2418
J . Phys. Chem. 1986, 90, 2418-2421
and the Na+ counterion. Alkali-metal cations have been shown to be capable of complexing with polyoxyethylenated nonionics in the presence of anionic surfactants and other large anions,14 and these complexes have been used as a basis for the analysis of this type of nonionic.15J6 In polyoxyethylenated anionics, the negative charge of the surfactant ion should increase the tendency of the ether oxygens to interact with Na+. Interaction with Na+ imparts partial zwitterionic character to the surfactant. Such zwitterionic character should result in a decrease in the cmc and (14) Toei, K.; Motomizu, S.; Umano, T. Talanra 1982, 29, 103. (15) Anderson, N. H.; Girling, J. Analyst (London) 1982, 107, 836. (16) Tsubouchi, M.; Yamasaki, N.; Yanigasawa, K. Anal. Chem. 1985, 57, 783.
C,, values and an increase in the cmc/C2, ratio3,when compared to those of the corresponding non-oxyethylenated materials. All
these changes are observed in the oxyethylenated compounds studied. Moreover, as would as expected from an interaction involving Na', these changes increase with the Na+ content of the solution, providing support for the complex formation hypothesis. Acknowledgment. This material is based upon work supported in part by the National Science Foundation under Grant No. ENG-7825930. Registry NO. ClOEOS, 101225-35-8; C12EOS, 20829-85-0; CIZEOSO, 15826- 16-1; Cj2EOZS0, 3088-31-1.
Size of Sodium Dodecyl Sulfate Micelle in Concentrated Salt Solutlons Jin-Ming Chen, Tzu-Min Su, and Chung Yuan MOU* Department of Chemistry, National Taiwan University, Taipei, Taiwan, Republic of China 107 (Received: October 28, 1985; In Final Form: January 8. 1986)
We investigate the effect of high salt concentration on the average aggregation number of sodium dodecyl sulfate (SDS) over the temperature range 30-70 O C . The method is based on the increase of self-quenching of the fluorescence of micelle-solubilized pyrene through excimer formation. Transient fluorescence decay is measured and analyzed. It is shown that an exponent weighted averaged aggregation number ( n ) eis obtained by this technique; it is smaller than weight average aggregation number for a polydisperse micelle system. For SDS in NaCl solution, we observe an increase of ( n ) , as the temperature is lowered and ionic strength is increased. We use the thermodynamic model developed by Missel et al. to calculate ( n ) e . Agreements between theory and our experimental results are quantitative.
1. Introduction
The formation of micellar aggregates in amphiphile solutions is a well-known phenomenon clearly established in early lightscattering studies.' Usually, ionic amphiphiles form small nearly spherical micelles at low ionic strength. When one increases the concentration of counterion, above some ionic concentration the aggregation number can increase up to 20-fold and the micelle is interpreted to undergo a sphere-to-rod shape transition. The most studied system is sodium dodecyl sulfate (SDS) in NaCl solution by either statiS4 or dynamic light-scattering techniquesw For aqueous solutions of SDS plus NaCl, in the range C(NaC1) = 0-0.8 M at 30 OC, it is found that aggregation number ranges from 60 to 1000; it drastically decreases at higher temperature. In fact, a t 80 OC, the micelles are again small with an average aggregation number around 100 at C(NaC1) = 0.8 M. Around the same time, fluorescence quenching of the micelle-solubilized fluorophore was investigated to obtain an aggregation number of SDS in NaCl solution.1w12 It was found (1) Mysels, K.J.; Princen, L. H. J . Phys. Chem. 1959, 63, 1699. (2) Emerson, M. F.; Holtzer, A. J . Phys. Chem. 1967, 71, 1898. (3) Anacker, E. W. In Solution Chemistry of Surfactants. Vol. 1, Mittel,
K. L., Ed.; Plenum: New York, 1979. (4) Ikeda, S.; Hayashi, S.; h a c , T. J . Phys. Chem. 1981, 85, 106. ( 5 ) Mazer, N. A.; Benedek, G. B.; Carey, M. C. J. Phys. Chem. 1976,80, 1075. ( 6 ) Missel, P. J..; Mazer, N. A.; Benedek, G. B.; Young, C. Y.; Carey, M. C. J . Phys. Chem. 1980, 84, 1044. (7) Missel, P. J.; Mazer, N. A,; Benedek, G. B.; Carey, M. C. J . Phys. Chem. 1983,87, 1264. (8) Corti, M.; Degiorgia, V. J. Phys. Chem. 1981, 85, 711. (9) Flamberg, A.; Pecora, R. J. Phys. Chem. 1984, 88, 3026. (IO) Turro, N. J.; Yekta, A. J . Am. Chem. SOC.1978, ZOO, 5951.
0022-3654/86/2090-2418$01 SO10
that the apparent average size measured is much less than the light-scattering results when a large rodlike micelle is detected at high salt concentrations. For example, at 0.8 M NaCl and 35 OC fluorescence quenching experiment gives an average aggregation around 240 while light scattering gives an average size about 1000. Many workers"-13a'4 suspected that the fluorescence technique gives too low a value for the micelle size. Lianos and Zana" believe that fluorescence quenching technique is limited to a size of n less than 200 because of incomplete excimer formation within its own lifetime (-400 ns), and the method simply fails at [NaCl] = 0.8 M. Because of this, the fluorescence quenching technique has not been applied to large rodlike micelles since then. However, there is another perfectly reasonable explanation: the large rodlike micelle is very polydisperse and the difference in the measured average aggregation size reflects different ways of averaging. In fact, this is indicated by Missel et al.;6,7they have a simple thermodynamical model that gives the size distribution function P ( n ) . They applied the model to their QLS study and explained their measured average aggregation of SDS very well. We therefore think it is necessary to reopen this question again using the available distribution to examine the average size determined by the fluorescence quenching technique. In this paper, we use solubilized pyrene as a fluorescene probe. We monitor the time-resolved fluorescence quenching due to excimer formation. The relative importance of monomer fluorescence and excimer formation is determined by the partition of pyrene among the micelles. By assuming random partitioning, ( 1 1 ) Lianos, P.; Zana, R. J . Phys. Chem. 1980, 84, 3339. (12) Atik, S. S.; Nam, M.; Singer, L. A. Chem. Phys. Let?. 1979, 67, 75. (13) Kfatohvil, J. P. J . Colloid Interface Sci. 1980, 75, 271. (14) Lindman, B.; Wennerstrom, H. Top. Current Chem. 1980, 87, 1.
0 1986 American Chemical Society
The Journal of Physical Chemistry, Vol. 90, No. 11, 1986 2419
SDS Micelles in Concentrated Salt Solutions we show in section I1 that the fluorescence quenching technique measures an exponent average aggregation number that is heavily weighted toward the low n part. We then in section 111 present our results of measurement for SDS at C[NaCl] = 0.5 and 0.8 M over a large temperature range. In section IV, we show that the exponent average aggregation number can be fitted very well by the same set of thermodynamic parameters in the model of Missel et aL6s7 Therefore, we believe the fluorescence quenching technique is useful in the study of micelle size distribution for the polydisperse situation since it furnishes a very different way of averaging the size. The question of micelle size distribution is discussed in the last section. 11. Material and Methods A . Reagents and Solutions. The SDS (Merck A.G.) used in this study was purified by precipitation from ethanol solution; its purity (-99.5%) was checked by HPLC. Sodium chloride was dissolved in deionized water and chlorine was bubbled to remove any trace of bromide and iodide since they are probable fluorescence quenchers. It was then recrystallized twice. Pyrene (Riedel-Dehaen) was dissolved in benzene, and maleic acid anhydride was added and heated at 80 OC to remove color impurities. The solution was column separated through silica gel packing. Finally, pyrene was collected by vacuum sublimation at 160 OC and 30 millitorr. Pyrene was dissolved in n-hexane and then n-hexane was pumped out to leave a thin layer of pyrene on the flask surface. Surfactant solution was then added to the flask and stirred at 50 OC for 1 day to ensure complete solubilization. Oxygen was removed by a special nitrogen bubble scheme to ensure no lost of surfactant solution. B. Measurements. A Nd:YAG laser (Quanta-Ray DCR-2) was used to excite pyrene at 355 nm. Fluorescence of wavelength 380 nm was collected at 90 OC through a 0.5-m Jarell-Ash monochromator and detected by a RCA 1P28 photomultiplier. The fluorescence decay was recovered by a transient waveform recorder (Gould-Biomation 6500, 2-11s resolution) which is interfaced to computer. The sample was kept at the desired temperature in a thermostat to within 0.2 K. Inmost cases, data were iveraged over 300 laser shots. C. Data Analysis. We monitor the monomer fluorescence decay of pyrene; it consists of two decay components: a slow exponential component corresponding to micelles having sohbilized one pyrene molecule, and a fast component associated with excimer formation within micelles having solubilized two or more pyrene molecules. We assume that (1) pyrene dissolves only in the micellar phase, (2) solubilization of pyrene is only in minor quantities (- 1 per micelle) it does not change the size and structure of the micelle, and (3) intermicelle exchange of pyrene is slow compared to the lifetime of excited pyrene. We measure from fluorescence decay curves the fraction of unquenched first-order decay. This comes from those micelles having only one excited pyrene without any other pyrene in it. Let m,, be the average occupation member of unexcited pyrene in micelles of aggregation number n. If we assume that the distribution is random, the distribution of m' unexcited pyrene molecules in micelles class of size n is Poissonian
Since excited pyrene during each shot is of negligible population compared to the total number of pyrene, the fraction of only one excited pyrene in micelle of size n is (see Appendix) fn(0)=
e-mn
(2)
Given a polydisperse micelle solution with size distribution P(n), the fraction of only one excited pyrene in all micelles is (ffl(0)) = U"(0) P(n)
(3)
fl
This quantity is proportional to the intensity of pure monomer fluorescence. Atik, Nam, and Singer'* showed that the time
dependence of the fluorescence intensity decay is I( t )/ I ( ( ) ) = emiex~(-k,O-l I-kit
(4)
for a monodisperse micelle system with average occupation number of fluorophers per micelles m. k3 and k , are the rate constants for excimer formation and monomer pyrene decay, respectively. The long time behavior from eq 4 is r(t)/z(o)N
(5)
In this work, we will have to replace the factor e-m by cffl(0)). Notice that we do not assume any particular kinetic scheme for excimer formation as long as it is fast compared to the k , process. Normally, we use the data points between t = 500 and t = 1000 ns to be represented by I ( t ) / I ( o ) = Cfn(o))e-khr
(6)
Now, let Cpbe the stoichiometric concentration of pyrene, C be the surfactant concentration, and cmc be critical micelle concentration; one has m n =- CP -
n
(7)
c-cmc
We then have
(fn(0)) =
xe-"cp/(c - cmc) n
p0 n
(8)
We define an average aggregation number ( n ) c which , we call exponent average aggregation number, by cfn(o))I e-(n)cCp/(C - cmc) (9)
( n ) , is the average aggregation size reported in this study; it is different from weight average ( ( n ) , ) or number average ( ( n ) , ) aggregation size reported in the literature. In ( n),, the averaging is more heavily weighted toward the lower end; therefore ( n ) , is always smaller than ( n ) , and (n),,. For a rod micelle in high salt concentrations, the difference can be substantial as will be shown in the next section. 111. Results We measure the exponent average aggregation over the concentration range of NaCl from 0 to 0.8 M; the concentration of SDS is 0.0347 M. Since at high salt concentration SDS can precipitate below 30 OC,we measure ( n ) ,over the temperature range 30-70 OC to avoid pre-precipitation secondary aggregation. M. The pyrene concentration is 1.8 X The average aggregation at 35 "C over different salt concentrations is reported in Figure 1. It follows the same trend reported The size increases from -50 to 240 over [NaCl] = 0 to 0.8 M. The uncertainty in ( n ) , is about 10%. To make sure that no residue excimer formation exists at long time, we observe approximately parallel decay (first order) at long times to cases without any excimer formation. We also studied the effect of pyrene by varying its concentration from 6 X 10-5 to 1.8 X 1O4 M. We find that the apparent ( n ) , does not change more than 10% for all the quenching cases. If there were incomplete excimer quenching due to slow diffusion, one would observe a much larger change of measured ( n ) , as the amount of pyrene changes. We also think that this furnishes evidence that the micelle structure changes little over the concentration range of pyrene we studied here. In order to study the thermodynamic behavior of a large rod micelle, we chose to measure ( n ) eat 0.5 and 0.8 M NaCl concentration over the temperature range 30-70 "C. These are reported in Figure 2 and Figure 3. Also in the same figures, we show the average aggregation number reported by Missel et aL6 by quasi-static light scattering. One can see that the aggregation size ( n ) ,decreases as the temperature increases, ( n ) eis much less than ( n ) , at low temperature end, and the difference is larger the higher salt concentration. We also list in Table I the monomer decay rate constants k , ; it is lower at higher salt concentration and larger the higher the temperature although it seems to approach a constant near the
The Journal of Physical Chemistry, Vol. 90, No. 11, 1986
2420
Chen et al.
""i
250
500
loop I
I 30
50
0
Figure 3. Variation of the average aggregation number (n), of SDS micelles upon increasing temperature: [SDS] = 0.0347 M, [NaCI] = 0.5 M. Solid lines represent calculations based on the thermodynamic ~ ; (n)"; D, ( r ~ ) ~The . cross represents our model: A, (n),,;B, ( r ~ ) C,
experimental data.
Figure 1. Variation of the average aggregation number (n), of SDS micelles upon increasing NaCl concentration. [SD] = 0.0347 M and 7 = 35
oc.
\
600
s
500
i
*O0I 100
I
01
1
1
30
44
I
I
I
M
60
IJ
70
TI'C
Figure 2. Variation of the average aggregation number (n), of SDS micelles upon increasing temperature: [SDS] = 0.0347 M, [NaCI] = 0.8 M. Solid lines represent calculations based on the thermodynamic model: A, (n),,;B, ( n ) w ;C, (n)";D, (n),. The circle represents our
inter-micelle repulsions are strongly screened out, and one can thus neglect the interaction. The best studied system is SDS in NaCl; Missel et al.697proposed a simple ladder model for the chemical potential of a monomer in a spherocylindrical micelle for such systems. We will show that this model, with the thermodynamic parameters determined by Missel et al., gives a exponent average aggregation number (n), that can explain our data well. Consider the following multiple equilibria between monomer surfactant S and micelle of size n, Sn,and let X I and X,, be mole fractions of monomer and micelle of size n; we have X , = Xlne-(r~-nrio~/RT (10) where :M and /llo are, respectively, the standard parts of the chemical potential for a micelle of size n and for a monomer. For a spherocylindrical micelle with n, monomers in the end caps and n - no in the cylindrical part, the chemical potential change can be separated into the cap part and the cylindrical part = FU,O - ~ u i ' = (pn,O - ~OFI') + ( n - ~O)(M' A + ( n - no)6 (11)
and 6 represents the equal-space change of free energy upon transfering each monomer from solution to the cylinder part of the micelle. Defining two parameters K and X B as
K = e(A-d)lRr
experimental data. TABLE I: ( n T , OC 30 35 40 45 50 60 70 a
)a
X B = ,AIR7
and k , Determined from SDS Solubilized Pvrene" 0.5 M NaCl 0.8 M NaCl (n)e 10"kl, s-l (n), 10-6kl, s-I 212 171 160 142 129 111 92
2.7 2.9 3.0 3.2 3.4 3.8 4.0
270 242 206 181 158 118 95
2.3 2.5 2.6 2.8 2.7 2.7 2.8
[SDS] = 0.0347 M.
high temperature end. Since it is known''-'4 that the interior environment of a micelle appears to be more nonpolar as the salt concentration is increased, one expects k l should approach the smaller value typical in hydrocarbon solvent. IV. Size Distribution of Rodlike Micelle-Comparison with Theory The present theories of micelle growth are mainly based on the free energy change in multiple chemical e q ~ i l i b r i a . ~ ' , ' ~It- ' ~is particularly suitable for micelles at high ionic strength since (15) Debye, P. Ann. N.Y. Acad. Sci. 1949, 51, 573.
70
60
1 IT I
1.0 (NaclIM
0.5
Eu
Lo
eq 10 can be rewritten as
(12) (13)
-( -)x "
X" = 1
XE In terms of the total surfactant concentration m
x = x , +"=no CnX,
(15)
eq 14 and 15 can be solved to write X , in terms of X , provided K and X , are known. Thus, we can calculate all kinds of average
size with the distribution ",
Missel et al. determined the thermodynamic parameters K and X Bfor SDS in NaCl solution by fitting the QLS data over a range of concentrations and temperatures. For the case [NaCI] = 0.8 M, we use their values of K , X B , and (40). We calculated (n),, (n),,,and (n), and compared them with the experimental results as shown in Figure 2. The (16) Tanford, C. The Hydrophobic Effecr; Wiley: New York, 1980, 2nd ed. (17) Porte, G.;Appell, J. J . Phys. Chem. 1981, 85, 51 1.
The Journal of Physical Chemistry, Vol. 90, No. 11, 1986 2421
SDS Micelles in Concentrated Salt Solutions
30 40 50 60 70
3.8 1.1 0.3 0.08 0.015
35 7.8 2.0 0.5 0.13
9.0 9.16 9.32 9.48 9.64
7.32 7.48 7.63 7.69 9.85
exponent average aggregation number determined experimentally agrees within experimental error with the calculated curve (lowest solid curve). W e also present the average aggregation number ( n ) h calculated from the hydrodynamic radius determined by a QLS experiment; (n)h is a little larger than (n),. The calculation is based on a prolate ellipsoidal model as done in ref 6. For the case [NaCl] = 0.5 M, we interpolate from the values reported in ref 6 the thermodynamic parameters K and X,. They are listed in Table XI. However, we find in this case that we have to shift no to a larger value no = 75 in order to fit our data well. We show this in Figure 3. The change of n, from 60 to 75 changes (n),,and ( n ) , relatively little; in fact, the latter value of no can also be used to fit the QLS data reasonably well. V. Conclusion We have shown that the fluorescence quenching technique can be used to study the sphere-to-rod growth of SDS micelles in high salt concentration. We resolve the discrepancy in average aggregation number reported by QLS and this technique; it comes from different ways of weighting in a polydisperse distribution. The fact that we can fit our measured aggregation number over a wide range of temperatures by using the well-tested thermodynamic model of Missel et a1.6 and their distribution function shows that the fluorescence quenching technique may be used for relatively large and polydisperse micelle system. It would be desirable to further test this technique on other well-understood systems. There is a good possibility that this technique can be used together with light scattering to study the size distribution and detailed thermodynamics of large micelles since they give very different weighted-averaged sizes. Given recent interests18-20in micelle thermodynamics, a new way to gain more experimental information on micelle distributions will be very useful. Acknowledgment. This research was supported by grants from National Science Council, The Republic of China (Grant No. NSC75-0201-M002C-07).
Appendix Here we give a detailed derivation of equations dealing with data analysis of the fluorescence quenching of pyrene in polydisperse micelles. Consider the following excitation and decay mechanism: (18) Stecker, M. M.; Benedek, G. B. J . Phys. Chem. 1984, 88, 6519. (19) Eriksson, J. C.; Ljunggren, S.;Hendriksson, U. J. Chem. SOC.,Faraday Trans. 2 1985, 81, 833. (20) McMullen IV, W. E.; Gelbart, W. M.; Ben-Shaul, A. J . Phys. Chem. 1984, 88, 6649.
-+ hu
TABLE II: Thermodynamic Parameters for SDS Size Distribution 107~ 106x, T. " C 0.5 M NaCl 0.8 M NaCl 0.5 M NaCl 0.8 M NaCl
A
A* A*
+ (m, - l ) A
A*
k,
A
k3h-I)
hv'
AA*
+ ( m , - 2)A
here m, represents the occupation number of pyrene in micelle of size n. The kinetics of the above scheme gives d[A*m,(t)l /dt = - [ k , + (mn - Ilk31 [A*mn(t)l (A-1) exp{-[kl + (mn - l)k,ltl (A-2)
[A*,"(?)] =
Let fn(m,) be the distribution of pyrene molecules among micelles of size n; it is Poissonian (A-3) a n
= CmlJn(mn) mn
Another average will be over the size distribution of micelles P(n). The initially excited pyrene will be distributed as
with Zo and At being the incident light intensity and its duration, and 4 being the excitation efficiency. The total time evolution of the excited pyrene concentration, [A*(?)], will be [A*(?)] = C C I A * m n ( t ) l= n m.
CdoA?qe-k"{CP(n)e-mnexp[M, exp(-k,t)]) = n
C 1Atq(em.[exP(-k,r)-l1-kir) P O
(A-5)
The bracket denotes the averaging over size distributions. Long-time behavior will be governed by [A*(?)]/ [A*(O)] = (e-'%)e-kll = (Ce-"cp/(c - cmc)p(n))e-klf n
('4-6) This is eq 8. One should note that the relevant quantity for long-time behavior in eq A-4 is just
which is the starting point of eq 2. Registry No. SDS, 151-21-3; NaC1, 7647-14-5.
