Oil Interface Inferred by

pubs.acs.org/Langmuir © 2009 American Chemical Society

Relaxation Processes of PGPR at the Water/Oil Interface Inferred by Oscillatory or Transient Viscoelasticity Measurements S
ebastien Marze* Nestl
e Research Center, Vers-chez-les-Blanc, CH-1000 Lausanne 26, Switzerland Received May 12, 2009. Revised Manuscript Received August 26, 2009 The rheological properties of PolyGlycerol PolyRicinoleate (PGPR) at the oil/water interface were studied using a drop-shaped tensiometer. Small deformation oscillations of the drop area allow the measurement of the interfacial viscoelasticity spectrum, that is, the elastic and viscous moduli as a function of frequency. Another way to obtain such a spectrum is to perform a transient relaxation measurement from which the relaxation modulus as a function of time is deduced and interpreted. Several models containing one or more relaxation times were considered, and their resulting spectra were compared to the oscillatory ones. Similar results suggest that one could in principle use oscillatory or transient relaxations indifferently. However, the transient relaxation technique proved to be more adapted for the determination of the relaxation times. At low PGPR concentrations in oil, the behavior is controlled by long relaxation times, whereas short ones take over when approaching and exceeding the saturation interfacial concentration. This was understood as a shift from a diffusion-dominated regime to a rearrangements-dominated regime.

Introduction Surface-active molecules (e.g., surfactants, emulsifiers, proteins) are widely used in many industries to form dispersions (e.g., foams, emulsions, suspensions, colloidal dispersions). Those can be used during processing or manufactured as finished products. Depending on the application, different levels of stability have to be achieved. Despite a significant number of studies focusing on how surface-active molecules at interfaces control dispersions stability, no definitive evidence was reached. 1-17 Some authors found that a high interfacial shear viscosity prevents emulsion1,2 or foam14 phase separation. For foam films, it was related to a high interfacial dilatational viscosity.3,11 Interfacial dilatational elasticity increases were found to correlate with improvements in many processes such as foam formation,6 coarsening7,14,15,17 or coalescence,9,17 and emulsion or foam phase separation.13,14 High interfacial shear viscoelasticity was also linked to enhanced foam formation10 or reduced coarsening.8,12

A few authors emphasized the importance of relaxation dynamics for interface stabilization.3,5,14,17 This implies a characterization of interfacial viscoelasticity in a wide frequency range. However, experiments usually allow its measurement in restricted and different frequency or time ranges. For dilatational perturbations, the drop shape or Langmuir trough techniques work at low frequencies, up to 1 rad.s-1, whereas the capillary pressure technique works in the range 10-103 rad.s-1 and the electrocapillary wave technique works in the range 102-104 rad.s-1. Surface quasi-elastic light scattering of thermally induced capillary waves works in the range 104-106 rad.s-1. Note that the wave perturbations usually are both of dilatational and shear natures. For pure shear perturbations, forced disk oscillations allow measurements at low frequencies, up to 102 rad.s-1.18,19 In most cases, the viscoelastic moduli are derived from mechanical, electrical, or thermal periodic perturbations (forced or damped oscillations), but can also be derived from instantaneous or continuous perturbations (steps or ramps).20-34

*Corresponding author. [email protected]. (1) Shah, D. O.; Djabbarah, N. F.; Wasan, D. T. Colloid Polym. Sci. 1978, 256, 1002. (2) Opawale, F. O.; Burgess, D. J. J. Colloid Interface Sci. 1998, 197, 142. (3) Fruhner, H.; Wantke, K. D.; Lunkenheimer, K. Colloids Surf., A 2000, 162, 193. (4) Wilde, P. J. Curr. Opin. Colloid Interface Sci. 2000, 5, 176. (5) Bos, M. A.; van Vliet, T. Adv. Colloid Interface Sci. 2001, 91, 437. (6) Beneventi, D.; Carre, B.; Gandini, A. Colloids Surf., A 2001, 189, 65. (7) Martin, A. H.; Grolle, K.; Bos, M. A.; Cohen Stuart, M. A.; van Vliet, T. J. Colloid Interface Sci. 2002, 254, 175. (8) Murray, B. S. Curr. Opin. Colloid Interface Sci. 2002, 7, 426. (9) Stubenrauch, C.; Miller, R. J. Phys. Chem. B 2004, 108, 6412. (10) Monteux, C.; Fuller, G. G.; Bergeron, V. J. Phys. Chem. B 2004, 108, 16473. (11) Koelsch, P.; Motschmann, H. Langmuir 2005, 21, 6265. (12) Cox, A. R.; Cagnol, F.; Russell, A. B.; Izzard, M. J. Langmuir 2007, 23, 7995. (13) Santini, E.; Ravera, F.; Ferrari, M.; Stubenrauch, C.; Makievski, A.; Kragel, J. Colloids Surf., A 2007, 298, 12. (14) Rodrı´ guez Patino, J. M.; S
anchez, C. C.; Rodrı´ guez Ni~no, M. R. Adv. Colloid Interface Sci. 2008, 140, 95. (15) Cervantes Martinez, A.; Rio, E.; Delon, G.; Saint-Jalmes, A.; Langevin, D.; Binks, B. P. Soft Matter 2008, 4, 1531. (16) Wierenga P. A.; van Nor
ela L.; Basheva E. S. Colloids Surf., A 2009, DOI:10.1016/j.colsurfa.2009.02.012 (17) Georgieva D.; Cagna A.; Langevin D. Soft Matter 2009, DOI: 10.1039/ b822568k

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(18) Miller, R.; Wustneck, R.; Kragel, J.; Kretzschmar, G. Colloids Surf., A 1996, 111, 75. (19) Ravera, F.; Ferrari, M.; Santini, E.; Liggieri, L. Adv. Colloid Interface Sci. 2005, 117, 75. (20) Kitching, S.; Johnson, G. D. W.; Midmore, B. R.; Herrington, T. M. J. Colloid Interface Sci. 1996, 177, 58. (21) Monroy, F.; Ortega, F.; Rubio, R. G. Phys. Rev. E 1998, 58, 7629. (22) Monroy, F.; Rivillon, S.; Ortega, F.; Rubio, R. G. J. Chem. Phys. 2001, 115, 530. (23) Freer, E. M.; Yim, K. S.; Fuller, G. G.; Radke, C. J. Langmuir 2004, 20, 10159. (24) Erni, P.; Fischer, P.; Windhab, E. J. Langmuir 2005, 21, 10555. (25) Babak, V. G.; Auzely, R.; Rinaudo, M. J. Phys. Chem. B 2007, 111, 9519. (26) Murray, B. S. Colloids Surf., A 1997, 125, 73. (27) Faergemand, M.; Murray, B. S. J. Agric. Food Chem. 1998, 46, 884. (28) Loglio, G.; Rillaerts, E.; Joos, P. Colloid Polym. Sci. 1981, 259, 1221. (29) Miller, R.; Loglio, G.; Tesei, U.; Schano, K. H. Adv. Colloid Interface Sci. 1991, 37, 73. (30) Cardenas-Valera, A. E.; Bailey, A. I. Colloids Surf., A 1993, 79, 115. (31) Serrien, G.; Geeraerts, G.; Ghosh, L.; Joos, P. Colloids Surf. 1992, 68, 219. (32) Boury, F.; Ivanova, Tz.; Panaiotov, I.; Proust, J. E.; Bois, A.; Richou, J. J. Colloid Interface Sci. 1995, 169, 380. (33) Saulnier, P.; Boury, F.; Malzert, A.; Heurtault, B.; Ivanova, Tz.; Cagna, A.; Panaiotov, I.; Proust, J. E. Langmuir 2001, 17, 8104. (34) Hansen, F. K. Langmuir 2008, 24, 189.

Published on Web 09/18/2009

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Here, the viscoelastic responses for forced area oscillations and area steps of a single drop are compared. We then analyze the results taking a mechanistic approach in order to understand the interfacial processes that are responsible for the viscoelasticity. We show that the interpretation of the transient relaxation following an area step reveals more mechanisms than forced area oscillations do. From the results of a preliminary study, we expect a promising link between those mechanisms and water/ oil emulsion stability.

Materials and Methods The PolyGlycerol PolyRicinoleate, a nonionic emulsifier, was provided by Danisco (GRINDSTED PGPR 90) and the oleic sunflower oil was provided by Nestl
e World Trade Corporation (8617.01). Milli-Q water having an electrical resistivity of 18 MΩ. cm was used. 3 wt % PGPR was dispersed in sunflower oil at room temperature. Other concentrations were obtained by successive dilutions. The TRACKER, a drop-shaped tensiometer from I.T. CONCEPT-TECLIS (France) was used to measure dynamic interfacial tension and viscoelasticity at room temperature (24 ( 1
C). A protocol was designed, in which (1) the drop size was set so that the initial Bond number35 was 0.1 ( 0.01; (2) a control area measurement was performed until the interfacial tension was constant; (3) after 4500 s, a rapidly increasing step (about 1 s) of 5 ( 1% of the drop area was done and the interfacial tension was recorded at the maximum acquisition rate (10 points/ s) until it came back to equilibrium (Figure 1). Even though the precision decreases with the interfacial tension level, we show in Figure 1 that it is still acceptable in the worst case of the highest PGPR concentration (typical fluctuations of 0.01 mN.m-1). For the PGPR concentrations in oil of 0.012 and 2 wt %, a fourth experiment followed, consisting of oscillation of the area with an amplitude of 2.5 ( 0.1% (peak-to-peak of 5 ( 0.2%) at several frequencies. For both types of perturbation, the linear regimes were determined. The relaxation modulus did not change between 4% and 12% area increase, and the viscoelastic complex modulus did not vary much between 2.5% and 20% amplitude at a frequency of 0.07 rad.s-1 (Figure 2). At a constant angular frequency ω, a change in the amplitude dA/A0 also changes the dilation rate ω.dA/A0 (and vice versa at a constant amplitude). Thus, some measurements were done where the frequency was decreased proportionally to the amplitude so as to keep the dilation rate constant.36-38 All types of measurement were highly repeatable, so each PGPR concentration was investigated only in duplicate and in triplicate for the PGPR concentrations of 0.012 and 2 wt %. Water/oil emulsions with different PGPR concentrations in oil were prepared by mixing with a Polytron (PT 10-35 from Kinematica, Switzerland) for 1 min. All emulsions had a total weight of 25 g and a dispersed-phase mass fraction of 0.3. Those were stored at 4
C for 5 months. The initial drop size distributions were determined using a Mastersizer S with a 300RF lens (Malvern, United Kingdom). Pictures were taken every month to follow their macroscopic destabilization.

Theoretical Basis The viscoelastic moduli39 were derived from several models reviewed elsewhere.19,40 Here, the bulk-interface diffusion (35) Bond number is defined as B = ΔFgL2/γ. (36) Wyss, H. M.; Miyazaki, K.; Mattsson, J.; Hu, Z.; Reichman, D. R.; Weitz, D. A. Phys. Rev. Lett. 2007, 98, 238303. (37) Krishnaswamy, R.; Majumdar, S.; Sood, A. K. Langmuir 2007, 23, 12951. (38) Marze, S.; Guillermic, R. M.; Saint-Jalmes, A. Soft Matter 2009, 5, 1937. (39) In the following, all moduli refer to interfacial dilatational ones. (40) van den Tempel, M.; Lucassen-Reynders, E. H. Adv. Colloid Interface Sci. 1983, 18, 281.

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Figure 1. Transient relaxation experiment of PGPR at the water/ oil interface (2 wt % PGPR in oil).

Figure 2. Water/oil interfacial elastic (filled symbols) and viscous (empty symbols) moduli measured by oscillations at a constant frequency of 0.07 rad.s-1 and increasing area dilation rate (equivalent to amplitude) at a PGPR concentration in oil of 0.012 wt %. The vertical lines show the linear regime (corresponding to amplitudes between 2.5% and 20%).

(Lucassen-van den Tempel, named lvdt) and the adsorption barrier theories will be compared. We restrict this study to these two models to follow the work of Kitching et al.20 Moreover, it is reasonable to exclude contributions from interfacial aggregation or reaction, as there are no signs from the bulk or interfacial tension behaviors. Briefly, the lvdt model assumes that adsorption/desorption are only controlled by diffusion, which is thus the only origin of relaxation. The calculations give E 0 ðωÞ ¼ E0

1þξ 1þ2ξþ2ξ2

and E00 ðωÞ ¼ E0

ξ 1þ2ξþ2ξ2

ð1Þ

where a characteristic relaxation time for diffusion λ = 1/ω0 can be introduced dc ξ ¼ dΓ

rffiffiffiffiffiffi! rffiffiffiffiffiffi D ω0 ¼ ¼ ð2ωλÞ -1=2 2ω 2ω

ð2Þ

with c and Γ the surfactant bulk and interfacial concentrations, D the surfactant bulk diffusion coefficient, ω the angular frequency, expressed in rad.s-1 and related to frequency f in Hz by ω = 2πf. In practice, the right-hand term of eq 2 is used to define ξ in eq 1. DOI: 10.1021/la9016849

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Figure 3. Water/oil interfacial tension as a function of time (highest interfacial tension curve) and with different PGPR concentrations (0.025, 0.037, 0.074, 0.22, 0.67, and 3 wt % from top to bottom).

Figure 4. Water/oil interfacial tension (circle) and parameters from the mþlvdt model as a function of PGPR concentration in oil. Data on top: the error bars are smaller than the symbols.

The measured relaxation modulus is expressed as EðtÞ ¼ ½γðtÞ -γ0 =f½AðtÞ -A0 =A0 g

ð3Þ

where γ0 and A0 are the interfacial tension and the drop area just before the step perturbation. The relaxation modulus for the lvdt model28,29 was calculated using an inverse Fourier transform EðtÞ ¼ E0 expð2t=λÞ erfc½ð2t=λÞ1=2 

ð4Þ

with E0 the Gibbs elasticity and erfc the error function. Briefly, the adsorption-barrier model assumes that surfactant sublayers form near the interface because of an energetic barrier to adsorption. It reduces to first-order kinetics when only one sublayer is considered to exchange matter with the interface. The viscoelastic moduli are then described by the one relaxation time Maxwell model40 (named m1), generalized with N relaxation times (named mN): E0 ðωÞ ¼

N X 1

EN

ðωλN Þ

2

1þðωλN Þ2

and E00 ðωÞ ¼

N X 1

EN

ωλN 1þðωλN Þ2

ð5Þ where EN and λN are the characteristic moduli and relaxation times of the system. For the relaxation modulus, an inverse Fourier transform gives EðtÞ ¼

N X

EN

expð -t=λN Þ

ð6Þ

1

Figure 5. Water/oil interfacial relaxation modulus measured from transient relaxation for different PGPR concentrations in oil. Full lines are for concentrations 0.0014, 0.0041, 0.012, and 0.025 wt % (increasing from pale gray to black with the full arrow), dashed lines are for concentrations 0.11, 0.67, 1, and 2 wt % (increasing with the dashed arrow).

(named mþlvdt) for the relaxation modulus, in eqs 4 þ 6, is transformed into eqs 1 þ 5 for the viscoelastic moduli. Some researchers did not assume any model a priori, using Fourier transforms20,23-30 to get the viscoelastic moduli from a measured relaxation modulus E0 ðωÞ ¼ ω

Z

¥

EðtÞ sinðωtÞ dt and E 00 ðωÞ ¼ ω

0

Note that the one relaxation time Maxwell model also describes the relaxation process of surfactant rearrangements (reorientations) at the interface in the case of an insoluble sublayer.19,20 The generalized Maxwell model was used empirically to account for multiple rearrangements processes.20-25 Although it was pointed out that diffusion and rearrangements processes could occur simultaneously,40 to our knowledge only one study coupled the lvdt and Maxwell contributions.20 Because of the linear property of Fourier transforms, such a mixed model 12068 DOI: 10.1021/la9016849

Z

¥

EðtÞ cosðωtÞ dt 0

ð7Þ

Results The water/oil interfacial tension decrease as a function of time for different PGPR concentrations is shown in Figure 3. Note that the sunflower oil is not completely free from surface-active molecules, as the interfacial tension without PGPR decreases down to ca. 20 mN.m-1. By removing those impurities using a Langmuir 2009, 25(20), 12066–12072

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Figure 6. Water/oil interfacial viscoelastic moduli measured by oscillations at constant amplitude, at constant dilatation rate (empty symbols), and deduced from the interfacial relaxation modulus using different models (see fitted parameters in Table 1) at a PGPR concentration in oil of 0.012 wt %. The insert shows the comparison of the mþlvdt model and the direct Fourier transforms of the relaxation modulus using eq 7.

column packed with Florisil 150-250 μm (Merck), it was checked that the interfacial tension did not decrease and, most of all, that the relaxation behavior was not modified, showing that no significant contributions originate from the unpurified sunflower oil. With increasing PGPR concentration, the interfacial tension shifts toward lower values. The values at 4500 s are reported as a function of PGPR concentration in Figure 4. This forms a classic Gibbs adsorption isotherm. In Figure 5, the relaxation modulus decays after the dilation step are shown at several PGPR concentrations. There are two typical curve shapes corresponding to low and high PGPR concentration ranges. Those relaxation curves were fitted with either the lvdt (2 parameters), the mN (2.N parameters, with N between 1 and 3), or the mþlvdt (4 parameters) models (respectively, eqs 4, 6, or 4 þ 6). Then, the fitted parameters were used in their viscoelastic moduli forms (respectively, eqs 1, 5, or 1 þ 5) which were plotted versus angular frequency (Figures 6 and 7). As examples, Table 1 gives the relaxation modulus averaged fitted parameters for the same PGPR concentrations as those reported in Figures 6 and 7. First, comparing the lvdt and mN fits of the relaxation modulus, much higher coefficients of determination were found using the lvdt model in the low PGPR concentration range. This range goes up to 0.037 wt %, at which the interfacial concentration is 1.1 mg.m-2. This is close to the saturation interfacial concentration determined to be 1.2 mg.m-2 at 0.074 wt % from a Gibbs model of the adsorption isotherm.42 Above 0.037 wt %, in the high PGPR concentration range, the coefficients of determination were, on the contrary, much higher for the mN model. This explains why two shapes of curve are observed. (41) Tschoegl N. W. The Phenomenological Theory of Linear Viscoelastic Behavior: An Introduction; Springer: Berlin, 1989. (42) Eastoe, J.; Dalton, J. S. Adv. Colloid Interface Sci. 2000, 85, 103.

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Then, using the mþlvdt model to fit the relaxation modulus, the same results were found with even higher coefficients of determination. The highest characteristic modulus indeed came from the lvdt part of the model in the low PGPR concentration range and from the Maxwell part of the model in the high PGPR concentration range. To go further, the complex viscoelastic modulus at 1 rad.s-1 (equivalent to the relaxation modulus at 1 s) and the main relaxation time (the one associated with the highest characteristic modulus) were extracted (Figure 4). The complex viscoelastic modulus varies within 1 order of magnitude. On the contrary, the main relaxation time undergoes a power law decrease of 2 orders of magnitude within 1 order of magnitude of concentration, even when the large error is taken into account. Together with the fact that the dominant part of the mþlvdt model shifts, we deduce that there is a change from a diffusiondominated regime to a rearrangements-dominated regime. The viscoelastic moduli obtained from the relaxation modulus fits, from direct Fourier transforms of the relaxation modulus, or measured by oscillatory perturbations, are compared in Figures 6 and 7 for one low and one high PGPR concentration. Although the viscoelastic moduli are in the same range, no calculations from the relaxation modulus are able to fully describe the oscillatory measurements. The agreement is generally better in the lowfrequency part. There is only a small difference between the lvdt and the mþlvdt models at low PGPR concentrations, because the diffusion process dominates. On the contrary, the Maxwell contribution dominates in the mþlvdt model at high PGPR concentrations, thus deviating from the lvdt model. The use of the mN model gives good results, although the choice of N is only based on the maximization of the coefficients of determination. This model can actually be rejected on the ground that it induces a moduli crossover at low frequency, which was never seen using the Fourier transforms or the oscillatory measurements in the investigated frequency and PGPR concentration ranges. In the high-frequency range, none of the models are really convincing for the viscous modulus and only the Fourier transDOI: 10.1021/la9016849

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Figure 7. Same as Figure 6 at a PGPR concentration in oil of 2 wt %.

form captures its increasing trend, although always shifted to higher frequencies. No quantitative agreement is found for this trend, as the Fourier transformed viscous modulus raises linearly whereas the oscillatory viscous modulus follows a power law with an exponent around 0.56. At the low PGPR concentration (Figure 6), this scaling law starts from a lower frequency than at the high PGPR concentration (Figure 7). This could indicate that both processes exist at any concentration, yet at different time ranges, which would explain the high coefficients of determination of the mþlvdt model. The oscillatory measurements at constant dilatation rate in Figure 6 only differ from the constant amplitude ones for the viscous modulus at the highest frequencies. At a double constant dilatation rate, only the viscous modulus above 1 rad.s-1 differs significantly (results not shown). In Figure 8, pictures of the water/oil emulsions after 5 months are shown. Below 0.11 wt % PGPR in oil, creaming was seen, and phase separation occurred as deduced by the presence of water at the bottom of the beakers. Above this concentration, only creaming occurred, and at high concentrations (from 3 wt %), there was no apparent destabilization.

Discussion The relaxation experiments analyzed by the mþlvdt model give similar viscoelastic parameters as the oscillatory experiments, with the advantage of identifying the relaxation times and their origins. The relaxation time varies in a much wider range than the viscoelastic moduli do. However, those parameters all behave as predicted by the lvdt model. Indeed, a similar power law decrease for the relaxation time as a function of the emulsifier concentration was deduced from adsorption experiments using the lvdt model in the low concentration range.43 Only the transition from a dominating lvdt term to a dominating Maxwell term using the mþlvdt model to fit the relaxation curves as a function of (43) Jayalakshmi, Y.; Ozanne, L.; Langevin, D. J. Colloid Interface Sci. 1995, 170, 358.

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Table 1. Fitted Parameters from the Relaxation Modulus Analyses Using the lvdt, mþlvdt, or mN Models for 0.012 and 2 wt % PGPR in Oila 0.012 wt % PGPR

2 wt % PGPR

11.9 ( 0.5 2.5 ( 0.6 E0 lvdt λ lvdt 1800 ( 700 32 ( 28 2 0.995 ( 0.001 0.857 ( 0.032 R lvdt 11.6 ( 0.4 1.27 ( 0.47 Elvdt mþlvdt 2000 ( 900 16 ( 2 λlvdt mþlvdt 0.57 ( 0.26 2.29 ( 0.22 Em mþlvdt 24 ( 8 2(1 λm mþlvdt 0.996 ( 0.001 0.949 ( 0.024 R2 mþlvdt 6.48 ( 0.52 1.7 ( 0.6 E1 mN 3550 ( 1150 7(4 λ1 mN 2.87 ( 0.21 0.51 ( 0.23 E2 mN 250 ( 50 290 ( 70 λ2 mN 2.25 ( 0.01 X E3 mN 30 ( 3 X λ3 mN 0.981 ( 0.014 0.923 ( 0.045 R2 mN a E are expressed in mN.m-1, λ in s, and R2 are the coefficients of determination.

emulsifier concentration demonstrates a deviation from the lvdt model. This indicates the transition from a diffusion-dominated regime to a rearrangements-dominated regime. This is in contrast with the results of Kitching et al.20 who found a rearrangementsdominated regime at low emulsifier concentrations, followed by a mixed regime, then a diffusion-dominated regime only above the critical micelle concentration of their nonionic emulsifier. However, they calculated a diffusion coefficient independent of the concentration (1.33  10-9 cm2.s-1), whereas we calculated from eq 2 with the adsorption isotherm data and the relaxation times that it decreases from 1.2  10-9 to 2.9  10-10 cm2.s-1 with the concentration (below 0.074 wt %). Those effective diffusion coefficients are quite low compared to the bulk value of 1.9  10-8 cm2.s-1 we found by NMR at a concentration of 8 wt % in sunflower oil, that is above the critical micelle concentration. So, micelles cannot be responsible for the low diffusion coefficients we found. This suggests a barrier to adsorption (in the form Langmuir 2009, 25(20), 12066–12072

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Figure 8. 30/70 water/oil emulsions after 5 months of storage at 4
C at various PGPR concentrations in oil (from left to right and top to bottom: 0.012, 0.037, 0.11, 0.33, 1, 3, 9 wt %).

of interfacial sublayers and/or rearrangements) at all concentrations. More work should be done to find what frequency range is needed to discriminate among these assumptions at a given emulsifier concentration. The range we investigated is indeed the low frequency range, as frequencies up to several kilohertz can be reached using other techniques.19 With those, one would maybe see a fast relaxation (bump in E00 , eventually decreasing at high frequencies) as seen by some authors.20-22 One would alternatively see both moduli following a common power law of typical exponent between 0.5 and 0.75 (presumably starting in Figure 7), as often seen in bulk viscoelasticity. The Rouse theory44 is the first one predicting such a behavior (with an exponent of 0.5). Then, other additions or theories45 refined the prediction. To our knowledge, only one effort tried to apply the Rouse theory at interfaces, in qualitative agreement with experiments.46 The effect of the dilatation rate shows that the measurement itself can induce an overestimation of the viscous modulus. This was discussed in the case of oscillating drop or bubble.47-49 For the present results, the maximum Weber and Capillary numbers are We = ΔF(ωΔL)2L/γ ≈ 5  10-7 and Ca = Δη(ωΔL)/γ ≈ 2  10-3, with drop length L and dilatation ΔL of 10-3 and 10-4 m, relative density ΔF and viscosity Δη of 100 kg.m-3 and 0.05 Pa.s, and interfacial tension γ of 2 mN.m-1. The inertia and bulk viscosity dissipations could then be discarded, as We is very low and Ca is just at the limit found by Freer et al.47 Working at a constant dilation rate allows We and Ca to be kept constant. So, the deviation of the frequency sweep data from the constant (44) Rouse, P. E., Jr. J. Chem. Phys. 1953, 21, 1272. (45) Larson R. G. The Structure and Rheology of Complex Fluids; Oxford University Press: New York, 1999. (46) Noskov, B. A.; Akentiev, A. V.; Bilibin, A.Yu.; Zorin, I. M.; Miller, R. Adv. Colloid Interface Sci. 2003, 104, 245. (47) Freer, E. M.; Wong, H.; Radke, C. J. J. Colloid Interface Sci. 2005, 282, 128. (48) Leser, M. E.; Acquistapace, S.; Cagna, A.; Makievski, A. V.; Miller, R. Colloids Surf., A 2005, 261, 25. (49) Yeung, A.; Zhang, L. Langmuir 2006, 22, 693.

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dilation rate data could indicate a bulk effect. The critical capillary number deduced from Figure 6 is thus 10-3, in agreement with Freer et al.47 For very high frequency measurements using mechanical perturbations, corrections are thus needed.3,47 Non-pertubative experiments would then be very interesting to investigate high frequencies without artifacts. In bulk, the use of multiple scattering optics allowed to recover the power law behaviors usually observed with mechanical perturbations.50,51 This proved the observations to be measurement-independent. So, it is also possible that the interfacial observations are measurement-independent, all the more since most theories for multiple relaxation times at high frequency are based on uncorrelated individual contributions,51 which might also be the case at interfaces. In this respect, the surface quasi-elastic light scattering would be a non-perturbative technique, but it is currently only able to investigate gas/water interfaces and limited to very high frequencies. For the water/oil emulsions stability, we calculated the PGPR concentration required to saturate the emulsion interfaces with a mean drop diameter of 1 μm and an interfacial concentration of 1.2 mg.m-2. We found a value of 0.3 wt %, a bit higher than that observed for water/oil emulsion phase separation stability. Above this concentration, the drop size distribution did not vary significantly, presumably due to the saturation of the interfaces by the emulsifier. Then, the full stability threshold seems to correspond to the critical micelle concentration one can infer from the interfacial tension plateau at high concentrations (around 1 wt %, close to previous results52). Comparing those preliminary observations together with our interfacial viscoelasticity results, we propose that, when the interfaces become saturated by the emulsifier, the rearrangements (50) Waigh, T. A. Rep. Prog. Phys. 2005, 68, 685. (51) Willenbacher, N.; Oelschlaeger, C. Curr. Opin. Colloid Interface Sci. 2007, 12, 43. (52) Bus, J.; Groeneweg, F.; van Voorst Vader, F. Prog. Colloid Polym. Sci. 1990, 82, 122.

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regime takes over the diffusion regime, leading to the emulsion stability increase. To assess this transition, we think the main relaxation time of the mþlvdt model should be a more appropriate indicator than the viscoelastic moduli.

Conclusions By comparing interfacial oscillatory and transient relaxation experiments, it was shown that the use of a mixed model accounting for both bulk-interface diffusion and rearrangements at the interface best describes the relaxation modulus. Then, we showed that this model actually discriminates between the two regimes as a function of the emulsifier concentration. However, the oscillatory measurements and direct Fourier transforms are not absolutely in agreement with the viscoelastic moduli deduced by this model from the relaxation modulus, especially at high frequencies. Measurements at higher frequencies are required to check the model prediction of two relaxation processes at a given emulsifier concentration. However, care must be taken when

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using mechanical perturbations, which could induce viscous and/or inertial effects. Preliminary observations of water/oil emulsions stability were also understood through the shift from the diffusion (long process) to the rearrangements (fast process) regimes. In this frame, we think that the main relaxation time deduced from a transient relaxation experiment should be a better stability indicator than the viscoelastic moduli. More work is being conducted with other emulsifiers in order to check the present results, notably for the ability of the mixed model to predict the stability increase above the saturation interfacial concentration and also above the critical micelle concentration. Acknowledgment. I thank Eric Hughes of NRC for NMR measurements. I thank Axel Syrbe, Martin Leser, Deniz Gunes of NRC, Reinhard Miller, J€urgen Kr€agel of Max-Planck-Institut, and Dominique Langevin of Universit
e Paris-Sud for helpful discussions.

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