J. Phys. Chem. 1987, 91, 1475-1481
1475
Expanding the left-hand side as a Taylor series to first order and substituting for An from (A2) one finds
Suppose now that the growth rate is not independent of crystallite size but rather is linearly dependent on its volume. Then
p( a N / an) = -NA-I( d N / at)
An = bNAn At
(A4)
After separating variables such that N(n,t) = ?(n) O(t) this integrates to
d n ) = d o ) exp(-fn) e(t) =
{em-1+ B,-l
exp(-s(o)
(A51
sE1e,t))-l
(A6)
In the present context the time dependence is of no concern; the essential feature in that one obtains an exponential distribution.
s(n) =
d o ) (n/no)-t
(A7) (A81
with O(t) given again by eq A6. Finally, we note that if the growth rate is independent of particle size for small crystallites but becomes volume dependent for larger particles then the model An = @NA(n it) At ('49)
+
yields the hyperbolic exponential distribution given by eq 9.
Intermicellar Migration of Reactants: Effect of Additions of Alcohols, Oils, and Electrolytes A. Malliaris, N R C "Demokritos", Aghia Paraskevi. Greece
J. Lang,* J. Sturm, and R. Zana Institut C. Sadron (CRM-EAHP} and Greco Microemulsion, CNRS, 67000 Strasbourg, France (Received: June 6, 1986; In Final Form: October 30, 1986)
Time-resolved excimer formation of micelle-solubilized pyrene has been used to investigate the intermicellar migration of pyrene. No intermicellar migration was detected on the probe fluorescence time scale, in moderately concentrated solutions of the investigated surfactants, in the absence of any additives. Probe intermicellar migration via coagulation-fragmentation reactions has been shown to be induced by addition of medium chain length alcohols to pure micellar solutions and inhibited by oil addition to the resulting mixed alcohol surfactant micellar solutions. Additions of electrolytes to some pure micellar solutions or to mixed alcohol + surfactant solutions also induce fragmentation-coagulation reactions taking place on the pyrene fluorescence time scale. The relationshipbetween micellar polydispersity and the occurrenceof fragmentation-coagulation reactions has been emphasized. This occurrence may strongly affect the determination of micellar aggregation numbers N by means of time-resolved fluorescence probing methods. The true N values are obtained only if the conditions K[micelle] >> 1 is fulfilled, K being the equilibrium constant of the fragmentation-coagulation reaction.
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Introduction The method based on the intramicellar quenching of a probe fluorescence has been extensively used for the study of micellar systems, mainly for the determination of the micellar aggregation number N.'" For some systems the rate constant for intermicellar migration of the probe or of the quencher (referred to as reactants in the following) has also been mea~ured.*~~-" In these systems reactant migration takes place either through the exit of the reactant from the micelle, followed by its diffusion in the water phase and association to another micelle or through collisions and (1) A great number of studies has now been devoted to the measurement of N in pure micellar solutions as well as in micellar solutions with additives dissolved in the bulk and/or incorporated in the micelles to form mixed micelles or microemulsions: see for instance ref 2-6 and references therein. (2) Roelants, E.; Geladt, E.; Smid, J.; De Schryver, F. C. J . Colloid Interface Sei. 1985, 107, 337. (3) Malliaris, A.; Lang, J.; Zana, R. J . Colloid Interface Sei. 1986, 110, 231. (4) Almgren, M.; Swarup, S. J . Phys. Chem. 1982, 86, 4212. (5) Lianos, P.; Lang, J.; Sturm, J.; Zana, R. J. Phys. Chem. 1984,88, 819. Lianos, P.; Lang, J.; Zana, R. J. Phys. Chem. 1982, 86, 4809. (6) Lafroth, J.-E.; Almgren, M. J . Phys. Chem. 1982, 86, 1636. (7) Dcderen, J. C.; Van der Anweraer, M.; De Schryver,F. C. Chem. Phys. Lett. 1979, 68, 451. (8) Grieser, F.; Tausch-Treml, R. J. Am. Chem. SOC.1980, 102, 7258. (9) Croonen, Y.; Geladt, E.; Van der Zegel, M.; Van der Anweraer, M.; Vandendrlessche,H.; De Schryver, F. C.; Almgren, M. J. Phys. Chem. 1983, 87, 1426. (IO) Atik, S . S.; Thomas, J. K. J. Am. Chem. SOC.1981,103, 3543; Chem. Phys. Lett. 1981, 79, 351. (1 1) Malliaris, A,; Lang, J.; Zana, R. J. Chem. SOC.,Faraday Trans. 1 1986, 82, 109.
transient merging of the micelles. More recently, we have shownI2 that in aqueous solutions of ionic surfactants, under appropriate experimental conditions, fast intermicellar exchanges of micelle-solubilized reactants can take place through a third mechanism which involves reactions of fragmentation and coagulation. In these reactions a micelle can lose a micellar fragment (fragmentation) or incorporate such a fragment (coagulation), which may eventually carry one reactant from one micelle to another. The existence of this new intermicellar migration mechanism was supported by the fact that its first-order rate constant increased very rapidly with the polydispersity of the system. The latter is related to the amount of micellar fragments, Le., submicellar aggregates present in the system. As previously pointed out,12 the fragmentation-coagulation mechanism for reactant exchange is very similar to the mechanism of micelle formation-breakdown proposed by Lessner et al,I3 which involves reactions such as Ai
+ Aj
Ai,
(1)
where Ai and Aj are submicellar aggregates containing i and j surfactants, respectively. For ionic micelles, reactions 1 become operative at high surfactant concentration and/or in the presence (12) Malliaris, A,; Lang, J.; Zana, R. J . Phys. Chem. 1986, 90, 655. (13) Lessner, E.; Teubner, M.; Kahlweit, M. J. Phys. Chem. 1981, 85, 3167. Kahlweit, M. (a) Pure Appl. Chem. 1981, 53, 2060; (b) J . Colloid Interface Sci. 1982, 90, 92; (c) in Physics of Amphiphiles, Micelles, Vesicles and Microemulsions; Degiorgio, V., Corti, M., Eds.; North-Holland: Amsterdam, 1985; p 212.
0022-3654/87/2091-1475$01.50/0 0 1987 American Chemical Society
1476 The Journal of Physical Chemistry, Vol. 91, No. 6,1987
of added electrolytes. It is clear that if in (1) A, is a submicellar aggregate (or a micellar fragment) and A , , is a full micelle (in which case i + j = N) then the two processes become formally identical. The work described in this paper has its origin in recent chemical relaxation (T-jump) investigations of the effect of additions of alcohols and oils on the dynamics of micelles.14 Thus, it has been found that the addition of medium chain length alcohols to micellar solutions induces a dramatic decrease of the micelle On the lifetime and a large increase of micellar polydi~persity.'~ contrary, additions of oils, particularly to mixed surfactant alcohol micellar solutions, bring about an equally dramatic increase of micelle lifetime and a large decrease of micellar polydispersity. In view of these results and the above ones, one would expect addition of alcohols and oils to micellar solutions to strongly affect the dynamics of intermicellar exchanges through fragmentation-coagulation and to do so in opposite fashions. The primary purpose of this paper is to show that indeed intermicellar migration of pyrene via fragmentation-coagulation processes becomes detectable on the fluorescence time scale upon addition of medium chain length alcohols to micellar solutions where this process was not observed prior to such additions. It will be also shown that oil additions to the mixed alcohol surfactant micellar solutions have an effect opposite to that of alcohol additions on the rate of pyrene intermicellar migration. Finally, additional results are given which confirm previous ones1, which showed that additions of electrolytes to some micellar solutions can also induce the occurrence of fragmentation-coagulation reactions.
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Experimental Section 1 . Materials. Hexadecyltrimethylammonium chloride (HTAC), sodium dodecyl sulfate (SDS), sodium p-octylbenzenesulfonate (OBS),and didodecyldimethylammonium chloride (DDDAC) were the same as in other s t ~ d i e s . " J ~ - ' ~ High-punty alcohols, ddecane, and salts (NaC1, CaC12,N02S04) were purchased from Fluka, Merck, or Aldrich. Pyrene (Aldrich, 99%) was extensively zone-refined. All solutions were prepared with deionized and distilled water and thoroughly deoxygenated prior to each fluorescence measurement by either purging with pure argon for 30 min or by 3-5 freeze-pump-thaw cycles. 2. Methods. The determination of the aggregation number N a n d of the fragmentation rate constant k- were made with the method of pyrene excimer formation at a [pyrene]/[micelle] molar concentration ratio close to 1. The fluorescence decay curves of micelle-solubilized pyrene were determined by the single photon counting techniquet8over a time span which in most cases stretched up to about 6ko-l (where k0-l = ' T ~ ,unquenched fluorescence lifetime of pyrene), that is more than 2000 ns after the exciting pulse. The fluorescence decay curves have been shown to obey the eq~ationl~.~~ Z ( t ) = I ( 0 ) exp(-A2t - A3[1 - exp(-A4t)]) (2) where Z ( t ) and Z(0) are the fluorescence intensities at time t and t = 0, following an excitation with a light pulse. A,, A,, and A4 are constants which were obtained together with Z(0) from the fitting of the decay curve to the eq 2, using a nonlinear weighted least-squares procedure. The experimental errors on A,, A,, and A , are =k2-3%, &lo%,and &lo%, respectively. In the case where the pyrene distribution is frozen on the fluorescence time scale ( k -
