1418
J. Phys. Chem. 1881, 85, 1418-1428
density, thus requiring a modification of LK and M approximate theories. Finally, it is remarked that, at least for limited number of data points of M A S in the range of a and concentration investigated, the AHD values are practically the same if obtained with Na+ or K+ despite the known selectivity of polycarboxylates toward such counterions. This fact, which is postulated by both LK and M theories in their
simplest form, was already found for poly(styrenesulfonates) at low concentrations.la
Acknowledgment. The authors are indebted to Professors D. Dolar, J. J. Hermans, and J. Skerjanc for stimulating discussions. The financial contribution of the Italian C.N.R. (Consiglio Nazionale delle Ricerche) is gratefully acknowledged.
Investlgatlons on Ionic Detergents wlth Unusual Aggregation Behavior H. Hoffmann," 0. Platz, and W. Ulbrlcht Lehrstuhl for Physlkallsche Chemle der Unlversldt Bayreuth, D8580 Bayreuth, West Qermany (Received: September 1 1, 1080)
The aggregation behavior of the two surfactants dodecylammonium trifluoroacetate (DATFA) and tetradecylammonium trifluoroacetate (TATFA) has been studied at different concentrationsand temperatures with several techniques. Rodlike aggregates are present in solutions of DATFA. The length of these anisotropic micelles which was determined by electric birefringence, viscmity, and quasielasticlight-scatteringmeasurements varies little with total detergent concentration but decreases rapidly with increasing temperature. The formation of anisotropic aggregates begins at a concentration which is about a factor 2 higher than the cmc. Kinetic measurements indicate that the residence times of a detergent ion inside the micelles have similar values as for spherical micelles that are found in other Clz detergents. The aggregation behavior of TATFA is very different from that of DATFA, Solutions of TATFA show no electric birefringence but the hydrodynamic radius for the micelles which is determined from the quasielastic light-scattering measurements is too large for normal spherical micelles. Furthermore, the residence times of the detergent ions inside the micelles are too long also. The data are explained on the basis of micellar aggregates that contain solubilized ion pairs of the detergent ion and its counterion in the interior of the micelles.
Introduction Recently it was found that some solutions of ionic perfluorodetergents contain aggregates which are much larger than normal spherical micelles.' It was shown by dynamic light scattering, kinetic, and electric birefringence measurements that the radii of these micelles must be far larger than the length of the hydrophobic group and it was postulated that the interior of these micelles is made up of solubilized ion These micelles are thus more like emulsion droplets than like normal micelles and solutions of these systems could really be looked upon as emulsions that are thermodynamically stable. The giant micelles were always observed when a perfluorocarboxylate ion was combined with an ammonium counterion that contained both a hydrophobic group and at least one H atom. The unsubstituted ammonium and the tetramethylammonium combined with the perfluorocarboxylate did not form giant micelles. These data suggested that giant micelles should also be formed when alkylammonium ions are combined with perfluoroacetate because the interaction of these ion pairs should be very similar to the investigated systems. For this reason the perfluoroacetates of the dodecyl- and tetradecylammonium ion were studied by light-scattering, conductivity, surface tension, and viscosity measurements in order to characterize the size of the aggregates formed and by kinetic and electric birefringence measurements to obtain information on their (1)H. Hoffmann, B. Tagesson, and W. Ulbricht, 2. Phys. Chem. (Frankfurt urn Main),113, 17 (1978). (2) H. Hoffmann, G. Platz, H. Rehage, K. Reizlein, and W. Ulbricht, Makrornol. Chem., 182, 451 (1981). 0022-3654/81/2085-1418$01.25/0
dynamic behavior. For comparison some measurements were also carried out with the Mono- and Difluoracetates and with the corresponding Chloracetates of alkylammonium detergents. The results on the investigated systems furthermore are compared with previous studies on the alkylammonium halide^.^ These investigations showed that the alkylammonium halides form normal spherical micelles. The formation of large aggregates by the alkylammonium perfluoroacetates was expected to be easily detectable by their different behavior.
Experimental Section and Results The compounds were prepared from dodecyl- and tetradecylamine (a Merck product of analytical purity), respectively. The amines were dispersed in water and titrated with a solution of pure trifluoroacetic acid until the pH value of the solution was 4. Above 40 "C the solutions were perfectly clear after the titration and the compounds crystallized from these solutions on cooling. After filtration the salts were twice recrystallized from water and then dried over P205at room temperature. The compounds had well-defined melting points that are given in Table I. It is remarkable that the melting points of the trifluoroacetates are closer to the melting points of the amines than to the halides. This can probably be taken as an indication that the compounds do not form a real ionic lattice but rather a molecular lattice and that the interaction between the surfactant ions and the counterions is very strong. (3)(a) H. Hoffmann, R. Lang, D. PavloviE, and W. Ulbricht, Croat. Chirn. Acta, 62, 87 (1979); (b) R. D.Geer, E. H. Eylar, and E. W. Anacker, J. Phys. Chem., 76, 369 (1971).
0 1981 American Chemical Society
The Journal of Physlcal ChernMy, Vol. 85, No. 10, 1981 1418
Detergents with Unusual Aggregation Behavior
TABLE I: Values for the Melting Points Tm, the cmc, the Apparent Dissociation Degree a, and the Surface Tension 7 at the cmc for Dodecyl- and TetradecylammoniumDetergents with Various Counterions compound Tm, "C T, "C cmc, mol/L LY 7 ,N/m
28 lsoa
C,zHz,"z C1ZH25NH3C1
C,,H,.NH, (Cl:CF,COO = C;;H;;NH; (C1:CFjCOO = C,,H,,NH, (C1:CF3C00 = C,,H,,NH,CF,COO C,zHz,NH,CF3CO0 + lo'* C,,H,.NH,CH,FCOO
19:l) 9:l) 4:l) '
76 m CF,COONa
73 40 1soa 82 80
25 25 25 25 25 25 25 25 25
1.5 X lo-' 1.32 X lo-' 1.26 X 1.17 X lo-' 6.75 x 10-3 3.7 x 10-3 1.23X lo-' 8.8 x 10-3 6.8 X
0.28 0.28 0.28 0.29 0.13
3.2 X
lo-*
3.0 X
lo-'
0.22 0.12 0.10
3.4 x
34 40 40
3.8 x 10-3 2.1 x 10-3 3.3 x 10-3
0.23
3.0 X lo-' 3.2x 3.4 x
0.08
0.22
Decomposition point. Critical micelle concentration (crnc) measurements were carried out on the investigated detergent solutions by measuring the electrical conductivity with a Wayne Kerr bridge and the surface tension with a Lauda tensiometer. The crnc values are also given in Table I. The table also contains values for the surface tension at the crnc and values for the apparent dissociation degree of the micelles a which is calculated as the ratio of the slopes of the conductivity plots against the total concentration above and below the cmc. The small a shows that the surface charge density on the micelles must be very small, which can only be caused by a strong interaction of the counterions with the micelles. If excess NaCF3CO0 is added to the surfactant solutions the crnc is shifted to smaller values in the usual way! The addition of the electrolyte causes the solutions to turn cloudy, even when the excess is still rather small (4 X rn in the case of dodecylammonium trifloroacetate DATFA). These turbid solutions seem to be thermodynamically stable. No precipitation was observed from the turbid solutions when they were kept at 25 (DATFA) or 40 "C (TATFA) for several days. Under these conditions the large aggregates causing the turbidity seem to be in equilibrium with the monomers. Relaxation measurements using the pressure jump and the shock wave apparatus with conductivity readout were carried out in the the clear and the turbid solutions. In the DATFA solutions one relaxation process was detected, while TATFA solutions showed two relaxation processes. The relaxation process for DATFA and the faster process for TATFA show typical features of the fast process which is present in micellar solution^.^^^ Figure 1gives a plot of the reciprocal relaxation times T~ as a function of the total concentration co for DATFA and TATFA. It shows a typical linear increase. The deviations of the points from straight lines is within an experimental error of &lo%. It is noteworthy, however, that the linear plot for TATFA has a break at a concentration which is about double the cmc. Additional results for relaxation times are summarized in Table 11. The values for the relaxation times are a little long for concentrations not too far above the crnc with respect to other CI2 and C14 detergent systems.38 Furthermore, the values for T~ became considerably longer on addition of an excess of NaCF3CO0. This behavior is
contrary to the results on other systems where it was observed that the addition of simple electrolytes shortened the short relaxation time.' For TATFA a slow relaxation process in the millisecond range could also be detected besides the fast process. The values of these relaxation times are also given in Table 11. No slow process was detectable in solutions of DATFA. Comparison measurements in mixtures of DATFA and dodecylammonium chloride (DAC1) showed that the slow process for DACl becomes longer with increasing amounts of DATFA and that it finally becomes too long for the pressure jump apparatus (longer than several seconds). Electric birefringence measurements were carried out in order to detect anisotropic aggregates that could be present.s The measurements were carried out with a commercial T-jump apparatus that was fitted with polarizers to detect the electric birefringence? Large birefringence effects were observed for solutions of DATFA but not for TATFA. For a given concentration the amplitude of the signal at the photomultiplier increased with the forth power of the electric field in the solution. Typical results are plotted in Figure 2. Unfortunately, the time constant for the build up of the birefrigence could not be determined with a high degree of accuracy because both the time constant for the orientation and the time constant for the detector were about 1ps. However, the recorded orientation times were temperature and concentration dependent, which clearly indicates that the orientation time could not have been significantly shorter than the time constant of the equipment. The electric birefringence decreased rapidly with increasing temperature and decreasing concentration as shown in Figures 3 and 4, where the square roots of the intensity i of the transmitted light are plotted against temperature and total concentration, respectively. The intensity i was measured as a voltage signal at the photomultiplier; its square root is proportional to the birefringence An. The decrease of the amplitudes was parallel to the shift of the orientation times to shorter values. Electric birefringence was also observed in turbid solutions of DATFA formed on addition of NaCF,COO. But both the concentration and the temperature dependence of the effect were very different in comparison with the clear solutions. The orientation times were considerably shorter
(4) K. Shinoda, T. Nagakawa, B. Tamamushi, and T. Isemura, "Colloidal Surfactants", Academic Press, New York, 1963, Chapter 1. (5)(a) E. A. G. Aniansson and S. N. Wall, J. Phys. Chem., 78,1024 (1974);(b) ibid.,79,857 (1975); (c) ibid., 84,727 (1980). (6) E. A. G. Aniansson, M. Almgren, S. N. Wall, H. Hoffmann, I. Kielmann, W. Ulbricht, R. Zana, J. Lang, and C. Tondre, J.Phys. Chem., 80,905 (1976).
(7)R. Folger, H. Hoffmann, and W. Ulbricht, Ber. Bunsenges. Phys. Chem., 78,986 (1974). (8)H. Benoit, Ann. Phys., 12e, SBr. 6,36 (1951). (9)(a) C. T. OKonski and A. J. Haltner, J. Am. Chem. SOC.,79,5694 (1957); (b) E. Fredericq and C. Houssier, "Electric Dichroism and Electric Birefringence", Clarendon Press, Oxford, 1973.
The Journal of phvsical Chemistry, Vol. 85, No. 10, 7987
1420
1
A
11 x 104
Hoffmann et ai. DAT FA
T
5
*
CO'C
0,lWl
'
ZS'C
0,04 H/I
10
15
x
10'
Figure 2. Plot of the square root of the relative amplitudes iof the orientation effect of DATFA solutions at different concentratlons and temperatures as a functlon of the square of the voltage of the applled electric pulse.
7 1 -
5
10
15
X ) .tu3
Figure 1. Plots of the reciprocal values of the short relaxation time 7 , for DATFA (a) and TATFA (b) solutions as a function of the total concentration co at different temperatures.
even though the aggregates must be much larger in these solutions. It is therefore likely that the operating mechanism for the building up of the birefringence must be different in the turbid solutions compared with the clear solutions. It is also worth mentioning that the birefrin-
gence effects for the highest studied concentrations did not decay in a single step but there was a second step present that decayed with a considerably longer time constant. The amplitude of this effect, which was only about 10% of the amplitude of the main orientation effect, increased linearly with increasing electric field, but decreased with decreasing concentration and was no longer detectable in m. solutions whose concentrations were below 8 X In order to obtain accurate orientation times we reported some measurements with an improved apparatus which allowed us to measure the building up of the birefringence and also its decay by applying an electric high-voltage pulse of rectangular form and variable length to the investigated solution. This apparatus, which had a time resolution far below 1p s , will be described in detail in another paper. Here it will only be pointed out that the results of the measurements obtained with the T-jump equipment could be confirmed by the new field jump apparatus. Orientation times are given in Table VII. Both classical and dynamic light-scattering measurementa were carried out on the DATFA and TATFA solutions.1° In order to clean dust particles from solutions, we intended to pass the solution through micropore filters with a pore diameter of 0.1 pm. But it turned out that this was difficult to perform because the filters represented a flow resistance for these solutions that was much higher than for solutions with normal spherical micelles. This observation is an indication that the particles had dimensions near the pore size and that there was danger of (10) B. J. Berne and R. Pecora, "Dynamic Light Scattering",Why, New York, 1973.
The Journal of Physical Chemistry,
Detergents with Unusual Aggregation Behavior DATFA
300
30
330
320
Plot of the square root of the relative amplitudes iof the orientation effect of DATFA solutions for an electric pulse of 30 kV as a function of the temperature at different total concentrations. Flgure 3.
DATFA U: 35 k V
/
I
Flgure 4. Plot of the square root of the relative amplitudes iof the orlentation effect of DATFA solutions for an electrlc pulse of 35 kV as a function of the total concentration coat different temperatures.
destroying the filters by pushing the aggregates through the filters. The solutions were therefore passed through
Vol. 85, No. 10, 1981 1421
filters with large diameter pores in the actual experiments. The dynamic light-scattering measurements could not be reconciled with a single correlation time constant. Even in the clear solutions several correlation times could be distinguished. The data are summarized in Table 111. They seem to indicate that the scattering is due to different particles or that the diffusion of the particles is controlled by several time constants. It is interesting to note that the clear solutions showed correlation times that were as long as in the turbid solutions. The amplitude of the fast correlation process seems to correlate with the amplitude of the birefringence effect. The classical light scattering data could not be evaluated because the forward scattering intensity was always fluctuating and no constant signal could be obtained. These data will therefore not be used in the discussion. Finally, viscosity measurements were carried out by using a low-shear viscosimeter (Contraves) which allowed the determination of low viscosities with an accuracy of a few percent at extremely small shear rates. Some of the values were repeated with a Zimm-Crothers viscosimeter (Krannich) which allowed us to measure the viscosity of aqueous solutions with an accuracy of 0.1% at a very low shear rate. These control measurements were important because it was found that in some surfactant solutions the viscosity is strongly dependent on the shear rate and sometimes also on the length of time for which the solutions is sheared. It can be seen that the viscosity for TATFA is not significantly higher than the water viscosity m. But is has to be even at concentrations of 5 X pointed out that the solutions were viscoelastic and at a shear rate above 25 s-' they seemed to become dilatant so that the measurements were only carried out below this shear rate. Below this value the solutions showed normal Newtonian behavior in spite of the visible viscoelasticity. In contrast, solutions of DATFA showed Newtonian behavior at all shear rates of the equipment (up to 100 s-l) even at concentrations of lo-' m. The value at the highest shear rate agreed very well with the values obtained with the Zimm-Crothers viscosimeter at the very small shear rate. As can be seen from Table IV,the viscosity increased considerably with total detergent concentration and reaches at lo-' m a value that is almost 100 times higher than the viscosity of pure water. Furthermore, the viscosity does not increase linearly with the concentration but with a higher power; the concentrated solutions also showed a very strong dependence of the viscosity on the temperature. The increased viscosity coincides with the appearance of the electric birefringence effect; solutions at temperatures above about 40 OC did not show orientation effects and also no significantly increased viscosity in comparison with water.
Theoretical Considerations and Discussion of the Data crnc Values. The cmc values of the TFA systems are smaller by a factor 2 than the cmc values of the previously studied alkylammonium halide~.~J'One is tempted to attribute this increased stability of the trifluoroacetates to H bonds between the counterions and the ammonium head groups. But a comparison with the results that have been obtained on alkylpyridinium salts shows that there also the cmc values of the trifluoroacetates are lower by a factor 2 compared with the cmc's of the chlorides.12 As (11)P. Mukerjee and K. J. Mysels, Natl. Stand. Ref. Data Ser., Natl. Ber. Stand., No.36 (1970). ( 1 2 ) H. Hoffmann, B. Tagesson, and W. Ulbricht, Ber. Bunsenges. Phys. Chern., 83, 148 (1979).
1422
The Journal of Physical Chemistry, Vol. 85, No. 10, 1981
Hoffmann et al.
TABLE 11: Values for the Relaxation Times for Dodecyl- and Tetradecylammonium Trifluoroacetate as a Function of the Total Concentration c, at Different Temperatures with Various Concentrations of Added CF,COONa CI2H2,NH3CF3COO 71,
c,, mol/L 7.0 x 10-3 7.5 x 10-3 8.5 x 10-3 1.0 x 1.2 x 10-2 1.5 X lo-' 4.0 x 10-3 5.0 x 10-3 7.5 x 10-3 1.0 x 10-2 1.5 X 2.0 x 4.0 X 1.0 x 10-2 1.0 x l o - z 1.0 x 1.0 x 1.0 x 1.0 x 10-2 1.0 x 2.0 x 2.0 x 2.0 x 1.5 X 1.5 X lo-'
CNaTFA
rn m rn rn m rn rn
25 "C 200 100 64 28 18 12.5 5000 1500 550 174 79 52 25 28 28 52 178 180 174 110
30 "C 140 77 41 23.3 14.3 10.7
-
NaTFA NaTFA NaTFA NaTFA NaTFA NaTFA NaTFA
2X rn NaTFA rn NaTFA 4X 6X rn NaTFA 8X rn NaTFA 1X m NaTFA 2X rn NaTFA C1:CF3C00= 1:0 C1:CF3C00= 19:l C1:CF3C00= 9 : l C1:CF3C00 = 9 : l C1:CF3C00= 4 : l
PS
-
23.3
25 r2,ms (at 25 "C)
35 "C 49 31 20 12.1 9.6
20
18 32 67 121 780
C,,H2,NH3CF3CO0 71,
c,, mol/L 2.5 x 10-3 3.5 x 10-3 5.0 x 10-3 7.5 x 10-3 1.0 x 2.0 x 3.0 x 10-3 3.0 x 10-3 3.0 x 10-3 3.0 x 10-3 3.0 x 10-3 3.0 x 10-3 3.0 x 10-3 3.0 x 10-3 3.0 x 10-3 3.0 x 10-3 1.0 x lo+ 1.0 x 10-2 1.0 x 1.0 x 101.0 x 1.0 x 10-1
CNaTFA
2x 4x 8X 1.2 X 1.6 X 2X 4X 6X 8X 1X
rn NaTFA rn NaTFA rn NaTFA m NaTFA rn NaTFA m NaTFA m NaTFA m NaTFA rn NaTFA m NaTFA
2x m NaTFA 4 X l o - ) m NaTFA 6X rn NaTFA 8X m NaTFA 1x m NaTFA
H bonds can be of no importance on these systems we have to conclude therefore that the strong binding of the TFA to the micelle must be due to the interaction of the hydrophobic CF3group with the micellar surface. This is also reflected in the fact that the cmc's of the acetates are higher than the cmc's of the monofluoroacetates which are higher again than the corresponding values of the trifluoroacetates. Obviously, the TFA must be able to bind to the interface with a gain in free energy which is larger than the electrostatic contribution alone. Some of this energy is probably due to the disappearance of the hydrocarbonwater and perfluorocarbon-water interface on the micelle and around the CF3 group. It is noteworthy to mention . . here that the CFSgroup is as effective in lowering the cmc of a system as the strongly hydrophobic group C5Hll in the C5HllS03- anion.
NS
721
35 "C 143 50 29 22.5 18 10.5
40 "C 111 36 22.5 16.6 14.6 7.2
18
57 75 95 210 > 300 14.6 18.5 24 36 68 125
35 "C 1.1 4 5.3 1.9 1.4
ms 40 "C 0.96 . . 6.2 6.5 2.4 1.6 2.1 1.3 1 -0.7
-0.4
1.9
2.4
The effect of the CF3group is also felt on the a values of the systems which are considerably lower than the a values of the chlorides. The TFA micelles appear to be weakly charged toward the bulk solution, at least much weaker than the chlorides. The real dissociation degrees that are determined from the shift of the cmc with the counterion concentration are very similar to the a values from conductivity measurements. This comparison shows that it seems to be justified to determine as a rough estimate the dissociation degrees from the conductivity data, It seems also possible that the effectiveness of TFA in lowering the cmc and the a value of an ionic detergent has nothing to do with the hydrophobic character of the CF8 group but is rather a consequence of the electron-withdrawing power of the CF3 group by which the charge density on the oxygen atoms of the carboxylate group is reduced. This could lead to weaker solvation of the TFA
The Journal of Physical Chemistry, Vol. 85, No. IO, 1981 1423
Detergents with Unusual Aggregation Behavior
TABLE 111: Values for the Diffusion Coefficient D and the Stokes' Radius r from Quasielastic Light-Scattering Measurements for Solution of C,,H2,NH3CF3CO0and C,,H2,NH3CF3CO0at Different Total Concentrations c,, Different Temperatures, and with Various Amounts of Added CF,COONa ( c N ~ )
c,, mol/L 1.0 x lo-2 1.0 x 1.0 x 1.0 x 1.0 x 1.0 x 1.0 x 1 0 - 2 1.0 x 1.0 x 10-2 2.0 x 10-1 2.0 x 2.0 x 2.0 x 2.0 x 10-2
T , "C 20.5 34.2 48.2 25' 20 34 34 34 34 24.9 29.6 34.3 43.4 51.3
C N ~ T F Amol/L ,
4.0 x 2.0 x 4.0 x 1.0 x 2.0 x
D,)o cm2/s
rl )o A
10-3 10-3
10-3
lo-z
c,, mol/L T , "C 39.4 1.0 x 101.0 x 45.7 51.9 1.0 x Calculated from the short correlation time. immediately after rapidly cooling a hot solution.
4.6 X lo-' 6.7 X lo-' 6.2 x 10-7 1.2 x 101.2 x 10-6 C14H2,CF3CO0
53 41 50 31 25
(TZ DZ2I/
D2,bcm2/s 2.0 x lo-' 4.2 X lo-' 5.4 x 4.0 X lo-' 2.5 X lo-' 4.1 x lo-'
4.1 X 3.9 x 4.2 X 4.4 x 5.1 X 3.0 X 4.7 x 6.4 X
r2vb
A
1000 730 610 600 850 760 750 800 730 550 540 1000 800 690
lo-' lo-' lo-' lo-' lo-'
lo-'
lo-' lo-'
D2'
0.8 0.6 0.8 1.0 0.4 0.6 0.6 0.7 0.5
A D2,bcm2/s r2,b '4 60 4.4 x lo-' 800 50 4.2 X lo-' 850 1.6 X lob6 24 4.8 X lo-' 820 Measurement carried out Calculated from the long correlation time.
D , )o cmz/s 7.0 X 10" 7.2 x 10-7
TABLE IV: Values for the Viscosity of Solutions of Dodecyl- and Tetradecylammonium Trifluoroacetate as a Function of the Total Concentration c, at Different Temperatures at Shear Rates between 0 and 100 s" (Newtonian Liquids) compound c,, mol/L T , "C q , mPa s water 25 0.89 water 30 0.80 water 0.67 40 C,,H,,NH3CF3CO0 1.0x 25 0.895 C,,HZ5NH3CF3COO 1.5 X lo-' 25 0.94 C,,H,,NH,CF,COO 2.0 x lo-' 25 1.00 1.13 C,,H,,NH,CF,COO 2.5 X lo-' 25 1.26 C,,H,,NH,CF,COO 3.0 x lo+ 25 C,,H,,NH,CF,COO 4.0x 25 1.74 C,,H2,NH3CF3CO0 5.0 x 25 2.62 C,,H,,NH,CF,COO 5.0X 30 1.69 ClZH,,NH3CF3COO 6.0X lo-' 30 2.67 C,,H2,NH3CF3CO0 7.0 X 30 3.92 C,,H2,NH3CF3CO0 8.0X lo-, 30 7.05 C,,H,,NH,CF,COO 9.0x 30 11.96 C,,H,,NH,CF,COO 10.0 X lo-* 30 21.5 C,,H,,NH,CF,COO 1.0X 40 0.67a C14H2,NH3CF3CO0 5.0X 40 0.80" Solutions showed viscoelasticity so that Newtonian behavior could only be observed with shear rates between 0 and 25 s-'.
ion and consequently could have the effect that the ions could approach closer to the micellar surface. This explanation is supported by the fact that other ions like ClOi or NO3- also give very low cmc and a values." These ions are certainly not hydrophobic but again have a small charge density on the oxygen atoms. So maybe there is nothing special with the TFA ion, but the discussed effects are due to its position in the Hofmeister series, where the TFA ion then would have to be placed close to the Clodion according to these results. Kinetic Parameters. The kinetic measurements were evaluated by using the theory of micelle formation of Aniansson and Wall.5 According to this theory two relaxation processes are present in micellar solutions. The faster process is due to the shift of the mean aggregation number of the micelles, while their number remains constant; the slower process is due to the change of the mi-
rl,a
TABLE V: Values for the Kinetic Parameters k-/nand k - l o for Dodecyl- and Tetradecylammonium Detergents with Trifluoroacetate and Halides as Counterions at Different Temperatures compound
T,
"C C12H25NH31 20 Cl2H2,NH3CF3COO25 C,,H,,NH,CF,COO 30 C,,H,,NH,CF,COO 35 C14H29NH3C1 40 C,,H,,NH,CF,COO 35 C,,H,,NH,CF,COO 40
k - / n , s-' 1.1 x 105 6.8 X lo4 7.5 x 104 8.7 x 104 5.0 x 104 2.3 x 1 0 4 3.2 x 104
k - / 0 2 ,s-l cmc, mol/L
1.4x 3.7X 6.1 x 1.0 x 1.8 x 2.5x 5.0 x
104 1.1 x 10-2 l o 3 6.75 X lo-' 103 104 104 4.0 x 10-3 103 103 2.1 x 10-3
cellar concentration. This change can take place only via the micellar nucleus, the oligomer with the lowest concentration. The concentration of nuclei is in most cases below 10-loM; it can thus be easily understood why this process can be very slow without having to assume the existence of a step with a small rate constant. Quantitatively, Aniansson and Wall derived for the two relaxation processes the following equations: ( 1 / r 2 )= (k-ci/c3)((cmc
+ n2c3)/(cmc + u2c3)) (11)
Here n means the mean aggregation number of the micelles¶ci the concentration of micellar nuclei, u the variance of the micellar distribution curve, k- the rate constant for the dissociation of a monomer from the micelle, and c3 = (co - cmc)/n the micellar concentration. When eq I is used it k possible to obtain the parameters k-/n and k - 1 2 from the plot of the reciprocal short relaxation time as a function of co in Figure 1.16 These values are given in Table V. For comparison the table also contains the values for the halides DAI and TAC1. The k - / n values are only slightly lower for the TFA salb than for the chlorides. This rather good agreement can be taken as evidence that the head groups of the detergents are located at the micellar interface and that all molecules in the micelles can directly participate in an exchange process. For TATFA it was possible to measure the r2 values. As previously shown these values taken together with infor-
1424
The Journal of Physical Chemistty, Vol. 85, No. 10, 1981
Hoffmann et al.
TABLE VI: Values for the Parameters n, u , k-, and k+ for Dodecyl- and Tetradecylammonium Trifluoroacetate at Different Temperatures, Calculated from the Two Relaxation Times r 1 and 7 ,
T, "C k+, L/mol s k - , s-l U n 25 8.6 X lo9 6.8 X'10' 126 849a ( 6 5 0 b ) 36 5.3 x 109 3.6 X 10' 60 410a 40 1.1 x 109 4.0 X lo6 28 126 6.3 X lo6 17 106 40 1.3 x 109 C14H29NH3a a Calculated with 7 , values obtained from a linear plot of log ( 1 / ~ , against ) log (cmc) for C,,H,,NH,' with various counterions. Calculated with T, = 1 0 s, the smallest relaxation time above the range of the pressure jump apparatus. compound C,,H,,NH,CF,COO Cl,H,,NH,CF3CO0 C,,H,,NH,CF,COO
mation from the short relaxation times permit the calculation of n and a directly from kinetic measurements without the help of any other inf0rmati0n.l~ The results of these calculations are given in Table VI. The n values thus obtained are only somewhat larger than the values we could expect for spherical micelles, which indicates that the micelles must be globular shaped. This result agrees well with the birefringence measurementa that were carried out on these systems and showed that anisotropic aggregates do not exist in these solutions. The n values in Table VI were calculated from the slope of the l / ~ ~ curves - c ~ at the cmc. As seen from Figure lb, the slope becomes much smaller at higher concentrations. This break in the curves occurs in a narrow concentration range. It could mean that from here on the concentration of the micelles increases slower with total concentration than before the break. Consequently, the micelles would have to be larger. But again as before the break no electric birefringence is observed even for concentrations as high as 5 X m. At this concentration the solution, which is still perfectly clear at 40 "C, shows weak viscoelasticity which can easily be observed by the small recoil of the solution that occurs, if the flask containing the solution undergoes a fast transient motion. In this way the solution of TATFA behaves in a rather unique way because all other detergent solutions that show viscoelasticity gave rise to electric birefringence. This shows that there must be different mechanisms operating in viscoelastic solutions. The hydrodynamic radii that are obtained for the micelles in this concentration range by quasielastic lightscattering measurement are considerably larger than for normal micelles with a tetradecyl chain. We have to conclude therefore that these aggregates which have large radii and no anisotropy must be able to solubilize detergent molecules with their counterions in the interior of the micelles. The TATFA system indeed seems to form the kind of micelles that was hoped to be found in this investigation. The very small k - / n values support these conclusions. According to this model, the low experimental k-/n and a! values are average values for these parameters for the molecules that are inside the micelle (q)and at the interface of the micelle (no).Because the ion pairs in the interior are not dissociated at all and also they cannot exchange directly we can write nisi + noao noao e!(111) %xpt = ni + no ni + no
The ratio of the slopes of Figure l b directly gives therefore the ratio of the molecules that are at the interface to the total number of molecules in a whole micelle. This ratio is about 1/2 for TATFA if we assume that the molecules (13)H. Hoffmann, Ber. Bunsenges. Phys. Chen., 82,968(1978).
a t the interface of the large micelles exchange with the same rate of those molecules in normal spherical tetradecylammonium micelles at concentrations close to the cmc. On the basis of both dynamic lighliscatteringand kinetic results the large micelles for TATFA do not seem to grow to such big aggregates as for the perfluorocarboxy1ates.l The aggregation process seems to come to an end when the radius of the micelles reaches about twice the normal radius and the question comes up why the aggregation process does not lead to complete phase separation if the ion pairs can be incorporated into the micelles. The answer to this question may have something to do with the interfacial tension of the aggregates. It could be conceivable that the interfacial tension of the aggregates approaches 0 for only a particular radius of the micelles and increases again for larger values. Rebinder et al. have put forward some arguments for the existence of such systems.14 Unfortunately, with solutions of DATFA the slow relaxation process could not be measured because the relaxation time was too long as the results of mixtures of solutions of DATFA and DACl indicate. From pure DACl to a mixture ratio of 4 1 the relaxation time increases from 18 to 780 ms at 26 OC. If we assume that the relaxation time keeps increasing in the same way we can extrapolate a relaxation time for the pure DATFA solution from a plot of log ( 1 / ~ against ~) log (crnc). It is, however, more likely that the 1/r2values go through a minimum with increasing DATFA content as has been observed in several cases.12 Table VI contains n and a values that were calculated for two extreme cases. In the first set it was assumed that T~ was 10 s, which is about the longest relaxation time that could be measwed or 2300 s which is an extrapolated value. Both assumptions lead to n values which are so large that they cannot be reconciled with the existence of normal globular aggregates. Large n values together with normal k - / n values can occur and have been observed for anisotropic micelles.16 We could expect therefore that such aggregates are formed at the cmc. However, as will be pointed out later, no anisotropic aggregates could be detected at concentrations slightly above the cmc. Only when the concentration was raised considerably above the cmc did we find anisotropic aggregates by electric birefringence and viscosity measurements. In this concentration range the data obtained by kinetic, electric birefringence, and viscosity measurements are in good agreement. The apparent discrepancy exists only for the small concentration range above the cmc. In this range, very large aggregates are also observed by dynamic light-scattering measurements as will be discussed later on. h judged from the experimental evidence obtained by the different methods the aggregates should have the following features to account for the observed results: large aggregation numbers; no anisotropy; head (14)V. M.Barboy, Y. M. Glazman, P. A. Rebinder, G. J. Fuks, and E. D. Shchukin, Kolloid. Zh., 32, 480 (1970). (15)H. Hoffmann and B. Tagesson, Z. Phys. Chem. (Frankfurt am Main), 110,113 (1978).
The Journai of Physical Chemistry, Vol. 85, No. 10, 1981 1425
Detergents with Unusual Aggregation Behavior
groups of the detergent ions situated at the micellar water interface. Aggregates that would fulfill these criteria would be vesicles, disklike aggregates, or torsoids as proposed by Ninham et a1.16 But of course there is also the obvious possibility that the assumptions that are made for the calculations of the n values do not hold for the present systems and the n values are really much smaller and can still be rationalized with normal globular micelles. The large particles that are observed by the quasielastic light-scattering technique could be due to minor concentrations of aggregates in which only a small fraction of the detergent molecules is present but these aggregates could be the dominant light scatterers. A good candidate for such aggregates could be coagulated micelles. Because of their low charge density, the micelles of the investigated systems seem to be able to agglomerate to rather loose particles in which the micelles can keep their identity. While such a coagulation normally requires the addition of high concentrations of supporting electrolyte, very small amounts of added electrolyte are sufficient for the investigated systems to facilitate agglomeration. This agglomeration can easily be observed visually by the appearance of a slight turbidity, if small m) are added to amounts of NaTFA (more than 4 X DATFA solutions. These turbid solutions seem to be thermodynamically stable; no precipitation can be observed on standing even for several days. It is likely that the agglomeration process can also occur, of course to a smaller extent, in the solutions with no added salt. Systems with Added Salt. For both systems, the short relaxation times became longer when small amounts of NaTFA are added to the solutions. The increase for DATFA occurs rather abruptly in a very small concentration range, while for TATFA the increase of the 7 values occurs smoothly with added salt. The change of the relaxation times with added electrolyte is in the opposite direction of what has been observed for NaDS and other systems.’ For these systems the decrease of the T~ values can be related to the increase of the micelle concentration that was caused by the shift of the cmc to smaller values while the aggregation number of the micelles remains constant for not too high salt concentrations. In the present systems this normal effect is obviously counterbalanced by another effect that is much larger. The decrease of the micelle concentration could come about by two different processes: The micelles could grow larger by the addition of electrolyte or more and more micelles could agglomerate to larger secondary aggregates while the individual micelles remain unchanged. The second process seems to be the more likely one because of evidence from the other measurements. The data from the quasielastic light-scattering experiments do not show a continuous change of the hydrodynamic diffusion coefficient with increasing concentration of added salt, but indicate that the small micelles disappear while the concentration of the very large aggregates increases. The kinetic data actually also favor this explanation because the increase of the short relaxation times is not large enough to account for the very large aggregates that are seen by light scattering. The radii of the large particles which cause the turbidity in the solution are more than a factor of 20 larger than the radii of the normal micelles. The concentration of these aggregates should therefore be at least by 10000 times smaller than the concentrations of the normal micelles and the relaxation time should vary by a similar factor which is clearly not the case. ~
~
~
~~~~
(16) I. N. Israelachvili, D. J. Mitchell, and B. N. Ninham, J. Chem. SOC.,Faraday Trans. 2, 72, 1525 (1976).
0.01M
TATM
0.OlM
QATFA
C.
40
25 .C
1
I 2
I 4
I
I
I
I
I
I
I
I
6
8
10
12
14
16
8
Xi
‘N~TFA [M’lJ
Figure 5. Plot of the reciprocal values of the short relaxation time 7 , for DATFA solutions at a total concentration co = mol/L and a temperature T = 25 O C and for TATFA solutions at a total concentration co = lo-* moi/L and a temperature T = 40 O C as a function of the concentration of added NaTFA.
The reciprocal values of the fast relaxation times are plotted as a function of the concentration of the added salt in Figure 5 for DATFA and TATFA. The drop of the l/rl values for DATFA occurs at the same concentration of added salt at which the solutions become turbid. While the drop of the 1 / values ~ ~ is quite large, it does not drop much below the k-/u2 values of the pure systems. This is an indication that there are a few normal micelles left in the turbid solutions that cause T~ and these normal micelles seem to be in a dynamic equilibrium with the large secondary aggregates. If temperature jump measurements are carried out in turbid solutions and the light intensity of the transmitted light at a wavelength of 470 nm is monitored, relaxation effects are indeed detectable in the millisecond time range. These effects indicate that the scattering particles in the solution are changed by the temperature jump. The relaxation processes must be caused by a change of the size or the number of the particles, for example, by secondary agglomeration. This agglogmeration of the micelles can be governed by the same processes as the formation of micelles of monomers. However, in this work these measurements and their evaluation shall not be presented; they will be described in a following paper. Electric Birefringence Measurements. Electric birefringence measurements have been carried out before on solutions of biopolymers and polyelectrolytes to determine the dimensions of the macromolecules.17 For the interpretation of the data it is usually assumed that the electric field induces a dipole moment on the polyion by displacing the counterions relative to the polyion and by orienting the dipole in the electric field.18 According to this model the length of the molecule is then determined from the orientation time according to the equation 1 6(3kT)(ln ( a / b ) - 0.8) -= 70
?ria3
(VI
where a is the length and b the width of the rod and 9 the viscosity of the solution. For rods having an orientation time T~ considerably shorter than the RC time constant of the discharge circuit, the light intensity at the detector is given by the following equation: (17) B. R. Jennings, Adv. Polym. Sci., 22, 61 (1977). (18) (a) G. S. Manning, Biophys. Chem., 9,65 (1978); (b) E. Charney, K. Yamaoka, and G. S. Manning, ibid., 11, 167 (1980).
1420
Hoffmann et al.
The Journal of Physlcal Chemistry, Vol. 85, No. IO, 198 1
I = IO -62(e-t/'0
- e-2t/'RC)2
(VI)
4 where S is the phase shift of the electric field vector of the electromagneticwaves that are parallel and perpendicular to the electric field in the cell. The phase shift is given by the birefringence An according to the equation 6 = 21rdAn/h (VI11 when d is the thickness of the solution and the birefringence is connected with the strength of the electric field by Kerr's law An E2.It is likely that in the present studies the electric birefringence is caused by the same mechanism. While it seems theoretically possible that the electric birefringence could be built up by growth of the aggregates in the direction of the electric field by kinetic processes, such a mechanism can be ruled out on the basis that the observed orientation time constants are considerably shorter than the chemical relaxation times. The aggregates have therefore no chance of changing their aggregation number during the short orientation times. Furthermore, the data obey Kerr's law that predicts a forth power dependence of the photodetector signal on the applied electric field for the birefringence that is orientation controlled. This law is clearly fulfilled as seen in Figure 2. The equation cited above can therefore be used with confidence to calculate the dimensions of the aggregates. It should be noted that eq V was derived for stiff rods, while micellar rods are likely to be flexible. However, the error by regarding the micelles as stiff rods cannot be very serious; if the flexibility of the micelles would influence the orientation in the electric field significantly, additional orientation effects should be observed, for example, an effect due to the stretching of the rods in the electric field. The lack of such effects justifies the use of eq V for calculation of the lengths of the rods; the same argument can be used for the validity of eq X and XI. The measured orientation times increase from 0.9 ps for a 2 x I t 2 m solution to 1.7 ps for a 5 X m solution at 25 "C. The change of a factor 2 is about the same as the change of the viscosity of the solutions as can be seen from table IV. It would follow therefore that the aggregates change very little with concentration, if the measured viscosity is used in eq V for the determination of the lengths of the rods. This result would be very surprising and in contradiction to a conclusion reached by Ninham et a1.16who in a theoretical treatment of the aggregation process predicted a strong increase of the length of rods with increase of total concentration. Evidence for a growth of the rods with concentration has been reported recently by Lindman et al.I9 on the basis of NMR data for cetyltrimethylammonium salicylate. In view of these theoretical considerations and experimental observations it is more likely that the viscosity of water should be used in eq V. The increase of the orientation times would then be due to a growth of the rods and their lengths would increase by a factor of z1I3= 1.26 between 2 X and 5 X m (see Table VII). In comparison to the results that have been obtained recently an other systems this is a very modest change in size of the aggregates. For these systems the lengths of the rods increased linearly with total concentration.20 The amplitudes of the birefringence effects support the conclusions which can be reached from the time constants. It is interesting to note that no electric birefringence can be ob-
-
TABLE VII: Values for the Length of the Anisotropic Aggregates Assuming Ellipsoids with a Short Axis of 40 A (Twice the Length of a Detergent Ion"), Calculated from Orientation Measurements ( l , ) , from Viscosity Measurements ( I , ) , and from the Hydrodynamic Radius (lh) Obtained by Dynamic Light-Scattering Measurement for Dodecylammonium Trifluoroacetate at 25 "C
lo-' lo-' 3 X lo-' 2X
360
42
67 76 113 170
4 X lo-'
1.5
410 450
5 X lo-'
1.7
475
1.2
53
320
320b {q} = (q
- q o ) / q o cwith respect to the result from the
orientation measurements that anisotropic aggregates are Average formed above c, = 1 . 5 X lo-' mol/L only. values, independent of c,.
served between the cmc and another critical concentration (cmcn)that is more than a factor 2 higher than the normal cmc (cmcl) (see Figure 4). The amplitude for the electric birefringence then increases linearly from the cmcIIwith the concentration over a large concentration range. This shows that globular micelles exist between the cmcI and cmcn, while for concentrations above the cmcn anisotropic aggregates are found, the size of which varies little with concentration, There is no evidence for a gradual transition from globular micelles to anisotropic ones taking place over an extended concentration range. The cmcn in the present system is more like a phase boundary. While the length of the rods is little dependent on the concentration it is strongly dependent on the temperature. The amplitudes decrease linearly with increasing temperature and disappear completely at a critical temperature (see Figure 3). The temperature where the amplitude disappears increases with increasing total concentration. For the evaluation of the birefringence data it was assumed that the short radius of the anisotropic aggregates is given by the extended length of the hydrocarbon chain and a reasonable value for the headgroup plus the counterion2l A total radius of 20 A was used. Thus the length of the aggregates could be calculated from eq V; the values obtained are listed in Table VII. The calculated length of the rods is consistent with the hydrodynamic radius that is determined from the quasielastic light-scattering data; the calculated values are given in Table VI1 and the good agreement between the data obtained by the different methods can be taken as evidence for the validity of the conclusions drawn. The question may be asked what happens when the concentration is increased to higher and higher values and the number of anisotropic aggregates becomes so large that the aggregates start to interact with each other. It is known from many investigations on various detergent systems that different kinds of mesophases can be formed at high detergent concentrations.22 While no information seem to be available on the systems in the present study, nmr measurements have been carried out on decyltrimethylammonium trifluoroacetate and it was concluded that a lamellar phase is formed in solutions of this system at a high concentration.2s Indeed, also a much slower orientation effect was observed for DATFA solutions with concentrations above 7 ~~
(19) J. Ulmius, H. Wennerstrbm, L. B. A. Johansson, G. Lindblom, and S. Gravsholt, J. Phys. Chem., 83, 2232 (1979). (20)H. Hoffmann and W. Schorr, unpublished results.
0.9
2.5 X
~
(21) C. Tanford, "The Hydrophobic Effect",Wiley, New York, 1973. (22)R.F. Gould, Adu. Chem. Ser., No. 162 (1976). (23)G.C.Levy, R. A. Komoroski,and J. A. Halstead, J. Am. Chem. SOC.,96, 5456 (1974).
The Journal of Mysical Chemistry, Vol. 85, No. 10, 1981 1427
Detergents with Unusual Aggregation Behavior
X m. The orientation times are in the millisecond range and the amplitude of this effect was linearly dependent on the electric field while for the fast process an increase with the electric field with the forth power was found. For small voltages therefore the total amplitude consists mainly of the slow process while at high voltages the amplitude of the slow process can practically be neglected beside the big amplitude of the fast process. If a long orientation time is used for the calculation of the dimensions of the anisotropic aggregates we obtain values in the range of some thousand angstroms. It is certainly unrealistic to assume that the rods really grow to such big length. If this would be the case it would be difficult to see why rods could not exist with dimensions in accordance with orientation times between the two observed time constants. It is more likely that the long time constant is due to a new species with a different structure. A possible alternative could be the existence of domains in which rods could be oriented with respect to each other. Such liquid crystalline structures have been predicted on theoretical arguments and have been confirmed by experiments on polyelectrolyte solutions." It is very likely that such structures can also be formed in detergent solutions. Preliminary measurements on other detergent systems have indicated the existence of two orientation times that vary by up to a factor 1000 in their time constants. In viscoelastic detergent solutions the slow orientation times can be observed already at rather small concentrations. For the formation of such domains in the present system evidence can also be taken from the fact that the fast orientation which disappears above a certain temperature appears again practically instantaneously when the temperature is lowered quickly below this temperature, The amplitude immediately has its final value and does not change with time. On the contrary, the amplitude of the slow orientation effect does not immediately appear when the temperature of the solution is rapidly lowered below the critical temperature. Depending on the concentration it takes up to several hours until the amplitude of the slow process has reached ita find value. This clearly shows that the formation of the particles giving rise to the slow process needs time, which can be understood if the particles are ordered domains or phases, but is not intellegible if the particles would only be longer rods, because longer rods should grow with a time constant similar to q. In solutions of TATFA no orientation effect was detected by the electric birefringence measurements. This leads to the conclusion that no anisotropic aggregates could be present in the solutions of this compound up to concentrations of 5X m or that disklike aggregate with only a small deviation from the globular shape are formed. This result is in accordance with the viscosity measurements, too, where a t low shear rates Newtonian behavior of all solutions was found up to 5 X m and the viscosity was at the highest concentration very slightly higher than the viscosity of pure water, which also is a proof that no rods are present in the solutions. The observed viscoelasticity which made measurements at shear rates above 25 s-l impossible could therefore not be caused by highly anisotropic aggregates, as already mentioned above. In the turbid solutions of DATFA with added NaTFA we know of the existence of large aggregates and therefore (24)(a)S.Lin, W. Lee,and J. M. Schurr, Biopolymers, 17,1041 (1976); (b) E.Senechal, G. Maret, and K. Dransfeld, Int. Biol. Macrornol., 79,
126 (1979); (c) L. Onsager, Ann. N. Y. Acad. Sci., 51,627 (1949); (d) D. Stigter, Biopolymers, 16, 1435 (1977); (e) ibid., 18,3125 (1979); (0 D. Stigter, private communication.
we could have expected to find long orientation times with the electric birefringence method. Contrary to our expectations the orientation times turned out to be even shorter than the short times measured in the clear solutions. The orientation times were in fact much too short to resolve with the available equipment. However, the decay of the birefringence signal has a time constant that was four times shorter than the RC time constant of the discharge circuit and because the amplitude of the signal was again proportional to the fourth power of the voltage it is clear that the signal had already reached its equilibrium value and decayed in phase with the voltage. Thus it follows that T~ must be much shorter than 1ps. For the fast process in the clear solution this was not the case. Because of this shortness we have therefore to conclude that the buildup and decay of the birefringence are not caused by the orientation of whole aggregates. Contrary to the amplitude of the birefringence effect in the clear solutions, the effect in the turbid solutions is very little affected by a change of the temperature. This is further evidence that the mode of operating is different in the clear and in the turbid solutions. Dynamic Light-Scattering Measurements. Diffusion Coefficients of aggregates may be determined by the dynamic light-scattering measurements. The method uses the fact that the time average value of the function G(At) is given by the equation
and depends only on At and the diffusion Coefficients of the scattering particles. k is the scattering vector and given by the equation
k=
4n
X,sin (6/2)
Here n is the refractive index, X the wavelength of the light, and 6 the scattering angle. From the diffusion coefficient it is possible to obtain hydrodynamic radii for the scattering particles with the Stokes-Einstein equation D = kT/(6nar). The obtained data are summarized in Table 111. In all solutions aggreates were found with a hydrodynamic radius of about 750 . For several concentrationsand for solutions with added NaTFA these aggregates were the main scatterers. Alm faster correlation effects were present with much smaller amplitudes. This was indicated by the fact that the correlation-time curves could not be fitted with a single time constant. Average diffusion coefficients were therefore determined according to the method of Koppel.26 For higher concentrations of DATFA the amplitudes for the fast effects increase considerably. The hydrodynamic radii m depend very much on temperature. For a 2 X solution r h decreases from 50 A at 25 "C to 25 A at 51 "C. The radii of the large aggregates seem to grow somewhat with the temperature. The fraction of the total amplitude for the fast process decreased with increasing concentration. Higher concentrations of DATFA than 2 X m gave similar results. It is necessary to point out that the intensity of a scattered light is proportional to the molecular weight of the scattering particles and to their concentration in g/mL. It is therefore likely that in these solutions, where radii of particles of both 50 and 750 A were found, the material in the particles with larger radii may also be less than 1% of the total detergent. If it is known that the particles whose diffusion coefficients are
x
(26)D. E.Koppel and D. W. Schaefer, Appl. Phys. Lett., 22,36(1973).
1428
The Journal of Physical Chemistry, Vol. 85, No. 10, 198 1
measured by the dynamic light scattering method are anisotropic, it is possible to calculate the ratio of the axes for cylindrical aggregates. This was done with the equation a rh = (X) (1 - p2)",5 In (1 (1 - p 2 ) 0 . s / p )
+
with p = b / a (see eq V), which was derived by P e r h Z 6 The calculated values are also included in Table VII. Again the values for the long axis a were obtained by assuming 40 A, Le., twice the length of a detergent molecule21for the short axis b. These values agree remarkably well with the values which were obtained from the birefringence and the viscosity measurements. Rheological Measurements. It is worthwhile to note that the conclusions which can be obtained from the rheological measurements agree very well with the conclusions reached from the other investigations. The anisotropy ratio of particles can be determined from the parameter {q] = limd (7 - qo)/qoc,using the Simha equation27 1
Here is d the density in g/mL, X = 1.8 (for rods), and p = a / b the ratio of the long axis a to the short axis b. Using this equation one obtains a value of about 8 for the anisotropy ratio p . Assuming the short axis b to be 40 A, i.e., twice the length of a detergent molecule again, we obtain for the length of the rods a value of 320 A which is also included in Table VI1 and is also in good agreement with the values which are calculated from light scattering and electric birefringence measurements. The viscosity values at small shear rates for the TATFA solutions point out that this compound forms spherical aggregates in aqueous solutions up to a concentration of 5 x 10" m. Conclusions The investigations were started with the aim of finding large emulsion dropletlike giant micelles in solutions of DATFA and TATFA. For DATFA all experimental evidence indicates that no such micelles are present. The dynamic light-scatteringmeasurements show the existence of rather small aggregates with hydrodynamic radii of 50 A at 25 "C. These radii which are too large for normal spherical micelles can easily be explained by the existence (26) (a) F. Perrin, J. Phys. Radium., 5, 497 (1934); (b) ibid., 7, 1 (1936). (27)(a) R. Simha, J.Phys. Chem., 44,25 (1940);(b)J. Chem. Phys., 13, 188 (1945).
Hoffmann et al.
of anisotropic aggregates having one axis considerably longer than the normal micellar radius. Such aggregates are indeed detected by electric birefringence and viscosity measurements. The kinetic measurements are also in accord with such aggregates. The average residence times which the detergent molecules spend inside the micelles before being released have such values that all headgroups of the surfactants must be located at the micellar surface and none are incorporated together with the counterions into the interior of the micelles. With the increase of temperature the anisotropic aggregates become smaller and finally disappear for a certain temperature. This specific temperature depends on the total concentration of the surfactant and moves to higher values with increasing concentration. Upon the addition of NaTFA the micelles seem to agglomerate in a reversible way to much larger secondary aggregates with hydrcdynamic radii of about 750 A. These solutions are slightly turbid but no new phase separates out when the solutions are left standing for days. Unfortunately, for TATFA the situation does not seem so clear. TATFA forms clear solutions above 40 "C, in which with the quasielastic light-scattering technique aggregates with radii of about 50 A are detected which decrease to about 25 A at 51 "C. The particles having a radius of 50 A are a factor of 2 larger than would be expected for normal globular micelles and it was thought again that they would form anisotropic ellipsoids. Surprisingly, however, no electric birefringence can be detected even at concentrations as high as 5 X m. The possibility can therefore not be ruled out that micelles are formed in the solutions which solubilize the detergent ions and their counterions into their interior. The kinetic data could also be explained by this model of the micelles. The k-f n values which are evaluated for concentrations above 4.5 X 10" m are at least a factor of 2 smaller than the values for normal spherical micelles. Furthermore, there is the fact that the solutions are viscoelastic which cannot be explained on the basis of simple globular micelles. Also small amounts of very large particles are present in the clear solutions. It is likely that these aggregates come about by agglomeration of the primary micelles. With an excess of NaTFA the small micelles disappear and large secondary aggregates are formed which do not seem to precipitate from the solution. Acknowledgment. We gratefully acknowledge financial support of this work by the Deutsche Forschungsgemeinschaft and the Fond der Chemischen Industrie. We are also indebeted to Mrs. R. Hammel and E. Stiebing for the preparation of the compounds and the conductivity and surface tension measurements.
