS chain is expected to be collapsed and form a tightly coiled molecule.15 If we assume that the shape of this tightly coiled molecule is spherical and its mass density is equal to the mass density of solid polystyrene, then the projection area A3 of such compact chains at δ∆ saturation should be that shown in column 3. As column 4 shows, the percentage of interfacial area that would be covered by such tightly coiled PS chains at δ∆sat is only 66% for 14K molecular weight copolymer and only 25% for 283K molecular weight copolymer. This indicates that the PS layer on the top of the A/W interface may be only diffusely populated under saturation conditions. Lin et al.16 found that hydrophobic PS blocks of their diblock copolymer came together to form thin diskshaped structures at the A/W interface. Plausibly, the PS molecules in our case may be forming flatter structures at the A/W interface. Turning our attention to the other side of the interface, we expect the PMAA to be completely ionized and stretched in water for pH values at and below 7. As was noted in ref 1, the estimated Debye screening length, LD, is much larger than the diameter of a methacrylic acid (MAA) monomer, which is ∼0.7 nm (for pH ≈ 7, LD ∼ 7 nm). The data presented herein are all for pH ≈ 7. An estimation of the chain to chain distance between PMAA chains hanging in water at δ∆ saturation shows that the PMAA chains for 14K molecular weight copolymer should be about 17 Å apart from each other while those for 283K molecular weight copolymer should be about 74 Å apart. So, for the lower (14K) molecular weight copolymer, the chain to chain distance between PMAA chains is much smaller than the Debye screening length of 70 Å while, for the higher (283K) molecular weight copolymer, the two values are comparable. In either case, weak repulsive forces are plausible. In an alternate possibility which seems very unlikely to occur,
we can assume that a PMAA chain performs a self-avoiding random walk in water.33 The projection area of such a configuration on the A/W interface is shown as A4 in column 5. Comparison between A2 and A4 indicates that the PMAA chains would under such conditions weakly overlap, with an overlap number approximately that shown in column 6 of Table 4. Such overlap numbers could yield weak repulsive forces. B. Capillary Wave Results. Our capillary wave measurements of the diblock copolymer at the A/W interface were performed in the same range of nominal number density of molecules as our previous study of the same diblock copolymer at the T/W interface. These nominal number densities of molecules are, over most of their range, much larger than the nominal number densities of molecules at which the A/W interface shows the saturation discussed above. However, the interesting changes in the viscoelastic moduli of the copolymer monolayers (both in the A/W case presented below and in the T/W case where there is reason to believe that a much larger fraction of the molecules in the sample does indeed populate the interface) occur only in the higher range of nominal number densities. This change in the surface viscoelastic properties of the copolymer monolayers at the A/W interface beyond the measured saturation of the A/W interface is difficult to explain. It could indicate a problem with interpreting the ellipsometric data, but these have been found to be accurate in other work with similar systems.7 Alternatively, the capillary wave modulations may be affected by interactions of the micelles in the bulk and the molecules at the interface and may not need to depend on any change in the population density of molecules at the interface. Clearly, we do not understand this completely, but there are a number of interesting comments that can be made with confidence, and these will constitute the remainder of this section. Surface tension data are presented below in the form of the surface pressure, π, the reduction of surface tension due to the presence of the polymer at the A/W interface. For convenience, we present our results as a function of the nominal number density of copolymer molecules added to the system even though ellipsometric results show that a very small and decreasing fraction of these molecules is actually adsorbed at the A/W interface. Figure 9 shows the extracted values of surface pressure π as functions of nominal polymer interfacial number density for PS-PMAA molecular weights of 14K, 38K, and 283K, respectively. The following points are easily noticeable from this figure: (1) The surface pressure values measured at the A/W interface are very small for all three molecular weights, indicating a very weak surfactant action of these macromolecules at the A/W interface. Also, (2) for the lower two molecular weight copolymers, there is only a weak sign of saturation of the surface pressure, while the highest molecular weight copolymer clearly shows no sign of saturation of the surface pressure with addition of more molecules to the system. This is in contrast with our measurements of the surface pressure of these diblock copolymers at the T/W interface, which showed much larger values as well as clear saturation of surface pressure for copolymers of all three molecular weights. Similar behavior of no saturation of the surface pressure has been observed by Sauer et al.17 in their study of very low molecular weight poly(ethylene oxide)-polystyrene block copolymer at the A/W interface. (3) The surface pressure keeps increasing beyond the nominal number density N1, at which δ∆ saturates (indicated in the figure by the arrows). As discussed above, we do not understand this effect of increase in the surface pressure of the A/W (33) Katchalsky, A.; Miller, I. J. Phys. Chem. 1951, 55, 1182.
Polystyrene-b-poly(methacrylic acid) Films
Langmuir, Vol. 13, No. 6, 1997 1599 Table 5. Saturation Surface Pressure as a Function of Molecular Weight of the Diblock Copolymer at the T/W Interface1
Figure 9. Surface pressure, π, as a function of the nominal interfacial polymer number density (in molecules/cm2) for each of the three molecular weights of PS-PMAA diblock copolymer. The arrow indicates the nominal number density N1 at which the ellipsometric phase angle δ∆ saturates (also refer to Table 3).
Figure 10. Surface pressure π, as a function of the nominal interfacial monomer number density (in monomers/cm2) for each of the three molecular weights of PS-PMAA diblock copolymer.
interface even though ellipsometry results indicate no or a very small amount of increase in the number of molecules present at the A/W interface beyond δ∆sat. For further comparison, we have also plotted the surface pressure data in Figure 10 for all three molecular weights as a function of the nominal number density of styrene monomers (some data points have been omitted for clarity). It should be noted that our copolymer has an equal proportion of styrene (Mw ) 104) and MAA (Mw ) 86) by weight, resulting in almost equal numbers of monomers of both types in a single copolymer chain. Ellipsometry results indicate that about the same number of styrene monomers are present at the A/W interface for both 14K and 283K molecular weight copolymers at the onset of δ∆sat. If we assume the surface number density behavior of the 38K molecular weight copolymer to be similar to that of the 14K molecular weight copolymer, then Figure 10 suggests that the 283K molecular weight copolymer is more efficient in reducing the surface tension as compared
Mw
πs, dyn/cm
14K 38K 283K
12 ( 1 16 ( 1 18 ( 1
to the copolymers of the lower two molecular weights. A somewhat similar dependence of saturation surface pressure on the molecular weight of the copolymer was seen at the T/W interface.1 As shown in Table 5, the saturation surface pressure at the T/W interface also increases with the molecular weight of the copolymer. Calculations of Lyatskaya et al.34 suggest that larger diblocks are more efficient at reducing the interfacial tension of two immiscible homopolymers. If copolymer block dissolution in homopolymer (somewhat analogous to dissolution in θ solvent) is similar to dissolution in a good solvent, then it is no surprise that similar results were seen in our double-good-solvent T/W case. In the present case of the A/W interface, the collapse of the PS block in air prior to formation of an equilibrium monolayer does not appear to contradict this trend. The magnitude of the copolymer’s surfactant effect seems to be reduced when toluene is replaced by air, as can be seen from Table 5 and Figure 10. The maximum reduction of surface tension at the A/W interface is only 9% for the 283K molecular weight copolymer as compared to the corresponding value of 50% surface tension reduction at the T/W interface. The values for the lower two molecular weights at the A/W interface are even lower. This trend becomes even more pronounced if we compare the surface pressure values at the number density where ellipsometry results indicate saturation of the A/W interface to the saturation surface pressure values at the T/W interface. The surface pressure values associated with the saturation of the A/W interface are approximately 1 dyn/cm for both 14K and 283K molecular weight copolymers. The corresponding saturation surface pressure values for the T/W case are 12 and 18 dyn/cm, respectively, as can be seen from Table 5. (Even though no ellipsometry was performed at the T/W interface, light scattering indicated too low a micelle density to be detected at even very large nominal surface densities in the T/W case, while the discussion above has already made clear that significant micellar scattering is observable even at low nominal densities in the A/W case.) Let us now compare the energy reduction per monomer at the saturation of the A/W and T/W interfaces. While the exact values of these energies are dependent upon the knowledge of the actual population of the molecules at the interface, nevertheless, the qualitative indication they convey is interesting. The energy reduction per monomer at the A/W saturation number density amounts to about 40 × 10-3kbT/monomer. This number is larger than the corresponding numbers at the saturation of surface pressure at the T/W interface, where the maximum energy reduction per monomer is about 15 × 10-3kbT/monomer for the 283K molecular weight copolymer. The above argument may indicate a very delicate energy balance present at the A/W interface. Since the environment of the PMAA chains remains the same (viz. water) at either the T/W interface or the A/W interface, the difference between the A/W case and the T/W case might plausibly be assumed to come from the difference in the energetics of the PS block when it is dissolved in a good solvent (toluene) and when it is dissolved in the bad solvent (34) Lyatskaya, Y.; Gersappe, D.; Balazs, A. C. Macromolecules 1995, 28, 6278.
1600 Langmuir, Vol. 13, No. 6, 1997
Figure 11. Longitudinal elasticity and longitudinal viscosity κ as a function of the interfacial polymer number density (in molecules/cm2) for the 14K molecular weight PS-PMAA diblock copolymer.
represented by either air when the polymer sits at the A/W interface or water when the polymer participates in a micelle. This may suggest that the PS block when in good solvent (toluene) makes a large contribution toward reduction of the surface energy through chain conformation energy (and possibly more effective solvent exclusion). In that case, the free energy reduction of adding a molecule to the T/W interface may be large enough to keep essentially all the added molecules at the interface and suppress micelle formation until the interface is very crowded. At the A/W interface, on the other hand, the free energy reduction of adding a molecule to the interface may be small enough that the micelle formation can compete once only weakly interacting molecules at the A/W interface produce weak repulsive forces. Similarly, the much larger time required for the A/W interface (as compared to the T/W interface) to come to an equilibrium might also be explained by a very small difference in free energy between interface population and micelle formation in the A/W case. Within the accuracy of our measurement method, the value of the transverse viscosity µ is always consistent with zero with an uncertainty of the order of 10-4 dyn‚s/ cm. We now turn our attention to the longitudinal wave moduli and κ. As has been discussed above, the density and viscosity contrast between air and water is sufficiently large that there is significant coupling between the transverse and longitudinal waves. This coupling makes it possible to determine both transverse and longitudinal viscoelastic moduli even though our apparatus primarily drives transverse waves. Figures 11-13 show the best fit values of the longitudinal elasticity and the longitudinal viscosity κ as a function of nominal polymer interfacial number density for molecular weights of 14K, 38K, and 283K diblock copolymer at the A/W interface, respectively. As the figures show, increases monotonically and with relatively small uncertainty as a function of nominal polymer number density until it reaches an intermediate value (typically e 10), above which value increases dramatically. As was discussed in section III, the large uncertainties in at these large values of are
Gandhi et al.
Figure 12. Longitudinal elasticity and longitudinal viscosity κ as a function of the interfacial polymer number density (in molecules/cm2) for the 38K molecular weight PS-PMAA diblock copolymer.
Figure 13. Longitudinal elasticity and longitudinal viscosity κ as a function of the interfacial polymer number density (in molecules/cm2) for the 283K molecular weight PS-PMAA diblock copolymer.
due to the insensitivity of observable capillary wave properties to changes in as becomes large. The daramatic increase in the longitudinal elasticity suggests the presence of a very stiff monolayer. As was indicated in the discussion of the ellipsometric results, at the A/W saturation, the PS on top of the A/W interface should only be able to cover the A/W interface diffusely. In that case, the measurement of such high stiffness for the diblock copolymers at the A/W interface for copolymers of all three molecular weights is puzzling.
Polystyrene-b-poly(methacrylic acid) Films
To turn our attention to the best fit values of κ, we refer again to Figures 11-13. These indicate that the value of κ at higher number densities is large with a large uncertainty. Just as in the case of , these uncertainties are not the uncertainties of the measurement but imprecision in the relation between the measured transverse wave properties and the longitudinal moduli. However, our results definitely indicate large values of κ for the copolymer film at the A/W interface over a range of nominal number density for each molecular weight. Nonzero values of the longitudinal viscosity have been conjectured to be due to the diffusional exchange of molecules between the bulk and the interface during contraction and expansion.28 In this picture, large values of the viscosity κ in our measurements would suggest that there is an exchange between the micelles in the bulk and the copolymer molecules at the interface, in which case our monolayer does not act like an insoluble monolayer. Our ellipsometric studies suggest enhanced micelle formation in the A/W case and hence indirectly support the above picture. The diffusional exchange of the molecules in such a case could short circuit any surface tension gradients created by the motion of the interface, resulting in effectively decreasing the longitudinal elasticity . Such a trend (of increasing κ as well as decreasing ) can be seen at least in the case of our 283K Mw copolymer at high nominal polymer number densities (Figure 13). The relaxation time for a diffusional exchange of molecules between the interface and the bulk should set a time scale for change of effective interfacial viscoelastic parameters, causing the measured viscoelastic parameters to depend on the frequency of the driven capillary waves used in the measurement. To address the question of the possible frequency dependence of our extracted viscoelastic parameters, it must be noted that we measure only two dependent variables, namely, the real and imaginary parts of the complex wavenumber as a function of the frequency of the capillary wave. With four unknown viscoelastic parameters (σ, µ, , and κ) in the dispersion relation, it becomes necessary to fit complex wavenumbers for all frequencies simultaneously, resulting in the loss of sensitivity to any frequency dependence of the viscoelastic parameters. Since all indications are that the transverse viscosity, µ, is very small, we have tested for evidence of frequency dependence in σ and by arbitrarily setting µ and κ to zero and fitting the complex wavenumber at each frequency to yield independent values of σ and . This analysis showed no dependence of the viscoelastic parameters (σ and ) on the frequency of excitation of the capillary waves (over a rather small frequency range of 500-2900 Hz). The lack of frequency dependence of these viscoelastic parameters in the frequency range explored by the experiment has been observed by other researchers in other A/W-polymer systems.35 V. Summary Following our previous experiment on the diblock copolymer PS-PMAA at a toluene-water interface,1 we have used the mechanically generated capillary wave method to measure the capillary wave properties of adsorbed monolayers of the same diblock copolymer at an air-water interface over a frequency range of 500 and 2900 Hz. Combining these measurements with the expected functional form of the dispersion relation for a thin viscoelastic interfacial layer between two simple fluids, we have determined the surface pressure π, surface transverse viscosity µ, surface longitudinal elasticity , and surface longitudinal viscosity κ, of the interfacial layer (35) Gau, C.-S.; Yu, H.; Zografi, G. Macromolecules 1993, 26, 2524. (36) Runge, F. E.; Kent, M. S.; Yu, H. Langmuir 1994, 10, 1962.
Langmuir, Vol. 13, No. 6, 1997 1601
as a function of nominal polymer number density and molecular weight of the copolymer. Significant light scattering from the bulk water indicated enhanced micelle formation in the air-water case, so we also measured the change in ellipsometric phase angle of the light reflected from the monolayer-covered interface to deduce the number of molecules adsorbed at the A/W interface. Ellipsometric studies showed that only a small fraction of the polymer was adsorbed at the interface (10% for the 14K and 5% for the 283K molecular weight copolymers). Beyond a certain nominal number density, the ellipsometric phase angle δ∆ reaches saturation, suggesting saturation in the number of polymer molecules adsorbed at the interface. However, in this saturation regime, interesting changes in π, , and κ have been observed with the addition of more copolymer molecules in the system. While the toluene-water case shows a clear saturation of surface pressure for all three molecular weight copolymers, no such clear saturation of surface pressure is seen in the air-water case for any molecular weight copolymer. Furthermore, the maximum surface pressure values of copolymer films at the air-water interface are very much smaller than the saturation surface pressure values at the toluene-water interface for the copolymers of all molecular weights. This difference in the strength of surfactant action, as well as enhanced micelle formation, may result from the change in the environment of the PS block from good solvent (toluene) to bad solvent (air). That is, the free energy reduction associated with adding a copolymer molecule to the T/W interface may be large enough to suppress micelle formation and keep essentially all the added molecules at the T/W interface until that interface is very crowded, while, in the A/W case, the free energy reduction at the interface is much smaller, so micelle formation can compete once a very small population of the A/W interface produces weak repulsive forces among weakly overlapping molecules. A similar free energy argument could explain the much slower progress toward equilibrium during sample preparation which characterizes the A/W interface in comparison with the T/W interface. That is, the free energy difference between interface population and micelle formation may be so small in the A/W case that metastable states can be very long lived. In all cases, the transverse viscosity µ is consistent with zero, with very small uncertainties of the order of 10-4 dyn‚s/cm. In the air-water case, there is a rather sudden transition of the longitudinal elasticity, , from intermediate to large values, which may indicate formation of a stiff monolayer. This is very puzzling when combined with the indication of the ellipsometric results that the monolayer at the A/W interface may be only diffusely populated at and after the onset of the saturation of the A/W interface. Large values of longitudinal viscosity κ are also observed, and these may suggest a diffusional exchange of molecules between the bulk and the airwater interface. Acknowledgment. We acknowledge helpful discussions with A. C. Balazs, J. S. Huang, and D. Jasnow. We also acknowledge Alan Esker and Hyuk Yu for their very helpful advice on performing Wilhelmy plate measurements. We also acknowledge Bruce Law and Xiao-Lun Wu for their helpful discussions on ellipsometric measurements. This work was supported by DOE Grant DE-FG02-84ER45131. LA9608324
