Langmuir 1996,11, 774-778
774
Micelle Formation of Binary Mixtures of Dodecylammonium Perfluoro Carboxylates Hiromi Furuya, Yoshikiyo Moroi," and Gohsuke Sugihara? Department of Chemistry, Faculty of Science, Kyushu University, Higashi-ku, Fukuoka 812, Japan, and Department of Chemistry, Faculty of Science, Fukuoka University, Jonan-ku, Fukuoka 814-01, Japan Received September 23, 1994. In Final Form: December 7, 1994@ The critical micelle concentrations (cmc's)and solubilitiesof dodecylammoniumperfluoroacetate (DAPA), perfluoropropionate (DAPP),and perfluorobutyrate(DAPB)were determined over the temperature range of 5-50 "Cfrom electrical conductance measurements, and the effect of the extent of the hydrophobicity of the counterion on solubility, cmc, and the micellization temperature was examined. The degree of counterion binding to micelles of DAPA and DAPP was near 1.0. Their micellar sizes were found to be very large from the static and dynamic light scattering measurements. The mixed cmc's were then determined for DAPA-DAPP, DAPA-DAPB, and DAPP-DAPB systems. The interaction between the perfluoro carboxylic acid anions in the mixed micellar state was investigated with use of the modified Rubingh's equations, which take the dissociation of the counterion in an aqueous solution into account. The interaction between the counterions was found to be small and they mixed almost ideally in the micellar state. The crystal structure ofthese surfactants was determined by X-ray diffractionto be arranged obliquely.
Introduction A mixed micelle is a micelle composed of surfactants capablethemselves of forming micelles. Many papers have appeared on mixed micelle formation. Most of them are based on the phase-separation models. For homologous surfactants mixtures, the models assume ideal mixing of the surfactants in the micelle.'-* But for nonhomologous surfactant mixtures, such as binary mixtures ofnonionicionic surfactants or of surfactants which have different head groups, deviations from the ideal model have been observed. Rubingh developed a pseudo-phase separation model, where nonideal mixing in the micelle was treated by means of a regular solution approximation.6 This model can elucidate binary mixtures of nonhomologous surfactants well using the single adjustable parameter. But micelles are not a separate phase but a chemical species, and mixed micelles also should be treated as a chemical species. Unfortunately, the interpretations of mixed micellization based on the mass-action model6 have not agreed well with experimentalvalues. Therefore a pseudophase model of the micelle is also of considerable practical importance for estimating cmc values of mixing surfactants. The discussion of the pseudo-phase model may be regarded as a practical effort to derive an empirical equation for mixed micelles. In the present paper, we further develop Rubingh's equations by taking into account the dissociation of counterion in an aqueous solution. The degree of counterion binding to mixed micelle is assumed to be unity. The dependence of the mixed micellization on counterion is investigated by use of the developed equations, paying much attention to the chain length of perfluoro carboxylate anion as counterion.
* Author to whom correspondence should be addressed. + @
Fukuoka University. Abstract published in Advance ACS Abstracts, February 15,
1995. (1)Lange, H. Kolloid 2. 1983,131, 96. (2) Shinoda, K.J . Phys. Chem. 1964,58,541.
Beck, K. H. Kolloid 2.2.Polym. 1973,251,424. (3)Lange, H.; (4)Clint, J. H.J . Chem. Soc. Faraday Trans. I , 1976,76, 1327. (5)Rubingh, D.N.In Solution Chemistry ofsurfactants; Mittal, K. L., Ed.; Plenum Press: New York, 1979;Vol. 1,p 337. ( 6 )Kamrath, R. F.; Franses, E. I. J . Phys. Chem. 1984,88, 1642.
The physicochemical properties of surfactants are strongly influenced by the kind of surfactant ion and counterion. Recently, the effect of hydrophobicity of counterions on aqueous solubility and micelle formation has been ~ t u d i e d . ~ -In l ~ this study, three kinds of surfactants having the same surfactant ion (dodecylammonium, DA)but different fluorocarbon counterions were examined. As the length of the fluorocarbon chain of the counterions, [perfluoroacetate (PA), perfluoropropionate (PP), and perfluorobutyrate (PB)] becomes longer, the hydrophobicity increases. The solution properties of a binary surfactant mixture fall either between or outside the solution properties of two single surfactants. This is also the case for the cmc of a binary surfactant solution. Most cmc's of binary surfactant mixtures fall between the cmc's of each component. First, cmc's and solubilitieswere determined over the temperature range from 5 to 50 "C by the electrical conductance of solutions. Secondly, cmc's of their mixtures, DAPA-DAPP, DAPA-DAPB, and DAPP-DAPB, were determined as a function of the composition of the binary mixtures at 30,40,and 50 "C by the same method. Since the aggregation number of the micelle was large (e.g., n values for DAPAof ~ 1 0 0 at 0 25 "C), these systems may be modeled using the pseudo-phase separation model of micelle formation. As for the degree of counterion binding to micelle, it was found to be about 0.8 for DAPA and 1.0 for DAPP and DAPB within experimental error. As will be made clear from the experimental results, the counterion composition in the mixed micelle shifts to the one of the longer fluorocarbon chain from the net composition in solute. Thus, the degree of counterion binding to a mixed micelle is assumed to be 1.0 in the present theoretical treatment. The interaction parameter (p)and the micellar composition, counterion composition (7)Mukerjee, P.; Mysels, K. J.; Kapauan, P. J . Phys. Chem. 1967, 71, 4166.
( 8 )hacker, E. W.; Underwood, A. L. J . Phys. Chem. 1981,85,2463. (9)Underwood, A.L.; hacker, E. W. J . Colloid Interface Sei. 1984, 100,128. (10)Underwood,A.L.;hacker, E. W. J . Phys. Chem. 1984,88,2390. (11)Moroi, Y.; Sugii, R.; Akine, C.; Matuura, R. J . Colloid Interface Sci. 1988,108,180. (12)Jansson, M.; Stilbs, P. J . Phys. Chem. 1987,91, 113. (13)Jansson, M.; Jonsson, B. J . Phys. Chem. 1989,93,1451.
0743-746319512411-0774$09.00/00 1995 American Chemical Society
Langmuir, VoE. 11, No. 3, 1995 775
Micelle Formation of Perfluoro Carboxylates in this case due to the same surfactant ion for these three surfactants,are obtained at the three temperatures. From the j3 values thus obtained, it will be made clear that the interaction between two surfactants is closely related to the chain length of the counterions.
Theoretical Section A mixed micelle in a solution of nonhomologous surfactant mixtures should be nonideal because the interaction between identical surfactants is different from that between nonhomologous ones. A simple way to take this nonideality into account is to employ the regular solution theory. In the present section, the Rubingh's equations are further improved. As the surfactants used are cationic, the chemical potential of the monomeric ionic surfactant in a bulk phase is given as the sum of the terms for the surfactant ion and counterion. The chemical potential +I) of monomeric surfactant 1 of a 1:l electrolyte in a bulk phase is expressed as pl = pS+ + pG1-
+
= pS+" pG1-"
+ RT In C,, + RT In cG1-
(1)
+ RT In Cs++ RT In c G 2 -
(2)
For surfactant 2
+
p, = psCo
pG2-O
where CS+and CG- are the concentration of a common surfactant ion and different counterion, respectively. The chemical potential of surfactant 1in a micellar phase is written as
plm = plo"
+ RT In y,x
(3)
where y1 is the activity coefficient due to nonideal mixing and x is the mole fraction of component 1 in the binary surfactant phase. A n important point here is that the degree of counterion binding to a micelle is assumed to be unity as mentioned above. From eqs 1 and 3, when a micelle of single component 1 is formed, the following relation results: plo" = p,"
+ 2RT In C,"
(4)
where C1"is the cmc of the single component 1 and plo= p ~ 1 - O . Then, from eqs 3 and 4, we have
ps-"
+
plm = p,"
+ R T In ylx(C,")2
(5)
At the cmc ( C ) of mixtures, the following relations are satisfied from the mass balances for components 1and 2. a C = CG1- and (1- a)C = CG2-
(6)
where a is a net mole fraction of component 1in the system. Substituting eq 6 into eqs 1 and 2 results in p, = p," pz = p,"
+ RT In aC2
+ R T ln[(l - a)C21
(7)
because C = CS+,due to a common surfactant ion. From the equilibrium of the components between the micellar phase and the intermicellar bulk phase, p = pm,we have aC2 = ylx(C,o)2 (1- a)C2 = yS(l - x)(c,")~
(8) (9)
Elimination of r from eqs 8 and 9 leads to
+
1/c2 = d y , ( ~ , ~ )(1 ~ - a)/y,(C,o)2
(10)
The case of y1 = yz = 1represents ideal mixing; thus,
+
I/C' = a / ( ~ , " ) ~(1- a)/(C,o)2
(11)
The values of C1"and C2" are obtained from the cmc values of single-surfactant solutions, and the activity coefficients are given by the regular solution theory as y1 = exp[p(l-
XYI
y z = exp(px2)
(12)
(13)
where j3 is the interaction parameter and is related to the molecular interaction in the mixed micelle:
p = N ( W l l + W,, - 2WJRT where Wll and W Zare ~ the energies of interaction between molecules in pure micelle, W12 is the interaction between the two species in a mixed micelle, and N is the Avogadro's number. Eliminatingj3 from eqs 8,9,12, and 13, we have
r2In[aC2/r(C,o)2Y{(1- 3 ~ ) ~ ln[(l - a)C2/(1- X)(C,")~I) = 1 (14) The j3 value can be evaluated by substituting eq 8 into eq 12:
p = In[aC2/x(C,a)2Y(1- x ) ~
(15)
If the cmc of a binary mixture ( C )is determined against the net mole fraction (a),then the micellar composition ( x ) is given by the solution of eq 14, andj3 may be obtained from eq 15 by using the 3c value for each mole fraction (a). A single parameter value of@was determinedby the leastsquares analysis over the entire composition range. The j3value is an index of interaction between two surfactants. A negative value indicates stronger attraction, whereas a positive value indicates less attraction compared with the mean value of the attractions between single components.
Experimental Section Materials. Three perfluoro carboxylate acids, CF3COOH (Kanto Chemical Co., Inc.), CzF5COOH (Merck-Schuchardt), and CsF7COOH(Aldrich Co., Inc.), were dissolved in water each and any contamination was removed from the solutions by centrifugation. The concentration of the aqueous acid solutions was determined by titration with NaOH solution. An equivalent amount of intact dodecylamine (Aldrich Chemical Co., Inc.) was added to the aqueous acid solution. The dodecylammonium perfluoro carboxylates thus formed were purified by repeated recrystallizations from the aqueous solution for DAPA and DAPP and from water-ethanol mixed solvent solution for DAPB. They were dried over P~05under reduced pressure, and DAPB was further dried by freeze-drying for about 5 h. Their purity was checked by elemental analysis, and the observed and calculated values were in satisfactory agreement: C 56.27 (56.17),H 9.49 (9.43),a n d N 4.62 (4.68)for DAPA; C 51.54 (51.56),H 8.04 (8.081, and N 4.11 (4.01)for DAPP; C 48.40 (48.121, H 7.09 (7.07),and N 3.49 (3.51) for DAPB, where the values in parentheses were calculated. The melting point was 74.1-74.5, 54.5, 38.9-39.6 "C for DAPA, DAPP, and DAPB, respectively. Solubility Measurement. A clear solution of known concentration above the cmc and above the micellization temperature (MT) was cooled below the MT, and the solid suspension thus formed was heated stepwise at temperature intervals of 3-4
Furuya et al.
776 Langmuir, Vol. 11, No. 3, 1995 1.oo
'
°
0
A
' 600-
Y
DAPP-DAPB
DAPA
5
ap=0.90
(14.4 mmol kg.')
Y . e:
0
500-
60
.
%
400U
!
2
*i
40°C
A 50°C
b 300-
v1
200I
I
I
1
10
20
30
40 0
Temperature / 'C
Figure 1. Change of specific conductance with temperature and temperature determination of specified solubility.
4
a
6
10
Surfactant concentration / mmol kg"
Figure 3. Change of ANAC with total concentration.
500
For the DAPA-DAPP mixture the cmc was determined by the same method as mentioned above for various compositions a t 30,40, and 50 "C. For the binary mixtures of DAPA-DAPB and DAPP-DAPB, their electrical conductances changed slowly around their cmc's, and two straight lines were not drawn. So the first differentials of conductancewith respect to concentration were plotted against surfactant concentration, and the cmc's were determined as the concentration a t an inflection point of the curves following Phillips' definition (Figure 3).14 The Degree of Counterion Binding to Micelles. The cmc was determined in the presence of excess counterion (CnFzn+lCOO-)by the same conductivity method, where the solution of CnF2,,+lC0ONaprepared by titration ofthe acids with NaOH solution using a pH meter was used for the counterion. The following equation can be given for micelle formation of monodisperse ionic surfactant micelles:15
DAPA
"0
2
5
10
15
Surfactant concentration / mmol kg'
20 1
Figure 2. Change of specific conductance with surfactant concentration. and 0.5 "C around the MT, each temperature being held for more than 15 min. The conductance was plotted against the temperature (Figure 1). Further temperature increase aRer disappearance of the precipitates resulted in only a slower increase of the conductance. The original concentration is the solubility at the temperature where the last slow increase starts. As for below the MT, a known concentration of concentrated surfactant solution which was still turbid after sonification around 50 "C was added stepwise to a measured volume ofwater (15 mL) maintained at a constant temperature. The electrical conductance of a solution at a specified temperature increased linearly with concentration up to a maximum value and then remained constant after a small hump with further increase in concentration, apparently being accompanied by precipitation. The solubility was determined as the concentration at which the initial linearity intersected the back-extrapolation of constant conductance (Figure 2). As for DAPA, 20 mL ofwater and a solid crystal of known weight were added together below the MT in a 20 mL injector tube with a filter of 0.2 ym pore size. The crystal suspension was agitated at a thermostated temperature for 3 h. Then the filtrate conductance was measured a t 35 "C and the solubility a t each temperature was determined from the conductance vs surfactant concentration relation at 35 "C. cmc Measurement. As for single surfactant systems, the electrical conductance values against surfactant concentration were measured and plotted at various temperatures. The cmc was determined as the concentration at the intersection of the two lines from the plots.
nS+ + mG-
5 M+(fl-m)
(16)
where S+, G-, and M are surfactant ion, counterion, and micelle of aggregation number n, respectively. From eq 16 the micellization constant K,, is written as
(17) From the logarithm of eq 17 one obtains
In [SI = -(m/n)ln [GI + (1ln)ln K,,
+ (l/n)ln [MI
Because surfactant monomer concentration can be set equal to the cmc for the micellization a t the cmc and the term In [MI can be easily estimated to be negligibly small in magnitude compared with In K,,, we have, In cmc = -(m/n)ln [GI
+ const
(18)
The value of the degree of counterion binding to a micelle (mln) is evaluated from the slope of the relation obtained by plotting In cmc against In [counterion]. X-ray Diffraction. The crystal structures of DAPA, DAPP, and DAPB were analyzed by an X-ray diffractometer (Shimadzu XD-D1) with a Geiger counter. The scanning speed was 1 deg/ min, and the range of measurement angle was 3.0-60.0'.
Results and Discussion Solubility and cmc of Single Surfactant. The solubilities a n d cmc's of DAPA, DAPP,and DAPB are (14)Phillips, 3. N. Trans. Faraday SOC.1956,51, 561. (15) Moroi, Y. In Micelles; Theoretical and Applied Aspects, Plenum Press: New York, 1992; Chapter 4.
Langmuir, Vol. 11, No. 3, 1995 777
Micelle Formation of Perfluoro Carboxylates 20
-5.0 4.8 I 0
b
DAPA
A
A
DAPP
I
b
-4.9
-4.7
-4.8
,
-4.6
.4.5
I
I
- -4.9
-5.0
'ii 15
E . .-5 E
k
-5.2
lo
I
C
8
50
- -5.0
.5.4
4
-
-5.1
-5.6
'c)
e 5U
Y-
4
-4.4 l .4.a
5
- -5.2
-5.8
C E
a
m
0
-6.0 I -5.4
0
10
20
30
40
50
1
4.2
.4.a
-4.6
'
-s.3
-4.4
60
Temperature / 'C Figure 4. Changes of solubilityand cmc with temperature for
In[GI Figure 5. Plots in In cmc vs In [GI of DAPA at 30 (0),40(A), and 50 "C (U) and of DAPP at 40 "C (A).
DAPA, DAPP, and DAPB.
shown in Figure 4. The MT values are 22.5 "C for DAPA, 33.5 "C for DAPP, and 28.4 "C for DAPB. From very careful measurement, the solubility above 35 "Cfor DAPB in the previous paper16 was found to be the cmc and a steep increase in solubility above MT was also ascertained. The MT values of homologous ionic surfactants have been reported to increase with increasing alkyl chain length of surfactant ion. The important feature of this increase is that MT values do not increase linearly with the number of carbon atoms of the alkyl chain.17J8 The relation between the number of fluorocarbon counterions and the MT of DAPA, DAPP, and DAPB is not monotonous but has a maximum for DAPP. Solubility is affected by the stability of the crystal. The stability is evaluated by the enthalpy change of dissolution for the surfactants, AHO, which is obtained from the slope of In S vs T -l below the MT. The AH" values for DAPA, DAPP, and DAPB are 23.5,25.7,26.8k J mol-l, respectively. Then A(AHO) are 2.2kJmol-lforDAPA-DAPPand 1.1kJmol-l forDAPPDAPB. This difference might be related to the stability difference in the solid state between an odd and even number of carbon atoms. That is, in the present case, the crystalline structures ofthe even series (DAPAand DAPB) are less stable than those of the odd series (DAPP). On the other hand, the cmc is not related to the stability of the crystal. The cmc decreased with the length of the fluorocarbon counterion, which is due to the hydrophobicity of the counterions. From the relation between the solubility and cmc, the MT of DAPP becomes highest. The Degrees of Counterion Binding. From the plots of In cmc vs In [GI, the degree of counterion binding to the DAPA micelle was determined to be 0.87 at 30 "C, 0.73 at 40 "C, and 0.77 at 50 "C Figure 5. At about 40 "C the binding was minimal,as in the former report.16 For DAPP, the degree of binding is about 1.0 at 40 "C. X-ray Diffraction. From the X-ray diffraction analysis, the long spacings between hydrocarbon head groups are 21.95 f 0.05 for DAPA, 23.03 f 0.06 for DAPP, and 21.5 f 0.1 for DAPB. The calculated value of twice the hydrocarbon chain length is 37.1 A according to the CPK atomic model. Hydrocarbon chains of surfactant are (16) Sugihara, G.;Nagadome, S.;Yamashita,T.; Kawachi, N.; Takagi, H.; Moroi, Y. Colloids and Surfaces 1991, 61, 111. (17)Ogino, K.; Ichikawa, Y. Bull. Chem. SOC.Jpn. 1976,49, 2682. (18)Moroi, Y. In Micelles; Theoretical and Applied Aspects; Plenum Press: New York, 1992; Chapter 6.
I
-5.0
Table 1. The Values of B
B 30 "C
40 "C
50 "C
DAPA-DAPP
0.39
DAPA-DAPB
-0.65
0.30 -0.11
0.32 -0.16 -0.51
binary system
DAPP-DAPB
-0.49
calculated to arrange obliquely at a 36.4"angle on average to the face made of head groups. As for fluorocarbon chains, well-defined peaks are not found, and further analysis has to be done for more detail. Perhaps they might also be arranged obliquely,judging from their bulky and more spherically shaped atomic models. Binary Mixtures. These three micelles are found to be very large from the static and dynamic light scattering, as mentioned above; the hydrodynamicradius of the DAPP micelle was about 70 nm, because both the hydrocarbon of the surfactant ion and the fluorocarbon of counterion are hydrophobic and the fluorocarbon does not mix with hydrocarbon.lg The values of the micellar composition ( X I and the parameter p are obtained from measured cmc's against the net mole fractions (a).One p value for one binary mixture at a certain temperature is obtained from the least squares method, and the results are shown in Table 1. The relationships between the mixed cmc and the mole fraction for three mixed systems at 40 "C are shown in Figures 6-8 together with the ideal relationships. Solid lines and dashed lines indicate the composition in solution and the composition in a micelle, respectively. The interaction of two surfactants, mainly of two counterions in this case, can be discussed in terms of parameter p. From Table 1, the change of the /3 value with temperature is quite small, and the temperature dependence is unclear. From Figures 6-8 and the p values in Table 1, the following can be said. 1. DAPA-DAPP System. The deviations from ideality are positive in Figure 6, which indicates that the interactions between molecules of different surfactants is smaller than the mean value of interactions between molecules of the same surfactant. It can be said that two kinds of counterions are supposed to orient independently, because the length of both fluorocarbon chains is short. 2. DAPP-DAPBSystem. From Figure 7, the nonideal curve almost coinsides with the ideal one. In comparison (19)Mukerjee, P.; Yang, A. Y. S. J . Phys. Chem. 1976, 80, 1388.
778 Langmuir, Vol. 11, No. 3, 1995
Furuya et al.
DAPA-DAPB(40’C) - solute _ _ _ _ micelle
DAPA-DAPP(40.C) - solute
___
micelle
, ,,‘’
,.-
/
0.0
0.2
0.4
/
fl= 0.0
0.6
0.8
1.0
1
4.0
PE 3 * 5
\
u
3.0
3 2.5
‘
0.0
I
I
0.2
0.4
‘/
//’ ’
4.5 1
2.0
0 /
’/
Mole kaction of DAPA Figure 6. Mixed cmc values of DAPA-DAPP system against the mole fraction of DAPA: x , experimental value.
3
1-
I
0.6
1
0.8
I 1.0
Mole fraction of DAPP Figure 7. Mixed cmc values of DAPP-DAPB system against the mole fraction of DAPP: x , experimental value.
with the DAPA-DAPP system, both fluorocarbon chains of the counterions become longer and the difference in the number ofcarbon atomsis one. Therefore, the interactions between the same and between different surfactant molecules are about the same, which results in almost ideal mixing in their mixed, micellized state. 3. DAPA-DAPB System. The deviations from ideal mixing are negative (Figure 81, which suggests that the interaction between different fluorocarbons strongly affects the shorter fluorocarbon. Although DAPA is not affected by DAPP, DAPB, which has a longer fluorocarbon chain than DAPP, greatly stabilizesthe shorter counterion,
0.0
0.2
0.4
0.6
0.8
1.0
Mole fraction of DAPA Figure 8. Mixed cmc values of DAPA-DAPB system against the mole fraction of DAPA: x , experimental value.
because the orientation of CF3COO- is restricted by the longer fluorocarbon, C3F&OO-. Compared with other mixtures, the interactions of these mixtures are, more or less, ideal, but the /Ivalues clearly depend on the combination of fluorocarbon chains. Conclusion The hydrophobicity of the fluorocarbon counterion was found to have a strong effect on the cmc and aqueous solubility. Regarding the micellization temperature, which is determined by the balance between the cmc and solubility, DAPP had the highest value among the three homologous surfactants due to its higher stability in the solid state. The degree of counterion binding to micelles of DAPA, DAPP, and DAPB was very large, ca. 1.0, which resulted in large aggregation numbers for the micelles. Therefore, the pseudo-phase separation model was applied to their micellizations, and the revised Rubingh’s equation was used to estimate the interaction between ionic surfactants from their mixed cmc, where both counterion and surfactant ion were taken into account. The surfactants used were composed of the same surfactant ion and different counterions and, therefore, the interaction depends mainly on their counterions. The followingconclusion was derived from the results; the larger the difference in length of the fluorocarbon counterions is, the more stable the mixed micelles become, while the smaller the former is, the more ideal the latter become. Acknowledgment. The authors are deeply indebted
to Prof. Tanaka’s laboratory of Fukuoka University for determination of the dynamic radius of DAPP. LA940755H
