856
J. Phys. Chem. lQ83, 87, 856-862
of T R ( T ~ and ) ~ ~ (of 1Aerosol ) IB in water are summarized taking into consideration the idea that the radius of a in Table V. Aerosol IB is 8 A in length along its longer micelle in water is 75% of the length of the extended axis and about 6 A in diameter a t its widest point. Now m0lecule,3~then ~ ( 1can ) be calculated to be 2.64 X we can approximate the shape of Aerosol IB to be a prolate s, which agrees well with T R ( T ~2.53 ), X s. Although ellipsoid with semiaxes of 4 and 3 A. When a geometrical we have now no precise data by which to calculate an accurate association number for the 2nd-micelle of Aerosol average of the semiaxes mentioned above is adopted as an effective radius of the Aerosol IB molecule, then ~ ~ (of 1 ) IB, we can roughly estimate an association number of 8 the Aerosol IB molecules can be calculated at 0.44 X from the rotational correlation time. This value satisfies the demand of geometric consideration that the association s in fair agreement with T ~ ( T ’0.32 ), X s. The 1stnumber must be less than 10, for Aerosol IB has short and micelle, whose micellar shape can be approximated as bulky hydrocarbon chains and forms a spherical micelle oblate, and which has an association number of 2 or 3, can as mentioned above. be considered to have semiaxes of 4 and 4.2 or 5.2 A, so that the effective volume of the 1st-micelle is two or three Acknowledgment. The authors express their thanks to times that of an Aerosol IB molecules. T R ( ~can ) be calthe Administration Committee of the 220-MHz NMR culated to be 0.88 X 10-lo or 1.32 X s, respectively. System at Department of Hydrocarbon Chemistry of Then 7R(T1), 1.08 X s, lies between these two TR(~)s. Kyoto University for measurements of the spectra. The It is reasonable to conclude from this that the micellar authors are indebted to Professor Y. Kyogoku of Osaka shape is approximated as oblate and that its association University for helpful discussion. number is 2 or 3. If it may be postulated that the shape of the 2nd-micelle of Aerosol IB is spherical and if it may (33)C. Tanford, Proc. Nutl. Acad. Sci. U.S.A., 71,1811 (1974). also be postulated that the radius of the micelle is 6 A by
Micelle Clusters of Octylhydroxyollgo(oxyethylenes) M. Zulauf” and J. P. Rosenbusch European Molecular Siology Laboratory. Grenoble Outstation, F-38042 Grenoble-Cedex, France, and Biozentrum, University of Basel, Microbiology Department, CH-4056 Basel, Switzerland (Received: April 13, 1982; In Final Form: October 5, 1982)
Aqueous micellar solutions of two nonionic detergents, a-octylwhydroxytetrakis(oxyethy1ene) (C,E,) and a-octyl-whydroxypentakis(oxyethy1ene)(C8E6), have been investigated as a function of temperature by photon correlation spectroscopy, viscosimetry, small-angle neutron scattering, and neutron spin-echo spectroscopy. Increase of scattering intensities and hydrodynamic radii with temperature is a critical phenomenon extending over a wide temperature range and is not due to micellar growth. The spatial arrangement of small micelles in loose clouds, caused by attractive intermicellar interactions, accounts for all observations.
Aqueous solutions of nonionic detergents often exhibit a critical phenomenon of demixing. When the isotropic micellar phase is heated, a critical temperature, Td, is reached at which solutions become suddenly turbid (cloud point). T d ,which we define as the phase boundary, depends on detergent concentration. Its minimum value corresponds to the lower consolution point. After some time, turbid solutions clear up and are fully separated into two isotropic liquids, one of which contains most of the detergent. This reversible phenomenon has been observed with various nonionic ~urfactants.’-~The existence of the phenomenon implies the existence of a critical region where static and dynamic parameters, such as scattering intensities and fluctuation times, increase and diverge as T d is approached. This is analogous to the phenomena observed in binary liquid mixture^.^ It is a particular feature of (1)N. Chakhovskoy,Bull. Soc. Chim. Belg., 65,474-93 (1956);R. R. Balmbra, J. S. Clunie, J. M. Corkill, and J. F. Goodman, Trans. Faraday SOC.,58, 1661-7 (1962);57, 1627-36 (1961). (2)K.W. Herrmann, J. G. Brushmiller, and W. L. Courchene, J. Phys. Chem., 70,2902-18 (1964). (3)J. M.Corkill and K. W. Herrmann, J. Phys. Chem., 67,934-7 (1963). (4)H. L. Swinney in “Photon Correlation and Light Beating Spectroscopy”,H. Z. Cummins and E. R. Pike, Eds., Plenum Press, New York, 1974;B. Chu, J . Am. Chem. Soc., 86,3557-61 (1964).
0022-365418312087-0856$0 1.50lO
micellar solutions that critical regions are very broad. It can therefore be expected that the physical properties of micellar solutions, unlike ideal solutions, are determined not by the size and shape of micelles alone, but also by intermicellar interactions. Although phase diagrams of detergents were determined many years ag0,1-31596and investigators have emphasized the high degree of nonideality of these systems, this aspect was often neglected when apparent molecular weights and micelle sizes were interpreted as true micellar parameter~.’-’~ Correspondingly, the increase of solution scattering in the critical region was interpreted as micellar growth, a concept which has found theoretical ~ u p p o r t . ~ Although nuclear magnetic resonance has revealed rapid orientational relaxations at all temperature^,'^ this has (5)F.Tokiwa and K. Ohki, J.Phys. Chem., 71,1343-8 (1967). (6)J. N. Phillips and K. J. Mysels, J. Phys. Chem., 59,325-30 (1955). (7)P. Mukerjee, J.Phys. Chem., 76,565-70 (1972);R. J. Robson and E. A. Dennis, ibid., 81, 1075-8,1977. (8)C. Tanford, ‘The Hydrophic Effect”, 2nd ed., Wiley, New York, 1980. (9)J. N. Israelashwili, D. J. Mitchell, and B. W. Ninham, J. Chem. Soc., Faraday Trans. 2,72,1515 (1976). (10)H. Wennerstrom and B. Lindman, Phys. Rep., 52, 1-86 (1979). (11)H. H. Paradies, J . Phys. Chem., 84,599-607 (1980). (12)C. Tanford, J. Phys. Chem., 78,2469-79 (1974);C. Tanford, Y. Nozaki, and M. F.Rohde, ibid., 81,1555-60 (1977).
0 1983 American Chemical Society
Micelles of Octylhydroxyoligo(oxyethylenes)
The Journal of Physical Chemistry, Vol. 87, No. 5, 1983 857
TABLE I : Physical Properties of Octylhydroxyoligo(oxyethy1enes)'
L, A
neat constituent detergents octane moiety (C,H,,) oxy ethylenes E4 (O,C,Hl,) (06C10H21)
detergents CRE4 C"E5
M, 113.2
exptl
193.2 237.3 306.5 350.5
ref 1.26=
monomers micelles
0.843b 0.843b 0.983' 0.992'
0.991d 0.9842' 0.972d 0.9495'
1.005' 0.975'
V, A ~ O " ( C b ( x ) ) ,cm 236.7 - 1.0406
e 11.6h
f
g
267.4 328.4
1.8614 + 1.0413~ 14.0 2.2752 + 1.0413~ 17.5
11.0 14.0
7.5 9.5
504.1 565.2
0.8208 t 1.0413~ 25.6 1.2346 + 1.0413~ 29.1
22.6 25.6
19.0 21.1
Reference 34. Reference 18. ' Reference 16. Theoretically. e Zig-zag conformation. Helical conformation. Meander conformation. Zig-zag conformation does not apply. Symbols: M,, molecular weight;T, partial specific volume;16 V = M,V/NaV,solvent-excluding volume ( N , = Avogadro's number); 2 b ( x ) , neutron scattering length at heavy water percentage x = [D,O]/[H,O] ;I9 L , approximate chain length.23
been interpreted to demonstrate secondary aggregation of nevertheless large asymmetric micelles.a More recently, results from light scattering studies of micellar solutions of Triton X-100 and a-dodecyl-w-hydroxyhexakis(0xyethylene) near Tdhave been analyzed as critical phenomena by Corti and Degi0rgi0.l~ They concluded that the apparent large size of micelles is due to the size of the spatial range over which fluctuations of micelle concentrations are uniform. The predictions of the theory of critical phenomena apply strictly only to the asymptotic region near T d and are independent of micelle structures. A complementary approach was taken by Hayter and Penf01d.l~ In their neutron study of concentrated sodium dodecyl sulfate micelles, they investigated the effects of ionic strengths on phenomena related to detergent crystallization. Using models to describe the scattering due to micelle structure, as well as their electrostatic repulsion, they found that salts affect micelle interactions rather than their size. In this report, we present results of our studies concerning the properties of micelle solutions of a-octyl-whydroxytetrakis(oxyethy1ene) (C8E4) and a-octyl-whydroxypentakis(oxyethy1ene) (CaE5). They show that with increasing temperature the micelles of the nonionic surfactants do not grow to form large structures with single hydrocarbon cores, nor do they form linear aggregates by secondary association.aJ2 We demonstrate that micelles interact loosely with others to form spherical statistical clusters, as postulated by Corti and Degi0rgi0.l~Molecular weights and equivalent radii at small scattering vectors may be ascribed to these clusters. The sizes of the constituent micelles, obtained from dynamic neutron measurements at large scattering vectors, do not increase significantly with temperature.
Materials and Methods Detergents. Synthesis and properties of CaE4and CaE5 are described in detail elsewhere.16 The detergents used were pure as judged by elemental composition, thin-layer chromatography, infrared spectra, and tensiometry. The latter was performed according to Du Nouy and revealed clean intersections of slopes at the critical micelle con(13)E. J. Staples and G. J. T. Tiddy, J. Chem. SOC.,Faraday Trans. I , 74,2530-41 (1978). (14)M. Corti and V. Degiorgio, Opt. Commun., 14,358(1975);Phys. Rev. Lett., 45,1045 (1980);in "Solution Chemistry of Surfactants", Vol. 1, K. L. Mittal, Ed., Plenum Press, New York, 1979;"Light Scattering in Liquids and Macromolecular Solutions", V. Degiorgio, M. Corti, and M. Giglio, Eds., Plenum Press, New York, 1980. (15)J. B. Hayter and J. Penfold, J.Chem. SOC.,Faraday Trans. 1,77, 1851-63 (1981). (16)M.Grabo, Ph.D. Thesis, University of Basel, Baael, Switzerland, 1982.
centration (cmc). Detergents were monodisperse with respect to alkyl chain length as well as to their hydrophilic moieties. Neutron scattering properties of detergent monomers were calculated from known parameters and are shown in Table I. The match point (i.e., the D20/H20 ratio at which the forward neutron scattering vanishes) is calculated to be 10.8%, in agreement with contrast variation experiments of CaE, (results not shown). Photon Correlation Spectroscopy. Solutions were filled into sealed scattering cells (quartz cuvettes of 40 X 10 X (1 or 2) mm; Hellma) by filtration through Nucleopore filters (0.1 pm; Shandon). Cells were placed in a thermostated toluene bath. All experiments were performed at scattering angles of 31.3' (q = 8.8 X lo4 em-'; cf. below) except for control runs. These were performed at angles between 21° and 120' to determine whether apparent diffusion coefficients and scattering intensities depended on the angle of observation. No such dependence was found. Correlations were performed with a 96-channel digital correlator (Malvern, England), interfaced to a Hewlett-Packard 9825 calculator which allowed on-line data ana1y~is.l~ The measured second-order correlation function of the fluctuating scattered intensities, observed at scattering vectors q, was analyzed in terms of the diffusion of monodisperse scattering centers: g,(q,t) = ( h t ? I ( q , t ' + t ) ) / ( l ( q , t ? ) 2 = 1 + Bgi2(q,t)
gi(q,t) = exp(-Dappq2t)
(1)
In these expressions, B is an instrumental constant, q = (4irn/X) sin 0/2 is the modulus of the scattering vector, X is the wavelength of the laser (514.5 nm), n is the refractive index of the solution, and 0 is the scattering angle. Dapp is the apparent diffusion coefficient. All spectra could be fitted by single exponentials; values of Dappwere independent of data analysis, i.e., fit to an exponential by nonlinear regression, or moment analysis.2o D, is related to the apparent hydrodynamic radius Rh by
Rh = (1 - $)kT/(Gx~(T)Dapp)
(2)
(17)A.Tardieu, V.Luzatti, and F. C. RBman, J.Mol. Biol., 75,711-35 (1973). (18)G. R.Anderson, Ark. Kemi, 20, 513 (1963). (19)P. Jacrot, Rep. Prog. Phys. 39,911-53 (1976). (20)M. Zulaf and H. F. Eicke, J. Phys. Chem., 83,430-6(1979);J. C. Brown, P. N. Pusey, and R. Dietz, J. Chem. Phys., 62, 1136 (1975). (21)G. D. J. Phillies, J. Chem. Phys., 60, 976 (1974). (22)Landolt-Bornstein, Vol. 11, 5A, Springer-Verlag, West Berlin, 1969;P. Pascal, "Nouveau Trait6 de Chimie Mincrale", Masson et Cie, Paris, 1956. (23)P. J. Flory, 'Statistical Mechanics of Chain Molecules", Wiley, New York, 1969.
858
The Journal of Physical Chemisfry, Vol. 87, No. 5, 1983
I
Zulauf and Rosenbusch
I
1
C 200
+- 401
I
\
I
/-
"
"
'
I
T
('0
I
II
i ,
I
I
01 1 10 [C, E,] 1% V/VI Figure 1. Phase diagram of C8E, in H,O at atmospheric pressure. Critical concentrations of micelllzation (cmc; squares) depend slightly on temperature (0.15% (4.3 mM) at 25 OC to 0.11% (3.0 mM) at 70 OC). Critical temperatures of demixing (T,; spheres) depend strongly on total detergent concentration. At concentrations smaller than the cmc, the detergent exists in a monomeric state (state I). Above the cmc, detergent monomers coexist wlth colloidal particles known as micelles, wlth monomer concentrations near the cmc (state 11). I n state 111, two phases coexist. The aqueous phase contains small amounts of detergent (slightly above the cmc), while most of the surfactant resides in the other phase.
where Tis the temperature (Kelvin),and q ( T ) the viscosity of the solvent as a function of temperature. 4 is the volume fraction of the particles in the solution. The excluded volume correction (1 - 6)is significant in concentrated solutions.21 Water viscosities were calculated for various temperatures by the interpolation vH2o(T)= 3.271
+ 14.261 exp(4.03697T)
(3)
Figure 2. Apparent hydrodynamic radii ( R h )as a function of temperature were obtained from photon correlation spectroscopy of aqueous micellar solutions of C8E, (open symbols) and C8E, (closed symbols). Triangles Indicate 30 % v/v solutions, circles 10% , squares 1% , and diamonds 0.4%. I n all cases, the correlation spectra were single exponentials. The ratio of the maximum delay time (t,) of the correlator to the observed correlation time (t,) could be varied over a broad range without affecting R h (0.5 < t,,/f, < 3).
Viscosimetry. Ubbelohde capillary viscosimeters were immersed in a thermostated bath (100 L) and connected to a MGW Lauda viscosimeter (Schott). Thermostating assured temperature stabilities to within 0.05 "C. Samples were carefully filtered before injection into the viscosimeter. If bubbles formed in the viscosimeter bulb, experiments were discontinued. Intrinsic viscosities were calculated from the viscosities of the sample and buffer according to
Here, T i s in degrees Celsius and the viscosity ( q ) is given (4) [a] = (%/?B - l ) / c in millipoise. The viscosity of DzOwas calculated from where c is the concentration in g/cm3. No extrapolation these values by using an interpolation of various published to zero concentration was made. values of the temperature-dependent ratio qD,o/qH,~.22 Small-Angle and Quasi-elastic Neutron Scattering. Results Small-angle scattering of C8E4was performed with the camera D11 at the Institute Laue-Langevin in G r e n ~ b l e , ~ ~ Phase Diagram. Figure 1 shows the phase diagram of using neutrons with X = 7.0 A,and a sample-to-detector C8E5 in H20 for concentrations below 30% v/v. It is distance of 9.77 m. The data obtained were converted to characterized by two phase boundaries: the critical conabsolute intensities, I(Q), with Q = (4a/X) sin 9/2, after centration of micellization (cmc) determined by tensiomcorrections for absorption, background, solvent scattering, etry (cf, ref 16), and the critical temperature above which and detector efficiency, according to standard procedures.25 a single isotropic micellar phase separates into two imTemperature control was achieved by circulating water miscible, isotropic phases. This reversible temperaturefrom a thermostated bath through the brass frame of the dependent phase separation is preceded by critical sample changer; the stability is estimated to be within 0.5 opalescence (clouding) which appears abruptly, and allows OC. Quasi-elastic neutron scattering measurements were rapid determination of Td. The minimal Tdof 60.6 "C was performed on solutions of C8E5,using the neutron spinobtained at a detergent concentration of about 7% v/v. echo spectrometer IN11 at the Institute Laue-Langevin. The two immiscible phases above T d appear after several The incident wavelength was 8.3 A. This instrument also hours of equilibration. At high temperatures, the boundary provides static scattering data. Corrections were made for of the micellar phase and the cmc converge. Indeed, phase solvent scattering only, since a single detector is moved separation has never been observed below the cmc. to obtain 1(Q). Sample temperatures were controlled to The corresponding phase diagram of C8E4 in H 2 0 is within 0.2 OC by electrical heating of the sample holder. essentially analogous to that shown in Figure 1 (cf. ref 16), Data analyses were performed with standard programs.26 except that the micellar phase boundary is shifted significantly to lower temperatures (minimum at 40.4 "C at (24) K. Ibel, J. Appl. Crystallogr., 9, 630 (1976). (25) R. E. Ghosh, "A Computing Guide for Small-angle Scattering", ILL Report 78GH247T, Grenoble, 1978. (26) M. E. Erskine and J. B. Hayter, "System User's Guide to the IN77 Spin-echo Spectrometer", ILL Report 80ER44T, Grenoble, 1980. (27) See, e.g.: Z. H. Cummins and E. R. Pike, Eds., "Photon Correlation and Light Beating Spectroscopy",Plenum Press, New York, 1973; 'Photon Correlation Spectroscopy and Velocimetry", Plenum Press, New York, 1977; B. Chu, "Laser Light Scattering",Academic Press, New York, 1974; B. J. Beme and R. Pecora, "DynamicLight Scattering",Wiley, New York, 1976. (28) K. Kuriyama,Kolloid-Z., 180,55 (1962);A. Goto, R. Sakura, and F . Endo, J . Colloid Interface Sci., 67, 491 (1978). (29) F. Perrin, J. Phys. Radium, 5, 497 (1934); 7, 1 (1936); S . H. Koenig, Biopolymers, 14, 2421-3 (1975). (30) C. Tanford, 'Physical Chemistry of Macromolecules",Wiley, New York, 1961.
(31) C. W. Pyun and M. Fixman, J.Chem. Phys., 41,937-44 (1964). (32) G. K. Batchelor, J.Fluid Mech., 52, 245 (1972); B. U. Felderhof, J. Phys. A: Math. Gen., 11, 929 (1978). (33) P. Debye and A. M. Bueche, J. Chem. Phys., 18,1423-5 (1950). (34) F. Reiss-Husson and V. Luzzati, J . Phys. Chem., 68, 3504-11 (1964). (35) A. Guinier and G. Fournet. "Small Angle Scattering- of X-rays". Wiley, New York, 1955. (36) F. Mezei, Z. Phys., 255, 146 (1972);J. B. Hayter and J . Penfold, 2. Phvs. E , 36, 199 (1979): J. B. Havter in "Neutron Diffraction", H. Dachi, Ed.; Springer:Verl& West Berlin, 1978; in 'Proceedings ofthe International Workshop on Neutron Spin-Echo",F. Mezei, Ed., Vol. 128. Springer Lecture Note Series, Springer-Verlag, West Berlin, 1980. (37) D. E. Koppel, J . Chem. Phys., 57,4814-20 (1972). (38) D. Stigter, J . Phys. Chem., 70, 1323 (1966).
Micelles of Octylhydroxyoligo(oxyethy1enes)
40
60
The Journal of Physical Chemistry, VOI. 87, No.
80
I d ,
,
10 Flgure 3. Relatiie scattered intensities (I,) vs. hydrodynamic radii (Rh) for 10% C8E4in H,O. Photon count rates, obtained from light scattering, are given by closed symbols: those obtained by scaling extrapolated neutron intensities at zero scattering angle are shown by open symbols. The hatched and dotted areas represent values of the scattered intensities expected for prolate and oblate ellipsoids of revolution, respectively. Calculations were according to Perrln," assuming Semiminor axes of 13 and 25 A. These values were fixed to account for the limitations imposed by the geometry of monomers, assuming the polar oxyethylene moieties to exist in either contracted (13 A) or extended (25 A) c o n f i g u r a t i ~ n . ~Two - ~ ~axial ratios (3:lat point A, and 11: 1 at point B) are indicated by arrows. The line, drawn through the experimental points, appears to reflect prolate ellipsoids of revolutions with semiminor axes near 23 A.
7% v/v; the phase diagram is shown in ref 39). The cmc depends more markedly on temperature (it decreases from 0.38% at 6 "C to 0.11%at 60 "C). Similar phase diagrams have been observed for various surfactants.'pZ@ We have found that the values of Td are strongly affected by salt and other additives.16 If H 2 0 was substituted by DzO in C8E5solutions, a decrease by 2.5 "C was observed, essentially independent of detergent concentration (within 0.5 "C). Hydrodynamic Radii and Scattered Light Intensities as Function of Temperature. Photon correlation spectroscopy was used to monitor the increase of the apparent hydrodynamic radii (Rh)with temperature. The results for C8E4and C8E5are shown in Figure 2 for various detergent concentrations. The correlation spectra were found to be single exponentials at any temperature and concentration, even near Td. The amount of light scattered by micellar solutions increases strongly with temperature, concomitant to an increase of Rh, as shown in Figure 3. Temperature variations of scattered neutron intensities a t zero angle coincided with photon correlation data. Provided intermicellar interactions are ignored, the results presented in Figure 3 suggest prolate geometry of the micelles with axial ratios increasing with temperature. As discussed el~ewhere?~ measurements up to Td - 0.1 "C show that the axial ratios diverge at Td. An interpretation of these results in terms of particle shape30would predict the intrinsic viscosity to diverge also at Td. Intrinsic Viscosity as a Function of Temperature. The dependence of viscosities of C8E4 solutions in H 2 0 on detergent concentrations appear linear at low temperatures (data not shown) but deviate significantly from linearity at temperatures close to Td (Figure 4a). At 36.5 "C, a complex concentration dependence is indeed expected: according to Figure 1, variation of concentration causes significant changes of the proximity of the phase boundary. Figure 4b shows the temperature dependence of the visthe viscosity reaches cosity of 7% v/v C g 4in H,O. At Td, a finite value. As has been mentioned above, light scat(39) M. Corti, V. Degiorgio, and M. Zulauf, Phys. Reu. Lett., 48, 1617-20 (1982). (40) S. Kaneshina, I. Ueda, H. Kamaya, and H. Eyring, Biochim. Biophys. Acta, 603,237-44 (1980). (41) T. Nakagawa in "NonionicSurfactants", M. J. Schick, Ed., Marcel Dekker, New York, 1966.
1
,
,
5, 1983 859
I
30
T ("0 Flgure 4. (a) Dependence of viscosity on detergent concentration for C8E4in H20 at 36.5 O C (cf. text). (b) Viscosities (7; squares) and intrinsic viscosities ([q]: triangles) of a 7 % CsE4solutlon in H,O as a function of temperature ( T ) . The broken line indicates water viscosity. The arrow pointing down indicates the position of T,. The sharp decrease of the viscosity thus occurs above this temperature and is due to the flow of the aqueous phase, while the detergent phase adheres to the glass wall. Points A and B correspond to their counterparts in Figure 3. According to Tanf~rd,~' the axial ratio of prolate micelles would be 3:l at A and 1O:l at B. The maximal axial ratio of the experimental point at T, is 12:1.
\ E
-
*
O
10
F
\. [C, E,]
(O/o
1 10
20
30
V/V)
Flgure 5. Relattve values of the scattered intensity divided by the total detergent concentration ( J l m ) of aqueous C8E4solutions are shown as a function of the total detergent concentration (circles). Open symbols represent measurements at 8.5 OC, and closed ones those at 30.9 "C. I n the insert, the dependences of apparent hydrodynamic radii from photocorrelation spectroscopy (R h) are shown as squares.
tering data, interpreted in terms of micellar growth, predict divergence of intrinsic viscosities at Td. This is in contradiction to the experimental findings. Therefore, the assumption on which this prediction relies must be questioned. Hydrodynamic Radii and Scattered Light Intensities as a Function of Concentration. Figure 5 shows the concentration dependence of the scattered relative light intensities per monomer ( I / m ) of C8E4at two temperatures. A linear variation is not observed at any concentration. A treatment in terms of virial correction^^^^^^ is therefore not applicable, and extrapolation of micelle size to the cmc remains undefined. Micellar solutions of C8E4 (and also of C8E5)do not possess dilute regimes but are thermodynamically highly n~nideal.'-~The values of the intensities per monomer, as well as of hydrodynamic radii (Rh; cf. insert of Figure 5), go through a maximum near a concentration of 7% at which the minimum Td in the phase diagram (Figure 1)is reached. These variations are therefore correlated to the proximity of the micellar phase boundary. Similar variations of scattered intensities or turbidities have been observed for other nonionic detergent~.~-~*~~ Small-Angle Neutron Scattering. Neutron scattering is ideally suited for the study of detergent micelle systems, since the coherent scattering properties yield very high count rates. Excess scattering densities relative to the solvent are only slightly different for the hydrocarbon cm/A3) and the oxyethylene head moiety (-0.0685 X groups (-0.0532 X cm/A3). This property is also
860
Zulauf and Rosenbusch
The Journal of Physical Chemistry, Vol. 87, No. 5, 7983
60 40 20
L--J 40
01
0
60
80
02 0
Flgure 6. Logarithms of scattered neutron intensities (I)are shown as a function of the scattering vectors (0). A 7 % solution of CE ,, in D,O was measured on the instrument IN1 1. Data have not been corrected for polychromaticityof neutrons. Temperatures were 25.0 (closed circles), 38.1 (open circles), 44.0 (closed triangles), 50.1 (open triangles), and 54.5 (closed squares) OC.
0
0001 0' [
0002
Figure 7. Logarithms of scattered neutron intensities ( I ) are shown in Guinier plots as a function of the square of scattering vectors (Q2). Solutions of 10% C8E4(open symbols) were examined with the instrument D 11. The data obtained allow an unambiguous determination of the radii of gyration. Temperatures were 8.5 (diamonds) and 30.9 (circles) OC. Solutions of 7% C8E, (closed symbols) were investigated with the instrument IN11. The smaller number of experimental points increases uncertainties, which are indicated as error bars in Figure 8. Temperatures used were 25 (triangles pointing up), 38.1 (triangles pointing down), 44.0 (circles), and 50.1 (squares) OC. The arrows indicate the points at which R,Q = 1. The values at Q = 0 were obtained from light scattering intensities, measured on the same sample at identical temperatures. The scaling procedure was as follows. Neutron intensities at 38.1 OC were extrapolated to Q = 0. The photon count rates were scaled such that the value at 38.1 OC corresponded to the extrapolated neutron intensity. Other points at Q = 0 were drawn according to scaled light scattering intensities.
pertinent to micelle aggregates in which the hydrocarbon cores exclude water, while oxyethylene moieties are hydrated. In D20, micelles therefore appear as objects of essentially homogeneous density whereas for X-rays scattering densities of the two moieties tend to cancel (results not shown; see also ref 34). In Figure 6, scattered neutron intensities are shown as a function of the scattering vector Q for 7% C8E5 in D 2 0 at various temperatures. It is apparent that temperature affects the scattering only in the forward direction (Q < 0.05 A-1). The measurements extend roughly to the first scattering minimum expected for spheres of 25-A radius. Although the increase of intensities at low angles could be due to nonsphericity, the resolution of the data is insufficient for unambiguous assignments. They allow, however, the conventional Guinier analysis at small angles, as shown in Figure 7. Therein, the intensities represented by open symbols pertain to C8E4and were measured on an absolute scale (cf. Materials and Methods Section). This allows calculation of the apparent molecular weights, yielding values of 29000 f 600 at 30.9 "C and of 6300 f 200 at 6.5 "C. These values do not reflect proper micelle mass, since intermicellar interactions are neglected.42 The intensities (42) M. Zulauf and J. (1982).
B. Hayter, Colloid Polym. Sci.,
260, 1023-28
Flgure 8. Radii of gyration (R,) obtained from the data shown in Figure 7 are plotted vs. hydrodynamlc radii (R,,). The hatched and dotted areas show the range of data expected for prolate or oblate ellipsoids of revolution (semiminor axes 13 and 25 A as in Figure 3). The solid line represents spherical scatterers, with R , = (3/5)1'2R,. Spheres pertain to C8E4,and circles to C8E5. For the deviations at small radii, cf. text.
represented by full symbols in Figure 7 pertain to C8E5and are shown on a relative scale (cf. legend to Figure 7). The radii of gyration of both detergents are shown in Figure 8 as a function of correspondinghydrodynamic radii. This representation allows a critical comparison with theoretically expected particle shapes. Hydrodynamic and mass radii of homogeneous ellipsoids of revolution were calculated with various axial ratios,29with values of their semiminor axes fixed at either 13 or 25 A (cf. legend to Figure 3). From this figure, it is immediately obvious that a prolate shape (but also an oblate geometry) of micelles can be excluded. Rather, the shape of the scattering particles appears to be spherical at high temperatures corresponding to Td- T < 15 OC, Rh > 45 A (solid line in Figure 8). At lower temperatures (correspondingto Rh < 45 A), the radii of gyration are smaller than those expected for spherical particles, which is likely due to interparticle interferences arising from excluded volume effects (cf. Discussion section). This observation, in conjunction with the dependence of light scattering intensities on temperature (Figure 3), is incompatible with the assumption that the scatterers are compact spherical structures. Alternatively, all our observations could be explained by assuming nonuniform distributions of small micelles, which interact to form loose clusters. Quasi-elastic Neutron Scattering. If the motions of individual particles within micelle clouds could be observed by measurements of their displacements over very short distances and times, the proposed hypothesis could be verified. Indeed, quasi-elastic neutron scattering, performed by neutron spin-echo measurements, allows evaluating such motions. The technique used has been described in In the present context it is pertinent that this method allows measurementsof the same physical quantities as photon correlation spectroscopy. For a single diffusional process, a characteristic relaxation time 7 is expected to be related to Q by 7 = DQ2. If this law were satisfied, the diffusion coefficient D would reflect Brownian motions over distances of 2a/Q. Figure 9 shows measurements of 7 as a function of Q2 in the range of 0.02 < Q < 0.13 A-1 for solutions of C8E5in D20. For Q > 0.05 A-1 (Q2> 0.0025 A-2),the relation given above is borne out, and the existence of a single diffusion process corresponding to a diffusion coefficient which is essentially independent of temperature is established. It is likely due to the Brownian motion of the individual detergent micelles. For Q < 0.05 .&-I, and with increasing temperature, the relaxations become eventually very slow and reach values inaccessible to quasi-elastic neutron scattering.
The Journal of Physical Chemistry, Voi. 87, No. 5, 1983 861
Micelles of Octylhydroxyoligo(oxyethy1enes)
0
001
002
Q2 ( A - 2 ,
Figure 9. Relaxationtimes (7 = Q'D), measured with the instrument IN1 1, as a function of the square of the scattering vector (0')for 7 % C,E, in D,O. The scale on the ordinate is arbitrary. Open and closed circles are used to allow distinction of points at various temperatures. Neutron correlation functions were determined at 9 or 10 points and analyzed by a cumulant method.37 The apparent polydispersity may thus be assessed. It is smallest at hgh Q values and increases toward smaller Q values with an increase of the second moment, ((D2) ( D ) 2 ) / ( D ) 2from , 0.1 to 0.8.
Furthermore, the apparent polydispersity increases toward small Q values (cf. legend of Figure 9). An estimation of the micelle size may be obtained by calculating hydrodynamic radii Rh from the experimental values of the diffusion constant D, using eq 2. The values of Rh increase linearly with temperature from 25.3 A at 25 OC to reach the finite value of 35.3 A at Td. Assuming that perturbations due to hydrodynamic drag and to increased local concentrations within clusters can be neglected, these values correspond to the physical parameters of the micelles. It follows that growth into long cylinders can be excluded. Even if it were assumed that cylindrical micelles were flexible38 and that internal flexing modes would dominate the neutron spectrum, the observed D values would be expected to decrease gradually with increasing Q. This is in clear contradiction to our experimental findings. If, near Td,the radius of 35 A were to reflect the radius of micelles, a rough surface of the core (due to temporary excursions of monomers) or slight nonsphericity would have to be assumed. Since the apparent increase in size is small, and its interpretation questionable as long as hydrodynamic corrections are neglected, it appears most reasonable to assume a basically spherical shape of micelles with the deviations reflecting their highly dynamic properties. At the present stage we cannot assign unambiguous values to the molecular weight and the monomer association number of micelles of this size, since such an assignment depends on model assumptions on their structure. In particular, it follows from the above observations that micellar weights cannot be obtained from the scattered intensity at zero angle. A quantitative analysis in terms of a model of interacting spherical micelles will be presented elsewhere.42
Discussion The light and neutron scattering experiments presented in this report fall into two classes. The first one includes elastic and quasi-elastic light scattering and neutron scattering experiments at low angles (Q < 0.05 A-1) and is characterized by strong temperature and concentration dependences of the scattering parameters. The second class comprises elastic and quasi-elastic neutron experiments at higher scattering angles (Q > 0.05 A-1); its results are independent, or at most weakly dependent, on temperature. Within the first class, the temperature-dependent values of the scattered neutron intensities at Q = 0 coincide with those obtained from light scattering. The apparent values of the molecular weights of scattering centers increase strongly with temperature and diverge at
Td, the critical temperature of demixing. Similarly, apparent hydrodynamic radii, determined by proton correlation spectroscopy, and the radii of gyration, evaluated by Guinier analysis of neutron scattering data, diverge. The combination of intensities and hydrodynamic radii could be interpreted as indicating that micelles grow into elongated shapes with substantial axial ratios. Such conclusions have often been drawn in studies of other detergents.&12,2sMeasurements of solution viscosities appear to support such an interpretation, except that they exhibit a finite value at Td,which is incompatible with the light scattering data predicting unlimited micellar growth. The comparison of the radii of gyration (R,) with hydrodynamic radii (Rh), shown in Figure 8, immediately reveals the incompatibility of the observed result with predictions based on micellar growth. If micelles were prolate ellipsoids, R, would exceed Rh at axial ratios larger than 4:1.29 Instead, Rh values were found to be larger than R, values at all temperatures tested. In fact, the experimental points coincide with values expected for spherical particles. Since spherical micelles with radii larger than the length of extended detergent monomers can be discounted, the scattering centers may represent loose clusters of small micelles which are interpenetrated by solvent. The size of these clouds would increase gradually with temperature. However, the existence of clusters implies a nonrandom distribution of micelles in space, which affects the scattering properties of the solution. In turn, clusters can arise only if micelles interact with each other. In the second class of experiments, the results of elastic neutron scattering are independent of temperature. Neutron spin-echo measurements reveal a unique diffusional process with diffusion coefficients varying very little with temperature and corresponding to small micelles of about 25-A radius (CsE,). With the concepts developed above, the two classes of experiments can now be discussed from a unified point of view. In the range of 0.1 < Q < 0.3 A-l, the static neutron scattering tests the distribution of matter on a spatial scale of 20-60 A, distances over which neutron spin-echo measurements perceive particle displacements due to Brownian motion. These distances are generally smaller than the extent of the clusters. In contrast, for Q C 0.05 A-l, static neutron scattering senses distances of 1000 8, and more and therefore detects concentration fluctuations of micelles. Photon correlation spectroscopy measures the corresponding dynamical processes pertinent to the clusters. These concentration fluctuations of small micelles are related to the critical phenomenon of demixing, a concept which was first proposed by Corti and Degi0rgi0.l~The spin-echo measurements confirm the validity of their hypothesis. In the intermediate range 0.05 C Q C 0.1 A-1, the scattering depends on the detailed nature of the intermicellar interactions. The temperature and concentration dependences of the scattering parameters may reflect a delicate balance of attractive and repulsive forces involved. The attractive forces, expected to increase with temperature, are likely to involve weak energies of short range compared to the radius of the micelles. If this were not the case, formation of stable, compact aggregates could occur. The effect of these forces could be described as follows: when micelles collide, they can adhere to each other for a limited period of time, before thermal energy disrupts the bonds again. The possibility of adhesion over short time intervals would lead to nonrandom spatial distribution, as observed in clusters. A plausible mechanism giving rise to such forces could be due to micellar hydration proper tie^.^^,^^ At low temperatures, extensive hydration of oxyethylene
J. Phys. Chem. 1983, 87,862-867
862
oxygens within single micelles may be postulated. Bound water would then prevent interpenetration of the head groups of neighboring micelles. At higher temperatures, dehydration would induce intermicellar hydrogen bonding by shared water molecules. The repulsive forces in nonionic detergent solutions are most likely due to excluded volume effects. Although micelles are dynamical structures without rigid boundaries, they are mutually impenetrable. For a 10% solution of micelles of radius R, the mean intermicellar distances are of the order of 4R. At such densities, the reduced accessible volume is equivalent to repulsive forces which counterbalance the attractive forces. Both influence the static and dynamic scattering and, thus, the value of the resulting parameters. The relations between these parameters may not be interpreted in terms of shape under all circumstances, as shown by the relation between Rh and R, at low temperatures in Figure 8. A quantitative analysis
of this concept of scattering from interacting particles will be presented elsewhere.42 In conclusion, we propose that micelles of the detergents C8E4and C8E6are small, spherical particles to which we can assign a radius of about 25 A. Small deviations from this value at high temperature may be due to hydrodynamic nonideality or to inherent dynamic properties of micelles. Experiments which provide results suggesting larger micelles would then be interpreted as being affected by micelle-micelle interactions.
Acknowledgment. It is a pleasure to thank Dr. J. B. Hayter for advice with quasi-elastic neutron experiments and many discussions. M. Grabo kindly performed the measurements of the critical micellar concentrations reported in Figure 1. This study was supported by a grant of the Swiss National Science Foundation (3.656.80). Registry No. CsE4, 19327-39-0; C8E5,19327-40-3.
Detection of a New Photoinduced Electron Paramagnetic Resonance Signal in Particle Dispersions of Metal-Free CY-, p-, and x-Phthalocyanines Roger L. Sasseville, James R. Bolton, Depam“
of Chemistry, University of Western Ontario, London, Ontario, Canada N6A 587
and John R. Harbour‘ Xerox Research Centre of Canada, Mississauga, Ontario, Canada L5L 1J9 (Received: April 19, 1982; In Final Form: October 19, 1982)
The electron paramagnetic resonance (EPR) characteristics of two preparations of the a , p, and x polymorphs of metal-free phthalocyanine (H,Pc) have been investigated. The first preparation consisted of dry powder samples of solid phthalocyanine in air. These samples exhibited a broad (3-5G)EPR signal (g = 2.0026) which increases moderately on light irradiation and decays slowly in the dark. In the second preparation, fine powders were dispersed in a nonsolubilizing fluid. Freshly prepared samples exhibited the same broad EPR signal as in the dry powder samples; however, after storage in the dark for 24 h, the broad signal completely disappeared. When these equilibrated dispersed samples were irradiated with visible light, a new narrow (1.0-1.3 G) EPR signal (g = 2.0026) is formed which decays rapidly in the dark. There are some variations, particularly in intensity and line widths, among the three polymorphs. The EPR signals are interpreted as arising from various electron and hole trap centers. A semiconductor band model is introduced to help interpret the results.
Introduction The study of dark and light-stimulated phenomena in inorganic and organic semiconductors, using the technique of electron paramagnetic resonance (EPR) spectroscopy, can, when complemented with the results of structural, optical, and other techniques, provide important information on the nature and location of paramagnetic centers, the type of dopant and/or defect, the crystalline morphology, and possibly also spin-phonon interactions in the (1) G. D. Watkin in “Point Defects in Solid”, Vol. 2, J. H. Crawford, Jr., and L. M. Slifkin, Eds., Plenum Press, New York, 1975; G. D. Watkins in “Lattice Defects in Semiconductors”, F. A. Huntley, Ed., Institute of Physics, London, 1975. (2) M. W. Brodsky, Ed., “Topics in Applied Physics”, Vol. 36, Springer-Verlag, West Berlin, 1979. (3) N. B. Vidi and J. W. Corbett, Eds., “Radiation Effects in Semiconductors”, Conference Series No. 31, The Institute of Physics, Bristol, 1976. (4) N. F. Mott and E. A. Davis, “Electronic Processes in Non-Crystalline Material”, Clarendon Press, Oxford, 1979. (5)Magn. Reson. Relat. Phenom., Proc. Congr. Ampere, ZOth, 1978 (1979) ‘ ( 6 ) s . G. Bishop, V. Strom, and P. C. Taylor, Phys. Reu. B , 15, 2278 (1977); Phys. Rev. Lett., 36, 543 (1976); 34, 1346 (1975); Philos. Mag., .m r t i E. 27. 241 m17a). (7jG.’A.Baraff, K. 0. Kane, and M. Schluter, Phys. Reu. E , 21,3563, 5662 (1980).
0022-3654/83/2087-0862$0 1.5010
In view of the above and the importance of phthalocyanines in both organic photoconductors and organic solar cells, we have chosen to reexamine the peculiar and anomalous EPR signals present in dark and illuminated metal-free phthalocyanines (H,Pc). Since the first observations by Ingram and Bennett,g these signals have variously been ascribed to broken T bonds,l0 diradicals,’l defect structures,12electronicallyactive centers,13oxidation products or impurities, the result of mechanical forces,l* and the formation of a charge-transfer complex between H2Pcand Oz(g) producing a phthalocyanine radical cation (8) H. J. Zeiger and G. W. Pratt, “Magnetic Interactions in Solids”, Clarendon Press, Oxford, 1973. (9) D. J. E. Ingram and J. E. Bennett, Philos. Mag., 45,545 (1954); J . Chem. Phys., 22, 1136 (1954). (IO) F. H. Winslow, W. 0. Baker, and W. A. Yager, J . Am. Chem. Sac., 77, 4571 (1955). (11) T. Fu. Yen, J. G. Erdman, and A. J. Saraceno, Anal. Chem., 34, 694 (1962); K. Wilksne and A. E. Newkirk, J. Chem. Phys., 34, 2184 (1961). (12) J. F. Boas, P. E. Fielding, and A. G. Mackay, Aust. J . Chem., 27, 7 (1974). (13) J. M. Assour and S.E. Harrison, J . Phys. Chem., 68,872 (1964); E. G. Sharoyan, N. N. Tikhomirova, and L. A. Blyumentas, Zh. Strukt. Khim., 6, 843 (1965). (14) K. M. More, G. R. Eaton, and S.S.Eaton, J . Magn. Reson., 37, 217 (1980); H. Harker, J. B. Horsley, and R. Robson, Carbon, 9 , l (1971).
0 1983 American Chemical Society
