2808
Langmuir 1993,9, 2808-2813
Structural Change and Micellar Composition in Aqueous Solutions of Binary Cationic Surfactant Mixtures As Deduced from Cross-Flow Ultrafiltration Experiments A. Makayssi,f D. Lemordant,SJ and C. Treiner*vt Laboratoire d'Electrochimie, UA CNRS 430, UniversitS Pierre et Marie Curie, 4 Place Jussieu, Bat. 74,Paris 75005,France, and Laboratoire d'EnergStique et RSactivitS aux Interfaces, Universitk Pierre et Marie Curie, Paris, 75005, France Received December 21, 1992. In Final Form: April 7,199P The variation of monomer surfactant concentration and mixed micelle composition with total surfactant concentration has been determined on the binary system of benzyl dimethyltetradecylaonium (TBzC1) and trimethyltetradecylammonium((TTA)Cl)chlorides using a cross-flowultrafiltration (UF)technique. It is shown that TBzCl undergoes a structural change at a concentration 3 times the critical micelle concentration (cmc)with a sudden increase of the monomer surfactant concentrationfollowed by a plateau value. This change may be identified with the so-called second cmc as determined for example by conductivity measurements: the micelle aggregation number increases with a concomitant increase of monomer concentration. Single (TTA)Cl micellar solutions do not show such a structural change, but when in mixtures with TBzCl, some (TTAIC1 monomers are salted out from the mixed micelles at the second cmc. In the presence of an additive such as 1-pentanol in dilute solutions, the magnitude of the second cmc effect is decreased. It is also experimentally shown that the change of mixed micellecomposition with totalsurfactant concentrationagreesremarkably well with that calculated using Clint's ideal surfactant mixing model as slightly modified with regular solution parameters. Thus, the structural micellar modification at the second cmc occurs with a continuous mixed micelle composition change. This type of behavior in dilute solutions is also observed with other long-chain cationic surfactants.
Introduction
It has been recently shown using conductivity measurements that some cationic surfactant solutions a t a concentration 3-10 times above the critical micelle concentration (cmc) undergo a structural micellar change1" which may be interpreted asthe consequence of an increase of counterion ass~ciation.~ This phenomenon occurs on a surfactant concentration interval narrow enough to be called a second cmc. The same behavior was found in mixed cationic solutions in the whole micellar composition range even when only one of the surfactants showed the double cmc b e h a ~ i o r . ~It is noteworthy that anionic surfactants such as sodium dodecyl sulfate (NaDS)show the opposite b e h a v i ~ ri.e., ; ~ the conductivity change with surfactant concentration a t the second cmc may be interpreted as the consequence of a decrease of counterion association. The aim of the present work is 2-fold: (1)to investigate the behavior of the monomer surfactants in single and mixed cationic surfactant solutions; (2) to determine the micellar composition in the region around the second cmc and compare the results obtained with the prediction of a mixed micellar model in order to determine if the structural change influences the micellar composition. The ultrafiltration (UF) method is ideal for such
* To whom correspondence should be addressed. t Laboratoire d'Electrochimie. t Laboratoire d'Energ6tique et RBactivit4 aux Interfaces. 8 Present address: Facult4 des Sciences et Techniques, Parc de Grandmont, 37200 Tours, France. e Abstractpublishedin Advance ACSAbstracts, October 15,1993. (1) Hoffman, H.; Platz, G.; Rehage, H.; Schorr, W.; Ulbricht, W. Ber.
Bunsen-Ges.Phys. Chem. 1981,85, 255. (2) Hoffmann, H.; Kalus, J.; Schwander, B. Ber. Bunsen-Ges. Phys. Chem. 1987,91, 99. (3)Malliaris, A.; Binana-Limbele, W.; Zana, R. J . Colloid Interface Sci. 1986, 110, 114. (4)Treiner, C.; Makayssi, A.; Langmuir 1992, 8, 794. ( 5 ) Miura, M.; Kodama,H.; Bull. Chem. SOC. Jpn. 1972,45, 428.
purposes and has been used before with the same goals,although some doubts have been raised upon the feasibility of this method to determine micellar composition for all surfactant pairs? However, these researchers used the batch-UF method, and we felt that the cross-flow UF technique was better suited to our experimental conditions. In particular, as the conductivity results on the degree of counterion condensation had been obtained in the absence of salt: it was considered that the UF method should also be used without added electrolyte with the complication of the occurrence of a streaming potential. Thus, a detailed account will be made of the technique used. The cationic surfactants chosen were trimethyltetradecylammonium chloride and dimethylbenzyltetradecylammonium chloride. The latter surfactant displays a second cmc, and the former does not.
Material and Methods All chemicals were of analytical grade and used as received trimethyltetradecylammoniumchloride ((TTA)Cl)was from TCIEP (Japan) with a cmc of 0.0053 mol/L. Dimethylbenzyltetradecylammonium chloride (TBzCI)was a 99 5% pure compound from Aldrich with a cmc of 0.0019 mol/kg. Both values have been obtained from conductivity measurements at 25.00 f 0.02 O C using a Wayne Kerr automatic conductance bridge (model 6425). 1-Pentanol (1-PeOH) from Aldrich was a 99% pure compound. The microporous UF membranes were sulfonated polysulfone (PSS),IRIS 3026 with a molecular weight cutoff (MWCO) of 5000 Da and an area of 106 cm2 (Rhone-Poulenc, France). It was experienced that the choice of the proper cutoff value was crucial for the applicability of this technique for the present purpose. All membranes were washed as recommended (6)Osborne-Lee, I. W.; Schechter, R. S.; Wade, W. H. J. Colloid Interface Sei. 1983, 94, 179. (7)Osborne-Lee, I. W.; Schechter, R. S.; Wade, W. H.; Barakat, Y.J. Colloid Interface Sci. 1985, 108, 60. (8)Asakawa, T.; Johten, K.; Miyagishi, S.; Nishida, M. Langmuir 1988, 4, 136. (9)Nguyen,C. M.;Rathman,J. F.;Scamehom,J. F. J.ColloidZnterface Sci. 1986,. 112, 438.
0743-746319312409-2808$04.00/0 0 1993 American Chemical Society
Solutions of Binary Cationic Surfactant Mixtures
Langmuir, Vol. 9, No. 11, 1993 2809 Table I. Monomer Surfactant Concentration C, versus Total Concentration G for Single Surfactant Solutione at
UFPP CELL
Recirculatingfluid (retentate)
I
298 K
A
(TI'A)Cl
-
Closed sample reservoir
TBZCl
C, (moVL)
CD(mol/L)
Cr(mol/L)
CD (moVL)
0.002 0.003 0.004 0.007 0.010 0.025 0.050 0.070 0.090
0.0019 0.0026 0.0032 0.0049 0.0050 0.0051 0.0055
0.0005
0.000 50 0.00100 0.001 40 0.00180 0.00190 0.00190 0.00260 0.00260 0.00270 0.00275 0.002 80 0.002 85
0.0066
0.0088
0.0010 0.0015 0.0020 0.0040 0.0060 0.0080 0.0100 0.0125 0.0150 0.0175 0.0200
Figure 1. Ultrafiltration cross-flow apparatus.
CP
( mmoVl )
4
2-1 0.0
I 0.2
0.4
0.6
AP ( bar )
Figure 2. Permeate concentration versus applied pressure for ~TTA)Cl:(a) Cr = 0.025 mol/L; (b) Cr = 0.004 mol/L. by the manufacturer prior to use and pretreated with the surfactant solution under investigation. The Plexiglas UF module (UFP2, Rhone-Poulenc, France) is a plate and frame system for cross-flow membrane filtration. The processed fluid circulates in a thin channel laminar flow, parallel to the membrane. A liquid channel of thickness 0.5 mm permits the use of a minumum solution volume of 22 mL. It has been found that this technique is one of the most effective for minimizing the concentration polarization a t the membrane surface. A schematic diagram of the apparatus is shown in Figure 1. Fluid circulation at a flow rate up to 500 L/h (corresponding to a channel flow rate of 4 m/s) is provided by a peristaltic pump. The desired flow and pressure are regulated by means of a valve followingthe UF module. A manometer is included in the circuit in front of the module input. Transmembranes operating pressures are usually well below 1 bar, and even lower pressures may be warranted for the optimal use of this analytical technique. As shown in Figure 1, the permeate is drained out to the spectrophotometer (Hitachi 100-80) or to the conductivity microcell for subsequent analysis and remixed with the retentate in order to avoid the undesirable concentration effects met with stirred cells. All readings were made a t a stationary state which is usually obtained about 15 min after the beginning of an experiment. As the permeate flow increases with rising pressure, hindered transport of low molecularweight ionicspeciesis usually observed. This phenomenon occurs when dilute solutions of strong electrolytes such as monomeric surfactant ions are filtered through the PSS membranes at low MWCO. At bulk concentrations higher than the cmc, the permeate concentration for surfactants having low cmc (below 0.02 mol/L) is less than expected (i.e., the cmc) and is a functionof the applied pressure. Results concerning (TTA)Cl a t bulk concentrations lower (0.004 mol/L) and higher (0.025 mol/L) than the cmc are reported in Figure 2. A t concentrations lower than the cmc, the permeate concentration
C,, is lower than the retentate concentration Cr and is a decreasing function of the pressure. At higher concentrations,the surfactant is micellized and C, is less than the cmc. This apparent retention is essentially due to a streaming potential effect which is usually eliminated by the addition of salt. It can also be suppressed by an extrapolation technique. For comparison purposes with the conductivity results which were obtained in the absence of salt, the latter technique was preferred. It has been found that in the case of the cross-flow filtration a t low transmembrane pressure (0.5 bar) that the relation between the applied pressure and C, is linear. Values extrapolated a t P = 0 for micellized (TTA)Cl agree remarkably well with the cmc as deduced from conductivity measurements. The same agreement was found for the other systems studied. A t bulk concentrations lower than the cmc, the C, value obtained for P = 0 is equal to Cr,which shows that no retention occurs under such experimental conditions. All experiments were performed with the same procedure; i.e., all solutions were analyzed at five different applied pressures from 0.5 to 0.1 bar and linearly extrapolated to P = 0. Using the data shown in Figure 2, an error analysis provides the following results: (1)above the cmc, C, = 5.20 X 10-3- 2.0AP with a standard deviation of 10.02 X 10-3mol/L. Below the cmc, C, = 4.05 X 10-3 - 2.6AP with a standard deviation of 10.03 X 10-3mol/L. No deviation from a straight line could be detected within experimental uncertainty. The analytical procedure in the case of surfactant mixtures, is as follows: the TBzCl concentration is determined by W spectra a t a wavelength of 262.4 nm using standardized solutions below the cmc after proper dilution of the permeate solutions; the total surfactant concentration is obtained likewise from conductivity versus concentration plots; the (TTA)Cl concentration is deduced from material balance. The presence of 1-pentanol did not interfere with this analytical procedure as long as the standardized solutions corresponded to surfactant concentrations below the cmc.
Results and Discussion 1. Monomer Concentrations in Single and Mixed Surfactant Solutions. Table I presents the results obtained for the two single surfactant solutions. Tables I1and I11present the results obtained for the two surfactant mixtures investigated, corresponding to stoichiometric solution compositions X,of 0.10 and 0.90 of TBzCl. The theoretical values for micellar composition and monomer concentrations are calculatedfrom eq 1as explainedbelow. The data for the (TTA)Cl monomers can be deduced from the tables as the difference between the total and TBzCl monomer concentrations. Figures 3 and 4 present the variation of surfactant concentration in the permeate (monomer concentration) versus concentration in the retentate (totalconcentration) for single surfactant solutions. In the case of (TTA)Cl, after an initial increase of monomer concentration, C, remains constant above a concentrationwhich corresponds to the cmc (hereafter called CI).It is equal to the value
2810 Langmuir, Vol. 9,No.11, 1993
Makayssi et al.
Table 11. Experimental and Theoretical Micellar Composition and Monomer Concentration in a Mixture of TBzCl + (TTA)Cl (X.(TBzCI) = 0.10)
X$
~,(mol/L) F$P 0.0010 0.0020 0.0030 0.0040 0.220 0.180 0.160 0.146 0.136 0.130 0.125 0.120
0.0060 0.0075 0.0085 0.0100 0.0125 0.0150 0.0175 0.0200
0.195 0.169 0.158 0.147 0.136 0.128 0.124 0.120
Cp(Bz)th cmcexp cmcth (mol/L) (mol/L) (mol/L) (moVL) 0.OOO 10 0.00090 0.OOO 19 0.OOO 27 0.OOO 38 O.OOO230 O.OOO185 O.OOO180 0.OOO 165 O.OOO135 O.OOO130 O.OOO120 O.OOO110
0.0018" 0.0027" 0.003P O.OOO27 0.0043 O.OOO23 0.0044 O.OOO21 0.0046 O.OOO19 0.0049 0.OOO 18 0.0050 O.OOO17 0.0051 O.OOO16 0.0052 O.OOO16 0.0053
0.0043
0.0044 0.0045 0.0045 0.0045 0.0046 0.0046 0.0046
Table 111. Experimental and Theoretical Micellar Composition and Monomer Concentration in a Mixture of TBzCl + (TTA)Cl (X.(TBzCl) = 0.90) C,
Cp(Wexp
P
(moVL)
0.910 0.905 0.902 0.900 0.904 0.903 0.903 0.900 0.902
0.OOO 41 0.OOO 87 0.001 25 0.001 50 0.001 65 0.00170 0.00170 0.00185 0.001 90 0.00190 0.00190 0.00193 0.00200
G
0.0005 0.0010 0.0015 0.0020 0.0030 0.0040
0.0060 0.0080 0.0100 0.0125 0.0150 0.0175 0.0200 a
0.930 0.925 0.918 0.915 0.912 0.909 0.909 0.908 0.907
20
Cr (
mmol/l )
Figure 4. Permeate versus retentate concentration for TBzCl solutions displaying the double cmc behavior; dotted line, conductivity versus total surfactant concentration (ref 4).
cp
( mmoM
0.0005"
0.00090 0.0018 0.0017 0.0017 0.0017 0.0017 0.0017 0.0017 0.0017 0.0017
0.0013" 0.00190 0.0019 0.0019 0.0019 0.0021 0.0022 0.0022 0.0022 0.0022 0.0023
0.002 0.002 0.002 0.002 0.002 0.002 0.002 0.002 0.002
40
Figure 3. Permeate versus retentate concentration for (TTA)C1 solutions.
C, = 0.005 mol/ kg. At a concentration equal to about 10 times the cmc, i.e., 0.05 mol/L, the situation becomes more complex and C, starts to rise slowly as the result of increased intermicellar interactions. No second cmc is found for this surfactant, nor was it found from conductivity measurements. It should be pointed out that batch-UF experiments in the case of NaDS show the same increase of monomer concentration, the threshold surfactant concentration being around 0.10 mol/L.'O The case of pure TBzCl is different. C, rises initially up to CI,as in the case of (TTA)Cl and remains constant found from conductivity determinations:
(10) Hafiane,A.;Issid,I.;Lemordant,D. J. ColloidlnterfaceSci. 1991, 142, 167.
10
0
Cp(Bz)th cmq, cmcth (moVL) (mol/L) (mol/L)
Permeate total concentration below the cmc.
0
I
Cp(Wexp
Permeate total concentration below the cmc.
(mol/L)
3 1
'
0
0
10
2 0 ~( rmmom
Figure 5. Permeate versus retentate concentration for TBzCl solutions: (a) pure TBzC1; (b) in the presence of 0.02 mol/L 1-pentanol.
in a small concentration interval. Again C1 is unambiguously identified with the cmc, and the value found is equal to that deduced from conductivity experimenta.4 Then C, increases again sharply at a concentration for which the second break in the conductivity versus concentration curve was observed (Figure 4). This is the second cmc, called CZ.Then finally, C, increases with a much slower rate above CZ. (Note the much smaller surfactant concentration interval investigated for TBzCl than for (TTA)Cl.) In Figures 4, 5, and 7-9 the value noted as C2 corresponds to the second break observed in the conductivityversus totalsurfactant concentration plot. It has been concluded previously4 from an analysis of the variation of the conductivity with surfactant concentration that two values of the degree of counterion association a1 and a2 can be calculated at the respective concentrations C1 and C2 with a1 > a2. This was the case for TBzCl but also for hexadecylpyridinium chloride and ita mixtures with benzyldimethylhexadecylauunonium chloride,trimethylhexadecylammonium bromide: or hexadecylpyridinium salicylate.2 Note that in the latter case it has been shown that the surfactant forms rodlike micelles above thesecond cmc. The mixtures of cationicsurfactants displayed much larger effecta than the single surfactant solutions. An increase of a is usually interpreted as the consequence of an increase of surface charge density" and hence of an increase of the aggregation number if the aggregate's spherical symmetry is retained. Thus, the UF (11) Gunnmon, G.;Jonsson, B.; Wennerstrom, H. J. Phys. Chem. 1980,84, 3114.
Langmuir, Vol. 9, No. 11, 1993 2811
Solutions of Binary Cationic Surfactant Mixtures results indicate that for TBzCl at CZ,while the micellar aggregation number increases, the monomer surfactant concentration decreases. The effect is relatively large in a very small surfactant concentration interval (see Figure 4) as the C, increase is about 25 % Thus, the micelles increase in size and at the same time decrease in number while the concentration is increased from C1 to C2. An order of magnitude of the increase in size of the aggregates may be evaluated using the dressed micelle model.12 This electrostatic theory enables the value of a to be calculated, knowing the cmc and the surfactant hydrocarbon chain length and assuming a micelle of spherical shape with 4nR2 = Nu, where R is the radius of the micelle, N the aggregation number, and a the crosssectional head group area. Conversely, if a and R are known, N and a can be calculated.13 The relevant equations may be found in the original paper. This model was applied to the present data for the TBzCl with R = 2.2 nm, a1 and cy2 being equal, respectively, to 0.32 and 0.28 at C1 and C2.4 N is found to vary from 66 to 75. The effect is larger for TBzCl + ('M'A)Cl mixtures: Hence, for a mole fraction X,(TBzCl) = 0.10, with a1 = 0.37 and a2 = 0.26, and the same assumptions as before, N varies from 68 to 100 while the surfactant surface area changes from 0.89 to 0.61 nm2. These numbers should be taken merely as indicative of the magnitude of the aggregation number changes. It was found interesting to investigate the effect of an additive which solubilizes in the TBzCl micelles on the variation of C, with C,. 1-PeOH was chosen as a model additive, as the partitioning of this alcohol between TBzCl micelles and water had been studied by a calorimetric method.14 A single 1-PeOH concentration of 0.02 mol/L was employed which corresponds to the alcohol concentration which had been used in these latter experiments. Figure 5 presents a comparison between the TBzCl solutions with and without 1-PeOH. The TBzClmonomer concentration decreases with the addition of alcohol as expected for a hydrophobic additive. However, the decrease is smaller between C1 and C2 than above CZ.The decrease of cmc is roughly twice as large at C1 than above CZ. This is the consequence of the C, concentration jump being smaller in the presence than in the absence of 1-PeOH. The decrease of nonmicellized monomer surfactant concentration due to the addition of 0.02 mol/L alcohol is about 55% at a total TBzCl concentration of 0.02 mol/L, which is an extremely large change indeed. Thus, it may be suggested that even at low micelle occupancy, additives which are solubilized in TBzCl micelles are much better aggregate stabilizers above C2 than at the regular cmc. This effect is amplified in the case of TBzCl + (TTA)Clmixtures. Figure 6 presents the variation of C,(TBzCl) in the case of a mole fractional composition X,= 0.10. C, first increases until the cmc of the mixedmicelle is attained, and then it decreases rapidly as the result of the mixed micelle formation. Since the cmc of TBzCl is lower than that of (TTA)Cl, the first micelles are richer in TBzC1; as the total surfactant concentration increases at constant X, and the mixed micelle composition XMapproaches that of the stoichiometric solution composition, the mole fraction of TBzCl in the mixed micelle decreases until it is equal to 0.10. The C, increase observed for the single TBzCl micelles has diasppeared.
0'4/
.
(12) Evans, D. F.; Ninham, B. W.J. Phye. Chem. 1983,87,5025.
(13) Treiner, C.; Nguyen, D. J. Phye. Chem. 1990,94, 2021.
(14)Bury,R.;Treiner, C.; Chevalet, J.; Makayssi, A. Anal. Chim. Acta
1991, 251, 69.
0.0 0
lo
C, ( m m o l A )
2o
Figure 6. Permeate versus total retentate concentration for TBzCl in a 10%TBzCl solution mixture of (TTA)Cl+ TBzC1.
VACl ) ( mmolA )
0
10
20
C, ( mmoVl)
Figure 7. Permeate versus total retentate concentration for (TTA)Clin a 10 % TBzCl solution mixture of (TTA)Cl+ TBzC1.
21
-
Cp( TBzCI (
mmoM )
0
10
C, ( mmoM )
20
Figure 8. Permeate versus retentate concentration for TBzCl in a 90% TBzCl solution mixture of (TTA)Cl+ TBzC1. Figure 7 shows the variation of C, with C,for (TTA)Cl at the same micellar composition. c, increases between C1 and CZalthough the single (TTA)Cl solutions showed no concentration effect in this concentration range. [Note the different C, scales in Figures 6 and 71. The main conclusion here is that some monomer (TTA)Cl ions are released above the regular cmc only when mixed with TBzc1. The results for XdTBzCl) = 0.90 confirm the above observations (Figure 8). When TBzCl is a major component, the two cmc's are clearly identified; although the effect is very small, the profile of the curve corresponding to (TTA)Cl (Figure 9) still displays the two CMC's with
2812 Langmuir, Vol. 9, No. 11,1993
XM
Cp ( T A C I ) ( mmol/l )
0.2
0.1
0
Figure 9. Permeate versus retentate concentration for ('ITA)C1 in a 90% TBzCl solution mixture of ("A)Cl+ TBzC1. a slight increase of (TTA)Cl monomer concentration a t the second cmc as was recorded previously from conductivity e~periments.~ One may conclude from this part of the study that in the case of pure TBzCl, larger micelles are formed when the concentration increases from C1 to CZ;however, the main effect is the increase in monomer concentration which implies that fewer micelles are formed. In the case of mixed micelles, although (TTA)Clby itself does not display a second cmc, an increase of (TTA)Cl monomers is observed due to the presence of a small fraction of TBzCl in mixed micelles. The TBzCl component may be considered as stabilized (by micellar solubilization) when present in small quantity in (TTA)Cl micelles while some of the (TTA)Cl monomers seem to be salted out from the mixed micelles. When TBzCl monomers are the major micelle component, the destabilization effect observed for the pure component dominates and the micelles behave much as the pure TBzCl ones. 2. Mixed Micellar Compositions. One of the main purposes of the present report is to investigate the possible consequence of the micellar structural change on micellar composition from C1 to the region of the second cmc. Experimental results regarding micellar composition as well as its change upon surfactant concentration may then be compared to calculated ones using Clint's thermodynamic approach in the case of ideality conditions16or as modified by RubinghlG in an attempt to incoporate nonideal mixing effects. The relevant equations are
XM = [-(C,- A)
+ {(Ct- A)' + 4X,CtA)"z1/2A
(1)
with and
fl = exp[B(1- XM)']
(3)
fz=exP(8XMz)
(4)
where /3 is a regular solution parameter which can be obtained from cmc determinations; in the present case B = -0.50: a number which quantifies the small attractive interaction between the two unlike surfactants. If B is 0, then Clint's ideal formulation is recovered. XMis the J. H. J. Chem. SOC.1976, 71,1327. (16) Rubingh, D. N. In Solution chemistry of surfactants; Mittal, K. L., Ed.; Plenum Press: New York, 1979; Vol. 1, p 337. (15) Clint,
A
4 10
C, ( mmoM )
20
Figure 10. Micellar composition versus total retentate concentration for a 10% TBzCl solution mixture: full line, eq 1.
0.85
0.00
0.01
c, ( moM)
0.02
Figure 11. Micellar composition versus total retentate concentration for a 90% TBzCl solution mixture: full line, eq 1. micellar composition, and Cl0 and Cz0 are the single surfactant cmc's (C1 values). More sophisticated models have been proposed in order to calculate the micellar c o m p o s i t i ~ n . ~ JThey ~ - ~ are ~ not necessary when small deviations from ideality are concerned as in the present case. Experimentally, the relevant equations are
where Cm(l)is the concentration of micellized surfactant 1 and CMthe total micellized Surfactant concentration. The micellar composition is defined by xM = cm(l)/cM (7) The experiments were performed as close as possible to and above the cmc for the two mixtures of 10% and 90% TBzC1. The results obtained are presented in Tables I1 and I11 and in Figures 10 and 11 where the experimental and calculated (eq 1)compositions are compared. The agreement is excellent for the 10% mole fraction TBzCl composition. The main conclusion which may be deduced from this observation is that there is no specific composition variation upon surfactant mixing in the C1 to CZ concentration range. Moreover, it can be seen that for (17) Kamrath, R. F.; Franses, E. I. Znd.Eng. Chem.Fundam. 1989,22, 230. (18) Rathman, J. F.; Scamehorn, J. F. Langmuir 1986,2, 364. (19) Motomura, K.; Yamanaka, M.; hatono, M. Colloid Polym. Sci. 1984,262,948. (20) Nagarajan, R. Langmuir 1985,1, 331.
Solutions of Binary Cationic Surfactant Mixtures this composition domain, the micellar composition approaches that of the stoichiometric one at about 5 times the cmc. In the case of the 90% TBzCl micellar composition, the agreement is stillvery satisfactory: the difference between experimentaland calculated values is of the order of 2-3 % , which is close to what may be expected with the analytical tools used. It is clearly seen that the micellar composition practically does not change with total surfactant concentration in this micellar composition range as predicted by eq 1,contrary to the results in the ('M'A)Cl-rich domain. One may thus confirm that, at least for quasi-idealmixed surfactant solutions, Clint's equation or a slight modification of it using regular solution parameters correctly predicts the composition change in the whole range of micellar composition. The situation may be different when strong departures from ideality are observed for the surfactant free energy of mixing.7 Clint's equation may also be used to calculatethe monomer concentration above the cmc: however, this can be achieved only under the condition that no structural change interferes with the mixing process. These structural changes have no influence on the micellar composition. It has been indicated above that other cationic surfactants either alone or in mixtures display the same conductivity behavior as the system under the present
Langmuir, Vol. 9, No. 11,1993 2813 investigation. It concerns surfactants with an alkyl chain with more than 16 carbon atoms. In the case of benzalkonium salts, it seems that the aromatic moiety on the head group should be considered as a short second hydrocarbon tail. It is usually accepted in standard thermodynamic calculationsthat a phenyl ring should be considered as equivalent to 3.5 methylene groups, hence the behavior of TBzC1. Finally, the UF results may help to interpret the intriguing adsorption behavior of TBzCl on silica dispersions at different pH values.21 It is usually observed that the adsorption isotherm of cationic surfactants at such solid/liquid interfaces levels off at a concentration close to the cmc ( C I ) . ~It~is not the case with TBzCl for which the saturation plateau value is observed at a higher surfactant concentration21which happens to be close to the second cmc as deduced from the present investigation. This result may be reconciled with the classical surfactant adsorption behavior, taking into account the above observation on the increasing monomer surfactant concentration up to a second cmc. (21) ullman,E.; Thoma, K.; Rupprecht, H.Arch. Pharm. Ber. Dtsch. .. Pharm. 1968,301,357. (22) Ingram, B.T.; Ottewill, R. H.In Cationic Surfactants;Rubingh, D. N.. Holland. P. M.. EMS.:' Surfactant Science Series: Dekker: New York,'1991; Vol. 37,p 87.
