and Microstructure of High-Internal Phase Emulsions Under Shear

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Nano- and Microstructure of High-Internal Phase Emulsions Under Shear Peter N. Yaron,† Philip A. Reynolds,† Duncan J. McGillivray,‡ Jitendra P. Mata,†,§ and John W. White*,† Research School of Chemistry, Australian National UniVersity, Canberra, ACT 0200, Australia, Department of Chemistry, The UniVersity of Auckland, Auckland 1142, New Zealand, and Bragg Institute, ANSTO, PMB 1, Menai, New South Wales 2234, Australia ReceiVed: September 01, 2009; ReVised Manuscript ReceiVed: February 11, 2010

High-internal phase aqueous-in-oil emulsions of two surfactant concentrations were studied using smallangle neutron scattering (SANS) and simultaneous in situ rheology measurements. They contained a continuous oil phase with differing amounts of hexadecane and d-hexadecane (for contrast matching experiments), a deuteroaqueous phase almost saturated with ammonium nitrate, and an oil-soluble stabilizing polyisobutylenebased surfactant. The emulsions’ macroscopic rheological behavior has been related to quantify changes in microscale and nanoscale structures observed in the SANS measurements. The emulsions are rheologically unexceptional and show, inter alia, refinement to higher viscosity after high shear, and shear thinning. These are explained by changes observed in the SANS model parameters. Shear thinning is explained by SANSobserved shear disruption of interdroplet bilayer links, causing deflocculation to more spherical, less linked, aqueous droplets. Refinement to higher viscosity is accompanied by droplet size reduction and loss of surfactant from the oil continuous phase. Refinement occurs because of shear-induced droplet anisotropy, which we have also observed in the SANS experiment. This observed anisotropy and the emulsion refinement cannot be reproduced by either isolated molecule or mean-field models but require a more detailed consideration of interdroplet forces in the sheared fluid. Introduction Emulsions with a volume fraction of the dispersed phase larger than the maximum packing fraction for monodisperse spheres are referred to as high-internal phase emulsions (HIPEs). A mixture of two immiscible Newtonian fluids often produces a non-Newtonian mixture due to the presence of an elastic interface between the two phases. The non-Newtonian behavior of a mixture is also often enhanced when a surfactant is added to cover and stabilize the interface.1 Above the critical micellar concentration, surfactant not covering droplets resides in the continuous phase as nanometer-sized micelles, micrometer-scale aggregates, or dissolved.2 The surfactant available as micelles in the oil phase plays an important part in stabilizing the emulsion, in addition to the stabilizing surfactant monolayer provided at the oil-droplet interface (see refs 3 and 4 and references therein). Minimizing the amount of surfactant through its economical distribution is of interest in commercial applications because the surfactant often comprises the most expensive component of the emulsion. This paper examines the effect of shear on the structure of a class of these emulsions consisting of saturated ammonium nitrate solution dispersed in hexadecane, stabilized by a low concentration of hexadecane-soluble polyisobutylene-based surfactant (polyisobutylene succinamide-PIBSA). It follows a series of small-angle neutron scattering (SANS) papers examining structural variation and stability of these and related emulsions as other parameters are varied (aqueous/oil phase ratios, * Corresponding author. Phone: 02 6125 3575. Fax: 02 6125 0750. [email protected]. † Australian National University. ‡ The University of Auckland. § Bragg Institute.

surfactant concentration, surfactant molecular weight, and polydispersity).3-8 In these emulsions, the high packing density is achieved by a large polydispersity in droplet size, as inferred from ultrasmallangle neutron scattering (USANS),9 cryo-FESEM, and confocal microscopy. In other HIPEs,10-17 substantial polyhedral distortion of the droplets has been observed and is related to their rheology. These distortions are observed here but are much smaller in extent. Indeed, at higher PIBSA concentrations, the droplets are insignificantly different from spherical. In these experiments, we observe and quantify the location of the surfactant, aqueous droplet size, and deformation as a function of surfactant concentration and applied shear. Utilizing a combination of contrast variation SANS and simultaneous insitu rheology, we relate the microscopic structural behavior of the emulsion to its macroscopic rheological behavior. The simultaneity was advantageous in minimizing variations in the emulsification procedure, shear history, sample transfer, etc. By then combining the SANS and rheology data with extant theories, a unified picture of the emulsion under shear has been established at all relevant length and time scales. Previous work on concentrated emulsions provides background for the present work. An excellent review of the rheology of emulsions has recently appeared.18 Related work on the rheology of supersaturated salt emulsions by Masalova and Malkin19 and references therein support the conclusions drawn here. Jansen et al.2 have included the effects of extra surfactant in the continuous phase in the calculation of a depletion energy, which we will relate to our contrast-matched SANS data. Welch et al.10 have studied emulsions of rheology similar to ours and shown that existing models are unable to account for their observations.

10.1021/jp9084525  2010 American Chemical Society Published on Web 02/24/2010

High-Internal Phase Emulsions Under Shear

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TABLE 1: Emulsion Sample Preparation Recipes (in mg), Corresponding Scattering Length (10-6 Å-2), and Physical Densities, (σ), (in g mL-1) sample

surfactant

C16D34

C16H34

AN/D2O

σAN/D2O

AN/D2O SLD

σC16H/D34

C16H/D34+ surfactant SLD

CM 1% UM 1% CM 0.3% UM 0.3%

151.0 150.8 45.4 45.3

931 0 938.7 0

122.1 922.6 280 1090.6

17 765 17 759 17 749 17 757

1.314 1.314 1.314 1.314

4.88 4.88 4.88 4.88

0.876 0.773 0.862 0.773

4.88 -0.42 4.73 -0.43

Langenfeld et al.11 have previously used simultaneous SANS and rheological experiments on a water-in-oil system. They showed that the two methods give consistent results in estimating interfacial surface area. They also related the effects of the shear rate and aqueous/oil phase volume ratio to the interfacial surface area and emulsification efficiency. Our work extends theirs to exploit contrast variation to directly observe surfactant at the interface and in micelles and quantify shear-induced anisotropy in the SANS scattering. These parameters provide additional self-consistency tests to the macro- nanolinking model by monitoring shear-induced droplet deformation and surfactant shifts among the interface, micelle, and solution. Experimental Section Emulsion Preparation and Microscopy. The HIPEs used in our experiments were prepared by fast shearing the oil-surfactant mixture at 80 °C while slowly dropping in the saturated ammonium nitrate solution. The procedure and materials have been described in previous papers.3-8 The samples were prepared using saturated ammonium nitrate (aqueous phase), hexadecane (oil phase), and PIBSA (surfactant), with varying neutron-scattering contrasts and two different surfactant concentrations. Previous SANS, rheological, and microscopic experiments show that all these emulsions are qualitatively similar to those used in the shearing experiments below. CryoFESEM electron micrograph images of emulsion surfaces produced by microtoming frozen emulsions at 77 K were obtained by use of a Cambridge S360 electron microscope. The confocal microscopy, using a Leica laser-scanning microscope, used saturated ammonium nitrate/diesel/PIBSA emulsions at room temperature. Diesel was used instead of hexadecane to provide fluorescence. The confocal images were slices from the surface down to about 20 µm into the emulsion. Each slice had a vertical resolution of a little better than 1 µm. Rheology. Rheology experiments were conducted in situ on the LOQ beamline (Rutherford Appelton Laboratory, ISIS Facility Chilton, UK) using an Anton-Paar Physica MCR501 Rheometer. This was of Couette cell geometry with two concentric quartz cylinders, an inner stator (radius 25 mm), and an outer rotor with a 0.5 mm gap between cylinders and a bottom gap of 0.56 µm. The rheometer allows continuous logging of the emulsion viscosity as the neutron beam passes through the vertical axis of the concentric cylinders perpendicular to the emulsion sample. All experiments were temperature-controlled at 25 ( 0.3 °C using the air-cooling system of the rheometer. To collect the desired rheological information from the sample while collecting scattering data, a series of time-interval tests was developed. Emulsion samples were sheared at a constant shear rate for a time interval that allowed for both the emulsion to reach a steady-state viscosity and reliable neutron scattering statistics. The evolution of both shearing and recovery runs was tracked to observe shear thinning/thickening, thixotropy, and other non-Newtonian behavior. A low shear rate (1 Hz) was first applied to establish a common starting point for all emulsion measurements by eliminating any shear history effects due to

sample handling or preparation. This shear was chosen to start from a destructured state without causing droplet breakage.20 Higher shear rates were then applied at 100, 500, 1000, and 2000 Hz with return to the low shear rate (1 Hz) to observe the recovery/regeneration of the emulsion after each. This test is a modification of a three-interval time test (3ITT) typically used to determine thixotropy in a sample.21 The postshearing 1 Hz “recovery” intervals were used to return the emulsion to a steady-state equilibrium viscosity value. There was no evidence of bubbles at the end of the test. A minimum of 24 h at 25 °C was allowed after manufacture for the emulsion to reach a stable structure and to ensure a consistent initial starting point for each scattering/rheology measurement. Sample transfers into the Couette cell were performed by placing the emulsion in the bottom of the rotor cup and very slowly introducing the stator to minimize shearing during sample transfer. Errors due to the rheometer’s Couette geometry, such as wall slippage, formation of Taylor vortexes, and end effects in the emulsion, were avoided by staying below the critical shear rate where these behaviors occur. The Reynolds numbers (Re) at each shear rate were calculated to avoid the formation of Taylor vortexes and end effects in this configuration. Values as low as Re ∼ 2000 can induce the onset of vortexes in the emulsion and alter the viscosity value recorded.22 At the highest shear rates (2000 Hz), the setup approached a Reynolds value of Re ∼ 500. Slippage was also checked by plotting the viscosity versus shear stress and checked for the appearance of shoulders or discontinuities and was cross-checked with a separate shear ramp experiment that used an identically prepared emulsion and found no slippage effects until well above 2000 Hz shear rate. Small-Angle Neutron Scattering Experiments. Measurements were conducted using incident neutron wavelengths between 2.2 and 10 Å, sorted by time of flight, with a sample detector distance of 4.1 m. This gives a Q range between 0.006 and 0.24 Å-1. The 1 mm sample total path length (front and back of Couette cell) ensured transmissions >90% and, thus, no need for multiple scattering corrections. To better understand the role of the surfactant in the emulsion structure, contrast matched (CM) and contrast unmatched (UM) samples were made at each concentration. CM samples reveal the hydrogenous surfactant situated at the aqueous-oil interface and in reverse micelles in the oil phase. Here, the high scattering length densities (SLD) of the aqueous phase ammonium nitrate/ deuterium oxide (AN/D2O) was matched with that of the oil phase (hexadecane/d-hexadecane) so that both then contrast strongly with the scattering from the low-SLD surfactant (-0.06 × 10-6 Å-2). UM samples were designed to highlight the aqueous/droplet interface. This was done using hexadecane of low SLD (-0.43 × 10-6 Å-2) almost matching that of the surfactant, both then contrasting with the high SLD of the AN/ D2O. A table of the emulsion constituents is shown in Table 1. Each emulsion had 90% dispersed aqueous internal phase and 10% continuous oil phase, by volume. Anisotropy in the scattering profiles was analyzed by partitioning the raw data collected from the 2D detector array

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Yaron et al. oil-aqueous interface (Q-4 dependence). The CM emulsions show scattering from the thin slab of low SLD at the interface due to adsorbed surfactant (Q-2 dependence).

I(Q)tot ) (1 - frac)I(Q)Porod + I(Q)micelle + I(Q)bk + (frac)I(Q)bilayer

Figure 1. Illustration of the simultaneous SANS/rheometry experimental setup. The dashed lines and shaded areas on the detector plate indicate the partition of the integrated signal into horizontal (Qx) and vertical components (Qy).

into horizontal and vertical components. The two vertical components were integrated radially between 60° and 120° and 240° and 300° and two horizontal slices taken from 150° to 210° and 330° to 30° to the horizontal where the +Qx axis is defined as 0°. The 60° partitions were chosen to ensure there was no overlap of the integrated intensity taken in the vertical and horizontal regions. Figure 1 illustrates how the detector signal was partitioned and radially integrated. The upper and lower slices give the vertical (Qy) data, and the left-right slices, the horizontal (Qx). The backgrounds were similarly treated. Unlike other systems that we have studied, the anisotropy is not clearly visible from the two-dimensional plots and must be obtained by the integrations defined above. Small-Angle Neutron Scattering Data Analysis. The samples were run, and data were processed in standard ways to obtain absolute intensity versus Q plots,23,24 where Q is the wavevector transfer. A D2O sample run was used for cell background subtraction. The sample incoherent background was subtracted using scaled H2O and D2O runs, with scaling appropriate to the hydrogenous content of the emulsions. The model used to fit the SANS data has been used extensively before.3-8 The total scattering intensity is approximated as the sum of four intensity components: scattering fromafreeaqueousdroplet/oilinterface,fromanaqueous-oil-aqueous bilayer formed by droplets touching and deforming, from reverse micelles in the oil-continuous phase, and the incoherent scattering background. The huge disparity in size between aqueous droplets and reverse micelles renders the interference term between them negligible. At this surfactant concentration in hexadecane, we do not expect the micrometer-scale aggregation of PIBSA that we have observed with other oil phases. The water droplets’ smallest mean radii are several thousand angstroms. The lowest accessible Q range of LOQ is insufficient to detect this droplet interface curvature. Thus, planar models fit the interfacial scattering. The UM emulsions show a Q dependence close to Porod scattering (Q-4 dependence) from the SLD step at the droplet interface and, thus, give the droplets’ specific surface area. There was a slight but significant deviation from a Q-4 Porod slope. This can be accounted for by invoking a small percentage of the surface area, where two droplets have touched and formed a planar aqueous-oil-aqueous bilayer, the beginning of droplet “polygonization”. The percentage of droplet surface flattened is defined in the model by the parameter “frac”. The resultant total scattering function is a summation of four components, as shown in eq 1. At the lowest Q values, frac is the percentage of scattering from a slab (Q-2 dependence) compared to the slab scattering plus the Porod scattering from the remaining step

(1)

The model used for the reverse micellar scattering is based on the Percus-Yevick approximation for micelle distribution within the oil with a micelle polydispersity given by a Schultz distribution. The model fits were applied to both the CM and UM data using IGOR routines. The instrumental resolution function was used to appropriately convolute the calculated intensity to compare with the experimental. The inclusion of the various scattering contributions discussed above introduces a large number of free parameters in this model. Previous SANS experiments and model fitting on the emulsions and corresponding hexadecane and other oil phase inverse micelle solutions allow many of these to be fixed. A mean micelle radius of 31 Å, micelle polydispersity of 0.25, shell and core SLD of 1.46 × 10-6 Å-2, and oil SLD of 4.79 × 10-6 Å-2 were fixed in the CM data; the reverse micelle volume fraction in the oil, micelle SLD, droplet interfacial, and incoherent background area remained as the four free parameters. In the UM fits, the model was constrained by entering the same fixed values, allowing background, Porod interfacial area, frac, and micelle SLD to vary, with the volume fraction of micelles in the oil phase, φmicelle, fixed at the value obtained from the analogous CM emulsion. The fits produced were satisfactory. We have tested the model-fitting procedure with even more constrained parameter refinements to ensure that a global minimum has been obtained with the least number of parameters. The standard errors quoted in the Supporting Information are smaller than the real errors. This is because we have, as is usual in SANS, included only errors due to neutron counting statistics and neglected the significant, but poorly understood, systematic errors. Some appreciation of the true errors can be obtained by comparison between the results of the different fits. The trends in parameter values are more reliable than the true errors (if known) would suggest, since the different data sets incorporate similar systematic errors; both the SANS and rheometer results are very reproducible. The refined values of oil interface scattering length densities, micellar volume fraction, and SLD can be used to calculate a total mass of surfactant detected by SANS. After augmentation by the proportion of surfactant dissolved in the oil, known from previous inverse micellar solution SANS studies,4-8 we can compare the total amount of surfactant found by scattering with that weighed into the emulsion mix. This is a further test of our modeling procedure. Results Microscopy. A typical FESEM image of a microtomed PIBSA- or SMO-containing emulsion surface is shown in Figure 2a. Such images show spherical droplets with a high polydispersity in droplet diameter, from ∼1 to 20 µm. Figure 2b shows a typical image slice obtained by the confocal microscopy, ∼21 µm down from the emulsion surface. Again, spherical droplets are present. When the complete stack of slices is viewed sequentially, the sphericity is even more apparent. The images are insensitive to the small distortions from sphericity that have been invoked in the frac fitting parameter needed for the neutron small-angle scattering.



Figure 2. Cryo-FESEM (a) and confocal microscopy (b) images of the unsheared emulsion in its quiescent state. We see that large polydispersity and not polyhedral distortion is responsible for the highly dispersed phase volume fraction.

Figure 4. Steady-state equilibrium viscosities extrapolated from final viscosity values (red circles, a) by determining the time needed to reach a point at which the change in apparent viscosity was negligible (∼∆η ) (0.3 Pa · s). Values of all shearing (squares, b) and resting runs (open circles, b) are shown for the 1% (red) and 0.3% (black) UM emulsions. Note the slightly different time periods due to fluctuations in neutron beam flux, which causes some variation in run intervals.

Figure 3. A plot of the shear rate versus time (a) and viscosity versus time (b) of a typical emulsion experiment (CM 0.3% active surfactant).

Rheology. The profile of a typical rheology experiment is shown in Figure 3. The top figure illustrates the shear rates, D, applied by the stator as a function of time, and the bottom figure shows the corresponding recorded viscosity, η. The times of the individual runs are slightly different due to slight changes in the neutron beam flux affecting total time needed to accumulate the deemed minimum total integrated intensity needed for an acceptable signal-to-noise ratio. All the emulsions show the same qualitative behavior, with some changes to the degree of shear thinning and increase in effective viscosity. The overall changes in viscosity for each sample are shown by plotting the extrapolated equilibrium viscosity values versus time reached at the end of each individual run interval (Figure 4). Where there is obvious relaxation in the viscosity after high shear intervals (e.g., near 1.8 × 104 s in Figure 4), extrapolated viscosity values in each interval were calculated by fitting an exponential to the data. The viscosity was assumed to be equilibrated when change in the apparent viscosity was negligible in that interval. For intervals that displayed oscillations (due to instrument control feedback) and behavior that could not be fitted by an exponential, the final viscosities were taken as the steady-state values. The changes in viscosity for both the recovery and shearing runs are more pronounced in the 1% active surfactant emulsions.

Small-Angle Neutron Scattering. Isotropically Averaged Scattering. Scattering patterns from the experiments are shown in Figure 5. Analysis of the SANS data was performed using the model described in the data analysis section and in previous papers.3-8 In both the CM and UM data, the low-Q intensities increase in value, even in the 1 Hz recovery interval measurements. This effect becomes more pronounced as the applied shear is increased above 500 Hz. In the UM scattering data, the intensity at low Q defines the total interfacial surface area, AV, of the droplet-oil interface in the emulsion. The increasing low Q intensity as a function of applied shear of the UM data indicates that a new surface area is being created through refining emulsion droplets to smaller sizes. The CM data, however, also reflect increasing surfactant loading at the interface, as well as an increase in the surface area. The surfactant loading in the CM data may be estimated using the UM-derived interfacial surface area combined with the intensity of scattering at low Q in the corresponding CM emulsion data. The CM data also show a pronounced “hump” centered at ∼Q ) 0.055 Å-1 that is indicative of scattering from the reverse micelles in the oil phase. The drop in this intensity at ∼Q ) 0.1 Å-1 shows the micelle diameters are on the order of ∼60 Å. As the shear rate is increased, the intensity of the micelle peak changes, showing a shear dependent change in φmicelle. The location of the emulsion-stabilizing surfactant and its redistribution by the shear field can be quantified from the SANS model fits for the CM and UM data. The values for φmicelle, AV, loading, total amount of surfactant, and frac for each shearing interval are the indicators of the changing nanostructure. These are plotted in Figures 6 and 7 and listed in the Supporting Information of this article. The effects detected in the isotropic analysis of the SANS patterns are not small.

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Figure 5. SANS contrast matched (left column: a, c) and contrast unmatched (right column: b, d) data collected during a shearing of a 1% (top row: a, b) and 0.3% (bottom row: c, d) active surfactant emulsion and the best model fits to each scattering intensity (lines).

Figure 6. Parameters extracted from analysis of SANS model fits as a function of the shear profile superimposed in gray and shown in Figure 3a. The red and black represent the 1% and 0.3% active emulsions during shearing (squares) and recovery (open circles) intervals. These plots illustrate the dependence of the micelle volume fraction (a), total droplet surface area (b), surfactant loading at the droplet interface (c), and total surfactant found (d) as a function shearing and recovery.

Anisotropic Scattering as a Function of Q. Examination of the 2D scattering patterns shows slight asymmetry of the scattering under shear. The integrated vertical scattering intensity (I(Qy)), increases relative to the horizontal scattering (I(Qx)), indicative of elongation along the direction of the applied shear field. To measure this splitting of the intensity in the two directions, 200(I(Qy) - I(Qx))/(I(Qy) + I(Qx)) (the percentage relative anisotropy) is plotted against Q for both UM and CM emulsions in Figure 8. The data are for 2000 Hz shear and the final 1 Hz resting states.

Because the shear response is only very weakly dependent on Q, the statistics were improved by calculating the Q averaged splitting for the first 14 data points with Q less than about 0.04 Å-1. The CM emulsions show no anisotropy, but the UM data at 2000 Hz have a measurable anisotropy of ∼10%, independent of Q. This arises because the amount of specific surface in the horizontal direction is higher than in the vertical direction, and thus, there is more scattering in the vertical direction. The dependence on shear rate of this splitting for the 1% and 0.3% active emulsions is shown in Figure 9. That the CM



Figure 7. “Frac” parameter extracted from analysis of SANS model fits as a function of the shear profile are shown in Figure 3, top. The red and black represent the 1% and 0.3% active emulsions during shearing (squares) and recovery (open circles) intervals. These plots illustrate the dependence of droplet partial flattening on shear.

Figure 9. The top image (a) is the anisotropy of the UM horizontal and vertical scattering data for 1% and 0.3% surfactant emulsions as a function of the shear profile superimposed in gray and in Figure 3a. The bottom image (b) shows the anisotropy in the 1% and 0.3% emulsions as a function of shear only.

value at around 500 Hz. The result is similar in both 1% and 0.3% emulsions. Discussion

Figure 8. Anisotropy of the horizontal and vertical scattering data for UM (a) and CM (b) 1% surfactant emulsions at 2000 Hz shear (red) and 1 Hz (blue). “Anisotropy” is defined in the text.

data do not follow this splitting indicates that at this contrast, the amount of surfactant per square meter of vertical and horizontal surface is the same, or the difference is unmeasurable. Since our distance resolution in the SANS experiment is much less than the droplet diameter, we would expect and do observe that the proportional splitting should be independent of Q. The lack of splitting at higher Q in the CM plot, however, shows that our micelles remain spherical. In many other systems, shear can induce a transition to an oriented wormlike phase with large scattering anisotropy.25,26 Variation of Anisotropic Scattering with Shear. This is shown in Figure 9, plotting Q-averaged splitting against shear interval number and shear rate for both 1% and 0.3% UM emulsions. All the 1 Hz data still show no significant anisotropy, even after averaging. As we increase the shear rate, the splitting increases, faster for lower shear rates, indicating that elongation occurs at low shear rates and gradually reaches a maximum

We will begin with a short discussion of the initial droplet microstructure, then show that our emulsions are not unusual but, following various empirical rheological models, behave in a typical way. We then discuss by a combination of the rheology and the small-angle data the refinement of droplet distribution by increasing shear the mechanism of this refinement and transient effects, such as droplet deformation as shear rates are increased. Microstructure at Rest. The microscopy data show no evidence of droplet distortion from spherical. This is unusual for such high-internal-volume fraction emulsions in whichthere is usually clear evidence of distortion to form extensive planar areas where droplets touch.11-17 A small flatness needs to be assumed to model adequately the difference from -4 in the Porod slope at low Q in the small-angle scattering data. The frac parameter suggests interference effects in areas of planarity that constitute about 15-25% of the total interfacial area. The almost complete sphericity, however, points to the ability of PIBSA to produce a high interfacial surface tension, which resists deformation. It is this surfactant property that links the rheology and nanostructures observed in the neutron scattering experiments. We look first at what macroscopic rheology theory reveals about the sheared structure. Shear Thinning, Viscosity Scaling, and the Emulsion Structural Model. The most obvious feature of Figures 3 and 4 is the great drop in emulsion viscosity (shear thinning) of our HIPE from the lowest shear imposed. Through this phenomenon, a basis for the rheological and small-angle scattering responses is established. Jansen et al. give an appropriate theory of emulsion stability2 relating the interplay of depletion and viscous

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Figure 10. A plot of the depletion flow number, Fld, versus relative viscosity, ηr, for 1% (red) and 0.3% (black) emulsions. The lines show rheological data from other emulsions at internal phase volume fractions (Φ) and viscosity ratios (λ) similar to the emulsions studied here. Adapted from ref 2.

energies. These are, respectively, the attractive and repulsive forces between droplets. This molecular level description of the role the surfactant plays in the stability of the emulsion under an applied shear also provides a universal scaling parameter. The depletion energy for a particular droplet (of a Sauter radius R32 ) 3/Av, where Av is the specific surface area of the emulsion (m2/m3) determined from small-angle neutron scattering) and rmicelle is the micelle radius) is defined as Edepletion) ((3/ 2)kTφmicelleR32)/rmicelle. This is the attractive force between two touching droplets in an oil phase containing micelles. The opposing viscous energy, Eviscous ) 6πηoilDR323, is the energy needed to overcome the depletion energy and allow relative droplet motion, where ηoil is the viscosity of the oil phase and D is the shear rate (Hz). It consists of a viscous friction force multiplied by the distance over which the force is applied.2 The unitless ratio of these two energies (Eviscous/ Edepletion) is defined as the depletion flow number, Fld. Many micellar stabilized emulsions follow the same “universal” curve when the relative viscosity, ηr ) ηem/ηoil, is plotted against Fld. Figure 10 shows that the scaling of our data (for the 1% and 0.3% systems) fits this model. Data for an emulsion with a similar volume fraction (Φ ) 0.9) and viscosity ratio, λ ) ηoil/ ηAN/D2O (λ ) 0.4)2 is also shown. By this test, our emulsions are typical micelle-stabilized emulsions. Droplet Cluster Break-Up. The overall behavior of our emulsions under shear can be classified as pseudoplastic. As here (Figure 4), pseudoplastic systems display a shear thinning behavior in which viscosity decreases as the shear rate increases. The model developed by Cross27 successfully describes pseudoplastic flow under shear as the property of a “system which contains elements which are capable of assuming some structural formation which is wholly or partially disrupted by shear”. The question is whether drop clusters or single aqueous drops or both are disrupted. In the Cross case, the model was one of a chain of “particles”, with each “particle segment” having a segmental friction through its interaction with the surrounding medium. The emulsion viscosity (η) under a shear rate D (in Hz) is related to the zero and infinite shear viscosities (η0, ηinf) by the formula

η ) η0 + (η0 - ηinf)/(1 + RD2/3)

(2)

In applying this simple formula to parametrize the shear response of our HIPE, we take the model to refer to complexes of linked droplets in different configurations with different stabilities and average sizes, both affected by shear. A 2/3 power scaling in D is found for our system, as in Cross’s systems.

Figure 11. Cross fits of the shearing data. Fits give alpha values of 1.8 and 1.4, respectively.27

Figure 12. Off-line amplitude sweep rheology results used to measure G′ and G′′.

This is not so for other HIPEs of various volume fractions.28 The model relates the shear thinning to a constant, R, associated with the rupture rate of linkages (R ) k1/k0), where k1 is the rupture rate constant due to shear and k0 is the Brownian rupture rate constant due to thermal fluctuations. Figure 11 applies the Cross model to our shearing data and indicates that most of the “emulsion structure” is lost at shear rates of about 1 Hz. This is consistent with the sharp drop in viscosity at low shear (Figures 3 and 4) and the limiting values at high shear for both the 1% and 0.3% active systems, for which the R values are 1.8 and 1.4, respectively. Given the good fit to the Cross model and sensible values for R, we can conclude that our HIPEs do not behave unusually rheologically, but as typical emulsions. The applicability of the Cross model to thinning at low shear rates is supported by the “off-line” measurements of the real, G′, and imaginary, G′′, parts of the shear response at 25 °C for our emulsions. Figure 12 plots the data and shows that both G′ and G′′ versus shear stress give similar values of the yield stress (the stress needed to induce flow), 43 Pa (∼20 Hz shear rate) for 0.3% system and 143 Pa (∼200 Hz) for the 1% system. These low-yield stresses are consistent with the Cross fits with high R values, indicative of the low shear freeing of droplet networks.20 Yield Stress and Droplet Interfacial Tension. To get a deeper understanding of possible droplet breakup mechanisms, our data have been analyzed with the theoretical model of emulsion elasticity by Princen et al.,12-14 as extended to three dimensions by a semiempirical equation based on experimental data of well-characterized emulsions. For such emulsions, the experimental G′ values are related to the experimental SANS specific surface area and experimental interfacial tension, σinterface of the emulsion by Princen’s equation.


G′ ) 1.77σint /R32Φ1/3(Φ - 0.71)


(3)

A calculation of the interfacial tension, σint, from G′ and the specific surface area gives values of 8.1 and 11.2 mN/m, which correspond well to the measured value of about 9 mN/m measured for an almost identical emulsion with a surface tensiometer.29 Again, these emulsions behave like many others, with G′, σint, and Av being mutually related. In conclusion, this section has shown that for shear rates below 500 Hz, shear thinning fitted by standard models is the predominant macroscopic physics of the HIPE. Looking at Figures 5 and 6, little also happens at the nanostructural level. The relative constancy of the scattering functions (e.g. the intensity at Q ) 0, the φmicelle, and AV) is noted. Three observations from the SANS correlate closely with the shear thinning at low shear rates: (1) a low frac value for all sheared states, indicating high curvature aqueous droplets; (2) the appearance of anisotropy below ∼500 Hz and its saturation above this shear rate (Figure 9); and (3) the alternation of frac between shear and no shear (Figure 7). These, then, we take as indicators of the mechanism of the fragilization of the aqueous droplet clusters shown by the Cross analysis. Before considering this, we treat the other major rheological outcome of shearing the emulsion above ∼500 Hz. This is the emulsion refinement. Refinement of the Droplet Distribution and Small Angle Neutron Scattering. (Figure 3b) shows the progressive increase in viscosity at each 1 Hz “rest” period after a shearing interval for both 1% and 0.3% surfactant emulsions, especially above 500 Hz (Figure 4b). The SANS data (Figure 6b) provide an explanation, because there is a nearly 70% increase in droplet specific surface area, Av, for both the 1% and 0.3% systems from 500 Hz shear to 2000 Hz shear. The “resting” viscosity increase is thus attributed to shear refinement of the emulsion to smaller droplet sizes. The slow relaxation to lower viscosity in the 1 Hz shear regions shows that this refinement is partially reversible. There must be some droplet recombination occurring. Capillary Numbers and Droplet Breakup. For “destructive” droplet deformation, a critical capillary number, Cacrit, and corresponding shear rate has been empirically observed in emulsions by Grace. At Cacrit, not only elongation but also rupture of droplets begins.30 Consistent with our logic (above) to find what macroscopic rheology theory reveals, we now apply this model to our HIPE rheology data. Figure 13 shows the corrected critical capillary number, Cacrit*, defined as 〈η(D)DR32〉/σint, where η(D) for concentrated emulsions is the emulsion viscosity at shear rate D.30 The two plots illustrate the dependence of Cacrit* on the shear rate (Figure 13b) and on the corrected viscosity ratio, λ* (Figure 13a). The corrected viscosity, λ*, is defined in Jansen as λ* ) ηAN/D2O/η.31 For a monodisperse system of isolated droplets, the droplets break up when the experimental curve crosses the experimentally derived Grace curve. Figure 13 utilizes a mean radius defined by R32. Clearly, this model fails for our HIPEs: DR32 would have to be nearly 10 times larger than found from small-angle scattering. One possible explanation comes from Figure 2 and consideration of previous papers,3-8 which demonstrate the high polydispersity in droplet size of PIBSA HIPEs. The Grace curve would predict that droplet sizes 10 times R32 would break under shear, and as the shear rate increased, droplets of smaller and smaller sizes would be disrupted, and the emulsion, refined. At a shear rate of 500 Hz, the Sauter radius is 7 µm, but there are no droplets of radius 10 times this in our system, (the maximum

Figure 13. Corrected critical capillary numbers, Cacrit* ) 〈η(D)DR32〉/ σint, of the 1% (red) and 0.3% (black) emulsions, plotted as a function of the corrected viscosity ratio, λ* ) ηAN/D2O/η (a), and shear rate (b).

radius is about 20 µm). Thus, the “droplet disruption” process in our system would have to be more efficient than Grace would predict. The explanation, already proposed by Jansen et al.,30 is simple. The droplets are not isolated, and interdroplet interactions destabilize the droplets more efficiently than oil shear forces. Thus droplet-droplet interactions are important in the refinement process in our emulsions. Relating Scattering Parameters to Refinement mechanism. The SANS parameter frac indicates, indirectly, the reality of droplet size refinement by shear. For perfectly spherical droplets, it would be zero, and for droplets fully polygonized, it would be close to 100%. Figure 7 plots frac against the shear regime of Figure 3. Frac for the 1 Hz data varies between 15 and 25% and overall shows a decrease across the shear regime, whereas the frac in any sheared state is lower and about constant. This decrease in the unsheared frac is consistent with droplet refinement to smaller sizes. Smaller droplets are harder to deform from spherical shape for a given aqueous-oil interfacial tension. There is a further consequence of droplet refinement. The values of φmicelle decrease with shear (Figure 6a), an indication of the diminishing content of the micelle reservoir that confers emulsion stability. Up to 40% of surfactant in micelles is lost due to migration to the increasing aqueous interfacial area. Using the loadings of Figure 6c and the surface areas of Figure 6b, we find for the 1 Hz resting data that the calculated changes in φmicelle match those observed well. For example, the change in droplet surface area, Av, from 0.45 to 1.2 m2 mL-1 between initial and final shear interval, together with the change in surfactant loading at the interface from 1.7 to 2.5 mg m-2, gives an increase in the PIBSA amount at the droplet interface of 33

3508


mg for the whole 15 mL sample. The decrease of 0.027 in φmicelle, allowing for a micelle PIBSA content of 50%, and dissolved PIBSA, gives a decrease of 27 mg in PIBSA in the oil phase. The numbers match well. Another way of expressing this is shown in Figure 6d. The total amount of PIBSA found in the SANS experiment can be calculated again assuming a percent ratio of 75:25 for PIBSA in micelles to dissolved PIBSA (as found in previous experiments3-8). The amounts found for the 1% and 0.3% emulsions correspond quite well to the 130 and 40 mg PIBSA actually weighed into the emulsions. Transient Shear Effects. The exact style of interdroplet configurational breakdown is not clear. A possibility is reordering of the polydisperse droplets into layers of large and small objects, as proposed by Saiki and Prestige,28 but such reordering is difficult to achieve at constant volume when, as in our HIPEs, the internal volume fraction is very high. A clue from the smallangle scattering is in the systematic variation of fitting model parameters with shear. For example, the value of frac alternates strongly exactly out of step with the viscosity. When sheared, its value decreases to about 10%, recovering to 15-25% when the shear is set back to 1 Hz. This increase in sphericity on shear is just what we would expect on deflocculation of a floc. There is also for the 1% system a 10% alternation in the micelle volume fraction as shear is applied then stopped (Figure 6a). This effect is present for the 0.3% data, but weaker. The strength of this alternation increases with increasing shear rate, and the change in micelle volume fraction is much larger than the small, if any, alternation in total interfacial area would require. The total amount of PIBSA involved in this alternation up to 20 mg of PIBSA is unaccounted for in the 1% data when sheared. The only other available reservoir for surfactant would be as molecules dissolved in the oil phase affecting the micelleto-dissolved ratio. A change from 75:25 to 65:35 in PIBSA in micelle to dissolved PIBSA ratio is enough to account for the alternation. That this is not the explanation is shown by recent experiments to shear a dispersion of hydrogenous surfactant reverse micelles in deuterated hexadecane up to 2000 Hz at room temperature. No change in the micelle content, even at the highest shear rate, was detected, so the micelles are stable to the shears imposed. Scattering Anisotropy and Droplet Deformation. From the scattering data, the refining of droplet size and the consequent increase in specific surface area, Av, by a factor of 3 times is attributed to rupture of larger droplets. Droplet ellipsoidal deformation under shear can be ruled out because a 10% deformation at 2000 Hz from spherical to prolate ellipsoids (Figure 9) would only correspond to 0.20% increase in Av, as compared to a sphere of the same volume. Under shear, the degree of droplet deformation of an isolated droplet is determined by the balance between the viscous shear stress of the oil phase and the Laplace pressure, which resists the deformation.32,33 The ratio between these two forces provides a useful measure of the ability of the shear field to deform an isolated droplet. The extent of deformation of an isolated droplet can be estimated from the unitless capillary number, Ca ) ηoilDR32/ σint. The increase in Ca is rapid up to 500 Hz, being proportional to D, then leveling off as a function of shear as the decrease in R32 (increase in Av) begins to occur, compensating the increase in D. The increase in Ca approximately mirrors the shape of the SANS anisotropic splitting parameter changes with shear (Figure 9b).

Yaron et al. Using the equations of Taylor,32,33 a value for the deformation parameter, D, can be calculated from Ca and the emulsion’s components’ viscosities. Maffetone and Minale1 have elaborated this theory, but change the Taylor values little. The deformation parameter is defined as (L - B)/(L - B), where L and B are the lengths of the droplets’ major and minor axes. For D ) 2000 Hz, we obtain a D of about 0.002 for both 0.3% and 1% emulsions. This corresponds to a small-angle scattering anisotropy “splitting parameter” of 0.4%. This is about 5% of the observed SANS splitting parameter of 8%, indicating that the theory is not adequate in this case, and so droplet deformation cannot be treated by isolated droplet theories. Clearl,y such a deformation is also inadequate for droplet fission. For a very small droplet, the surrounding medium may be effectively oil, and use of the oil viscosity may be appropriate. However, at the other extreme, for a very large droplet, a “meanfield”-like approximation may be adopted. Here, the appropriate viscosity to use would be the emulsion viscosity, that is, Cacrit* ) 〈ηem(D)DR32〉/σint, where ηem(D) is the emulsion viscosity at shear rate D. Grace’s empirical observations discussed above suggest this is a better approximation. Again, as for the isolated droplet theory, Ca increases initially with D and then reaches an approximate plateau (Figure 13b), resembling the SANS splitting plot. If we identify R with the Sauter radius R32, that is, assume the formula is correct for all droplet radii, we obtain a splitting parameter at D ) 2000 Hz of 50%. This is a factor of 6 larger than is observed by SANS. We conclude that in our emulsions, collective interdroplet deformation forces leading to fission, and refining must operate. Their effect is, as expected, intermediate between isolated droplet theory and a mean-field theory. Neither theory is a good approximation for calculating the observed droplet mean deformation. We propose that controlled effects of cosurfactants on the interfacial tension with a combination of rheology and small-angle scattering may resolve this issue. Conclusions The combination of contrast variation SANS measurements with simultaneous rheology measurements provides a powerful method for understanding emulsion behavior at all relevant length scales, tracking all components of the emulsion as a function of applied shear rate. This method of observation also allows for the physical explanation of the emulsion behavior at various time scales. The variation of micelle volume fraction, interfacial surface area and flattening, amount of surfactant at the aqueous oil interface, and total surfactant found with the simultaneously observed viscosity have been correlated throughout the shear rate regime illustrated in Figure 3. The other variables (e.g., micelle size) are much less sensitive to shear and have been discussed before.3-8 Under electron and optical microscopy, the dispersed phase micrometer-scale droplets appear spherical, but the more sensitive SANS measurements show that there is a small fraction (

and Microstructure of High-Internal Phase Emulsions Under Shear

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