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Langmuir 1991, 7, 1585-1589
Morphologies and Inversions of Emulsions of Conjugate Microemulsion and Oleic Phases in an Amphiphile/Oil/ Water System between Its Critical Endpoint Temperatures Duane H. Smith,’*+G. L. Covatch, and Kyung-Hee Lim* US.Department of Energy, Morgantown Energy Technology Center, Morgantown, West Virginia 26507-0888 Received September 28,1990. In Final Form: January 8,1991 A study has been made of emulsions formed within the two-phase miscibility gap that borders the middle phase-top phase side of the tietriangle in an amphiphile/oil/water system (2-butoxyethanol/ndecane/aqueous 10 mM NaCl system at 35.0 “C).The study includes emulsions formed by six different conjugate oleic-microemulsion phase-pairs, ranging from the top phase-bottom phase tieline to a tieline very close to the plait point. Electrical conductivity measurements were used to infer emulsion morphologies and to detect morphology changes (emulsion inversions). The results are compared to the dispersion morphology diagram previously postulated for amphiphile/oil/water systems.
Introduction Emulsions and other dispersions of one fluid phase in another are used in so many industrial products and processes that it is surprising how little is known about some of their most elemental properties. In particular, the number of possible dispersion morphologies,and where in the phase diagram these morphologies form, has not yet been fully determined.’ Theoretically, two conjugate fluid phases, A and B, may form the two “simple” morphological types: A-in-B (A/B) and B-in-A (B/A). Multiple dispersions,such as in A-in-B-in-A (A/B/A) and B-in-A-in-B (B/A/B), sometimes occur.2 The ubiquitous ”oil-in-water”(O/W) and “water-in-oil” (W/O) nomenclature implies the existence of only two nonmultiple morphologies in systems that contain “oil” (or some other hydrophobic component) and water. However, as illustrated by Figure 1, many amphiphile/ oil/water systemssimultaneouslyform three liquid phases (the top, middle, and bottom phases, 7,A, and 3, respectively). By the phase rule, the tietriangle for these three phases is bounded on each of ita sides by a different two-phase miscibility gap. (These gaps are the loci of the oleic-microemulsion, aqueous-microemulsion, and oleicaqueous conjugate phase-pairs, respectively.9 Thus, as pointed out by Smith, the phase diagram of Figure 1 theoretically contains six different nonmultiple, two-phase dispersion morphologie~.~*~ These are the OL/MI, MI/ OL;AQ/MI, MI/AQ; and OL/AQ, AQ/OL morphologies, respectively, for the oleic-microemulsion, aqueous-microemulsion, and oleic-aqueous miscibility gaps. Recently, the present authors postulated the model dispersion morphology diagram shown in Figure 2 for systems that exhibit the phase behavior of Figure 1.‘ In Figure 2, each two-phase region is subdivided into three different dispersion morphology regions: For example, in the oleic-microemulsion miscibility gap, only dispersions ‘Adjunct, School of Chemical Engineering and Materials Science and Institute for Applied Surfactant Research, University of Oklahoma, Norman, OK. t Present address: Department of Chemical Engineering, West Virginia University, Morgantown, WV 26506. (1) Smith, D. H.;Lim, K.-H. J . Phys. Chem. 1990,94,3746. (2) Sherman, P. In Emulsion Science; Sherman P., Ed.;Academic Press: New York, 1968;p 131. (3) Smith, D. H. J. Colloid Interface Sci. 1986,108, 471. (4) Smith, D. H.In Microemubion Systems; b a n o , H. L., Clausse, M., Eds.; Marcel Dekker: New Yok, 1987; p 83.
Amphiphile
Water
Oil
Figure 1. Phase diagram and nomenclature for a model amphiphile/oil/water system that forms three conjugate liquid phases. Amphlphlle
Oil
Water
Figure2. Previously postulated dispersion morphology diagram for the system of Figure 1.1
of the oleic in the microemulsion phase (OL/MI morphology) are predicted in the region closest to the microemulsion ends of the tielines. In the region closest to the oleic ends of the tielines, only the MI/OL morphology is expected. These two regions are separated by the third, intermediate region, the boundaries of which are two
This article not subject to U.S.Copyright. Published 1991 by the American Chemical Society
Smith et al.
1586 Langmuir, Vol. 7, No. 8, 1991
curvedlines that meet in a cusp at the plait Within this intermediate, hysteresis region, either morphology may be observed: Under some conditions, the morphology in this region clearly depends on the history of the system (i.e., the experimental whereas in other cases, the hysteresis is manifested as the apparently random appearance of the A/B or B/A morphology>JOwhen a series of emulsions is prepared from a single sample by a technique that seems to be invariant from one preparation to the next.gJO The postulated morphology diagram appeared to be consistent with the experimental results of various researchers (who used a variety of chemically different systems and emulsification techniques),116*s12 although none of these experimenta was performed in either the oleic-microemulsion or the aqueous-microemulsion miscibility gap and between the critical endpoints. (The critical endpoints are the values of some "additional" variable, such as temperature, pressure, or salinity, not included in Figure 2, a t which the tietriangle collapses to an ordinary tieline.) Moreover, a partial experimental test of Figure 2 was subsequently performed, in which the emulsion inversion hysteresis region along each side of the tietriangle was determined by means of electrical conductivity measurements.' For two of the three two-phase regions of Figure 2, the latter experiments supported the postulated dispersion morphology behavior a t its three-phase limit.' However,"anomalous" conductivities were found for some emulsions formed along the top-middle phase tieline, which bounds the oleic-microemulsion two-phase region. Hence, the present study tests the postulated dispersion morphology diagram of Figure 2 by means of a series of measurements within the oleic-microemulsion miscibility gap. As in the tietriangle study,' the present measurements were performed on the 2-butoxyethanol/n-decane/ aqueous 10 mM NaCl system at 35.0 OC. This temperature is approximately midway between the lower and upper critical endpoint temperatures1J3 of the 2-butoxyethanol/n-decanelaqueous10 mM NaCl system (lower and upper temperatures, respectively, at which the tietriangle collapsesto a twephase tieline). Emulsions prepared from the oleic and microemulsion phases of amphiphiles of larger molecular weights eventually may be found to invert at larger volume fractions of the internal phase than those measured for the 2-butoxyethanol/n-decane/ aqueous 10 mM NaCl system; however, we believe that the topology of the dispersion morphology diagram of such emulsions, as first demonstrated here, will prove to be valid for those emulsions, also. All emulsions were prepared from conjugate (Le., preequilibrated) phases. Electrical conductivity measurements were used to detect changes of dispersion morphology. Where possible, theoretical emulsion conductivities were calculated from equations that contained no adjustable parameters, and agreement between measured and theoretical conductivities furnished quantitative (5) Lim, K.-H.; Smith, D. H. J. Colloid Interface Sci. 1991,142,278. (6) Smith, D. H.; Lim, K.-H. Longmuir 1990,6,1071. (7) Smith, D. H.; Nwoeu, S. N.;Johnson, G. K.; Lim, K.-H. Morphologiw of Emulsions of Conjugata Phase-Pain,of Amphiphile/Oil/Water
'Microemulsion" Tietrianglee. In preparation. (8) Salager, J.-L. In Encyclopedia of Emulsion Technology; Becher, P.,Ed.;Marcel-Dekker: New York, 1988, p 79. (9) Seaaki, T. Bull. Chem. SOC.Jpn. 1989,14.63. (IO)€&a,S.; Kornbrekke, R. E. J. Colloid Interface Sei. 1981,81,68. (11) Smith, D. H.;Lim, K.-H. In Society of Petroleum Engineers International Symposium on Oilfield Chemistry; Houston, TX,Feb. 8-10; Society of Petroleum En ineen,: D U , TX, 1989; SPE 18496. (12) Lim, K.-H.; Smith, D. If. J . Dispersion Sci. Technol. 1990,11, 529.
(13)Kunieda, H.;Shinoda, K. Bull. Chem. SOC. Jpn. 1982,55,1777.
r
1 R U
0 I
0.06
I
0.10
I
0.14
I
0.18
I
0.22
I
I
0.26
Weight Fraction, Brine
Figure 3. Electrical conductivities from which tielines were obtained and regressions to the data. evidence for assignment of the dispersion morphology. Experiments were performed on six different tielines between the top-middle phase tieline and the oleic-microemulsion plait point. The experimental results tend to supportthe postulated dispersion morphology diagramlvs of Figure 2 for OL/MI and MI/OL emulsions. However, unexpected behavior was also observed, which suggests that the dispersion morphology diagram may need to be extended to include multiple dispersions.
Experimental Section The limiting oleic-microemulsion tieline was determined (in a previous study') by means of a titration calorimetry technique,"Js and the oleic-microemuleion miscibility gap was determined by a conventional titration and visual observation method. The other tielinen were determined from electrical conductivity measurementa on the microemulsion phases of a series of samples located on two different (known) composition paths. As in previous studies,1aJJ*each conjugate phase-pair for the emulsion experimenta was prepared by mixing a sample of twophase Composition in a thermostated separatory funnel, waiting for separation of the emulsion into bulk phases, and careful separationof the layers. Thisprocess ensuredthat the emulsions were obtained from conjugate phases, independent of experimental uncertainties in the tieline compositions, when the emulsions were subsequently prepared from measured volumes of each phase. Samples for measurement of single-phase conductivities were prepared in the same way. The phase volume fraction at which inversion occurred was measured for both directions along each of the six tielines. The chemicals and apparatus used for the emulsion preparation and electrical conductivity measurementa have been described in greater detail elsewhere.' Results and Data Analysis Tieline Measurements. Figure 3 shows the electrical conductivity of the microemulsion phase, plotted against the concentration of brine in the sample, for two series of samples that fell on different compositional paths. (See Figure 4 for a plot of the two paths.) Any two system compositions on paths 1 and 2, respectively (Figure 31, that have some microemulsion phase conductivity must have microemulsion phases of the same composition and thus be on the same tieline. Hence, in Figure 3 the tieline condition is simply (14) Smith, D. H.; Allred, 0.C. J. Colloidlnterface Sci. 1988, IN, 199. (15) Smith, D. H.;Covatch, G. L. In Proceeding8 of the Society of
Petroleum Engineers Intemtional Symposium on Oilfield Chemistry; Houston, TX, Feb. 8-10; 1989, SPE 18498.
Langmuir, Vol. 7, No. 8, 1991 1587
Morphologies and Inversions of Emuhiom
C, Hg OC2 H4 OH
K, = K, where K1 and K2 are microemulsion conductivities for paths 1 and 2, respectively. Equation 1, along with the measured conductivities for the two paths, gives pairs of different system compositions that are on the same tieline; since two points define a line, the tielines (but not their ends) are determined. The compositions of the set of samples on path 1 fell on the line
H1/A1= Cl and the compositions of the second series of samples were along the path A, = C,
Here Ai is the (weight fraction) concentration of amphiphile and Hi is the concentration of hydrocarbon and the subscripts denote the two different paths C1= 1.243 and C2 0.5000. The microemulsion conductivities along paths 1 and 2 are accurately described by the equations K, = m, W,+ b,
'
(3) v
v
v
v
v
v
v
v
Brine
Figure 4. Miscibility gap and tielines for conjugateoleic phases and microemulsions of the 2-butoxyethanol/n-decane/aqueous 10 mM NaCl system at 35.0 "C; also shown are the three-phase tietriangle and the experimental paths for Figure 3.
(4)
and
K, = m2W, + b, where Wi is the weight fraction of the aqueous pseudocomponent and mi and bi are the slope and intercept, respectively. Regressions of eqs 4 and 5 to the data of Figure 3 gave ml = 658.85, bl = -42.495, m2 = 383.97, and b2 = -32.323 with regression coefficients rl = 0.9996 and r2 = 0.9991, respectively. Point Q (filled circle in Figure 3) was measured as a check on the method. The composition of sample Q (on path 2) was calculated from eq 5 to have the same conductivity as sample P (path l ) , and the electrical conductivity of a sample of composition Q was measured. As illustrated by Figure 3, the conductivity of Q fell very close to the predicted value, showing that the method accurately predicted which pairs of points on paths 1and 2, respectively, fell on the same tieline. For brine concentrations W2 I0.10, path 2 exits the miscibility gap and enters the single-phase region; for W2 10.25, path 2 reaches the top phase-middle phase limiting tieline and enters the tietriangle. However, an equation may be calculated for any tieline for any composition, 0.10 IWZI0.25, between these limits. For the emulsion studies, a series of samples along path 1was prepared, and emulsions were prepared from the conjugate phase-pairs into which the samples separated. Therefore, it is for samples along path 1 that we require tieline equations. After some algebraic manipulation, eqs 1-4, together with the values for Ci, mi, and bi, give A = W(0.05417 + o.4458w1)/(o.7159w1 - 0.02649) + 0.44583 (1 - W) (6) This provides an equation for the tieline through any specified point (A,, W,)along path 1. The tielines (I, J, L, M, N)used in the emulsion studies are shown as dashed lines in Figure 3. Figure 4 shows the oleic phase-microemulsion tielines of Figure 3 for the 2-butoxyethanol/n-decane/aqueous 10 mM NaCl system at 35.0 OC replotted in conventional triangular coordinates, along with the oleic phase-microemulsion miscibility gap. For reference of the miscibility gap to the three-phase region, the top-middle-bottom phase tietriangle is also shown in Figure 4.7 The exper-
0.2 4 0.0
I
0.1
I
I
I
1
0.2
0.3
0.4
0.5
0 i
Volume Fraction Oleic Phase,
Figure 5. Comparison (for tieline J) of measured emulsion conductivities and conductivities calculated (solid line) for the OL/MI morphology with Bruggeman's model." imental temperature, 35.0 "C,is approximately midway between the lower and upper critical endpoint temperatures. Emulsion Morphologies. Once the tielines and conjugate phase compositions had been measured, the next step was to determine the emulsion morphologies. For nonmultiple emulsions in which the phase of the greater conductivity is the continuous phase, we had found in previous work that the theoretical conductivitiescalculated from effective medium models agreed very well with the measured ccondu~tivities.~*6J~J6J~ Figure 5 illustrates similar agreement of theory with experiment for OL/MI (oleic phase-in-microemulsion phase) emulsions. (The data are for emulsions formed along tieline J.) Here the dimensionless conductivity is the emulsion conductivity divided by the microemulsion conductivity, and the emulsions were prepared by successive additions of the oleic phase to the microemulsion phase. In effective medium models the theoretical conductivity is calculated from the volume fractions and conductivities of the conjugate phases and contains no adjustable parameters. (Details of the equations of the effective medium models and of the equations have been published elsewhere.12) Aa illustrated by Figure 5, excellent agreement between theory and experiment was found for tieline J for volume (16) Smith, D. H.;Lim, K.-H. SPE Prod. Engr. 1990,6,266. (17) Smith, D. H.; Covatch, G. L.; Lim, K.-H.J. Phys. Chem. loSl,SS, 1463.
Smith et al.
1588 Langmuir, Vol. 7, No. 8, 1991 22 20
6
18
.-2 .->
14
3
-
16
12
3
10
:.
6
4-
D
4
LJ+---0.45
0.47
0.49
0.53
0.51
Volume Fraction Oleic Phase,
0.55
eW
Figure 6. Inversion hysteresis measured for tieline N. fractions of the oleic phase up to nearly 0.5 (where a large drop in the conductivity occurred). Similar agreement was found for tielines I and L. Thus, for these tielines we can conclude with considerable confidence that OL/MI emulsions formed for allvolume fractions of the oleic phase between zero and some limiting value, at which a change of emulsion morphology occurred. Similar to the behavior observed in other regions of the phase diagram,' the phase volume fractions for the OL/ MI MI/OL inversion and the MI/OL OL/MI inversion were slightly, different; that is, inversion hysteresis was observed. Figure 6 illustrates the hysteresis along tieline N. For the composition range of Figure 6, the larger conductivity indicates that the morphology is OL/MI, whereas the smaller cconductivity is indicative of the MI/OL morphology. (The emulsion morphology a t volume fractions of the oleic phase above the limiting value can only be inferred qualitatively, because effectivemedium and other conductivity models do not give accurate emulsion conductivities when the ratio of the conductivity of the dispersed p h e to that of the continuous phase is very large. However, where conductivity measurements show a change of morphology from the OL/ MI morphology, we assume that the change is a simple inversion to the MI/OL morphology.) When oleic phase was successively added (with mixing) to the OL/MI emulsion, the OL/MI MI/OL inversion occurred at @i = @OL = 0.507 0.002 (where @pi is the volume fraction of the internal, or dispersed, phase). However, when microemulsion was added to MI/OL emulsion, the MI/OL OL/MI inversion occured at @i = @MI = 1 - @OL = 1 - (0.492 0.004) 0.508 f 0.004. Thus, for the two different directions along the tieline, the difference in the volume fractions of the oleic phase a t which inversion occurred was A@OL= 0.015 0.006. The volume fractions (01and 49, respectively) of oleic phase at which inversion occurred for additions of microemulsion phase (@I) and for additions of oleic phase (@2) were measured for six different tielines. Figure 7 shows the inversion hysteresis lines, @I and @2, measured MI/OL and MI/OL OL/MI for the OL/MI inversions, respectively. Small differences, A@OL= (P2 @I, were found for the emulsions of all of the conjugate phase-pairs studied. Figure 8 shows the conductivity of emulsions formed along tieline N by addition of oleic phase to microemulsion. The emulsion conductivity as calculated for the OL/ MI morphology from the phase conductivities and volume fractions is shown, also. In contrast to Figure 5 (tieline J),it is evident that the calculated conductivities in Figure 8 do not agree with the experimental results. Agreement
-
Figure 7. Measured phase and dispersionmorphology diagram for oleic and microemulsion phases of the 2-butoxyethanol/ndecane/aqueous 10 mM NaCl system at 35.0 "C, including approximate boundaries (hatched area) for the tentatively identified MI/OL/MI region. 1.0
+,
-
*
-
-
*
*
-
-
0.0
0.1
0.2
0.3
0.4
0.5
0 i
Volume Fraction Oleic Phase,
Figure 8. Comparison (for tieline N) of measured emulsion conductivitieswith conductivities (solid line) calculated for the OL/MI morphologywith Bruggeman's mode1.a The differences at emall volume fractions of the oleic phase suggest formation of MI/OL/MI emulsions. similar to that of Figure 5 was found for tielines I and L; differences similar to those of Figure 8 were found for emulsions on the top phase-middle phase (I-&) tieline' and tielines M and N. Substantial differences between the calculated and measured conductivities at smallvolume fractions of the oleic phase may indicate formation of MI/ OL/MI emulsions along the latter tielines. This region of postulated multiple emulsions is shown as the hatched region in Figure 7. Discussion The electrical conductivity method of measuring tielines (Figure 3) proved to be very simple and precise. In the present work it was particularly convenient, because the phase-conductivity measurements needed for calculation of the theoretical emulsion conductivities also gave the tieline equations, without requiring any additional experimental work. Furthermore, although the subject of percolation phenomena in microemulsions falls outside of the scope of this paper, we note that the conductivity data in Figure 3 show no evidence of any percolation threshold within the range of microemulsion compositions studied. The basic principle of the measurements is simply that, when multiphase samples of different system composition
Morphologies and Inversions of Emulsions
have equal values of some physical property of either the denser or less-dense layer, the two samples must, in fact, be on the same tieline. The two sample compositions define the tieline. The principle holds for all ternary and pseudoternary systems and for any physical property (although mistaken assignments could occur if the values of the physical property chosen did not change monotonically with distance from the plait point). We believe that the basic principle will prove useful with many different physical properties, not just the electrical conductivity. Comparison of the experimental results summarized in Figure 7 with the behavior predicted by Figure 2 shows that the experimental data confirm several of the predictions' of the dispersionmorphology diagram previously postulated for the 2-butoxyethanol/n-decane/aqueous 10 mM NaCl system. In particular, the experiments confirm that the dispersion morphologydiagram for emulsionsof the conjugate microemulsions and oleic phases includes (at least) three different regions: (1) a region in which all emulsions have the OL/MI morphology; (2)a region in which very low emulsion conductivities indicate the MI/OL morphology; (3) a narrow hysteresis region, in which the morphology depends on the direction along the tieline from which the hysteresis region was entered. These results are in accord on emulsions formed in other with measurement81~~~11~12~16~17 regions of the diagram. In addition,' the width of the hysteresis region, A ~ o L , decreased as the distance of the tielines from the plait point became smaller, and to within the uncertainties in the measurements, the limiting value of the inversion volume fractions as the plait point was approached was equal to the theoretical value, 3 = 0.5.5J0 Both of these findings also are in accord with Figure 2. The present results apparently differ from the findings of Schechter and co-workers for more complex chemical mixtures. In one study they concluded that for macroemulsions in which one of the conjugate phases is a microemulsion "the microemulsion phase is generally the continuous phase irrespective of the volumetric proportions blended,"l*Jg and in another study they stated that "when a microemulsion and its excess phase are vigorously agitated to create an ordinary emulsion, the microemulsion will be the continuous phase.'" We anticipate that when amphiphiles of greater molecular weight are studied systematically, both inversion hysteresis lines may be found to occur at substantially different volume fractions than were found for the 2-butoxyethanol/n-decane/ aqueous 10 mM NaCl system. At present, it is clear that the statements of Schechter et al.'83 did not hold for the emulsions that we formed from conjugate microemulsion and oleic phases of the 2-butoxyethanol/n-decane/ aqueous 10 mM NaCl system at 35.0 "C. Instead, for the latter system a change of emulsion morphology occurred for all of the phase pairs studied. The volume fraction of the internal phase at which the morphology change occurred depended slightly on the tieline and on whether the internal phase were oleic or microemulsion, but was always between 0.465and 0.529. In fact, as judged by the average volume fractions of internal phase at which the change occurred (0.514vs 0.4901,the microemulsion was only very slightly "preferred" over the oleic phase as the continuous phase. Although most of the previous predictions' of the (18) Hazlett, R. D.; Schechter, R. S. Colloids Surf. 1988,29, 63. (19) Grnciaa,A.; L a c e , J.; Bowel, M.;Schechter,R. S.;Wade, W.
H.J. Colloid Interface Scr. 1986,119, 583. (20) Graciaa, A.; Lachaiee, J.; Marion,G.; Schechter, R. S. Langmuir 1989,6, 1316.
Langmuir, Vol. 7, No. 8, 1991 1589
dispersion morphology diagram were confirmed, the experiments of the present study do suggest that an important addition to the diagram may be needed. The previously postulated dispersion morphology diagram included only nonmultiple dispersions.' The most plausible explanation for the conductivity behavior illustrated in Figure 8 is that multiple emulsions of the morphology MI/OL/MI (microemulsion-in-oleic-phasein-microemulsion)were formed. Unlike the equationsused to calculate the conductivity curve of Figure 8 (which contain no adjustable parameters), the equations for the conductivityof multiple emulsions2'contain one parameter that was not measured independently (the volume fraction of microemulsiondispersed within the oleic phase). Hence, to explore the validity of the multiple-emulsionhypothesis, we calculated the volume fraction of dispersed microemulsion from the measured emulsion conductivities.22 These calculations confirm that the multiple-emulsion hypothesis can account for the "anomalous" emulsion conductivities measured for the top phase-middle phase tieline' and tielines M and N. In each case the calculated fraction of microemulsion that is dispersed within the droplets of oleic phase goes to zero before a discontinuous drop in the conductivity is observed; hence, even with this hypothesis lines 31 and 3 2 represent inversions between nonmultiple OL/MI and MI/OL emulsions. Figure 7 illustrates the approximate boundaries of the (postulated) MI/OL/MI region (hatched). The (postulated) multiple emulsions of Figure 7 also may be contrasted to the emulsion behavior of other chemical systems. Hazlett and Schechter18reported the formation of OL/MI/OL emulsions in a system that contained butanol, sodium dodecyl sulfate,toluene, sodium chloride, and water; but they did not observe the MI/ OL/MI morphology for which we find strong circumstantial evidence. Moreover, according to our results the multiple MI/OL/MI emulsionsform only a band of tielines that terminates at the top phase-middle phase limiting tieline and do not form for tielines that lie closer to the oleic phase-microemulsion critical point. Thus, our findings differ from those of Schechter and co-workers in two ways: (1) For nonmultiple emulsions we did not find the microemulsion to always be the continuous phase; instead, OL/MI emulsions always inverted when the volume fraction of the microemulsion became less than half. (2) For multiple emulsions the limitations of the conductivity technique did not allow us to determine if OL/MI/OL emulsionsformed;but possible evidence for the MI/OL/MI morphology was found in a portion of the oleic phase-microemulsion miscibility gap. In summary, the results of the present study (1)appear to confirm the predictions of the dispersion morphology diagram1p5 for nonmultiple emulsions and (2) suggest possible additions to the dispersion morphology diagram to include the appearance of multiple emulsions. We believe that the volume fractions at which inversions occur will prove to be different for other chemical systems but that the dispersion morphology diagram topology demonstrated here will prove valid for those systems.
Acknowledgment. This research was supported by the US. Department of Energy and, in part, through an appointment of K.-H. Lim to the U.S. Department of Energy, Fossil Energy, Post-Graduate Research Program administered by Oak Ridge Associated Universities. (21) Pauly, H.; Schwan, H.P. Z. Naturforsch. 1969, 146, 126. (22) k m , K.-H.; Smith, D. H. Unpublished. (23) Bruggeman, V. D.A. G. A n d . Phys. 1935,24,636.
