Langmuir 1996, 12, 2303-2307
2303
Properties of Surfactant Monolayers Studied by Surface Light Scattering Donal Sharpe and Julian Eastoe* School of Chemistry, University of Bristol, Cantock’s Close, Bristol BS8 1TS, United Kingdom Received November 27, 1995. In Final Form: February 21, 1996X Properties of monolayers, formed by soluble surfactants of widely differing chemical structure, have been investigated by surface light scattering over the frequency range ω0 104-105 s-1. For all surfactants studied, negative values for the dilational viscosity (′) were found, implying that the dilational waves are destabilized. This behavior is consistent with the presence of an adsorption barrier (Hennenberg, M.; et al. J. Colloid Interface Sci. 1992, 150, 7). This barrier can be altered by mixing dodecane into C16TAB and C10E8 monolayers, and ′ then assumes positive values. Furthermore, the characteristic time for monomer adsorption into the pure film (τads) may be estimated as about 10-5 s-1.
1. Introduction Thermally-generated capillary (transverse) waves exist at the interface between two fluids. Dilational (longitudinal) waves may be supported by the presence of a monolayer adsorbed at the interface and are coupled to the capillary waves.1 Surface light scattering (SLS) can be used to study these waves over the frequency range ω0 104-106 s-1.2 A sophisticated analysis of SLS data, developed by Earnshaw et al.,3 allows four surface properties to be obtained simultaneously (see below). Of interest here is the dilational viscosity (′). Insoluble monolayers (e.g., pentadecanoic acid) show positive values of ′.4,5 However, for some alkanol and soluble surfactant monolayers (e.g., C16TAB), ′ is found to be systematically negative.6-8 Lucassen and Van den Tempel predicted that a diffusive exchange of surfactant molecules between bulk and interface will have an important effect on the dilational viscosity.9 Furthermore, the recent theory of Hennenberg et al. shows that the presence of an adsorption barrier can cause destabilization of the dilational waves,10 which, it is believed, also results in negative ′.5,6 Recently, we have found that addition of dodecane to the surface of a C16TAB monolayer causes a transition to positive ′.11 The change in sign may arise if the adsorption barrier, and thus the characteristic time for adsorption (τads), increases. This would be expected when the density of the surface film increases. Here we have studied a wide range of surfactants by SLS to see if different chemistries have any effect on the dilational waves. Anionic, cationic, catanionic, zwitterionic, and nonionic surfactants were investigated. A fluorocarbon surfactant has also been included in the X
Abstract published in Advance ACS Abstracts, April 15, 1996.
(1) Lucassen-Reynders, E. H.; Lucassen, J. Adv. Colloid Interface Sci. 1969, 2, 347. (2) Langevin, D., Ed. Light Scattering by Liquid Surfaces and Complementary Techniques; Marcel Dekker: New York, 1992. (3) Earnshaw, J. C.; McGivern, R. C.; McLaughlin, A. C.; Winch, P. J. Langmuir 1990, 6, 649. (4) Earnshaw, J. C.; Winch, P. J. J. Phys.: Condens. Matter 1990, 2, 8499. (5) Sharpe, D. J. Ph.D. Thesis, Queen’s University, Belfast, U.K., 1995. (6) Earnshaw, J. C.; McCoo, E. Langmuir 1995, 11, 1087. (7) Earnshaw, J. C.; Sharpe, D. J. J. Chem. Soc., Faraday Trans. 1996, 92 (4), 611-618. (8) Earnshaw, J. C.; McLaughlin, A. C. Prog. Colloid Polym. Sci. 1989, 79, 155. (9) Lucassen, J.; Van den Tempel, M. Chem. Eng. Sci. 1972, 27, 1283. (10) Hennenberg, M.; Chu, X.-L.; Sanfeld, A.; Velarde, M. G. J. Colloid Interface Sci. 1992, 150, 7. (11) Sharpe, D.; Eastoe, J. Langmuir 1995, 11, 4636.
S0743-7463(95)01078-X CCC: $12.00
study. For pure films, the sign of ′ is negative. However, at low frequencies (ω0 ∼ 3 × 104 s-1), ′ is about a factor of 2 lower for the ionic monolayers as compared with the neutral ones. This suggests that counterion dissociation plays a discernible role. For mixed surfactant-dodecane films, positive ′ is observed. 2. Theoretical Background A liquid surface scatters light because it consists of a thermally-agitated diffuse molecular layer.12 Conceptually, this interface can be considered as a Fourier series of surface waves, where each has a well-defined wavelength Λ. The temporal behavior of the waves depends on both bulk and surface properties. Each capillary wave has a certain frequency ω and decays with time
ω ) ω0 + iΓ
(1)
Γ being the damping constant. The wavenumber q is given by
q ) 2π/Λ
(2)
For a monolayer-covered liquid surface, ω and q are related by a dispersion equation,13
D(ω) ) 0
(3)
where
D(ω) ) {q2/ω + iη(q + m)}{γq2/ω + gF/ ω - ωF/q + iη(q + m)} + [η(q - m)]2 (4) and
m ) x(q2 + iωF/η)
Re(m) > 0
(5)
η and F are the bulk liquid viscosity and density. The two moduli, transverse (γ) and dilational (), can be expanded to take into account viscous dissipation within the film, γ0 + iωγ′ and 0 + iω′. The parameters γ0 and 0 are elastic moduli, γ0 being identified with the surface tension and 0 with the equilibrium dilational elastic modulus, (12) Von Schmoluchowski, M. Ann. Phys. 1908, 25, 225. (13) Langevin, D. J. Colloid Interface Sci. 1981, 80, 412.
© 1996 American Chemical Society
2304 Langmuir, Vol. 12, No. 9, 1996
0 ) -dγ0/d ln Γs
Sharpe and Eastoe
(6)
where Γs is the surface excess. What are γ′ and ′? They may be considered to be surface viscosities, the transverse shear (γ′) and dilational (′) viscosity, respectively. As such, they act to increase the damping of the capillary14 and dilational15 waves, respectively. 2.1. Surfactant Monolayers. For soluble monolayers, the frequency dependence of the dilational modulus () has been given by Lucassen and Van den Tempel9
1+φ 0 ) ∞ 1 + 2φ + 2φ2
(7)
∞ φ ω 1 + 2φ + 2φ2
(8)
′ )
The parameter ∞ is the value of the dilational modulus for ω f ∞. The parameter φ reflects diffusive exchange of surfactant molecules between the subsurface and interface,
φ)
dc dΓs
x2ωD
(9)
where D is the diffusion coefficient of the molecules. The subsurface surfactant concentration is c. (The frequency ω may be identified with ω0.6) The parameter φ is dimensionless and essentially depends on the ratio of the experiental time scale to that for diffusion. Recently, Hennenberg et al. have shown that any barrier to adsorption can have a significant effect on the dilational waves.10 Primarily, a barrier may affect the rate of adsorption of surfactant molecules, thus perturbing the local diffusional equilibrium between surface and bulk. Over typical SLS wave frequencies, this barrier may act to reduce the stability of the dilational waves. What would cause this barrier? Two possibilities are (i) an adsorbing molecule must do work against the surface pressure and (ii) ionic surfactants must do added work against the surface potential. Both of these may serve to reduce the rate of adsorption from the subsurface. 3. Experimental Section 3.1. Materials. The chemical purity of all the surfactants was determined by elemental analysis and NMR. Where necessary, the materials were purified using established methods. All surfactants were stored in a dessicator, over refreshed P2O5, until used. The critical micelle concentrations (cmc’s) were checked by du Nouy tensiometry (Kru¨ss K10) and/or electrical conductivity (Jenway 3410 electrochemical analyzer). Where literature values for the cmc’s were available, there was good agreement.16-20 No impurities were evident from the du Nouy surface tension vs concentration data. Ionic Surfactants. Sodium bis(2-ethylhexyl)sulfosuccinate (AOT) (Sigma 99%) was used as received. Hexadecyltrimethylammonium bromide (C16TAB) (Aldrich) was washed 3 times in diethyl ether before use. Hexylammonium dodecyl sulfate (C12C6) was prepared by acidifying an ethanolic solution of sodium dodecyl sulfate (Aldrich 98%) using an ion-exchange resin (Amberlite IR-120 plus) and then neutralizing with hexylamine (14) Earnshaw, J. C.; McGivern, R. C. J. Phys. D 1987, 20, 82. (15) Kramer, L. J. Chem. Phys. 1971, 55, 2097. (16) van Os, N. M.; Haak, J. R.; Rupert, L. A. M. Physio-Chemical Properties of Selected Anionic, Cationic and Nonionic Surfactants; Elsevier: Amsterdam, 1993. (17) Williams, E. F.; Woodberry, N. T.; Dixon, J. K. J. Colloid Interface Sci. 1957, 12, 452. (18) Eastoe, J.; Rogueda, P.; Harrison, B. J.; Howe, A. M.; Pitt, A. R. Langmuir 1994, 10, 4429. (19) Packter, A.; Donbrow, M. J. Pharm. Pharmacol. 1963, 15, 317. (20) Kabalnov, A.; Weers, J.; Arlauskas, R.; Tarara, T. Langmuir 1995, 11, 2966.
Figure 1. Schematic representation of SLS setup. (Aldrich). The product was recrystallized from absolute ethanol 3 times. Cesium pentadecafluorooctanoate (CsPFO) was prepared by neutralization of a methanolic solution of pentadecafluorooctanoic acid (Aldrich) with an aqueous solution of CsOH (Aldrich). The salt was recrystallized from absolute ethanol 3 times. After purification, all surfactants were dried in a vacuum oven at 50 °C and then transferred to a dessicator. Nonionic Surfactants. Poly(oxyethylene (5)) lauryl ether (C12E5) and poly(oxyethylene (8)) decyl ether (C10E8) were obtained from Sigma. The glucamide sugar surfactant, 7,7-bis[(1,2,3,4,5-pentahydroxyhexanamido)methyl]-n-tridecane (di-C6Glu), was a kind gift from Alan Pitt (Kodak, Harrow, U.K.).21 Zwitterionic Surfactant. 1,2-Dioctyl-sn-glycero-3-phosphocholine (di-C8-PL) was obtained from Avanti Polar Lipids and used as received. The water came from a Milli-Q purification system. Octanol (99+%) was supplied by Aldrich and the dodecane (99+%) by Lancaster. Surface tensions, checked by both du Nouy ring and SLS, were in accord with literature values. Furthemore, the γ0 values determined by both methods were the same within experimental error. The watch glasses, used to hold the solutions for the SLS measurements, were first thoroughly cleaned with Decon solution in an ultrasonic bath. After rinsing with distilled water, they were placed in 30% nitric acid to remove all traces of detergent and then thoroughly rinsed with distilled and Milli-Q water. 3.2. Surface Light Scattering. The SLS setup was based on the design of Ha˚rd and Neuman22 (Figure 1) and modified to allow for normal incidence of light on the liquid surface. The light source used was a Spectra Physics He-Ne unit with a maximum power output of 5 mW at 633 nm. The laser beam was first spatially filtered before passing through a “weak” transmission grating that generates a series of diffracted beams. The lenses imaged the grating at the liquid surface. The diffracted orders converged at the surface and then diverged to form a series of reference beams at the detector, a Malvern Instruments photomultiplier tube (PMT). To improve the signal-to-noise ratio at the higher wavenumbers, appropriate Kodak Wratten gel neutral-density filters were positioned in the setup such that the reference beam intensity was reduced with respect to the scattered intensity. Normal incidence geometry was achieved (21) Briggs, C. B. A.; Newington, I. M.; Pitt, A. R. J. Chem. Soc.: Chem. Commun. 1995, 3, 379. (22) Ha˚rd, S.; Neuman, R. J. Colloid Interface Sci. 1981, 83, 315.
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Table 1. Surfactant Concentrations (c) Used in This Worka material C16TAB AOT CsPFO C10E8 C12E5 di-C6-Glu di-C8-PL C12C6 octanol
c/mmol dm-3
cmc/mmol dm-3
γ0/mN m-1
∆γ0
0.72 1.26 6.12 0.10 0.0052 0.80 0.0633 0.43 6.56
0.9016
37.5 35.8 40.1 54.4 57.1 35.3 32.0 30.7 28.9
0.05 0.08 0.09 0.14 0.13 0.04 0.10 0.05 0.05
2.3017 22.4 1.2816 0.064216 1.9018 0.2020 0.9219
a Surface tension (γ ) and associated uncertainties (∆γ ) deter0 0 mined by SLS measurements at 20 ( 0.1 °C. Experimental cmc’s agree well with the literature values referenced.
by using a polarizing beamsplitter and a quarter-wave plate;23 these components allowed the light to reach the liquid surface but prevented reflected light from returning to the laser. At the PMT, one of four reference beams, corresponding to 235 cm-1 < q < 613 cm-1, was selected to mix with the scattered light. The resultant “beats”, due to the small frequency differences between the reference and scattered light, were detected in heterodyne mode. The temporal evolution of the scattered light (g(τ)) was then determined by photon correlation using a 128-channel Malvern Instruments (K7025) correlator. Judicious setting of the PMT high voltage allowed the instrument to be operated in the “multiphoton counting regime”, enabling relatively rapid data acquisition.24 At the highest wavenumber, where the scattered intensity was smallest, a good correlation function could be obtained in about 20 min. The liquid sample, all optical components, and the PMT were mounted on a heavy (1-ton) Melles Griot optical table with horizontal and vertical vibration isolation capability. Samples were contained within a thermostated box, and the relative humidity was controlled. All experiments were carried out at 20 ( 0.1 °C. An equilibration time of about 1 h was allowed before SLS data were recorded. The data obtained at different q values were analyzed in two ways: (i) a damped cosine fit to obtain frequency ω0 and damping Γ25 and (ii) a more thorough (spectral) fit to determine the four surface viscoelastic parameters γ0, γ′, 0 and ′, which has been developed and extensively tested by Earnshaw et al.3 Typically, 10 g(τ) functions were averaged before fitting. Individual functions were also fitted as a consistency check. Repeated fitting with differing starting points would eventually produce the best quality fit, judging by a number of relevant fit criteria.3 The noise levels of the averaged correlation functions were generally about 0.5%. Under these conditions, it has been shown that the spectral fit can distinguish between ′ > 0 and ′ < 0.8
Figure 2. Dilational elastic modulus (0) and dilational viscosity (′) for ionic surfactant solutions. [C16TAB] ) 0.72 mmol dm-3, [AOT] ) 1.26 mmol dm-3, and [CsPFO] ) 6.12 mmol dm-3.
4. Results The SLS surface tension values (γ0) for the different surfactant solutions, averaged over four q vectors, are given in Table 1. Also included are surfactant concentrations (c), the cmc’s, and uncertainties in γ0. The concentrations were chosen to be below the respective cmc of each surfactant so that direct comparisons could be made with the nonmicellizing octanol and that any effects of the micelles ignored. However, data for c > cmc (not shown) were essentially identical to the lower concentrations. The transverse shear viscosity (γ′) could not be determined; this may be due to the small effect of γ′ on the capillary waves at low q as γ′ ∝ q3.14 Figures 2-4 show the frequency dependence of the dilational elasticity (0) and dilational viscosity (′) for pure films of the different surfactants. The solid lines on Figures 2 and 3 represent theoretical calculations, and these are discussed in more detail below. Data for the (23) Dorshow, R. B.; Hajiloo, A.; Swofford, R. L. J. Appl. Phys. 1988, 63, 1265. (24) Winch, P. J.; Earnshaw, J. C. J. Phys. E: Sci. Instrum. 1988, 21, 287. (25) Earnshaw, J. C.; McGivern, R. C. J. Colloid Interface Sci. 1988, 123, 36.
Figure 3. Dilational elastic modulus (0) and dilational viscosity (′) for nonionic surfactant solutions. [C10E8] ) 0.10 mmol dm-3, [C12E5] ) 0.0052 mmol dm-3, and [di-C6-Glu] ) 0.80 mmol dm-3.
octanol solution are given in Figure 5. Figure 6 shows data for mixed surfactant-dodecane monolayers, with either C10E8 or C16TAB. The bars on the figures are representative of the errors. For pure films, broadly speaking, the behavior of 0 falls into two main categories. AOT, C16TAB, and octanol show some frequency dependence but not the other surfactants. For the hydrocarbon amphiphiles, at 3 × 104 s-1, the mean value of 0 is about 45 mN m-1 for the ionics, but for the noncharged ones, it is around 25 mN m-1. However, for both types at higher frequencies (∼9 × 104 s-1), the 0 values are more alike. Clear trends are evident in the variation of ′ with ω0, and the data are surprisingly similar for the different surfactants. The frequency dependence of 0 and ′ is discussed below. For mixed films with dodecane (Figure 6), the magnitude of 0 is slightly lower than for the pure films. The most
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Sharpe and Eastoe
Figure 4. Dilational elastic modulus (0) and dilational viscosity (′) for [di-C8-PL] ) 0.0633 mmol dm-3 and [C12C6] ) 0.43 mmol dm-3. Figure 6. Dilational elastic modulus (0) and dilational viscosity (′) for two surfactants with added dodecane. [C10E8] ) 0.10 mmol dm-3 and [C16TAB] ) 0.72 mmol dm-3.
observation is that octanol behaves in a very similar way to the surfactants. 5. Discussion
Figure 5. Dilational elastic modulus (0) and dilational viscosity (′) for an octanol solution at 6.56 mmol dm-3.
striking change is in the sign of ′, which now assumes positive values. This transition suggests that increasing the film density, by incorporating dodecane in the layer,26 has an important effect on the dilational waves. Since in this case the dilational parameters do not show any obvious frequency dependence, we do not attempt to account for them here. 4.1. Effect of Surfactant Type. Changing the surfactant chemistry seems to have little effect on the trends in 0 and ′, although there is some scatter evident on the 0 data of AOT, C16TAB, and octanol. Consideration of the ′ data for the various materials shows that at the lowest wave frequency, the magnitudes for the ionic monolayers are about twice those of the neutral ones. This will be discussed in the next section. An interesting (26) Lu, J. R.; Thomas, R. K.; Aveyard, R.; Binks, B. P.; Cooper, P.; Fletcher, P. D. I.; Sokolowski, A.; Penfold, J. J. Phys. Chem. 1992, 96, 10971-78.
For insoluble monolayers, where bulk-to-surface diffusion is essentially absent, positive ′ values are always found when using the dispersion equation (eq 3).4,5 Why then is negative ′ found for soluble materials? This would suggest that, in its present form, the dispersion equation does not fully account for the behavior of soluble monolayers; i.e., ′ acts as an effective parameter.6 Below, we consider two different models that can explain negative ′. 5.1. Diffusive Exchange Model. The Lucassen and Van den Tempel diffusive exchange model9 (eqs 7-9) may be modified to give negative ′.8 This requires φ, and therefore dc/dΓs, to be negative. At first sight, this may seem surprising, given that, at equilibrium (ω0 f 0) and concentration about cmc, a typical value for dc/dΓs would be approximately +6 × 104 m-1.27 How then could dc/dΓs change its sign? Over the SLS frequencies, the concept of a phase difference between c and Γs has been introduced to account for this.8 This lag would mean that a molecule leaving the surface, and populating the subsurface, is not immediately replaced in the monolayer by another molecule. This may also be thought of as an adsorption barrier. Theoretical values of 0 and ′ were generated by setting D ) 1 × 10-9 m2 s-1, ∞ ) 22 mN m-1, and dc/dΓs ) -1 × 105 m-1, and these are shown on Figures 2 and 3 as lines. In the experimental frequency range, the generated 0 values decrease by about 2 mN m-1, while the ′ values are negative and approach zero at high ω0. In general, the experimental and generated 0 values agree well, especially so for the nonionics. Certainly, this approach has its limitations. However, in principle, it supports the idea that dilational wave damping is reduced for the soluble surfactants at these high frequencies. (27) Lu, J. R.; Thomas, R. K.; Penfold, J.; Flitsch, S. L. Langmuir 1993, 9, 1352.
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pressure. The lower ′ values for ionics indicate an additional electrostatic contribution to the barrier. What about the change in sign of ′ in the mixed monolayers? This can also be explained in terms of a changing adsorption barrier. An increase in Z from, say, 0.01 to 1 drives the instability threshold to lower frequencies,10 away from our experimental M-ω0 values. For the mixed film, the transition to positive ′ could be brought about by either an increase or decrease in Z.10,11 However, owing to the increased surface packing in the mixed film,26 an increase in Z and τads is the more likely reason. 6. Conclusions
Figure 7. Loci of neutral stability for dilational waves (adapted with permission from ref 10). Z ) 0 corresponds to no adsorption barrier, while Z ) 0.01 and Z ) 1 represent barriers of two different strengths. The shaded region shows the experimental values calculated using eq 12 and assuming D ) 1 × 10-9 m2 s-1.
5.2. Adsorption Barrier Model. Recently, the importance of Marangoni effects have been highlighted.10,28 At high frequencies, local temperature or concentration gradients in the film may be converted to mechanical energy. If energy is supplied to the dilational waves at a faster rate than it can be dissipated, the waves grow in amplitude.28 Particularly over SLS frequencies, the presence of an adsorption barrier can affect the dilational wave stability,10 which in turn results in reduced damping.6 Dilational wave stability can be considered in terms of the Marangoni elasticity number (M) and frequency.10,28 Loci corresponding to neutral stability of the dilational waves can be plotted in the M-ω0 plane (Figure 7). Inside a locus, the waves are self-sustaining and ΓD would be negative, which is impossible. On a locus, ΓD would be 0. Far outside, ΓD would presumably be unaffected. In the proximity of a locus, ΓD would be reduced, resulting in negative ′ values. The barrier can be represented by a ratio of two characteristic times Z: that for adsorption (τads) and that for diffusion from the bulk to a subsurface layer (τdiff). The loci for Z ) 0 (no barrier), Z ) 0.01, and Z ) 1 are shown on Figure 7. It is clear that increasing Z has a notable effect on the loci. Marangoni numbers for our experimental data may be estimated using28
M ) -0γ0m/FgηD
(10)
where m is defined by eq 5 and D is the diffusion coefficient of the solute (set at 1 × 10-9 m2 s-1). The experimental region has been marked on Figure 7. This regime is intercepted by the Z ) 0.01 locus, so this Z value is unlikely for these systems. However, if Z was slightly greater or less than 0.01, then the data would lie just outside the locus. The dilational wave damping would then be reduced. It can be seen that on moving to higher frequencies, the waves are more stable, as shown by the experimental ′ values. What do the differences in ′ for the ionic monolayers, as compared to the neutral ones, tell us? Since the values of M are almost identical for the different surfactants, these changes are consistent with slightly different Z values for the two categories. For the neutrals, there is apparently a “natural” barrier, perhaps owing to surface (28) Chu, X.-L.; Velarde, M. G. Physicochem. Hydrodynam. 1988, 10, 727.
Our studies of a wide range of soluble amphiphiles, with very different chemical structure, have improved the understanding of SLS from these monolayers. In general, for pure monolayers of compounds that either aggregate or do not, negative dilational viscosities (′) are found. This arises owing to a destabilization of the dilational waves. The observations are consistent with the presence of an adsorption barrier, which is important over the SLS frequency range. The frequency dependence of ′ may be understood in terms of two different models. A diffusive exchange model (Lucassen and Van den Tempel) can account for the observed negative ′ values but only if the quantity dc/dΓs is allowed to assume negative values at high frequencies. This condition would occur if the characteristic time for desorption was less than that for adsorption. In order to reflect the observations, a radical switch in dc/dΓs, as compared to that at equilibrium, is required. However, this seems doubtful. Although it is more complex, the adsorption barrier model (Hennenberg) does offer a more comprehensive understanding of the changes we have observed. The dilational wave stability, and thus the magnitude and sign of ′, can be influenced by the time ratio (Z), which is a manifestation of the barrier. For SLS, this effect will be most evident at the lower frequencies. With the neutral monolayers, ′ values are less negative than those for charged monolayers, suggesting that the dilational waves in the former are more stable. Furthermore, this indicates that there is a separate electrostatic contribution to the adsorption barrier. When dodecane is added to monolayers of C16TAB or C10E8, the dilational viscosities are systematically positive, and the waves become stable. The increased film density26 is expected to lead to an increase in τads and, so, Z. Returning now to the pure film systems, we can tentatively assign Z as either slightly greater or less than 0.01. With this in mind, τads may be crudely estimated to be of the order of 10-5 s for the soluble surfactants. Owing to the complexity of the Hennenberg model, we are not able to take the analysis any further at this stage. In order to advance, a dispersion equation, modified to take into account the specific properties of soluble monolayers, will be required. Acknowledgment. We thank the BBSRC for support via a research grant and postdoctoral associateship (D. S.). We warmly thank the following: Kodak European Research, Harrow, U.K., for providing the di-C6-Glu surfactant; Eveline Bollen, Jinfeng Dong, Alia Lodhi, and Philippe Rogueda (Bristol) for preparing surfactants and carrying out preliminary measurements; Prof. J. C. Earnshaw (Queen’s University, Belfast, U.K.) for providing the analysis programs; and Dr. Spence Taylor (BP, Sunbury, U.K.) for donating some equipment. LA951078+
