5994
Langmuir 1998, 14, 5994-5998
Articles Mutual Diffusion Measurements in a Ternary System: Ionic Surfactant-Nonionic Surfactant-Water at 25 °C M. Castaldi, L. Costantino, O. Ortona, L. Paduano, and V. Vitagliano* Dipartimento di Chimica dell’Universita` di Napoli, Federico II, Via Mezzocannone 4, 80134 Napoli, Italy Received April 28, 1998. In Final Form: July 1, 1998 The four diffusion coefficients describing the isothermal transport process in ternary systems have been measured in aqueous solutions of mixed surfactants. Measurements have been made on the system pentaethyleneglycol 1-hexyl ether-sodium 1-hexanesulfonate-water at various mean compositions. The analysis of diffusion data allows a reasonable interpretation of the behavior of mixed surfactant solutions, showing the evidence of the presence of mixed micelles.
Introduction Diffusion measurements have become a widely used technique for characterizing surfactant solutions. In the last 20 years several papers appeared in the literature dealing with the transport properties of systems containing surfactants that have been studied with a variety of methods: NMR, quasielastic light scattering, tracer measurements, and boundary spreading. The former techniques allow measurement of intradiffusion coefficients1 and the latter technique allows measurement of interdiffusion (or mutual diffusion) coefficients.1 Mutual diffusion studied by boundary spreading was successfully used in the past to characterize aggregation processes as well as micelle formation. As pointed out in the past,2-5 the value of the mutual diffusion coefficient measured in the presence of micelles is weighted by the micelle number of aggregation, while the experimental value of the intradiffusion coefficient is just a numerical average between the values of monomer and aggregate intradiffusion coefficients. Since surfactants used in practical applications are never pure, there is an increasing interest in understanding the structure and properties of systems containing more than one surfactant and forming mixed micelles.6 Furthermore, micelles show the property to solubilize many compounds in their core improving their solubility in an aqueous medium. The transport of solubilized compounds together with micelles is called mutual transport. Leaist and Hao7 published recently an interesting paper on diffusion in ternary systems sodium dodecyl sulfate* To whom correspondence may be addressed: fax, +39081 5527771; e-mail,
[email protected]. (1) Tyrrell, H. J.; Harris, K. R. Diffusion in Liquids; Butterworth: London, 1984. (2) Leaist, D. G. Can. J. Chem. 1988, 66, 1129. (3) Leaist, D. G. J. Colloid Interface Sci. 1986, 111, 230. (4) Leaist, D. G. J. Solution Chem. 1992, 20, 3415. (5) Paduano L., Sartorio R.; Vitagliano, V.; Costantino, L. J. Colloid Interface Sci. 1997, 189, 189. (6) Randal M. H. in Mixed Surfactant Systems; Ogino, K., Abe, M., Eds.; Dekker: New York, 1993; Vol. 46, p 317. (7) Least, D. G.; Hao, L. J. Chem. Soc., Faraday Trans. 1995, 91, 2837.
various alcohols with chains of different length-water. These systems bear some similarity to that discussed in the following pages. Nevertheless, the present work is the first paper, to our knowledge, on the interpretation of mutual diffusion coefficients of a ternary system containing two different surfactants. Mutual transport in ternary systems is based on Fick’s phenomenological equations that include four experimental diffusion coefficients, two main coefficients accounting for the transport of each component due to its own concentration gradient, and two cross-diffusion coefficients that take into account the motion of each surfactant caused by the concentration gradient of the other. The sign and magnitude of the cross-diffusion coefficients are related to the interactions between solutes in solution. The two surfactants studied here are the nonionic pentaethylene glycol 1-hexyl ether, CH3-(CH2)5-(OCH2-CH2)5 -OH (C6E5, defined as component 1), and the ionic salt sodium 1-hexanesulfonate, CH3-(CH2)5-SO3Na (C6SNa, defined as component 2). Experimental Section Materials. Bakem analytical reagent grade C6E5 and Sigma reagent grade C6SNa were used without further purification, the dye Orange-OT from Sigma was purified as described in the literature. The molar masses used for C6E5, C6SNa, and water were 322.4, 188.22, and 18.016 g mol-1, respectively. All solutions were prepared by weight, using doubly distilled water. Diffusion Experiments. The experiments were performed with a Gouy diffusiometer, which has been automated to scan Gouy patterns and record the fringe positions during the experiment. A model “II fx” MacIntosh computer was used to control the scanning apparatus and to calculate the fringe positions from the fringe intensity profile. The temperature bath was regulated at 25.00 ( 0.01 °C. A single-channel cell was used, and the initial boundary was formed with the siphoning technique. The light source was a Unifas PHASE 0.8-mW neon-helium laser operating at λ ) 632.8 nm. Fringe position data for each experiment were analyzed with a series of computer programs described in the literature. The value of Jm (experimental Gouy fringe number), was determinated
S0743-7463(98)00457-0 CCC: $15.00 © 1998 American Chemical Society Published on Web 09/22/1998
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Langmuir, Vol. 14, No. 21, 1998 5995
using the XMQD8 and F4J9 or F3JP9 computer programs (the choice of code followed the criteria given in ref 9). The appropriate Jm value plus the positions of fringe minima were used to calculate Da (reduced height-area ratio)10,11 and Qo (integral of the fringe deviation graph)10,11 with the F3 or F2M, F2P codes.9 Values of Jm, Da, and Qo for all the experiments are given in Table 1. From these data and the concentration differences from the top and bottom solutions, ∆Ci, a preliminary set of Dij values were obtained by using the RFG program.12,13 All the runs used to compute the diffusion coefficients were controlled to be in the range of gravitational stability.14 Diffusion measurements were performed at five mean compositions (see Figure 1); comprehensive results are given in Table 2. Density Measurements. The densities of all solutions were measured with an Anton Paar DMA 602 density meter with an accuracy of (5 × 10-6 g cm-3. The temperature of the density meter was regulated at 25.00 ( 0.005 °C and calibrated with air, at known pressure and humidity, and water, where the density of air-saturated water was assumed to be 0.997 044 kg dm-3. The following equation, obtained with the method of leastsquares, was used to interpolate experimental density data of each mean concentration studied:
F ) Fo + H1(C1 - C1o) + H2(C2 - C2o)
(1)
where Fo is the density (kg dm-3) at the average concentration, Hi the differential density increment with concentration, and Cio (mol dm-3) the mean concentration where the diffusion runs were performed. All the values of the parameters Fo, H1, and H2 are listed in Table 2. Phase Separation. At low C6SNa concentration there is a range of compositions where the ternary system shows some turbidity.15 The phase separation range was approximately estimated by diluting at constant temperature a homogeneous solution at fixed C6SNa/C6E5 ratio and registering the composition where opalescence appeared and that where it disappeared by further dilution. The range of the miscibility gap is shown in Figure 1; this range is only indicative because, due to kinetic effects, it was not easy to detect the exact limits of the phase separation. Determination of the Critical Micelle Concentration. The micellization process of a surfactant S can be described either as a phase separation, so that the concentration of the monomer species becomes constant and equal to the critical micelle composition (cmc) at higher concentrations, or as a chemical equilibrium
nS ) Sn Both models are good enough to allow a reasonable insight on the behavior of surfactant solutions through the micellization process,16 although more sophisticated models are described in the literature.17,18 The choice of the model is mainly related to the discussion of experimental results. We used both models in the past;5,19 here we prefere to choose the phase separation model.
(8) Miller, D. G.; Sartorio, R.; Paduano, L. J. Solution Chem. 1992, 96, 7478. (9) Albright, J. G.; Miller, D. G. J. Phys. Chem. 1989, 93, 2163. (10) Fujita, H.; Gosting, L. J. J. Am. Chem. Soc. 1956, 78, 1099. (11) Fujita, H.; Gosting, L. J. J. Phys. Chem. 1960, 64, 1256. (12) Revzin, A. Ph.D. Thesis, University of Wisconsin, Madison, WI, 1969. (13) Vitagliano, V.; Sartorio, R.; Spaduzzi, D.; Laurentino, R. J. Solution Chem. 1977, 6, 671. (14) Vitagliano, P. L.; Della Volpe; Vitagliano, V. J. Solution Chem. 1984, 13, 549. (15) Sadaghiania, A. S.; Khan, A. J. Colloid Interface Sci. 1991, 144, 191. (16) Zana, R. Surfactants Solutions, New Methods of Investigation; M. Dekker, New York, 1987. (17) Mukerjee, P. J. Phys. Chem. 1972, 76, 565. (18) Desnoyers, J. E.; De Lisi, R.; Roberts, D.; Roux, A.; Perron, G. J. Phys. Chem. 1983, 87, 1397. (19) Ambrosone, L.; Costantino, L. D’Errico, G.; Vitagliano, V. J. Colloid Interface Sci. 1997, 189, 286.
The cmc of the ternary solutions was measured by a spectrophotometric technique using the dye Orange OT.20,21 The measurements were carried out at 25 °C by a Perkin-Elmer Lambda 17 UV/VIS spectrophotometer. This dye is completely insoluble in aqueous medium while it dissolves into the micelles. Excess Orange OT was added to a solution of the two surfactants of known composition. The solution was shaken to reach saturation; part of it was filtered through a Millipore HV filter (pore size 0.45 µm), and its absorption spectrum was registered. The remaining solutions were weighted again and diluted with water, and the previous procedure was repeated. At constant molality ratio m2/m1 the molality of one surfactant plotted as a function of the measured dye absorbance is a straight line whose intercept gives the cmc (in terms of molality) of the ternary solution at the corresponding m1 and m2 molalities. Figure 2 is an example of such a plot. It must be pointed out that measuring the cmc by the Orange OT method, we did not observe any phase separation effect when concentration entered the miscibility gap composition. A plot of the cmc as a function of both surfactants composition is approximately a straight line (see Figure 1) ranging from the C6SNa cmc to that of the C6E5. In the literature an expression was proposed relating the (cmc)i of binary surfactant solutions to that of the cmc in the ternary systems were mixed micelles are present.22-24 In terms of molalities of the two surfactants this expression becomes:
m2,cmc ) γ2(cmc)2 -
γ2(cmc)2 γ1(cmc)1
m1,cmc
(2)
where γi is the activity coefficient of species i in the micelle, and the monomers in solution are assumed to have ideal behavior. If also micelles behave as ideal systems (γi ) 1), eq 2 is a straight line ranging from m1 ) (cmc)1, m2 ) 0 to m1 ) 0, m2 ) (cmc)2, as found in our case. Recent intradiffusion measurements in D2O solution for our system24 were interpreted in terms of regular solutions. This interpretation leads to slightly different values for the cmc, as shown in Figure 1; however, considering the different experimental techniques and the different solvent medium and allowing for the accuracy of the various experiments, the agreement obtained can be considered very good.
Discussion The results of diffusion measurements allow a reasonable interpretation of this ternary system behavior. As can be seen from Table 2, this ternary system shows quite large changes in the sign and magnitude of the crossdiffusion coefficients. This suggests a transition to different diffusion behaviors as the tenside concentrations change. At low concentration of the solutes (point 1) the main diffusion coefficients are quite close to those of the corresponding binary systems (DC6SNa ) 0.910 × 10-5/cm2 s-1, DC6E5 ) 0.464 × 10-5/cm2 s-1).5 This evidence ensures that, in this region, micelles are not present, so that the main diffusion coefficients are due only to the diffusivity contribution of nonassociated surfactants. As shown in Figure 1, the spectrophotometric measurements agree with this evidence. Moreover, point 1 is near to the solubility gap; this fact justifies the positive values of the cross-diffusion terms with a quite large D21 value. Large values of cross terms were observed in other systems at compositions approaching a critical mixing region25 or, (20) Schott, H. J. Phys. Chem. 1964, 68, 3612. (21) Schott, H. J. Phys. Chem. 1966, 70, 2966. (22) Clint, J. M. J. Chem. Soc. 1975, 71, 1327. (23) Holland, P. M.; Rubingh, D. H. J. Phys. Chem. 1983, 87, 1984. (24) Ciccarelli, D.; Costantino, L.; D’Errico, G.; Paduano, L.; Vitagliano, V. Submitted for publication in Langmuir. (25) Vitagliano, V.; Sartorio, R.; Scala, S.; Spaduzzi, D. J. Solution Chem. 1978, 7, 605.
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Castaldi et al. Table 1. Data of All Diffusion Runsa Point 1
run
m1 (mol kg-1)
m2 (mol kg-1)
F (kg dm-3)
run
m1 (mol kg-1)
m2 (mol kg-1)
F (kg dm-3)
1 top 1 bottom 2 top 2 bottom
0.0407 0.0409 0.0297 0.0512
0.0262 0.0555 0.0226 0.0581
0.999 277 1.000 867 0.998 876 1.001 215
3 top 3 bottom 4 top 4 bottom
0.0232 0.0587 0.0188 0.0631
0.0334 0.0483 0.0405 0.0411
0.999 296 1.000 818 0.999 638 1.000 539
C1o/mol dm-3 ) 0.0399,
C2o/mol dm-3 ) 0.0399
∆C1 (mol dm-3)
∆C2 (mol dm-3)
Jm
Da × (cm2 s-1)
Qo × 103
∆C1 (mol dm-3)
∆C2 (mol dm-3)
Jm
Da × 105 (cm2 s-1)
Qo × 103
0.00004 0.0206
0.0286 0.0344
66.35 73.6
0.9013 0.6149
-13.4 83.3
0.0343 0.0428
0.0141 0.0000
82.16 86.47
0.5179 0.4702
62.8 24.8
105
Point 2 run 1 top 1 bottom 2 top 2 bottom
m1 (mol
kg-1)
m2 (mol
0.1029 0.1059 0.0969 0.1113
kg-1)
F (kg
0.0251 0.0586 0.0159 0.0676
dm-3)
1.000 58 1.002 50 0.999 98 1.003 05
C1o/mol dm-3 ) 0.1002, ∆C1
∆C2 (mol dm-3)
Jm
Da × 105 (mol dm-3)
Qo × 103 (cm2 s-1)
0.0023 0.0127
0.0319 0.0493
32.60 65.60
0.7750 0.5125
-40.3 223.1
run
m1 (mol kg-1)
m2 (mol kg-1)
F (kg dm-3)
3 top 3 bottom
0.0925 0.1158
0.0232 0.0603
1.000 32 1.002 72
C2o/mol dm-3 ) 0.0401 ∆C1
∆C2 (mol dm-3)
Jm
Da × 105 (mol dm-3)
Qo × 103 (cm2 s-1)
0.0213
0.0352
66.71
0.3511
269.3
Point 3 run 1 top 1 bottom 2 top 2 bottom 3 top 3 bottom
m1 (mol
kg-1)
m2 (mol
0.0256 0.0641 0.0372 0.0523 0.0444 0.0450
kg-1)
F (kg
0.5493 0.5687 0.5274 0.5908 0.5156 0.6028
dm-3)
1.024 560 1.025 501 1.023 796 1.026 290 1.023 378 1.026 726
C1o/mol dm-3 ) 0.0409, ∆C1 (mol dm-3)
∆C2 (mol dm-3)
Jm
Da × (cm2 s-1)
Qo × 103
0.0347 0.0132 0.0001
0.0110 0.0516 0.0738
65.46 62.93 58.84
0.1820 0.3228 0.5538
-65.0 180.2 43.2
105
run
m1 (mol kg-1)
m2 (mol kg-1)
F (kg dm-3)
4 top 4 bottom 5 top 5 bottom 6 7
0.0351 0.0544 0.0426 0.0470 0.0300 0.0596
0.5322 0.5854 0.5273 0.5910 0.5402 0.5783
1.023 977 1.026 098 1.023 818 1.026 256 1.024 222 1.025 847
C2o/mol dm-3 ) 0.5117 ∆C1 (mol dm-3)
∆C2 (mol dm-3)
Jm
Da × 105 (cm2 s-1)
Qo × 103
0.1715 0.0036
0.0426 0.0634
62.06 48.56
0.2728 0.4582
162.0 138.1
Point 4 run
m1 (mol kg-1)
m2 (mol kg-1)
F (kg dm-3)
run
m1 (mol kg-1)
m2 (mol kg-1)
F (kg dm-3)
1 top 1 bottom 2 top 2 bottom
0.0839 0.1047 0.0799 0.1088
0.5451 0.5840 0.5514 0.5775
1.024 320 1.025 678 1.024 520 1.025 478
3 top 3 bottom 4 top 4 bottom
0.0899 0.0987 0.0918 0.0967
0.5356 0.5935 0.5324 0.5967
1.024 020 1.025 977 1.023 920 1.026 077
C1/mol dm-3 ) 0.0850,
C2o/mol dm-3 ) 0.5090
∆C1 (mol dm-3)
∆C2 (mol dm-3)
Jm
Da × (cm2 s-1)
Qo × 103
∆C1 (mol dm-3)
∆C2 (mol dm-3)
Jm
Da × 105 (cm2 s-1)
Qo × 103
0.0178 0.0250
0.0295 0.0177
51.60 52.70
0.2163 0.1716
130.4 15.2
0.0071 0.0036
0.0470 0.0529
49.60 49.81
0.3435 0.4332
146.7 81.6
105
Point 5 run
m1 (mol kg-1)
m2 (mol kg-1)
F (kg dm-3)
run
m1 (mol kg-1)
m2 (mol kg-1)
F (kg dm-3)
1 top 1 bottom 2 top 2 bottom 3 top 3 bottom
0.1645 0.1757 0.1672 0.1729 0.1652 0.1750
0.5561 0.5983 0.5444 0.6101 0.5477 0.6068
1.025 186 1.026 726 1.024 689 1.027 276 1.024 920 1.027 115
4 top 4 bottom 5 top 5 bottom 6 7
0.1693 0.1709 0.1537 0.1879 0.1570 0.1832
0.5412 0.6133 0.5673 0.5868 0.5606 0.5937
1.024 497 1.027 384 1.025 744 1.026 152 1.025 493 1.026 456
C1o/mol dm-3 ) 0.1500, ∆C1 (mol dm-3)
∆C2 (mol dm-3)
Jm
Da × 105 (cm2 s-1)
Qo × 103
0.0086 0.0036 0.0072
0.0329 0.0530 0.0470
40.96 49.96 50.77
0.3379 0.4799 0.3904
145.2 -8.7 100.1
C2o/mol dm-3 ) 0.5088 ∆C1 (mol dm-3)
∆C2 (mol dm-3)
Jm
Da × 105 (cm2 s-1)
Qo × 103
0.0000 0.0286
0.0589 0.0109
49.57 52.44
0.6088 0.1676
-205.6 -10.4
a ∆C /mol dm3, concentration difference of component i between bottom and top solutions for each diffusion run (C i bottom - Ctop); Jm, total number of Gouy fringes, in terms of refractive index difference, ∆n, between bottom and top solutions at the He-Ne laser red light (λ ) 632.8 nm) Jm ) 3.951 × 106 ∆n; Da, reduced height-area ratio;10,11 Qo, integral of the fringe deviation graph.10,11
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Langmuir, Vol. 14, No. 21, 1998 5997
Table 2. Diffusion Coefficients and Related Data of All Compositions Studied o/mol
dm-3
C1 C2o/mol dm-3 Fo/kg dm-3 H1/kg mol-1 H2/kg mol-1 R1 R2 D11 × 105/cm2 s-1 D12 × 105/cm2 s-1 D21 × 105/cm2 s-1 D22 × 105/cm2 s-1 DC6E5 × 105/cm2 s-1 DC6SNa × 105/cm2 s-1
C1o/mol dm-3 C2o/mol dm-3 Fo/kg dm-3 H1/kg mol-1 H2/kg mol-1 R1 R2 D11 × 105/cm2 s-1 D12 × 105/cm2 s-1 D21 × 105/cm2 s-1 D22 × 105/cm2 s-1 DC6E5 × 105/cm2 s-1 DC6SNa × 105/cm2 s-1 D1m × 105/cm2 s-1 D2m × 105/cm2 s-1
point 1
point 2
0.0399 0.0399 1.000065 ( 6 × 10-6 0.02108 ( 4 × 10-4 0.05563 ( 5 × 10-4 2013.5 ( 3.3 940.4 ( 2 0.4393 ( 0.0049 0.0059 ( 0.0047 0.1189 ( 0.0240 0.8834 ( 0.0172 0.464 0.910
0.1002 0.0401 1.000530 ( 5 × 10-6 0.01596 ( 4 × 10-4 0.05839 ( 3 × 10-4 1643.3 ( 11.8 901.4 ( 4.3 0.1893 ( 0.0045 0.0486 ( 0.0015 -0.0379 ( 0.0027 0.7475 ( 0.0127 0.325 0.910
point 3
point 4
point 5
0.0409 0.5117 (1.025040 ( 3) × 10-6 (0.01310 ( 4) × 10-4 (0.04503 ( 1) × 10-4 1638.4 ( 3 795.2 ( 1 0.1973 ( 0.0036 0.0055 ( 0.0012 -0.2240 ( 0.0150 0.5806 ( 0.0201 0.462 0.725
0.0850 0.5090 1.024998 ( 6 × 10-7 0.01007 ( 1 × 10-5 0.04005 ( 3 × 10-5 1704.3 ( 3 860.8 ( 1 0.1618 ( 0.0024 0.0076 ( 0.0006 -0.2096 ( 0.0094 0.4898 ( 0.0117 0.405 0.725
0.1500 0.5088 1.025970 ( 1 × 10-6 -0.00585 ( 0.001 0.04867 ( 5 × 10-4 1515.9 ( 13 832.9 ( 5 0.1590 ( 0.0090 0.0218 ( 0.0036 -0.1183 ( 0.0239 0.4870 ( 0.0300 0.155 0.725
0.125 0.215
a C o, average concentrations of each point; Fo, density at the average concentrations; H , concentration increments of density (eq 1); R , i i i concentration increments of the refractive index at the He-Ne laser light 639 nm in terms of fringe number Jm; Dij, measured diffusion coefficients of the ternary system; Dim diffusion coefficient of the micelles.5
Figure 1. mi/mol kg-1 molality of component i: b, average composition of diffusion runs; [, measured critical micelle composition; O, critical micelle composition from intradiffusion measurements taken in D2O solutions.24 L is approximate range of miscibility gap.
generally, in systems where salting out effects are present. Noting that in the binary system C6E5-H2O there is no solubility gap, it can be argued that it is the presence of C6SNa to cause this gap.15 From the transport point of view the positive values of the cross terms can be interpreted as due to the tendency of the solutes to diffuse away from the cloud area. At point 2 the main diffusion coefficient D11 drops drastically near the value of the C6E5 micelles diffusion coefficient, D1m. D22 also decreases, although not so drastically. This is evidence that micelles are present; they are mainly C6E5 micelles that solubilize some amount of C6SNa. The quite high value of D22 indicates that a reasonable large amount of C6SNa is still free. The cross term D12 is positive and fairly large. As in the previous case the sign can be interpreted as the tendency of
Figure 2. Molality of C6E5, m1, plotted as a function of the absorbance, A, of Orange OT dye at the wavelength of the absorption maximum: 1, m2/m1 ) 0; 2, m2/m1 ) 1.01; 3, m2/m1 ) 3.20. The intercepts of the straight lines correspond to the cmc at each m2/m1 ratio.
component 1 to move apart from the phase separation area, namely, toward a region where the C6SNa concentration is lower. A different interpretation can be given to the negative sign of D21, in this case we have an overall diffusion of C6SNa against the C6E5 concentration gradient. At total constant C6SNa concentration we are in the presence of a concentration gradient of C6SNa adsorbed into the micelles and an opposite concentration gradient of free C6SNa.26 The stoichiometric transport of C6SNa is a balance between the surfactant carried by the micelles and that diffusing as a monomer in the opposite direction. A local redistribution of surfactant between micelles and solution does also contribute to the total transport process. (26) Paduano, L.; Sartorio, R.; Vitagliano, V. J. Phys. Chem. 1998, 102, 5023.
5998 Langmuir, Vol. 14, No. 21, 1998
Figure 3. Diffusion coefficients Dij of systems 3, 4, and 5 drawn as a function of C6E5 molality.
In the presence of the C6E5 concentration gradient most of the C6E5 transport is due to micelles diffusion, because the monomer concentration is almost constant and the micelles also carry C6SNa with them. At point 2 the concentration of free C6SNa is much larger than that of the bound one, so that the negative sign of the cross term D21 is due to the prevailing effect of the faster moving monomer C6SNa that diffuses toward the higher C6E5 concentration region. Intradiffusion coefficients and stoichiometric distribution between free surfactants and micelles were measured in D2O with PGSE NMR.24 On the basis of these results the molalities of C6SNa at point 2 are about (m2)Free = 0.038 mol kg-1 and (m2)Mic = 0.004 mol kg-1. Points 3, 4, and 5 also correspond to compositions where micelles are present. The analysis of the trend of the Dij diffusion coefficients gives a reasonable insight on the system behavior. Both D11 and D22 are slightly decreasing functions of C6E5 concentration (see Figure 3); D11 approaches the value of the C6E5 micelles diffusion coefficient in the binary system as the C6E5 concentration increases (D11 f 0.125 × 10-5 cm2 s-1 ) D1m).5 On the other hand, as m1 f 0, D11 f 0.215 × 10-5 cm2 s-1, which is the diffusion coefficient of C6SNa micelles.5 This is strong evidence for the presence of mixed micelles. In the absence of C6E5, the main diffusion coefficient D22 corresponds to that of C6SNa in its aqueous binary solutions (DC6SNa ) 0.725 × 10-5 cm2 s-1),5 its value decreasing with C6E5 increasing concentration. The decreasing of D22 with C6E5 concentration is due to the increasing dimensions of micelles that include increasing amounts of nonionic surfactant. It is worth while to note that intradiffusion measurements have shown that, adding C6E5 from a zero concentration to that of point 5, the fraction of C6SNa present into the micelles changes from 1 to about 0.75.24 The presence of a relevant amount of free C6SNa is responsible for the high D22 value that does not approach D2m. In the binary C6SNa-water system the amount of monomer surfactant is always quite high, even in the presence of micelles; this fact quenches the amount of free Na+ counterions coming out from the micelles and the diffusion process can be treated as that of nonionized surfactants.5 If the amount of free ionic surfactant (27) Evans, D. F.; Mukherjee, S.; Mitchell, D. J.; Ninham, B. W. J. Colloid Interface Sci. 1983, 93, 184. (28) Deng, Z.; Lu, M.; Leaist, D. G. J. Chem. Eng. Data 1996, 41, 214.
Castaldi et al.
decreases, this treatment does not hold anymore and a more complicated expression must be used that accounts for the training effect of free Na+ counterions on ionized micelles.2,27,28 As a result of this effect, if the monomer surfactant concentration is low, the diffusion coefficient of surfactant increases by increasing the micelles concentration. This fact was found in sodium-dodecyl sulfate (SDS) solutions3,27 where the cmc is very low. In our case,raising the amount of C6E5 into the micelles dilutes the adsorbed C6SNa; as a consequence the concentration of free C6SNa in equilibrium with the bound surfactant decreases, increasing the fraction of excess free Na+ counterions responsible for the training effect on micelles. However, this effect is not large enough to promote a growing of the D22 value, although such a tendency seems evident on the graph of Figure 3. The positive and growing trend of D12 values can be attributed to the same cause. The reduced concentration of free C6SNa also reduces the fraction of sodium ions adsorbed in the Stern layer. As a consequence the diffusivity of micelles increases due to the training effect of free sodium ions. The possible counterflow of free C6E5 is not enough to balance the transport due to the higher micelles diffusivity, so that positive values of D12 are found, which increase with micelles concentration. The negative values of D21 can be interpreted as done for point 2. Their absolute value decreases by raising the C6E5 concentration because, as a consequence of the C6SNa partition between the free component and the micelles, the concentration of free C6SNa decreases and so does the backward flow of this component. In their recent research on diffusion in ternary systems sodium dodecyl sulfate-various alcohols with chains of different length-water,7 Leaist and Hao found both positive cross coefficients for systems with short chain alcohol, but the D21 terms became negative with hexanol and longer chains alcohols. The long-chain alcohol-SDS systems are very similar to ours, which differ only by the much larger hydrophilic head. This head promotes the surfactant-like behavior of C6E5 as compared to that of alcohols; however, the diffusional behavior of these systems and that of ours is comparable, and the interpretation given by the previous authors agrees with that suggested in our paper. Conclusions The analysis of the isothermal diffusion transport in surfactant and mixed surfactant solutions gives quite a bit of information on the behavior of these solutions. The data obtained are important for understanding the kinetics of detergency, solubilization, and other mass transport processes involving ionic and nonionic surfactant systems. Our system shows a lowering of the critical micelle composition with respect to the binary surfactant solutions due to the mixed micelle formation. The mutual diffusion coefficients measured for the system C6E5-C6SNa-H2O indicate a strong coupling between the diffusing species that have been interpreted in terms of mixed micelle formation. Acknowledgment. This research was carried with the financial support of the Italian MURST (Cofin. 97 GFSIB) and the Italian CNR. LA980457A
