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water interface
JOURNAL OF
COLLOID AND INTERFACE SCIENCE 2 3 , 1 6 5 - 1 7 3
(1967)
A Theory of Aqueous Emulsions I. Negative Interfacial Tensionat the Oil/Water Interface L E O N M. P R I N C E
Lever Brothers Company, Research Center, Edgewater, New Jersey Received November 18, 1965 It was proposed that negative interracial tension due to high film pressure is responsible for the formation of micro emulsions. It now appears that the initial, negative interfacial tension v~ in mixed films of soap and long-chain alcohols is the result not so much of a high initial film pressure 7r0 as of a large depression of the interfacial tension (7o/~)a between the water and the oil phase with its adsorbed alcohol monolayer in accordance with the equation v¢ = (q,o/w)~- 7r . This depression is brought about by the spontaneous distribution of alcohol between the interface and the oil phase. I t is pointed out that this distribution is dependent upon the initial chemical potential of the particular alcohol in the given oil and that it may vary within wide limits. The fraction of the alcohol that remains in the oil phase is available to depress the oil/water interfacial tension while the remainder of it forms a mixed film with emulsifier adsorbed from the water phase. It is submitted that the interaction of coulombic, hydrogen bonding and van der Waals forces among the heads and tails of the tenants of this film develops an initial pressure gradient across the flat interface which generates the initial film pressure ~r0 . Three stages of pressure development are postulated, the maximum pressure corresponding to an intermediate concentration of alcohol. Hypothetical plots of (vo/~,)~and 7r0 as ordinates versus concentration of alcohol as abscissa provide a graphical characterization of the process of mieroemulsification.
INTRODUCTION Consideration has been given to the influence of the chemical nature of both the alcohol and oil phase upon the formation of micro emulsions stabilized with oleate soap and long-chain alcohols (1). It was shown that oil-in-water (o/w) micro emulsions were formed o n l y when the chain l e n g t h of the tail of the alcohol was a t least as long as t h e molecules of t h e oil phase. T h i s suggested t h a t oil phase molecules could p e n e t r a t e the m i x e d film owing to the strong association a m o n g the long alcohol tails a n d the oil phase molecules a n d t h a t such p e n e t r a t i o n would s p o n t a n e o u s l y increase the pressure ~r in the film. T h i s m o l e c u l a r concept subseq u e n t l y (2) inspired a differentiation bet w e e n m a c r o a n d micro emulsions based on the t h e r m o d y n a m i c relationship
where 7~ is the t o t a l interfacial tension, v o/~ is the o i l / w a t e r interfaeial t e n s i o n w i t h o u t a d d i t i o n of stabilizing agents, a n d 7r is the spreading pressure in the m o n o l a y e r of adsorbed species. According to this equation, if as a result of the a d s o r p t i o n of the soap a n d alcohol at the interface a n d its p e n e t r a t i o n b y oil phase molecules, ~r b e c a m e greater t h a n
7o/~, then energy -wdA (A = surface area) would be available to increase the total interfaeial area. This was considered to be the condition for the formation of a micro emulsion. When ~ < 7o/w only a macro emulsion would form. In this view, the temporary existence of a film pressure greater than 7o/~ would be the
165
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PRINCE
driving force which reduced the droplet size of the fixed volume of oil until no more energy was available to increase the interfacial area. Equilibrium would be attained when the negative interracial tension returned to zero by virtue of the uncrowding of the molecules and loss of pressure in the interface. Such systems have been characterized (3-6) by droplet diameters of the order of magnitude of 80 A to 800 A, optical isotropy, faint light scattering, and longterm stability. When ~o/~ > 7r, droplet diameters of the order of magnitude of 10,000 A are usually observed and the systems, which now appear milky white, achieve equilibrium by separating into two phases. Energy input in the form of mechanical work (agitation or homogenization) may ternporarily increase the total interfacial area but is not capable p e r se of changing the values of ~r or Vo/w. Modification of this theory is now required. Recent studies (3) have given strong indication that hydrocarbon molecules would be ejected from mixed films of soap and alcohols at the high pressures necessary for negative interracial tension, i.e., greater than 55 dynes/era, for alkanes or greater than 35 dynes/era, for benzene. Furthermore, the original proposal overlooked evidence that water-in-oil (w/o) micro emulsions could be made with alcohols the tails of which were shorter than the length of the hydrocarbon (7). It is presently submitted that suitable relationships for negative interracial tension can be achieved between ~r and 7o/w by a substantial depression of vo/~ within the context of the thermodynamic concepts expressed in Eq. [1]. The new arguments are based upon a reassessment of previous experimental data in the light of the full implications of this equation.
ing a micro emulsion became narrower until, abruptly, no micro emulsion would form. It was similarly shown that when the amount and kind of soap as well as alcohol was held constant, abrupt transitions from micro to macro emulsions took place with changes in the molecular weight of the oil in a given homologous series. The data illustrating these transitions are presented in Table I. The point at which the transition occurs is denoted by an x. Table I (A) indicates the amount of alcohol required to produce the smallest particle sized o/w micro emulsion of each oil using a fixed amount of soap. On either side of this optimal amount of alcohol, particle size was larger. This is illustrated in Fig. 1, in which the range of effectiveness of cetyl alcohol in forming micro emulsions of n-alkanes is shown. Two alcohols, eetyl and myricyl, were used in the experiments reported in Table I(A). The data clearly demonstrate that it became increasingly more difficult to make a micro emulsion as the molecular weight of the oil was increased and that lengthening the chain of the alcohol substantially extended its range of effectiveness. Table I(B) indicates the amount of myricyl and eetyl alcohol required to produce the smallest particle sized micro emulsion of kerosene using a given amount of soap. No micro emulsion was made at any concentration of lauryl alcohol. The minimum volumes of n-hexanol required to titrate equal volumes of three n-alkanes to transparent w/o micro emulsions are shown in Table I(C). Table I(D) catalogs the minimum volumes of four nalkanols which Bowcott and Schulman (5) found were required to titrate benzene to a transparent w/o micro emulsion with a fixed amount of water. No micro emulsion was observed in these systems with n-dodecanol. THE DATA The narrowing range of effectiveness of Data on micro emulsion systems stabilized these alcohols with increasing chain lengths with mixed films of soap and alcohol have is amply documented by the experiments of been developed by a number of investigators these authors. In recapitulation, it seems to be more than (3, 5, 6, 8). This experimental evidence indicated that, at constant amount of soap, coincidence that a certain symmetry is reas the molecular weight of the alcohol in- vealed by the arrangement of the data of creased for w/o emulsions or decreased for these four tables. Observe that when the o/w emulsions, the range of concentration kind of alcohol is fixed as in Tables I(A) over which the alcohol was effective in form- and (C), the amount required to yield a
167
A THEORY OF AQUEOUS EMULSIONS TABLE I TRANSITION FROM MICRO TO MACRO EMULSIONS
Oil-in-Water Systems A. Effect of different oils (6) Oil
Alcohol (g.) Cetyl
n-IIeptane n-Dodecane Kerosene n-Hexadecane n-Octadecane Nuj ol Paraffin wax Microcrystalline wax
B, Effect of different alcohols Oil:Kerosene Myricyl
Alcohol
1.0
Lauryl Cetyl Myricy!
1.5 2.0 2.0 3.0 3.0 N N X
Grams
X 2.0 1.0
3.0 4.5 × Water-in-Oil Systems
C. Effect oJ different oils (3)
D. Effect o] different alcohols (5) Oil: Benzene
Oil
n-ttexanol (ml.)
Alcohol
Milliliters
(Ethane) n-ttexane n-Decane n-Hexadecane
(N) 2.6 3.1 4.3
n-tIexanol n-tteptanol n-Oetanol n-Decanot n-Dodecanol
6.0 4.3 3.5 3.4 X
micro emulsion increases with the molecular weight of the oil phase. In a similar manner, when the oil phase is fixed as in Tables I(B) and (D), the amount of alcohol required decreases as the molecular weight of the alcohol increases. These variations with molecular weight appear to be in the same direction whether the system is o / w or w/o. But the direction in which the transition from micro to macro emulsion takes place, reverses itself from o / w to w/o, Tables I(A) and (C), to (B) and (D). Thus, although it is not demonstrated experimentally, it m a y reasonably be deduced that n-hexanol in Table I(C) would fail to produce a micro emulsion when the molecular weight of the hydrocarbon fell to that of (liquid) ethane. Finally, several important differences between the o/w and w/o emulsions should be noted. The w/o emulsions were titrated just to transparency. Smaller sized droplets could be made by the addition of more alcohol (3). This was not the ease for the
.0.1-
.01-
FIG. 1. The effect of cetyl alcohol concentration on the droplet diameter in microns of n-alkanein-water emulsions. o/w emulsions. The low fixed ratio of soap to oil limited particle size to translucent systems, exhibiting a pronounced Tyndall effect (6). B y increasing the soap to oil ratio, transparency was achieved in similar
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PRINCE
systems in which the oil phase was an alkyd TABLE II (2). By staining this unsaturated compound INTERFAeIAL TENSIONS OF HYDROCARBONS AGAINST WATER AT 20°C., dynes/era. (9) with osmium tetroxide, the oil phase was seen directly in the electron microscope in Hydrocarbon 'Yo l w droplet form. A further difference between these systems n-Hexane 51.1 n-Heptane 50.2 lies in the kind of cation used with the soap. n-Octane 50.8 A stoichiometric amount of potassium was n-Decane 51.2 employed with the oleic acid in the w/o sysn-Tetradecane 52.2 tems so that all the fatty acid existed as S~anolax ~ 55.55 oleate ion (soap). The use of an amine oleate (Nujol) (55.55) in the o/w systems, as previously pointed Benzene 35.0 out (1), formed amphiphile in situ so that the fatty acid existed as both oleate ion and A medicinal grade of mineral oil substantially free fatty acid in approximately equal equivalent to Nujol. proportions. Since free acid may be considered to act as an alcohol under such octadecane. In a similar way, 4.5 g. of circumstances, it means that a 1/1 ratio of myricyl alcohol is less effective in microalcohol to soap existed in these systems emulsifying Nujol than paraffin wax in spite before addition of the alcohols shown in of the lower 7o/w of the Nujol. Tables I(A) and (B). This is a matter of Such behavior indicates that the distribuconsiderable consequence to the discussion tion of alcohol between the oil phase and the interface is different for each oil (3). In which follows. this way the effectiveness of the alcohol in INTERPRETATION OF THE DATA raising ~r depends upon its actual concentraThe arrangement of data in Table I tion in the mixed film rather than upon its derives theoretical significance from its total concentration in the system. Support for this contention is available explicit definition of the criteria which determine whether or not micro emulsions are from additional data obtained on the w/o formed in these systems. The abrupt transi- emulsions. After the original emulsions were tions from micro to macro emulsions in made by titrating to transparency with Tables I(A) and (C) might, for example, be alcohol, additional oil was added and the explained by higher values of "Yo/~ as the systems were titrated to transparency again molecular weight of the n-alkane increases, with more alcohol. Repeating this process as shown in Table II. This would be true determined the alcohol volume per hydroproviding the interactions among the soap carbon volume to produce a transparent and alcohol (including free acid) species in system, and extrapolation of the curve to the mixed film produced the same value of zero hydrocarbon determined the amount of ~r for each oil. As it turns out, this is not the alcohol in the interface. These data are shown in Table III. case. On the basis of this information it may be If ~r must be greater than ~/o/wfor a micro emulsion, then according to Table I(A), inferred, for example, that the chemical the value of ~r developed at 3 g. of cetyl potential of hexyl alcohol in hexane is lower alcohol must be greater than the ~'o/~ for than it is in hexadecane, assuming that the n-octodecane, which is seen from Table II changes in values of the activity coefficients to be approximately 53 dynes/era. But of the alcohol in the two oil phases are small when cetyl alcohol was used with n- in comparison with those of the partial dodecane, it is obvious from Fig. 1 that 3 g. molal free energy. By the same token, one of this alcohol was considerably less effective may assume that the initial chemical poin microemulsifying n-dodecane than n- tential of cetyl alcohol in Nu]ol is greater octadecane in spite of the fact that than in kerosene; this is another way of n-dodecane has a lower ~oI~ than n- saying that as the molecular weight of the
A T H E O R Y OF AQUEOUS E M U L S I O N S III
TABLE MOLE
RATIO
OF ALCOHOL
AND
THE
TO SOAI" IN THE
INTERFACE
Alcohol
Oil
n-Hexanol n-Hexanol n-ttexanol n-Hexanol n-Heptanol n-Oetanol n-Decanol
n-Hexane n-Deeane n-Hexadeeane Benzene Benzene Benzene Benzene
SYSTEM
(3, 5) In
In
3.2 3.9 5.4 7.5 4.8 3.5 2.8
1.7 2.0 3.6 2.0 1.5 1.25 1.0
system interface
oil increases the distribution ratio will favor the interface so that there will be less alcohol available in the oil to lower 7o/~. The same arguments apply when the oil phase is constant as in Tables I(B) and I(D). One would expect, for example, the initial chemical potential of hexanol in benzene to be higher than that of decanol in benzene, implying that at equilibrium more hexanol would be in the interface than decanol (el. Table III). These arguments indicate that 7o/~ may no longer be considered as determining 7i. For systems containing long-chain alcohols, the criterion must now be considered to be the interracial tension against water of the oil plus its fraction of alcohol. Let this be (%/~)a. In general, this interracial tension falls very rapidly at low concentrations of alcohol and then levels off. The extent of the depression and the rate at which it occurs will be different for each class of alcohol and oil and will be substantially independent of the chain length of the alcohol in any homologous series (10, 11). It follows that negative interracial tension may be achieved not so much by a great increase in ~r as by a substantial depression of ('~oi~)~. This thesis removes the requirement for film pressures of over 53 dynes/em, and places the demand for pressure values at levels more consistent with those to be expected to be spontaneously developed at an emulsion interface. Let us now therefore consider the manner in which such film pressures may be developed. In mixed films of soap and alcohol, the tails may be attracted by van der Waals forces and the heads by hydrogen bonding.
169
At the water side of the film of the o/w emulsions, the heads of the oleate ions are negatively charged so that there is also a strong electrostatic force of repulsion among them, which repulsion is transmitted longitudinally from the heads of the molecules along their axes, weakening the attraction among the tails. If these were no alcohol molecules interspersed among these ions, the coulombic repulsion would be so great that an expanded film of low pressure would result. The introduction of alcohol molecules among the charged heads not only serves to reduce the repulsion among the oleate ions but actually bonds alcohol to oleate ion. This allows closer adlineation of the tails, which, owing to the seventh power inverse law, greatly increases the force of attraction among them. As more alcohol molecules enter the film, the electrostatic repulsion at the water side of the film will be further decreased and hydrogen bonding among the alcohol and oleate ions increased. Because of the relative strength of these forces, which are proportional to the concentration of the two species at the interface, three stages of pressure development may occur in o/w systems. In the first, with zero or only a low concentration of alcohol, the film will be expanded and its pressure will be low. In the second stage, the concentration of alcohol will be high enough to reduce the electrostatic repulsion so that a liquid condensed film of high spreading pressure will develop. It is in this stage that maximum pressures will be developed. In the third stage, alcohol molecules will be in excess and although the film will remain condensed, the strong electrostatic repulsive forces will be diluted so that the pressure will be lower than in the second stage. This conception of the way in which film pressures may develop also changes the meaning of the term 7r in applying Eq. [1] to these systems. As soon as the molecular species have become adsorbed at the interface, they are oriented parallel to one another. For simplieity's sake, let all the soap be considered adsorbed at the interface (12). Concomitant with the initial adsorption, the physical forces acting among them will exert a pressure gradient across the flat film. In the o/w systems, the electrostatic
170
PRINCE
force of repulsion is gradient determining. In the w/o systems the concentration of soap in the water phase is very high so that the ionic diffuse layer is suppressed and the soap exists as an ion pair. There will be strong hydrogen bonding among the heads of the soap and alcohol molecules at the water side of the interface, so that the gradient-determining force here may be considered to be a lack of attraction among the tails, the shorter the alcohol tails, the less the attraction. Thus, depending upon the relative strength of the forces acting at the water side or the oil side of the flat film, a curvature will develop which relieves the excess pressure at the high side. Coineidentally, a packing gradient or wedge will develop among the fihn tenants. In the flat film, the pressure gradient generates the initial pressure which, in iuxtaposition to (%/,)a, determines whether the emulsion will be macro or micro. A more descriptive term than ~r for this pressure would therefore be ~ro,the pressure generated by the difference in magnitude of the forces acting among the heads and tails of the freshly adsorbed film tenants or the initial pressure resulting from the initial pressure gradient across the interface. This term implies the spontaneous development of pressure at an emulsion interface in situ rather than artifically, as in a film balance. It follows that at the emulsion interface the initial pressure gradient is responsible for the difference in magnitude between ~ra, the film pressure before curvature, and ~r, the film pressure after curvature. Likewise, if the total potential (minimum) interracial tension corresponding to ~ro be ~ , then after curvature the higher interfacial tension 7i will correspond to the lower pressure 7r. The equation based on this terminology
of the foregoing concepts may be widened to include nonionic emulsifiers. Emulsions corresponding to those of Table I can readily be made using commercially available nonionie emulsifiers of the polyoxyethylene class. Such emulsifiers are inhomogeneous with respect to the length of the ethylene oxide chain and thus may act as both alcohol and soap. The shorter chain fractions which are less water soluble behave as alcohols. Increasing the ethylene oxide chain makes the molecules more water dispersible and at the same time enlarges their spatial requirements in the water phase. This has the same effect as increasing the ionic repulsion among the polar heads of soap molecules (13). To return to the graphical representation, an informative picture of the criteria which determine the transitions of Table I may be obtained by plotting on the s~me axes, hypothetical curves of ~ro and @o/~)~ as ordinates versus concentration of alcohol as abscissas. Intersection of these curves indicates micro emulsion formation; failure to intersect, a macro emulsion. This is illustrated in Fig. 2 in which Figs. 2A, 2B, 2C, and 2D correspond to Table I(A), (B), (C), and (D), respectively. In these graphs the concentration of alcohol shown on the abscissas represents the total in the system. For the (~'o/~)a curves, the alcohol concentration is plotted as that fraction of the total alcohol that is in the oil phase. For the ~ra curves, the alcohol concentration is plotted as that fraction of the total amount of alcohol in the interface. By referring both of these fractions to the total amount of alcohol in the system, the abscissas, the plots may be validly superimposed upon one another. It is understood, of course, that the locations of points on these graphs are only educated guesses. With this in mind, let us consider the im~ (~oi~)o - ~o [2] plications of Fig. 2A. These graphs correspond to the data of Table 1A and Fig. 1. more accurately expresses the thermody- The vo curves state that the maximum namic conditions at the interface before pressure in the interface between each oil curvature than does Eq. [1]. The new equa- and water is the same for all emulsion systion also makes possible a graphical char- tems and that this maximmn pressure acterization of the process of mieroemulsi- corresponds to the same ratio of alcohol to fication. oleate ion in the interface. The curves are Before considering this, however, the scope of the same shape; the reason for the shift =
A THEORY OF AQUEOUS EMULSIONS
171
B
55 52 kerosene
...
cety] alcoho; Ig-
2
3
lg.
4
2
3.,.
53
\\ \
c/oho'~Odeeeoe
35 benzene
~-o~k
"¢~2`%
hexanol
,/"
x\%
/% f
n hexanol lml.
;~ 2
3
4
...
L
3ml.
,4
5
6
Fla. 2. Characterization of the process of emulsification. Upper curves represent depression of @o/w)a; lower curves, variation of ~r0.Effect of the Meohol-oil relationship upon the formation of: (A) o/w emulsions of various oils, (B) o/w emulsions of various Meohols, (C) w/o emulsions of various oils, and (D) w/o emulsions of various alcohols. in their position from left to right corresponds to the increase in the ratio of alcohol at the interface to total alcohol in the system as the molecular weight of the oil phase increases. The (7 o/.)~ curves show how eetyl alcohol depresses the oil/water interfacial tension in proportion to the amount left in each different oil after the chemical potential in each phase has been equalized by partitioning. I t will be noticed that each of these curves begins at a different point on the ordinate corresponding to the 7oh of each oil as shown in Table II. When the ratio of alcohol in the oil phase to the total in the system falls to a point, as with Nujol, where the maximum pressure at the interface has been reached before (~/o/~)~ can be depressed to this level, no micro emulsion will form. Also where the ~r0 and (1'o/~)~ curves do intersect, the area between the curves decreases as the molecular weight of the oil increases. This implies that these areas are proportional to the free energy available to form micro emulsions. The curves of Fig. 1 clearly demonstrate that the micro emulsion range decreases as the molecular weight of the oil increases,
corresponding to such an interpretation of Fig. 2A. When myricyl alcohol replaces cetyl in the Nujol system, Table I(A), the chemical potential of alcohol in the oil is lowered. This favors a lower ratio of alcohol to soap in the interface and a greater depression of (7oi~)~ with the result that the curves intersect again. This prevails through the paraffin waxes.
The rapid change in distribution coefficient k with the chemical potential tt of the alcohol in the oil phase stems from the strict thermodynamic relationship (14) #°--#°
e-(O
,)/~ T
= /~_ cra~
[3]
Co 0/o
where co and cs, ao and ar are the concentration and activity coefficients in the oil phase and interface, respectively, and /~° 0
and ~° are the respective chemical potentials Y in a standard state. The data of Table III illustrate these interrelationships. Bowcott and Schulman (5) also made a rough estimation of the standard free energy decrease associated with one mole of alcohol
i72
PRINCE
as it enters the interface from the benzene phase. Assuming that the activity coefficients of the alcohol were the same in both phases, they obtained a value of 1330 calories for n-deeanol whereas n-hexanol varied from 740 to 1000. The effect of different alcohols upon the mieroemulsification of kerosene in water is shown in Fig. 2B. At low concentrations of the longest alcohol (lowest chemical potential in kerosene) a substantial depression of (Vo/w)a is effected and at the same time ro is relatively high, in spite of the low alcohol to soap ratio in the interface, because of its close adlineation of its long tails with those of the soap. The magnitude of the van der Waals forces is thus shown to be very sensitive to an increase in chain length, offsetting a deficiency in concentration. Under these circumstances, it is a relatively easy matter for the value of (Vo/~)a to drop to below that of ss. Cetyl alcohol, with its higher chemical potential in kerosene, is less effective than myricyl alcohol in depressing (vo/~)a. Moreover, cetyl alcohol produces a lower maximum ~ro owing to the lower attraction of its shorter tails with those of the soap. Finally, with lauryl alcohol its low concentration in kerosene fails to sufficiently depress (7o/w)~ before its maximum pressure development in the interracial film is passed. The foregoing considerations apply with equal force to w/o emulsions except that the alcohol values shown in Tables I(C) and (D) are, differing from those in the o/w systems, dependent upon the volume of both the oil and water phases. Under conditions favoring mieroemulsification, as alcohol is titrated into one of these systems, the film pressure will develop slowly at first and then more rapidly as the attraction among the tails decreases. When alcohol is in excess, ~'o can be expected to decrease again owing to the formation of a more condensed film. In Fig. 2C hexadeeane has the highest film pressure corresponding to its high alcohol to soap ratio (cf. Table III). Since the chemical potential of n-hexanol in hexadecane is higher than for the other hydrocarbons of this series, it will be least effective in depressing ('ro/~)~. As the molecular weight of the oil phase decreases, the maxi-
mum ~ro will decrease but the effectiveness of the total alcohol in the system in depressing (3'o/~)~ will increase. But by the time (liquid) ethane is reached, as more alcohol is titrated into the system, the excess will begin to decrease vo so rapidly that the curves will never intersect. Figure 2D corresponds to Table I(D). Hexanol is the most effective of all the alcohols in this series in raising ~ro and least effective in depressing the tension of benzene. Of all the alcohols, dodecanol is the most effective per volume in the system in depressing (7o/~), because of its relatively low initial chemical potential in benzene. But because of this it does not partition efficiently to the interface. Combined with relatively strong attraction among its tails and those of the soap in the interface, ~r0 reaches its maximum value and is falling off before it can intersect the (3'o/~), curve. In conclusion, Table III shows that the n-decane emulsion of Table I(C) and the n-hexanol emulsion of Table I(D) both have 2 moles of hexyl alcohol per mole of soap at the interface. From this it may be presumed that the value of ~o is the same in both interfaces although the effectiveness of such a value in producing a micro emulsion is different in each case. Since the 7o/w of benzene is 35 dynes/cm., it may be deduced --not unexpectedly--that these alcohols depress the interfacial tension of n-alkanes against water much more than that of benzene against water and that the values of 7r~ and (7o/~)~ that we are talking about are probably of the order of magnitude of 10-20 dynes/era. At such low pressures, penetration of the mixed films by nonpolar oil species might take place. The theory as embodied in Eq. [2] encompasses such a possibility but is equally adequate without it. REFERENCES 1. SCI-IULM2~N, J. H., STOEC:KENIUS, W., A_ND
PRINCE, L. M., J. Phys. Chem. 63, 1677
(1959). 2. STOECKENIUS, W., SCHULMAN, J. H., AND PRINCE, L. M., Kolloid Z. 169, 170 (1969).
3, COOKE,C. E., JR., ANDSCnVLM~,J. H., Proe. 2nd Scandinavian Syrup. Surface Activity, Stockholm, November 1964.
A THEORY OF AQUEOUS EMULSIONS 4. SCHULMAN,J. H., AND MONTAGNE, J. B., Ann. N . Y . Aead. Sci. 92, Art. 2,366-371 (1961). 5. BOWCOTT,J. E., SCHULMAN,J. H., Z. Elektrochem. 59, Heft 4, 283 (1955). 6. PRINCE, L. M., Soap Chem. Specialties, 36, Sept., Oct. (1960). 7. HOAR, T. P., AND SCttULMAN, J. H., Nature 152, 102 (1943). 8. SCHULMAN, J. H., AND McRo~ERTS, T. S., Trans. Faraday Soe. 42B, 165 (1946). 9. GInAFALCO,L. A., AND GOOD, R. J., J. Phys. Chem. 61,904 (1957).
173
10. JASPER, J. L., AND HOUSEMAN, ]3. L., J. Phys. Chem. 67, 1548-1551 (1963). 11. VALENTINe, R. S., AND HEIDEGER, W. J., J. Chem. Eng. Data 8, 27-30 (1963). 12. VAN DER WAARDEN, J. Colloid Sci. 7, 140 (1952); ibid. 9, 215 (1954). 13. SCHICK,M. J., ATLAS, S. M., AND EIRICH, F. R., J. Phys. Chem. 66, 1326 (1962). 14. tt~_~Ew~:, Lo~JIS P., "Introduction to the Study of Physical Chemistry," p. 251. McGraw-Hill, New York, 1952.
COLLOID AND INTERFACE SCIENCE 2 3 , 1 6 5 - 1 7 3
(1967)
A Theory of Aqueous Emulsions I. Negative Interfacial Tensionat the Oil/Water Interface L E O N M. P R I N C E
Lever Brothers Company, Research Center, Edgewater, New Jersey Received November 18, 1965 It was proposed that negative interracial tension due to high film pressure is responsible for the formation of micro emulsions. It now appears that the initial, negative interfacial tension v~ in mixed films of soap and long-chain alcohols is the result not so much of a high initial film pressure 7r0 as of a large depression of the interfacial tension (7o/~)a between the water and the oil phase with its adsorbed alcohol monolayer in accordance with the equation v¢ = (q,o/w)~- 7r . This depression is brought about by the spontaneous distribution of alcohol between the interface and the oil phase. I t is pointed out that this distribution is dependent upon the initial chemical potential of the particular alcohol in the given oil and that it may vary within wide limits. The fraction of the alcohol that remains in the oil phase is available to depress the oil/water interfacial tension while the remainder of it forms a mixed film with emulsifier adsorbed from the water phase. It is submitted that the interaction of coulombic, hydrogen bonding and van der Waals forces among the heads and tails of the tenants of this film develops an initial pressure gradient across the flat interface which generates the initial film pressure ~r0 . Three stages of pressure development are postulated, the maximum pressure corresponding to an intermediate concentration of alcohol. Hypothetical plots of (vo/~,)~and 7r0 as ordinates versus concentration of alcohol as abscissa provide a graphical characterization of the process of mieroemulsification.
INTRODUCTION Consideration has been given to the influence of the chemical nature of both the alcohol and oil phase upon the formation of micro emulsions stabilized with oleate soap and long-chain alcohols (1). It was shown that oil-in-water (o/w) micro emulsions were formed o n l y when the chain l e n g t h of the tail of the alcohol was a t least as long as t h e molecules of t h e oil phase. T h i s suggested t h a t oil phase molecules could p e n e t r a t e the m i x e d film owing to the strong association a m o n g the long alcohol tails a n d the oil phase molecules a n d t h a t such p e n e t r a t i o n would s p o n t a n e o u s l y increase the pressure ~r in the film. T h i s m o l e c u l a r concept subseq u e n t l y (2) inspired a differentiation bet w e e n m a c r o a n d micro emulsions based on the t h e r m o d y n a m i c relationship
where 7~ is the t o t a l interfacial tension, v o/~ is the o i l / w a t e r interfaeial t e n s i o n w i t h o u t a d d i t i o n of stabilizing agents, a n d 7r is the spreading pressure in the m o n o l a y e r of adsorbed species. According to this equation, if as a result of the a d s o r p t i o n of the soap a n d alcohol at the interface a n d its p e n e t r a t i o n b y oil phase molecules, ~r b e c a m e greater t h a n
7o/~, then energy -wdA (A = surface area) would be available to increase the total interfaeial area. This was considered to be the condition for the formation of a micro emulsion. When ~ < 7o/w only a macro emulsion would form. In this view, the temporary existence of a film pressure greater than 7o/~ would be the
165
166
PRINCE
driving force which reduced the droplet size of the fixed volume of oil until no more energy was available to increase the interfacial area. Equilibrium would be attained when the negative interracial tension returned to zero by virtue of the uncrowding of the molecules and loss of pressure in the interface. Such systems have been characterized (3-6) by droplet diameters of the order of magnitude of 80 A to 800 A, optical isotropy, faint light scattering, and longterm stability. When ~o/~ > 7r, droplet diameters of the order of magnitude of 10,000 A are usually observed and the systems, which now appear milky white, achieve equilibrium by separating into two phases. Energy input in the form of mechanical work (agitation or homogenization) may ternporarily increase the total interfacial area but is not capable p e r se of changing the values of ~r or Vo/w. Modification of this theory is now required. Recent studies (3) have given strong indication that hydrocarbon molecules would be ejected from mixed films of soap and alcohols at the high pressures necessary for negative interracial tension, i.e., greater than 55 dynes/era, for alkanes or greater than 35 dynes/era, for benzene. Furthermore, the original proposal overlooked evidence that water-in-oil (w/o) micro emulsions could be made with alcohols the tails of which were shorter than the length of the hydrocarbon (7). It is presently submitted that suitable relationships for negative interracial tension can be achieved between ~r and 7o/w by a substantial depression of vo/~ within the context of the thermodynamic concepts expressed in Eq. [1]. The new arguments are based upon a reassessment of previous experimental data in the light of the full implications of this equation.
ing a micro emulsion became narrower until, abruptly, no micro emulsion would form. It was similarly shown that when the amount and kind of soap as well as alcohol was held constant, abrupt transitions from micro to macro emulsions took place with changes in the molecular weight of the oil in a given homologous series. The data illustrating these transitions are presented in Table I. The point at which the transition occurs is denoted by an x. Table I (A) indicates the amount of alcohol required to produce the smallest particle sized o/w micro emulsion of each oil using a fixed amount of soap. On either side of this optimal amount of alcohol, particle size was larger. This is illustrated in Fig. 1, in which the range of effectiveness of cetyl alcohol in forming micro emulsions of n-alkanes is shown. Two alcohols, eetyl and myricyl, were used in the experiments reported in Table I(A). The data clearly demonstrate that it became increasingly more difficult to make a micro emulsion as the molecular weight of the oil was increased and that lengthening the chain of the alcohol substantially extended its range of effectiveness. Table I(B) indicates the amount of myricyl and eetyl alcohol required to produce the smallest particle sized micro emulsion of kerosene using a given amount of soap. No micro emulsion was made at any concentration of lauryl alcohol. The minimum volumes of n-hexanol required to titrate equal volumes of three n-alkanes to transparent w/o micro emulsions are shown in Table I(C). Table I(D) catalogs the minimum volumes of four nalkanols which Bowcott and Schulman (5) found were required to titrate benzene to a transparent w/o micro emulsion with a fixed amount of water. No micro emulsion was observed in these systems with n-dodecanol. THE DATA The narrowing range of effectiveness of Data on micro emulsion systems stabilized these alcohols with increasing chain lengths with mixed films of soap and alcohol have is amply documented by the experiments of been developed by a number of investigators these authors. In recapitulation, it seems to be more than (3, 5, 6, 8). This experimental evidence indicated that, at constant amount of soap, coincidence that a certain symmetry is reas the molecular weight of the alcohol in- vealed by the arrangement of the data of creased for w/o emulsions or decreased for these four tables. Observe that when the o/w emulsions, the range of concentration kind of alcohol is fixed as in Tables I(A) over which the alcohol was effective in form- and (C), the amount required to yield a
167
A THEORY OF AQUEOUS EMULSIONS TABLE I TRANSITION FROM MICRO TO MACRO EMULSIONS
Oil-in-Water Systems A. Effect of different oils (6) Oil
Alcohol (g.) Cetyl
n-IIeptane n-Dodecane Kerosene n-Hexadecane n-Octadecane Nuj ol Paraffin wax Microcrystalline wax
B, Effect of different alcohols Oil:Kerosene Myricyl
Alcohol
1.0
Lauryl Cetyl Myricy!
1.5 2.0 2.0 3.0 3.0 N N X
Grams
X 2.0 1.0
3.0 4.5 × Water-in-Oil Systems
C. Effect oJ different oils (3)
D. Effect o] different alcohols (5) Oil: Benzene
Oil
n-ttexanol (ml.)
Alcohol
Milliliters
(Ethane) n-ttexane n-Decane n-Hexadecane
(N) 2.6 3.1 4.3
n-tIexanol n-tteptanol n-Oetanol n-Decanot n-Dodecanol
6.0 4.3 3.5 3.4 X
micro emulsion increases with the molecular weight of the oil phase. In a similar manner, when the oil phase is fixed as in Tables I(B) and (D), the amount of alcohol required decreases as the molecular weight of the alcohol increases. These variations with molecular weight appear to be in the same direction whether the system is o / w or w/o. But the direction in which the transition from micro to macro emulsion takes place, reverses itself from o / w to w/o, Tables I(A) and (C), to (B) and (D). Thus, although it is not demonstrated experimentally, it m a y reasonably be deduced that n-hexanol in Table I(C) would fail to produce a micro emulsion when the molecular weight of the hydrocarbon fell to that of (liquid) ethane. Finally, several important differences between the o/w and w/o emulsions should be noted. The w/o emulsions were titrated just to transparency. Smaller sized droplets could be made by the addition of more alcohol (3). This was not the ease for the
.0.1-
.01-
FIG. 1. The effect of cetyl alcohol concentration on the droplet diameter in microns of n-alkanein-water emulsions. o/w emulsions. The low fixed ratio of soap to oil limited particle size to translucent systems, exhibiting a pronounced Tyndall effect (6). B y increasing the soap to oil ratio, transparency was achieved in similar
168
PRINCE
systems in which the oil phase was an alkyd TABLE II (2). By staining this unsaturated compound INTERFAeIAL TENSIONS OF HYDROCARBONS AGAINST WATER AT 20°C., dynes/era. (9) with osmium tetroxide, the oil phase was seen directly in the electron microscope in Hydrocarbon 'Yo l w droplet form. A further difference between these systems n-Hexane 51.1 n-Heptane 50.2 lies in the kind of cation used with the soap. n-Octane 50.8 A stoichiometric amount of potassium was n-Decane 51.2 employed with the oleic acid in the w/o sysn-Tetradecane 52.2 tems so that all the fatty acid existed as S~anolax ~ 55.55 oleate ion (soap). The use of an amine oleate (Nujol) (55.55) in the o/w systems, as previously pointed Benzene 35.0 out (1), formed amphiphile in situ so that the fatty acid existed as both oleate ion and A medicinal grade of mineral oil substantially free fatty acid in approximately equal equivalent to Nujol. proportions. Since free acid may be considered to act as an alcohol under such octadecane. In a similar way, 4.5 g. of circumstances, it means that a 1/1 ratio of myricyl alcohol is less effective in microalcohol to soap existed in these systems emulsifying Nujol than paraffin wax in spite before addition of the alcohols shown in of the lower 7o/w of the Nujol. Tables I(A) and (B). This is a matter of Such behavior indicates that the distribuconsiderable consequence to the discussion tion of alcohol between the oil phase and the interface is different for each oil (3). In which follows. this way the effectiveness of the alcohol in INTERPRETATION OF THE DATA raising ~r depends upon its actual concentraThe arrangement of data in Table I tion in the mixed film rather than upon its derives theoretical significance from its total concentration in the system. Support for this contention is available explicit definition of the criteria which determine whether or not micro emulsions are from additional data obtained on the w/o formed in these systems. The abrupt transi- emulsions. After the original emulsions were tions from micro to macro emulsions in made by titrating to transparency with Tables I(A) and (C) might, for example, be alcohol, additional oil was added and the explained by higher values of "Yo/~ as the systems were titrated to transparency again molecular weight of the n-alkane increases, with more alcohol. Repeating this process as shown in Table II. This would be true determined the alcohol volume per hydroproviding the interactions among the soap carbon volume to produce a transparent and alcohol (including free acid) species in system, and extrapolation of the curve to the mixed film produced the same value of zero hydrocarbon determined the amount of ~r for each oil. As it turns out, this is not the alcohol in the interface. These data are shown in Table III. case. On the basis of this information it may be If ~r must be greater than ~/o/wfor a micro emulsion, then according to Table I(A), inferred, for example, that the chemical the value of ~r developed at 3 g. of cetyl potential of hexyl alcohol in hexane is lower alcohol must be greater than the ~'o/~ for than it is in hexadecane, assuming that the n-octodecane, which is seen from Table II changes in values of the activity coefficients to be approximately 53 dynes/era. But of the alcohol in the two oil phases are small when cetyl alcohol was used with n- in comparison with those of the partial dodecane, it is obvious from Fig. 1 that 3 g. molal free energy. By the same token, one of this alcohol was considerably less effective may assume that the initial chemical poin microemulsifying n-dodecane than n- tential of cetyl alcohol in Nu]ol is greater octadecane in spite of the fact that than in kerosene; this is another way of n-dodecane has a lower ~oI~ than n- saying that as the molecular weight of the
A T H E O R Y OF AQUEOUS E M U L S I O N S III
TABLE MOLE
RATIO
OF ALCOHOL
AND
THE
TO SOAI" IN THE
INTERFACE
Alcohol
Oil
n-Hexanol n-Hexanol n-ttexanol n-Hexanol n-Heptanol n-Oetanol n-Decanol
n-Hexane n-Deeane n-Hexadeeane Benzene Benzene Benzene Benzene
SYSTEM
(3, 5) In
In
3.2 3.9 5.4 7.5 4.8 3.5 2.8
1.7 2.0 3.6 2.0 1.5 1.25 1.0
system interface
oil increases the distribution ratio will favor the interface so that there will be less alcohol available in the oil to lower 7o/~. The same arguments apply when the oil phase is constant as in Tables I(B) and I(D). One would expect, for example, the initial chemical potential of hexanol in benzene to be higher than that of decanol in benzene, implying that at equilibrium more hexanol would be in the interface than decanol (el. Table III). These arguments indicate that 7o/~ may no longer be considered as determining 7i. For systems containing long-chain alcohols, the criterion must now be considered to be the interracial tension against water of the oil plus its fraction of alcohol. Let this be (%/~)a. In general, this interracial tension falls very rapidly at low concentrations of alcohol and then levels off. The extent of the depression and the rate at which it occurs will be different for each class of alcohol and oil and will be substantially independent of the chain length of the alcohol in any homologous series (10, 11). It follows that negative interracial tension may be achieved not so much by a great increase in ~r as by a substantial depression of ('~oi~)~. This thesis removes the requirement for film pressures of over 53 dynes/em, and places the demand for pressure values at levels more consistent with those to be expected to be spontaneously developed at an emulsion interface. Let us now therefore consider the manner in which such film pressures may be developed. In mixed films of soap and alcohol, the tails may be attracted by van der Waals forces and the heads by hydrogen bonding.
169
At the water side of the film of the o/w emulsions, the heads of the oleate ions are negatively charged so that there is also a strong electrostatic force of repulsion among them, which repulsion is transmitted longitudinally from the heads of the molecules along their axes, weakening the attraction among the tails. If these were no alcohol molecules interspersed among these ions, the coulombic repulsion would be so great that an expanded film of low pressure would result. The introduction of alcohol molecules among the charged heads not only serves to reduce the repulsion among the oleate ions but actually bonds alcohol to oleate ion. This allows closer adlineation of the tails, which, owing to the seventh power inverse law, greatly increases the force of attraction among them. As more alcohol molecules enter the film, the electrostatic repulsion at the water side of the film will be further decreased and hydrogen bonding among the alcohol and oleate ions increased. Because of the relative strength of these forces, which are proportional to the concentration of the two species at the interface, three stages of pressure development may occur in o/w systems. In the first, with zero or only a low concentration of alcohol, the film will be expanded and its pressure will be low. In the second stage, the concentration of alcohol will be high enough to reduce the electrostatic repulsion so that a liquid condensed film of high spreading pressure will develop. It is in this stage that maximum pressures will be developed. In the third stage, alcohol molecules will be in excess and although the film will remain condensed, the strong electrostatic repulsive forces will be diluted so that the pressure will be lower than in the second stage. This conception of the way in which film pressures may develop also changes the meaning of the term 7r in applying Eq. [1] to these systems. As soon as the molecular species have become adsorbed at the interface, they are oriented parallel to one another. For simplieity's sake, let all the soap be considered adsorbed at the interface (12). Concomitant with the initial adsorption, the physical forces acting among them will exert a pressure gradient across the flat film. In the o/w systems, the electrostatic
170
PRINCE
force of repulsion is gradient determining. In the w/o systems the concentration of soap in the water phase is very high so that the ionic diffuse layer is suppressed and the soap exists as an ion pair. There will be strong hydrogen bonding among the heads of the soap and alcohol molecules at the water side of the interface, so that the gradient-determining force here may be considered to be a lack of attraction among the tails, the shorter the alcohol tails, the less the attraction. Thus, depending upon the relative strength of the forces acting at the water side or the oil side of the flat film, a curvature will develop which relieves the excess pressure at the high side. Coineidentally, a packing gradient or wedge will develop among the fihn tenants. In the flat film, the pressure gradient generates the initial pressure which, in iuxtaposition to (%/,)a, determines whether the emulsion will be macro or micro. A more descriptive term than ~r for this pressure would therefore be ~ro,the pressure generated by the difference in magnitude of the forces acting among the heads and tails of the freshly adsorbed film tenants or the initial pressure resulting from the initial pressure gradient across the interface. This term implies the spontaneous development of pressure at an emulsion interface in situ rather than artifically, as in a film balance. It follows that at the emulsion interface the initial pressure gradient is responsible for the difference in magnitude between ~ra, the film pressure before curvature, and ~r, the film pressure after curvature. Likewise, if the total potential (minimum) interracial tension corresponding to ~ro be ~ , then after curvature the higher interfacial tension 7i will correspond to the lower pressure 7r. The equation based on this terminology
of the foregoing concepts may be widened to include nonionic emulsifiers. Emulsions corresponding to those of Table I can readily be made using commercially available nonionie emulsifiers of the polyoxyethylene class. Such emulsifiers are inhomogeneous with respect to the length of the ethylene oxide chain and thus may act as both alcohol and soap. The shorter chain fractions which are less water soluble behave as alcohols. Increasing the ethylene oxide chain makes the molecules more water dispersible and at the same time enlarges their spatial requirements in the water phase. This has the same effect as increasing the ionic repulsion among the polar heads of soap molecules (13). To return to the graphical representation, an informative picture of the criteria which determine the transitions of Table I may be obtained by plotting on the s~me axes, hypothetical curves of ~ro and @o/~)~ as ordinates versus concentration of alcohol as abscissas. Intersection of these curves indicates micro emulsion formation; failure to intersect, a macro emulsion. This is illustrated in Fig. 2 in which Figs. 2A, 2B, 2C, and 2D correspond to Table I(A), (B), (C), and (D), respectively. In these graphs the concentration of alcohol shown on the abscissas represents the total in the system. For the (~'o/~)a curves, the alcohol concentration is plotted as that fraction of the total alcohol that is in the oil phase. For the ~ra curves, the alcohol concentration is plotted as that fraction of the total amount of alcohol in the interface. By referring both of these fractions to the total amount of alcohol in the system, the abscissas, the plots may be validly superimposed upon one another. It is understood, of course, that the locations of points on these graphs are only educated guesses. With this in mind, let us consider the im~ (~oi~)o - ~o [2] plications of Fig. 2A. These graphs correspond to the data of Table 1A and Fig. 1. more accurately expresses the thermody- The vo curves state that the maximum namic conditions at the interface before pressure in the interface between each oil curvature than does Eq. [1]. The new equa- and water is the same for all emulsion systion also makes possible a graphical char- tems and that this maximmn pressure acterization of the process of mieroemulsi- corresponds to the same ratio of alcohol to fication. oleate ion in the interface. The curves are Before considering this, however, the scope of the same shape; the reason for the shift =
A THEORY OF AQUEOUS EMULSIONS
171
B
55 52 kerosene
...
cety] alcoho; Ig-
2
3
lg.
4
2
3.,.
53
\\ \
c/oho'~Odeeeoe
35 benzene
~-o~k
"¢~2`%
hexanol
,/"
x\%
/% f
n hexanol lml.
;~ 2
3
4
...
L
3ml.
,4
5
6
Fla. 2. Characterization of the process of emulsification. Upper curves represent depression of @o/w)a; lower curves, variation of ~r0.Effect of the Meohol-oil relationship upon the formation of: (A) o/w emulsions of various oils, (B) o/w emulsions of various Meohols, (C) w/o emulsions of various oils, and (D) w/o emulsions of various alcohols. in their position from left to right corresponds to the increase in the ratio of alcohol at the interface to total alcohol in the system as the molecular weight of the oil phase increases. The (7 o/.)~ curves show how eetyl alcohol depresses the oil/water interfacial tension in proportion to the amount left in each different oil after the chemical potential in each phase has been equalized by partitioning. I t will be noticed that each of these curves begins at a different point on the ordinate corresponding to the 7oh of each oil as shown in Table II. When the ratio of alcohol in the oil phase to the total in the system falls to a point, as with Nujol, where the maximum pressure at the interface has been reached before (~/o/~)~ can be depressed to this level, no micro emulsion will form. Also where the ~r0 and (1'o/~)~ curves do intersect, the area between the curves decreases as the molecular weight of the oil increases. This implies that these areas are proportional to the free energy available to form micro emulsions. The curves of Fig. 1 clearly demonstrate that the micro emulsion range decreases as the molecular weight of the oil increases,
corresponding to such an interpretation of Fig. 2A. When myricyl alcohol replaces cetyl in the Nujol system, Table I(A), the chemical potential of alcohol in the oil is lowered. This favors a lower ratio of alcohol to soap in the interface and a greater depression of (7oi~)~ with the result that the curves intersect again. This prevails through the paraffin waxes.
The rapid change in distribution coefficient k with the chemical potential tt of the alcohol in the oil phase stems from the strict thermodynamic relationship (14) #°--#°
e-(O
,)/~ T
= /~_ cra~
[3]
Co 0/o
where co and cs, ao and ar are the concentration and activity coefficients in the oil phase and interface, respectively, and /~° 0
and ~° are the respective chemical potentials Y in a standard state. The data of Table III illustrate these interrelationships. Bowcott and Schulman (5) also made a rough estimation of the standard free energy decrease associated with one mole of alcohol
i72
PRINCE
as it enters the interface from the benzene phase. Assuming that the activity coefficients of the alcohol were the same in both phases, they obtained a value of 1330 calories for n-deeanol whereas n-hexanol varied from 740 to 1000. The effect of different alcohols upon the mieroemulsification of kerosene in water is shown in Fig. 2B. At low concentrations of the longest alcohol (lowest chemical potential in kerosene) a substantial depression of (Vo/w)a is effected and at the same time ro is relatively high, in spite of the low alcohol to soap ratio in the interface, because of its close adlineation of its long tails with those of the soap. The magnitude of the van der Waals forces is thus shown to be very sensitive to an increase in chain length, offsetting a deficiency in concentration. Under these circumstances, it is a relatively easy matter for the value of (Vo/~)a to drop to below that of ss. Cetyl alcohol, with its higher chemical potential in kerosene, is less effective than myricyl alcohol in depressing (vo/~)a. Moreover, cetyl alcohol produces a lower maximum ~ro owing to the lower attraction of its shorter tails with those of the soap. Finally, with lauryl alcohol its low concentration in kerosene fails to sufficiently depress (7o/w)~ before its maximum pressure development in the interracial film is passed. The foregoing considerations apply with equal force to w/o emulsions except that the alcohol values shown in Tables I(C) and (D) are, differing from those in the o/w systems, dependent upon the volume of both the oil and water phases. Under conditions favoring mieroemulsification, as alcohol is titrated into one of these systems, the film pressure will develop slowly at first and then more rapidly as the attraction among the tails decreases. When alcohol is in excess, ~'o can be expected to decrease again owing to the formation of a more condensed film. In Fig. 2C hexadeeane has the highest film pressure corresponding to its high alcohol to soap ratio (cf. Table III). Since the chemical potential of n-hexanol in hexadecane is higher than for the other hydrocarbons of this series, it will be least effective in depressing ('ro/~)~. As the molecular weight of the oil phase decreases, the maxi-
mum ~ro will decrease but the effectiveness of the total alcohol in the system in depressing (3'o/~)~ will increase. But by the time (liquid) ethane is reached, as more alcohol is titrated into the system, the excess will begin to decrease vo so rapidly that the curves will never intersect. Figure 2D corresponds to Table I(D). Hexanol is the most effective of all the alcohols in this series in raising ~ro and least effective in depressing the tension of benzene. Of all the alcohols, dodecanol is the most effective per volume in the system in depressing (7o/~), because of its relatively low initial chemical potential in benzene. But because of this it does not partition efficiently to the interface. Combined with relatively strong attraction among its tails and those of the soap in the interface, ~r0 reaches its maximum value and is falling off before it can intersect the (3'o/~), curve. In conclusion, Table III shows that the n-decane emulsion of Table I(C) and the n-hexanol emulsion of Table I(D) both have 2 moles of hexyl alcohol per mole of soap at the interface. From this it may be presumed that the value of ~o is the same in both interfaces although the effectiveness of such a value in producing a micro emulsion is different in each case. Since the 7o/w of benzene is 35 dynes/cm., it may be deduced --not unexpectedly--that these alcohols depress the interfacial tension of n-alkanes against water much more than that of benzene against water and that the values of 7r~ and (7o/~)~ that we are talking about are probably of the order of magnitude of 10-20 dynes/era. At such low pressures, penetration of the mixed films by nonpolar oil species might take place. The theory as embodied in Eq. [2] encompasses such a possibility but is equally adequate without it. REFERENCES 1. SCI-IULM2~N, J. H., STOEC:KENIUS, W., A_ND
PRINCE, L. M., J. Phys. Chem. 63, 1677
(1959). 2. STOECKENIUS, W., SCHULMAN, J. H., AND PRINCE, L. M., Kolloid Z. 169, 170 (1969).
3, COOKE,C. E., JR., ANDSCnVLM~,J. H., Proe. 2nd Scandinavian Syrup. Surface Activity, Stockholm, November 1964.
A THEORY OF AQUEOUS EMULSIONS 4. SCHULMAN,J. H., AND MONTAGNE, J. B., Ann. N . Y . Aead. Sci. 92, Art. 2,366-371 (1961). 5. BOWCOTT,J. E., SCHULMAN,J. H., Z. Elektrochem. 59, Heft 4, 283 (1955). 6. PRINCE, L. M., Soap Chem. Specialties, 36, Sept., Oct. (1960). 7. HOAR, T. P., AND SCttULMAN, J. H., Nature 152, 102 (1943). 8. SCHULMAN, J. H., AND McRo~ERTS, T. S., Trans. Faraday Soe. 42B, 165 (1946). 9. GInAFALCO,L. A., AND GOOD, R. J., J. Phys. Chem. 61,904 (1957).
173
10. JASPER, J. L., AND HOUSEMAN, ]3. L., J. Phys. Chem. 67, 1548-1551 (1963). 11. VALENTINe, R. S., AND HEIDEGER, W. J., J. Chem. Eng. Data 8, 27-30 (1963). 12. VAN DER WAARDEN, J. Colloid Sci. 7, 140 (1952); ibid. 9, 215 (1954). 13. SCHICK,M. J., ATLAS, S. M., AND EIRICH, F. R., J. Phys. Chem. 66, 1326 (1962). 14. tt~_~Ew~:, Lo~JIS P., "Introduction to the Study of Physical Chemistry," p. 251. McGraw-Hill, New York, 1952.