Article pubs.acs.org/Langmuir
Coalescence in Double Emulsions Martín Chávez-Páez, Carla M. Quezada, Laura Ibarra-Bracamontes,† Héctor O. González-Ochoa,‡ and José Luis Arauz-Lara* Instituto de Física “Manuel Sandoval Vallarta”, Universidad Autónoma de San Luis Potosí, Alvaro Obregón 64, 78000 San Luis Potosí, S.L.P., Mexico ABSTRACT: Coalescence processes in double emulsions, waterin-oil-in-water, are studied by optical microscopy. The time evolution of such systems is determined by the interplay of two coalescence processes, namely, between inner water droplets and between the inner water droplets and the continuous external water phase. The predominance of one of those processes over the other, regulated by the relative amount of hydrophilic and lipophilic surfactants, leads to different evolutions of the system. We present here results for a class of systems whose evolution follows a master behavior. We also implemented a computer simulation where the system is modeled as a spherical cavity filled with smaller Brownian spheres. Collisions between spheres allow coalescence between them with probability Pi, whereas collisions between a sphere and the wall of the cavity allow coalescence with the external phase with probability Pe. The phenomenology observed in the experimental systems is well reproduced by the computer simulation for suitable values of the probability parameters.
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INTRODUCTION Double emulsions are systems in which two immiscible liquids are dispersed one into the other, in the form of droplets, in a double sequence. The main processes of interest in such systems are the controlled production, stabilization, and destruction. The understanding of the physical grounds of the mechanisms involved in each of those processes poses challenging questions whose elucidation is of current interest in science and technology.1 Here we are concerned with one of the main mechanisms responsible for the destabilization of emulsion systems, namely, coalescence. Coalescence is by itself a complex process, and the possibility of understanding and controlling it suggests interesting technological applications for a variety of industries such as food, pharmaceutical, cosmetics, agriculture, petroleum, and so forth.1−6 We present here a study, experimental and by computer simulations, of coalescence processes in double emulsions. The experimental systems considered here are double emulsions of the form water-in-oil-in-water (W/O/W), consisting of small (submicrometer) water droplets dispersed in larger oil globules which are themselves dispersed in a continuous water phase. A very interesting characteristic observed in W/O/W double emulsions is that the addition of an excess of hydrophilic surfactant, above its critical micellar concentration (cmc), in the external continuous water phase destabilizes the system. Under such conditions, the inner water phase is gradually released to the continuous external water phase, transforming the double emulsion in a more stable direct oil-in-water (O/W) emulsion.7−9 Two types of coalescence occur during such process: coalescence of the internal water droplets with the external water phase (external coalescence) and coalescence © 2012 American Chemical Society
between internal water droplets (internal coalescence). The former produces the release of the water droplets content to the external phase, whereas the latter produces the uneven grow of the internal water droplets. Depending on the amount of hydrophilic surfactant added to the external water phase, those processes can happen within minutes or they can be controlled to occur gradually during a time span of weeks.10 Such interesting behavior of these systems makes them suitable for industrial applications and technology development, for instance, for the encapsulation of substances incorporated in the internal water phase (drugs, nutrients, flavors, enzymes, cosmetics) and their gradual release for prolonged efficiency.3,6,11−17 Let us note here that Ostwald ripening is another mechanism for emulsion destabilization. Such mechanism is, however, much slower than the one reported here, and it is only important at surfactant concentrations below 1 cmc.8 External coalescence in double emulsions has been described as being driven by interface instabilities, occurring when the excess of hydrophilic surfactant in the continuous phase penetrates the oil phase and replaces part of the lipophilic surfactant at the oil−water droplet interface. At some surfactant ratio, the bending energy is expected to favor a change of the interface curvature of the droplets in contact with the oil globule interface, producing an opening and a sudden release of the droplet content to the continuous water phase.8,18 Nevertheless, a microscopic understanding of the mechanism Received: December 30, 2011 Revised: March 17, 2012 Published: March 19, 2012 5934
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results are presented in the Results section. Figure 1a shows a picture of a single oil globule of diameter 50 μm in a double emulsion. In this
behind this process, and that of internal coalescence, is still missing. It is, however, a complex task since various quantities of interest in these systems are not easy to determine and probably they change with time. For instance, the composition of surfactants at the interfaces, between the inner water droplets and oil, and between the oil globule and the external water phase, are unknown. Both interfaces are likely to be mixtures of both species of surfactants but their compositions are not simple to determine. Furthermore, it is not clear whether those interfaces are single layers of surfactants or more complex structures.9,19 Thus, although internal and external coalescence are rather complex mechanisms, here we propose model computer simulations that incorporate internal and external coalescence in a simple manner, that is, by introducing two probability parameters, one for each type of coalescence process. By tuning such parameters, the simulations are able to reproduce the main trends observed experimentally. In the following sections, we present a description of the sample preparation, the simulation details, the experimental and simulation results, and finally the conclusions.
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Figure 1. (a) Picture of single oil globule of diameter 50 μm in a double emulsion prepared at 2% of Span 80 and 30 cmc of SDS. (b) Schematic representation of the coalescence events considered in the simulations. Inside the globule two particles coalesce with probability Pi, whereas particles in contact with the spherical cavity coalesce with the exterior with probability Pe. image, the large circle is the oil globule, the nonuniform texture inside the circle is produced by the small water droplets filling up the globule, and the outer uniform area is the external continuous water phase.
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EXPERIMENTAL PREPARATION
SIMULATIONS The model system simulated here consists of spherical particles enclosed in a spherical cavity of radius R. The particles in the cavity are allowed to move according to the classical Brownian dynamics (BD) algorithm proposed by Ermak.22 In BD, the equation of motion of particle i is given by
Double emulsions in this work are prepared following a two-step standard procedure.8,9,20 In the first step, an inverse water-in-oil (W/ O) emulsion is produced consisting of water droplets, stabilized by a lipophilic surfactant, dispersed in oil. In the second step, the double emulsion is produced by dispersing globules of the inverse emulsion in water with a hydrophilic surfactant. By varying the amount of both surfactants, one can produce double emulsions with different stability properties which are regulated by the interplay of internal and external coalescence of the inner water droplets. For the sake of clarity, we concentrate here only in the study of the evolution of double emulsion where the effect of both coalescence processes can be distinguished separately. Let us now describe the system preparation. The inverse emulsion is prepared as follows. A 1 M NaCl water solution and the lipophilic surfactant Span 80 (sorbitan monooleate, with a hydrophilic−lipophilic balance HLB = 4.3) are mixed in a proportion of 4:1 by weight, by gentle shearing in a mortar. The creamy product is then mixed with dodecane (used here as the oily phase) at 10% (w/w), by fast stirring. With this procedure, we produce a W/O emulsion with water droplets with a narrow size distribution (hydrodynamic diameter 208 nm ± 6%, determined by dynamic light scattering, DLS). In order to avoid multiple scattering, the hydrodynamic size is measured in samples diluted using oil with the same concentration of Span 80. In order to fix the lipophilic surfactant concentration in the oil phase, four cycles of gentle centrifugation of the water droplets and resuspension in fresh oil with a known concentration of Span 80 were performed. After each cycle, the size distribution of the water droplets was determined by DLS; no changes were observed. We varied the amount of lipophilic surfactant in the range of 0.5−2.0% w/w, but we present here results only for the higher concentration. In the second step, the inverse emulsion is dispersed in pure water with hydrophilic surfactant; we use sodium dodecyl sulfate (SDS, HLB = 40). The proportion of the inverse emulsion to water is 1:9 by volume. The concentration of SDS was fixed at 30 cmc (cmc = 8 × 10−3 mol/L). Ultrapure water was used throughout sample preparation. Thus, the double emulsion produced here consist of submicrometer water droplets, encapsulated in oil globules of diameter in the micrometer range, dispersed in a continuous water phase. The osmotic pressure mismatch between the water in the droplets and the continuous phase induce an initial swelling of the oil globules.21 This does not affect the coalescence processes and helps to increase the proportion of the internal water phase. All samples were prepared and studied at a temperature of 20 °C. Right after preparation, the sample is loaded in a rectangular cell 2 cm × 2 cm × 200 μm and placed on the stage of an optical microscope for observation. Standard video equipment is coupled to the microscope to record the process. Our
ri(t + Δt ) = ri(t ) + βD0i Fi(t )Δt + R i
(1)
where β = (kT)−1, with kT being the thermal energy; ri, D0i, and Fi are the position, diffusion coefficient, and total force acting on particle i (including the interaction particle−particle, particle−wall, and gravity), respectively. The time interval is Δt, and Ri is a random displacement whose components Riα are chosen independently from a Gaussian distribution with zero mean and variance ⟨(Riα)2⟩ = 2D0iΔt. The interaction between particles is modeled by the simple, short-range, repulsive potential βuij(r ) = ε exp[−z(r − σij)]
(2)
where σij = (σi + σj)/2 is the contact distance between particles i and j with diameters σi and σj, ε is a dimensionless energy parameter, and z a screening constant. The cavity’s wall is modeled as a hard wall. We also considered soft cavities by using the Lennard−Jones potential22 as the interaction between the wall and the particles; since the observed trends are similar, here we report only those for the hard wall. Equation 1 is used to move particles inside the cavity. In order to incorporate internal and external coalesce, we implemented a simple stochastic criterion as follows. When two particles with diameter σi and σj do overlap, they are allowed to coalesce with probability Pi.22 In such a case, a new particle is created, at the center of mass of the coalescing particles, with a size determined from the volume conservation condition, that is, the size of the new particle is given by σnew = (σi3 + σj3)1/3. On the other hand, if a droplet overlaps with the wall, it is allowed to coalesce with the external phase with probability Pe. In this case, the droplet disappears from the group of particles in the simulation and the size of the cavity decreases accordingly. Naturally, the higher the values of Pi and Pe, the more likely particles will coalesce. As limiting cases we 5935
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have Pi = 0.0, when particles are not allowed to coalesce internally, and Pi = 1.0, when any overlap between particles will produce immediately a new particle. Similarly, when Pe = 0.0 the particles are not allowed to leave the cavity, and when Pe = 1.0 any collision with the wall will lead to the escape of the colliding particles. Thus, within this model, we can simulate pure internal coalescence (Pe = 0 and Pi ≠ 0), pure external coalescence (Pi = 0 and Pe ≠ 0), or the combination (Pi ≠ 0 and Pe ≠ 0), where the evolution of the system will depend on the competing effects introduced by these coalescence parameters. Figure 1b shows schematically the model used here. At the beginning of a simulation run, a specified number of particles are placed inside a spherical simulation box of radius R. The number of particles N is determined from the required value of particles’ volume fraction ϕ and the initial size σg0 = 2R of the cavity using the relation N = ϕ(σg0/σ0)3, where σ0 is the size of the particles at the beginning of the simulation. Note that for small systems and/or low volume fractions, N is of the order of a few hundred and the simulation runs can be quite fast. However, for intermediate and high volume fractions, N is in the range 104−106 and the runs require much longer times. In our case, the initial N identical particles are placed randomly, or in a lattice, over the entire volume inside the cavity and then allowed to equilibrate for several thousand cycles before allowing particles to coalesce. This initial stage is performed to avoid significant overlaps that might be present in the initial configuration (or to melt the initial configuration if we start from a lattice). Here we take the parameter ε = 1, that is, the amplitude of the interactions equals kT at contact. The screening is taken as z = 20/σ0, and the simulation time step as Δt = 5 × 10−4t0, where t0 = σ02/D0 and D0 is the diffusion coefficient of particles before coalescence is allowed. The value of these parameters are taken from our experimental values: D0 = 1.58 × 10−12 m2/s2, σ0 = 208 nm, and t0 = 2.52 × 10−2 s. Note that the diffusion coefficient changes as particles coalesce. For a new particle, its diffusion coefficient is obtained through the relation Dnew = (σ0/σnew)D0. The force due to gravity, on the other hand, is calculated through the relation Fg = Δρg(πσp3/6), where Δρ is the density difference between the oil and water phases, g is the magnitude of the gravity field, and σp is the diameter of the particle.
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Figure 2. Time evolution of double emulsions, prepared at 2% of Span 80 and 30 cmc of SDS. (a) Diameter of oil globules of different sizes vs time. (b−e) Pictures taken from a side view (see text) of a single oil globule of initial diameter σg0 = 30 μm, taken at the different time regimes separated by the dashed lines. (f) shows in more detail the time evolution of smaller oil globules, where the four regimes are better appreciated.
The results in Figure 2 show that the oil globules lose material with time and, more interestingly, that their size decreases following a similar behavior for a wide range of initial values σg0 ≡ σg(t = 0). As one can see here, σg(t) evolves following four time regimes. In the initial one, σg(t) has a fast decrease. In the second regime, the change of the globule’s size is much slower. The third regime is characterized by an accelerated release of water droplets to the continuous phase, producing an appreciable reduction of σg(t). Finally, in the fourth regime, the globule size decreases slowly again. The dashed straight lines in Figure 2a are guides to the eye, separating the different regimes. The state of evolution of the system at each regime is illustrated in Figures 2b−e. These figures show images of a single oil globule, of initial size σg0 = 30 μm, taken from a side view at times within the different time regimes. Observation of the samples from a side view is attained by rotating the optical microscope by 90°. As one can see here, this setup allows us to appreciate the effect of gravity pointing downward in these pictures. As pointed out above, the phenomenology reported in Figure 2 can be understood as the interplay of the two main processes observed here, namely, external coalescence and internal coalescence. Initially, there is a large number of water droplets in contact with the external water/oil globule interface. Thus, in the initial regime, the frequency of external coalescence events is high and the reduction of the globule’s size is determined by the rate of external coalescence. This process depletes small water droplets close to the interface and the frequency of external events eventually goes down; that is, the decrease of σg(t) slows down. At the same time, internal coalescence is taking place producing inner water droplets of larger size, but not large enough to be clearly distinguished at this stage by
RESULTS
Figure 2 shows the time evolution of the diameter σg(t) of oil globules in double emulsions, prepared at 2% (w/w) of Span 80 in the oil phase and 30 cmc of SDS in the external water phase. At this concentration of the hydrophilic surfactant, the phenomenon of interest occurs within a time scale from few hours to few days. A lower amount of SDS slows down the coalescence processes, prolonging the experimental time, but the phenomenology is the same as that being reported here. On the other hand, higher amounts of SDS speeds up the processes and make them difficult to quantify. The oil/water proportion is kept low in order to produce very dilute dispersions of oil globules and in that way avoid any effect from interglobule interactions. Various samples were prepared; in each of them, the evolution of σg(t) is monitored only in a single spot containing a few disperse oil globules. Thus, each curve in Figure 2a represents the average behavior of different oil globules, of roughly the same initial size, and is also an average over different realizations of the system. 5936
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optical microscopy. Thus, during the first time regime, the main process observed here is the reduction of σg(t), due to coalescence of the inner water droplets toward the external water phase, without much change in the texture of the globule. During the time span of the first regime, the system looks like the image in Figure 2b. As internal coalescence proceeds, the inner water droplets grow larger and they can reach sizes in the range of micrometers with a broad distribution. This process diminishes the number of internal droplets and therefore their number of collisions with the globule’s interface. Thus, the rate of external coalescence decreases and the globule’s size stabilizes. Figure 2c shows an image of the oil globule in the second regime. At this stage, the main evolution observed is a change in the texture of the globule as the inner water droplets grow due to inner coalescence. As the evolution proceeds, one can observe the presence of inner water droplets with sizes as large as few micrometers settled down at the bottom of the globule due to gravity; see Figure 2d. The large water droplets are eventually also released to the continuous phase, in the third regime, producing an appreciable reduction of the globule size. Finally, in the last regime, most of the inner droplets have been released and the globule encloses only a small amount of diffusing individual water droplets; see Figure 2e. These droplets also coalesce with the external water phase, and no significant internal coalescence is observed. For comparison, Figure 2f reproduces partially results reported in a previous work.9 As one can see here, the phenomenology observed in the case of small oil globules is preserved as the size of the globules increase for about 1 order of magnitude. One can also see here that the four regimes are better differentiated in the curves for σg(t) for smaller globules. Larger globules contain a much larger number of inner water droplets and the change in size is smoother. The predominance of one coalescence process over the other depends on the interaction between the water−oil and oil− water interfaces, that is, coalescence processes depend on the surfactant composition of both interfaces, which are unknown. Here, instead of pursuing the elucidation of those compositions, we assume the simple model of double emulsions described above and implement a computer simulation algorithm (Brownian dynamics22) to assess the relative contribution of both coalescence processes in the stability of such systems. As we show below, this simple model can reproduce qualitatively the experimental observations when appropriate values of the coalescence parameters Pi and Pe are chosen. Figures 3 and 4 show our simulation results for σg(t) for different coalescence conditions. In all cases considered here, the volume fraction of small spheres is ϕ = 0.4 and they are enclosed in a cavity of radius R = 30σ0, leading to a initial number of spheres of N = 86 400. Figure 3 illustrates four cases where the internal and external coalescence parameters are equal, namely, Pi = Pe = 10−1, 10−2, 10−3, and 10−4. The inset presents the same results in a log−log scale. From this figure, we see clearly that σg(t) exhibits fast and slow regimes. In the former, particles in the system are rapidly released to the exterior as a result of a large number of collisions with the wall of the cavity which take place due to the high concentration of particles close to the wall. As this process takes place, the remaining particles in the system are able to diffuse more freely throughout the available space, decreasing the collision rate with the wall and therefore contributing to slow down the
Figure 3. Simulation results for σg(t)/σg0 for different values of the coalescence parameters Pi and Pe: Pi = Pe = 10−1, 10−2, 10−3, and 10−4, circles, squares, diamonds, and triangles, respectively. Inset, same results in log−log scale.
reduction of the cavity size. All the curves in Figure 3 exhibit this trend; reducing the rate of internal and external coalescence only make the process slower, as observed here. The inset in Figure 3 shows the data in a log−log scale which allow us to plot larger times and to appreciate more clearly the time scale separation between the two regimes for the different systems. As one can see here, the time to reach the final stage of the simulations, that is, the release of all particles, can be increased by orders of magnitude by reducing appropriately the coalescence parameters. Figure 4 shows the main features of the model, as determined by the competition between both coalescence
Figure 4. Simulation results for σg(t)/σg0 for different values of the coalescence parameters Pi and Pe as indicated in the figure. Inset shows σg(t)/σg0 for 20 different simulation runs in system S3. The thick line represents the average of 50 independent runs.
processes. Here σg(t) is presented for four combinations of Pi and Pe. Such systems, labeled here as Sj ≡ (Pi,Pe), are S1 = (10−1,10−1), S2 = (10−3,10−1), S3 = (10−1,10−3), and S4 = (10−3,10−3). In systems S1 (diamonds) and S2 (squares), external coalescence occurs at the same rate, but the rate of internal coalescence is different, being slower for S2. As one can see here, the initial decay of σg(t) is practically the same for both systems but the decay at longer times differs owing to the difference in the value of Pi. Similarly, in systems S3 (circles) and S4 (triangles), the value of Pe is the same and Pi is different. Here too, one can see an identical initial decay of σg(t), but quite a different behavior at later times. Thus, it is clear that external coalescence determines the initial decrease of σg(t), being faster for higher values of Pe. On the other hand, for fixed Pe, the value of Pi determines the evolution of σg(t) at longer times. Let us consider here in more detail the case where internal coalescence is the predominant process (system S3). This system is particularly interesting, since under such conditions the evolution of the cavity’s size resembles qualitatively the behavior of the experimental system in Figure 5937
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dashed lines in Figure 2, drawn to separated the different stages in the experimental curves. Thus, Figure 5b shows that the simulation model could reproduce the experimental results by decreasing appropriately the probability parameters. The scaling parameter for the simulation time used here is 2.4 × 104. Although we did not find a direct relation between the probability values and the simulation time scale, it is likely that one needs to lower the probabilities by several orders of magnitude in order to reach in the simulation the experimental times scales. On the other hand, in the cases where the rate of external coalescence is higher or similar to that of internal coalescence, the practically continuous release of small spheres through the cavity’s boundary produces a smooth decrease of σg(t). Scenarios like this are also observed in our experiments for much higher concentrations of SDS in the external continuous water phase (data not shown).
2; that is, it exhibits four stages as in the experiment: an initial fast decrease, a regime of slow evolution, a regime of abrupt drops and a final slow decay. As we show below, in this case, the state of evolution of the internal spheres is also similar to the experimental system. In the simulation, the coalescence criterion allow spheres of all sizes to have the same chance to escape from the cavity once they reach the boundary by diffusion. Since in S3 it is much less likely that the spheres leave the cavity, internal coalescence produces the uneven growth of internal spheres. However, when large spheres escape, the change in the cavity’s size is larger than when small spheres do. Nevertheless, different realizations of the simulation lead to different evolution of the system and of its corresponding size distribution of the internal spheres, and in turn to different curves for σg(t). This is observed in the inset of Figure 4, where the curves from 20 (out of a total of 50) different runs are shown (lines) together with the average curve (thick line). As mentioned above, the behavior of the simulated system S3 closely resembles that of the experimental one in Figure 2, not only in the average curve for σg(t) but also in the evolution of the internal droplets. Thus, for comparison, in Figure 5a is
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CONCLUSIONS Here, we study coalescence in double emulsions experimentally and by means of a computer simulation. As observed in the experiments, the time evolution of such systems is determined by the interplay of two coalescence processes, namely, internal and external coalescence of the inner water droplets. As it is shown in the present work, an understanding of such interplay is provided by a numerical simulation using a simplified model system, where those processes are taken into account via their probabilities of occurrence. Variation of these two probability parameters, produces different behavior of the model system. It is found that the phenomenology is defined mainly by the relative values of those parameters, that is, an entirely different kind of behavior is produced when Pe > Pi than that when Pe < Pi. As it is shown here, this simple model reproduces qualitatively the evolution of our experimental system when one assumes the latter. Although the simulation time scale is much shorter than the experimental one, the latter should be reached by taking much lower values for the probability parameters maintaining the relation Pe < Pi. In the experimental system, the actual frequency of occurrence of both coalescence processes depend on the surface properties of water/oil interfaces where they occur, for instance, the surfactant composition of those surfaces. Such quantities are difficult to assess experimentally, but the simulation model developed here provides us with a way to obtain some insight on the coalescence processes and in turn on the properties of those interfaces for different experimental conditions.
Figure 5. (a) Average value of σg(t)/σg0 for the system where Pi = 10−1 and Pe = 10−3 as obtained from the simulation (symbols). Inset pictures are illustrative snapshots of the simulated system at different times, showing the evolution of the size distribution of particles in the globule at different stages of the simulations. The color of particles indicate different sizes. One can also see here the effect of gravity, driving the larger particles toward the bottom of the cavity. (b) Rescaled simulation data as explained in the text.
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AUTHOR INFORMATION
Present Addresses
shown σg(t) for system S3 in linear scale, together with snapshots of the state of the simulation system at different times for one of the runs. As one can see here, the snapshots of the simulation and the experimental systems are quite similar, including the effect of gravity. The large difference between experimental and simulation time scales does not allow us a direct quantitative comparison between both results. However, by doing a simple rescaling of the simulation time, one can corroborate that the simulation curve for σg(t) fits very well within the behavior of the experiments. Since the diameter of the internal spheres in the simulation is taken as that of the experiment, 208 nm, the diameter of simulation globule is then 12.5 μm. The simulation curve for the globule’s diameter (in actual units) is plotted in Figure 5b against a rescaled time. The dashed straight lines in this figure are extrapolations of the
†
Universidad Michoacana, Mexico. ́ y Tecnológica A. Instituto Potosino de Investigación Cientifica C., Mexico.
‡
Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS ́ We acknowledge technical support from A. Ramirez-Saito and financial support from Consejo Nacional de Ciencia y Tecnologiá (Conacyt), Mexico, Grants 84076 and 58470.
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REFERENCES
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