CHEMICAL PHYSICS LElTERS
volume 56. number 1
DISTRIBUTIONAL
15 May 1978
EFFECTS ON EXCIMER FORMATION IN
MICELLAR SURFACTANT
SOLUTIONS
BX. SELINGER of Cizemistg?, AustmEan National University. Canberm. Australia 2600
Department
and
A.R. WATKINS Restnrch School of Chemistry, Austmltin National University. Gzrtberra, Austmlti 2600 Received 26 July 1977 Revised manuscript received 27 February 1978
An analysis is presented of excimer formation of molecules solubllized in mice&r surfactant solutions. This treatment takes account of both the statistical distriiution of solubihzate molecules among the mice&s and the kinetic factors affect
ing excimer formation. By using this analysis to interpret the results of steadystate fluorescenceintensity measurements, where the excimer and monomer emissions of pyrene solubilized in a num.wzrof surfactants are mred, it is possible to gaininformation about mice&r size and about the mobility and disposition of pyrene molecules within the micelle.
Over the past decade, photochemical reactions in micellar environments have attracted growing interest, because of the possibility of using surfactant mice!ies as prototypes of biological membranes. It has been shown that a considerable
amount
of otherwise
inac
cessible information, such as micellar surface charge and mobility of solubilizate molecules, can be gained by studying the properties of fluorescent “probe” molecules solubilized in micelles [I]. One reaction which has received a good deal of attention in the investigation of micelle properties is the excimer formation of aromatic hydrbcarbons, in particular of pyrene
[2]. The pyrene excimer
is charac
terised by its fluorescence emission, which is shifted to the red of the emission of the pyrene monomer. Excimer formation and decay usually occur on a time scale measured in some hundreds of nanoseconds; most surfactant micelles, on the other hand, are stable for periods of tenths of miliiseconds 131. The parameters of excimer formation thus provide a “snapshot” of the properties of the mlcelle itself, independently of the rate at which it forms or decays.
On this time scale, micelles thus form physically discrete “compartments”, among which the pyrene molecules can distribute themselves. Since excimer formation can only occur when two or more pyrene molecules occupy the same micelle, those micelles having no or only one pyrene molecule will make no contribution to the excimer formation process, and the characteristics of excimer formation will depend on the way in which pyrene molecules are distnbuted among the available micelles. If we assume that the probability of a pyrene molecule going into a micelIe does not depend on whether pyrene molecules are already there or not, we arrive at a relatively simple expression (the Poisson distribution) for the distribution of pyrene molecules among the available micelles [4] :
P(x) = px ep/x!
,
(1)
where P(x) is the probability of finding a micelle con
taining x pyrene molecules, and CLis the ratio of the bulk number of pyrene molecules to the bulk number of micelles. The relation between p and the bulk con
99
Volume 56. number 1
CHEMICAL
PHYSICS LETTERS
we obtain for the ratio of excimer to monomer quantum yields
centrations of pyrene and surfactant, cpy and cs, is given by ir = A cpyIcs ,
15 May 1978
(2)
whereA is the aggregation number of the surfactant. It should be noted that the pyrene molecules are solubilized almost entirely in the micellar phase [4]. The quantum yield of excimer fluorescence will, however, not only depend on the occupation number x, but also on the rate at which the excimer formation reaction 1pY* +pY 5 l(pY*)’
(3)
takes place. For the purely mtramiceliar excimer formation studied here, we can write (4) where 4; is the quantum yield of excimer fluorescence at infinitely high pyrene concentration, K is the StemVoider constant for excimer formation, N is the total number of micelles in the system, and cpy is the concentration of pyrene available for excimer formation. In a micelIe of occupation number x, cpY wilI correspond to (x  1) pyrene molecules. The sum is over micelles with occupation numbers from 2 upwards, since only in these micelles wiii excimei formation take place. The presence of the factor x weights each term for the number of pyrene molecules in the micelle. The monomer quantum yield will be given by a similar expression:
1
xP(x)
1

In any experiment fluorescence intensities rather than fluorescence quantum yields are measured; these are related to one another by an instrument constant. Since we are concerned here solely with ratios of quantum yields, the instrument constants cancel out, and we have
I’ Qi =
(9)
Er,
I
wherex’=xI
and
d=EfK.
(10)
P(x) in the previous expression has been substituted by eq. (1). Since fl1 et = [dl
5
tx’lx’! = C
x'=O
tx*+dljX1! ,
x'=O
we have
j
+1
etdr=
5 x*=0
0
6+d x’!(x’ + d)’
(11)
so that 9 = X$I $0 Ml
+
~cpy)lxJYx)~r >
(5) =pd
where the sum in this case begins at x = 1, since singly occupied micelles, although making no contribution to the excimer emission, will still give rise to monomer emission. Using the relaYon cpy=(x
 1)/E,
(6)
where E=AhfM’/ltXKID,
=
rdr(d, dCWd ,
(12)
where 7 represents the incomplete gamma function [5 1. This, in turn, can be related to the confluent hypergeometric function, for which computer programs and tables are available [S]. Thus
(7’7)
where D is the density of the micelle, A its aggregation number and MW the molecular weight of the surfactant, loo
jtdlet&
0
=d‘M(d,d+l,p),
(13)
Volume 56, number1
CHEMICAL PHYSICSLETTERS
where M represents the confluent hypergeometric function. The denominator of eq. (9) can then be transformed into
m.
,jo$;
x,)
=
ElgdlM(dn
d*U)
9
15 May 1978
PYRENE IN CTAB d = O571
(14)
and the numerator, after some manipulation, becomes a,
g
O
x’=l
4
x’px’ x’!(d +x’)
=KpI;(d+
I’IO
11:
1)lM(d+l,d+2,Cr)

(1%
Using eqs. (14) and (1 S), eq. (9) then becomes I’ ‘6 p =I &,d+l
M(d+ l,d+2,1.L) M(d,d+l,,u) 
(16)
There still remains the problem of determining fh/Io_ This may be dealt with by observing that, since the processes leading to the deactivation of monomer and excirner remain constant throughout the experiment, the relation &o
* @‘/&I = 1
(17)
must hold 161. If intensities are substituted for quantum yields, as above, and the expression rearranged, we obtain I’ = I;,  I(I&j,
)
08)
from which individual values of 16 and lo may be obtained by plotting the intensity data for monomer and
50
loo
I’ Fig. 1. The plot of I’ versuslfor pyrene solubilized in CTAB at room temperature. The units of both axes are arbitrary.
Fig. 2. f’f&f& as a function of g, the ratio of the bulk number of pyrene moleculesto +fiebulk number of micelles,for pyrenesolubilkedia CTAB. The continuouscurve represents the theoretical fit of eq. (16) with the parameters4 = 53.7 andd = 0.571.
excimer over a range of pyrene concentrations. Some representative results are given in figs. 1 and 2 for pyrene in a solution of cetyltrimethylammoniurn bromide, CTAB. This solution was diluted with the same concentration of surfactant in water, which had the effect of changing the quantity cr in eq. (16). After each dilution the emission intensities of the pyrene monomer and excimer were measured. Then, in order to correct for the changing excitation conditions, the experiment was repeated, this time by diluting with water, the effect of which was to disperse the micelles without changing either the distribution of pyrene molecules or the parameters affecting the excimer formation process [2] _ The data from the first experiment, corrected using the results from the second, were then fitted to eq. (18) (shown in fig. 1) from which I&, is obtained. The aggregation number of the surfactant is not known, and so it is not possible to fit eq. (16) to the data as it stands. Consequently, a fitting process was adopted which was essentially to start from the data lot
Volume 56, number 1
CHEMICAL
PHYSICS
Table 1 Values of the parameters A and d for pyrenc in aqueous surfactant
Surfactant a)
solutions
d
Surfactant concentration
15 May 1978
LETlEKS
at room temperature A
(M) this work
CTAB
0.0563
0.571
54
CDBC N10
0.0129 0.047 1
1.016 0.979
97 81
Triton X 100
0.172
0.728
120
literature 61[1],72[15], 74flOJ. 801161, 85[17],91[18], 95[19) 100[201,125[213, 152[7], 276[22] 111[23], 121[24], 125[24]
a) Abbreviations used. CTAB = cetyltrimethylammonium bromide, CDBC = cetyldimetbylbenzylammonium (oxyethylene)nonylphenol, Triton X 100 = (oxyethylene)g,5isooctylphenol.
as a series of values of I’I,/IIk at various values of cpy/cs, and to fit these numerically to eq. (16) by adjusting the parameters A [which appears in fi, cf. eq. (2)] and d. The fact that the experimental points, in contrast to the same experiment in homogeneous solution, lie on a curve (see fig. 2) ensures that the fit is unique to the particular surfactant being studied. Table 1 lists the surfactants studied here together with the values of A and d found in this work; also shown are the available literature values for the aggregation numbers A number of comments can be made about the re
sults contained in table 1: (i) For two surfactants (NlO and CTAB)
the values
of aggregation number measured in the present work disagree with the literature values which, however. disagree quite markedly among themselves. Our value of A for Triton X 100 lies within the range of the iiterature values; no previously measured aggregation numhers could be found for CDBC. in the case of CTAB, the high temperaturecoefficient of A [7 ] may be the cause of the discrepancies between our results and the literature values. The measured aggregation numbers for N 10, if our results are included, vary from 8 1 to 276, an effect which may result from the fact that these nonionic surfactants contain molecules having varying numbers of ethylene oxide units n(EO), and the distribution of n(EO) values may vary between samples having the same average number of ethylene oxide units. (ii) The value of d obtained will, from eqs. (7) and 102
chloride,
NlO = deca
depend on K and also on E, which is proportional to a quantity representing the volume of the micelle accessible to the solubilized pyrene molecules. Any preference of the pyrene for a specific part of the micelle will be reflected in the value of E obtained from the experimentally determined values of d (from this work) and K. The volume so calculated: (lo),
F$, = E/No
(19
will be less than the nominal micellar volume V, : Vm = A MW,‘lOOOh’OD
(20)
if the solubilized pyrene is confmed to one particular part of the micelle. This must be taken into consideration for the surfactants studied here, particularly for the nonionic micelles, where the pyrene has two domains available, the hydrocarbon core and the ethylene oxide pallisade layer. The solubilization sites of organic molecules in charged micelles appear to depend to a large degree on the polarity of the solubilized molecules. Polar molecules are generally solubilized near the surface of the micelle, whereas nonpolar molecules, such as aromatic hydrocarbons, occupy the inner hydrophobic regions of the micelle [8]. Pyrene derivatives appear to behave in the same way [9], suggesting that almost the entire volume of the micelle will be available to the dissolved pyrene molecules in the cases of CTAB and CDBC. We can thus set VP,= V, and so derive values of K, obtaining 38.5 Ml for CTAB and 42.6 M1 for CDBC. These are considerably lower than the corresponding
Volume56, number 1
CHEMICAL
PHYSICS
values in organic solvents, which are of the order of 5000 Ml. A similar calculation can be made for the other three smfactants, although the justification for equating VP, with V, is less certain, since little is known about solubilization sites in micelles having not only a region made up of hydrophobic aliphatic chains but also a region of ethylene oxide chains. One obtains 51.4 Ml for NlO, and 96.8 Ml for Briton X 100. However approximate the values of K obtained here may be, they represent a considerable departure from those found in lowviscosity homogeneous solvents. This may be due to changes in the monomer lifetime on going to a micellar environment, but is most likely due to the much higher viscosity of the relatively ordered micelle interior. In this connection it should be noted that viscosities derived from studies of the rotational diffusion of probe molecules [IO], which were generally in the range 17 to 40 cP, are lower than the viscosities that would be indicated by the values of K given above (of the order of 50 to 100 cP)_ The reason for this could well lie in the fact that the molecular motion involved in translational diffusion will be considerably different from that involved in rotational diffusion. It is not unreasonable to expect that there might be a considerably larger barrier to gross movement of pyrene molecules through the relatively highlyordered interior of the micelle, than to rotational motion which can take place in a “cavity” in the interior of the micelle. (iii) Dynamic quenching has been assumed throughout this derivation. A static contribution leads to a modified StemVolmer equation [ 1 I] : I/I,, = exp( k'cpy
)/( 1 + Kcpy ) ,
(21)
the effect of which will be to replace fl in eq. (16) with cr exp(k’/Kd). Values of A derived from eq. (16) would have to be divided by exp(k’/Kd), which would have the effect of making them larger. In a situation where the excimer formation process is purely static, and no dynamic quenching occurs, eq. (16) is replaced by 1’1&;
= exp [;((l  ebk’Q]
 1.
(22)
Pyrene has a relatively long excited singlet lifetime, and although the term exp(k’c ) may differ from unity in the
PY
concentration range studied here, dynam
ic quenching will still predominate, making the application of eqs. (2 1) and (22) unnecessary.
LETTERS
15 May 1978
A number of other authors have studied pyrene formation in surfactant rnicelles. However, at least some of their work is open to criticism, on the grounds that they have disregarded distributional effects and the variation of 16/&, with changing surfactant [ 121, or that they assume, for their model, that the bulk rate of exchange of aromatic hydrocarbons between micclles (occurring in times of the order of lOA s [3]) is much faster than the excited state processes being studied (these take place in the region of tens to hundreds of nanoseconds) [I 31. Other studies [ 141 assume a distribution based on an upper limit of 2 pyrene molecules per micelle; these gave plausible aggregation numbers, presumably because pyrene was solubilized relatively inefficiently in sodium dodecyl sulphate micelles. The methods presented here hold out prospects for gaining not only information about micellar size but also about the movement and deployment of solbbilized molecules within the micelle. We are hoping to measure K by independent means and thus determine Vpy and the r&cellar viscosity. It is also hoped to extend the methods outlined here to quenching experiments and to kinetic experiments in the nanosecond time range. Thanks are due to Dr. Liam Healy and Dr. David Walker for help with the theoretical part of this work,
and to Dr. U. Khuanga for helpful discussions. We express our gratitude to ICI of Australia for the gift of the samples used in this work.
References J.H. Fender and EJ. Fender, Catalysis in mice’larand macromo!ecularsystems (Academic Press, New York, 1975). Th. Fcrster and B.K. Selinger, Z. Naturforsch. 19a (1964) 38. 131 T. Nakagawa and K. Tori, KoUoidZ. Z. Polymere 194 (1964) 143. 141 U. Khuanga, BK. Selinger and R. McDonald, Australian J. Chem. 29 (1976) 1. [51 hi. Abramowitz and LA. Stegun, Handbook of mathematical functions (Dover, New York, 1965). [61 AR. Watkins, J. Chem. Sot Faraday Trans. 168 (1972)
PI
28. [71 KS. Birdi, KolloidZ. 2. Polymere 250 (1972) 731: 252 (1974) 551.
103
[S]
B. Svens and B. Rosenhohn, J. CoUoid Interface sci. 44 (1973) 495; PT. Jacobs, R.D. Geer and EW. Anacker, 3. CoBoid Interface Sci. 39 (1972) 611. 191 M. Grstzel, K. Kalyanasundaram and JK. Thomas, J. Am. Chem. Sot. 96 (1974) 7869. [lOI G. Weber. M. !3hinitzky, AC. Dianoux and G. Gitler, Biochemistry 10 (1971) 2106; M. Shinitzky, Israel J. Chem. 12 (1974) 879. [ 111 Th. Fikster, Flu~reszenz Grganischer Verbindungen (Vandenhoeck und Ruprecht, Giittingen, 1951) p 215. 1121 HJ. PownaB and LC. Smith, J. Am. Chem. Sot. 95 (1973) 3136. fl3j R.C. Dorrance and T.F. Hunter, J. Chem. Sot. Faraday Trans. 170 (1974) 1572; 68 (1972) 1312. [I41 hf. Hauser and U. KIein, Acta Phys. Chem. 19 (1973) 363; Z. Physik. Chem. 78 (1972) 32.
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Hyde and D.J.M. Robb. Proce&iiqs of the 4th international Congress on Surface Active Substances, 1964 (Gordon and Breach, London. 1967). WI P. Debye and EW. Anacker, J. Phy% Chem. 55 (1951) 644. r171 H.V. Tarter, J. Colioid Sci. 14 (1?59) 115. WI BW. Barry, JC. Morrison and G.F.J. Russ& L CoBoid Interface Sci. 33 (1970) 554. WI P. Ekwall, L. Mandell and P. Solyom, J. ColIokl Interface sci. 35 (1971) 519. ml P. Becher, J. Colloid Sci. 16 (1961) 49. 121I CW_ Dwiggins Jr.. RJ_ Bolen and HN Dunning, J. PhYS. Chem. 64 (1960) 1175. WI M.J. Schick, SM. Atlas and F.R. Eirich. J. Phys. Chem. 66 (1962) 1326. 1231 A.M. Mankowich, J. Phys. Chem. 58 (1954) 1027. 1241 C.J. Biaselle and D.B. MiBar, Biophys. Chem. 3 0975) 355.