2866
J. Phys. Chem. 1981, 85, 2866-2869
Scheme I1
HOz
OH
+
+
CI
For HCI
-
E (10.6 i 0 . 2 )
(HOOCI)*
HCI
+
4
C1+ OH S -4 O(3P) + HC1
On(’A)
+
O*?Z)
2 [02.*.H.**CI] (HCIO)*
O(D2)
-
*
HOz
-* -
+
CI
+ CI = OH + C I - 4 (9.7)
(HOC17
Cl]
(4)
Because of the spin conservation rule, this reaction cannot occur through recombination and indeed the A factor derived from the experimentally found A(-4) = L/ (mol s)15 and AS‘”(4),log A(4) = 9.7 L/(mol s), is consistent with the A factor estimated for a bent transition state L/(mol s)) and somewhat lower than the H-atom collision frequency (1010.2L/(mol 9)).
( i f energy surface crossing exists)
4- 0 the channelsare
+
-
HOOCI secondary reactions i important in the stratosphere )
OCI HCI
HCI
r
The singlet oxygen elimination is, as seen in Figure 4, endothermic by 44.1 kcal/mol and therefore not competitive with the triplet oxygen formation pathway (4).
OH
higher than the H-atom collision frequency (lo9.’ L/ (mol s)), the estimated A factor for a linear (108.9L/(mol 5)) or bent L/(mol s)) H-metathesis transition state but is consistent with the estimated A factor for the recombination transition state (lO1l.o L/(mol s)).’O The O(lD,) HC1 consequently should be a recombination as well. Two paths are available, a three-center triangular path which would surprisingly have zero activation energy, or a direct recombination path to form excited HClO*, an isomer of HOC1. HC10* would then rearrange to HOCl* which would further split into HO + C1. The normal molecule HClO is not known, but it could be analogized to the known higher valence state species of Cl.
+
Conclusions “Abnormal ” high cross sections found experimentally for several radical-radical reactions are consistent with the proposed mechanism being the recombination through loose transition states. When the energetics of a particular reaction do not activate the radical adduct sufficiently toward a further reaction, the recombination cannot lead to distinct products and the metathesis through a tight transition state becomes the only efficient reaction path. The cross sections and rate constants for these reactions are consequently smaller. The selected pathways and log [k (L/(mol s))] values (in parentheses) which were obtained for the reactions C1 H 0 2 and 0 + HC1 are given in Scheme 11. Acknowledgment. This work has been sponsored by grants from the National Science Foundation (No. CHE7826623) and U.S. Army Research Office (DAAG 29-79G-0022).
+
(15)R. D.Hudson and E. I. Reed, Ed., NASA RP 1049,Dec, 1979. (16)S. W. Benson and J. Buss, J. Chem. Phys., 27, 1382 (1957). (17)P. J. Robinson and K. A. Holbrook, “Unimolecular Reactions”, Wiley-Interscience, New York, 1972.
~
(14)J. A. Davidson, H. I. Schiff, G. E. Streit, J. R. McAfel, A. L. Schmeltekopf, and C. J. Howard, J. Chem. Phys., 67,5021 (1977).
Transient Electric Birefringence Study of CTAB Micelles. Implications for Rodlike Growth D. F. Nlcoll,” Physics Depafjment, Unlverslty of Callfornia at Santa Barbara, Santa Barbara, Californla 93 106
John 0. Ellas, and Don Eden Chemistry Department, Yale Unlverslty, New Haven, Connecticut 065 1 1 (Received: May 4, 198 1; In Final Form: July 7, 198 1)
Using the technique of transient electric birefringence we have measured the field-freedecay times for the micellar system 0.035 M CTAB + 0.1 M NaBr as a function of temperature T (20-30 “C). We observe both a fast (1.4-2.6 ps) and a slow (14.7-17.7 ps) decay time, however, neither characteristic time is appreciably T dependent. This result suggests a negligible T dependence of the CTAB micellar rod length (in the range 20-30 “C), assuming that the birefringence decay is due to the rotational diffusion of rod-shaped micelles which become partially aligned by the brief application of an electric field. Introduction There have been numerous reports of measurements of the translational diffusion coefficient D,and associated Stokes-Einstein hydrodynamic radius Rh of aqueous micelles by use of the technique of photon correlation spectroscopy (PCS).l Mazer et al.,2s3Corti and Degiorgio$6 (1)B. Chu, “Laser Light Scattering”, Academic Press, New York, 1974. 0 0 2 2 - 3 6 w a 1/2085-2866$01m
o
Nicoli et al.6~’and others have sought to measure the size of these self-assembling surfactant aggregates as a function (2) N. A. Mazer, G. B. Benedek, and M. C. Carey, J.Phys. Chem., 80, 1075 (1976). (3)N. A. Mazer, M. C. Carey, and G. B. Benedek in “Micellization, Solubilization and Microemulsions”, Vol. I, K. L. Mittal, Ed., Plenum, New York, 1977. (4) M. Corti and V. Degiorgio, Ann. Phys., 3, 303 (1978). (5)M.Corti and V. Degiorgio, J. Phys. Chem., 85,711 (1981).
0 1981 American Chemical Society
The Journal of Physical Chemistry, Vol. 85, No. 20, 7987 2887
Letters
TABLE I : Apparent Hydrodynamic Radius, &, for CTAB Micelles Plus the Corresponding Rod Length, L, and Mean Micelle Separation, S , as a Function of Temperature' 35
69 97 124 141
30 25 20
270 480
700 850
yr = 1.45 - 7(1/ln p - 0.27)2
295 36 0 405 43 5
of temperature, pressure, salt and surfactant species, and concentration. From these studies it has been generally concluded that micelles can grow extensively upon cooling in the presence of added salt. For the present study we used the cationic surfactant CTAB, C16H33N(CH3)3Br, in water. For the system 0.035 M CTAB + 0.1 M NaBr, we have shown7 that the apparent Rh determined by PCS grows monotonically with decreasing T, from roughly 30 A at 55 "C to almost 150 A at 20 "C, as indicated in Table I (column 1). These values are obtained from the measured translational diffusivity Dt (Stokes-Einstein relation), assuming that intermicellar interactions can be neglected: Rh = kT/GrqD,. If we assume that CTAB micelles grow in cylindrical fashion,8 then the cylinder length L corresponding to a given Rh value can be obtained fromg
kT Dt = -(In 3aqL
2p - rt)
where Yt
= 0.373 - 0.57(l/p)
Ob)
where q is the solvent viscosity and d the rod diameter (twice the monomer surfactant length, =60 A). The computed L values are shown in Table I (column 2). As noted p r e v i o u ~ l ythe , ~ ~striking ~ prediction is that there is a very large increase in micelle length with decreasing T, assuming that the mean Rh as determined by dynamic light scattering describes the intrinsic aggregate size (i.e., is not greatly perturbed by interaction^^^^ or collective diffusion). It must also be appreciated that the predicted micellar lengths imply a highly crowded system, in which the mean separation S between micelles is given' in Table I (column 3). (For simplicity we have assumed a monodisperse distribution and a minimum aggregation number no of 80.) To obtain an independent measurement of micellar growth in this region where large rod lengths are expected, we sought to measure the perpendicular rotational diffusion coefficient DrL. This quantity is a much more sensitive function of length L for a rod-shaped particle of large axial ratio p than is the translational diffusivity D,. From Broersma,'O we obtain 3kT DIL = -(ln
aqL3
2p - rr)
where (6) D. F. Nicoli, D. R. Dawson, and H. W. Offen, Chem. Phys. Lett., 66, 291 (1979). (7) D. F. Nicoli, R. Ciccolello, J. Briggs, D. R. Dawson, H. W. Offen,
L. Romsted, and C. A. Bunton in "Scattering Techniques Applied to Supramolecular and Non-Equilibrium Systems", S. H. Chen, B. Chu, and R. Nossal, Ed., Plenum, New York, 1981. (8)P. J. Missel, N. A. Mazer, G. B. Benedek, C. Y. Young, and M. C. Carey, J. Phys. Chem., 84, 1044 (1980). (9) M. M. Tirado and J. Garcia de la Torre, J. Chem. Phys., 71, 2581 (1979). (10) S. Broersma, J. Chem. Phys., 32, 1626, 1632 (1960); 74, 6989 (1981). ~~
(2b)
To measure DIL we employed the technique of transient electric birefringence (TEB). This methodll is able to achieve much higher signal/noise ratios than depolarized dynamic light scattering. It has been used to measure the lengths of a variety of macromolecules, including TMV'l and DNA fragments.12J3 We have made several implicit assumptions in our use of TEB to study micelles. Although micellar aggregates are self-assembling, we assume that application of a brief, weak external electric field will not seriously distort the micellar shape (e.g., due to perturbations of the surrounding counterions). Furthermore, we assume that the rod-shaped micelles are polarizable and will partially align in the applied field and upon release of the field will rotationally diffuse like cylinders of fixed shape and size. Materials and Methods The salient features of the apparatus have been reported elsewhere;12only the sample cell was modified. The field electrodes consisted of 4 mm X 8 mm platinum plates of fixed spacing, designed to be inserted into a thermostated cuvet (8-mm active path length). Since the NaBr concentration required to produce significant apparent growth in Rh for CTAB is high by TEB standards, special care in cell pulsing was required to avoid excessive Joule heating. We applied alternating-polarity dc pulses (50-100 V, fields of 175-350 V/cm) of short duration (typically 8-32 pus) at low pulse repetition rates (0.6-1.6 Hz). Transient accumulation was accomplished with a LeCroy Model 2256 digitizer (&bit, 1024 channel, dwell times of 50,100, and 200 ns) and a DEC LSI-11 minicomputer for averaging, data storage, and display. CTAB (MCB) was purified as reported;14 the water was distilled, deionized, and filtered (0.22 pm Millipore) before use. Results and Discussion Using the technique of TEB we measured the exponential time constants which characterize the field-free decay in birefringence of the micellar system 0.035 M CTAB + 0.1 M NaBr in the temperature range 20-30 "C. This choice of surfactant and salt concentrations represented a compromise, made necessary by a set of conflicting experimental constraints (peculiar to micellar systems). The dominant consideration was the problem of excessive solution conductivity; at 0.1 M NaBr the cell impedance was only 35 ohm at 30 "C (increasing to 45 ohm at 20 "C). High voltage pulser loading and solution Joule heating ruled out higher salt molarities. However, significantly lower NaBr concentrations were not used because dynamic light scattering reveals15 that CTAB micelles do not grow measurably (i.e., beyond "minimum sphere") at NaBr molarities below approximately0.05-0.07 M. Hence, 0.1 M NaBr represents a compromise between excessive solution conductivity and insufficient birefringence due to inadequate micellar growth. We chose the CTAB molarity (0.035 M) to be the lowest value consistent with an acceptable TEB signal/noise ratio. From estimates of micellar rod lengths and mean separations (Table I, columns 2 and 3), it is apparent that we were operating in a concentrated regime. The likely con(11) J. Newman and H. L. Swinney, Biopolymers, 15, 301 (1976). (12) J. G. Elias and D. Eden, Macromolecules, 14, 410 (1981). (13) J. G. Elias and D. Eden, Biopolymers, in press. (14) C. A. Bunton, L. S. Romsted, and C. Thamavit, J. Am. Chem. SOC.,102, 3900 (1980). (15) R. Dorshow, J. Briggs, C. A. Bunton, and D. F. Nicoli, manuscript
in preparation.
2060
The Journal of Physical Chemistry, Vol. 85,No. 20, 1981 I
l
l
I
I
I
I
Letters
I
2
Ec
I
I
I
0
I
I
I
20 40 TIME (usec)
I
I
60
t-I
i
/
I
80
Figure 1. Normallzed birefringence vs. time for 0.035 M CTAB M NaBr at 20 O C (32-ps pulses with E = 350 V/cm).
-
+ 0.1
12-
20 40 TIME (usec)
0
60
Flgure 3. Normalized TEB signal vs. time for 0.035 M CTAB i- 0.1 M NaBr for T = 20, 25, and 30 O C (16-ps pulses).
TABLE 11: Summary of Two-Exponential Analysis of TEB Dataa A t , PS
8 16 32 64 1 0.8
I
0
I
I
5
I
I
10
I
I
15
I
20
1
' 25
I
TIME (usec)
Flgure 2. Birefringence (log scale) vs. time for fleid-free decay region, data of Figure 1.
sequences of intermicellar interactions on the measured TEB decay times will be discussed later. Figure 1shows a good example of our TEB data (average of 150 32 Ns-long pulses, 350 V/cm) taken at 20 "C, where micelle growth should be significant. We observe that the time constants for the rise and fall of the birefringence signal appear to be roughly the same. This symmetry is expected, since it is unlikely that a large permanent dipole moment (as opposed to the field-induced moment) exists in a micelle. Upon closer examination of the TEB data of Figure 1, shown as a semilog plot in Figure 2, it is evident that the field-free decay is best described by a sum of two exponential decays f ( t ) = Af exp(-t/d + A, exp(-t/~,) (3) where subscripts f and s represent the fast and slow components, respectively. The resulting parameters for the data of Figures 1 and 2 are 7f = 1.6 ps (Af = 2.8) and T , = 12.4 ps (A, = 9.8). The slower component is clearly dominant. Interestingly, this decay time is in close agreement with the predictions of Table I (20 "C)and eq 2a and 2b; for L = 850 A (d = 60 A) we expect rrOt= 1/6Or1 = 14 ps. Of course, both the original L estimate in Table I and the resulting 7r0tcalculation assume an ideal system of dilute, noninteracting, relatively rigid rods. Some of these conditions are probably violated to some extent in our micellar system.
8 16 32 64 a Mean and T.
7f
3 0 "C
2 5 "C
20 " C
Fast Decay Time ( 7 f ) 1.4
1.73
2.08
2.6
2.6
2.09 2.5
8 Slow Decay Time 14.9 15.6 15.9 15.2 14.7 (fast and
T~
77 (slow) vs.
( T ~ )
17.7 17.1
A t , (field pulse w i d t h )
We now exam ne the TEB decay times as a function of temperature. Representative plots at 20, 25, and 30 "C, obtained by using a field pulse width of 16 ps, are shown in Figure 3. Two experimental artifacts occurred, contributing to uncertainty in the measured decay times. First, there existed optical birefringence anomalies associated with either the solution or the cell which resulted in discrepancies between the initial and final baselines. The shifts were not systematic in either sign or magnitude and did not obviously correllate with the measured decay times. Second, we observed oscillations superimposed on the main signal structure, which occurred in both the field-on and field-free regions. The amplitude of the ringing structure appeared to be independent of temperature but was more prominent a t higher temperatures where the magnitude of the TEB signal was smaller. We speculate that these oscillations may be the result of a perturbation of the micellar shape or of the surrounding Stern layer of mobile counterions, or a consequence of convection in the cell due to pulsed Joule heating. Efforts are underway to try to identify the origin of this unusual structure in the TEB data. If CTAB micelles exist as rods which can be partially aligned by application of a brief electric field (remaining relatively rigid and intact in the process), then from the lengths predicted by dynamic light scattering (Table I) we expect roughly a fivefold increase in the mean rotational
Letters
decay time in going from 30 to 20 "C. As is evident from Figure 3, we do not observe such a change in decay characteristics. In Table I1 we list the average values for 7f and 7,for each of the three temperatures as a function of field pulse duration At ( 8 4 4 ps). (No results are given at higher T because the %E'B signal/noise ratio deteriorated rapidly above 30 "C, presumably because of a rapid decrease in micellar size.) A number of systematic trends emerge. It is clear that At, = 64 ps produces a drastic perturbation of the micelle and/or its environment; both Tf and 7, are much larger than their values at all shorter Aty We therefore confine our analysis to the regime At, = 8-32 KS. For the fast decay we find values which vary between 1.4 and 2.6 ps, which correspond to rod lengths between roughly 350 and 450 A. However, we find at any given T that 7f increases monotonically with pulse width, increasing by roughly a factor of 2 over the range At, = 8 to 32 ps (25 "C). In addition, for a given At there is no consistent increase in 7f upon cooling. Final&, as seen in Figure 2, the fast component represents only a small fraction of the birefringence signal. Hence, we tentatively conclude that time rf is not associated with micellar rotation per se but perhaps is due to an intrinsic structural relaxation. Next we examine the slow decay values. We observe no significant pulse width dependence in 7,)given the measurement uncertainty (at least f l - 2 ps). From eq 2a and 2b the rod lengths corresponding to these decay times are 930-950 A for both 20 and 25 "C and 980 A for 30 "C. We conclude that there is negligible T dependence in T, over the limited range examined. The theoretical rod length above agrees quite well with the value of 850 A predicted in Table I for 20 "C but is substantially higher than the values deduced from dynamic light scattering at 25 and 30 "C. This study represents the first application of the TEB technique to a micellar system. More extensive measurements are needed before any firm conclusions can be reached concerning the behavior of micelles in transient electric fields. Nevertheless, our preliminary TEB results raise interesting questions. For example, we observe two birefringence decay times, neither of which is appreciably T dependent. It is unclear whether either is associated with the rotational diffusion of nonspherical micelles per se, although the slower time 7,is in reasonable agreement
The Journal of Physical Chemistry, Vol. 85, No. 20, 198 1 2869
at 20 "C with a value suggested by dynamic light scattering. In this first report we have not considered the effects of polydispersity, rod bending and flexing, or the kinetics of micelle formation and dissolution. If we assume that CTAB micelles can be represented as rod-shaped aggregates, it seems unlikely that the mean rod length could increase by as much as a factor of 2 in going from 30 to 20 "C, as suggested by dynamic light-scattering results (Table I). If that were the case, we would expect some evidence of temperature dependence of the birefringence decay, regardless of the detailed response of the micelles in a TEB experiment. The condition of "crowding", alluded to earlier, would yield a rod-length dependence of DrL which is even stronger than L3, as predicted by the steric hindrance theory of Doi and Edwards,16and supported by a recent TEB study of Maguire et al.17 At our relatively high surfactant concentration, micellar diffusion (both DrL and Dt)can be seriously affected by nearest-neighbor interaction^.^^^ As discussed recently by Nicoli et a1.,18 it is possible that much of the decrease in Dt upon cooling is a manifestation of interactions among micelles which lead to critical-type behavior (with cooperative diffusion of small micelles), in which individual micelles never achieve the large axial growth predicted in Table I. In that case, smaller rods in a crowded environment could yield a much longer decay time than would be predicted by eq 2a and 2b for a dilute solution. The challenge remains to successfully isolate the effects of interactions from determinations of intrinsic micellar size and shape by using techniques such as TEB and dynamic light scattering.
Acknowledgment. We thank C. A. Bunton and colleagues a t University of California, Santa Barbara (Chemistry Department) for providing us with purified surfactant. D.F.N. expresses his gratitude to Don Eden for his hospitality during visits to Yale, where the experimental work was performed. This work was supported in part by National Institutes of Health Grant RR-07015. (16)M. Doi and S. F. Edwards, J . Chem. SOC.,Faraday Trans. 2,74, 560 (1978). (17)J . F.Maguire, J. P. McTague, and F. Rondelez, Phys. Reu. Lett., 45, 1891 (1980). (18)D.F.Nicoli, F. de Buzzaccarini, L. Romsted, and C. A. Bunton, Chem. Phys. Lett., 80,422 (1981).
