N . MULLER, J. H. PELLERIN, AND
3012 Nowever in general we believe that the method C described above is more logical than s, resulting in a somewhat shorter: program yielding more accurate rewits; and that these results are obtainable in less comecause sophisticated numerical methods
. CHEN'
can be used, which are upset by the discontinuous cutoff conditions needed in s. Because it lacks Sch~varz's empirically determined parameter a,method G may be safer to use in cases very different from those used in fixing the value of CY-
~ n v e s t i ~ af tMicelle ~ ~ ~ ~Structure by Fluorine Magnetic Resonance. uaternary Ammonium Salts'
y Norbert Muller,* John H. Pellerin, and Winston W. Chen Department of Chemistry, Purdue University, Lafayette, Indiana
47907
(Received March 16, 1973)
Publication costs assisted by the National Science Foundation
The cationic surfactants 12,12,12-trifluorododecyltrimethylammonium bromide (I-Br) and 10,1O110-trifluoroclecyltrimethylammonium bromide (11-Br) have been prepared, and fluorine chemical shifts have been measured for these and for the corresponding fluorides, chlorides, and hydroxides as a function of concentration in aqueous solutions. The data yielded monomer and miceile chemical shifts closely similar to those for related anionic and nonionic detergents, and critical micelle concentration (cmc) values roughly twice as large as those of unfluorinated compounds of similar structure. When fluoride serves as the counterion its chemical shift is concentration dependent and can be used to evaluate the cmc, but with low acruracy. Attempts to measure counterion binding by a method using the line-broadening effect of added manganous chloride were unsuccessful. Determinations of the cmc in the presence of simple electrolytes show that fluoride and bromide are bound about equally by micelles of I-F and I-Br. The Lrifluoromethyl group chemical shifts for I-F with added potassium fluoride reveal a "second cmc," tentatively interpreted using a double equilibrium model involving micelles with an aggregation number near 25 in the more dilute solutions and micelles containing about 60 cations above the second cmc.
Introduction Although the association of detergent molecules in water solutions has been investigated very extensively during several decades, most experimental approaches have yielded vnly thermodynamic quantities, usually the free energy of micellization AG," and sometimes also the corresponding enthalpy and entropy changes, AH," and AS,". Continuing efforts to use such data as a basis for undmtanding the role of hydrophobic interactions in stabilizing the native conformations of proteins and in denaturation processes13and the recent upsurge of interest in micellar c a t a l y ~ i shave , ~ made it more than ever desirable t o elucidate the mode of organization of micellar material, including water of hydration. The present series of studies was undertalten with this goal in view, since it was anticipated that fluorine nmr cnemical shifts and line widths for micelles of fluorine-labeled detergents would provide at least a modicum of useful nonthermodynamic information. For a variety of anionic5-' arid nonionic8 detergents having CF8(CH2). groups in place of the The Journal of Physical Chemistry, Vol. 7 6 , No. 21, lQ72
usual hydrocarbon chains, and also for perfluoro~ c t a n o a t eit, ~was shown that nmr measurements yield values of AG,,", AH,", and As," which agree with results of conventional methods. Exchange of molecules or ions between the monomeric and micellar states was found invariably to be fast on the nmr timescale, that is, involving lifetimes less than lW3 see. For the CFS(1) Financial support by the National Science Foundation under Grant No. G P 19551 and by the Purdue Research Foundation is gratefully acknowledged. A preliminary account of this work appears in the abstracts of the 162nd National Meeting of the American Chemical Society, Washington, D. C., Sept 1971. (2) P. Mukerjee, Advan. Colloid Interface Sw., 1, 241 (1967). (3) J. E'. Brandta in "Structure and Stability of Biological Macromolecules," s. N. Timasheff and G. D. Fassman, Ed., Marcel Dekker, New York, N. Y., 1969, p 255. (4) E. J. Fendler and J. H. Fendler, Advan. Phyr. Ory. Chem., 8 , 271 (1970). ( 5 ) N. Muller and R. H. Birkhahn, J. Phys. Chem , 71, 957 (1967). (6) N. Muller and R. H. Birkhahn, ibid., 72, 583 (1968). (7) N. Muller and T.W. Johnson, ibid., 73, 2042 (1969). (8) N. Muller and E'. E. Platko, ibid., 75, 537 (1971). (9) N , Muller and H. Simsohn, ibid., 75, 942 (1971).
hVEYl"GATI0N OF *!I
CELLE fhRUCTUREs BY
3013
FMR
2)71 compounds the chemical shift of the monomeric species was indspendent of the nature of the solubilizing group and (at IPast, for 6 5 n 5 12) of the chain length, suggesting tha, tho dkyl chains exist primarily in extended c o ~ f ~ r ~ ~ a ~ ~ o n s The Auorinc chemical shift for a micellized CFa(CH,), det ergenl lies very nearly halfway between the shift for the monomzr in water and the shift expected when the ohaino are dissolved either in pure hydrocarbon solvcnls or in partially fluorinated materials such as GF'a(CHz)8QZ3. This would seem to imply that 011 the average Idle CP3groups find their surroundings to he abo1A 505, aqueous and 50% hydrocarbonlike, and t h a t rnicellization is not as effective in eliminating hydmsarbon-water contact as one might have supposed. Jniplicit in this interpretation is the assumption t 933 t e iectrostatic int>eractions involving charged groupij at thr: micelle surface do not produce a major effect, vhicii it; supported by the observation of rlosel.). similar micelle shifts for anionic and nonionic detergents. 'The present study of cationic species was begun in part >,,o provide a more rigorous test of this assiimpt,ion, Moreover, quaternary ammonium surfactants can be - x e p a r d in which fluoride serves as the counterion, arrd we wished to explore the utility of chemical shift and line width measurements for the counterions a': a means of determining critical micelle concentrationk (cinc) and the extent of counterion binding. PVc also determined the dependence of the cmc on the concentration of added fluoride ions and in so doing found evidence for a moderately abrupt change m the micellc size ai, detergent concentrations considerably larger than She cmc. The materials prepared for this study were the fhoride, chloride, bromide, and hydroxide of 12,12,12trifluorodociecvltrilr.ethylammonium ion, designated I,, and 1-013,and analogous salts of 10,10,i:plirir~~ethylammoniumion, designated 11-F,E t @ .
epared from the appropriate, commercially available a,@-dibromoalkanes according t o the following scheme.1°
SF4, ll0", 10 hr
Br(CH2) ,GO(C?IEI-~--t Br(CH2).CF3 excew h (CHdy, O " , 4 days
r (C X 2 ).CF3 ----
--f
CFdCH2).N(CH&Br
(3)
Tn the first step of (1) the dissolved sodium diethylmalonate (typically 0.25 mol) was added slowly t o the dibromoalkane (0.50 mol) in order to minimize the probabilit) of attack by diethylmalonate ion at both ends of the dibromoalkane. Distillation of the product mixture alioved the excess dibromoalkane to be recov-
ered and the ethyl bromocarboxylate to be isolated, The w-bromocarboxylic acids next formed were isolated as crystalline solids with melting points in good agreement with values from the literadlure. The bromotrifluoroalkanes formed in (2) were colorless liquids, the dodecane derivative boiling at 72-74" and the decane derivative at 61-63", each a t 1 Torr. Reaction 3 then gave I-Br and 11-Br as sold products which were purified several times by dissolving them in acetone and adding benzene to reprecipitate them, and finally dried under vacuum. Anal. Calcd for C1SK31BrF3N:6 , 49,%2;ITj 8.62, Found: C, 49 36; €3, 8.57, CaYcd for Cj3H2; C, 46.71, B, 8.14. Found: C, 46.56; El 8-34. I-Br W R S extremely hygroscopic, IS-Br somewhat less so. KOimpurity peaks were found in their proton iamr spectra irr water solution. Although other possibilities are not absoliite1y excluded, it seems iikeiy that mater was the major impurity in each product. The oalculated analysis for a mixture containing 99*37&Iand 0.7'35 HZO is C, 49.37; I-I,S.64. Solutions of I-OH and Il-ON[ were prepared from the bromides by ion exchange using owex 2-X4 resin previously converted to the hydroxi forni. The fluoride and chloride salts were p r e p a d by neutralizing the hydroxides in solution with the appropriate acid. Eventually it proved more eatisfact ory to prepare solutions of .(,hefluorides by adding equivalent amounts of standard soluiions of silver fluorjde to the respective bromide or hydroxide and filtering off thc precipitate. I-CI and 11-CI were isolaLed in crystalline lorn?, but attempts to do this with tbe fluorides brought about their decomposition. When line width measurements for rqueous F- are t o be made it is essent,ial that paramagnetic impurities, especially Cu2+, be rigorously excluded. l1 Accordingly, triply distilled deionized water was used, and the quaternary fluoride solutions were treated with Chelex 100 re5in,11 which was then reMOT7ed by millipore filtration. To avoid introduction of paramagnetic ions by leaching from glass surfaces, these solutions were prepared and stored in plastic laboratory ware, and in. Teflon spagheltr tubing were used liners made of in the nmr sample tubes. When desired, portions of 1.0 X M MnC12solution n7ere added from a microM liter syringe to make samples containing 2 0 X added ;IlnC12. Most of the spectra were obtained at 56.445 MHz with a Varian HA-60-IL spectrometer, a few at 94,007 MHz with an XL-100 spectrometer. Shifis are upfield from the signal of 1,l12-trichlorotri uoro-1-propene in a capillary which also contained a trace of l,2-difluorotetrachloroethane to allow the temperature to be deter(10) J. H. Pellerin, Ph.D. Thesis, Purdue University, 1972. (11) M. Eisenstadt and H. L. Friedman, *J. Chem. Ph,ys., 48, 4445 (1968).
The Journal of Physical Chemistry, Vol. "5,N o . 21, 1972
N. MULLER, J. W.PELLERIN, AND W, W. GHEN
3014 mined,12 Bulk magnetic susceptibility corrections should be constant to within about 0.01 ppm over the range of concentrations used and were therefore neglected.
Solutions zvilhou,t Added Electrolyte. The fluorine nrnr spectra of the trifluoroalkyltrimethylammonium ions in aqueoixs s~lutionare closely similar to those de. scribed carlier for anionic and nonionic trifluoroalkyl As before, plotting the chemical shifts against 1/[soj,IJhe reciProcal the surfactant concentrabtion, allows one to evaluate the monomer shiftJS(S), the xullceile shift S(s,), and the cma for each material.Io T h e results, given in Table I, conform to two generalizat>ionsbased on earlier data. The monomer shifts are independent of the chain length and the n:+,tixre of the solubilizing group, and the cmds are about twice as large as those for analogous unfluorinated compounds. Thc dscrease of the erne's as the counr;erion is varied in the sequence F-, Cl-, Br- is parallel for dodecyltrimethylammonium to the trend repor%ect13 t NaX, which was taken as an indication salts in 0.5 A that F- i s the least tightly bound counterion, perhaps because it, is the most strongly hydrated. We offer no explanation for the finding that the plnce of OH- is not quite the same in the I sequence as in the 111 sequence. Tsble I ; Fluorirre Chemical Shifts (Upfield from External 1,1,2-TrichlorotriP,uoro-l-propene) and cmc Values for Salts of CF1(CH2)11N (CW8)3 (I) and CFdCHla)sN(CHa)a+ (11)at 31Qa Monomer ahif t ,
Micelle shift.
Coinpd
PP"1
ppm
I-F I-Cl I-Br 1-OH 11-F IE-Gl
3 . '70 3 .'70 3.70 3.70 3.71 3.71 3.71 3 71
4.73 4.73 4.73 4.73 4.63 4.63 4.63 4.63
XI-& 11-OH
M
cmc, x 10%
5.13 4.17 (1.72b) 2.72 (1.53,"1.46d) 3.95
18.9 14.7 ( 6 . l l b ) 9.9 (6.8")
18.3
For comparison, C ~ values L for corresponding unfluorinated alkyl trimethylammonium halides are given in parentheses. H. W. Woyer and A. lllizrmo, J . Phys. Chem., 65, 807 (1961). E'. Debye, ibid., 53, 1 (1949). Reference 17. Q
The micelle shifts :ire independent of counterion and only slightly dependent on chain length. When they are compared with earlier results, such as 4.87 ppm (at 35") for trduorododecyl sulfate' and 4.81 ppm (at 32.5') for triauorooctyl hexaoxyethylencglycol monoit 1s apparent that electric field effects arising from charged groups at the micelle surface indeed makc no major contribution t o thevalue of S(SJ. The nmr signals from the F- ions in solutions of 1-3' and 11-F yield plots of chemical shift against reciprocal The Journal of Physical Chemistry, Val. 7'6, N o . 21, 197.9
i/S, (liters /mole)
Figure 1. Fluoride ion chemical shift, of molar suifactant fluoride minus shift of is,]nlolar potassium fluoride, as a function of I/ is,]: open circles, CF,(CB&N (CH&F; filled circles, CFa(CHz)sN(CH,)aF.
concentrationlo which are strongly curved and resemble plots of the shift of aqueous potassium fluoride solutions14 over the same concentration range. To focus on the effect of micelle formation one may plot the difference in chemical shift for I-E' and KF, each at concentration [So], as a function of 1 i[So], with results shown in Figure 1. Cmc values may indeed be estimated from such a plot, but because of the nonlinearity of the curves the accuracy is low and the results agree only very roughly with values derived from the CFS shifts. Since the fluoride shift of simple salts becomes essentially independent of concentration below 0.05 M , fluoride shift measurements for quaternary fluoride surfactants should be much more useful for compounds having cmc's of 0.01 M or less. hro such materials were included in this study because the spectrometer used for most of the work does not provide the required sensitivity. The data could not be used to evaluate the shift for fluoride ions bound to the micelles, but they suggest that the difference ?)bound - ?)free is hss than 1ppm. Effect of Added Manganous Chloride. We attempted to investigate the binding of fluoride ions by the cationic micelles using the following approach, suggested by the work of Mildvan, Leigh, and Cohn. l5 The signal from dilute RE' solutions has a width, Av, of about 2 Hz in the absence of paramagnetic species and becomes about six times as broad in the presence of 1.0 X 10-5 M &In2+. The same should be true for suriactant fluorides if no counterions are bound by the micelles. However, it seemed plausible to suppose that a bound fluoride ion should interact less effectively with Mn2+, since the paramagnetic ion should be repelled by the net positive charge of the micelle. In such a situation the observed line width should be a weighted average A V ~ Y== fboundAVbound (12) (13) (14) (15)
+
j'freehvfres
(4)
N. Muller and T,W. Johnson, J . Phys. Ckem., 73, 2460 (1969). E. W. Anacker and H. M. Ghose, ibid., 67, 1713 (1963). R. E. Connick and R. E. Poulson, ibid., 62, 1002 (1968). A. S. Mildvan, J. 8 . Leigh, and M. Cohn, Biochemistry, 6, 1805
(1967).
and appropriate manipulation of the data might then be used t o evaluate the fractionfbound. Solutions of KF. k-F, and II-F were examined both M added A h 2 + and it was found, witli and without that the broadening effect of Mn2f as shown in Table I I, was ementially the same for all three sahs. Since it seems unreasoiiablc to suppose that no fluoride ions are bound by the rnicellci, (see below) we are forced to concltade that A ~ b ~ is , ~very ~ d nearly the same as Anree in the presence of _jJn2+, implying that) the "bound" fluoride ions a-e in liict rather loosely associated with the mieellies a :d remain accessible to the perturbing paramagnetic cpeci
Table YI: Effect, of 1.0 X 10-6 M Mn2+on the Line Width of the Fluoride IFesonance from Solutions of Potassium Fluoride and ihs'actant Fluorides ,----Line width, Hz"Without 10-6 M Mnz Mnz
Concn,
1M
Compd
KF
+
0.2
1.8 1.8 1.6 1.8 1.6 1.7 1.5 1.6 1.7 1.6
0.3 0.4 0.5 I-E"
0.3
0.4 0.5
II-F
+
0.3 0.4 0.5
13 12 12 12 14 13 12 14 13 12
-
~
~
.~~ ~
I-F I-F I-F I-F I-F 11°F 11-F II-F I-%I. I-Br
Water 0.20 KF 0.40 f&fKF 0.80 M NF 1.00 M KF Water 0.20 M KF 0.40 n/l KF Water 0.20 M KRr
-
where A is a constant characteristic of the surfactant and counterion. The data points for I-F in water, 0.20 M KF, and 0.40 M RF lie on. such a line log cmc"
=
-1.922 - 0.49 log (crnc*
+ [F*])
(7) but this line does not pass through the points for 0.80 and 1.0 M added KF. Similar deviations a t high electrolyte concentrations were found in ref 6. They probably arise because the derivation of eq 6 Is good only as lung as the activity coefhient of each species present is independent of concentration. For I-Br only one concentration of added electrolyte was used, Le., 0.20 M KBr, the main purpose of the experiment being to establish whether or not the dilution shift plot showed a second cmc (see below) , but>assuming that an equation like (6) holds the observed effect on the cmc requires ~ C "=
-2.349 - 0.50 log (cmc*
+
omc. x 10%
5.13 2.40 1.84 1.12 0.82 18.9 16.4 15.4
2.72 0.78
____I__
used for the surfzctant cations and the counterions, and micelle formation is represented by the equilibrium
+ [Br"])
(9)
which represents light-scattering for dodecyltrimethylammonium bromide with KRr. The data for II-E' in water and 0.20 and 0.40 ,!if KF yield the equation log cmc"
M
= A
log cmc* = -2.958 - 0.610 log (erne*
Table TI1 : Effect of Added Electrolyte on the cmc Values Electrolyte
CMC"
These results are very similar to the equation
Effect o i Added R F a7td KBr. As an alternative approach to thc study of counterion binding we determined ends in tho presence of added simple salts, with results given in Ta,ble 1x1. If the symbols S and X are
Compd
log
log C
a Averages of two to five determinations for each solution; estimated uncertainties are about b 0 . 2 Hz for the unbroadened Jines, 1 Hz €or the broadened lines.
-
straightforward application of the law of mass action implies16 that cmc" (the crnc found uhen the concentration of added count,erion is [X*])should obey
=
-0.861 - 0.19 log (cmc*
+ [I?*])
(10)
We have not been able to rationalize the surprisingly low apparent value of n/u in this system. The dilution curves for I-F with added KF, shown in Figure 2 , are unusual in that, points for surfactant concentrations larger than about 0.2 A4 deviate markedly from the line drawn through the points for more dilute solutions. We remeasured the curve for 0.40 2 1 1 KIF' at two other temperatures and found that at 13' the points define two fairly good straight lines intersecting at 1/ [So] S 83, while a t 44" the sharp break is replaced by a gradual change of slope (see Figure 3 ) . Similar behavior was briefly noted several years ago6 for CF3(CH2)loC00Xawith added NaCl, but no detailed analysis was attempted. I-Br with 0.20 d l IC and 44' gave only linear plots of shift against reciprocal concentration up to a surfactant concentration of 0.50 N. It seems likely that these observations are attributable t o a phenomenon extensively studied by Ekwall (16) M. L. Corrin, J . Colloid Sci.,3 , 333 (1948). (17) E. W. Anaclrer, R. M. Rush, and J. S . Johnson, J . Phys. Chem., 68, 8 1 (1964).
The Journal of Physical Chemistry, Vol. 78, L\To. 21, 1972
3016 -t
1
I
the chemical shifts of the various species, S(S>,S(S,X,), and S(S,X,). In practice, it is found that S(S) depends somewhat on the added electrolyte concentration, but the required values can be obtained directly from solutions below the cmc. The system of equation which need to be solved then includes the defining equations for Kl and K z and the followjvii~g
IS01 = [SI
[Sol 3 50 IO
2C
30
50
40
60
70
80
6 =
Figure 3. Chemical shift of the trifluoromethyl groups of CF~(CH~)IIN(CE~&)~F with 0.40 M added K F as a function of the reciprocal of the detergent concentration at 13, 31, and 44’.
and coworkersE8 using sodium carboxylates and referred to as a “seconid cmc.” For these amphiphiles, it appears that i,he average micelle size varies little with concentration above the first cmc until, a t a considerably higher concentration, there is a rather abrupt increase in aggregation number accompanied by an increase in the n / a ratio. This suggests that the totality of the data can most simply be represented by a double equilibrium model with smaller micelles formed according to eq 5 and larger ones according to the anal3gous equation bS
+ 1nX :I? sax,;
K2
=
[S,x,]/[s]b[x]m (11)
R here b > a, (inlbj > (%/a),and the values of K1 and Kz are such 1 hat only the smaller micelles are present in appreciable amounts between the first and second cmc. To compute a dilution-shift curve €or this model one need? the set of parameters K1, Kz, a, n, b, and 7% and
irhe Journal of Phyaical Chemistry, Vol. 7 6 , N o . $1, 197%
+ [X*l = [XI -4-
%[saxn] k .niSaX;,]
(12)
(13)
and
US, (liters /mole)
Figure 2. Chemical shift of the trifluoromethyl groups of CFl(CHz)l~N(Cl13)3F as a function of the reciprocal of the detergent concentration. Open circles are values obtained in the presence of 0.40 M added KF, filled circles, 0.20 I !4KF. The solid curves represent calculated points for the model described in the text.
+ a[SaXnl + b!S,X,I
{ [SIN9 -4- a[SaXnIG(SaX,)
+
b[SaX,J~(&Xd]/[Sol (14) Here again [X*] is the concentration of added counterion, while [XI represents the concentration of free counterions. For each point on the curve, a convenient iterative procedure is to pick a value of [XI,guess a trial value of [ X I , calculate the two micelle concentrations from eq 5 and 11, and then use (12) a i d (13) to find [So]and an “output” value of [XI. The latter is used t o fix an improved trial value, the process is repeated until the input and output values of iX] are the same, and the final values of the various concentrations are used with (14) to compute the chemical shift, After a number of trials, we found a ‘%be~t’~rnodel with a = 25, ?I = 12, b = 60, ?TI = 30, K l = 4.885 X M-s6, Kz = 2.613 X lo1’’ JW-’~,S(S,Xn) = 11.35, and S(S,X,) = 4.75. For S(S) we used 3.66 in 0.20 M K F and 3.65 in 0.40 1%’ KF. The solid cuyves in Figure 2 are the calculated shifts with these parameters in 0.20 and 0.40 M KF. The calculated and observed shifts agree very well, but it is not possible to reproduce the data at higher added K F concentrations with the same parameters. This is not surprising, since eq 7 is built into the model by the choice of a and n and the data at high KF concentrations do not conform t o (7’). The model accounts automatically for the absence of a second cmc when there is no added electrolyte, since with [X*] = 0 the calculated concentration of the large micelles is only l/2000 of that of the small ones at [So]= 0.40 144. Kote however that the observed micelle shift without added electrolyte, 4.73 ppm, is sornen-hat higher than the shift assigned to the small micelies in the presence of KF. The model also shows that for a given value of KI a second cmc can be observed only if KT falls nithin a rather narrow range.. Since these constants should be significantly altered by changing the identity of the counterion, it is not surprising that substitution of for F- eliminates the phenomenon. It seems obligatory to explain somewhat more fully what we mean by calling the above seherne a “best” (18) P. Ekwall and P. Stenius, Acta Chem. Scand., 2 1 , 1767 (1967), and references given there.
301%
KLNETWCS OF MICELI,~ DISSOCIATION model Obviously, our data do not suffice to fix all of t,he required parameters, so that the final choice is not uniquely determined: for that mat)ter, there is no way to exclude more elaborate multiple-equilibrium models involving a,n e x w larger number of parameters. The present model is hesi in the sense that (1) a twoequilibrium model is the simplest one which gives an adequate fit for the data in Figure 3; (2) the curvature or” the dilution shift plots near t h e first cmc suggests that a = 25 is; about right, a n d then eq 7 requires n = 12; and (3) the choice Z, --- 60 reflects the fact that
the model cannot give good results unless b is substantially larger than a, but in the systems studied by Ekwall the larger micelles still appeared to be spherical.l* We chose to try to incorporate this feature into the model, tanking note also of the fact that spherical micelles cannot be formed by detergents having twelvecarbon chains when the aggregaliorx xiurxiber is much higher than 60. Once a, n, and b are selected in this way, the remaining parameters are indeed ‘(best” values in the srnse that other choices produced c z ~ r v e s ~ ~ which agree less well with the experimental points.
icelllle Dissociation by Temperature-JumpTechniques.
y Norbert Muller Department of Chemistry, Purdue University, Lafayette, Indiana .47907
(Received June 1.4, 1QYW)
Pi~hlicalioncosts assisted by the National Science Foundation
Sei-eral authors have reported that when the monomer-micelle equilibrium in an aqueous detergent solution is perturbed by a temperature jump the relaxation time lies between 1 and 300 msec. Rate constants for the dissociation of one molecule from the micelle have been derived from such data and stated to be no larger than 120 sec-I. Since other evidence, especially line widths in nmr spectra, appears to hhow that the rate constants must be several orders of magnitude larger a reexamination of the procedures used t o interpret the T-jump data was undertaken. It was found that the mathematical development involves an approximation usually not admissible under the conditions of the T-jump experiments, but even when allowance is made for rhis the T-jump and nmr results cannot be reconciled while retaining a mechanism for micelle dissolution wkmh involves a single slow step. An approximate treatment based on the assumption that dissolution proceeds by a sequence of many steps of nearly equal rate shows that with this mechanism the reported relaxation times are compatible with rate constants in the 106-10e sec-l range when the aggregation numbers are larger than 50.
Introduction The formation and dissolution of micelles in aqueous detergent solutions is so rapid that quantitative measurements of the rdevant rates have become available only relatively recenl ly. Since 1966, rakes of dissocia-
0 ~y~sec.The data mrere interpreted on the ztssurnpl ion t h a t micelle dissociation (1)
is the rate-limiting step in the formation and dissolution processes and used to derive values of i%n,n-l ranging from 0.4 to 120 sec-l. These results stand in flat contradiction to the repeated observationst7that process 1 i s “fast on t h e nmr
(4) B. C. Bennion and E. M. Eyring, J . Colloid Interfuce Sci., 32, 236 (1970). (5) J. Lang and E. M . Eyring, J . Polgmer Sci., Part A-2, 10, 89 (1972). (6) H. Inoue and T. Nakagawa, J . Phys. Chem., 70, 108 (1966). (7) N. Muller and I?. E. Platlro, (bid.,75, 547 (1971). The Journal of Phgsical Chemistry, V G ~ 76, . N o . 21, 1572
