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Synergism in binary mixtures of surfactants
Synergism in Binary Mixtures of Surfactants VIII. Effect of the Hydrocarbon in Hydrocarbon/Water Systems MILTON J. ROSEN AND DENNIS S. M U R P H Y Department of Chemistry, Brooklyn College, City University of New York, Brooklyn, New York 11210 Received March 4, 1988; accepted June 22, 1988 The surfactant mixture CI2H25SO~Na+-CI2H25N+(CH2CrH~)(CH3)CH2COO- (CI2BMG) was investigated at various hydrocarbon/water interfaces. The hydrocarbons used were hexadecane, dodecane, heptane, cyclohexane, heptamethylnonane, isooctane, and toluene. Using nonideal solution theory, the molecular interaction parameters for mixed monolayer and mixed micelle formation, 3[L and 3LML, respectively, and parameters determining synergism in interfacial tension reduction efficiency, mixed micelle formation, and interfacial tension reduction effectiveness were calculated. It was found that, for this surfactant mixture, the replacement of air by a hydrocarbon as the second phase against water reduced molecular interaction in the mixed monolayer or mixed micelle and reduced synergism in interfacial tension reduction efficiency, mixed micelle formation, and interfacial tension reduction effectiveness. © 1989AcademicPress,Inc.
INTRODUCTION
In a recent publication (1), we extended the nonideal solution theory for binary mixtures of surfactants (2-4) to liquid-liquid systems at low surfactant concentrations. The degree of interaction between two surfactants in mixed monolayer or mixed micelle formation in a liquid-liquid system can be measured by calculating the molecular interaction parameters 3[L and 3LML,respectively, from inteffacial tension measurements. For these calculations, the interfacial tension-log total concentration curves of the two individual pure suffactants and at least one mixture of them are required. Either when (i) the phase volume ratio, ¢ ( = V b / V w where Vb and Vw are the volumes of the nonaqueous and aqueous phases, respectively), is kept constant in all solutions used to evaluate 3[L and 3ML and ( ii ) the partition coefficient, K ( = Cb / Cw), of each suffactant remains essentially unchanged when the two surfactants are mixed, or when K4~ ~ 1, then Eqs. [ 1] and [2 ] can be used to
calculate ~ L (Eq. [1] is solved numerically for Xl,l, which is used in Eq. [2 ] to evaluate 3[L). These conditions are met in the system investigated here. ( X l ,I ) 21n ( C1 ,t/C°l,tXl ,I )
(1 - Xl,021n[Cz,t/C°t(l
- Xl,x)]
= 1
[1]
3[L = ln( Cl"t/ C°l'tXI'I) (1 - X I , I ) 2
'
[2]
where XI,I is the mole fraction of surfactant 1 in the mixed surfactant in the interfacial region; Cl.t and C2.t are the total molar concentrations (in the two-phase system) of surfactams 1 and 2, respectively, in their mixture to produce a given interfacial tension (reduction); and C°t and C°t are the total molar concentrations of individual surfactants 1 and 2, respectively, to produce the same interfacial tension (reduction). Analogous equations hold for the calculation of 3LMLusing the critical micelle concentrations of the individual surfactants and their mixture. 208
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Journalof Colloidand InterfaceScience,Vol. 129,No. 1, April 1989
209
SYNERGISM IN SURFACTANT MIXTURES
Synergism in interfacial tension reduction efficiency is present when a mixture of two surfactants can yield an interfacial tension (reduction) at a concentration less than that required of either individual surfactant. When the conditions of phase volume ratio and partition coefficient mentioned above are met, synergism in this respect exists when (1)
(ii) [fl~_LI > Iln C ol,t/ C 02,t I.
M,.
Analogous conditions hold for synergism in mixed micelle formation. The mole fraction ofsurfactant 1 in the total surfactant in the entire system at the point of maximum synergism in interfacial reduction efficiency is given by =
In(C°l,t/"Co2,t]~ "~ # ~ L 23~L
[3]
When C~,t o < C2,t o (as is the convention chosen in this paper), a~' > 0.5. The minimum total surfactant concentration required to produce a given interfacial tension (reduction) is given by Cl2,t,min ~- C°,t
X expl~[L[t3~L- ln( C°'t/ C°'t) ]
[4]
Analogous equations hold for calculation of a,,M and C~2,t,n~in, M the corresponding quantifies for mixed micelle formation. Synergism in interfacial tension reduction effectiveness is present when the following conditions are satisfied (1):
]/3~L -- /3LML[ >
C12,t =
CMC°,t + CMC°t tiME 2 ' • exp --~--,
[6]
and the lowest interfacial tension attainable at the CMC of any mixture of the two components is given by , 0 Tcmc, 12,t = "Ycmc,l(2),l -S
a -- 3 ~ D / 4 , 1(2)(3LL
[7]
where 3'cmo, 0 l(2),t is the interfacial tension in a pure surfactant 1 (or 2) system at the CMC for the entire system, and S~(2) is the slope of the 3q vs In C°t (or In C°,t) plot for pure surfactant 1 (or 2). Equation [ 7 ] works best when the pure surfactant having the larger (negative) slope is used. In the present paper, we investigate the effect of different hydrocarbon phases on synergism in a zwitterionic/anionic binary surfactant mixture. The surfactants used were C12 H25 SO~ Na + - Cl2 H25 N + (CH2 C6 Hs) (CHa)CH2COO- (C~2BMG); the hydrocarbons used were hexadecane, dodecane, heptane, cyclohexane, heptamethylnonane, isooctane, and toluene.
Materials
(ii) 3[L -- 3LML< 0 0 [~CMC, I,t 0 -- ']eCMC,2,t/S[ ,
and ~/CMC.2,t 0 are the interfacial tensions at the critical micelle concentrations for the entire pure surfactant 1 and 2 systems, respectively, and S is the slope of the -y~-ln Ct plot of the individual surfactant having the larger (negative) value. w h e r e ~tOMc, l,t
[5]
EXPERIMENTAL
(i) 3~_L < 0
(iii)
CMC°,t a *'E = CMCOt + CMCO,t,
the critical micelle concentration for the entire system at this point is given by
(i) 3~c < 0
a*
The mole fraction ofsurfactant 1 in the total mixed surfactant solution at the point of maximum synergism (when it is assumed that X = 0.5 at this point) in interfacial reduction effectiveness is given (1) by
Sodium dodecanesulfonate (C1zH25SO~Na + > 99% purity; Research Plus, Bayonne, N J) and N-dodecyl- N-benzyl- N-methylglycine (CI2HEsN+(CH2C6Hs)(CHa)CH2CO0
-)
(5) were used. Before being used for interfacial tension measurements, aqueous solutions of the surfactant (in water that had first been deionized and then distilled twice, the last time through Journal of Colloid and Interface Science, Vol. 129,No.
1, April 1989
210
ROSEN AND MURPHY
a 1-m-high Vigreaux column with quartz condenser and receiver) were further purified by repeated passage (6) through minicolumns of octadecylsilanized silica gel to remove any traces of impurities more interfaciaUy active than the parent compound. The hydrocarbons used were hexadecane, heptamethylnonane, >99% (Humphrey); dodecane, isooctane, >99% (Aldrich); heptane, spectro grade (Eastman); cyclohexane, toluene, certified A.C.S. spectranalyzed (Fisher Scientific). The UV absorbance of each of the saturated hydrocarbons was measured at 255 nm against a blank of 95% ethanol when received. If the absorbance was less than 0.015, the saturated hydrocarbon was used as received. If the absorbance was greater than 0.015, the saturated hydrocarbon was passed through a 31 × 3.4cm column (Fisher and Porter Co.) of silica gel 922 (Wills Corp. ) that had been heated at
120°C for 3 h before use, until the absorbance fell below 0.015. The toluene was used as received.
Interfacial Tension Measurements All interfacial tension measurements were made by the spinning drop technique using a Model 500 spinning drop interfacial tensiometer (University of Texas). The solutions to be measured were allowed to stand for 2 weeks after which equilibrium was achieved (7). Shaking was avoided to prevent emulsion formation. K~ Va/ues The ~b value was kept the same for all the experiments performed, at ¢ = 0.025. The partition coefficient of C~2BMG was previously measured (1) to be 8.62 × 10 -3 with heptane as the oil. This yields a K~b value of
22
20 D
-
15
E Z E
~7 IO
.
.
-2.7
.
r ~
.
-2.6
-2.5
-2.4
-2.5
- 21~ log C t
i -2.1
"~l -2.0
, -I.9
J,
-I.8
FIG. l. Interfacialtension vs log total surfactantconcentrationfor Cl2SO3Na at 25.0°C. Hydrocarbon phase: [] hexadecane,® heptamethylnonane,A dodecane,--12t---isooctane,--®-- heptane, --A-- cyclohexane, and xytoluene. Journal of Cotloid and Interface Science, Vol. 129,
No.
1, April 1989
211
SYNERGISM IN SURFACTANT MIXTURES ,.
17
15
IC
TE z E
5
- 4 . 6I
- 4 , 41
-
4 2.
.
4 0.
.
.
3.8
.
. 3 6. 34 log Clz,t
-
3 2.
I)
-
30 .'- ~ 2 4 .
.
.
2.2
2 [0 .
- t8 .
FIG. 2. Interfacial tension vs log total surfactant concentration for Cj2BMG-CI2SO3Na mixtures at 25.0°C and ~t~,e = 0.945. Hydrocarbon phase: [] hexadecane, ® heptamethylnonane, & dodecane, - - [ ] - - isooctane, - - ® - - heptane, - - & - - cyclohexane, and ~ toluene. ~3CI2SO3Na at 25.0°C; hydrocarbon phase, cyclohexane. (~ C~2BMG at 25.0°C; hydrocarbon phase, cyclohexane.
2.16 × 10 -4. C 1 2 S O ~ N a + partitions into oil to a much smaller degree and thus the above condition of Kq~ ~ 1 is met in all systems investigated here. RESULTS AND DISCUSSION
Interaction Parameters On the basis of interfacial tension data (Figs. 1-3) (the Tl-lOg Ct plots for pure C]2BMG have been published previously (8)) and using Eqs. [ 1], [ 2 ], and their analogs for mixed micelle formation,/~[L and ~L~Lvalues at 25.0°C were calculated and appear in Table 1. As found previously (1), all the values are slightly less negative in the hydrocarbon/water systems than in the water/air system. This is attributed to the hydrocarbon molecules intercalating between the hydrophobic groups of
the surfactant molecules at the interface and in the miceUes, increasing the distance between them as compared to the mixture in the water/ air system, and consequently decreasing interaction between them. The variation of the interaction for the hydrocarbon/water systems is slight, except for the toluene/water system which shows a marked decrease in interaction both at the interface and in the micelles. The former effect is attributed to a large increase in the area per surfactant molecule (this occurs in both the pure and the mixed surfactant systems); the latter is attributed to solubilization of the toluene molecules in the palisade layer (9, 10) of the micelles (which results in larger distances between the surfactant molecules and a less negative ~LMLvalue). Although the variation in the interaction parameters among the saturated hydrocarbon/water systems is slight, Journal of Colloid and Interface Science, V o l .
1 2 9 , N o . 1, A p r i l 1 9 8 9
212
ROSEN AND MURPHY
T
E z E
IO
I
-3.6
|
-3.4
-3.2
-3.0
-2.8
-2.6
-2.4
-2.2
log C l I , !
FIG. 3. Interfacial tension vs log total surfactant concentration for CI2BMG-CI2SO3Na mixtures at 25.0°C and a~ta~ne = 0.0277. Hydrocarbon phase: [] hexadecane, @ heptamethylnonane, A dodecane, - - [ ] - - isooctane, - - ® - - heptane, - - A - - cyclohexane, and ~7 toluene.
it appears that the larger the cohesive energy density, 6, of the hydrocarbon, and thus the smaller its tendency to penetrate an interfacial film, the more negative is the ~[L value. Thus, hexadecane and cyclohexane which have larger ~ values than isooctane or heptane yield #[L values that are more negative. No such trend is observed for the #L~Lvalues.
Interfacial Tension Reduction Efficiency As indicated by the data in Table I, all of the systems met the conditions for this type of synergism, except the toluene/water system. Conditions at the points of maximum synergism are listed in Table II. The O/~etain e values in the hydrocarbon/water systems are all greater than those in the air/water system. This follows from Eq. [ 3 ] and the data in Table I, since as ln(C°t/C°t) --~ ~ L , C~* --~ 1, and in the hydrocarbon/water systems which show Journalof Colloidand InterfaceScience,Vol.
129, No. 1, April 1989
synergism in this respect, In (C °t/C°t) values are closer to their respective ~ L values than those in the air/water system. The quantity (C°t - Cl2,t,min)/C°,t ( = 1 o - C12,t,mi,/C1,t), where C°t < C°t, is a measure of the degree of synergism; the larger this quantity, the larger the synergistic effect. This quantity is related to Eq. [4], which determines the value of the Cl2,t,min/f°,t ratio. As the difference between B~L and ln(C°t/C°t) becomes larger, the Cl2,t,min/f°,t ratio decreases and the degree of synergism increases. As indicated by the data in Table I and shown in Table II, the degree of synergism is smaller for the hydrocarbon/water systems than for the air/water system. The hexadecane/water system has the largest difference between/~[L and In (C°t/C°t) and therefore the largest degree of synergism of the hydrocarbon/water systems studied. For the straight-chain hydrocarbon phase systems, the synergistic effect in
213
SYNERGISM IN SURFACTANT MIXTURES TABLE I Interaction Parameters for Mixed Monolayer and Mixed Micelle Formation ~ Second phase (against water)
fl~.t,
ln(C°,dC~,t)
Heptane Dodecane Hexadecane Isooctane Heptamethylnonane Cyclohexane Toluene Air b
-4.7 -4,8 -5.2 -4.4 -4.4 -5.0 -3.2 -5.7
-4.2 -4.0 -4.0 -4.2 -4.2 -4.5 -4.6 -4.0
,8~c
-4.0 -3.6 -4.0 -4.0 -3.4 -4.2 -2.1 -5.0
In(CMC~,dCMC%)
-3.1 -3.1 -3.0 -3.1 -3.0 -3.3 -3.3 -3,0
At 25.0°C. b Data from Ref. (3). this respect b e c o m e s weaker as the chain becomes shorter.
Mixed Micelle Formation All o f the systems m e t the conditions for synergism in this respect, except the t o l u e n e / water system. D a t a appear in Table III. The ,,M abetai,e values, like the o/betaine* values, are all greater in the h y d r o c a r b o n / w a t e r systems than in the a i r / w a t e r system. This follows f r o m the equation analogous to [3 ] for mixed micelle formation and the data in Table I, since as In(CMC°,t/CMC°,t ) .-~ tiME, a *'M --~ 1. The quantity (CMC°,t - C M 0l,t 12,t,min ) / C M C
(=1
M 0 -- Cl2,t,min/CMfl,t), where CMC°,t, < C M C ° t , is a measure o f the degree o f synergism in this respect; the larger this quantity the larger the synergistic effect. This quantity is related to the equation for mixed micelle formation analogous to Eq. [4]. As the difference between flLML and l n ( C M C ° J C M f ° , t ) becomes larger, the degree o f synergism increases because o f the decrease in the M 0 Cl2,t,min/CMCl,t ratio. As was true for interfacial tension reduction efficiency, the l n ( C M C ° t / C M C 2 ° t ) values for the hydrocarb o n / w a t e r systems are m o r e negative and the fl LMLvalues are less negative than those for the air/water system (Table I). The degree o f
TABLE II Synergism in Interfacial Tension Reduction Efficiencya Cj2,~mi~× 104 (M) Second phase (against water)
a~.~i,~
(Calcd.)
Heptane Dodecane Hexadecane Isooctane Heptamethylnonane Cyclohexane Air c
0.95 0.92 0.88 0.98 0.97 0.95 0.85
1.11 1.42 1.67 1.14 1.46 0.76 1.7s
(Exptl.)b
(1 - G2,~.~./C%)
1.07
0.01 0.03 0.07 0.01 0.01 0.01 0.12
1.44 1.66
1.10 1.38 0.92 1.7o
At 25.0°C. b At a~tai,~ = 0.945. c Data from Ref. (3). Journal of Colloid and Interface Science, Vol. 129, No. 1, April 1989
214
ROSEN A N D M U R P H Y TABLE III Synergism in Mixed Micelle Formation ~ C~.t.~, × 104 (M) Second phase (against water)
a ~*.M i.e
(Caled.)
(Exptl.) t'
(1 -- C~2,t~o/CMC M o~,t)
Heptane Dodecane Hexadecane Isooctane Heptamethylnonane Cyclohexane Air ~
0.89 0.93 0.87 0.89 0.94 0.89 0.80
4.0 4.4 4.6 4.0 4.8 3.4 4.5
3.2 3.7 4.3 3.3 3.8 3.0 4.0
0.05 0.02 0.08 0.04 0.01 0.05 0.18
At 25°C. b At a~taine = 0.945. Data from Ref. (3).
synergism is consequently smaller than that for the air/water system, and this is shown in Table III. In contrast to that observed in synergism in interfacial tension reduction efficiency no correlation of the synergistic strength in this respect with length of the straight-chain alkane is observed.
lnterfacial Tension Reduction Effectiveness All of the systems studied met the conditions for synergism in this respect. However,
although the toluene/water system met the conditions, no synergism was found experimentally at the predicted mole fraction. Data appear in Table IV. The ot~ine values in the hydrocarbon/water systems are both above (0.048 in the heptamethylnonane/water system) and below (0.037 in the cyclohexane/ water system) the value of 0.047 for the air/ water system but the variation is not great. Thus, the presence of the hydrocarbon instead of air as the second phase against water does not affect the a~'~tZai,evalue significantly. There
TABLE IV Synergism in Interfacial Reduction Effectivenessa 3'*~a2,~ (raN m -l) Second phase (against water)
a*~.n©
C M2.~m*n × 103 (M)
(Calcd.)
(Exptl.) b
~x-,/(mN m -1)
Heptane Dodecane Hexadecane Isooctane Heptamethylnonane Cyclohexane Toluene Air a
0.042 0.044 0.047 0.042 0.048 0.037 0.038 0.047
1.85 2.05 1.96 1.83 2.14 1.69 1.71 |.69
0.6 0.7 1.4 1.3 1.1 0 0 31.6
1.1 1.8 1.4 1.0 1.3 0.1 ~ 29.8
0.7 1.0 2.1 1.0 1.5 0.9 -4.9
At 25.0°C. b At a~t~i.o = 0.0513. c Data at a~t~i.e = 0.945 are within experimental error. a Data from Ref. (3).
Journal of Colloid and Interface Science, V01. 129, No. 1, April t 989
SYNERGISM IN SURFACTANT MIXTURES
is also not much effect on the C~;*m~nvalue. Calculated and experimental values of 3'cmc,12,t a r e i n g o o d
(iii) Synergism decreases in the order longchain alkanes > short-chain alkanes.
agreement.
The degree of synergism in this respect is measured by the (3"°me,lowest- - 3" crrlc, * 12,t = A 3 " ) / 3'¢0mc,~owestratio. The larger the A3' value the larger the synergistic effect. A3" is related to [7], viz. A3" = S l ( 2 ) ( f l ~ L --
APPENDIX: NOMENCLATURE
a*, a*'M, a ~'E
flMC)/4.
From this relation it is observed that A3" becomes larger when S~(2) becomes more negative and/or (/3~L -- /3LML)becomes more negative. As shown in Table IV, A3, is smaller in all the hydrocarbon/water systems (which exhibit synergism) than in the air/water system. The hexadecane/water system has the largest A3" value of the hydrocarbon/water systems studied. As the alkane length is shortened in the straight-chain alkane series, the A3, value becomes progressively smaller. It is interesting to note that A3" is related to the minimum work necessary to create a given interfacial area between two phases. This work can be defined as
/~-L, /3LML
0 C~,t, C°,t
Cl,t, C2,t
W = 3'i" AREA, from which it is seen that a larger A3" value results in a larger reduction in the amount of work necessary to produce a given interfacial area. CONCLUSIONS
(i) The values of the interaction parameters for mixed monolayer and mixed micelle formation,/3 [L and/3 LML,respectively, in this surfactant mixture are less negative in the hydrocarbon/water systems than in the air/water system. (ii) In all the types of synergism investigated, the presence of a hydrocarbon phase instead of air decreases synergism. When toluene is the hydrocarbon phase, no synergism is obtained.
215
mole fraction of surfactant 1 in the total surfactant in the system at the point of maximum synergism in interfacial tension reduction efficiency, mixed micelle formation, and interfacial tension reduction effectiveness, respectively. molecular interaction parameters for mixed monolayer formarion at the liquid/liquid interface and for mixed micelle formation in a liquid/ liquid system, respectively. total molar concentrations (in the two-phase system) of individual surfactants 1 and 2, respectively, required to produce a given interfacial tension (reduction). total molar concentrations of surfactants 1 and 2, respectively, in their mixture to produce the same interfacial tension (reduction) as C°,t
(c°A. C12,t,mi., M C12,t, mi.,
The concentration of total surfactant in the mixed, twoC~'t*.min phase surfactant system at the point of maximum synergism in interfacial tension reduction efficiency, mixed micelle formation, and interfacial tension reduction effectiveness, respectively. CMC°,t, total molar concentrations ofinCMC°t dividual surfactants 1 and 2, respectively, at their respective CMCs in the two-phase system. 3'C0MC,Lt, interfacial tension values of ino 3"CMC,2,t dividual surfactants 1 and 2, respectively, at their CMCs. Journal of Colloid and Interface Science, Vol. 129,No. 1, April 1989
216 "Y~MC,12,t
A'y
K
Xl,i
ROSEN AND MURPHY the lowest inteffacial tension attainable at the C M C o f a n y mixture o f the two c o m p o nents. the difference between the lower interfacial tension value o f either individual surfactant (i.e., 0 0 ~CMC, I,t o r ~YCMC,2,t) at its C M C and ~/~MC,12,t. the partition coefficient o f either surfactant between the aqueous and n o n a q u e o u s phases, defined as the concentration in the n o n a q u e o u s phase divided by the concentration in the aqueous phase. t h e v o l u m e o f the n o n a q u e o u s phase divided by the v o l u m e o f the aqueous phase. the slopes o f the ~/~ vs In C ° t (In C2,t, 0 respectively) plots. the m o l e fraction o f surfactant 1 in the total surfactant in the mixed interfacial m o n o l a y e r in the two-phase system.
Journal of Colloid and Interface Science, Vol. 129, No. 1, April 1989
,:,~, ACKNOWLEDGMENTS
This material is based upon work supported by the National ScienceFoundation under Grant CBT-8413162, by PSC-CUNY Research Award Program Grant 66-7273, and by grants from Exxon Research and Engineering, GAF Corp., Shell Development, and Shulton Research. REFERENCES 1. Rosen, M. J., and Murphy, D. S., J. Colloidlnterface Sci. 110, 224 (1986). 2. Hua, X. Y., and Rosen, M. J., J. Colloid Interface Sci. 90, 212 (1982). 3. Rosen, M. J., and Zhu, B. Y., J, ColloidlnterfaceSci. 99, 427 (1984). 4. Zhu, B. Y., and Rosen, M. J., J. Colloid Interface Sci. 99, 435 (1984). 5. Dahanayake, M., and Rosen, M. J., in "Structure/ Performance Relationships in Surfactants" (M. J. Rosen, Ed.), ACS Symposium Series 253. Amer. Chem. Soc., Washington, DC, 1984. 6. Rosen, M. J., J. ColloidlnterfaceSci. 79, 587 (1981). 7. Warr, G. G., Grieser, F., and Healy, T. W., J. Phys. Chem. 87, 4520 (1983). 8. Murphy, D. S., and Rosen, M. J., J. Phys. Chem. 92, 2870 (1988). 9. Mukerjee, P., and Cardinal, J. R., J. Phys. Chem. 82, 1620 (1978). 10. Cardinal, J. R., and Mukerjee, P., J. Phys. Chem. 82, 1614 (1978).
INTRODUCTION
In a recent publication (1), we extended the nonideal solution theory for binary mixtures of surfactants (2-4) to liquid-liquid systems at low surfactant concentrations. The degree of interaction between two surfactants in mixed monolayer or mixed micelle formation in a liquid-liquid system can be measured by calculating the molecular interaction parameters 3[L and 3LML,respectively, from inteffacial tension measurements. For these calculations, the interfacial tension-log total concentration curves of the two individual pure suffactants and at least one mixture of them are required. Either when (i) the phase volume ratio, ¢ ( = V b / V w where Vb and Vw are the volumes of the nonaqueous and aqueous phases, respectively), is kept constant in all solutions used to evaluate 3[L and 3ML and ( ii ) the partition coefficient, K ( = Cb / Cw), of each suffactant remains essentially unchanged when the two surfactants are mixed, or when K4~ ~ 1, then Eqs. [ 1] and [2 ] can be used to
calculate ~ L (Eq. [1] is solved numerically for Xl,l, which is used in Eq. [2 ] to evaluate 3[L). These conditions are met in the system investigated here. ( X l ,I ) 21n ( C1 ,t/C°l,tXl ,I )
(1 - Xl,021n[Cz,t/C°t(l
- Xl,x)]
= 1
[1]
3[L = ln( Cl"t/ C°l'tXI'I) (1 - X I , I ) 2
'
[2]
where XI,I is the mole fraction of surfactant 1 in the mixed surfactant in the interfacial region; Cl.t and C2.t are the total molar concentrations (in the two-phase system) of surfactams 1 and 2, respectively, in their mixture to produce a given interfacial tension (reduction); and C°t and C°t are the total molar concentrations of individual surfactants 1 and 2, respectively, to produce the same interfacial tension (reduction). Analogous equations hold for the calculation of 3LMLusing the critical micelle concentrations of the individual surfactants and their mixture. 208
0021-9797/89 $3.00 Copyright© 1989by AcademicPress,Inc. All fightsof reproductionin any formreserved.
Journalof Colloidand InterfaceScience,Vol. 129,No. 1, April 1989
209
SYNERGISM IN SURFACTANT MIXTURES
Synergism in interfacial tension reduction efficiency is present when a mixture of two surfactants can yield an interfacial tension (reduction) at a concentration less than that required of either individual surfactant. When the conditions of phase volume ratio and partition coefficient mentioned above are met, synergism in this respect exists when (1)
(ii) [fl~_LI > Iln C ol,t/ C 02,t I.
M,.
Analogous conditions hold for synergism in mixed micelle formation. The mole fraction ofsurfactant 1 in the total surfactant in the entire system at the point of maximum synergism in interfacial reduction efficiency is given by =
In(C°l,t/"Co2,t]~ "~ # ~ L 23~L
[3]
When C~,t o < C2,t o (as is the convention chosen in this paper), a~' > 0.5. The minimum total surfactant concentration required to produce a given interfacial tension (reduction) is given by Cl2,t,min ~- C°,t
X expl~[L[t3~L- ln( C°'t/ C°'t) ]
[4]
Analogous equations hold for calculation of a,,M and C~2,t,n~in, M the corresponding quantifies for mixed micelle formation. Synergism in interfacial tension reduction effectiveness is present when the following conditions are satisfied (1):
]/3~L -- /3LML[ >
C12,t =
CMC°,t + CMC°t tiME 2 ' • exp --~--,
[6]
and the lowest interfacial tension attainable at the CMC of any mixture of the two components is given by , 0 Tcmc, 12,t = "Ycmc,l(2),l -S
a -- 3 ~ D / 4 , 1(2)(3LL
[7]
where 3'cmo, 0 l(2),t is the interfacial tension in a pure surfactant 1 (or 2) system at the CMC for the entire system, and S~(2) is the slope of the 3q vs In C°t (or In C°,t) plot for pure surfactant 1 (or 2). Equation [ 7 ] works best when the pure surfactant having the larger (negative) slope is used. In the present paper, we investigate the effect of different hydrocarbon phases on synergism in a zwitterionic/anionic binary surfactant mixture. The surfactants used were C12 H25 SO~ Na + - Cl2 H25 N + (CH2 C6 Hs) (CHa)CH2COO- (C~2BMG); the hydrocarbons used were hexadecane, dodecane, heptane, cyclohexane, heptamethylnonane, isooctane, and toluene.
Materials
(ii) 3[L -- 3LML< 0 0 [~CMC, I,t 0 -- ']eCMC,2,t/S[ ,
and ~/CMC.2,t 0 are the interfacial tensions at the critical micelle concentrations for the entire pure surfactant 1 and 2 systems, respectively, and S is the slope of the -y~-ln Ct plot of the individual surfactant having the larger (negative) value. w h e r e ~tOMc, l,t
[5]
EXPERIMENTAL
(i) 3~_L < 0
(iii)
CMC°,t a *'E = CMCOt + CMCO,t,
the critical micelle concentration for the entire system at this point is given by
(i) 3~c < 0
a*
The mole fraction ofsurfactant 1 in the total mixed surfactant solution at the point of maximum synergism (when it is assumed that X = 0.5 at this point) in interfacial reduction effectiveness is given (1) by
Sodium dodecanesulfonate (C1zH25SO~Na + > 99% purity; Research Plus, Bayonne, N J) and N-dodecyl- N-benzyl- N-methylglycine (CI2HEsN+(CH2C6Hs)(CHa)CH2CO0
-)
(5) were used. Before being used for interfacial tension measurements, aqueous solutions of the surfactant (in water that had first been deionized and then distilled twice, the last time through Journal of Colloid and Interface Science, Vol. 129,No.
1, April 1989
210
ROSEN AND MURPHY
a 1-m-high Vigreaux column with quartz condenser and receiver) were further purified by repeated passage (6) through minicolumns of octadecylsilanized silica gel to remove any traces of impurities more interfaciaUy active than the parent compound. The hydrocarbons used were hexadecane, heptamethylnonane, >99% (Humphrey); dodecane, isooctane, >99% (Aldrich); heptane, spectro grade (Eastman); cyclohexane, toluene, certified A.C.S. spectranalyzed (Fisher Scientific). The UV absorbance of each of the saturated hydrocarbons was measured at 255 nm against a blank of 95% ethanol when received. If the absorbance was less than 0.015, the saturated hydrocarbon was used as received. If the absorbance was greater than 0.015, the saturated hydrocarbon was passed through a 31 × 3.4cm column (Fisher and Porter Co.) of silica gel 922 (Wills Corp. ) that had been heated at
120°C for 3 h before use, until the absorbance fell below 0.015. The toluene was used as received.
Interfacial Tension Measurements All interfacial tension measurements were made by the spinning drop technique using a Model 500 spinning drop interfacial tensiometer (University of Texas). The solutions to be measured were allowed to stand for 2 weeks after which equilibrium was achieved (7). Shaking was avoided to prevent emulsion formation. K~ Va/ues The ~b value was kept the same for all the experiments performed, at ¢ = 0.025. The partition coefficient of C~2BMG was previously measured (1) to be 8.62 × 10 -3 with heptane as the oil. This yields a K~b value of
22
20 D
-
15
E Z E
~7 IO
.
.
-2.7
.
r ~
.
-2.6
-2.5
-2.4
-2.5
- 21~ log C t
i -2.1
"~l -2.0
, -I.9
J,
-I.8
FIG. l. Interfacialtension vs log total surfactantconcentrationfor Cl2SO3Na at 25.0°C. Hydrocarbon phase: [] hexadecane,® heptamethylnonane,A dodecane,--12t---isooctane,--®-- heptane, --A-- cyclohexane, and xytoluene. Journal of Cotloid and Interface Science, Vol. 129,
No.
1, April 1989
211
SYNERGISM IN SURFACTANT MIXTURES ,.
17
15
IC
TE z E
5
- 4 . 6I
- 4 , 41
-
4 2.
.
4 0.
.
.
3.8
.
. 3 6. 34 log Clz,t
-
3 2.
I)
-
30 .'- ~ 2 4 .
.
.
2.2
2 [0 .
- t8 .
FIG. 2. Interfacial tension vs log total surfactant concentration for Cj2BMG-CI2SO3Na mixtures at 25.0°C and ~t~,e = 0.945. Hydrocarbon phase: [] hexadecane, ® heptamethylnonane, & dodecane, - - [ ] - - isooctane, - - ® - - heptane, - - & - - cyclohexane, and ~ toluene. ~3CI2SO3Na at 25.0°C; hydrocarbon phase, cyclohexane. (~ C~2BMG at 25.0°C; hydrocarbon phase, cyclohexane.
2.16 × 10 -4. C 1 2 S O ~ N a + partitions into oil to a much smaller degree and thus the above condition of Kq~ ~ 1 is met in all systems investigated here. RESULTS AND DISCUSSION
Interaction Parameters On the basis of interfacial tension data (Figs. 1-3) (the Tl-lOg Ct plots for pure C]2BMG have been published previously (8)) and using Eqs. [ 1], [ 2 ], and their analogs for mixed micelle formation,/~[L and ~L~Lvalues at 25.0°C were calculated and appear in Table 1. As found previously (1), all the values are slightly less negative in the hydrocarbon/water systems than in the water/air system. This is attributed to the hydrocarbon molecules intercalating between the hydrophobic groups of
the surfactant molecules at the interface and in the miceUes, increasing the distance between them as compared to the mixture in the water/ air system, and consequently decreasing interaction between them. The variation of the interaction for the hydrocarbon/water systems is slight, except for the toluene/water system which shows a marked decrease in interaction both at the interface and in the micelles. The former effect is attributed to a large increase in the area per surfactant molecule (this occurs in both the pure and the mixed surfactant systems); the latter is attributed to solubilization of the toluene molecules in the palisade layer (9, 10) of the micelles (which results in larger distances between the surfactant molecules and a less negative ~LMLvalue). Although the variation in the interaction parameters among the saturated hydrocarbon/water systems is slight, Journal of Colloid and Interface Science, V o l .
1 2 9 , N o . 1, A p r i l 1 9 8 9
212
ROSEN AND MURPHY
T
E z E
IO
I
-3.6
|
-3.4
-3.2
-3.0
-2.8
-2.6
-2.4
-2.2
log C l I , !
FIG. 3. Interfacial tension vs log total surfactant concentration for CI2BMG-CI2SO3Na mixtures at 25.0°C and a~ta~ne = 0.0277. Hydrocarbon phase: [] hexadecane, @ heptamethylnonane, A dodecane, - - [ ] - - isooctane, - - ® - - heptane, - - A - - cyclohexane, and ~7 toluene.
it appears that the larger the cohesive energy density, 6, of the hydrocarbon, and thus the smaller its tendency to penetrate an interfacial film, the more negative is the ~[L value. Thus, hexadecane and cyclohexane which have larger ~ values than isooctane or heptane yield #[L values that are more negative. No such trend is observed for the #L~Lvalues.
Interfacial Tension Reduction Efficiency As indicated by the data in Table I, all of the systems met the conditions for this type of synergism, except the toluene/water system. Conditions at the points of maximum synergism are listed in Table II. The O/~etain e values in the hydrocarbon/water systems are all greater than those in the air/water system. This follows from Eq. [ 3 ] and the data in Table I, since as ln(C°t/C°t) --~ ~ L , C~* --~ 1, and in the hydrocarbon/water systems which show Journalof Colloidand InterfaceScience,Vol.
129, No. 1, April 1989
synergism in this respect, In (C °t/C°t) values are closer to their respective ~ L values than those in the air/water system. The quantity (C°t - Cl2,t,min)/C°,t ( = 1 o - C12,t,mi,/C1,t), where C°t < C°t, is a measure of the degree of synergism; the larger this quantity, the larger the synergistic effect. This quantity is related to Eq. [4], which determines the value of the Cl2,t,min/f°,t ratio. As the difference between B~L and ln(C°t/C°t) becomes larger, the Cl2,t,min/f°,t ratio decreases and the degree of synergism increases. As indicated by the data in Table I and shown in Table II, the degree of synergism is smaller for the hydrocarbon/water systems than for the air/water system. The hexadecane/water system has the largest difference between/~[L and In (C°t/C°t) and therefore the largest degree of synergism of the hydrocarbon/water systems studied. For the straight-chain hydrocarbon phase systems, the synergistic effect in
213
SYNERGISM IN SURFACTANT MIXTURES TABLE I Interaction Parameters for Mixed Monolayer and Mixed Micelle Formation ~ Second phase (against water)
fl~.t,
ln(C°,dC~,t)
Heptane Dodecane Hexadecane Isooctane Heptamethylnonane Cyclohexane Toluene Air b
-4.7 -4,8 -5.2 -4.4 -4.4 -5.0 -3.2 -5.7
-4.2 -4.0 -4.0 -4.2 -4.2 -4.5 -4.6 -4.0
,8~c
-4.0 -3.6 -4.0 -4.0 -3.4 -4.2 -2.1 -5.0
In(CMC~,dCMC%)
-3.1 -3.1 -3.0 -3.1 -3.0 -3.3 -3.3 -3,0
At 25.0°C. b Data from Ref. (3). this respect b e c o m e s weaker as the chain becomes shorter.
Mixed Micelle Formation All o f the systems m e t the conditions for synergism in this respect, except the t o l u e n e / water system. D a t a appear in Table III. The ,,M abetai,e values, like the o/betaine* values, are all greater in the h y d r o c a r b o n / w a t e r systems than in the a i r / w a t e r system. This follows f r o m the equation analogous to [3 ] for mixed micelle formation and the data in Table I, since as In(CMC°,t/CMC°,t ) .-~ tiME, a *'M --~ 1. The quantity (CMC°,t - C M 0l,t 12,t,min ) / C M C
(=1
M 0 -- Cl2,t,min/CMfl,t), where CMC°,t, < C M C ° t , is a measure o f the degree o f synergism in this respect; the larger this quantity the larger the synergistic effect. This quantity is related to the equation for mixed micelle formation analogous to Eq. [4]. As the difference between flLML and l n ( C M C ° J C M f ° , t ) becomes larger, the degree o f synergism increases because o f the decrease in the M 0 Cl2,t,min/CMCl,t ratio. As was true for interfacial tension reduction efficiency, the l n ( C M C ° t / C M C 2 ° t ) values for the hydrocarb o n / w a t e r systems are m o r e negative and the fl LMLvalues are less negative than those for the air/water system (Table I). The degree o f
TABLE II Synergism in Interfacial Tension Reduction Efficiencya Cj2,~mi~× 104 (M) Second phase (against water)
a~.~i,~
(Calcd.)
Heptane Dodecane Hexadecane Isooctane Heptamethylnonane Cyclohexane Air c
0.95 0.92 0.88 0.98 0.97 0.95 0.85
1.11 1.42 1.67 1.14 1.46 0.76 1.7s
(Exptl.)b
(1 - G2,~.~./C%)
1.07
0.01 0.03 0.07 0.01 0.01 0.01 0.12
1.44 1.66
1.10 1.38 0.92 1.7o
At 25.0°C. b At a~tai,~ = 0.945. c Data from Ref. (3). Journal of Colloid and Interface Science, Vol. 129, No. 1, April 1989
214
ROSEN A N D M U R P H Y TABLE III Synergism in Mixed Micelle Formation ~ C~.t.~, × 104 (M) Second phase (against water)
a ~*.M i.e
(Caled.)
(Exptl.) t'
(1 -- C~2,t~o/CMC M o~,t)
Heptane Dodecane Hexadecane Isooctane Heptamethylnonane Cyclohexane Air ~
0.89 0.93 0.87 0.89 0.94 0.89 0.80
4.0 4.4 4.6 4.0 4.8 3.4 4.5
3.2 3.7 4.3 3.3 3.8 3.0 4.0
0.05 0.02 0.08 0.04 0.01 0.05 0.18
At 25°C. b At a~taine = 0.945. Data from Ref. (3).
synergism is consequently smaller than that for the air/water system, and this is shown in Table III. In contrast to that observed in synergism in interfacial tension reduction efficiency no correlation of the synergistic strength in this respect with length of the straight-chain alkane is observed.
lnterfacial Tension Reduction Effectiveness All of the systems studied met the conditions for synergism in this respect. However,
although the toluene/water system met the conditions, no synergism was found experimentally at the predicted mole fraction. Data appear in Table IV. The ot~ine values in the hydrocarbon/water systems are both above (0.048 in the heptamethylnonane/water system) and below (0.037 in the cyclohexane/ water system) the value of 0.047 for the air/ water system but the variation is not great. Thus, the presence of the hydrocarbon instead of air as the second phase against water does not affect the a~'~tZai,evalue significantly. There
TABLE IV Synergism in Interfacial Reduction Effectivenessa 3'*~a2,~ (raN m -l) Second phase (against water)
a*~.n©
C M2.~m*n × 103 (M)
(Calcd.)
(Exptl.) b
~x-,/(mN m -1)
Heptane Dodecane Hexadecane Isooctane Heptamethylnonane Cyclohexane Toluene Air a
0.042 0.044 0.047 0.042 0.048 0.037 0.038 0.047
1.85 2.05 1.96 1.83 2.14 1.69 1.71 |.69
0.6 0.7 1.4 1.3 1.1 0 0 31.6
1.1 1.8 1.4 1.0 1.3 0.1 ~ 29.8
0.7 1.0 2.1 1.0 1.5 0.9 -4.9
At 25.0°C. b At a~t~i.o = 0.0513. c Data at a~t~i.e = 0.945 are within experimental error. a Data from Ref. (3).
Journal of Colloid and Interface Science, V01. 129, No. 1, April t 989
SYNERGISM IN SURFACTANT MIXTURES
is also not much effect on the C~;*m~nvalue. Calculated and experimental values of 3'cmc,12,t a r e i n g o o d
(iii) Synergism decreases in the order longchain alkanes > short-chain alkanes.
agreement.
The degree of synergism in this respect is measured by the (3"°me,lowest- - 3" crrlc, * 12,t = A 3 " ) / 3'¢0mc,~owestratio. The larger the A3' value the larger the synergistic effect. A3" is related to [7], viz. A3" = S l ( 2 ) ( f l ~ L --
APPENDIX: NOMENCLATURE
a*, a*'M, a ~'E
flMC)/4.
From this relation it is observed that A3" becomes larger when S~(2) becomes more negative and/or (/3~L -- /3LML)becomes more negative. As shown in Table IV, A3, is smaller in all the hydrocarbon/water systems (which exhibit synergism) than in the air/water system. The hexadecane/water system has the largest A3" value of the hydrocarbon/water systems studied. As the alkane length is shortened in the straight-chain alkane series, the A3, value becomes progressively smaller. It is interesting to note that A3" is related to the minimum work necessary to create a given interfacial area between two phases. This work can be defined as
/~-L, /3LML
0 C~,t, C°,t
Cl,t, C2,t
W = 3'i" AREA, from which it is seen that a larger A3" value results in a larger reduction in the amount of work necessary to produce a given interfacial area. CONCLUSIONS
(i) The values of the interaction parameters for mixed monolayer and mixed micelle formation,/3 [L and/3 LML,respectively, in this surfactant mixture are less negative in the hydrocarbon/water systems than in the air/water system. (ii) In all the types of synergism investigated, the presence of a hydrocarbon phase instead of air decreases synergism. When toluene is the hydrocarbon phase, no synergism is obtained.
215
mole fraction of surfactant 1 in the total surfactant in the system at the point of maximum synergism in interfacial tension reduction efficiency, mixed micelle formation, and interfacial tension reduction effectiveness, respectively. molecular interaction parameters for mixed monolayer formarion at the liquid/liquid interface and for mixed micelle formation in a liquid/ liquid system, respectively. total molar concentrations (in the two-phase system) of individual surfactants 1 and 2, respectively, required to produce a given interfacial tension (reduction). total molar concentrations of surfactants 1 and 2, respectively, in their mixture to produce the same interfacial tension (reduction) as C°,t
(c°A. C12,t,mi., M C12,t, mi.,
The concentration of total surfactant in the mixed, twoC~'t*.min phase surfactant system at the point of maximum synergism in interfacial tension reduction efficiency, mixed micelle formation, and interfacial tension reduction effectiveness, respectively. CMC°,t, total molar concentrations ofinCMC°t dividual surfactants 1 and 2, respectively, at their respective CMCs in the two-phase system. 3'C0MC,Lt, interfacial tension values of ino 3"CMC,2,t dividual surfactants 1 and 2, respectively, at their CMCs. Journal of Colloid and Interface Science, Vol. 129,No. 1, April 1989
216 "Y~MC,12,t
A'y
K
Xl,i
ROSEN AND MURPHY the lowest inteffacial tension attainable at the C M C o f a n y mixture o f the two c o m p o nents. the difference between the lower interfacial tension value o f either individual surfactant (i.e., 0 0 ~CMC, I,t o r ~YCMC,2,t) at its C M C and ~/~MC,12,t. the partition coefficient o f either surfactant between the aqueous and n o n a q u e o u s phases, defined as the concentration in the n o n a q u e o u s phase divided by the concentration in the aqueous phase. t h e v o l u m e o f the n o n a q u e o u s phase divided by the v o l u m e o f the aqueous phase. the slopes o f the ~/~ vs In C ° t (In C2,t, 0 respectively) plots. the m o l e fraction o f surfactant 1 in the total surfactant in the mixed interfacial m o n o l a y e r in the two-phase system.
Journal of Colloid and Interface Science, Vol. 129, No. 1, April 1989
,:,~, ACKNOWLEDGMENTS
This material is based upon work supported by the National ScienceFoundation under Grant CBT-8413162, by PSC-CUNY Research Award Program Grant 66-7273, and by grants from Exxon Research and Engineering, GAF Corp., Shell Development, and Shulton Research. REFERENCES 1. Rosen, M. J., and Murphy, D. S., J. Colloidlnterface Sci. 110, 224 (1986). 2. Hua, X. Y., and Rosen, M. J., J. Colloid Interface Sci. 90, 212 (1982). 3. Rosen, M. J., and Zhu, B. Y., J, ColloidlnterfaceSci. 99, 427 (1984). 4. Zhu, B. Y., and Rosen, M. J., J. Colloid Interface Sci. 99, 435 (1984). 5. Dahanayake, M., and Rosen, M. J., in "Structure/ Performance Relationships in Surfactants" (M. J. Rosen, Ed.), ACS Symposium Series 253. Amer. Chem. Soc., Washington, DC, 1984. 6. Rosen, M. J., J. ColloidlnterfaceSci. 79, 587 (1981). 7. Warr, G. G., Grieser, F., and Healy, T. W., J. Phys. Chem. 87, 4520 (1983). 8. Murphy, D. S., and Rosen, M. J., J. Phys. Chem. 92, 2870 (1988). 9. Mukerjee, P., and Cardinal, J. R., J. Phys. Chem. 82, 1620 (1978). 10. Cardinal, J. R., and Mukerjee, P., J. Phys. Chem. 82, 1614 (1978).