744
J. Phys. Chem. 1980, 84, 744-751
(4) Funasaki, N.; Hada, S. J . Ph,ys. Chem. 1979, 83, 2471, and references cited therein. (5) Mukerjee, P.; Mysels, K. J. ACS Symp. Ser. 1975, No. 9 , 239. (6) Mukerjee, P.; Yang, A. Y. S. J. Phys. Chem. 1976, 80, 1388. (7) Funasaki, N.; Hada, S. Chem. Lett. 1979, 717. (8) Hildebrand, J. H.; Scott, R. L. "The Solubility of Nonelectrotytes"; Dover Publications: New York, 1964; Chapters 7 and 16 and Appendixes 1 and 4. (9) Pagano, R. E.; Gershfeld, N. L. J. Phys. Chem. 1972, 76, 1238. (10) The chemical structure of NF is (CFa 12 C F\
c,=c'
(CF3)zCF
\",Lo_, -
0 ,No
(11) (12) (13) (14) (15) (16) (17)
Funasaki, N.; Hada, S. Bull. Chem. SOC.Jpn. 1976, 49, 2899. MatijeviE, E.; Pethica, B. A. Trans. Faraday SOC.1958, 54, 1382. Mysels, K. J. J . Colloid Interface Sci. 1978, 66, 331. Shinoda, K.; Soda, T. J. Phys. Chem. 1963, 67, 2072. Tanford, C. J . Phys. Chem. 1972, 76, 3020. R. L. Scott, J . Am. Chem. SOC. 1948, 70, 4090. Hildebrand, J. H.; Fisher, B. B.; Benesi, H. A. J . Am. Chem. SOC. 1950, 72, 4348. Jolley, J. E.; Hildebrand, J. H. J. Phys. Chem. 1957, 61, 791. Shinoda, K.;Hildebrand, J. H. IbM. 1958, 62, 481; 1961, 65, 1885. (18) Funasaki, N.; Hada, S., unpublished results. (19) Menger, F. M.; Jerkunica, J. M.; Johnston, J. C. J . Am. Chem. SOC. 1978, 700,4676. Muller, N.; Birkhahn, J. H. J . Phys. Chem. 1967, 77, 957. SvenS, B.; Rosenholm, B. J. ColloidInterfacs Sci. 1973, 44, 495. Corkill, J. M.; Goodman, J. F.; Walker, T. Trans. Faraday
SOC.1967, 63, 768. Clifford, J. Ibid. 1965, 67,1276. (20) Menger, F. M. J. Phys. Chem. 1979, 83, 893. Acc. Chem. Res. 1979, 72, 111. (21) Mukerjee, P. J. Colloid Sci. 1964, 79, 722. (22) Overbeek, J. Th. G.; Stigter, D. Recl. Trav. Chim. Pays-Bas 1956, 75,1263. Mukerjee, P. Adv. ColloldInterface Sci. 1967, 7, 241. Anacker, E. W. In "Cationic Surfactants"; Jungermnn, E., Ed.; Marcel Dekker: New York, 1970; p 203. Tanford, C. "The Hydrophobic Effect: Formation of Micelles and Biologlcal Membranes"; WileyInterscience: New York, 1973; p 45. (23) Hall, D. G.; Pethica, B. A. In "Nonionic Surfactants"; Shick, M. J., Ed.; Marcel Dekker: New York, 1967; p 516. (24) Hill, T. L. "Thermodynamics of Small Systems"; W. A. Benjamin: New York, 1963-1964; Vol. 1 and 2. (25) Mukerjee, P. Kolloid Z. 2. Polym. 1970, 236, 76. (26) Metheson, I. B. C.; King, A. D., Jr. J . Colloid Interface Sci. 1978, 66,464. (27) Goodrich, F. C. "Proc. Int. Congr. Surf. Act., 2nd, 79571957, 7, 85. Defay, R.; Prigogine, I.; Bellemans, A,; Everett, D. H. "Surface Tension and Adsorption"; Longmans: London, 1966; Chapter 12. Lucassen-Reynders, E. H. J . Colloid Interface Sci. 1973, 42, 563. Nakagaki, M.; Funasaki, N. Bull. Chem. SOC.Jpn. 1974, 48, 2094, 2482. Funasaki, N.; Nakagaki, M. Ibid. 1975, 48, 2727. Goddard, E. D. Adv. Chem. Ser. 1975, No. 744, Chapters 3, 12, and 13. Gershfeld, N. L. Annu. Rev. Phys. Chem. 1976, 27, 349. Motomura, K.; Yoshino, S.; Fujii, K. Matsuura, R. J. Collokl Interface Sci. 1977, 60, 87. Garrett, P. R. Ibid. 1977, 62, 272. (28) Stigter, D. J . Phys. Chem. 1975, 79, 1008; 1964, 68, 3603. Fgat, G. R.; Levine, S. Adv. Chem. Ser. 1975, No. 744, Chapter 8.
Micelle Size and Shape of Sodium Dodecyl Sulfate in Concentrated NaCl Solutions Shoji Hayashi and Sholchi Ikeda" Department of Chemistry, Faculty of Science, Nagoya University, Chikusa, Nagoya 464, Japan (Recelved April 2, 1979; Revised Manuscript Received December 12, 7979)
Light scattering from aqueous solutions of sodium dodecyl sulfate has been measured in the presence of NaCl of different concentrations at different temperatures. In NaCl solutions more concentrated than 0.45 M, surfactant micelles fbrmed at the critical micelle concentration further associate into large micelles with increasing surfactant concentration. In 0.60 and 0.80 M NaCl at 25 "C, light scattering exhibits anomalous dissymmetry attributable to the formation of trace amounts of microgel particles. In 0.80 M NaCl at 35 "C, light scattering is normal and gives the micelle aggregation number as high as 1410 at 1.10 X g ~ m - The ~ . angular dependence indicates formation of a rodlike micelle having a length of 597 A. It is concluded that sodium dodecyl sulfate forms spherical micelles at low NaCl concentrations (10.45 M), but it associates into rodlike micelles at high NaCl concentrations when its micelle concentration is high.
Introduction Recently Mazer, Benedek, and Carey1 measured quasielastic light scattering from aqueous solutions of sodium dodecyl sulfate (SDS) in the presence of NaCl of different concentrations and found that the micelle aggregation number increases from about 80 in 0.15 M NaCl to about 1000 in 0.6 M NaCl a t 25 "C. The small micelle having an aggregation number less than about 100 has been assumed to be spherical or globular in ~ h a p e . ~However, -~ the large micelle cannot be accommodated to a globular micelle but has been assigned a rodlike shape.' The same workers together with their co-workers6further observed angular dependence of light scattering and confirmed the formation of rodlike micelles. Unfortunately it proved that the SDS samples they used were not sufficiently pure but contained considerable amounts of higher alkyl homologues.6 Furthermore, they did not examine variation of light scattering and micelle size with SDS concentration in detai1.l These workers measured light scattering at various temperatures from 11to 85 "C, but the temperatures in0022-3654/80/2084-0744$01 .OO/O
cluded the range that was considerably lower than the temperature of solubility limit or the critical micelle temperature of SDS in 0.6 M NaC1.' This fact could cast suspicion if the SDS solutions that they studied and in which they found the rodlike micelles were unstable and contained small crystallites. The formation of rodlike micelles first proposed by Debye and Anacker7i8has long been accepted with serious reservation by other worker^.^#^ In the present work we have measured light scattering from aqueous solutions of SDS in the presence of concentrated NaCl at different temperatures and examined their behavior as a function of SDS concentration at temperatures above and below its solubility limit. Conditions for preparing and clarifying SDS solutions and for lightscattering measurements have been carefully defined, and, especially, the temperatures for all these stages have been strictly regulated. A series of SDS solutions of concentrations c (g ~ m - has ~ ) been prepared by dissolving SDS solid in an NaCl solution of a given concentration, C, (M). We have found that a transition of micelle shape from sphere to rod occurs in SDS solutions of concentrations 0 1980 American Chemical Society
Micelle Size arid Shape of Sodium Dodecyl Sulfate
well above the critical micelle concentration (cmc) when the NaCl concentration is higher than 0.45 M. In the temperature range below the solubility limit and even above but not far from it, anomalous angular dependence of light scattering has been observed with SDS solutions containing medium amounts of micelles, and this has been attributed to the formation of trace amounts of microgel particles, possibly each composed of a network of spherical micelles linked by some cations and occluding solvent, but not to the presence of small crystallites.
Experimental Section Materials, SDS was purchased from the Nakarai Chemical Co., Inc., Kyoto, as the special reagent for protein analysis, lot no. M7K6587. The reagent was extracted with dry ethyl ether for 12 h on a Soxhlet extractor, and then it was recrystallized from ethanol as follows. About 17 g of the material was dissolved in 1 L of ethanol a t 70 "C, and after filtration the solution was cooled to 18 "C. About 11g of SDS was collected. It was dried at 100 "C in vacuo for 10 h and stored over P205. The SDS sample was analyzed for dodecanol and distribution of lnydrocarbon chain length. It was extracted with ethyl ether, and the ethereal solution was applied to gas chromatography. It was found that the content of dodecanol WEISless than 0.01%. The sample was refluxed with 2 N H2S04for 2 h and then extracted with ethyl ether. The ethereal solution was subjected to gas chromatography. The results showed that the sample consisted of 0.24% Clo,98.10% CI2,and 1.66% CI4. The gas chromatographic analysis was performed on a Shimadzu 4BM gas chromatograph using a Chromosorb W column at 120 "C. Reagent grade NaCl (Tomita Chemical Co., Inc., Tokushima) waR ignited on an evaporating dish for 1h and stored in a desiccator until use. The amounts of divalent cations in the NaCl were determined by atomic absorption spectroscopy, and the reagent was found to contain 1.5 ppm of Ca and 1.0 ppm of Mg. Water was glass-redistilled from alkaline KMn04. A stock solution of SDS was prepared volumetrically by dissolving a weighed amount of SDS solid into an NaCl solution, either at room temperature (25 f 2 "C) or 35 f 0.01 "C, depending on whether the NaCl concentration was less than 0.50 M or higher. After a day the stock solution was diluted by the same NaCl solutions to prepare the solutions for measurements. The SDS solutions in 0.60 and 0.80 M NaCl were kept at 35 f 0.01 "C for more than overnight before clarification for light-scattering measurements. Solutions aitid solvents for light scattering were filtered by a Sartorius membrane filter, SM 113, having a pore size of 10 nrn, in an air bath kept at 36 f 1 "C. The filtration was performed under pressure of about 2 atm, and the filtrate was directly poured into the light-scattering cell along its wall, About 10 cm3 of the filtrate was used to rinse the cell, and the remaining 40 cm3 of filtrate was filtered further three to four times, when it was dust-free. For filtration of concentrated SDS solutions, close to 2 X lom2g cmW3,in 0.80 M NaC1, however, it took about 3 h, and they were, therefore, filtered only once. Light Scattering. Light scattering was measured at 436 nm of a mercury lamp on a Shimadzu PG-21 light scattering photometer with a constant temperature bath and a small-slit system. A cylindrical cell was put in a temperature bath made of brass similar to that of Trementozzi,1° througlh which water of constant temperature was circulated from a Haake FS thermobath. The temperature of solution or solvent was monitored by a dipped ther-
The Journal of Physical Chemistry, Vol. 84, No. 7, 1980 745
mistor tip and maintained constant within f0.05 "C. The reduced intensity of light scattered in the angle 0 is calculated with eq 1,where Ioand IB are the intensities sin 0 10 1 cos2 6 of incident and scattered light, respectively, measured by the deflection of galvanometer and calibrated for the attenuation by neutral filters, and 4 is the calibration constant of the apparatus. The constant, 4,was determined by measuring the light scattered from purified benzene at 25 and 30 "C, using the values Rw = 48.5 X and 49.5 X lo4 cm-l a t the respective temperaturell and taking account of the refractive index of the solvent. The value of 4 was found to be common a t the two temperatures within 0.3%) and consequently it was assumed in the present work that the calibration constant is unchanged by temperature from 20 to 35 "C. Refractive Index Increment. The refractive index increment was measured on a Shimadzu DR-3 differential refractometer of Brice type with a photoelectric attachment. The apparatus was calibrated by aqueous solutions of NaCl at 25 "C. The temperature was regulated within fO.O1 "C by circulating water of constant temperature around an oil bath and putting the cell therein. At least four SDS solutions of the same NaCl concentration !were measured against an NaCl solution of the same concen~, measured tration. Thus the increment, ( a f i / a c ) ~actually was Afi/c at constant temperature and NaCl concentration. For solutions in 0-0.80 M NaCl a t 25 "C, it was found that
Rg =
+
(ace c,)= 0.121
lo
- O.O22C,
For solutions in 0.80 M NaCl at 35 "C, the increment was 0.103.
Results Figure 1shows the reduced intensity of light scattered by aqueous SDS solutions in the presence of dilute NaCl a t 25 "C. The dissymmetry of these solutions is 1.02 or less. Although the curves are concave downward at 0.01 and 0.10 M NaC1, the curve turns concave upward at 0.50 M NaC1. All of them give linear Debye plots, but the plot for 0.50 M NaCl has two sections having negative slopes, as shown in Figure 2. The Debye equation is given by (3) where the subscript or superscript, zero, refers to the cmc, K is the optical constant, M is the apparent micelle molecular weight, and B is the second virial coefficient. Values of the apparent molecular weight, M , and the apparent aggregation number, m' = M/288, of the micelle are given in Table I, together with those of the cmc, co, and the second virial coefficient, B. As can be seen in Figures 7 and 8, values of M are in harmony with those of Emerson and Holtzer12and of Kuriyama,13but they are somewhat higher than those of the o t h e r ~ . ~ J Recently '>~~ Corti and DegiorgiolGgave a value of M in 0.1 M NaCl in agreement with ours. The Debye equation does not take account of the effect of micelle charge on light scattering, and the micelle molecular weight given by M is apparent in this respect. The necessary correction for the charge effect can be made by applying the equation of Prins-Hermans-Princen-Mysels17Jsto obtain the micelle molecular weight, but the results are valid only for an ideal charged micelle without
746
The Journal of Physical Chemistry, Vol. 84, No. 7, 1980
Hayashi and Ikeda
TABLE I: Micelle Characteristics of SDS in Low NaCl Solutions at 25 "C C.. M
c,. g cm-3
0.01 0.10 0.50
0.15 X lo-' 0.042 X lo-' 0.013 X
10
M 20 200 27800
m' 70 97
42600
148
B, cm3 g-l 5.89 x 10-3 0.65 x 10-3 -0.085 X
____--
M, 22 100 29100
m 76.7 101
P
P/m
12.7 15.1
0.17 0.15
4
1.10 1.05
-
98 -
7-
-I
6 -
E
u
In
5 -
I
0 r
-
4 -
0
m
3 1.6
I
0
I
,
0.2
0.4
c
I
I
1
1
1
0.6 0.8 1.0 (10-2 g c m - 3 )
Figure 1. Reduced intensity, Reo,of SDS solutions at 25 "C and at the following NaCl concentrations: 0.01, ( 0 )0.10, and (0)0.50
(0)
0
c
M.
mutual equilibrium between monomers and micelles. Values of the micelle molecular weight, M,, the aggregation number, m = Mm/288, and the micelle charge, p , obtained by this theory are also given in Table I. In more concentrated (20.5 M) NaCl solutions, SDS tends to cease to be soluble at 25 "C. The temperature of solubility limit was termed the critical micelle temperature,l which was determined as the midpoint of the temperature range of dissolution of SDS when solid SDS was shaken and warmed with aqueous NaCl solution. The temperature is reported to be 24.7 "C in 0.50 M NaCl and 25.4 "C in 0.60 M NaC1, as shown in Figure 3, and it is almost independent of SDS concentration. In our experiments aqueous solutions of SDS were filtered at 36 f 1 "C and brought to temperatures for light-scattering measurement successively by cooling, each time after a series of measurements. We could keep the solutions clear down to a temperature several degrees lower than the critrical micelle temperature. Mazer and his co-workers1B6 measured light scattering of solutions even at 18 "C in 0.6 M NaC1. Undoubtedly these solutions must have been in supercooled states, as they also noted. Such solutions are suspected to contain crystallites portending imminent pre~ipitation.~,~ Figure 2 shows reduced intensity, RW,and dissymmetry, .z4 = R4/R13S, of SDS solutions in 0.60 M NaCl at different temperatures. While the reduced intensity, RgO,smoothly
0.4
0.8 (
10-2
1.2 1.6 g cm-3 )
2.0
Figure 2. Reduced intensity, R,, and dissymmetry, q5, of SDS solutions in 0.60 M NaCl and at the following temperatures: ( 0 )23, (0) 25, ( 0 ) 27, and 30 OC.
(0)
increases with increasing concentration, high dissymmetry values are exhibited by solutions containing moderate amounts of micelles at temperatures lower than 30 "C. The dissymmetry is about 1.02 or less a t 30 "C. Similar behavior of dissymmetry was observed for the solutions in 0.50 M NaCl at temperatures lower than 25 "C. High and anomalous dissymmetry was also associated with SDS solutions in 0.80 M NaCl when the temperature was lower than 35 "C. However, even at 35 "C the SDS solutions in 0.80 M NaCl showed dissymmetry around 1.1,but this was found to be normal from the measurements of angular dependence of light scattering, as shown later. The high anomalous dissymmetry can be distinguished from the normal dissymmetry by observing angular dependence of scattered light, and it is seen that the anomaly comes mainly from strong scattering a t low angles. This will be discussed in more detail in the Discussion section. In those solutions containing moderate amounts of micelles and showing high anomalous dissymmetry, the dissymmetry value increased with time even after the solution reached the temperature of light-scattering measurement. Nevertheless, it attained a steady value within a few hours, which remained constant during the period of measurement for about 3 h. In contrast, the reduced
Micelle Size and Shape of Sodium Dodecyl Sulfate
The Journal of Physical Chemistry, Vol. 84, No. 7, 1980 747
TABLE 11: Micelle Characteristics of SDS in Concentrated NaCl Solutions ~~
~~
a t cmcap
~
a t maximumC I____
C,, hul ---
m'
M
c,, g cm-?
temp, "C
M
m'
____I
0.501
25 30 25 30 25 30 35
0.60
0.80
0.013 0.014 0.012 0.013 0.011 0.012 0.013
a Equation 3, or eq 5 and 4 with B tions 5 and 4 with B = 0. I
I
~2
X X
lo-'
lo-'
x X
x x
low2
3 48 136 (1 74) (151)
152 000 111000 470 000 352 000 262 000
X
528 385 1630 1220 909 Equa-
Values in parentheses obtained by smooth extrapolation to the cmc.
0.
I
42 600 39 300 (50 OOQ) (43 500)
I
-
Y)
I0
0
. d
2 IB
Y
I 0
I
I
I
I
I
0.2
0.4
0.6
0.8
1.0
(c-co)
(
1 0 - 2 g cm-3
h
*
O "
Flgure 4. Debye lots for SDS solutlons In 0.50 M NaCl at the following temperatures: 25 and (a)30 OC.
(6)
24
d E
c
20
I "
0
0.2
0.4
0.6
0.8
Figure 3. Relaticins of temperature for anomalous dissymmetry and critical micelle temperature with NaCl concentration. Ovals indicate points where light scattering was measured. Values circumscribed are the largest values of dissymmetry, and values underneath are the SDS concentrations (X lo-' g cm3) where they were observed: (-) threshold curve for normal and anomalous dissymmetries, (- -) critical micelle temperature defined by Mazer et al.,' and its extension. (-.a)
intensity, RN,did not show such a perceptible change with time. In view of its normal behavior with respect to SDS concentration and temperature, as seen in Figure 2, the value of RgOitself would be free from the anomaly and could be considered to reflect the micelle characteristics. The anomalous dissymmetry decreases as the SDS concentration increases beyond some value, and it becomes difficult to distinguish the anomalous behavior from the normal one, foir example, in 2 X g cm-3 SDS solution in 0.60 M N a C l at 25 "C, which Mazer and his co-workers' investigated in detail. Figure 3 shows the relations of the temperature of anomalous disaiymmetry and the critical micelle temperature with NaCl concentration. The threshold curve between normal and anomalous behavior can be drawn rather clearly, and it is seen to differ from the curve for solubility limit. The anomalous behavior appears even a t temperatures higher than the critical micelle temperature.
Nevertheless, we could keep the SDS solutions free from precipitation even at temperatures several degrees lower than the critical micelle temperature. That is, the SDS solution can be readily supercooled and retained in the metastable state for a sufficiently long time, even in the presence of concentrated NaC1. Figure 4 shows the Debye plots of SDS solutions in 0.50 M NaCl at 25 and 30 "C, for which the dissymmetry is less than 1.02. The micelles formed at the cmc gradually associate into larger micelles with increasing micelle concentration. Table 11gives values of the apparent molecular weight, M , of the micelle at the cmc as well as those of the cmc. Each Debye plot consists of two linear ~ e c t i o nand , ~ the break cannot be eliminated by choosing any other cmc value. Consequently, we may infer that the micelle growth is further promoted by the increase in micelle concentration above a certain yalue. Such an observation can be compared with the results of two groups of workers on SDS solutions of almost equal NaCl concentration: Mysels and Princen,14who worked a t low SDS concentrations, 0-0.5 X g ~ m - found ~ , a weakly positive slope, B = 0.15 X cm3 g-l, whereas Emerson and HoltzerI2 reported a negative slope, B = -0.56 X cm3 g-l, a t the concentration range (0.4--1.2) X g cm-3. Figure 5 shows the Debye plots of SDS solutions in 0.60 and 0.80 M NaC1, for the scattering at 90a direction. In 0.60 M NaCl the solutions showed anomaly in dissymmetry at temperatures lower than 30 "C, and in 0.80 M NaCl the solution was normal only at 35 "6. However, even with the solution showing high anomalous dissymmetry, the value of reduced intensity at 90" angle, RgO,can be regarded as free from the anomaly and would stand for the micelle characteristics if the internal interference could be corrected. Then the Debye plots suggest that the micelles formed at the cmc sharply associate into large micelles with increasing micelle concentration. The observed micelle
748
The Journal of Physical Chemistry, Vol. 84, No. 7, 1980
2.5
I
I
I
Hayashi and Ikeda
c-co
I
i 1 0 - 3 g cm-3)
1.7 0
3.53
I
0
0.5 (
c -cg)
I
I
I
1.0
1.5
2.0
(
5.36
1 0 - 2 g cm-3
18.2 11.0
Flgure 5. Debye plots for SDS solutions in 0.60 and 0.80 M NaCI. Light scattering at 90" direction. Upper: 0.60 M; 25 OC, ((3) 30 'C. Lower: 0.80 M; 25 "C, (a)30 'C, (0) 35 'C.
(0)
(0)
growth and the formation of large micelles in concentrated NaCl are in agreement with those found by other workerdJ6 in 0.6 M NaCl. The small micelle has a molecular weight of 2000030 000, whereas the large micelle has a much larger size characteristic of NaCl concentration, and it grows very sensitively with increasing NaCl concentration. Since the reduced intensity at 90' direction, Rw, would not be influenced by the anomaly in dissymmetry, we assume that an approximate molecular weight of micelle is given by the value of M defined by eq 4,even when the
M = MwP(90) (4) dissymmetry is anomalous. Here M , is the micelle molecular weight, P(90) is the value of particle scattering factor at 90°, and the intermolecular interaction is assumed to be negligible, Le., B = 0. Table I1 gives values of M at the cmc and the largest value of M at n finite micelle concentration in 0.60 and 0.80 M NaC1. The value of M in eq 4 for concentrated NaCl solutions will be employed together with that of M in eq 3 for low NaCl solutions in the Discussion section, although the former is subject to optical interferences. The correct values of various micelle parameters can be estimated by extrapolating the Debye plots to zero scattering angle, unless angular dissymmetry is anomalous. In such cases the light-scattering equation is given by
Here the particle scattering factor, P(@,is expanded in the form
where X is the wavelength of light (436 nm), Ro the refractive index of solvent, and RG the radius of gyration of micelle. If the micelles are polydisperse, M , is their weight-average molecular weight and RG is their somehigher-order-average radius of gyration.
3
0
0.2
0.4
0.6
0.8
1.0
sin24 L
Flgure 6. Angular dependence of light scattering from SDS solutions in 0.80 M NaCl at 35 'C.
Since the size of a large micelle is defined by the NaCl concentration, as can be seen from the curves in Figure 5 leveling off at high SDS concentrations, it is presumed that the SDS solution contains, at least, two kinds of micelle, i.e., the small spherical micelle formed at the cmc and the large micelle, and that the latter fraction increases with increasing SDS concentration. Thus the largest value of M cited in Table I1 can be taken as the apparent molecular weight of the large micelle. Figure 6 shows angular dependence of light scattering from SDS solutions in 0.80 M NaCl at 35 "C. The intercept of the curve gives the reciprocal of the weight-average molecular weight, M,, of the micelle at a given micelle concentration when B = 0 is assumed. Although the micelle formed at the cmc would have a molecular weight of about 50000, the apparent micelle molecular weight at 1.10 X IOv2g amounts to 284000, which cannot be accommodated to a spherical micelle. The angular dependence of light scattering shows the difference in micelle size clearly, the limiting slope being zero at low micelle concentrations but finite at high micelle concentrations. The finite slope can be assigned to the large micelle, and the contribution of the small micelle to the slope would be negligible. The slope gives the radius of gyration, 172 A, at 1.10 X g ~ m - ~This . corresponds to the length of a rigid rod, L = 597 A, which can be fit well to the apparent micelle molecular weight, 284000, or the apparent micelle aggregation number, 986. Apart from the possible dynamic character of the rodlike micelle, as in the case of spherical micelles,lg we may derive a more exact structure of the rodlike micelle, assuming a rigid rod. In order to derive the exact value of the mo-
Micelle Size arid Shape of Sodium Dodecyl Sulfate
The Journal of Physical Chemistry, Vol. 84, No. 7, 1980 749
lecular weiglht of the rodlike micelle, we have to take account of the contribution of the second virial coefficient, B, in a manner proposed by Prins and H e r m a n ~ and l~~~~ adapted by Pvhkerjee22for the multiple-step micellization. Since the NaC1 concentration concerned is high enough to suppress the electrostatic effect between charged micelles, it is assumed that the second virial coefficient comes from the excluded volume effect alone. For a solution of rigid spheroicylindrical particles it is given by 4NA v m n B=------f (7) MW2 where N A is Avogadro's number, V,, the volume of the spherocylincler, and f its shape factor f = l t
P
Br(4r 1 Z
t1
)
r being the radius of the cylindrical part, and 1 its length.23 The length of the spherocylinder is equal to L = 1 t 2r, when applied to the rodlike micelle. Assuming r = 20.5 A, using L = 597 A, and solving eq 5 for B = 0, we obtain the micelle rr~olecularweight, M, = 405 000, or the micelle aggregation number, mn = Mw/288 = 1410. The second virial coefficient is then calculated to be 0.48 X cm3 g-l from eq 7 and 8. Theee results lead to the molecular pitch of the rodlike SDS micelle, Limn = 0.42 A. Assuming the crms-sectional diameter of SDS molecule to be 6.7 A, the micelle should contain about 16 molecules in its cross section, and thus the rodlike micelle of SDS in 0.80 M NaCl at 35 "C consists of a stack of 88 such disklike layers.
Discussion We have shown that the rodlike micelles are formed in SDS solutions at concentrations well above the cmc if the NaCl concentxation is high, whereas the spherical micelles are stable in dilute NaCl solutions. The transition of micelle shape from sphere to rod is induced by a change in NaCl concentration when the micelle concentration is finite. Figure 7 shows the relation of the logarithm of apparent micelle molecular weight, M , with the logarithm of ionic strength, Co t C,, where Co is the cmc in molar unit. It includes data of M at different temperatures for high NaCl concentrations. Figure 7 indicates different logarithmic relations for spherical and rodlike micelles. At 25 "C two linear relations intersect at the point of 0.45 M NaC1, and M = 33 100 or m' = 115. The linear relations can be represented by eq 9a and 9b. Below 0.45 M the log M := 0.118 log (C, t C,) + 4.54 C, I 0.45 (9a) log M
E-
4.68 log (C,
+ C,) t 6.15
C, 1 0.45
(9b)
micelle size can be fit to the spherical or globular micelle, whereas above 0.45 M it has to be assigned the rodlike shape, as can be imagined from the results derived in 0.80 M NaCl a t 35 "C. It is seen that the data of Emerson and Holtzer12 also fit eq 9a. In a previous paper20we have shown that similar logarithmic relations of apparent micelle molecular weight with ionic strength hold for a series of some cationic surfactants in NaCl solutions. If one compares the coefficients of eq 9, 0.118 and 4.68, with those for dodecyldimethylammonium chloride, 0.105 ahd 2.64, it is seen that rodlike micelles of SDS increase their size about 1.8 times more sharply than those of dodecyldimethylammonium chloride as the ionic strength is increased. This would be caused by different degrees of counterion binding on rodlike
-2
-1
-1.5
-0.5
0
log( C O * C S ) Flgure 7. Logarithmic relation of apparent micelle molecular weight with ionic strength: and -) 25 O C ; (A) 30 O C ; (e)35 "C;(0)data of Emerson and Holtzer.'*
(0
micelles between the two surfactants. Such a difference could be revealed in their solubility behavior a t 25 "C: SDS is soluble only in low NaCl solutions, but dodecyldimethylammonium chloride dissolves in NaCl solut,ions concentrated as high as 4.00 M. From the above results it can be presumed that the micelle formation of SDS in concentrated NaCl solutions occurs in two steps when the SDS concentration irJ increased. The steps can be represented by eq 10a and lob, mD nD,
G
D,
(loa)
G
D,,
(Lob)
where D is the monomer, D, the spherical micelle, and D, the rodlike micelle. The molecular weights of spherical and rodlike micelles are determined by NaCl concentrakion and temperature, and the molecular weight derived from light scattering at an SDS concentration represents the weight-average molecular weight of the two kinds of micelle, as was already noted above. Next we will see the effect of temperature on micelle size of SDS. Figure 8 shows the relation of apparent micelle molecular weight with temperature a t different NaC1 concentrations. The value of micelle molecular weight in 0.10 M NaCl is consistent with that of Kuriyamaf3 and of Corti and Digiorgio.16 Generally, the micelle size decreases with the rise of temperature. This trend is in accord with that found for ionic s u r f a c t a n t ~ and ~ ~ is J ~in~contrast ~~~~~ with that for nonionic surfactant^.^^,^^^^ It is noticed that the rodlike micelle formed a t high NaCl concentrations decreases its size about 5 times more sharply than the spherical micelle as the temperature is raised. Finally we will discuss the nature of anomalous dissymmetry of light scattering. Figure 9 illustrates the angular dependence of scattered light for SDS solutions in 0.60 M NaCl at 25 "C, for which anomalous dissymmetry is observed a t low micelle concentrations. Just above the cmc, where the dissymmetry is the largest, the curvature of the scattering curve is very large and concave downward at low
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The Journal of Physical Chemistry, Vol. 84, No. 7, 1980
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Figure 8. Relatl,on of logarithm of apparent micelle molecular weight with temperature at different NaCl concentratlons: (0) 0.01, ( 0 )0.10, (a)0.50, 0.60, and ( 0 )0.80 MI (A)data of Kuriyama13 at 0.10 M,
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Flgure 3. Angular dependence of light scattering from SDS solutions in 0.60 M NaCl at 25 O C and at the following SDS concentrations (XlO-' g ~ r n - ~ ) : 0.19, ( 0 )0.40, (0) 0.60, (131) 1.01, and (A) 2.01.
(0)
Hayashl and Ikeda
aqueous solution^,^^-^^ and such behavior has been attributed to the presence of trace amounts of microgel Furthermore, anomalous angular dependence of light scattering has often been observed during the course of either association or dissociation of polymers after dissolved in s o l ~ t i o n . " ~ ~Linear ~ ~ ~ ' polymers themselves cannot form microgels but associate into crystalline bundles of linear chain^.^^"^ However, cross-linking between linear or branched polymers would lead to such microgel particles consisting of polymer network and occluded solvent. Although SDS is soluble in 0.60 and 0.80 M NaCl and the solutions are stable at 35 "C, lowering of temperature induces the association of spherical micelles. Before transforming into rodlike micelles, however, some of the spherical micelles associate into other types of aggregates, Le., microgels, which would be metastable. The presence of such a bypass could be facilitated by the following two facts: (1)SDS has a high Krafft point and high critical micelle temperatures, so that its micelle is unstable in concentrated NaCl solution, and (2) an SDS molecule has a large polar head group, so that it can accommodate to a spherical micelle more favorably.20 Thus the spherical micelles would tend to link with one another to form microgel particles, possibly by some interaction of their charged groups through cations. However, the amount of microgel particles is so small that the reduced intensity, RBO,may not be influenced by their presence.3g It is known that the reduced intensity as well as the dissymmetry of the solutions of impure SDS containing 0.1% dodecanol shows large increases just below the cmc,21~40~41 However, in the present SDS sample no dodecanol was detected, but the anomaly was observed for dissymmetry only. Furthermore, the anomalous dissymmetry occurred only when the micelles were present and also when the NaCl concentration was higher than 0.45 M at 25 "C. These are not necessarily amenable to the suspected contamination of SDS with dodecanol either. Some amounts of higher alkyl homologues in the SDS sample cannot be responsible for the anomalous dissymmetry, since it disappeared at higher temperatures or a t lower NaCl concentrations. It seems more likely that some contaminant divalent cations in NaCl link the negatively charged spherical micelles to form a network. Such effects can be readily reduced by increasing SDS concentration or raising temperature, in accord with the observed results. The results of trace analysis of metals in the NaCl used revealed contamination of only trace amounts of various divalent metals, but it is also likely that trace amounts of contaminant cations are sufficient to link small amounts of spherical micelles present around tho crnc to form microgel particles. The effect of such trace amounts of contaminant could be made negligible or eliminated by the conversion into rodlike micelles when the SDS concentration increases. Acknowledgment. We thank Kenji Okahashi of the Kao Soap Co., Inc., for gas chromatographic analyses of the SDS sample.
angles. With increasing concentration, the curvature beReferences and Notes comes less distinct and the scattering becomes normal. (1) N. A. Mazer, G. B. Benedek, and M. C . Carey, J . Pbys. Cbem., 80, 1075 (1976). We may then ascribe the observed anomalous dissym(2) D. Stlgter, R. J. Williams, and K. J. Mysels, J. Pbys. Cbem., 59, 330 metry to the strong reduced intensity at low angles. The (1955). curvature downward at high angles may be, at least, partly (3) L. M. Kushner and W. D. Hubbard, J . ColloidSci., 10, 428 (1955). (4) H. V. Tartar, J . Pbys. Cbem., 59, 1195 (1955). attributable to the Fresnel reflection of intense scattered (5) H. V. Tartar, J . Colloid Sci., 14, 115 (1959). light at low angles. This kind of large curvature of scat(6) C. Y. Young, P. J. Missel, N. A. Mazer, G. B, Benadek, and M. C. tering curve has been observed with solutions of many Carey, J . Pbys. Cberni., 82, 1375 (1978). polymeric substances, either in organic ~ o l v e n t s or ~ ~in- ~ ~ (7) P. Debye and E. W. Anacker, J. phys. CollOM. Chem.,55, 644 (1951).
J. PhyS. Chem. 1980, 84,751-756 (8) E. W. Anacker and H. M. Ghose, J . Am. Chem. Soc., 90, 3161
(1968). (9) C.Tanford, J. Phys. Chem., 78, 2469 (1974). (10) Q. A. Trementozzi, J . Polym. Sci., 23,887 (1957). (11) C. I. Carr, Jr., and B. H. Zimm, J. Chem. Phys., 18, 1616 (1950). (12) M. Emerson and A. Holtzer, J . Phys. Chem., 71, 1898 (1967). (13) K. Kuriyama, Kolloid Z. Z. Polym., 180, 55 (1962). (14) K. J. Mysels and L. H.Princen, J . Phys. Chern., 63, 1696 (1959). (15) H. F. Huisman, Proc. K . Ned. Akad. Wet., Ser. B, 67, 388 (1964). (16) M. Corti and V. Degiorgio, Chem. Phys. Left., 53, 237 (1978);Ann. Phys. (Pnrls), 3, 303 (1978). (17)W. Prlns and J. J. Hermans, Proc, K . Ned. Akad. Wet., Ser. B , 59, 162 (1956). (18) L. H. Princen and K. J. Mysels, J. Colloid Scl., 12, 594 (1957). (19) G. E. A. Aniansson, J . Phys. Chem., 82, 2805 (1978). (20) S Ikeda, S.Ozeki, and M. Tsunoda, J . Colloid Interface Sci., 73, 27 (198OJ1. (21) W. Prinssind J. J. Hermans, Proc. K . Ned. Akad. Wet. Ser. B, 59, 298 (1956). (22) P. Mukerjoe, J . Phys. Chem., 76, 565 (1972). (23) T. Klhara, J . Phys. Soc. Jpn., 8, 289 (1951).
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(24) P. Debye, Ann. N.Y. Acad. Scl., 51, 575 (1949). (25) K. W. Herrmann, J . Phys. Chem., 68, 1540 (1964). (26)T. Nakagawa, H. Inoue, K. Torl, and K. Kuriyama, J , Chem. Soc. Jpn., Pure Chem. Sect., 79, 1194 (1958). (27) C. W. Dwiggins, Jr., and R. J. Bolen, J. Phys. Chem., 65, 1787 (1961). (28) R. R. Balmbra, J. S. Clunie, J. M. Corkill, and J. F. Goodman, Trans. Faraday Soc., 60,979 (1964). (29) P. H. Elworthy and C. B. MacFarlane, J. Chem. Soc., 907 (1963). (30) P. H. Elworthy and C. MacDonald, KolbklZ. Z. Polym., 195, 16 (1964). (31) D. Attwood, J. Phys. Chem., 72, 339 (1968). (32) K. W. Herrmann, J . Phys. Chem., 66, 595 (1962). (33) L. D. Moore, J . Polym. Scl,, 20, 137 (1956). (34)L. H. Peebles, Jr., J . Am. Chem. Soc,, 80, 5603 (1958). (35) N. Eliezer and A. Silberberg, Biopolymers, 5, 95 (1967). (36) D. W. Tanner and G. C. Berry, J . Polym. Scl., 12, 941 (1974). (37) T. Matsuo and H. Inagaki, Makromol. Chem., 53, 130 (1962). (38) K. Walenfels, H. Sund, and W. Burchard, Biochem. Z., 335, 315
(1962). (39) P. Kratochvil, Collect. Czech. Chem. Commun., 30, 1 1 19 ('1985). (40) J. N. Phillips and K. J. Mysels, J . Phys. Chem., 59, 325 ('1955). (41) L. H. Princen and K. J. Mysels, J . Phys. Chern., 63, 1781 ('1959).
Electronic Structure of a Porphyrin Solid Film and Energy Transfer at the Interface with a Metal Substrate K, Tanlmura, T. Kawal, and T. Sakata" Instltute for Molecular Science, MyodaJi, Okazakl444, Japan (Recelved February 5, 1979; Revised Manuscrlpt Recelved August 6, 1979) Publlcatlon costs asslsted by the Institute for Molecular Sclence
The electronic structure and the interaction with a metal substrate of amorphous solid films of free base tetraphenylporphine (H,TPP) and its Zn derivative (ZnTPP) have been studied. The visible absorption spectra resemble those of solutions, although the Soret band is greatly weakened and broadened in the film.The lifetime of the SI state in an amorphous HzTPP film is less than 2 ne and is much shorter than that of solutions. This quenching is attributed to enhancement of the nonradiative decay rate in the solid phase. The typical effect of the metal substrate on the film is a strong quenching both of sensitized chlorin emission in ZnTPP and of fluorescence in H2TPP. Forster type energy transfer to the metal substrate explains most of the quenching, but an additional long-range effect in the H2TPP film is attributed to exciton diffusion within the film. The metal-dye system is discussed in terms of a device for solar-energy conversion.
Introduction Special attention has recently been attracted, because of interest in solar-energy conversion mechanisms, to the interesting phenomena exhibited by organic dyes at their interface with other materials. A solid thin film of dye in contact with mlids (metal, semiconductor, and insulators) is one of the most common systems in which these interfacial phenomena have been ~ t u d i e d . l -Such ~ an organic film plays a central role in the conversion of light into other forms of energy through, in general, the following processes: capture of photons and the transfer of the excitation energy to the interfaces where carrier generation and/or chemical reactions mainly take place. Thus, clarification of excited-state behavior of dye film interfaces with other solids, liquids, and gases is crucial for elucidating the mechanisms of the various kinds of reactions concerned, and hence for developing a system with highconversion efficiency. Nevertheless, detailed properties of such excited states of dye films with interfaces are far from being well understood. In this paper, we study the electronic structure of the porphyrin film and its interaction with a metal substrate. The use of porphyrin (tetraphenylporphine and its metal derivatives in this study) as an organic dye gives us several advantages, since a great deal of data has already been 0022-3654/80/2084-0751$01 .OO/O
reported for porphyrin molecules in solutions as to their electronic structure, photochemical behavior, etcS8Properties of solid thin films of porphyrins are also interesting as simple analogues to the chlorophyll aggregates in photo~ynthesis.~J~
Experimental Section Tetraphenylporphine (H,TPP) of chlorin-free grade and the Zn derivative (ZnTPP) were obtained from Strem Chemicals, Inc. and were used after recrystallization three times from ethanol. Quartz plates polished to optical grade and platinum (99.9%) plates were used as substrates after cleaning their surfaces by an ultrasonic cleaner in tetrahydrofran. Films were prepared in vacuo (1 X lo4 torr) with a controlled deposition rate of 1 A/s. The thickness of the film was monitored and determined by a Sloan thickness meter (DTM 200). The optical absorption spectrum of the film deposited on quartz was measured by a Hitachi 556 spectrophotometer. The amount of porphyrin deposited was found to be the same for both substrates, which was confirmed by measuring the solution spectra of materials recovered from the film. Excitation of the porphyrins was made by means of a 100-W tungsten lamp with a grating monochromator (Nickon P-250). Exciting light intensity was calibrated @ 1980 American Chemical Society
