Langmuir 1993,9, 3345-3351
3345
Articles Mixing of Nonionic Surfactants at Water-Oil Interfaces in Microemulsions Hironobu Kunieda’ and Motoo Yamagata Department of Physical Chemistry, Division of Materials Science and Chemical Engineering, Faculty of Engineering, Yokohama National University, Tokiwadai 156, Hodogaya-ku, Yokohama 240, Japan Received January 25, 1993. In Final Form: July 2 2 , 1 9 9 P Different from a single-surfactant system, a three-phase body consisting of excess water, surfactant (microemulsion), and excess oil phases is largely skewed to higher temperature with decreasing total surfactant concentration in a multisurfactant system of water/R2E02/R12EOJR12EO$R12EO$heptane, where RI~EO,,indicates homogeneous polyethylene glycol dodecyl ether. The surfactants are mainly distributed between a microemulsion phase and an excess oil phase. Inside the microemulsion, the surfactants are considered to exist in the micro-oil domain and at the interface between the bicontinuous oil and water domains, if the solubility of surfactant in water is negligible. Considering this condition, the mixing ratios of surfactants at the interface were obtained using the phase diagram and the solubilities in the excess oil phase at each temperature. It is confirmed that the weight additivity of three-phase (HLB) temperatures of each surfactant hold in this mixed surfactant system. The meaning of the weight addivitiyis discussedaccordingto the correlation between R-theory,hydrophilic-lipophile-balanced(HLB) number, and HLB temperature. It was found that there is a compensating tendency of solubilitiesof each surfactant in oil phase. With the rise in temperature, the solubilities of lipophilic surfactants largely decrease although that of hydrophilic surfactant increases. As a result, the total solubility of the mixed surfactant decreases at higher temperature.
Introduction Nonionic surfactants are changed from hydrophilic (forming aqueous micelles) to lipophilic (forming reverse micelles) with a rise in temperature.l4 At the transition temperature, a three-phase body consisting of microemulphases appears. sion (surfactant, D), water (W), and oil (0) The three-phase body exists a t temperatures between two critical end temperatures of D-W and D-0 in single nonionic surfactant systems, and the hydrophile-lipophile lipophile property of surfactant is just balanced at the mid temperature. The HLB (hydrophile-lipophile-balanced) temperature is defiied as the temperature at which a single D phase containing equal weights of water and oil touches the three-phase body.5 In most practical nonionic surfactant systems, the HLB temperature is very close to the mid temperature of the three-phase body because the three-phase body exists in a very narrow temperature range at a fixed composition. Kahlweit et al. also emphasizes the importance of this particular temperature.6 The solubilizing power of surfactant reaches its maximum and the ultralow interfacial tensions are attained around the HLB t e m p e r a t ~ r e . ~The * ~ *defined ~ HLB temperature is independent of surfactant concentration and water/oil ratios in a single homogeneoussurfactant system according to the phase rulee6
* Corresponding author. @
Abstract published in Advance ACS Abstracts, November 1,
1993. (1) Shinoda, K.; Kunieda, H. J. Colloid Interface Sci. 1972,42, 381. (2) Kunieda, H.; Friberg, S. E. Bull. Chem. SOC.Jpn. 1981,54, 1010. ( 3 ) Kunieda, H.; Shinoda, K. Bull. Chem. SOC.Jpn. 1982, 55, 1777. (4) Kunieda, H.; Shinoda, K. J. Dispersion Sci. Technol. 1982,3,233. ( 5 ) Kunieda, H.; Shinoda, K. J. Colloid Interface Sci. 1985,107,107. (6) Kahlweit, M.; Strey, R.; Buese, G. J. Phys. Chem. 1990,94,3881. (7) Saito, H.; Shinoda,K. J . Colloid Interface Sci. 1971, 35, 359. (8) Shinoda, K.;Friberg, S.Emulsions and Solubilizations;John Wiley & Sons: New York, 1986; Chapter 1.
Since most of commercial nonionic surfactants are usually mixtures of homologs or isomers, it is important to predict the phase behavior of the system with more than single surfactant quantitatively. However, their phase behavior is more complicated due to the increase in the degree of f r e e d ~ m . ~In ~ ”general, ~ ~ the three-phase body is largely skewed to higher temperatures with decreasing surfactant concentration, although the opposite tendency is observed in a few systems.14 Therefore, the Griffin HLB number system15J6cannot be directly applied to mixed surfactant systems. The HLB number system is based on the weight additivity of surfactants as to HL (hydrophile-lipophile) property of a mixed surfactant. If it is correct, the weight additivity of the three-phase temperature should also hold. These relations have never been clearly verified in a multi-surfactant system.5~~7 Hence, there is a question on this matter.’SJg The surfactant phase (or microemulsion) is considered to be a “bicontinuous”structure in the three-phase region.20 The mixed surfactant layers are present at the interface between two micro-water and oil domains. The mixing (9) Mitaui, T.;Machida, Y.; Harusawa, F. Bull. Chem. SOC.Jpn. 1970, 43, 3044. (10)Kunieda, H.; Igarashi, K. Yukagaku 1982,31,949. (11) Kunieda, H.; Ishikawa, N.J. Colloidlnterface Sci. 1985,107,122. (12) Kunieda, H.; Shinoda, K. Yukagaku 1986,34,367. (13) Kunieda, H.; Sato,Y. Organized Solutions; Lindman, B.,Friberg, S., Eds.; Marcel Dekker Inc.: New York and Basel, 1992; Chapter 6. (14) Kunieda, H.; Ushio, N.; Nakano, A.; Miura, M. J . Colloidlnterface
Sci., in press. (15) Griffin, W. C. J. Soc. Cosmet. Chem. 1949, 1, 311. (16) Griffin, W. C. J. SOC.Cosmet. Chem. 1964,5, 249. (17) Kunieda, H.; Yamagata, M. Colloid Polym. Sci., in press. (18) Raney, K. H.; Miller, C. A. J . ColloidInterface Sci. 1987,119,539. (19) Wormuth, K. R.; Geissler, P. R. J. Colloid Interface Sci. 1991, 146, 320. (20) Olsson, U.; Shinoda, K.; Lindman, B. J. Phys. Chem. 1986, 90, 4083.
0743-7463/93/2409-3345$04.00/00 1993 American Chemical Society
Kunieda and Yamagata
3346 Langmuir, Vol. 9,No. 12,1993
A 50 -
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)resent
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X
Figure 1. Phase diagram of a water/RlzEO$heptane solution as a function of temperature. The weight fraction of heptane in
+
water heptane (R,) is kept at 0.5. x means the weight fraction of RlzEOe in system. The broken line indicates the HLB temperature.
04 0
'
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fraction of surfactants at the interface may be directly X related to the three-phase temperature in a mixed surFigure 2. Effect of mixing ratios of surfactants on the threefactant system. Since surfactants are also dissolved in phase behavior in a water/R~zEOzlR~~EOJR~~EOdR~zEOdheptane system: 0, W1 = WZ= W3 = W4 = 0.25;0,W1 = 0.5,W Z the oil and water domains, one cannot measure the real = W3 = W, = 0.167. The water/oil ratios are 50/50(w/w). The mixing fraction at the interface, directly. HLB temperature (the broken curve) is skewed to higher In this context, we have investigated the phase behavior temperature. Wi is the weight fraction of each surfactant in and the solubilities of each surfactant in the excess oil total surfactants. x is the weight fraction of total surfactants in phase in a water/R1~EOz/R~~EO$R~~EOs/R~~EO$heptane system. I, 11, and I11 are one-, two-, and three-phase regions, system to evaluate mixing fractions of each surfactant at respectively. "LC present" is a region including a liquid crystal. the water-oil interface in microemulsions. The meaning of the weight additivity of three-phase temperature is HL property of surfactant is just balanced in the midst discussed according to the concepts of R theory,21HLB of the three-phase body.3 The three-phase body consists number,l5J6 and HLB temperatures5 of a stack of three-phase triangles in which a surfactant phase (microemulsion, D)coexists with excess water (W) and oil (0)phases. In order to evaluate the three-phase Experimental Section behavior, we choose the particular three-phase triangle Materials. Homogeneous di-, tetra-, hexa-, and octaethylene on which a single surfactant phase contains equal weights glycol dodecyl ethers (abbreviated as RlzEOZ, RIZEOI,R1zE06, of water and oil touches the three-phase body.S16 The HLB and R12EOs) were kindly supplied from Nihon Surfactant Co. temperature is defined as a temperature at which the Extra-pure grade heptane was obtained from Tokyo Kasei Kogyo triangle exist$, and it is invariant in a three-component Co. These materials were used without further purifications. system containing a single surfactant at constant pressure. Procedures. Procedures to determine phase boundaries are The HLB temperature is 46.9 O C in a water/RlzEOs/ described in the previous paperas The solubilities of surfactants heptane system and is independent of water/oil ratios and in oil phases were measured as follows. After the samples reached surfactant concentrations as is shown in Figure 1. The equilibrium in a thermostat, the oil phases were sampled by a HLB temperatures for a water/RlzEO$heptane system syringe. Heptane was removed by rotary evaporator. The remained surfactants were determined by means of highand water/R12EO$heptane system are also experimentally Japan Optics, BIPperformance liquid chromatography (HPLC, determined to be 9.8 and 72.4 "C, respectively. The HLB 1). A gel column (GS-310, Asahi Chemical Industry) was used. temperature for a water/RlzEOdheptane system is below The elution liquid is a mixed solvent (50 wt % water and 50 w t 0 OC and cannot be measured experimentally. There is % methanol). A differential refractometer (Shodex RI,SE-11) a linear relationship between the HLB temperature and was used as a detector. the Griffins HLB number for a single surfactant system.6 By use of this relation, the HLB temperature is calculated Results to be -42.2 "C for the last system. Three-phase Behavior i n a Water/Rl2EOalRlzEOJ HLB Temperatures of Each Surfactant. The phase RlzEOs/R12EO$Heptane System. Phase diagrams of a diagram of a water/R~zEOs/heptane system at a fixed water/Rl2EOz/R~~EO$Rl2EOs/R~~EO$heptane system as water/oil ratio (the weight fraction of oil in water + oil, a function of temperature are shown Figure 2. The water/ Row = 0.5) is shown in Figure 1. It is considered that the oil ratio is fixed to unity (Row= 0.5) and total surfactant concentration ( x ) is plotted horizontally. In this paper, (21) Bourrel, M.; Schechter, R. 5. Microemulsions and Related Systems; Marcel Dekker: New York and Basel, 1988; Chapter 1. R12E02, R12E04, R12E06, and R12E08 are represented by
Langmuir, Vol. 9, No, 12,1993 3347
Mixing of Nonionic Surfactants
/
I1
I I
0
d 02
o.ol/
Lc present 04
0.6
0
08
0.2
0.4
0.6
0.8
1.0
0.6
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1 .o
Row
Row Figure 3. Three-phasebehavior as a function of Rowat constant total surfactant concentration (x) in a waterlRlzEOdRlzEOd RlzEO$RlzEO$heptane system. W1 = WZ= Ws = W4 = 0.25.
0.05
The concentrations are given in weight fractions.
0 04
( 1 ), (2), (3), and (4), respectively. The weight fractions
of each surfactant on a total surfactant basis are indicated by WI, WZ, W3,and W4, respectively. The concentrations and mixing fractions are given in weight fractions. Different from a single nonionic surfactant system, the threephase body is largely skewed to higher temperature with the decrease in surfactant concentration at a fixed mixing ratio.of surfactant (fixed Wi). In the presence of a large amount of lipophilic surfactant, the three-phase body is more skewed as is shown in Figure 2. Therefore, it is meaningless to estimate the hydrophile-lipophile balance (HLB) of commercial surfactant by measuring the threephase temperature or PIT (phase inversion temperature in emulsions) at one composition. A microemulsion phase separates from a water phase at the left-hand boundary of the three-phase body which corresponds to the lower part of the three-phase region in Figure 1. With increasing surfactant concentration, the microemulsion dissolves oil and, finally, merges with the excess oil phase at the righthand boundary. Therefore, it is considered that the microemulsion phase contains equal weights of water and oil at certain composition at each temperature in Figure 2. In other words, there is only one particular three-phase triangle related to the HLB temperature at constant temperature when the surfactant mixingratio ( Wi)is fixed. The HLB temperature is very close to the mid temperature of the three-phase body judging from the phase behavior and ita narrowness. The mid temperature of the threephase body (the broken curve) is regarded to be the HLB temperature in Figure 2. The HLB temperature is a function of composition in a multisurfactant system. We also determined the three-phase behavior as a function of the mixing fraction of oil (R,) at fixed surfactant concentration ( x ) as is shown in Figure 3. With increasing the oil content, the three-phase body goes up to higher temperature. It is suggested from these facts that a mixed surfactant acts as a more hydrophilic surfactant in the presence of a large amount of oil. This tendency is a general phenomenon for a commercial surfactant although there is an exception.5J3J4 At each temperature, a linear relationship almost holds between x / ( l - x) and the water/oil ratio (Row)to form a
%O O3 %
I
h
0 02
0 01
0
0
0.2
0.4
Row Figure 4. Three-phase body in a space of R, and xl(1- x) at constant temperature: (a, top) W1 = W Z= WS = Wr = 0.25; (b, bottom) W1= 0.5, WZ= WS = Wd = 0.167. The broken lines are
calculated by eq 1using Si and S: values.
three-phase body as is shown in Figure 4. The threephase bodies are oriented toward a water apex. The reason will be discussed later. At constant temperature, a microemulsion phase separates from a water phase at the lower boundary whereas the microemulsion and oil phases merge at the oupper boundary. Inside the three-phase body, it is observed that the dissolution of oil in the microemulsion increases with increasing surfactant concentration. Again, when the surfactant mixing ratio is fixed, only one particular three-phase triangle exists at each temperature. As described later, the linearity of the three-phase shape in Figure 4 also supports this idea. Effect of Temperature on the Monodisperse Solubilities in Excess Oil Phases. The three-phase behavior is influenced by the distribution of each surfactant between microemulsion and excess oil phases.5 In the midst of the three-phase body, the excess oil phase contains monodisperse surfactant.6 I t is known that the property of solubilized water or oil in aggregates is similar to that
3348 Langmuir, Vol. 9, No. 12, 1993
of bulk water or oil when the solubilizationis large.22Hence, it is considered that the solubility of surfactant in the oil phase is similar to that in micro-oil domain in the microemulsion. The effect of temperature on the solubilities of each surfactant, Si, in the excess oil phase forming the threephase body was measured at Row= 0.5 in the midst of the three-phase body (the broken curve) in Figure 2 and the results are shown in Figure 5. The data at 35 O C in Figure 5a were measured at Row= 0.41 because there is no threephase region at Row = 0.5. However, the error may be small since there is only one particular triangle at constant temperature. As described in the former section, the mid temperature of the three-phase body is regarded as the HLB temperature. Si means the weight fraction of the ith surfactant in the excess oil. The solubilities of hydrophilic surfactant increase monotonically, whereas that of lipophilic surfactant decreases at higher temperature. As a result, the total solubility (SI+ Sp + Sa + Sq) decreases with the rise in temperature as is shown in Figure 5. This tendency is also observed in a commercial surfactant system including more than four surfactants.lg This compensating effect is remarkable in comparison with the change in monodisperse solubility of a single surfactant. Monodisperse solubility of nonionic surfactant in an oil phase in a singlesurfactant system monotonically increases with increasing t e m p e r a t ~ r e . Note ~ ~ ? that ~ ~ the ratios of Si (SilCSj) values approach the original mixing fractions, Wi,at the highest temperature of the three-phase region (the top of the threephase body in Figure 2). We also measured Si values at different Rowin the midst of the three-phase body in Figure 3 and the result is shown in Table I. The Si are almost the same values at a fixed temperature and are independent of water/oil ratios or total surfactant concentrations as is shown in Table I. These data also support the existence of only a particular three-phase triangle in which the microemulsion contains equal weights of water and oil in case the surfactant mixing ratio is fixed.
Kunieda and Yamagata 0,04
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Discussion Three-phaseBehavior in a Multisurfactant System. An isotropic surfactant phase (middle-phase microemulsion phase, D)coexists with excess water (W) and oil (0)phases in a three-phase region. The three coexisting phases in the multisurfactant system are schematically shown in Figure 6. Since the cmc's of each surfactant in water are negligibly small, we assume that the excess water phase is pure water. Each surfactant is distributed among the excess oil phase, oil- and water-microdomains, and the surfactant layer at the oil-water interface inside the surfactant phases. The excess oil phase contains no water judging from the former result.l7 It is also assumed that the compositions of the oil and water microdomains inside of the surfactant phase are the same as that in the excess oil and water phases. As described before, when the solubilization is large, the property of solubilized water or oil in microemulsions is similar to that of bulk water or Hence, this assumption is reasonable and the water domain can be regarded as pure water. Consequently, it is assumed that surfactant distributes between excess oil phase, micro-oil domain, and interface a t the oil and water domains inside of the surfactant phase. (22) Kawai, K.; Hamada, K.; Shindo, N.; Konno, K. Bull. Chem. SOC. Jpn. 1992,65, 2715. ( 2 3 ) Saito, H.; Shinoda, K. J. Colloid Interface Sci. 1971, 35, 359.
0 4
20
30
40
50
Temperature/ "C Figure 5. Effect of temperature on the solubilities of RlzEOn (SI),RIZEOI(Sd, RlzEOe (SS), and RIzEO~ (S4) in an excess oil phase in the midst of the three-phase body at each temperature along the broken curve in Figure 2 except the data at 35 O C in Figure 5a: (a, top) WI = W2 = W S= W4 = 0.25; (b, bottom) Wl = 0.5, W Z= W3 = W4 = 0.167. The data at 35 O C were measured at R, = 0.51. 0, B, 0,and 0 indicate SI,Sp, Sa,and S4, respectively. A indicates the h u m of the solubilities of each surfactant.
The monodisperse solubilities of each surfactant in oil is represented by Si, the weight fraction of ith surfactant in the excess oil phase the HLB temperature. The weight fraction of the ith surfactant at the oil-water interface inside of microemulsion is indicated by St. In a whole multisurfactant system, a three-phase body exists at each temperature between the highest HLB temperature for a hydrophilic surfactant and the lowest one for a lipophilic surfactant in a space of temperature and compositions.6 Of course, the three-phase body does not practically appear below the freezing temperature of water. The three-phase
Langmuir, Vol. 9, No. 12, 1993 3349
Mixing of Nonionic Surfactants Three coexisting phases
Bicontinuous structure of microemulsion
water domain oil domain ( S )
lwl
.--
Figure 6. Schematic representation of three coexisting phases in a multisurfactant system at the HLB temperature. The model of "bicontinuous" microemulsion phase is represented on the right-hand side. It is assumed that the excess water phase and the water domain inside of microemulsion are pure water and the compositionsof excess oil phase and oil domain inside of the microemulsion are the same.
0.2 -
0.1
-
Table I. Si Values at Different l'kW temp,OC R, 40.0 0.28 0.50 45.0 0.37 0.50 0.71
S1
s2
1.44 X 9.9 X 103 1.49 X 1CF2 1.02 X 1.23 X 9.6 X 103 1.24 X 10-2 9.7 X 103 1.21 X 9.8 X 103
s 3
o !
s4
4.8 X 103 1.5 X 4.9 X 103 1.9 X 6.0 X 103 2.4 X 5.5 X 103 2.4 X 5.6 X 103 2.1 X
30
103 103 103 103 10-3
body appears in a certain temperature range between the two temperatures if the surfactant mixing ratio is fixed, because the degree of freedom decreases. At constant temperature, there is only one particular three-phase triangle consisting of a surfactant phase which contains equal weights of water and oil, when Wi is fixed. This three-phase triangle is located almost in the midst of the three-phase body at that temperature. Since Si and Si8are the solubility in oil and the mixing fraction at the water-oil interface for ith surfactant in this particular three-phase triangle, three composition points (a water apex, an excess oil phase, and a surfactant mixture whose composition is Sis)determine one plane called the HLB plane5 in a space of compositions at constant temperature. An equation of the plane is obtained by a simple geometrical calculation and is expressed as follows13
,
1
40
50
60
Temperature/ "C 0.6
0.5
0.4
v, '_
0.3
0.2
0.1
0 20
where Rowis the weight fraction of oil in water + oil and x is the weight fraction of total surfactant, respectively. Equation 1 indicates the condition to observe three coexisting phases. The Si and Si8should be independent of water/oil ratios and surfactant concentration at constant temperature as is shown in Table I because only one particular three-phase triangle exists. The surfactant phase just disappears at the highest temperature of the three-phase body (the top of the three-phase region in Figure 2), at which surfactants are considered to dissolve only in the excess oil phase because we regard the water phase as pure water. Therefore, Wi = Si/CSj holds at the top as is shown in Figure 5. By using eq 1, we obtain the mixing fractions of each surfactant, Si8,at the water-oil interface as is shown in Figure 7. It is clear from Figure 7 that hydrophilic surfactant increases at the water-oil interface inside of the surfactant phase with the increase in temperature. From eq 1, the following relation holds
30
40
50
Temperature/ "C Figure 7. Effect of temperature on the mixing fractions of each surfactant at the water-oil interface inside of surfactant phases, S:: (a, top) W1= Wz = W3 = W4 = 0.25; (bybottom) W I= 0.5, W2 = W3 = W4 = 0.167. 0,W, 0 , and 0 indicate Slay Ssa,and Sd8, respectively.
(W, - S,8)(1-
pJ-
s, - s:csj
(W, - S,")(l-
s, - s,"csj
-- ... = A (constant)
(2)
If the three-phase body is mapped in a Rowand x space, the straight line is obtained at constant temperature. This prediction is in good agreement with the experimental results shown in Figure 4. This result also supports that there is only one HLB plane a t constant temperature if the surfactant mixing ratio is fiied. If a three-phase region is narrow enough, the terms in eq 2 can be also obtained from phase equilibria.
Kunieda and Yamagata
3350 Langmuir, Vol.9,No. 12,1993
types of oils, additives, etc. For ethylene glycol-type surfactants, it is considered that A , is proportional to the number of methylene units and A , is proportional to the number of ethylene glycol units. When three-phase bodies appear in single homogeneous surfactant (RmEOJ and a mixture (R,,EO,,, ...,RmiEO,, ...) at the same temperature, both surfactants have the same R values at the water-oil interface. The m and n are the numbers of methylene units and ethylene glycol units in a surfactant, respectively. The molar average hydrocarbon chain length and ethylene glycol units should be equal to those of the homogeneous surfactant. ' Then, the average hydrocarbon chain length and ethylene glycol chain length of the mixed surfactant are equal to the single surfactant. Hence, the following relation is needed to attain the same R for single and mixed surfactants at the same temperature
20
10 10
20
30
40
50
60
70
Temperature / "C Figure 8. 1Tt-S: and ET."BX: as a functionof temperature. The open -marksrepresent kT,J'WS: whereas the filled marks 0,a, Wl= Wz = Ws = W4 = 0.25; 0 , E, WI indicate CT,-X:: = 0.5, Wz Wa = Wd = 0.167.
Weight Additivity of HLB Temperatures. There is a disagreement on the validity of the additivity of HLB temperatures in a multisurfactant s y ~ t e m . ~ J *In J ~ the former section, we obtained the real mixing fractions of each surfactant at the water-oil interface in a surfactant phase as is shown in Figure 7. Hence, we can verify whether the weight additivity or the molar additivity is valid in and CTimBXt this four-surfactant system. The CTiHTIBSt as a function of temperature are shown in Figure 8. The TiHLB is the HLB temperature for ith surfactant in a given water-oil: -42.2 "C for R12E02; 9.8 "C for R12E04; 46.9"C for R12E06; 72.4 "C for R12E08. The X,B is a mole fraction of ith surfactant at the interface calculated from Sia and molecular weights of surfactants. I t is clear from Figure 8 that the weight additivity holds T = CTFLBsr (3) The weight additivity of HLB temperatures is valid in this system of an ethylene glycol-type surfactant mixture. However, there is a tendency to deviate the linearity at lowest and highest temperatures in Figure 8. It is known that B cloud temperature or three-phase temperature tends to saturate at higher temperatures if very hydrophilic surfactant is used.6 Hence, eq 3 would not hold in a very wide temperature range exceedingthe boiling temperature of water. In the following section, the correlation between R theory, HLB number, and HLB temperature is discussed to inquire as to the meaning of the weight additivity. Correlation between R-Theory,HLB Number, and HLB Temperature. The simple form of Winsor's R theory can be written as follows21
R = A,,,JA, (4) where A,, means the hydrophobic interactions between the surfactant layers and oil. A , indicates the hydrophilic interactions between the surfactant layers and water. R is the ratio of both interactions and phase behavior of surfactant in water-oil is decided by the R ratio at the water-oil interface. In the present discussion, we do not consider the additional factors to influence the R ratio:
maMH C m i a M H X : R=-= (5) nbMEO ~nibMEoX,s where M H and MEO are the molecular weights of a methylene group and an ethylene glycol unit, respectively. a and b are the arbitrary constants to combine the interactions and the molecular weights. Xis is the mole fractions of ith surfactant in the mixed surfactant at a water-oil interface. In eq 5, the end OH- group is omitted. Even if the term is included, the following discussion is essentially the same. The a and b can be omitted from the eq 5, which can be deduced to the following equation nMEO + nMEO
-
c n i M E 6 i s
x m i M H X :+ x n i M E o X / (=HLB numbed201 (6) The term on the left-hand side is called the Griffin HLB number.14J5 To be exact, one has to multiply it by 20. Therefore, the basic concepts of the R-theory and HLB number system are identical as for ethylene glycol type surfactants. The term on the right-hand side can be rewritten as follows: (HLB number of the single surfactant)/20 = mMH
niMEO CmiMH
(miMH
+ niMEo)Xt -
+ niMEO x ( m F H
+n,.M~o)x~
C H L B number of ith surfactant X S:/20 = (HLB number of the mixed surfactant)/20 (7) A three-phase body appears at the same temperature in both systems, when both HLB numbers of single and mixed surfactants are equal. It is known that a linear relationship between HLB number in eq 7 and the three-phase temperature holds in a single ethylene glycol-type surfactant system including the same oiL6 Hence, it is clear from eq 7 that eq 3 is theoretically valid for ethylene glycoltype surfactant systems. In the present discussion, it is assumed that the contribution of an ethylene glycol unit to Acw is regarded as the same at any position in a surfactant molecule. This assumption may not be exactlyvalid for a surfactant having an extremely long hydrophilic chain. In fact, the deviation from the weight additivity is observed in the case where the HLB temperature is very high.6
Conclusion The three-phase body is largely skewed to higher temperatures with decreasing total surfactant concentra-
Mixing of Nonionic Surfactants tion at a fixed water/oil ratio in a water/RlzEOdRl2EOJ R12EOs/Rl2EOs/heptane system. The difference in distribution .of each surfactant in microemulsion and oil phases cause this three-phase behavior. The HLB temperature at which a microemulsion phase containing equal weights of water and oil touches the three-phase body expresses the three-phase behavior in a space of temperature and compositions. In the present paper, the mid temperature of three-phase body is regarded as the HLB temperature. At constant temperature, only one threephase triangle of this condition exists in a multisurfactant system if the surfactant mixingratio is fixed. We proposed an equation of the HLB temperature as a function of total surfactant concentration, water/oil ratio, and surfactant mixingratio according to the geometrical relation in phase equilibria, assuming that the composition of excess oil phase is the same as that in oil domain inside of the
Langmuir, Vol. 9, No. 12,1993 3351
microemulsion. By applying the equation to the real phase behavior, we can calculate the mixing fractions of each surfactant a t the water/oil interface inside of the microemulsion, which cannot be directly measured. The HLB temperature is directly related to the mixing ratio of surfactant at the water-oil interface inside of the microemulsion phase. The weight additivity of the HLB temperature holds in a certain temperature range. The meaning of the weight additivity is related to the concepts of R theory and Griffin’s HLB number.
Acknowledgment. Financial support by the Ministry of Education, Science, and Culture (Japan) (Grant-inAid, No. 03453005) is gratefully acknowledged. The authors wish to thank Mr. M. Akimara (Nihon Surfactant Co.) for supplying homogeneous surfactants.
