17558
J. Phys. Chem. 1996, 100, 17558-17562
Temperature Dependence of Emulsion Morphologies and the Dispersion Morphology Diagram. 3. Inversion Hysteresis Lines for Emulsions of Middle and Bottom Phases of the System C6H13(OC2H4)2OH/n-Tetradecane/“Water” Duane H. Smith,*,†,‡ Ramanathan Sampath,§,| and Dady B. Dadyburjor§ U.S. Department of Energy, Morgantown Energy Technology Center, Morgantown, West Virginia 26507-0880, and Department of Chemical Engineering, West Virginia UniVersity, Morgantown, West Virginia 26506 ReceiVed: May 14, 1996; In Final Form: August 21, 1996X
The morphologies and phase volume fractions at which inversion occurred for (macro)emulsions formed by the middle-phase microemulsion (M) and water-rich bottom phase (B) were determined by means of electrical conductivity measurements for the amphiphile/oil/“water” system C6H13(OC2H4)2OH/n-tetradecane/aqueous 10 mM NaCl at temperatures from 25 °C down to 12 °C, near the lower critical end-point temperature (Tlc )10.4 °C). The M/B and B/M morphologies and their inversion hysteresis lines conformed to the previously postulated dispersion morphology diagram; that is, within experimental uncertainties, the two emulsion inversion lines in phase volume-temperature space met at a “critical point” that coincided with the lower critical end point for the phases.
Introduction Manysif not mostsof the two-phase emulsions commonly encountered at various temperatures in systems of nonionic surfactant, oil, and water form1 in systems that also can form triconjugate oil-rich top phase (T), water-rich bottom phase (B), and middle-phase microemulsion (M). For such systems, twophase emulsions may form in any of the various two-phase regions2,3 that surround a stack of tie triangles in the triangularprismatic phase diagram. For temperatures between Tlc and Tucsthe range over which phases T, M, and B coexiststhere are three two-phase regions (not just one) and thus six nonmultiple, two-phase emulsion morphologies (not just “water-in-oil” and “oil-in-water”).4 For such systems the plotting of phase boundaries and of boundaries between different emulsion morphologies in accordance with the phase rule introduces a rigorous way of showing how the occurrence of each of the six two-phase morphologies depends on temperature and composition. The dispersion morphology diagram that results when this is done for nonmultiple, two-phase emulsions is illustrated by Figure 1.1,5 For the limiting tie lines (i.e., the sides of the tie triangle), where the three-phase and two-phase regions meet, the six twophase morphologies are formed by the triconjugate phases taken pairwise: T/M, M/T; B/T, T/B; and M/B, B/M. One of the widely observed phenomena of emulsion inversion is inversion hysteresis;6 for example, the phase volume fractions at which the inversions A/B f B/A and B/A f A/B occur are somewhat different. If the pair of phase volume fraction points at which the pair of conjugate inversions occur are measured at different temperatures, the resulting measurements form a pair of inversion hysteresis lines in phase volume fraction-temperature space. The original two-phase dispersion morphology diagram1 hypothesized that wherever a phase critical point occurs, there will be a “critical point” for dispersion inversion, also; that is, †
U.S. Department of Energy. Also, Department of Physics, West Virginia University, Morgantown, WV 26506. § West Virginia University. | Current address: Clark Atlanta University, Atlanta, GA 30314. X Abstract published in AdVance ACS Abstracts, October 1, 1996. ‡
S0022-3654(96)01385-8 CCC: $12.00
Figure 1. Dispersion morphology diagram for nonmultiple emulsions in the various two-phase regions that surround a stack of tie triangles in surfactant/oil/water-temperature coordinates.1
pairs of dispersion inversion hysteresis lines meet at a point, and this point coincides with the critical point for the two phases of the dispersion. As illustrated by Figure 2, this behavior is easily visualized for two-component systems that have an upper or lower consolute point. Figure 2 shows experimental data7 for the system C4H9OC2H4OH/“H2O” near its lower consolute point. For volume fractions of AM (the “amphiphile-rich” phase) less than Φ1, the morphology is AM/AQ (where AQ is the aqueous phase); for volume fractions of AM greater than Φ2 the morphology is AQ/AM; and in the hysteresis region between Φ1 and Φ2 either morphology may occur, depending on the emulsion history. As accurately as can be determined from the experiments, inversion hysteresis lines Φ1 and Φ2 meet at an emulsion morphology “critical point” (Φc, Tc), which coincides with the critical point for the phases.7 Previous to the experiments of Figure 2, Ross and Kornbrekke8 found experi© 1996 American Chemical Society
Temperature Dependence of Emulsion Morphologies
J. Phys. Chem., Vol. 100, No. 44, 1996 17559 (Φuc, Tuc) for the phases, respectively; that is, Φilc ) Φlc ) 0.5, Tilc ) Tlc, Φiuc ) Φuc ) 0.5, and Tiuc ) Tuc. However, it has been suggested that the inversion critical point composition need not be identically at Φic ) 0.5. Moreover, in a study10 of three-phase emulsion morphologies in the system C6H13(OC2H4)2OH/n-tetradecane/aqueous 10 mM NaCl, threephase “inversions” were not detected when the temperature was “too close” to the critical end-point temperature of the two different continuous phases. It was not clear whether the apparent “disappearance” of the three-phase morphology changes was a “trivial” result of conductivity differences between different morphologies becoming too small to detect or an indication of the need for revisions in the dispersion morphology diagram for both three phases and two. Hence, measurements of electrical conductivities, emulsion morphologies, and emulsion inversions were undertaken for the middle and bottom phases of the system C6H13(OC2H4)2OH/n-tetradecane/aqueous 10 mM NaCl; the results are reported here.
Figure 2. Emulsion inversion points AQ/AM f AM/AQ (circles) and AM/AQ f AQ/AM (diamonds) for the (pseudo) binary system C4H9OC2H4OH/10 mM aqueous NaCl. The inversion hysteresis lines, Φ1 and Φ2, were obtained by fits of critical scaling theory to the measured points.7
Experimental Section The materials, apparatus, and basic methods of this study have been described elsewhere.11-14 Briefly, electrical conductivities were measured for phases and for steady-state emulsions formed by mixing measured volumes of the pre-equilibrated phases. Emulsion morphologies then were identified by comparison of the measured emulsion conductivities with conductivities predicted by equations that contain no adjustable parameters.13,14 Inversions were detected as abrupt, discontinuous jumps of the measured emulsion conductivities between the two theoretical curves. As before,11,12,14 all compound purities were 99%, or better. Results
Figure 3. Hysteresis lines predicted by Figure 1 for M/B T B/M and M/T T T/M inversions, respectively.
mental evidence for the analogous existence in a threecomponent, isothermal system of an emulsion morphology critical point and its coincidence with the plait point of the phases.9 Figure 3 illustrates the inversion hysteresis lines predicted by Figure 1 for M/B T B/M and M/T T T/M inversions in (Φ, T) coordinates (as viewed from outside the stack of tie triangles). As illustrated by Figure 3, if one prepares emulsions at, for example, T ) Tuc by starting with the bottom phase and adding middle phase (with agitation), the emulsion morphology is M/B until line Φ2 is reached, at which composition the morphology inverts to B/M. Emulsions formed by addition of bottom phase to middle phase will have the B/M morphology until line Φ1 is reached, where the B/M f M/B inversion occurs. Hence, inversion hysteresis occurs between lines Φ1 and Φ2, because the morphology formed depends on the history of the emulsion. The hysteresis width becomes narrower as the critical point, (Φilc, Tilc), for B/M T M/B inversions is approached, where the inversion lines meet. As illustrated by Figure 3, the M/T T T/M inversion hysteresis lines were postulated1 to meet at a similar critical point, (Φiuc, Tiuc). In the originally postulated dispersion morphology diagram (Figure 11), the emulsion inversion critical points for the M/B T B/M and M/T T T/M inversions coincide with the lower critical end point (Φlc, Tlc) and the upper critical end point
The value of the phase lower critical end-point temperature, Tlc, in the system C6H13(OC2H4)2OH/n-tetradecane/aqueous 10 mM NaCl was determined from measurements of the electrical conductivity of phases M and B. The ability of electrical conductivity measurements to distinguish between different emulsion morphologies and to detect morphology changes depends on the emulsion conductivities, which in turn depend on the conductivities of the phases. The phase conductivities are described by the theoretical equations
KB - KM ) K1β
(1)
KB + KM ) 2K21-R + 2Kc
(2)
where KB and KM are the phase conductivities at absolute temperature T, Kc is the conductivity at the critical point, and K1 and K2 are conductivity parameters that depend on the chemical system. The values of the universal critical-scaling exponents are R ) 0.11 and β ) 0.324.15 The parameter is defined by
≡ (T - Tc)/Tc
(3)
where Tc is the critical temperature (in this study, Tlc, the lower critical end-point temperature). To obtain the value of Tlc we rewrote eq 1 as
(KB - KM)1/β ) (K1)1/β(T - Tc)/Tc
(4)
and fit eq 4 to the data. Figure 4 illustrates a fit (r2 ) 0.999) of eq 4 to the data. The regression yielded Tlc ) 283.6 K (10.4
17560 J. Phys. Chem., Vol. 100, No. 44, 1996
Smith et al.
Figure 4. Fit of scaling theory (eq 4) to the phase conductivities to get the value of the lower critical end-point temperature, Tlc ) 283.6 K.
Figure 6. (a) Conductivities at 25.0 °C of emulsions of the bottom and middle phases of C6H13(OC2H4)2OH/n-tetradecane/aqueous 10 mM NaCl: squares, emulsions titrated with M; triangles, emulsions titrated with B; lines, predictions of the Maxwell equation for M/B and B/M morphologies, respectively. (b) Same as part a, except T ) 12.0 °C. Figure 5. Conductivities of the bottom and middle phases of C6H13(OC2H4)2OH/n-tetradecane/aqueous 10 mM NaCl: points, measured; line, fit of eqs 1 and 2.
°C) and Kc ) 474 µS/cm. This value of Tlc then was used in the fits of Figure 5. The measured phase conductivities and their averages are plotted vs temperature in Figure 5, along with the fits (r2 ) 0.9998) of eqs 1 and 2 to the experimental data and to their average, (KB + KM)/2. As shown below, the comparatively large differences (Figure 5) between the conductivities of the conjugate bottom and middle phases made it possible to detect emulsion inversions at temperatures within 1.6 K of Tlc. Figure 6a illustrates the dimensionless conductivities, k, measured at 25.0 °C for emulsions of the bottom and middle phases of C6H13(OC2H4)2OH/n-tetradecane/aqueous 10 mM NaCl. Also shown in Figure 6a are the dimensionless emulsion conductivities predicted for the M/B and B/M morphologies, respectively, by the Maxwell equation,16
k/kc ≡ K ) (1 + 2BΦ)/(1 - BΦ)
(5)
Here B is defined by
B ≡ (kd - kc)/(kd + kc)
(6)
where k is the emulsion conductivity, kd is the conductivity of the dispersed phase, kc is the conductivity of the continuous phase, and Φ is the volume fraction of the dispersed phase. Because kc, kd, and the various values of Φ were all measured individually, the theoretical conductivities in Figure 6a were calculated from eqs 5 and 6 without any adjustable parameters.
Thus, the excellent agreement between the predicted emulsion conductivities and the measured values provides considerable confidence that the morphology assignments are correct. The volume fractions of phase M at which inversion occurred were found to be ΦM/BfB ) 0.705 and ΦB/MfM/B ) 0.735. These results are in good agreement with the values previously reported17 for inversions to the B/M and M/B morphologies, Φ ) 0.698 ( 0.012 and Φ ) 0.729 ( 0.004, respectively. Figure 6b is similar to Figure 6a, except the results were obtained at T ) 12.0 °C, about 1.6 °C above Tlc. Because the conductivities of the two phases (Figure 5) are much closer at this temperature, the change of emulsion conductivity at inversion is much smaller than at 25 °C. Nevertheless, we were able to detect the inversions at this relatively small distance from the critical point. The temperatures and phase volume fractions at which inversions were found are summarized in Table 1. Figure 7 illustrates tie triangles at several temperatures for the C6H13(OC2H4)2OH/n-tetradecane/aqueous 10 mM NaCl system.18 Obviously, the composition of the bottom phase is somewhat temperature-dependent and the composition of the middle phase changes by a large amount with temperature. Hence, the temperature-dependent emulsion inversion lines cannot be plotted in two dimensions if the component concentrations are used. However, the use of phase concentrations, such as “Ostwaldian” phase volume fractions, easily overcomes this problem. The emulsion inversion phase volume fraction and temperature data of Table 1 are plotted in Figure 8, along with the phase lower critical end point (Φlc ) 0.5, Tlc ) 283.6 K). In
Temperature Dependence of Emulsion Morphologies
J. Phys. Chem., Vol. 100, No. 44, 1996 17561 as the distance from the critical point increases, and (4) in each case the critical point for emulsion inversion coincides with the phase critical point. For the hysteresis lines of the C4H9OC2H4OH/aqueous 10 mM NaCl system (Figure 2) a catastrophe theory for the emulsion inversion was tested.7 However, catastrophe theory could not match the curvature of the midline of the inversion hysteresis, because it predicts (Φ1 + Φ2)/2 ) Φc ) 0.5 at all temperatures. Moreover, this test7 supported the belief that a more accurate treatment might lead to values of the exponents more like those of modern scaling theory. Thus, a scaling approach appeared both experimentally and theoretically to be more promising. Hence, as an exploration of these ideas, the equations7
∆Φ ) Φ2 - Φ1 ) Φ′F′
(7)
ln ∆Φ ) F′ log[(T - Tic)/Tic ] + ln Φ′
(7a)
Φ2 + Φ1 ) 2Φ′′F′′ + 2Φic
(8)
ln |Φav - Φic| ) F′′ ln[(T - Tic)/Tic] + ln Φ′′
(8a)
Figure 7. Tie triangles, showing the compositions of top, middle, and bottom phases at several temperatures, for the ternary C6H13(OC2H4)2OH/n-C14H30/H2O.18
TABLE 1: Temperatures and Volume Inversions
a
Fractionsa
of
T (K)
ΦM/BfB/M
ΦB/MfM/B
∆Φ
318.2 298.2 298.2 293.2 288.2 285.2 283.6
0.731b 0.729c 0.735 0.710 0.680 0.605 0.5d
0.707b 0.698c 0.705 0.685 0.660 0.590 0.5d
0.024b 0.031c 0.030 0.025 0.020 0.015 0.000d
Of middle phase. b References 10, 11. c Reference 17. d Theoretical.
were fit to the experimental data for the emulsions of middle and bottom phases. Here Φav ) (Φ2 + Φ1)/2 and Φ′ and Φ′′ are system-dependent parameters. Equations 7 and 8 correspond to critical-scaling equations (1) and (2), respectively; however, instead of assuming that the exponents have critical-scaling values, we treat these parameters as unknowns, the values of which are to be found from the inversion data. To perform these fits, we assumed Tilc ) Tlc and Φilc ) Φlc. The fit of eq 7a to the data of Table 1 and Figure 8 yielded the value F′ ) 0.31 (r2 ) 0.992). The corresponding fit of eq 8a yielded F′′ ) 0.38 (r2 ) 0.950) for the exponent. By combining the fits of eq 7 and eq 8, we can calculate the inversion hysteresis lines Φ1 and Φ2 individually, to compare directly with the experimental data. These comparisons are illustrated by Figure 8, which shows the fitted Φ1 and Φ2 (solid lines), as well as the measured points. Discussion
Figure 8. Hysteresis lines for M/B T B/M inversions of the system C6H13(OC2H4)2OH/n-tetradecane/aqueous 10 mM NaCl: points, measured; lines, fit of eqs 7 and 8.
drawing Figure 8, we have assumed that the emulsion inversion lower critical end point occurred at Φilc ) Φlc, Tilc ) Tlc. As illustrated by Figure 8, this is a plausible, and perhaps a rigorously correct, assumption. With this assumption, the inversion hysteresis lines of Figure 8 closely resemble those of Figures 2 and 3: (1) in each case the emulsion inversion hysteresis lines meet at a cusp that defines an inversion critical point, (2) the width of the hysteresis region increases with distance from that critical point, (3) both inversion hysteresis lines bend toward the phase of greater amphiphile concentration
Measurement of the phase conductivities (Figure 5) was experimentally convenient for this study, because these data allowed us both to determine the lower consolute solution temperature (Figure 4) and to predict emulsion conductivities (Figures 6) without any adjustable parameters. The scaling equations (eqs 1 and 2) used to fit the phase conductivities and to obtain Tlc ) 283.6 K are theoretically well established. The fits of equations of similar form yielded the values F′ ) 0.31 and F′′ ) 0.38, respectively, for the emulsion inversion hysteresis lines. These values are much different from the corresponding values, F′ ) 1.26 and F′′ ) 0.53, found7 for emulsions in the binary system C4H9OC2H4OH/10 mM aqueous NaCl (Figure 2). Although eqs 7 and 8 gave good fits to both sets of emulsion inversion data, the large differences in the values of F' and F" for the two data sets emphasize that a more intensively developed theory for emulsion inversion hysteresis lines is needed. The question of whether the phase critical point and the emulsion inversion critical point coincide now has been investigated experimentally in four chemically different systems with four “different” types of two-phase critical point: plait point of aqueous and oleic phases, plait point of oleic and microemulsion phases, consolute point in a two-component system, and critical end point (in a three-component system).7-9,19
17562 J. Phys. Chem., Vol. 100, No. 44, 1996 In all of these cases, the emulsion inversion critical point, to within the limits of experimental uncertainty, coincided with the phase critical point. There remain several reasons why it is difficult, if not impossible, to experimentally prove with absolute certainty that the critical points for conjugate phases and for inversion of their emulsions are identical. A fundamental problem is that the physical properties of the near-critical pair of inversion morphologies approach each other as the inversion critical point is approached. This happens, of course, whenever the inversion critical point lies close to the phase critical point, because the properties of the phases also approach each other as their critical point is approached. Thus, both the phase critical point and the emulsion inversion critical point must be found by measuring small differences at finite distances from the critical point that go to zero as the critical point is approached, then fitting a theoretical equation to the data, and extrapolating to where the differences go to zero. Nevertheless, measurements7-9,19 on four different types of critical points in four chemically different systems are all consistent with and support the theory that the phase and emulsion inversion critical points should be identical. A comparison of the inversion hysteresis lines (Figure 8) for M/B T B/M inversions in the ternary system C6H13(OC2H4)2OH/n-tetradecane/aqueous 10 mM NaCl and the hysteresis lines (Figure 2) for AM/AQ T AQ/AM inversions in the binary system C4H9OC2H4OH/10 mM aqueous NaCl makes it clear that the two emulsion morphology diagrams are at least naively similar. In each case (1) the inversion lines meet at a cusp that defines an inversion critical point, (2) the width of the hysteresis region increases with distance from that critical point, (3) both inversion hysteresis lines bend toward the phase of greater amphiphile concentration as the distance from the critical point increases, and (4) the critical point for emulsion inversion appears to coincide with the phase critical point. The behavior (Figure 8) of the emulsions of middle and
Smith et al. bottom phases also appears to be exactly that predicted by the dispersion morphology diagram,1 Figure 3. This agreement augments the many previous experimental confirmations of the predicted dispersion morphology diagram.5,7,9,10,12,17,19-23 References and Notes (1) (1) Smith, D. H.; Lim, K.-H. J. Phys. Chem. 1990, 94, 3746. (2) Kunieda, H.; Friberg, S. E. Bull. Chem. Soc. Jpn. 1981, 54, 1010. (3) Smith, D. H. J. Colloid Interface Sci. 1985, 108, 471. (4) Smith, D. H. In Microemulsion Systems; Rosano, H. L.; Clausse, M., Ed.; Marcel Dekker: New York, 1987; p 83. (5) Smith, D. H.; Lim, K.-H. Pure Appl. Chem. 1993, 65, 977. (6) Becher, P. J. Soc. Cosmetic Chem. 1958, 9, 141. (7) Smith, D. H.; Lim, K.-H. Langmuir 1990, 6, 1071. (8) Ross, S.; Kornbrekke, R. E. J. Colloid Interface Sci. 1981, 81, 58. (9) Lim, K.-H.; Smith, D. H. J. Colloid Interface Sci. 1991, 142, 278. (10) Johnson, G. K.; Dadyburjor, D.; Smith, D. H. J. Phys. Chem. 1994, 98, 12097. (11) Johnson, G. K. A Study of Three-Phase Emulsion Behavior; Ph.D. Dissertation, West Virginia University, 1993. (12) Smith, D. H.; Johnson, G. K.; Dadyburjor, D. Langmuir 1993, 9, 2089. (13) Johnson, G. K.; Dadyburjor, D.; Smith, D. H. Langmuir 1994, 10, 2523. (14) Smith, D. H.; Johnson, G. K.; Wang, Y.-C.; Lim, K.-H. Langmuir 1994, 10, 2516. (15) Rowlinson, J. S.; Widom, B. Molecular Theory of Capillarity; Clarendon Press: Oxford, 1984; p 327. (16) Maxwell, J. C. A Treatise on Electricity and Magnetism; Dover: New York, 1954. (17) Smith, D. H.; Nwosu, S. N.; Johnson, G. K.; Lim, K.-H. Langmuir 1992, 8, 1076. (18) Smith, D. H.; Covatch, G. L. J. Colloid Interface Sci. 1995, 170, 112. (19) Smith, D. H.; Covatch, G. L.; Lim, K.-H. Langmuir 1991, 7, 1585. (20) Smith, D. H.; Covatch, G. L.; Lim, K.-H. J. Phys. Chem. 1991, 95, 1463. (21) Smith, D. H.; Reckley, J. S.; Johnson, G. K. J. Colloid Interface Sci. 1992, 151, 383. (22) Smith, D. H.; Wang, Y.-C. J. Phys. Chem. 1994, 98, 7214. (23) Smith, D. H.; Johnson, G. K. J. Phys. Chem. 1995, 99, 10853.
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