J . Chem. SOC., Faraday Trans. I, 1986, 82, 109-118 Dynamic Behaviour of Fluorescence Quenchers in Cetyltrimethylammonium Chloride Micelles Angelos Malliaris,? Jacques Lang and Raoul Zana* C. R. M . , Grkco Microkmulsions, CNRS, 6 rue Boussingault, 67000 Strasbourg, France The kinetics of quenching of the fluorescence of pyrene solubilized in cetyltrimethylammonium chloride (CTAC) micelles by three different types of quenchers [pyrene or cetylpyridinium chloride (immobile quenchers), dodecylpyridinium chloride (mobile, hydrophobic quencher) and iodide ion (mobile, hydrophilic quencher)] has been investigated by means of time- resolved fluorescence measurements. The results obtained with the two immobile quenchers have permitted the first determination of the mean micellar aggregation number N of CTAC at high concentration up to 1.2 mol dmP3.These N-values have then been used for a quantitative evaluation of the kinetic and equilibrium quenching parameters for the other two types of quenchers. The results concerning the quenching by the iodide ion are discussed on the basis of the available models proposed for this type of quenching. They appear to favour the electrostatic model of Almgren et al. The kinetics of quenching of the fluorescence of micelle-solubilized probes by various quenchers both organicl-s and inorganic7* 9-13 has been recently the subject of extensive investigations. Taking into account the fact that the hydrophobic fluorescent probes such as pyrene or methylpyrene used in most of these investigations have a residence time inside the micelle much longer than their fluorescence lifetime, the mechanism of the quenching process depends exclusively on the nature of the quencher. Thus three situations can be distinguished.(i) The distribution of the quencher is ‘ frozen on the time scale of the fluorescence, i.e. when the residence time of the quencher in the micelles is much longer than the probe fluorescence lifetime. This is the case of pyrene excimer for ma ti or^^^^^^ where the pyrene fluorescence is quenched by pyrene in the ground state, or the quenching of pyrene fluorescence by cetylpyridinium i o n P (CP;), the so-called ‘immobile’ quenchers.l79 l8 (ii) The quencher is hydrophobic and partitioned between the micelle interior and the aqueous phase. The quencher may then be exchanged between two micelles in a time comparable to the fluorescence lifetime. This is the case of the ‘ mobile ’ quenched7 7 l8 such as m-dicyanobenzene,8 and dodecylpyridinium ion (DPC).(iii) The quencher is hydrophilic and ionic such as I-, Cu2+, etc. and is partitioned between the micelle Stern layer and the aqueous phase. This case is by far the most complex7~ l3 and it is observed that the rate of intermicellar quencher exchange increases rapidly with the surfactant concentration.13 Two different interpretations have been given to this observation. In the first one this increase is attributed to ‘close encounters’ of micelles during which the quencher effectively ‘hops’ from micelle to mi~elle.~O-~~9 l9 The rate constants for the association of the quencher to a micelle, and its dissociation from a micelle, k+ and k-, respectively, are assumed to remain constant and the increase in the exchange rate with increasing surfactant concentration C (and thus micelle concen- tration [MI) then results from the increase of the number of close encounters.The second interpretation is based on a numerical solution of the Poisson-Boltzmann equation using a cell model for the micellar so1ution.203 21 These calculations show that a large increase t On leave of absence from N.R.C. ‘Demokritos’, Athens, Greece. 109110 Fluorescence Quenching in CTAC Micelles in k- with C results from the decrease of the electrostatic potential at the micelle surface as [MI increases, which facilitates the release of the counterions located in the micelle Stern layer.In the present study we have investigated the quenching of pyrene in aqueous micellar solutions of cetyltrimethylammonium chloride (CTAC) up to very high surfactant concentration (1.2 mol dm-3, i.e. just below the range of liquid crystal phases) by means of two immobile quenchers, pyrene and CP;, a mobile hydrophobic quencher DP;, and the hydrophilic ionic quencher I-. The objective of this work was to investigate the quenching mechanisms for the various types of quenchers, with emphasis on ionic quenchers, particularly at the high [MI range where intermicellar quencher exchange becomes very important.20* 21 Moreover we have examined the possibility of obtaining the mean micelle aggregation number N and rate constants of the quencher-micelle association-dissociation process, for the various types of quenchers.Finally we have used our experimental data to test the various assumptions most often adopted for the extraction of micellar parameters from quenching experiments. 7 , l3 CTAC was selected for this study, because (i) it is easily prepared and purified, (ii) it has a Krafft temperature which allows the use of concentrated solutions at 298.15 K and (iii) its micelles are dynamically stable on the time scale of fluorescence.22 Materials and Methods The sample of CTAC was obtained by exchanging the bromide ions of hexadecyltri- methylammonium bromide for chloride ions with an ion exchange resin (Merck 111). CTAC was purified by three crystallizations in ethanolkthylacetate mixtures.The c.m.c. of CTAC (1.38 x 1 0-3 mol dmP3 at 298.15 K) was determined by electrical conductivity using a Wayne-Kerr conductometer operating at 1.592 KHz. Dodecylpyridinium chloride (DP,C) was purchased from K and K and purified by boiling its methanol solution with carbon black and by several crystallizations in ace tone-e thylace ta te mixtures. Hexadecylpyridinium chloride (CP,C) was obtained by reacting pyridine with chloro-1-hexadecane in dry ethanol for 4 h at 408.15 K in an autoclave and purified by two crystallizations in ethylacetate and two crystallizations in acetone. Pyrene (Aldrich 99 % ) was purified by extensive zone refining. Potassium iodide (Prolabo > 99.5%) was used as received. Pyrene was dissolved into the micellar solutions following aclassical procedure.23 For the pyrene excimer experiments the [pyrene]/[micelle] molar concentration ratio was kept close to unity.For the measurements based on the quenching of pyrene fluorescence by DP;, CP; or I-, the [pyrene]/[micelle] and the [quencher]/[micelle] ratios were about 0.05 and 1, respectively. These conditions ensured negligible perturbation of the micelle by either the probe or quencher and accurate determinations of N . All micellar solutions were purged with pure argon in quartz cuvettes for 30 min. All measurements were performed at 298.15 K. The fluorescence decay curves of micelle-solubilized pyrene were obtained by the single photon counting technique24 and analysed using a non-linear weighted least-squares procedure. Theoretical The equations which govern the decay of a fluorescence probe in the presence of a quencher in a micelle have been given in several 10,12, 1 7 9 18, 2 5 9 26 We shall briefly recall the main equations and assumptions involved in order to facilitate the discussion of the results.In all situations, the fluorescence decay curves have been shown to obey the equation 2 5 3 2 6 I ( t ) = I(0) exp(-A,t--A,[l -exp(-A4t)]) (1)A . Malliaris, J . Lang and R. Zana 111 where I ( t ) and I(0) are the fluorescence intensities at time t and t = 0, following an excitation with a &light pulse. A,, A , and A , are constants whose expressions in the [QI k, k+ + KkJM] general case are given by:l09 A , = k,+- A , l+K[M] A4 = k, + kJM] + k- (4) where [Q] is the total quencher concentration, k, is the rate constant for the decay of the fluorescence of the micelle-solubilized monomeric probe, k , is the pseudo first-order rate constant for intramicellar quenching, k+ and k- are the rate constants for the association and the dissociation of the quencher to/from a micelle, respectively, K = k + / k - is the equilibrium association constant of the quencher to the micelle, and k, is the second-order rate constant for the exchange of quencher between micelles through micellar collisions or close encounters. Here it should be pointed out that through rearrangement of eqn (2)-(4) one obtains A3 k Q = A2-k0+A3A,' This equation allows the estimation of k , from the values of the experimentally available parameters.Therefore from eqn (4) and (5) k , and k,[M] + k- can be obtained directly from the fluorescence decay parameters for all types of quenchers, independently of any assumptions or approximations made.It has been shown17 that the time-resolved fluorescence method can be used to obtain information on micelle aggregation numbers only when k, 3 k,. The three situations discussed in the introduction can now be considered more quantitatively. (a) Immobile Quencher This corresponds to k,, k , % k- +k,[M]. Provided that K[M] % 1 , which is fulfilled for the quenchers used in the present work, eqn (2)-(4) then reduce to A , = k, A, = [QI/[Ml A , = k,. Analysis of the decay curve thus permits the calculation of the value of [MI and, in turn, of the mean micelle aggregation number N from N = (C-c.m.c.)/[M]. (9) (6) Mobile Hydrophobic Quencher If it is assumed that the intermicellar repulsions between ionic micelles nearly prevent collisions, then k,[M] 6 k- and eqn (2) and (4) reduce to k, k+ A, 1 + K[MJ A , = k,+- A , = k, + k- (1 1) whereas eqn (3) is unchanged.The main difference between the cases of mobile and immobile quenchers is that whereas A , is in both situations independent of [Q], A ,112 Fluorescence Quenching in CTAC Micelks becomes a linearly increasing function of [Q] at constant [MI in the case of a mobile quencher. This provides an easy test of the type of system under investigation. In any case it is important to realize that there are four unknowns, k,, k+, k- and [MI, for only three experimentally available quantities, A,, A, and A,. However, as was mentioned earlier, k , and k- can always be calculated from eqn (4) and (9, but in general it is not possible to obtain k+ and [MI, and thus N , from the data pertaining to the mobile hydrophobic quencher.Some additional assumption must therefore be made. Thus [MI can be assumed to be proportional to C-c.m.c., which is equivalent to assuming that N is independent of C. [MI is then obtained from the slope of the plots of A , uersus [Q] at different C. This method permits one to obtain both k+ and [MI. It can also be assumed that K[M] + 1, i.e. k+[M] + k-. On this assumption only [MI can be obtained from the results. It will be seen below that either assumption may not be valid in many instances. If no assumptions are made, k+ can be obtained from eqn (10) only if N has been determined in an independent experiment with an immobile quencher. (c) Mobile Hydrophilic Quencher The experimental results show that both A , and A , are increasing functions of [Q].If the intermicellar exchange of quencher is attributed only to the hopping of a quencher from micelle to micelle upon close encounter of micelles, then k,[M] % k-. This situation (pure hopping) has never been encountered in practice, but cannot be excluded. With hydrophilic ionic quenchers such as I- or Cu2+ it has been assumed that together with the hopping mechanism, the quencher is also exchanged ilia the aqueous phase and the full eqn (2) and (4) must be used to describe the system.7, R~ l3 k was considered to be a true rate constant, i.e. independent of both [Q] and [MI.In this case k , is still given by eqn ( 5 ) , and Thus, in principle both k , and k can be obtained from the plot of A , - k , L’ersus [MI provided [MI is known. This takes us back to the discussion at the end of the paragraph concerning the mobile hydrophobic quencher. If close encounters of ionic micelles are assumed to be prevented by intermicellar repulsions, the intermicellar exchange of quencher can only occur cia the aqueous phase. In the ‘electrostatic’ model developed by Almgren et al.z0.21 k- is shown to be an increasing function of [MI. Eqn (3), (10) and (1 1) describe this situation and k , and k- can be obtained at each surfactant concentration from eqn (5) and (1 l), provided [MI is known. There is however a basic difference with the case of the hydrophobic mobile quencher: k- as well as k+ are now dependent on [MI, and K is not a true equilibrium constant.Recall that the binding of counterions to micelles has the characteristics of a condensation 28 as in the case of polyelectrolyte solutions.29 This fact alone would exclude the use of an equilibrium constant to describe counterion binding to micelles. The situation is different for non-ionic solutes (such as fluorescence probes) or hydrophobic mobile quenchers such as DP:, the binding of which involves forces other than electrostatic forces. Both the ‘hopping’ model and the ‘electrostatic’ model predict qualitatively similar dependence of the quencher exchange rate on the micellar concentration at low [MI. However, at high [MI the electrostatic model requires a steep non-linear increase of exchange rate with [MI while the hopping mechanism always predicts a linear relationship between [MI and the exchange rate.The experimental evidence published thus fars* 21 deals exclusively with low [MI where both mechanisms predict similar behaviour and do not permit a choice between these mechanisms. Moreover since the important parameter is the micellar concentration [MI and not the overall surfactant concentration C it is imperative to know the change of N with C. In previous studies13 N was assumed to be independent of C, which introduced some error in the calculation of the rate constants of interest. This is avoided in the present work. k,[M]+k- = A , - k , . (12)A . Malliaris, J . Lang and R. Zana 113 Results and Discussion (a) Immobile Quencher (Pyrene Excimer Formation and Quenching of Pyrene by CP?) The values of A,, A , and A , are listed in table 1.It is seen that A , is independent of both C and [Q], and equal, within the experimental error, to k,, the rate constant of fluorescence decay of pyrene solubilized in CTAC micelles (k, = 2.94 x lo6 s-l was obtained in a preliminary experiment at a pyrene concentration of ca. lop5 mol drn-,, at which concentration excimer formation is negligible). These results indicate that pyrene and CP; can be considered as immobile quenchers. Eqn (7) and (8) have been used to obtain the micelle aggregation numbers and the quenching rate constants which are listed in table 1 under headings N and k,, and plotted in fig.1. The N-values obtained with pyrene only (excimer formation) and with the pyrene/CP$ system (quenching) are seen to fall on the same curve. The aggregation number shows a sizeable increase with C, with a nearly linear increase in a fairly large range of concentration between 0.2 and 1 mol dm-3. Above 1 mol dmP3, N increases rapidly possibly owing to the approach of the phase boundary limit. Aggregation numbers for CTAC have been reported for low surfactant concentrations. Values of 80-1 15 were found by fluorescence quenching measurements for CTAC concentrations 0.0065-0.05 mol dm-3.7r l4 These values agree, within experimental accuracy, with the ones reported here. On the other hand, a small aggregation number of 59 was found by e.s.r.,O for [CTAC] z 0.01 mol dm+.However, a discrepancy in the value of the c.m.c. compared to the one reported in the literature was also found by the same e.s.r. method (4 x c.f. 1.38 x lop3 mol dm-3). In any case this aggregation number is very small for a surfactant with a 16 carbon atom aliphatic chain31 and appears to be in error. To the authors’ knowledge there are no reported N-values at high C with which the present measurements can be compared. Although the value N = 154 obtained at C = 1 mol dm-3 is significantly larger than the value 94 which corresponds to the minimum spherical micelle for a surfactant with a 16 carbon atom alkyl chain,31 the shape of the CTAC micelle does not differ much from that of a sphere. Thus, if for the sake of discussion we assume a spherocylindrical shape, the ratio between the overall length and diameter of the micelle is found to be only ca.1.7 on the assumption of a surface area of 0.7nm2 per surfactant head group in the cylindrical part of the micelle. The near-spherical micellar shape at high concentration is further suggested by the k , data listed in table 1. Even though k , decreases significantly upon increasing C , and thus N , the quantity NkE is constant, within the experimental error, as predicted by theoretical treatments of intramicellar quenching kinetics in spherical micelle~.~~ Thus, our results show that, contrary to CTAB micelles, which become very elongated at C > 0.2 mol dm-3,33 CTAC micelles remain nearly spherical, even at concentrations as high as 1.2 mol drn-,. This conclusion provides additional evidence of the strong influence of the nature of the counterion on the micelle size and shape in the case of cationic surfactant s o l ~ t i o n s .~ ~ ~ 35 (b) Mobile Hydrophobic Quencher (DPT) The values of A,, A , and A , for the pyrene/DP,+ system are also listed in table 1. It is seen that the two systems having about the same surfactant concentration (0.47 mol drn-,), but largely differing [Q] values are characterized by different A , values and nearly equal A , values, as is expected from eqn (10) and (1 1) which apply to the case of a mobile hydrophobic quencher. The [MI values obtained in the case of the immobile quenchers have been used for the analysis of the data by means of eqn (3), (10) and (1 1) to yield the values of k,, k- and k+ listed in table 1 .It can be seen thatTable 1. Experimental parameters for quenching of the fluorescence of CTAC-solubilized pyrene -~ . ~ C [QI 4 A3 A4 kQ 4 - k , k+ K / lo5 s-I / lo9 dm3 mol-I s-l / lo3 dm3 mo1-l K[M] /mol dm-3 /I0 mol dm /I06 s-1 /I06 SS' / 106 s-1 Nb 0.016 0.03 1 0.064 0.123 0.254 0.300 0.465 0.740 0.991 1.204 0.12 0.205 0.46 0.73 0.051 0.193 0.458 0.499 0.017 0.050 0.052 0.052 0.052 0.100 0.246 0.303 0.505 0.840 1.36 2.64 5.17 8.15 16.7 30.5 25.9 38.3 51.0 44.9 7.9 12.7 26.0 37.1 3.74 12.2 64.9 29.1 1.74 3.67 2.79 3.96 5.15 6.7 15.97 17.16 28.6 49 3.04 3.03 2.94 2.90 2.93 3.06 2.99 3.01 3.18 3.01 3.01 3.03 3.05 3.01 3.1 3.2 3.4 3.16 3.45 3.52 3.44 3.65 3.8 3.73 4.44 4.52 5.29 6.12 0.84 0.88 0.87 0.79 0.82 1.30 0.75 0.74 0.79 0.7 0.80 0.74 0.77 0.76 0.51 0.66 1.62 0.72 0.95 0.71 0.54 0.7 0.87 0.63 0.49 0.42 0.3 0.17 pyrene excimer formation 8.4 8.4 7.9 7.9 6.8 6.8 6.1 6.1 5.7 5.7 5.7 5.7 5.2 5.2 5.0 5.0 4.4 4.4 3.6 3.6 quenching by CP; 10.2 10.2 10.0 10.0 8.8 8.8 8.4 8.4 quenching by DP; 12 11.8 11.5 11.2 9.15 8.9 8.7 8.5 8.77 7.94 8.7 8.9 8.9 7.8 9.3 8.9 9.5 13.4 quenching by I 8.3 7.3 8.0 8.1 8.0 6.8 7.I 6.3 5.3 5.5 91 99 106 118 124 128 134 143 154 187 I17 119 135 145 103c 70d 122 100 133 120 135 130 9Ic 89d 104 100 105 102 105 108 105 1!2 114 117 125 126 126 136 135 140 145 155 - ~ ~ - - ~ - _ _ ~ ~ ~ - 2.2 3.2 2.5 2.4 4.7 6 4 7.0 8.0 9.0 10.0 12.0 26.0 42.0 79.0 a Accuracy+4%. Accuracy$lO%. r N-values from the immobile quencher measurements. N-values from the corresponding mobile quencher on the assumption k[M] 9 1A .Malliaris, J. Lang and R. Zana 115 I I I I I I I I 1 ~ - 1 1 lo ~~ 0 0.2 0.4 0.6 0.8 1.0 1.2 C/mol dm-3 Fig. 1. Micellar aggregation numbers N for CTAC obtained by various quenchers (see text). Quenching by @, excimer; A, CP;; A, DP; and +, I-. 0, k , for excimer formation. k- = (2.7 kO.5) x lo5 s-l and k+ = (1.2 0.5) x lo9 dm3 mol-1 s-l. These values, how- ever, cannot be compared directly to those obtained from chemical relaxation interpreted on the basis of Aniansson and Wall theory3' for the exchange process, and which are k ~ , z 4.5 x lo7 s-l and k& 2 3 x lo9 dm3 mol-1 s-l. Indeed in chemical relaxation, k,, corresponds to the exchange of DP; between DP, C micelles and the bulk. Thus all the surfactant ions making up the micelles are exchanged whereas, in fluorescence, only probe exchange is observed and k- must be compared to hz-- / N e R Y ln5 c-1 Ctill the waliipc nf Ir- anrl L-Y- / N A i f f e r h x i a fartnr nf rn 2 Thic "('K, 1.- " ,, I" " . "LIII, L l l V . U I U V U "I rb UIlU ,b CR, . 1 1 U l l l V l "J u L U V L W L W I L.U. J . 1 l l l . J difference may reflect differences in the properties of the DP,C and CTAC micelles. The latter are more compact and less ionized than the former. Indeed both the surface area per head group3' and the micelle ionization degree as N increases. Both factors - . L _ 1 L 1 1 * 11 1 r i i 1 1 - r .i 1 0 -nL * --I- I - are expecrea 10 resuit in smaller values or K ana tz ror me excnange or ur; in L I HL than in DP,C micelles as is indeed observed in this work.The values of k+, k- and N listed in table 1 provide a check of the validity of the assumption k+[M] 9 k- which is usually made to obtain [MI and, thus N , when these quantities have not been determined using an immobile quencher. The calculations show that the above approximation would result in an error of 30% at C = 0.055 mol dmP3 and ca. 5% at C 2 0.47 mol dm-3. This is illustrated in fig. 1 by the data points corresponding to DP;. Clearly, the above approximation may introduce large errors at low surfactant concentration and should be avoided whenever possible. Finally, we note that the values of K are fairly inaccurate. This results from the fact that for the present system the condition k- 4 k+[M] is nearly fulfilled. Then K is calculated as the difference between two nearly equal and large numbers, with a large error.(c) Hydrophilic Ionic Qwncher (I-) Eqn (5) has been used to obtain the values of k , and A , - k , which are listed in table 1. The quantity A , - k , which represents the rate of intermicellar exchange of I- [see eqn (1 2)] is plotted against [MI in fig. 2. This rate is seen to increase rapidly and linearly t No value of k,, is given for dodecylpyridinium chloride; however, from the given value of k& for dodecylpyridinium iodide at 25 "C (k& = 3 x lo9 dm3 mol-' s-l) and the relation k,,/k& = c.m.c., with c.m.c. = 1.5 x lo-* mol dm-3, k,, is found to be 4.5 x 10: s-l.116 Fluorescence Quenching in CTAC Micelles 8 7 6 5 v) 3 h W Y I 3 4 2 1 0 I I I I [MI/ 1 0-3 mol dm-3 Fig.2. Variation of A , - KQ = k- (or k,[M] + k-) with micellar concentration. Quenching by A, DP; and +, I-. Dotted line shows the predictions of the ‘hopping’ mechanism. with [MI at low [MI and the plot shows an upward curvature at [MI > 2 x mol dm-3. A linear increase of A , - k , is expected in the whole range of [MI on the basis of the ‘hopping’ mechanisms [see eqn (1 2)], contrary to the present finding. On the other hand, model calculationsz0* 21 predict a strong upward curvature in the change of A , - k , with [MI, even at low [MI, contrary to the results of fig. 2, as well as the results reported by others for the quenching of the fluorescence of pyrenell- l2 and 1-methylpyrene lo by divalent ions in sodium dodecylsulphate micellar solutions, and also for the quenching of pyrene by I- in dodecyltrimethylammonium chloride (DTAC) micellar solutions. Thus the results of fig.2 do not permit a choice between the ‘hopping’ model, and ‘electrostatic’ model. Indeed, both the linear part and the curved part of fig. 2 may be attributed to factors which were not taken into the two models, such as micelle size and shape variations, polydispersi ty, influence of the added ionic quencher, etc. An element of choice between the two mechanisms can however be extracted from the results of fig. 2 when considering the rate of increase of A , - k , with [MI. In the hopping model this rate corresponds to the second order rate constant k , for micelle close encounter with hopping of I- from one micelle to another [see eqn (12)].The plot of fig. 2 yields k, = (1 kO.1) x lo9 dmP3 mol-l s-l at low [MI, and a value about twice as large at high [MI. Our value at low [MI is in excellent agreement with that reported for the pyrene/I- system in DTAC mi~e1les.l~ The rate of diffusion-controlled micellar collisions in the absence of intermicellar interactions is ca. 7 x lo9 dm3 mol-1 s-l at 298.15 K. The strong intermicellar repulsions must significantly decrease this rate, well below the experimental value of lo9 dm3 mol-1 ~ - ~ . t ~ ~ The fact that quencher hopping does not occur at every collision has the same decreasing effect on this rate. Thus, the interpretation of the increase of A , - k , with [MI in terms of micelle close encounters leads to the physically unsound conclusion that the rate for such encounters with I- t This is based on the use of the Debye-Schmoluchowski equation for the rate of diffusion-controlled collisions3@ using for the reaction distance the centre-to-centre intermicellar distance (6 nm) at C = 1 mol dm-‘.The calculations show that if the micelles are assumed to behave like point-charges of charge 6, the rate of collision is already 10 times lower than for electrically neutral micelles. A micelle charge of 8 would result in a reduction of rate by a factor close to 100. Note that the charge of CTAC micelles is ca. 25.A . Malliaris, J. Lang and R. Zana 117 hopping is larger than the rate of diffusion-controlled micellar collisions. This inter- pretation must therefore be discarded and we are led to the conclusion that the increase of A , - k , with [MI probably has its origin in the electrostatic effects postulated by Almgren et al.20,21 Whichever the model adopted for the quencher exchange, the extrapolation of the plot of fig.2 to [MI = 0 yields the rate constant k; for the dissociation of I- from CTAC micelles, in the absence of intermicellar interactions [see eqn (12)]. The value of k; = 2.5 lo5 s-l obtained in the present study is one order of magnitude smaller than that found by Grieser13 for the pyrene/I-system in DTAC (a shorter homologue of CTAC) micelles. This large difference may reflect the smaller surface area per head group of the CTAC micelles with respect to DTAC micelles, which results in a tighter binding of counterions including I-, and thus in a smaller k- value, in the absence of intermicellar interactions. Attempts made to calculate k+ from the results produced largely scattered values, some even negative.This effect results from the fact that the approximation k+[W B k- is nearly fulfilled at all [MI in the case of I- quenching, and thus, k+ cannot be obtained by the fluorescence method with any accuracy. The fact that this approximation is fulfilled explains that the two sets of data in columns (c) and (6) in table 1 are nearly coincident. The value of k , for quenching by iodide is slightly larger in CTAC (this work) than in DTACL3 micelles. The difference probably reflects the fact that the latter study was performed at 22 "C. The k, values for I- quenching show the same decreasing trend upon increasing N than for CP; or DP; quenching, and the product Nk, is also nearly constant.At a given N the k , value for pyrene is smaller than for the other three quenchers. This probably reflects the well known interaction between arenes, such as p~rene,~O* 41 and the trimethylammonium head group, which restricts the mobility of pyrene. This interaction is also reflected in the much lower k , values found for all cationic micelles than for anionic micelles such as SDS (k, z 2 x 10' s-l),'? in the case of pyrene quenching . Conclusions This study has permitted us to show that CTAC micelles remain nearly spherical up to a concentration of 1.2 mol dm-3, i.e. at concentrations very close to those for the formation of liquid crystal phases. lu'evertheless, the aggregation number is increased by a factor of two in going from the c.m.c.to 1.2 mol dmP3. Thus, the assumption sometimes made13 in similar studies that N remains constant over large C range is not valid. We have also shown that great care should be exercised in the approximations made for the evaluation of N by means of transient fluorescence quenching methods. 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