4448
J. Phys. Chem. B 2000, 104, 4448-4456
Percolation in Concentrated Water-in-Carbon Dioxide Microemulsions C. Ted Lee Jr., Prashant Bhargava, and Keith P. Johnston* Department of Chemical Engineering, The UniVersity of Texas at Austin, Austin, Texas 78712 ReceiVed: NoVember 22, 1999; In Final Form: February 16, 2000
The phase behavior and electrical conductivity of water-in-carbon dioxide (W/C) microemulsions are reported over a range of temperatures (5-65 °C), pressures (100-450 bar), and droplet volume fractions (φ ) 0.03470.483) at a constant water-to-surfactant molar ratio (Wo) of 12.5. A φ of 0.483 is a 5-fold increase over those reported previously. A critical point is observed at a droplet volume fraction of approximately 0.12, at which the single-phase microemulsion splits into two microemulsion phases of similar volume upon lowering the pressure (upper critical solution pressure). At low temperatures, a lower critical solution pressure is also observed upon increasing the pressure. Both of the critical solution pressures result from an increase in the attractive interdroplet interactions; consequently, pressure has little effect on the conductivity in the onephase region. The conductivity increases nearly 3 orders of magnitude with changes in the droplet concentration or temperature. Scaling analysis of the conductivity data supports a dynamic percolation model, whereby the attractive interdroplet interactions form clusters of discrete droplets with rapid charge transport.
Introduction Together, water and carbon dioxide (CO2) constitute the two most abundant and environmentally benign solvents on earth. Liquid or supercritical CO2 (Tc ) 31 °C, Pc ) 73.8 bar) exhibits solvent properties that are tunable with pressure, and it is essentially nontoxic and nonflammable. Dense CO2 is nonpolar (unlike water) and has weak van der Waals forces1 (unlike oils) and, as such, may be considered a third type of fluid phase in nature, somewhat similar to fluorocarbons. Dispersions of H2Oin-CO2, whether on the nanometer (microemulsions)2-4 or micrometer (emulsions)5 scale, offer new possibilities for separations on the basis of polarity and as media for reactions between polar and nonpolar molecules.6,7 The low viscosities and high diffusivities occurring in near-critical or supercritical CO2 8 may result in enhanced separation9 or reaction rates6 in these media. Furthermore, the formation of nanometer-sized metallic and semiconductor particles in water-in-Co2 (W/C) microemulsions10,11 may potentially be influenced by enhanced collision among water droplets in a low viscosity supercritical fluid. For the development of these applications, a fundamental knowledge of the microstructure, stability, and exchange processes of W/C microemulsion systems would be highly beneficial. The structure of microemulsions has often been determined from conductivity measurements.12 For some systems, an increase in conductivity with φ has been attributed to changes in the microstructure (e.g., from droplets of water dispersed in the oil to a bicontinuous structure).13-15 For example, smallangle X-ray scattering (SAXS),16 freeze-fracture electron microscopy (FFEM),17 and water self-diffusion NMR18 measurements confirm a transition from bicontinuous structures to discrete water droplets, as the amount of water is increased at constant surfactant-to-oil ratio in water-in-alkane microemulsions formed with the didodecyldimethylammonium bromide (DDAB) surfactant. On the other hand, W/O microemulsions formed with sodium bis(2-ethylhexyl) sulfosuccinate or AOT have been shown to exist as discrete water droplets in oil for droplet volume fractions
up to φ ) 0.588 by FFEM,17 as well as small angle neutron scattering (SANS),19 NMR,20 and time-resolved fluorescence quenching21 methods. For this type of system, a dynamic percolation model22,23 has been proposed in which the formation of droplet clusters allows for the transport of the charge carriers and leads to an increase in the microemulsion conductivity.24 As the volume fraction of water droplets increases, attractive interdroplet interactions increase, leading to droplet clustering and thus percolation. Droplet clustering can also result from changing the system temperature or pressure. For ionic surfactants, increases in temperature can lead to attractive interdroplet interactions25,26 and thus percolation27 and phase separation28 in W/O microemulsion systems. For near-critical or supercritical fluids, decreasing the pressure lowers the density and solvent power of the fluid,29 thus increasing the attractive interdroplet interactions.30,31 This effect can also be seen in liquid solvents near a phase transition at which changing the pressure can have a marked effect on the phase behavior of the system, which is normally considered incompressible.28,32-34 SANS experiments performed on dilute (volume fraction of droplets φ < 0.1) water-in-compressible fluid microemulsions were used to show direct evidence of spherical droplet formation, as well as information on the primary (droplet size) and secondary (aggregation) structure of this class of microemulsions.30,31 Later, conductivity35 and luminescence quenching36 experiments performed on concentrated (φ up to 0.3) microemulsions formed in near-critical propane with the surfactant DDAB illustrated a percolation mechanism whereby attractive interdroplet interactions result in droplet aggregation as the droplet volume fraction is increased. SANS, dynamic light scattering (DLS),37,38 conductivity,35 and luminescence quenching36 measurements on water-in-near critical and supercritical alkane microemulsions have all demonstrated that lowering the pressure of these systems can also result in strong interdroplet interactions at the cloud point. The phase behavior of microemulsion systems is a function of two factors, namely the interdroplet interactions and the natural
10.1021/jp9941357 CCC: $19.00 © 2000 American Chemical Society Published on Web 04/08/2000
Percolation in H2O-in-CO2 Microemulsions
J. Phys. Chem. B, Vol. 104, No. 18, 2000 4449
curvature (i.e., the curvature in the absence of these interactions). As described theoretically,39 lowering the pressure reduces the solvent power of near-critical or supercritical fluids, resulting in enhanced attractive interdroplet interactions and separation into two phases, one with a large and one with a small droplet concentration.30,39 Phase separation can also result from an increase in the curvature of the interface about water whereby an excess water phase is expelled from the microemulsion phase, resulting in a Winsor II system.39,40 Although reasonably well established for the supercritical hydrocarbon fluids, little is known about these two mechanisms of phase separation in W/C microemulsions or the regions in which they are expected to occur. The existence of bulk water domains in W/C microemulsions was first demonstrated by several spectroscopic techniques with an ammonium carboxylate perfluoropolyether surfactant (PFPENH4).3 SANS experiments41 later confirmed the existence of spherical water droplets dispersed in CO2. Subsequently, microemulsions in CO2 have been formed for only a select few surfactants.2,4 To date, microemulsions have been formed in CO2 for volume fractions below 0.1, and the attractive interdroplet interactions have not been studied quantitatively in these systems. In the present work, the phase behavior, percolation phenomena, and microstructure of concentrated (φ > 0.1) W/C microemulsions are studied. Electrical conductivity measurements are used to describe interdroplet interactions as a function of the temperature, pressure, and droplet volume fraction. Extensive phase-behavior measurements are used to identify regions of percolation, as well as to explain the observed trends in electrical conductivity. Specifically, the existence of critical points in the microemulsion phase behavior will be sought as evidence for attractive interactions between droplets. Finally, from scaling analysis of the effect of droplet volume fraction, temperature, and pressure on the electrical conductivity, the morphology of the microemulsion (discrete droplets or bicontinuous structures) upon approaching a phase boundary will be determined. Theory Percolation in Water-in-Oil Microemulsions. The conductivity (σ) of water-in-oil microemulsions can be described by the asymptotic laws of the dynamic percolation model22,23
σ ) C1σ1(φ - φp)µ
(1)
above the percolation threshold (φ > φp + δ) and
σ ) C2σ2(φp - φ)-s
(2)
below the percolation threshold (φ < φp - δ ′). In eqs 1 and 2, C1 and C2 are prefactor terms, whereas σ1 and σ2 correspond to the conductivity of the droplets and the continuous phase, respectively. The volume fraction at the percolation threshold (φp), defined as the point at which an “infinite” cluster spans the length between the two electrodes,42 is determined from the inflection point in the plot of the log of conductivity versus φ. Once φp has been determined, the scaling exponents µ and s can be determined from plots of the log of conductivity versus the log of (φ - φp) and (φp - φ), respectively. The width of the transition interval ∆ ) δ + δ ′ can be approximated by ∆ ≈ (σ2/σ1)1/(µ + s).43 Therefore, for W/O microemulsions in which σ2/σ1 , 1, the width of the transition interval is small.
Percolation with temperature or pressure can be understood in terms of the dynamic percolation model by considering the fact that φp is a function of T, P, and Wo. At constant droplet volume fraction, P and Wo, the effect of changing the temperature on the percolation volume fraction is given by
K)
( ) ∂φp ∂T
(3)
The percolation threshold temperature Tp is defined as the temperature at which φ ) φp and is determined in a similar manner as φp (i.e., the point of inflection on a log of conductivity versus temperature plot). Thus, the effect of changing the temperature on microemulsion conductivity, to a first-order approximation, is given by44
σ ) C1σ1[- K(T - Tp)]µ
(4)
above the percolation threshold temperature (T > Tp) and
σ ) C2σ2[- K(Tp - T)]-s
(5)
below the percolation threshold temperature (T < Tp). In AOT microemulsion systems, φp has been found to be essentially linear in T,44,45 thus K is independent of temperature, and the scaling exponents µ and s can be determined from plots of the log of conductivity versus the log of (T - Tp) or (Tp - T), respectively. Percolation with pressure can be described in a similar manner, except now Kp ) (∂φp/∂P) at constant φ, T, and Wo is used.34 For systems that exist as discrete droplets clustering in a continuum (dynamic percolation), the scaling exponents are expected to be µ ≈ 2 and s ≈ 1.2, showing that these systems “belong to the same class of universality”.27,34 For water/AOT/ alkane systems, numerous experimental examples indicate that the dynamic scaling exponents above are indeed observed.27,42,45 For the transition to bicontinuous structures (static percolation), different scaling exponents are expected, namely µ ≈ 2 and s ≈ 0.6-0.7.27,46,47 In water/DDAB/alkane systems,48 as well as other bicontinuous microemulsion systems,49 similar exponents were obtained. Furthermore, for these static percolating systems, the percolation threshold volume fraction is found to be independent of temperature (i.e., K ) 0) with φp ≈ 0.15 in all cases. This is consistent with the Talmon-Prager model14 for bicontinuous microemulsions and, as evident from eqs 3 and 4, would not be observed in a system undergoing dynamic percolation. By investigating the percolation phenomenon in W/C microemulsions through electrical conductivity measurements, insight into the structure of concentrated water-in-CO2 microemulsions can be obtained for the first time. Experimental Section Materials. An ammonium carboxylate perfluoropolyether (PFPE-NH4) surfactant
CF3-(O-CF2-CF(CF3))n-(O-CF2)-COO-NH4+ was used in all experiments. The surfactant with an average molecular weight of 672 was synthesized from the neutralization of the acid (Ausimont, Lot # D-5) with aqueous ammonium hydroxide, followed by the removal of water and excess ammonia under vacuum at 65 °C. FT-IR (Perkin-Elmer) was used to confirm the disappearance of the acid peak at 1780 cm-1 to ensure complete conversion. Instrument grade CO2 (Praxair)
4450 J. Phys. Chem. B, Vol. 104, No. 18, 2000 passed through an oxytrap (Oxyclear, model RGP-31-300) and Nanopure II water (Barnstead) were used in all experiments. Microemulsion Phase Behavior and Conductivity. Microemulsions were prepared in a high-pressure variable-volume view cell50 (2 in. o.d. × 11/16 in. i.d., 28 mL total volume) equipped with a sapphire window (1 in. diameter, 3/8 in. thick) which permitted visual observation of microemulsion formation and phase behavior. A piston inside the view cell was used to vary the pressure independently of temperature. The desired amounts of water and surfactant to form a Wo ) 12.5 were loaded into the view cell, which was then sealed. CO2 was then added to the cell with a computer-controlled syringe pump (Isco, Model 260D), such that droplet volume fractions of approximately 0.5 would be obtained. After phase behavior and conductivity measurements had been made at that surfactant concentration, more CO2 was added to the cell with the syringe pump so that the volume fraction of dispersed water droplets could be varied. Using this technique, droplet volume fraction, temperature, and pressure were all varied. The system pressure was controlled with the syringe pump to within 1 bar, using CO2 as the pressurizing fluid on the backside of the piston. The system temperature was controlled to within 0.1 °C by submerging the view cell in a water bath. The cell contents were mixed with a magnetic stir bar inside the cell. The microemulsion cloud point at each concentration was measured from 0 to 65 °C by decreasing the pressure from 450 bar until the clear, one-phase microemulsion became cloudy. In some cases, cloud points were also observed upon increasing pressure, in which case the upper cloud points were determined by increasing the pressure from the one-phase region. The most concentrated microemulsion studied (equal masses of surfactant and CO2) was viewed between two cross polarizers in a specially designed high-pressure cell equipped with isotropic quartz windows51 and no evidence of liquid crystalline phases was observed. The view cell was equipped with two 1/8 in. ports, on opposite sides, that allowed conductivity electrodes to be placed directly inside the high-pressure microemulsion system, as described previously.5 The electrodes were fashioned from approximately 2 mm diameter loops of 0.01 in. diameter 304 stainless steel wire that had been platinized. The opposing wire loops were approximately 1 mm apart, and measurements were made with a conductivity meter (YSI, Model 3100). The conductivity meter operated at a frequency of 70 Hz for conductivities up to 499.9 µS and 240 Hz for conductivities up to 4999 µS. The cell constant was calibrated with aqueous solutions of NaCl and a cell constant of 3.0 cm-1 was determined. The conductivity of the microemulsions was measured simultaneously with the phase behavior by successively decreasing the pressure, in 10-20 bar increments, and maintaining a constant pressure until the conductivity of the microemulsion phase had equilibrated (typically less than one minute). Results and Discussion Phase Behavior. The results of the phase behavior of the W/C microemulsions formed at various surfactant/CO2 (S/C) mass ratios at Wo ) 12.5 is shown in Figure 1. For simplicity, only five of the 17 S/C ratios studied are shown because the data were systematic. Two distinct types of phase separation were observed. The first type occurred at temperatures greater than about 15 °C as the pressure was reduced at constant temperature. This transition typically had a slope of 3.2-3.6 bar/°C in P-T space. The transition occurred gradually with the one-phase solutions developing a slight orange tinge within
Lee et al.
Figure 1. Phase behavior of the water/PFPE-NH4/CO2 system at Wo ) 12.5 versus the surfactant-to-CO2 ratio (S/C). Two distinct phase transitions are clearly evident, one at higher temperatures as the pressure is reduced at constant temperature or the temperature is increased at pressure (PL or TU) and one at lower temperatures as the temperature is reduced at constant pressure (TL). Only five of the 17 S/C ratios studied are included. However, the data were systematic.
10-20 bar of the cloud point (denoted here as PL). The color became more intense at higher S/C values (i.e., in more concentrated microemulsions). This phase transition was likely a result of an increase in interdroplet interactions as the density of CO2 decreased, producing relatively large droplet clusters that scattered light. As the pressure was further lowered, the solutions became rapidly opaque at PL, as indicated in Figure 1. Below this cloud point, two transparent phases with similar volumes resulted. As this phase transition also results as the temperature is increased at constant pressure, it will also be referred to as TU. Analogous PL and TU cloud points have been observed and shown with SANS and DLS to be the result of attractive interdroplet interactions in water-in-oil microemulsions formed with near-critical and supercritical alkanes.31,52,53 A second type of phase transition occurred at temperatures less than about 10 °C as the temperature was reduced at constant pressure (denoted here as TL). As seen from Figure 1, TL is essentially independent of pressure. Furthermore, the clear, onephase microemulsion did not become colored near this transition, unlike the PL transitions. For temperatures below TL, only small amounts of an excess phase were observed. The solubility of PFPE-NH4 in water decreases with decreasing temperature,54 whereas the solubility of PFPE-NH4 in CO2 increases with decreasing temperature (at constant pressure).55 Thus, TL is a consequence of the water-CO2 interface becoming more curved about water as temperature is decreased (resulting in the expulsion of a small volume of nearly pure water) and not interdroplet interactions. A similar explanation has been presented for the TL cloud point in water-in-near-critical and supercritical alkanes.31 Percolation with Droplet Volume Fraction. On a plot of the log of the conductivity of the one-phase microemulsion versus φ at constant temperature and pressure, the percolation threshold volume fraction φp was determined from the inflection point. An example of this threshold is shown in Figure 2 where the conductivity increased by nearly 3 orders of magnitude. For clarity, only one curve is shown; however, 75 similar curves were generated at various T and P. The droplet volume fraction φ was calculated in the typical manner56 as the ratio (volume
Percolation in H2O-in-CO2 Microemulsions
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Figure 2. Percolation phenomena of a water/PFPE-NH4/CO2 microemulsion at 20 °C and 379 bar, as represented by the increase in the microemulsion electrical conductivity with droplet volume fraction.
Figure 3. Determination of the scaling exponents µ and s for percolation with droplet volume fraction at 20 °C and 379 bar (see eqs 1 and 2).
of water + PFPE-NH4)/(volume of water + PFPE-NH4 + CO2). A density of 1 g/mL was used for water and 1.8 g/mL for PFPENH4, as measured by Chittofrati et al.57 The volume of CO2 was determined from the density of CO2 at the given T and P.58 Thus, in these microemulsions, the droplet volume fraction was a function of S/C, T, and P due to the compressible nature of the continuous phase solvent, unlike the case in traditional oil systems. The low mutual solubilities of water and CO2 59-61 were ignored in the above calculation; however, if included, the calculated volume fractions changed by only 2%. To determine if the increase in microemulsion conductivity is due to transport of the charge carriers between neighboring droplets in a cluster (dynamic percolation) or through water channels in a bicontinuous system (static percolation), the conductivity data was fit to the dynamic percolation model of eqs 1 and 2. The percolation volume fraction φp was determined at each T and P by fitting the log σ to a fourth-order polynomial in φ and then setting the second derivative equal to zero.34 Once φp had been determined, log σ was plotted against the log of the absolute value of (φ - φp) as shown in Figure 3. For volume fractions sufficiently removed from the transition interval ∆, two straight lines were fit to the data with slopes equal to µ above and -s below the percolation threshold, respectively. Table 1 contains the values of µ and s determined at each T and P investigated using the methods described above. The average values for the scaling exponents are µ ) 1.99 and s ) 1.18 with standard deviations of 0.07 and 0.1, respectively, which are in excellent agreement with values expected from the dynamic percolation model and those obtained for water/AOT/liquid alkane systems (µ ≈ 2 and s ≈ 1.2).27,34,42,44,45 Thus, the increase in electrical conductivity in concentrated W/C microemulsions is due to the clustering of discrete droplets from attractive interdroplet interactions and not static percolation (bicontinuous structures). Similarly, a water-in-oil microemulsion stabilized with a PFPE-NH4 surfactant (MW ) 710 g/mol) in an unfunctionalized PFPE oil (MW ) 900 g/mol) has also been shown to undergo dynamic percolation according to conductivity62,63 and SANS experiments.64-66 In dynamic percolating systems, conduction has been attributed to the formation of transient water channels formed between droplets in a cluster.21,24,67 The formation of water channels requires the opening of the surfactant monolayer and, thus, is expected to be a function of the film rigidity. In
TABLE 1: Values of the Scaling Exponents µ and s Obtained at Each T and P Studieda T
µ
P
10 138 172 207 241 276 310 345 379 414 25 138 172 207 241 276 310 345 379 414 40 138 172 207 241 276 310 345 379 414 55 all
s
1.77 1.97 2.02 1.95 1.90 1.86 1.92 1.82
b
b
b
d
d
d
d
1.82 1.99 2.02 1.99 2.05 2.05 1.93
c
d
d
d
d
d
d
d
d
d
d
d
d
0.90 0.90 1.39 1.38 1.34 1.21 b
1.30 1.08 1.10 1.16 1.11 1.13
1.94 c 1.99 1.06 2.00 1.08 d
d
T
µ
P
15 138 172 270 241 276 310 345 379 414 30 138 172 207 241 276 310 345 379 414 45 138 172 207 241 276 310 345 379 414 60 all
s
b
b
1.97 2.00 1.98 1.96 1.96 1.95 1.92 2.05
1.34 1.12 1.18 1.12 1.11 1.34 1.27 1.17
d
d
d
d
1.94 2.13 2.09 1.97 1.98 2.03 2.07
1.11 -c 0.92 0.96 0.95 1.01 0.97
d
d
d
d
d
d
d
d
d
d
d
d
2.02
c
d
d
d
d
d
d
T
µ
P
20 155 172 207 241 276 310 345 379 414 35 155 172 207 241 276 310 345 379 414 50 138 172 207 241 276 310 345 379 414 65 all
s
2.08 2.09 2.05 2.05 2.04 2.02 1.99 1.95 1.94
c
d
d
d
d
d
d
d
d
d
d
d
d
c
1.10 1.27 1.27 1.30 1.32 1.27 1.24
1.93 c 2.03 0.90 1.99 1.11 d
d
d
d
d
d
d
d
d
d
1.95 c 1.95 c 1.98 c 2.09 1.03 d
d
a Temperature in units of °C; pressure in units of bar. b Could not be determined accurately from the available data. c The value of φp was too low to accurately determine s from the available data. d The value of φp was too low to be accurately determined from the available φ range (see Figure 1).
static percolation, relatively small values of the film rigidity (< kT) allow for greater fluctuations in the interfacial curvature and, thus, zero net curvature or bicontinuous structures.13,68,69 Theory predicts that film rigidity is determined primarily by the configurational entropy of the flexible surfactant tail region,70 which is a function of the surfactant tail length70,71 and headgroup electrostatic interactions,72,73 surface area per surfactant molecule,70 and solvent penetration into the surfactant tail region.74,75 Although the area per PFPE-NH4 molecule has been shown to be larger in the W/C microemulsion (100 Å2/
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Lee et al.
Figure 5. Fit of conductivity data to a 3-D surface along a constant T and φ mesh at 276 bar. Figure 4. Effect of temperature on the volume fraction at the percolation threshold at various pressures.
molecule)76 as compared to the water-in-PFPE oil microemulsion (50 Å2/molecule).64 The effect of area on film rigidity is predicted to be important only at smaller values of the surface area per molecule (
