2656
Langmuir 2001, 17, 2656-2663
Shear-Induced Formation of Ordered Monodisperse Emulsions Stabilized by an Associating Amphiphilic Polyelectrolyte Patrick Perrin,* Nicolas Devaux, Philippe Sergot, and Franc¸ ois Lequeux Ecole Supe´ rieure de Physique et Chimie de Paris (ESPCI), CNRS, Universite´ Pierre et Marie Curie (UPMC), UMR 7615, Physico-Chimie des Polyme` res, 75005 Paris, France Received October 23, 2000. In Final Form: January 29, 2001 An associating amphiphilic polyelectrolyte was used as an emulsifier of the n-dodecane-water system. First, the dynamic rheological behavior of polydisperse concentrated direct emulsions with dispersed phase volume fractions up to 0.91 was investigated. Both the Princen and Kiss (J. Colloid Interface Sci. 1983, 91, 160; 1986, 112, 427) and Mason et al. (Phys. Rev. Lett. 1995, 75, 2051) approaches on emulsion elasticity give an adequate fitting of the rheological behavior leading to the conclusion that the emulsion elasticity mainly arises from droplet compression. Second, the shear-induced formation of ordered monodisperse emulsions was studied. More specifically, the conditions under which ordered structures are obtained by shearing polydisperse premixed emulsions within the two-parallel circular glass plates of a homemade shear apparatus were reported. The light scattering patterns, first-order ring, first-order diffuse ring with 6 bright spots, and second-order diffuse ring with 12 bright spots successively observed while shearing the emulsion samples reveal the progressive formation of ordered layers of hexagonal close-packed planes of oil droplets as the shear rate increases. The observation of the diffraction patterns also shows that the level of droplet organization decreases after cessation of flow thus suggesting that the droplets occupy well-defined spatial positions within a sample under shear as compared to a sample after cessation of flow. The radius of the droplets forming the colloidal crystal was systematically measured under shear as a function of the radial distance from the center of the glass slides, the gap spacing, the polymer concentration, and the oil content to follow the development of long-range ordering within the emulsions. The formation of the droplet crystal was found to depend only on the shear rate. Smaller droplets are obtained with increasing both the shear rate and the polymer concentration, and only a slight change in the droplet size could be detected upon varying the volume fraction of the dispersed phase. The results are in qualitative agreement with a coalescence-fractionation mechanism of the droplets under shear.
Introduction Concentrated emulsions or high internal phase emulsions (HIPE) are systems where the volume fraction of the dispersed phase is larger than about 0.74, which is the close-packing volume fraction of monodispersed hard spheres. The dispersed soft entities of a concentrated emulsion are no longer spherical. They deform into polyhedra separated by thin films of continuous phase. The structure is thus analogous to conventional gas-liquid foams with low liquid content. The structure, properties, stability, and applications of highly concentrated emulsions were recently reviewed by Cameron and Sherrington.1 Kunieda and co-workers2 have also published a book chapter on this topic. Concentrated emulsions are classically stabilized by surfactants. However, there has been recent interest in using polymeric surfactants. Taylor3 has investigated the effect of an anionic surfactant (sodium dodecyl benzene sulfonate) on the stability and dynamic rheological behavior of moderately concentrated emulsions (φoil ) 0.65-0.8) stabilized by poly(vinyl alcohol). Pons and coworkers4 used PEO/PPO/PEO (PEO, poly(ethylene oxide); PPO, poly(propylene)) nonionic triblock copolymers * To whom correspondence may be addressed. (1) Cameron, N. R.; Sherrington, D. C. Adv. Polym. Sci. 1996, 126, 165. (2) Kunieda, H.; John, A. C.; Pons, R.; Solans, C. In StructurePerformance Relationships in Surfactants; Esumi, K., Ueno, M., Eds.; Surfactant Science Series; Marcel Dekker: New York, 1997; Vol. 70, p 359. (3) Taylor, P. Colloid Polym. Sci. 1996, 274, 1061. (4) Pons, R.; Solans, C.; Tadros, Th. F. Langmuir 1995, 11, 1966.
(Symperonic L92 and L64) to prepare concentrated direct emulsions of decane in water up to a dispersed phase volume fraction of 0.94. The rheological behavior of the emulsions was investigated as a function of the oil content and temperature (20-80 °C). Ganguly and co-workers5 have compared the stability behavior of concentrated water in oil (white mineral oil or mixture of mineral oil and waxes) emulsions at various salt (ammonium nitrate or mixture of ammonium and sodium nitrate) concentrations for two types of surfactant. One is sorbitan monooleate (SMO), a nonionic surfactant, while the other one is a small (M ) 2500 g/mol) polymeric emulsifier (code name LZX). According to the authors, LZX must be considered as a zwitterionic surfactant as a result of the reaction of poly(butenyl succinic anhydride) with alkanolamine. The study reveals that the presence of salt is required to prepare stable emulsions using the nonionic surfactant. The stability enhancement of emulsions formulated with LZX due to the addition of salt is much more important than for SMO. The authors showed that the interactions between the surface-active agent and the added electrolyte are held responsible for stability improvement. The uncharged emulsifier and electrolyte can only interact through hydrogen bonding while the zwitterionic character of the polymer chains would enable the macrosurfactant to develop more intense interactions therefore explaining the greater stability enhancement observed for the polymer. The dynamic rheological behavior of both concentrated direct and inverse emulsions (5) Ganguly, S.; Krishna Mohan, V.; Jyothi Bhasu, V. C.; Mathews, E.; Adiseshaiah, K. S.; Kumar, A. S. Colloids Surf. 1992, 65, 243.
10.1021/la001492w CCC: $20.00 © 2001 American Chemical Society Published on Web 04/05/2001
Emulsion Stabilization with a Polyelectrolyte
stabilized by twin-tailed amphiphilic polyelectrolytes was found to be adequately described by the Princen and Kiss theoretical model6,7 on emulsion elasticity.8 The charged polymeric surfactants allow the preparation of direct and inverse emulsions with dispersed phase volume fractions up to φ ) 0.94 and 0.93, respectively. It was also shown recently that both types of concentrated emulsions with φ up to 0.90 can be prepared using an original ioncontaining polymeric surfactant with balanced hydrophilic-lipophilic properties.9 The author attributed the different rheological behavior exhibited by the direct and inverse concentrated emulsions to the different interactions observed between oil (repulsive) and brine (attractive) droplets. The concentrated emulsions investigated above are polydisperse. There has been a recent growing interest in producing monodisperse emulsions using various techniques such as fractionated crystallization,10 membrane extrusion,11 emulsification in viscoelastic media,12-15 and drop break-off in a coflowing stream.16 From an academic point of view, the preparation of liquid-liquid dispersions with narrow droplet size distribution is crucial to give a better understanding of emulsion rheology.17 Furthermore, monodisperse emulsion templating represents an attractive method to produce solid porous materials with uniform pore diameters ranging from 0.04 µm to several micrometers.18,19 Such materials are predicted to possess new optical properties and, hence, are technologically important systems.20 Interestingly, it was recently demonstrated that concentrated monodisperse emulsions stabilized by hydrophobically grafted polyelectrolyte surfactants can efficiently be prepared by manually shearing concentrated polydisperse emulsions between glass slides.8,13 Moreover, near the critical aggregate concentration of the associating polymeric surfactants, a similar method was used to locally prepare both ordered monodisperse emulsions and foams.21 It was also shown how to build a covalent gel around droplets to immobilize the ordered liquid-liquid structure using a one-step emulsification method.21 In this paper, we continue our work initiated in ref 13 and present qualitative experimental features regarding the formation of shear-induced ordered monodisperse direct emulsions stabilized by a polyelectrolyte emulsifier. First, we examine the dynamic rheological properties of the polydisperse emulsions. Attempts are made to fit the experimental data using the Princen and Kiss6,7 and Mason22 models. Second, the conditions under which ordered structures are obtained by shearing polydisperse premixed emulsions within a homemade device are reported. In (6) Princen, H. M. J. Colloid Interface Sci. 1983, 91, 160. (7) Princen, H. M.; Kiss, A. D. J. Colloid Interface Sci. 1986, 112, 427. (8) Perrin, P.; Monfreux, N.; Thierry, F.; Lafuma, F.; Lequeux, F. Proc. ACS Div. Polym. Mater. Sci. Eng. 1999, 81, 492. (9) Perrin, P. Langmuir 2000, 16, 881. (10) Bibette, J. J. Colloid Interface Sci. 1991, 147, 474. (11) Yamano, Y.; Kagawa, Y.; Kim, K. H.; Ghotani, S. Food Sci. Technol., Int. 1996, 2 (1), 16. (12) Mason, T. G.; Bibette, J. Phys. Rev. Lett. 1996, 77, 3481. (13) Perrin, P. Langmuir 1998, 14, 5977. (14) Mabille, C.; Schmitt, V.; Gorria, Ph.; Leal Calderon, F.; Faye, B.; Deminie`re, B.; Bibette, J. Langmuir 2000, 16, 422. (15) Mason, T. G.; Bibette, J. Langmuir 1997, 13, 4600. (16) Umbanhowar, P. B.; Prasad, V.; Weitz, D. A. Langmuir 2000, 16, 347. (17) Lequeux, F. Curr. Opin. Colloid Interface Sci. 1998, 3, 408. (18) Imhof, A.; Pine, D. Adv Mater 1998, 10, 697. (19) Imhof, A.; Pine, D. J. Nature 1997, 389, 948. (20) Joannopoulos, J. D.; Villeneuve, P. R.; Shanhui, F. Nature 1997, 386, 143. (21) Perrin, P. Langmuir 2000, 16, 4774. (22) Mason, T. G.; Bibette, J.; Weitz, D. A. Phys. Rev. Lett. 1995, 75, 2051.
Langmuir, Vol. 17, No. 9, 2001 2657
particular, the effect of changing the gap spacing, the polymer concentration, and the dispersed phase volume fraction is investigated. Experimental Section Materials. The polymeric surfactant used to stabilize the oilin-water emulsions is a hydrophobically modified poly(sodium acrylate) with the following chemical structure:
The molar degree of hydrophobic modification is 0.1. The n-dodecylamine (Fluka) was chemically grafted onto the hydrophilic poly(sodium acrylate) (Polysciences). The molecular weight of the polymer precursor given by the supplier is Mw ) 50 000. The synthesis of the amphiphilic polyelectrolyte has been reported previously.23 It is important to recall that the chemically grafted dodecyl chains are randomly distributed along the polymer backbone. The resulting amphiphilic polyelectrolyte is a watersoluble associating polymer with a critical aggregate concentration (cac) of about 1.5% (weight of polymer/volume of water) as shown from viscosity measurements. The viscometric behavior and the determination of the cac of this series of polymers as a function of the degree of grafting, polymer backbone molecular weight, length, and shape of the graft have already been detailed in previous papers.24-26 Emulsions were prepared using doubledistilled deionized water (Milli-Q system from Millipore) and n-dodecane (Prolabo). Methods. The preparation of the concentrated oil in water emulsions can be described as follows. First, we prepared 4 mL of a Cp % (Cp %, polymer concentration given in weight of polymer/ volume of solvent) concentrated aqueous polymer solution by dissolving the appropriate quantity of polymer in water. Four milliliters of n-dodecane was then added to the aqueous phase. The two phases were mixed using a rotor-stator type of homogenizer (Heidolph Diax 600) for 5 min at 8000 rpm to form an emulsion with an oil phase volume fraction of φ ) 0.5. To increase the dispersed phase volume fraction, oil was progressively added to the premixed emulsion (φ ) 0.5) and fractionated into droplets by gently stirring the dispersion with a spatula in a way similar to the preparation of a mayonnaise. The droplet size distribution of the various samples was determined by laser granulometry (Malvern Mastersizer X) and optical microscopy (Olympus BH-2). The rheological measurements were performed at T ) 298 K on a strain-controlled rheometer (Rheometrics RFS II) equipped with a cone-plate geometry. To observe the in-situ formation of the colloidal crystal of oil droplets, we have built a device to shear the polydisperse emulsions under controlled conditions. The apparatus consists of two transparent parallel circular glass slides. The upper plate is fixed while the lower plate rotates at a controlled angular velocity Ω. The shear rate is thus given by γ˘ ) Ωr/e where r is the radial distance from the center of the glass slide to the point of observation of the emulsion sample (where the laser beam hits the sample) and e is the gap between the two slides. The parallelism of the plates is adjusted using the reflection of a laser beam (typically 10-3 rad). The gap spacing is measured as the height (volume-to-surface ratio) of a silicone oil (viscosity ) 1000 mPa‚s) cylinder formed between the glass slides. The lowest attainable value of e is 30 ( 10 µm. The mobile plate always rotates in the same direction and thus does not move back and forth as in the case in ref 13. While the (23) Wang, T. K.; Iliopoulos, I.; Audebert, R. Polym. Bull. 1989, 20, 577. (24) Wang, T. K.; Iliopoulos, I.; Audebert, R. In Water-Soluble Polymers: Synthesis, Solution Properties and Applications; Shalaby, S. W., McCormick, C. L., Butler, G. B., Eds.; ACS Symposium Series 467; American Chemical Society: Washington, DC, 1991; p 218. (25) Perrin, P.; Lafuma, F.; Audebert, R. Prog. Colloid Polym. Sci. 1997, 105, 228. (26) Perrin, P.; Lafuma, F. J. Colloid Interface Sci. 1998, 197, 317.
2658
Langmuir, Vol. 17, No. 9, 2001
Perrin et al.
Table 1. Average Droplet Radius, R32, Measured as a Function of the Oil Volume Fraction (O) and Aqueous Phase Polymer Concentration (Cp %) Cp (%)
φ
R32 (µm)
4.0 4.5 4.5 4.5 4.5 4.5 4.5 4.5 4.5 4.5 4.5 4.5 5.0
0.75 0.50 0.60 0.70 0.75 0.80 0.83 0.85 0.87 0.89 0.90 0.91 0.75
3.70 2.20 2.30 2.60 2.70 2.90 2.80 2.85 2.80 2.80 2.80 2.80 2.50
sample is sheared, a He/Ne laser light with a wavelength of 632.8 nm is sent perpendicular to the sample shear plane. Photographs of the diffraction pattern are taken using an Agfa ephoto 1680 digital camera. Let us now describe the shear procedure of the emulsion samples. Once the setup is adjusted to fit the desired values of r and e, the angular velocity was increased by 5 rpm steps from 10 to 45 rpm. At a given velocity, the sample was observed for 2 min. From Ω ) 60-140 rpm, a step increase of 20 rpm was performed, the sample being left at a given velocity for 2 min.
Results and Discussion The Polydisperse Concentrated Emulsions. First, the droplet size distribution and the volume-surface mean radius, R32, of a large number of emulsion samples were determined right after the sample preparation using laser granulometry. The values of R32 are reported in Table 1. At a constant polymer concentration of Cp ) 4.5%, R32 increases slightly from 2.20 to 2.70 µm as the oil dispersed phase volume fraction increases from φ ) 0.5 to 0.75. Above φ ) 0.75, n-dodecane is incorporated without changing the droplet size distribution (not shown here) and thus R32 remains constant with φ within the experimental error. As discussed later, the final droplet size arises essentially from the competition between coalescence and droplet fractionation. On one hand, the aqueous polymeric surfactant film separating two adjacent droplets is expected to become thinner as φ increases. As a consequence, increasing the dispersed phase volume fraction a priori favors the coalescence process. On the other hand, the fractionation of the droplets becomes more efficient as φ increases since added oil experiences a more and more viscoelastic medium during emulsification. In their study of n-decane in water-concentrated emulsions stabilized by PEO-POP-PEO L92 triblock copolymer (Mw ) 3650), Pons et al.4 did not observe a significant change in the measured values of R32 with increasing φ from 0.849 to 0.964. A slight decrease of R32 from 3.67 (φ ) 0.849) to 3.04 µm (φ ) 0.964) was reported by the authors when using L64 (Mw ) 2900) instead of L92. In our system, Table 1 shows that the mean droplet radius, R32, decreases with increasing polymer concentration. At φ ) 0.75, the mean droplet radius is 3.7, 2.7, and 2.5 µm at Cp equal to 4, 4.5, and 5%, respectively. In general, this observation is attributed to an improved stabilization of the fractionated droplets during emulsification due to the presence of a larger amount of interface active macromolecules available to cover the interface. For instance, CardenasValera27 reported that the average size of toluene droplets dispersed in water decreases with increasing the con(27) Cardenas-Valera, A. E.; Bailey, A. I.; Doroszkowski, A. Colloids Surf., A 1995, 97, 1.
Figure 1. Elastic modulus G′-frequency sweeps at a strain of 1% (linear domain). The oil volume fractions, φ, of the n-dodecane in water emulsions are indicated above. The polymer concentration is 4.5%.
centration of the polymeric emulsifier (poly(methyl methacrylate)-graft-poly(ethylene oxide)) within a range of 0.51.25%. Above Cp ) 1.25%, which corresponds to the saturation of the surface, the average droplet size levels off. The excess amount of our polymer at the n-dodecanewater interface is not known. However, we have studied the surface adsorption of a series of hydrophobically grafted poly(sodium acrylate)s combining X-ray reflectivity and surface tension measurements.28 Both methods are in good agreement and give an excess surface concentration of about 1 mg/m2. In addition, at Cp ) 4%, the surface is saturated as shown by the Gibbs isotherms.28 So, the decrease of R32 with Cp cannot be attributed to a larger amount of polymeric surfactant chains available to cover the interface as Cp increases. It is more likely to be due to an improved rupturing of the droplets as the viscous forces become more efficient with increasing the quantity of associating polyelectrolyte surfactant in the external aqueous phase. Moreover, once the emulsification is completed, the ruptured droplets are trapped into a physical polymer gel the strength of which increases with Cp.26 In addition, it was shown that the thickness of vertical free-standing films of the amphiphilic polyelectrolyte increases rapidly with the polymer concentration above the cac.29 This is due to the structure of the film, which consists of a physical microgel made of connected hydrophobic aggregates.13,29 Hence, the droplet recombination is prevented at higher Cp. All these remarks could explain why R32 decreases with increasing Cp. The dynamic rheological behavior of a series of emulsion samples with various oil volume fractions was investigated. The polymer concentration in the continuous aqueous phase was kept constant equal to 4.5%. We were able to prepare emulsion samples with φ up to 0.91. The elastic modulus, G′, was measured for each sample as a function of the frequency at a strain of 1% (linear domain) (Figure 1). The regular increase of G′ with φ shows that oil was suitably incorporated. At oil contents higher than 0.91, it seems that the high viscosity of the dispersion prevents the incorporation of oil as already observed by Chen and Ruckenstein.30 We now analyze our results using the theoretical model of Princen and Kiss6,7 and the approach of Mason et al.22 According to the former model,6,7 (28) Millet, F.; Nedyalkov, M.; Renard, B.; Perrin, P.; Lafuma, F.; Benattar, J. J. Langmuir 1999, 15, 2112. (29) Millet F.; Benattar, J. J.; Perrin, P. Phys. Rev. E 1999, 60, 2045. (30) Chen, H. H.; Ruckenstein, E. J. Colloid Interface Sci. 1991, 145, 260.
Emulsion Stabilization with a Polyelectrolyte
Langmuir, Vol. 17, No. 9, 2001 2659
Figure 2. Princen and Kiss analysis of our experimental data: From the linear regression, the values of B ) 0.72-0.73 and σ ) 18.5 mN/m were calculated.
Figure 3. Variation of the shear stress with the shear rate for Cp ) 4.5% concentrated emulsions with various oil volume fractions indicated above.
the emulsion elasticity is determined by the deformation of the interface under shear and the elastic modulus is given by
G′ ) Aσ/R32φ1/3(φ - B)
(1)
where σ is the interfacial tension. The constants A ) 1.769 and B ) 0.712 are experimental values obtained by Princen. Polydisperse emulsions were used to determine the constants A and B. B represents the volume fraction at which the droplets start to deform so that B is also often known as the close-packing volume fraction. The volume fractions of hexagonal and randomly close-packed spheres are φC ) 0.74 and φC′ ) 0.635, respectively. Mason et al.22 have studied the elastic modulus φ dependence of emulsions consisting of monodisperse droplets of radius R. According to the authors, the elastic modulus varies with φ as follows:
G′ ) 1.64σ/Rφ(φ - φC′)
(2)
The Princen analysis is presented in Figure 2. The reasonable values of B and σ, 0.72-0.73 and 18.5 mN/m, respectively, indicate that the Princen model describes adequately our experimental data at least from a semiquantitative point of view. Unlike surface tensions, interfacial tension measurements are unfortunately not available for the polyelectrolyte surfactant used here. Our study on the adsorption of a series of hydrophobically grafted poly(sodium acrylate)s gives a surface tension value of about 55 mN/m at concentrations above Cp ) 0.2% for a polymer with an identical hydrophobic modification (10%) but a slightly higher molecular weight (Mn ) 50 000 and Mw ) 120 000).28 Consequently, a value of the interfacial tension of 18.5 mN/m is realistic. Between φ ) 0.5 and 0.7, our data show that G′ is not equal to zero as predicted by the Princen model (Figure 2). To the best of our knowledge, within this range of dispersed phase volume fractions, there is no satisfactory model to describe the rheological behavior of emulsions. Although our emulsions do not exhibit a narrow droplet size distribution, an attempt was made to fit our experimental data using the eq 2. The Mason model also provides a good description of the experimental results since values of φC′ and σ equal to 0.66 and 15.6 mN/m, respectively, are determined from the G′R32/φ-φ plot (not shown here). The results are similar to those obtained using the Princen model. It is thus clear that the elasticity of the emulsion arises mainly from droplet compression. Finally, to complete the description of the polydisperse emulsions, the variation of the shear stress as a function of the shear rate is presented
Figure 4. Bragg diffraction pattern observed while shearing an initially polydisperse emulsion (Cp ) 4% and φ ) 0.75) at γ˘ ) 8000 s-1 using a homemade device. The first two orders of the diffraction pattern are clearly observed. They reveal the presence of ordered layers of hexagonal close-packed planes of oil droplets. A sketch of the shear device is also presented.
in Figure 3 for samples with various oil contents. The macroscopic shear stress of the emulsion is not much dependent on φ. For shear rates exceeding 100 s-1, we did not succeed in getting appropriate measurements as the sample was most often ejected from the rheometer geometry. The Shear-Induced Formation of Ordered Monodisperse Emulsions. The behavior of the above prepared polydisperse emulsions under shear is now reported. In our previous papers,8,13 the samples were manually sheared so that the relationship between the shear rate and the structure of the emulsion (level of droplet organization, droplet size, ...) could not be investigated in detail. So, a homemade device was built in order to shear the emulsion samples under controlled conditions as explained in the Experimental Section. The first step was to test the efficiency of the shear apparatus. Figure 4 displays the Bragg diffraction pattern of an initially polydisperse emulsion with Cp ) 4% and φ ) 0.75 sheared using the plane-plane geometry of the device at a shear rate of γ˘ ) 8000 s-1. A sketch of the shear device is also
2660
Langmuir, Vol. 17, No. 9, 2001
Perrin et al.
Figure 5. Droplet radius, R, measured under shear as a function of the shear rate at a constant gap spacing of 80 µm. The distance from the center of the glass plates at which the laser beam hits the sample, r, is varied as indicated above. The polymer concentration and the oil volume fraction of the emulsions are 4% and 0.8, respectively.
presented in Figure 4. The diffraction pattern consists of two diffuse rings of 6 bright spots (first order) and 12 spots (second order) which indicates the presence of ordered layers of hexagonal close-packed planes of oil droplets. Obviously, the droplet radius R can be calculated from the diffraction pattern using Bragg’s law. It is important to remember that the ordered structure is obtained using only a small amount (4%) of the amphiphilic polyelectrolyte. The vorticity (the neutral shear direction) and shear velocity directions are also indicated in the Figure 4. Consequently, ordered monodisperse emulsions can actually be created by shearing polydisperse emulsions using the homemade device. We now give a more detailed analysis of the shear-induced formation of the droplet crystal. As mentioned earlier, the shear rate for the planeplane geometry of the shear device is given by
γ˘ ) Ωr/e
(3)
To obtain quantitative information regarding the emulsion structure-shear conditions relationship, it is essential to check that our experimental observations are similar at given gap spacing and shear rate whatever the distance from the center of the plates at which the sample is observed. Consequently, a polydisperse emulsion with Cp ) 4% and φ ) 0.8 was sheared between the glass slides at a constant gap spacing of 80 µm and the light scattering pattern simultaneously observed to follow the formation of the ordered monodisperse emulsion. Three sets of experiments were then performed at r ) 12.5, 15, and 17 mm, the angular velocity being increased as described in the Experimental Section. In Figure 5, the droplet radius measured from the Bragg diffraction pattern is plotted as a function of the shear rate for the three values of the distance from the center of the glass slide to the point of observation of the emulsion sample. The three curves superpose onto a master curve within experimental error. As a consequence, as the sample is sheared, a sufficiently good parallelism of the glass plates is observed at least up to a radial distance of 17 mm. The distance from the center at which the sample is observed can thus be used as a parameter to control the range of attainable shear rates. The effect of the gap spacing on the formation of the monodisperse emulsion is now presented. We sheared a polydisperse emulsion with φ ) 0.8 and Cp ) 4.5% between the plates and observed the scattering pattern of the samples at a constant value of r ) 20 mm while changing the gap spacing. Three values of e, 30 ( 10, 50 ( 10, and 70 ( 10 µm, were studied. Figure 6 presents the droplet radius-shear rate dependence. A master curve can be
Figure 6. Dependence of R with γ˘ at a constant value of r ) 20 mm. The gap spacing is varied as indicated above. The polymer concentration and the oil volume fraction of the emulsions are 4.5% and 0.8, respectively.
built from the superposition of the three curves obtained at different gap spacing values. Interestingly, this demonstrates that the formation of the droplet crystal is not affected upon changing the gap spacing in the 30-70 µm range. Thus, like the radius r, the gap spacing can also be used as a parameter to monitor the desired range of shear rates. In Figures 5 and 6, it is important to point out that the values of the monodisperse emulsion droplet radius obtained at shear rates lower than 1000 s-1, 6-13 µm, are unexpectedly high. According to our droplet size measurements (Table 1), the droplet mean radius of φ ) 0.8 and Cp ) 4.5% polydisperse emulsion, 2.90 µm, is smaller. The value of the radius of the emulsion with φ ) 0.8 and Cp ) 4% is not available, but it must be of the order of 4 µm since an average droplet radius of 3.70 µm was measured for the emulsions with φ ) 0.75 and Cp ) 4%. Consequently, the radii of the monodisperse emulsions determined at low shear rates are significantly higher than the mean droplet radii of the polydisperse emulsions at same oil content and polymer concentration. At high shear rates the measured droplet radius (about R ) 2-3 µm for the φ ) 0.8 and Cp ) 4.5% emulsion, Figure 6) is of the same order as the average droplet radius of the corresponding polydisperse emulsions (R32 ) 2.9 µm, Table 1). Consequently, the mechanism determining the droplet size of the monodisperse emulsions certainly arises from the competition between the fractionation and the coalescence of the droplets. In addition, a single fractionation process would lead to a steplike variation of the droplet radius, which we did not observe (Figures 5 and 6). We now examine how the shear rate modifies the structure of the liquid-liquid dispersion. There exists a range of shear rates (400-9000 s-1) in which the development of a long-range ordering within the emulsion occurs (Figure 7). More specifically, the successive Bragg diffraction patterns observed with increasing the shear rate are presented in Figure 7. These observations are general, although the values of the shear rates given in the figure are indicative. With a change in the composition of the emulsion, the delimited shear rate ranges can slightly be modified, but the general pattern of the observed sequence described below remains identical. Pictures of the light scattering pattern were taken while shearing the sample. They reveal the progressive formation of the colloidal droplet crystal as the shear rate increases. Below 400 s-1, no ordering could be detected within the sample. Between 400 and 700 s-1, the width of the droplet size distribution is sufficiently narrow to observe a diffuse ring. At higher shear rates (700-4000 s-1), a crystalline structure is revealed by the presence of a diffuse ring with 6 bright
Emulsion Stabilization with a Polyelectrolyte
Langmuir, Vol. 17, No. 9, 2001 2661
Figure 8. Effect of the polymer concentration and dispersed phase volume fraction on the formation of the shear-induced ordered monodisperse emulsions. Experiments were run with e ) 30 µm and r ) 20 mm. (A) The droplet radius-shear rate plot for emulsions with various polymer concentrations (Cp ) 4 and 4.5%) and a same oil content (φ ) 0.7). (B) The droplet radius-shear rate dependence for emulsions with various oil contents (φ ) 0.7, 0.75, and 0.8) and a same polymer concentration (Cp ) 4.5%).
Figure 7. Successive Bragg diffraction patterns observed with increasing the shear rate. The four pictures presented on the right-hand side were taken under shear while the pictures on the left-hand side were taken after cessation of flow.
spots. Increasing the shear rate above 4000 s-1 leads to a better ordering of the structure with the appearance of a Bragg diffraction pattern consisting of a first-order diffuse ring with 6 bright spots and a second-order ring with 12 spots at shear rates higher than 7500 s-1. Above 9000 s-1, the breakdown of the emulsion is observed. This is due to the coalescence of the droplets which prevents the formation of an ordered monodisperse structure with smaller size droplets. We continue to describe the pictures presented in Figure 7. Once an ordered structure was obtained under given shear conditions, the shear was stopped. A few seconds later, the emulsion sample is at rest and photographs of the diffraction pattern were taken again. They are also presented in Figure 7. By comparing the two sets of pictures (scattering patterns of emulsions under shear and after cessation of flow) for a given range of shear rates, we come to the conclusion that the relaxation of the droplets causes the emulsion to be less ordered. While the sample is sheared, it thus seems that the droplets are constrained to occupy well-defined spatial positions. They possibly move by following preferential flow planes so that the emulsion ordering is more important under shear. However, the droplet size distribution is still probably too large for the crystalline structure to be completely preserved after the cessation of shear. It is now appropriate to discuss the decrease of the droplet radius with increasing the shear rate (Figures 5, 6, and 8). Figure 8A presents the dependence of the oil droplet radius with the shear rate for emulsions with
various polymer concentrations (Cp ) 4 and 4.5%) but the same oil content (φ ) 0.7). Over the whole range of investigated shear rates, the droplet radius of the Cp ) 4% emulsion is larger than that of the Cp ) 4.5% emulsion. Let us first recall that the average droplet radii of the premixed polydisperse emulsions are not the same. The average droplet radius of the 4% concentrated emulsion, R32 ) 3.2 µm (not reported in Table 1), is larger than that of the 4.5% concentrated emulsion, which is 2.6 µm (Table 1). The difference in size arises from the water-soluble associating behavior of the polymeric emulsifier. The Newtonian viscosity of a 4% concentrated aqueous polymer solution is about 2000 mPa‚s. The viscosity of the 4.5% concentrated solution is higher by at least 1 order of magnitude. Consequently, the droplet rupturing which occurs during the preparation of the sample is more efficient at high polymer concentrations. The difference in the droplet size arising from emulsion preparation is still observed while shearing the samples (Figure 8A). Also, a droplet of an emulsion at Cp ) 4.5% will experience a larger shear stress contribution from the emulsion than a droplet of a 4% concentrated emulsions.26 Hence, the droplet breaking is improved with increasing Cp. The coalescence is another possible reason to explain the difference in the droplet size for the two polymer concentrations (Figure 8A). As already discussed above, the recombination of the droplets is certainly less favored as the polymer concentration increases. These remarks are qualitatively coherent with our experimental data presented in Figure 8A. Finally, the droplet radius-shear rate dependence is presented in Figure 8B for emulsions with various dispersed phase volume fractions (φ ) 0.70, 0.75, and 0.80), the polymer concentration being constant and equal to 4.5%. The droplet size distributions of the three polydisperse emulsions are nearly similar (not shown here) and thus the values of R32 are close as shown in Table 1. It can be concluded from Figure 8B that the
2662
Langmuir, Vol. 17, No. 9, 2001
Perrin et al.
variation of the droplet size with the shear rate is not much dependent on the dispersed phase volume fraction within the narrow range of investigated oil contents. However, it is possible to observe a slight change of R with φ after a careful examination of the experimental results given in Figure 8B. If so, it appears that at a given shear rate the samples with the lower dispersed phase volume fractions exhibit larger droplet radii. These observations must be related again to the competition between droplet fractionation and coalescence. On one hand, the decrease of R with increasing the oil content at a same shear rate can be attributed to a slightly larger compression (Figure 3) and to a reduced mobility of the droplets as the dispersed phase volume fraction increases. The same arguments hold to explain that the minimum value of the shear rate required to observe an ordered structure is lower for the emulsions containing a larger amount of oil (Figure 8B). On the other hand, due to coalescence, larger droplet radii are expected with increasing φ. In the end, increasing the oil content from 0.7 to 0.8 changes only slightly the droplet size. To summarize, we suggest the following scenario to describe our observations shown in Figure 8. For shear rates up to about 40005000 s-1, the radius decreases rapidly therefore indicating that the rupturing of the droplets is dominating over the coalescence mechanism. Within the range of shear rates from 5000 to 9000 s-1, the competition between the fractionation and the coalescence processes becomes more effective and the decrease of R with γ˘ progressively slows down. The radii of the ordered monodisperse emulsions converge to an identical value of about 2-3 µm in the high shear rate limit whatever the polymer concentration or the dispersed phase volume fraction (Figure 8). So, before the ordered structure breaks down, the fractionation and the coalescence processes counterbalance each other leading to a droplet radius which thus seems to be characteristic of the emulsion system. At shear rates higher than 9000-10000 s-1, the coalescence process is predominant and the structure is broken down. We continue our discussion regarding the coalescencefractionation mechanism of the droplets. Let us first consider that the fractionation process is solely responsible for the decrease of the droplet size. The shear-induced fractionation of an isolated droplet of an emulsion can a priori occur if the viscous stress (τ) exceeds the droplet Laplace pressure. This leads to the following equation
(τ ) ηγ˘ ) g σ/R
(4)
where η is the viscosity of the emulsion. Consequently, the qualitative description of our experimental observations (Figures 5, 6, and 8) is well accomplished using eq 4 since R scales like the inverse of the shear rate. However, as discussed below, it is much more difficult to give a quantitative analysis of the results. According to Figure 8, the radius of the monodisperse emulsions is about 2-3 µm in the limit of high shear rates. The interfacial tension in the presence of the amphiphilic polyelectrolyte is around 15-20 mN/m as determined using the Princen (18.5 mN/ m) (Figure 2) and the Mason (15.6 mN/m) approaches. The droplet Laplace pressure is thus within a range of 5000-10000 Pa. However, as shown in Figure 3, the shear stress within the emulsion sample is of the order of 200 Pa, which is between 1 and 2 orders of magnitude lower than the Laplace pressure. We are aware that the shear rate at which a radius of 2-3 µm was observed, γ˘ ) 3000 s-1, is far out of the range of shear rates for which an almost constant value of the shear stress equal to 200 Pa was measured (below 100 s-1). Nevertheless, it is also
difficult to argue that the shear stress would probably increase by 1 or 2 orders of magnitude with increasing the shear rate from 100 to 3000 s-1. Consequently, a reasonable estimate of the measured droplet radius R of the sheared emulsions cannot certainly be given by injecting the value of the macroscopic shear stress in the eq 4. With τ ) 200 Pa, the expected value of the radius is then equal to 75-100 µm using an interfacial value of 15-20 mN/m. We can only suggest that the droplets may experience local stresses higher than the sample macroscopic shear stress. Assuming the propagation of the local stress over the entire sample would possibly explain the observation of emulsions with droplet radius of the order of 1 µm. To end up our discussion, as explained above, it is essential to consider again the occurrence of droplet coalescence under shear. Since the presence of coalescence increases the droplet size, we again come to the conclusion that the droplets have to experience a shear stress larger than the macroscopic shear stress of the emulsion. Finally, even if the radius of the droplets is effectively controlled by local constraints, we still do not have an explanation for the fact that the droplets are fractionated down to a unique size. Let us examine how our results correlate to those reported in refs 14 and 15. Mason and Bibette15 reported qualitative maps over the dispersed phase (oil) volume fraction (φ) and surfactant concentration (C) of uniformity of ruptured droplets at various shear rates. As a general result, they found that monodispersity is favored by large effective viscosities, high φ and C. However, the coalescence of highly concentrated emulsions (φ f 1) is observed immediately after shearing. Coalescence also occurs at high C when the surfactant forms inverse lamellar phases in water. Within this range of surfactant concentrations, Mason and Bibette observed that the coalescing droplets of the premixed emulsion can still be ruptured down to a uniform size. After the shear is stopped, coalescence is again observed. Hence, within this particular regime, fragmentation and coalescence occur simultaneously and still lead to a shear-induced monodisperse emulsion. We also observe a droplet fragmentation-coalescence mechanism in our experiments but not coalescence after shear. The comparison of the two sets of experiments is somewhat hazardous since our premixed emulsions at rest do not present visible coalescence. Our polymeric surfactant does not exhibit any structural change in the continuous medium within the range of investigated concentrations that would lead to the destabilization of the direct emulsions. In contrast, it is much more relevant to compare our experimental data to the results obtained by Mason and Bibette within the more darkly shaded areas of their map (Figure 5 in ref 15). In this range of φ and C, the premixed emulsions exhibit a viscoelastic behavior and have a good stability at rest. Consequently, they can reasonably be compared to our emulsion samples. Mason and Bibette observed a decrease of the radius of the uniform droplet with increasing the shear rate up to 3000 s-1. At a given shear rate, the radius of the monodisperse emulsion decreases with increasing the dispersed phase volume fraction and the surfactant concentration (Figures 12-14 in ref 15). So, our data correlate well with the results of Mason and Bibette: monodispersity is favored by large effective viscosities, high φ and C. However, they came to the conclusion that within the darker regions of their map, the monodispersity arises solely from the rupture of the droplets. Our experimental results are in agreement with a description of a droplet fragmentation-coalescence mechanism. We also suggest that the droplet size is controlled by local constraints more important than the emulsion shear stress. The quality of the ordered structure
Emulsion Stabilization with a Polyelectrolyte
of our emulsion samples decreases after the shearing is stopped. Hence, we do not come to the same conclusion as Mason and Bibette regarding the mechanism leading to droplets with uniform size. Even if this is probably due to the presence of a physical polymer gel between the oil droplets, no satisfactory explanation can actually be given at the present time. Conclusion The hydrophobically modified poly(sodium acrylate) emulsifier used in this study allows the preparation of polydisperse concentrated direct emulsions with an oil content up to 0.91. The models of Princen and Kiss6,7 and Mason et al.22 provide a good fitting of the experimental G′-φ dependence indicating that the elasticity of the emulsions is proportional to the density of interface. Shearing polydisperse emulsions leads to the formation of ordered monodisperse emulsions at sufficiently high shear rates. Remarkably, the formation of the crystalline structure is not affected by changing the gap spacing values from 30 to 70 µm. The level of organization of the droplets within the emulsion increases with the shear rate up to about 9000-10000 s -1. Above this threshold
Langmuir, Vol. 17, No. 9, 2001 2663
value, the ordered structure is broken down. The quality of the ordered structure decreases a few seconds after shear flow cessation. The droplets are probably forced to flow according to preferential shear planes thus explaining the higher level of droplet organization observed under shear. The high ordering of the structure is not totally preserved after cessation of shear. This is probably due to the fact that the droplets are still not monodispersed enough. Finally, the droplet size decreases with increasing the shear rate, the polymer concentration, and, to a lesser extent, the dispersed phase volume fraction. The results are only in qualitative agreement with a description of a droplet fractionation-coalescence mechanism in which the fractionation of the droplets occurs when the viscous stress becomes higher than the Laplace pressure. Accounting for the presence of both the coalescence and the fractionation processes, the measured values of the radius are smaller than expected leading to the conclusion that the droplet size is likely to be controlled by local constraints higher than the macroscopic shear stress of the emulsion. LA001492W
