1428
J. Phys. Chem. 1983, 87, 1426-1431
stirred for 1 h, the mixture was filtered and the filtrate cooled to 0 "C and acidified with 35 mL of concentrated HC1. Evaporation of the water in vacuo, followed by thorough drying of the residue at 100 "C in vacuo, yielded 40.3 g (73%)of HOPC1, mp 160-164 "C, Nh4R (D20)F 4.83 (s, 3 H), 8.50 (m, 2 H), 8.92 (m, 2 H), which gave a satisfactory equivalent weight on titration with AgNO,. Solution Preparation. The mixed solvents were prepared from weighed amounts of distilled water and ethanol or dimethyl sulfoxide. Dissolved carbon dioxide was removed from all solvents by passing C02-free nitrogen gas through a sintered glass bubbler immersed in the solvent. HOAI and HOPCl solutions were prepared by weight, followed by dilution when necessary. NaOH solutions were standardized by titration with HCl. Heats of Reaction. The heats of reaction were measured a t 25.0 "C with an LKB 8700-2 titration calorimeter. Solutions of HOPCl or HOAI, 1-10 mL, at concentrations
ranging from 0.005 to 0.05 M were added to 90 mL of NaOH solution having the same concentration as the phenol. In some cases, the procedure was reversed and the NaOH solution was titrated into an excess of phenol solution. Both procedures gave the same results. Heat of dilution corrections were found to be insignificant. In the aqueous cases, allowance was also made for the partial ionization of the phenol by using the ionization equilibrium constant of the phenol and the heat of dissociation of H20. This correction was found to be less than 170in all cases. Heats of Solution. Heats of solution were measured with an LKB 8700-1 reaction and solution calorimeter. (See Table IV.) Acknowledgment. This work was supported in part by a grant from the City University of New York Faculty Research Award Program. Registry No. HOA.1, 21405-07-2; HOP-C1, 7295-78-5.
Influence of Salt, Detergent Concentration, and Temperature on the Fluorescence Quenching of I-Methylpyrene in Sodium Dodecyl Sulfate with m-Dicyanobenzene Y. Croonen, E. Gelad0, M. Van der Zegel, M. Van der Auweraer, H. Vandendriessche, F. C. De Schryver,* and M. Almgrent KULeuven, hpadment of Chemistty, Ceiestl/nenlaan 200 F, 8-3030 Heveriee, Belgium and Division of Physlcai Chemistty I, Chemical Center, Uppsala, Sweden (Received: October 28, 1982; In Final Form: November 10, 1982)
The quenching of 1-methylpyreneby m-dicyanobenzenein sodium dodecyl sulfate micelles is studied as a function of the total detergent concentration, ionic strength, and temperature. Analysis of the time-dependent decay of the fluorescencegives information about the aggregation number and in addition permits the study of important rate constants characterizing interactions in or at the micelle. The aggregation number is found to increase either at higher soap concentration or upon adding salt. The rate constants k,+ and k,- are not affected by the size of the micelle nor by the ionic strength while k,, decreases as the aggregation number increases. A study of the parameters as a function of temperature shows a small decrease in aggregation number. The rate constants km+,km-, and k,, increase with increasing temperature. This permits an evaluationof the activation energies. Comparison of steady-state and time-correlated fluorescence measurements shows that a fraction of the 1-methylpyrene fluorescence quenching is due to static quenching at higher quencher concentrations. Introduction In the past few years the fluorescence quenching method has received much attention as a tool to study organized molecular systems. In particular, the quenching of arene fluorescence by neutral organic quenchers' and metal ions2$has been extensivelystudied. The kinetic formalism of this quenching process has been described.4* The kinetic scheme of fluorescence decay for quenching with neutral molecules in a micelle can be presented as in Scheme I, where Pn is a micelle with n quenchers and a Scheme I
*Address correspondence to this author at KULeuven. Division of Physical Chemistry I, Chemical Center. 0022-3654/83/2087-1426$01.50/0
probe, kf is the rate constant of fluorescence decay in a micellar solution without quencher, k,, is the rate constant for intramicellar quenching when only one quencher is present in the micelle, k,- is the rate constant for a quencher to leave the micelle, and k,+ is the rate constant for a quencher to enter the micelle. The time-dependent fluorescence decay function is given by I(t) = A, exp[-A2t - A3(l - exp(-A4t))] (5) AI = I(0) fluorescence intensity on t = 0 (6) 273
(1)M.Van der Auweraer, C. Dederen, C. Palmans-Windels,and F. C. De Schryver, J.Am. Chem. SOC.,104, 1800 (1982). (2)(a) M.A. J. Rodgers and M. F. da Silva e Wheeler, Chem. Phys. Lett., 53, 165 (1978);(b) N.J. Turro and A. Yekta, J . Am. Chem. SOC., 100,5951(1978);(c) M.Kalyanasundaram,M. Gratzel, and J. K. Thomas, ibid., 97,3915 (1975). (3)(a) S. S.Atik, M. Nam, and L. Singer, Chem. Phys. Lett., 67,75 (1979);(b) N.J. Turro, M. Aikawa, and A. Yekta, ibid., 14, 473 (1974); (c) M. Gritzel, K. Kalyanasundaram,and 3. K. Thomas, J . Am. Chem. SOC.,96,7877(1974);(d) F.Grieser and R. Tauach-Treml,ibid., 102,7258 (1980). (4)(a) P.P. Infelta, M. Grktzel, and J. K. Thomas, J . Phys. Chem., 78, 190 (1974);(b) A. M. Tachiya, Chem. Phys. Lett., 33, 289 (1975). (5)J. C.Dederen, M. Van der Auweraer,and F. C. De Schryver, Chem. Phys. Lett., 68, 451 (1979). (6)J. C.Dederen, M. Van der Auweraer, and F. C. De Schryver, J. Phys. Chem., 85, 1198 (1981).
0 1983 Amerlcan Chemical Society
The Journal of Physical Chemistty, Vol. 87,No. 8, 1983 1427
Fluorescence Quenching of I-Methylpyrene
TABLE I : Kinetic Constants Obtained from the Quenching of 1-Methylpyrene by mDCB in SDSa [SDS] cmc, M Kkqm2[Q1
A3 = (km-
+ kqnJ2(1 + K[Ml)
A4 = kqm
+ k,-
(8)
(9)
In this article the quenching of 1-methylpyreneand pyrene by m-dicyanobenzene (mDCB) is investigated. The value of the method of time-dependent fluorescence quenching in studying micellar systems has been examained by looking into the influence of the total detergent concentration, the ionic strength of the medium, and the temperature on the aggregation number (NWJof sodium dodecyl sulfate micelles. In addition to the micelle size data this kind of analysis permits a study of the different rate constants of eq 5. Experimental Section 1-Methylpyrene was purified by recrystallization from EtOH with carbon black, followed by column chromatography on silica gel with benzene as eluent. The purity was checked by a lifetime measurement in isooctane (255 ns) . Pyrene was purified by thin-layer chromatography. The purity was checked by a lifetime measurement in sodium dodecyl sulfate (370 ns). SDS (Merck fur biochemische Zwecke) contains a fluorescent impurity that can be removed by recrystallization from MeOH. The purity of SDS was checked by measurement of the critical micelle concentration (0.007 94 M, 25 "C). The quencher mDCB (Aldrich) was purified by recrystallization from EtOH followed by sublimation. The fluorescence decay curves obtained by excitation at 344 nm were measured with time-correlated singlephoton counting technique using a thyrathron-gated deuterium lamp as an excitation source run at 20 kHz (Applied Photophysics). The observed decay was fitted to eq 5 and convoluted with the lamp curve by using a modified nonlinear Levenberg-Marquardt algorithm.' The error margins on km+,k,-, and k,, are f25%. The error margin on the aggregation number is &lo%. Results and Discussion Quenching of 1-Methylpyrene and Pyrene by mDCB in SDS Micelles at 24 "C. The observed fluorescence decay can be analyzed according to eq 5 where (10) Az = kf + SdQ1
where
A4 = lz,,
+ It,-
(14)
A plot of A3 as a function of the quencher concentration yields a linear relationship out of which the slope S3 can (7) International Mathematical and Statistical Libraries, Inc., Houston, TX,routine ZXSSQ.
S,, M-1
s,,
M-1
s-1
S,/S,, s-' A,, s-1
1.2 x
lo-,
1100 6 . 2 2 x 109 5.7 X l o 6 3.9 x 107
2.2 x
lo-,
862 5 x 109 5 . 8 X lo6 5 x 107
3.2 x
lo-,
752 4.04 x 109 5.4 X l o 6 3 . 9 x 107
5.2 x
lo-,
578 2 . 9 3 x 109 5.1 X lo6 3.5 x 107
a S,, S,, S,/S,, and A , vs. [SDS]- cmc ( t = 24 "C). M; [ l - M e P y ] = M; [mDCB] = 1 x 1 0 - 3 - 5 x cmc = 8 x M.
be determined. A plot of A, vs. the quencher concentration yields a slope S2and an intercept that within experimental error is identical with kp Since [MI in eq 11 and eq 13 is equal to ([SDS] - cmc)/Nagr a plot of the experimental Scl and S z l values as a function of the SDS concentration minus the cmc gives a linear relationship. The values of S,, S2,S 2 / S 3 ,and A4 are reported in Table I. From S 2 / S 3and A , the rate constant k,- can be determined according to
When we equate k,, with A4 - km-, a value of kq, is obtained. Multiplication of S3 with A2/kqm2and S2with A4/kqmgives
c = A4, 7 s 3 =1 + KK[M] kw
A plot of B-l vs. SDSbt - cmc gives according to eq 19 an intercept equal to l / k m + and a slope equal to l/km-Nagg. A plot of C-l vs. SDS - cmc gives according to eq 17 an intercept equal to 1/K and a slope equal to l/Nagr This approach gives correct values for k,-, km+,N g, and K. These values are reported in Table 11. For &e system pyrene, mDCB, and SDS, the observed decay can be analyzed in the same way. The values for the different rate constants and the aggregation numbers are given in Table 11. Influence of the Total Detergent Concentration on the Aggregation Number of SDS Micelles. Quenching of 1-Methylpyrene by mDCB. In these fluorescence quenching experiments the influence of the total detergent concentration on the aggregation number and the different rate constants of eq 5 was investigated. All measurements were carried out at room temperature (24 "C). As for the above described system, the assumption is made that mDCB does not exchange between the micelles during the lifetime of the probe. S2 and S3 can then be determined by plotting A , and A , as a function of the total quencher concentration. The values of S2,S3, and A4 as a function of the total detergent concentration are given in Table 111. The micelle concentration [MI can be obtained from S3 if in eq 20 the above experimentally found value of K (Table 11) is used. Application of the above-mentioned
1428
The Journal of Physical Chemistty, Vol. 87, No. 8, 1983
Croonen et al.
TABLE 11: Kinetic Parameters Obtained from the Quenching of 1-Methylpyrene and Pyrene by mDCB in SDS Micellar Solutions ( t = 24 "C) probe p yrenea 1-methylpyrene
hm7, L mol-' s-' 9.8 x 109 1.05 X 10"
quencher mDCB mDCB
a [mDCB] = 6 i( 10-4-1.4 x lo-, M, [SDS] = 2 x 10-'-8 M, [SDS] = 2 x 10-'-8 x 10.' M, [l-MePy] = M.
k
k m - , s-l
6.3 5x
N,
lo6 lo6
K, L mol-' 1660 1900
73 66
X
M.
10.' M, [pyrene] =
kqm, s-'
4.4 x 107 3.5 x 107
[mDCB] = 1 x 10-3-5 x
lo-,
TABLE 111: Kinetic Constants Obtained from the Quenching of 1-Methylpyrene by mDCB in SDSa [SDS], M
__
0.07 0.28 0.49 0.73
S,,
M-'s - '
S,,
4.62 x 109 2.26 x 1 0 9 1.27 x 109 0.91 x 109
M-'
514 172 117 84
0
A,, s - '
4.3 4.4 4 x 2.9
x 107 x 107 107 x 107
0
70
S,, S,, and A , vs. the total detergent concentration M, [mDCB] = 1 x 10-,-1x ( t = 24 "C). [l-MePy] = M. cmc = 8 x lo-, M.
c
6 0 1
0
'
TABLE IV: Quenching of 1-Methylpyrene by mDCB in SDSa
I
I
I
02
06
04
Flgure 1. Quenching of 1-methylpyrene by mDCB in SDS. N,,
0.07 0.28 0.49 0.73
0.98 3.9 6.1 8.0
63 70 79 91
7.4 x l o 6 1 x 107 8.5 X l o 6 8 X
lo6
3.6 X l o 7 3.4 x 107 3.1 x lo' 2.1 x 107
a,,,A ' h , , and kqm as a function of the SDS concentration ( t = 24 "C). b The error on km- and kqm is 30% due t o the fact that they could only be determined at one detergent concentration.
procedure yields correct values for k,-, kqm, and Nagg (Table IV). In the concentration range studied (0.07-0.73 M) it appears that the aggregation number increases with the total SDS concentration (Figure 1). Since we are working with a neutral quencher the slight increase in the aggregation number cannot be ascribed to an electrolyte effect of the quencher. Recently Baumgardt and Strey8 studied the concentration dependence of the mean aggregation number of ionic micelles by stopped-flow experiments. The experiments were performed on H20-NaTS and H20-SDS. It turned out that the mean aggregation number of these detergents appears to increase with increasing detergent concentration. The results on SDS are in accord with the results found in this study. Lianos et al.9 studied oil-inwater microemulsions of SDS. In the absence of codetergent or oil they found the same small increase in aggregation number when increasing the detergent concentration. The experimental results also show a slight decrease if k,, when the SDS concentration increases. This is in agreement with the model for intramicellar quenching.1° Since the volume of the micelle increases, the probability that a quencher meets a probe becomes smaller. Influence of the Ionic Strength of the Medium on the Quenching of 1-Methylpyrene by mDCB in SDS Micelles. All measurements were carried out a t 24 f 1 "C. The observed fluorescence decay can be analyzed according to eq 5 as in the case without added electrolyte. The parameters A,, A,, and A , take the form described by eq 10, \
~~
~~~~~
(8) X. Baumgardt and R. Strey, Ber. Bunsenges. Phys. Chem., ac-
cepted for publication. (9) P. Lianos, J. Lang, C. Stranielle, and R. Zana, J.Phys. Chem., 86, 1019 (1982). (10) M. Van der Auweraer, J. C. Dederen, E. GeladB, and F. C. De Schryver, J . Chem. Phys., 74, 1140 (1980).
vs.
[ SDS] . *.3c 33 E 35
3 3 3 00
io3 3 c
100 00
-I
t
NaCl
005
GI5
035
055
Flgure 2. Variation of kqmwith the NaCl concentration.
12, and 14. A4 is 3.3 X lo7, 3.2 X lo7, 2.3 X lo7, and 1.92 X lo7 s-l at 0.1, 0.3, 0.45, and 0.6 M NaC1, respectively. The values of S3-land S2-las a function of the SDS concentration are for different salt concentrations reported in Table V. At each salt concentration it appears that S2/S3is independent of the SDS concentration. Application of the procedure mentioned above yields values for the aggregation number, k,+, km-, K , and k , , (Table VI). The variation of k,, with the NaCl concentration can been seen in Figure 2. It is clear that k,, decreases as the NaCl concentration increases. Influence of Temperature on the Quenching of 1Methylpyrene by mDCB in SDS Micelles. The quenching of 1-methylpyrene by mDCB in SDS was studied at 20, 32.6, 42.5, and 51.2 "C. The absorption spectrum of 1methylpyrene in SDS is identical at 20 and 50 "C. The fluorescence decay could a t all temperatures be analyzed according to eq 5 . The parameters A 2 ,A B ,and A, take the form described by eq 10, 12, and 14. The values of S1, S3,and S2/S3 at different temperatures are reported in Table VII. The values of A , are 4 X lo7, 6.7 X lo7, 9.2 X lo7, and 11.84 X lo7 ssl at 20, 32.6, 42.5, and 51.2 "C, respectively. Application of the above-mentioned procedure leads to the values of k,+, km-, kqm, and the aggregation numbers reported in Table VIII.
The Journal of Physical Chemistty, Vol. 87, No. 8, 1983
Fluorescence Quenching of 1-Methyipyrene
1429
TABLE V: Values of S,-' and Sz-' as a Function of the SDS concentration for Different Salt Concentrations Obtained from t h e Quenching of 1-Methylpyrene by mDCB in SDS Micellar Solutions ( t = 24 i. 1 "C)
[SDS I , M
2
x lo-,
4 x
8 x 10.'
lo-'
0.0008323 1.79 X lo-''
0.1 M NaCl 0.0 01046 2 2.35 X lo-''
0.00140552 2.4 X lo-''
S 3 - ' ,M S2-',M s
0.000972 1.56 X lo-''
0.3 M NaCl 0.00125 1.66 X 10.''
0.00158 1.79 X lo-''
1x
lo-,
3x
lo-,
5x
0.0019 2.50 X lo-''
lo-,
S 3 - ' ,M S2-', Ms
0.00079 1.24 X 10."
0.45 M NaCl 0.00107 1.46 X lo-''
0.00125 1.70 X lo-''
S,-I, M Sz-', M s
0.00079 9.23 X lo-''
0.6 M NaCl 0.00097 1.12 x lo-''
0.00115 1.13 X 10."
TABLE VI: Parameters Obtained from the Quenching of 1-Methylpyrene by mDCB in SDS Micelles as a Function of [ NaCl] M
km-, s-'
0 0.1
5 x lo6 4.4 x 1O6 6 X lo6 6 X lo6 7 X lo6
0.3 0.45 0.6
X
S 3 - ' ,M S,-', M s
[SDS I , M
[ NaCl I,
6
km', L mol-' s-'
K, kqm,L L mol-' mo1-Is-l
17 0 0 ,
1650
N,,
1 x 10" 7.4 x 109
1900 1680
3.5 X l o 7 2.9 x 107
8.6 X l o 9 1.1 X 10" 1.4 X 10''
1400 1800 2000
2.6 X lo7 110 1.7 X 10' 1 3 0 1.28 X 182
I
1
66 93
107
TABLE VII: Values of S,,S,, and S,/S, as a Function of the SDS Concentration at Different Temperatures Obtained from the Quenching of 1-Methylpyrene by mDCB in SDS Micellar Solutionsa
[SDS 1, M
2 x lo-'
S,, M-' S,, M - ' s - '
1100 6.22 x
sz/s,, s-l
5.7 x
109
4 x
lo6
6 x lo-,
t = 20.4 "C 752 578 4.04 x 2.93 x 109 109 5.4 x l o 6 5 X l o 6
8x
109
5
X
t = 42.5 "C
10" S,/S,,S-I
1 x 107
SJS,, a
S-I
1031 1.39 X 10''
1.4x 107
[I-MePy] =
792 1.06 x 10'O 1.3 x 107
000340
000350
Figure 3. In k,- as a function of 1/T. 1
23L0
23 2 0
722 7.34 x 109
489 5.76 x
1 x 107
1.1 x
1 0 9
107
t = 51.3 "C S,, M-I S,, M-' s-'
000330
23 6 0
1218 1.17 X
SC'
000320
lo6
S,, M-I S,, M-'
926 8.93 x 109 1 x 107
000310
I
466 2.33 x
S,/S,, s-'
S,, M - ' s - '
15 00 00030
I
1
23 8 0 I
t = 32.7 "C 600 525 1314 1008 9.39 X 6.25 X 5.96 x 4.72 x 109 109 109 109 7.2 X l o 6 6.5 x l o 6 9.9 X l o 6 9 x l o 6
S,, M-'
1/T __c 1
650 493 8.94 x 7.43 x 109 109 1.4 x 1 0 7 1.5 x 107
2 3 00 00030
Figure 4. In ',k
000310
000320
000330
000340
000350
0 003L0
0 00350
as a function of 1/T.
M, [mDCB] = 5 x 10-4-1.6 x
M. TABLE VI11 : Parameters a t Different Temperatures Obtained from the Quenching of 1-Methylpyrene by mDCB in SDS Micellar Solutions
t , "C N, 20.4 32.7 42.5 51.5
66 61 62 58
K, L mol-' 1900 1700 1580 1480
h,, s-I 3.5 X l o 7 6 X lo7 8.3 X l o 7 1.1 X l o 8
km', L mol-'s-I
k&, s-'
1 X 10'" 1.2 X 10" 1 . 5 X 10" 1.9 X 10"
5 X lo6 7.3 X l o 6 9.3 X l o 6 1.3 X l o 7
P l o t t i n g of the logarithm of k,+, k,-, and k,, as a function of 1/ T shows a linear dependence (Figures 3-5)
'
173G 0 0030
0 00310
000320
0 0033C
Figure 5. in k,, a s a function of 1 / T .
The Journal of Physical Chemistty, Voi. 87, No. 8, 1983
1430 7 50 I
I
Croonen et al.
TABLE X: I,lI (Steady State) and I,/I (Calculated)vs. the Quencher Concentration for the Quenching of 1-Methylpyreneby mDCB at 0.04 M SDSa
steady state
[QI,M 0 4.68 x 10-4 6.24 X
7.8 x 1.17 x 1.56 x a
t1
720 000303
30C31C
000320
000330
5~ J 0003LC 000350
Flgure 8. In K a s a function of 1 / T .
TABLE IX: Parameters Obtained from the Quenching of 1-Methylpyreneb y mDCB in SDS Micellar Solutions in the Presence of 0.01 M CaCI, ( t = 51 "C) N, 90
K, L mol-'
k m - , s-l
1650
1.3 X lo'
2
X
10"
6.7 X
lo'
from which the activation energies can be determined. The rate constant k,- has an activation energy of 24 kJ mol-' while for k,+ and k,, values of 16 and 28 kJ mol-', respectively, are derived. A plot of the logarithm K as a function of 1/T is linear (Figure 6). Values of -6.3 kJ mol-' for AHo and 42 J mol-' K-' for AS" are derived indicating that at 25 "C AGO equals -18.82 kJ mol-'. Influence of Temperature and Ionic Strength. The influence of temperature and ionic strength together were studied by analyzing the fluorescence decay at 24 and 30 "C at 0.3 and 0.6 M NaCl concentration. The values for the different parameters are reported in Table VI. The influence of these parameters was also studied by using CaClz instead of NaC1. In view of the salting-out effect of Ca2+ions one has to use lower salt concentrations (0.01 M) and higher temperatures (51 "C). Although the obtained data, reported in Table IX, cannot be related directly with the parameters of SDS at room temperature they nevertheless show that k,+ and k,- are not affected by the nature of the electrolyte and that the obtained values for these rate constants are identical with those obtained in the system containing no NaCl at 50 "C (Table VIII). The rate constant lz,, in the presence of CaClz at 51 "C is smaller than that in the absence of added salt at that temperature. This can be explained by the larger aggregation number (vide supra). Relation between Steady-State and Time-Correlated Fluorescence Intensity Measurements. Steady-state quenching measurements were made with a 0.04 M SDS solution. The relative emission yield Io/I as a function of the concentration of quencher can be related to the kinetic quenching behavior in the forml1J2
where I(t) = I(t=O) exp(-A2t - A3[1 - exp(-A4t)]) (22) (11) P. P. Infelta, Chem. Phys. Lett., 61, 88 (1979). (12) F. Grieser, Chem. Phys. Lett., 83, 59 (1981).
[l-MePy] =
1 1.97 2.4 2 3.5 5 7.2
calculated
1 1.91 2.3 2.7 4.4 5.2
M.
SomI(t)Q,o dt is equal to I(t=O)/kf and the denominator of eq 21 can be written as L m I ( t ) , dt = [I(t=O)/A,](l - A,eMA3L 1~ ~ z I ~ dx) 4e~3~ (23)
Thus
I o / I = (A,/k,)[l
- A,e-A3& 1~
~ 2 / ~ d4x e] ' ~ (24) 3~
The integral above can be solved by using Simpson's approximation, to give I,,/I. Table X shows I o / l values obtained from steady-state quenching experiments. The parameters A2, kf, A,, A4 obtained from time-correlated single-photon counting experiments were then introduced in the right-hand side of eq 24 and the Io/I values were calculated. These values are also reported in Table X.
Discussion Time-Dependent Fluorescence Measurements. The present study clearly shows that analysis of the time-dependent decay of the fluorescence of an adequately chosen probe,13 quenched in an irreversible process, gives information about a micellar system that is consistent with other known methods. The variation of the aggregation number with added electrolyte has been studied by using light ~cattering,'~ excimer f~rmation,'~ and stationary2bJ6a and time-resolved16bfluorescence quenching. The results on the growth of the micelle with the concentration of added salt are in quantitative agreement with some other s t ~ d i e s ' yielding ~ ~ ' ~ ~ the same type of average.', In addition to the micelle size data this analysis permits the study of important rate constants characterizing interactions between organic molecules and the micelle on the one hand and the interaction between two organic molecules in the micelle on the other. The rate constants ',k and k,- are in the present study affected neither by the size of the micelle nor by the ionic strength, and they are also independent of the probe. The constancy of k,+ justifies the method to calculate the aggregation number as a function of SDS concentration: there is no transfer (13) M. Almgren and J. E. Loefroth, J. Chen. Phys., 76, 2734 (1982). (14) (a) K. J. Mysels and L. H. Princen, J. Phys. Chem., 68, 1599 (1959); (b) M. F. Emerson and A. Holtzer, ibid., 69, 3718 (1965); 71, 1898 (1967); ( c ) A. Rohde and E. Sackmann, ibid., 84, 1598 (1980); (d) S. Hayashi and S. Ikeda, ibid., 84,749 (1980); (e) M. Corti and C. Degiorgio, ibid., 85,711 (1981); (f) S. Ikeda, S. Hayashi, and T. Imae, ibid., 85, 106 (1981); (9) N. A. Mazer, G. B. Benedek, and M. C. Carey, ihid., 80, 1075 (1976); (h) P. J. Miasel, N. A. Mazer, G. B. Benedek, C. Y. Young, and M. C. Carey, ibid., 84, 1044 (1980). (15) (a) P. Lianos and R. Zana, J. Phys. Chem., 84, 3339 (1980); (b) D. J. Miller, U. K. A. Klein, and M. Hauser, Ber. Bunsenges. Phys. Chem., 84, 1135 (1980);( c ) D. J. Miller, ibid., 85, 337 (1981). (16) (a) M. Almgren, F. Grieser, and J. K. Thomas, J. Am. Chem. Soc., 101, 279 (1979); (b) M. Almgren and J. E. Loefroth, J . Colloid Interface Sci., 81, 486 (1981).
Fluorescence Quenching of 1-Methylpyrene
The Journal of Physical Chemistry, Vol. 87, No. 8, 1983
1431
of quencher on micelle collisions. The constancy of k,-, and of the ratio K = k,+/k,- = n / [ Q w ]is , quite remarkable. One would expect that the distribution of quencher between micelles and water followed a two-phase distribution equilibrium in the first approximation. This would imply that KINw was constant as long as [&,Imt remained constant. The thermodynamic parameters obtained from a temperature-dependent study of k,+ and k,- indicate a negative and relative small enthalpy which can be attributed to different kinds of interactions between the water, the ionic head groups of the detergent, and the quencher mDCB. However, it is clear that the association of the quencher is largely governed by the positive entropy (42 J mol-' K-'). This positive entropy is usually associated with the elimination of hydrocarbon-water interfaces and thus the freeing of water molecules from a highly structured environment." Estimation of the values of these parameters with other quenchers will lead to a better insight into the nature of the binding of organic molecules to micelles. Increase of the aggregation number either at high SDS concentration or upon adding salt leads to a decrease of the quenching rate constant, in accordance with the theory.1° The product of the quenching constant and aggregation number remains almost constant (or varies without trend) in agreement with previous observations for the quenching of Ru(bpy),2+by 9-methylanthracene in SDS micelles.16bIt is furthermore clear that Ca2+exerh a larger effect on the micelle size'* than Na+. Even at a tenfold lower concentration than the lowest NaCl concentration and at higher temperatures is the effect of Ca2+ more important. The small decrease of the aggregation number with the increasing temperature is in accordance with the results by Mazer et al.14g for small micelles. Given the almost constant aggregation numbers, a study of the rate parameters as a function of temperature will allow the evaluation of activation energies. If the quenching is a diffusioncontrolled processlo then the activation energy in k,, reflects the activation energy of viscous flow in the micelle, keeping in mind that one uses ideas developed for homogeneous systems and extends these to this inhomogeneous system. Combination of variation in temperature and ionic strength emphasizes the statement that k,+ and k,- are
independent of the ionic strength since their values are the same within experimental error at all salt concentrations at 30 "C. Comparison of Steady-State and Time-Correlated Fluorescence Measurements. From Table X it is clear that the values of Io/Isht and 10/Icdcd correspond very well for the lowest quencher concentrations used. When the quencher concentration exceeds 6.24 X M, it can be seen from Table X that the values of Io/Idddeviate from the values of Io/Istat. This deviation becomes larger when the quencher concentration increases. This is most probably due to the fact that a fraction of the l-methylpyrene fluorescence quenching occurs in a static way. Because the decay curve obtained in time-resolved fluorescence studies contains only information concerning molecules engaged in dynamic quenching processes, the contribution of static quenching shows up if one also considers the absolute fluorescence intensity. The only experimental evidence for static effects in fluorescence quenching in micellar systems that has been reported until now comes from the work of Mataga et al.,19Atik et a1.,20 and Martens and Verhoeven.21 In the study of the quenching of pyrene fluorescence by amines, Mataga et al. showed the occurrence of static quenching, however, without the occurrence of ground-state complexation. Martens and Verhoeven studied the quenching of pyrene fluorescence by N,N'-dimethyL4,4'-bipyridinium dichloride (paraquat, pq2+)in SDS solutions and showed that due to the enhanced ground-state complexation the quenching of pyrene fluorescence should not only be discussed on the basis of a dynamic mechanism only, but that static and dynamic mechanisms contribute almost equally to the overall fluorescence quenching. It is clear that the use of steady-state fluorescence data to obtain information on the micellar systems is only permitted under conditions where all parameters of the probe-quencher pair are known from time-correlated measurements.
(17)(a) J. B. S. Bonilha, T. K. Foreman, and D. G.Whitten, J. Am. Chem. Soc., 104,4215(1982);(b) R. B. Loftfield, E. A. Eigner, A. Pastuszyn, T. N. E. Lovgren, and H. Jakubowski, Biochemistry, 77,3374 (1980). (18)J. M. Corkill and J. F. Goodman, Trans. Faraday SOC.,58,206 (1962).
(19) Y. Waka, K. Hamamota, and N. Mataga, Chem. Phys. Lett., 53, 242 (1978). (20)S. S. Atik, C. L. Kwan, and L. A. Singer, J.Am. Chem. Soc., 101, 5696 (1979). (21)F. M. Martens and J. W. Verhoeven, J. Phys. Chem., 85,1773 (1981).
Acknowledgment. The authors are indebted to the I. W.O.N.L. (fellowshipto Y.C., MvdZ), the Belgian National Science Foundation (fellowship to E.G., MvdA), and to the F.K.F.O. and the University Research Fund for financial aid to the laboratory. Registry No. mDCB,626-17-5;SDS, 151-21-3;1-methylpyene, 2381-21-7.
