3484
J . Phys. Chem. 1988, 92, 3484-3488
Photoelectrochemtstry of Cadmium Sulfide. 2. Influence of Surface-State Charging Dieter Meissner,* her Lauermann, Riidiger Memming, ISFH, Institut f u r Solarenergieforschung, Hannover. Sokelantstrasse 5, 0-3000 Hannover 1, FRG
and Bertel Kastening Institut f u r Physikalische Chemie der Uniuersitat, Bundesstrasse 45, 0-2000 Hamburg 13, FRG (Received: May 5, 1987; In Final Form: January 28, 1988)
The energy bands at the surface of clean CdS become unpinned upon illumination and are shifted in the anodic direction by several hundred millivolts. The same effect occurs in the dark after addition of the oxidized species of certain redox systems whose standard potentials are located in the bandgap of CdS. A model is presented in which the band movement is interpreted by positive charging of surface states. In the case of light excitation a hole in the valence band is captured by the surface state; in the case of a suitable oxidizing agent the surface state is charged by direct electron transfer from this state to the acceptor in the electrolyte. The potential dependence of photocurrents and dark currents can be explained semiquantitatively in terms of charge transfer via surface states, which means that both minority carrier (anodic photocurrent) and majority carrier transfer (cathodic dark current) occurs via these states. The model and the possible nature of these states are discussed in detail.
Introduction A reanalysis of the CdS photoelectrochemistry given in part 1 revealed a striking potential difference between the flat-band potential of this material in the dark and the onset of cathodic dark currents in the presence of oxygen or Cd2+ions in the solution. Actually, considerable cathodic currents were already observed at an upward band bending of about 0.8 V. To prove whether this is a general phenomenon at CdS, we report here on corresponding investigations with a number of other typical redox systems. The main question behind these experiments was whether the electron transfer occurs via the conduction band or whether majority carrier transfer via surface states is involved. The latter has been postulated by Tributsch and Bennett2 for the reduction of Fe3+ and by Hengleid and later by Bard and co-workers4 for the reduction of methylviologen (MV2+). Previous investigations of the minority carrier transfer from CdS electrodesS had lead us and others to the conclusion that the hole transfer occurs via surface states. On the other hand, the surface-state charging causes a change of the potential drop across the Helmholtz double layer in the solution, and this should shift the energetic position of the surface states itself. The aim of the investigation presented here was to develop a qualitative model for these effects. Experimental Section The experimental conditions used in this study are reported in part 1.l Phototransients were measured by using a photoshutter triggering a multichannel analyzer (Nicolet Instrument computer, Model 1074, with high-speed digitizer, Model SD-77, and highspeed sweep control, Model SW-77) connected to the current (1) ,Meissner, D.; Memming, R.; Kastening, B. J. Phys. Chem., preceding paper in this issue. (2) Tributsch, H.; Bennett, J. C. J . Chem. Technol. Biotechnol. 1981,31, 565. ( 3 ) Henglein, A. Ber. Bunsen-Ges. Phys. Chem. 1982, 86, 301; J . Phys. Chem. 1982, 86, 2291. (4) Finlayson, M. F.; Wheeler, B. L.; Kakuta, N.; Park, K. H.; Bard, A. J.; Campion, A,; Fox, M. A,; Webber, S. E.; White, J. M. J . Phys. Chem. 1985, 89, 5616. (5) (a) Memming, R. J . Electrochem. SOC.1978, 125, 117. Memming, R.; Kelly, J. J. Photochemical Conversion and Storage of Solar Energy; Connolly, J . S., Ed.; Academic: London, 1981; p 243. (b) Tyagai, V. A,; Kolbasov, G. Y . Surf. Sci. 1971, 28,433. (c) Ellis, A. B.; Kaiser, S. W.; Bolts, J. M.; Wrighton, M. S. J. Am. Chem. SOC.1977, 99, 2839. (d) Inoue, T.;
Watanabe, T.; Fujishima, A,; Honda, K.; Kohayakawa, K. J . Electrochem. SOC.1977, 224, 719. (e) Nagasubramanian, G.; Wheeler, B. L.; Bard, A. J. J . Elecfrochem. SOC.1983, 130, 1680. (f) Fujishima, A,; Suda, Y . ;Honda, K. Denki Kagaku Oyobi Kogyo Bufsuri Kagaku 1983, 51, 69.
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output of a fast Wenking potentiostat (POS 73) via a preamplifier (Tektronix 7A22 for oscilloscope 72/3). The run-up signal of a number of scans was observed by using an oscilloscope (Tektronix R5 103) and transferred to an X / Y recorder after a satisfying signal to noise ratio was achieved. All experiments in the dark were performed in a carefully sealed black box. The electrochemical cell for photocurrent measurements was a Teflon cylinder with a quartz window at its bottom. The electrode was illuminated through this window by use of a quartz fiber optic light cable on which the light of a 450-W Xe lamp was focused. Neutral density filters were used to obtain low light intensities. All experiments reported in this paper were obtained from CdS electrodes exposing their (0001) Cd surface to the electrolyte. The results of corresponding experiments using the (0001) S surface depended on the pretreatment of the surface as reported in ref 1. Before all experiments the CdS electrodes were polished with diamond powder of decreasing size down to 0.5 wm and etched for 5-10 s in 20% HC1. So that the electrodes could be cleaned from rest sulfur on the surface,6 the electrodes were transferred into oxygen-flushed redox-couple-free electrolyte and either prepolarized at about -1.1 V(SCE) or cycled between about -1.5 and about +1 V(SCE) for at least 1 h. The latter procedure has the advantage that progress in cleaning the electrode surface can be easily followed by observing the shape change of the current/potential curve. After a clear step for the oxygen reduction was obtained, the electrode potential was adjusted to a potential where no net current was seen (about -0.5 V(SCE)). The electrolyte was then flushed with purified nitrogen for about 15 min, and a concentrated, oxygen-free stock solution containing the redox couple was added to obtain the desired concentration.
Results Majority Carrier Transfer. To investigate the electron-transfer reaction from CdS electrodes to redox couples in the electrolyte, we recorded current/potential curves in the presence of different oxidized species. Figure 1 shows as typical results the curves obtained from the reduction of oxygen, H202, Fe(CN)63-, and C ~ ( s e p ) ~(sep + = sepulchrate). Corresponding results were obtained by adding Fe3+,Co(NH3),, Fe(EDTA)3+,V3+, and Cr3+. However, in addition to the reduction of the 3+ state to the 2+ state, further reduction to the metal occurs in the case of iron, cobalt, and chromium, leading to a further increase of the cathodic current to give a second reduction step. (6) Meissner, D.; Benndorf, C.; Memming, R. Appl. Surf, Sci. 1987, 27, 423.
0 1988 American Chemical Society
CdS: Surface-State Charging
The Journal of Physical Chemistry, Vol. 92, No. 12, 1988 3485 -1 0
-05
0 IVISCEll -E
-0 2 N2-bubbled
-.-oL ---06
_--0 8 Im A k m 2 1 -1 0
I{
-0 5
OOIM H202
t-06
N 2 - bubbled
-0 8 -1 0 -1 2
Fimue 1. Cathodic dark currents at CdS-(0001) Cd in the presence of the indicated redox couples (concentration 0.01 M, scan rate 100 mV/s, electrolyte 0.7 M Na,SO,).
Besides the reduction of these redox couples, we also investigated the deposition of metals on the surface of CdS. In these experiments special attention was paid to the first scan in the cathodic direction, starting from potentials where no reduction current is seen. During this scan the metal is deposited directly onto the CdS. In further scans metal deposition can occur onto the metal islands already formed. In this case the surface energetics become complicated because they are determined by the semiconductor metal and the metal electrolyte contact. However, examination of the surface by light microscopy (magnification about 1OOX) showed a very homogeneous layer of metal after the deposition of larger amounts, indicating that the metal is not preferentially deposited onto itself, which should lead to more needlelike metal growth. The deposition of Pt or Cd on CdS leads to diffusion-controlled reduction steps as was found for the further reduction of the iron, cobalt, and chromium complexes previously mentioned. In these cases the cathodic currents detected in the first sweep start at about the same potentials where the reduction of the redox couples (from their 3+ into their 2+ state) occurs. In addition anodic stripping peaks are seen on the back sweep by using higher scan rates (compare ref 1). In the absence of all oxidizing species, the dark current at CdS starts to rise around -1.3 V(SCE) due to hydrogen formation and the reduction of CdS itself.' Zn2+ and even A13+are reduced at about the same potentials, as can be seen from additional reoxidation peaks in the case of zinc and by concentration-dependent shifts of the reduction currents in the case of A13+.' The reduction of AI3+ in neutral aqueous solution at CdS, although expected from the very negative position of the conduction band edge at CdS in the dark, surprised us. Therefore, we used X-ray photoelectron spectroscopy to analyze the surface after polarizing the electrode at -1.3 V(SCE) in AI3+-containingsolution for 20 min. The electrode surface was then carefully washed with distilled water and transferred into the XPS lab (compare ref 6). For comparison we used the same CdS electrode after immersing it into the solution for 60 min under open-circuit conditions. Only the electrode polarized at -1.3 V(SCE) showed a peak at about (7) Lauermann, I. Diploma Thesis, Institut fur Physikalische Chemie der Universitat: Hamburg,1986.
-06V
-05v
pl
Figure 2. Photocurrent transients on CdS-(0001) Cd recorded at different electrode potentials in oxygen-saturated solution (current scales
as indicated). 75-eV binding energy due to aluminum. The electrode was covered with a shiny metallic layer that turned white after the electrode was exposed to air due to aluminum oxide formation. Photocurrents. Photocurrent transients were measured with carefully etched electrodes after prepolarization at -1.1 V(SCE) in the presence of oxygen. These transients start near the flat-band potential as determined in the dark, Le., at potentials where the reduction of oxygen or other suitable oxidized species is already diffusion controlled. Figure 2 shows photocurrent transients recorded at low light intensity. The overall photocorrosion was kept as small as possible by minimizing the time and intensity of illumination and by prepolarizing the electrode again at -1.1 V(SCE) before each new measurement. Assuming quantitative formation of sulfur (although in the oxygen-containing solution sulfate is the main photocorrosion product), the total amount of charge passed through the electrode (less than 10 pC/cm2) could have formed only less than 10% of a monolayer of sulfur on the surface of the electrode per measurement. The rise time of the photocurrent transients shown in Figure 2 is determined by the opening time of the shutter. The absolute
3486 The Journal of Physical Chemistry, Vol. 92, No. 12, I988
Meissner et al.
Figure 5. Energy model of the surface-charging effects of surface states at clean CdS electrodes polarized between E,(d) and Ew(l). Upper row: photocurrent transient: sequence of hole formation (a), surface-state charging (unpinning of bands) (b), and charge recombination via the surface state (c). Lower row: stationary reduction current in the presence of appropriate electron acceptors: sequence of electron transfer (d), band movement (e), and electron supply via the conduction band (f).
'15
- i j
-1-
-'?
-1:
-33
-jC
-;L
-:?
i ! i: E
Figure 3. Plot of the peak currents (Imax) and the plateau currents (I,,,,,) versus potential on a linear (a) and on a logarithmic (b) current scale.
Figure 4. Idealized current/potential curves found at clean (sulfur-free) CdS electrodes: IN*= dark current in N2-flushed solution; Io* = dark current, e.g., 0,-flushed solution; I , = peak photocurrent at low light intensities and photocurrent in the presence of, e.g., S2-;I,, = stationary photocurrent at low light intensities.
currents at the peak maxima are therefore arbitrary and should be taken only for the purpose of comparison. A plot of these peak currents and of the plateau currents taken from the transients in Figure 2 as a function of potential is shown in Figure 3. As seen from the logarithmic plot, the peak currents saturate about 0.6 V cathodic of the saturation potential of the plateau currents (around -0.4 V(SCE)). Discussion
Illumination of the electrode leads on one hand to transient photocurrents (peak currents I,) starting near the flat-band potential in the dark (Efb(d)). On the other hand, the light shifts the band edges up to about 0.6 V in the anodic direction to Efb(l), as described in ref 1. Anodic of the light value of Efb(l) the steady-state photocurrent ( I h) rises. In the presence of appropriate redox couples (especially S4-) the steady-state photocurrent rises at E,(d), and no shift of the capacity values during illumination occurs as was reported in ref 5 . This current/potential behavior is outlined in an idealized scheme in Figure 4. It is based on current/potential curves as shown in Figures 1 and 3. This behavior is understood on the basis of the following model: In a microscopic picture a number of sequential events occur upon
illumination as illustrated in Figure 5 , parts a-c. In the first step (Figure Sa) the holes created by light excitation move toward the surface and are trapped in surface states, leading to a downward shift of the band edges at the surface by a few tenths of a volt (Figure 5b). The anodic phototransients reflect this charging process (see Figure 2 and compare also with ref 8). The new flat-band potential Efb(l) now prevents a current flow via the valence band, if the electrode is polarized at a potential between Efb(d)and Efb(l). On the other hand, the new band position allows electron flow toward the surface. Here the electrons recombine with the holes in the surface states, shifting the flat-band potential back to its dark value (Figure 5c). This process will continue as long as the illumination is turned on. Reduced species in the solution can interfere with this process if they are able to transfer their electron to the positively charged surface state. By this they change the amount of positive charge in the surface and shift the flat-band potential back toward its dark value.5a The best example at CdS is the sulfide ion. Adding S2-to the solution actually leads to a stationary photocurrent curve as depicted in Figure 4 for the peak currents of the phototransients (ZJ seen in the absence of a redox couple. The hole transfer to such stabilizing electron donors as, e.g., sulfide occurs via the surface states (compare ref 5 and 9). Depending on the relative rates of current flow toward the surface and of recombination, an average net positive charge will be found in the surface, which is seen as the anodic phototransient. The compensation of this charge can be seen as the cathodic transient after switching off the light. The excess surface charge changes the potential drop across the Helmholtz double layer by A ~ =H QSS/CH with QS = net charge trapped in surface states and CH= capacity of the Helmholtz double layer. For AUH = 0.6 V (seen as maximum shift of the flat-band potential) about 4 X lOI3 charges are needed, assuming a Helmholtz capacitance of 10 hF/cm2. With this change of the potential drop across the Helmholtz double layer, the energy states in the surface will also change their position relative to those in the electrolyte, Le., with the band edges and also the surface states. Their position relative to the band edges is assumed to remain unchanged. Another interesting result is the observation that the cathodic dark currents obtained with various redox couples occur in two (8) (a) Iwanski, P.; Curran, J. S.; Gissler, W.; Memming, R. J. Electrochem. SOC.1981, 128, 2128. (b) Abrantes, L. M.; Peter, L. M. J. Elecrroanal. Chem. 1983, 1-70, 593. (c) Peter, L. M.; Li, J.; Peat, R.J . Electroanal. Chem. 1984, 145, 29. (d) Li, J.; Peat, R.; Peter, L. K. J . Electroanal. Chem. 1984. 145, 41.
(9) (a) Miller, B.; Heller, A. Nature (London) 1976, 242, 680. (b) Wilson, R . H. J . Elecrrochem. Sor. 1979, 126, 1187.
The Journal of Physical Chemistry, Vol. 92, No. 12, 1988 3487
CdS: Surface-State Charging i ISCEI -2
-Al/Al
"
Figure 6. Comparison between positions of the energy band edges at the surface ( E ( s ) )of clean CdS-(0001) Cd with positively charged surface formed, Ew = Ew(l),left) and with uncharged surface states states (S(S2-, Elb = E,(d), right) with redox potentials of the redox couples
investigated. different potential regions. In one case, for the reduction of Zn2+, Mn2+,AI3+,and water, the corresponding currents occur at rather negative potentials, Le., near the flat-band potential in the dark. At this potential CdS itself is also reduced.' This result is easily understood in terms of electron transfer directly from the conduction band to the acceptor. With other redox systems such as oxygen, peroxide, Fe3+,Fe(CN)6f, Co(NH,):+, Fe(EDTA)-, V3+, C ~ ( s e p ) ~Cd2+, + , Fez+,Cr3+,Cr2+,and MV2+,however, a cathodic dark current on the order of tenths of a milliampere was found around -0.9 V(SCE), Le., at a potential at which the energy bands are expected to be bent upward by about 0.8 V. A correlation of the redox potentials of the couples and the band positions of CdS in the dark and under illumination is given in Figure 6. As indicated, a reduction-current onset for most of the redox couples at about -0.8 V(SCE) is much too anodic compared to a flat-band potential of about -1.75 V(SCE), as found in the dark.' To estimate a reasonable limit for a majority carrier current anodic of the flat-band potential, we can measure the current/potential behavior of solid-state Schottky barrier devices.I0 In the case of majority carrier flow it is assumed that all electrons reaching the semiconductor surface are actually collected by an acceptor in the electrolyte. The current is then limited only by the electron transport through the space-charge region and is not determined by the interface kinetics. A corresponding limiting current/potential dependence can be derived from the thermionic emission model using the Richardson equation i; = A ~ ( m * / m , ) - ' ~ 2 ( n o / N , )exp(-eUsc/kT)
with m* being the effective electron mass, no the bulk density of electrons and N, the state density in the conduction band, and Us, the band bending as explained in ref 10. With A = 120 A ~ ,= l o i 7~ m - and ~ , the effective mass cm-2, Nc = 6 X l O I 9 ~ m - no m*/m, = 0.27, the band bending to get a current density of 1 mA cm-2 has to be smaller than 0.43 V even for this limiting case. Accordingly, in the presence of such a redox couple the flat-band potential cannot be more cathodic than about -1.2 V(SCE) to obtain a dark current of about 1 mA/cm2 at -0.8 V(SCE). At first sight this conclusion seems to be in contradiction to results obtained by capacity measurements according to which the flat-band potential in the dark occurs at -1.8 V(SCE) (see part 1, ref 1). Therefore, we had some doubt at first concerning the latter value, which was derived by extrapolating the Mott/ Schottky plot over a relatively large potential range. The very negative flat-band potential was supported, however, by the (10) Memming, R. Be?. Bunsen-Ges. Phys. Chem. 1987, 91, 353.
photocurrent transients discussed above, which also indicated a flat-band potential being more negative than at least -1.6 V(SCE). In addition the reduction of Mn2+ and even of A13+ observed experimentally is only possible if the flat-band potential is very negative (compare Figure 6). It should be emphasized that the very negative flat-band potential of -1.75 V(SCE) was determined in an electrolyte free of any redox system. We then repeated the capacity measurements in the dark in the presence of oxidizing agents such as Fe3+ and C ~ ( s e p ) ~and + found a shift in the flat-band potential of about 0.5 V in the anodic direction. The latter result resolves the discrepancy between the flat-band potential and the onset of the majority carrier current, i.e., in the dark U, occurs around -1.2 V(SCE) in the presence of redox systems that lead to reduction currents at a potential around -0.8 V(SCE). Therefore, the majority carrier currents remain within the limits given by the Richardson equation. However, the question arises as to the origin of this latter shift of U,. This effect can be interpreted by assuming that electron transfer via surface states is the main process of majority carrier currents as already postulated for Fe3+ (ref 2) and MV2+ red ~ c t i o n . ~A, corresponding ~ model for this process as depicted in the three sequential steps in Figure 5, parts d-f, is completely analogous to that for the phototransient (Figure 5 , parts a-c). In the first reaction step an electron transfer from the surface state to an acceptor (oxidized species of a redox system) is assumed as indicated in Figure 5d, which leads to a positively charged urface state. This positive charge in the surface changes the potential drop across the Helmholtz double layer in the electrolyte (unpinning of bands) and shifts all surface energies in the anodic direction (Figure 5e) exactly as found during illumination (Figure 5b). The corresponding macroscopic flat-band potential depends on the density of charged surface states. As a consequence of the downward shift of the band edges at the surface, the electron density at the surface (ns) increases, and (depending on the applied electrode potential) electrons recombine with the positive charge in the surface state, which shifts the band back in cathodic direction (Figure 5f). Under stationary conditions a certain current can occur (see Figure 4). At more cathodic potentials (e.g., in the potential range where the cathodic current is diffusion controlled) the electron supply from the bulk of the semiconductor and the recombination rate is so fast that under stationary conditions nearly no surface states are positively charged, so that the bands shift back to their original value (Figure 5f). At anodic potentials, Le., anodic of about -0.8 V(SCE), the surface states remain positively charged because no electrons are available at the surface for recombination. With respect to the absolute values of the cathodic dark currents observed, we want to emphasize that they reach high values within a rather small potential range (between -0.7 and -0.9 V(SCE)), although the band bending at these potentials is still large with respect to the flat-band potential U,(l) = -1.2 V(SCE). As already discussed, these high currents can be understood only on the basis of the thermionic emission model, Le., the current is limited by the electron transport across the space-charge region to the surface. Accordingly, it can be concluded that the following step, the recombination of electrons at the surface with the hole in the (positively charged) surface state, must be very efficient. Concerning the chemical nature of the surface state, we assume it to be the surface bound So-as described above. The energy of the surface state of CdS has been determined by luminescence experiments to about 1.5-1.9 V above the valence band.3,4 The lower value has been taken in Figure 6 to show the position of the negatively charged surface state. As seen from this figure, the position is just negative enough to enable electron transfer to all redox couples with redox potentials more positive than that of Zn2+, and indeed we have found that electron transfer to all the species depicted below this ion occurs starting at about E,(1) (far anodic E,(d)), as expected. Zn2+and All+, on the other hand, are not able to take electrons out of the surface states and by this to enable electron flow towards the surface by shifting the flat-band potential in the anodic direction. This means that electrons will
3488
J. Phys. Chem. 1988, 92, 3488-3492
not reach the surface before the applied potential gets near to E,(d). Current flow to both species starts at about -1.3 V(SCE). Our model as shown in Figure 5 is based on the result that the flat-band potential of CdS in the dark is much more negative than generally assumed. It is confirmed by the fact that, e.g., A13+ can be reduced, and it is further supported by completely independent and previously not understood measurements by Streckert and co-workers published in 1980." They investigated the electroluminescence of CdS in the presence of SO4'-, which is known to inject holes into the valence band. Pulsing the electrode potential from 0 V(SCE) with its depleted space-charge layer to more cathodic potentials where electrons can reach the surface, they report" the electroluminescence intensity as a function of the negative potential limit of the pulse. Their Table I shows results for the two luminescence wavelengths corresponding to recombination of electrons from surface states (at 700 nm) and from the conduction band (at 510 nm) with holes in the valence band. The assignment of the low-energy emission at 700 nm was left open. It was proven later by Finlayson and co-workers4that it is the result of a recombination process between electrons in the surface state and valence-band holes. Increasing the negative potential limit from -1.3 to finally -2.0 V(SCE), Streckert et al. found that the long-wavelength luminescence had reached its (relative low intensity) maximum at -1.3 V(SCE) and disappeared completely between -1.8 and -2.0 V(SCE). On the other hand, the luminescence caused by the band-to-band transition at 510 nm increased dramatically between -1.3 and -1.5 and further at -1.8 V(SCE). (11) Streckert, H. H.; Karas, B. R.; Morano, D. J.; Ellis, A. B. J . Phys. Chem. 1980, 84, 3232.
These results are in perfect accordance with our model. At potentials near &(d) the number of electrons getting trapped in surface states reaches its highest number, the electroluminescence intensity coming from these states saturates. Yet the number of electrons in the conduction band at the surface will further increase at even more negative potentials. On the other hand, the number of holes trapped at the surface by the band bending decreases as Efb(d) is approached, so that no further increase of the bandto-band transition can be expected negative of Efb(d). The luminescence intensity saturates at -1.8 V(SCE). The model presented in this paper is assumed to be valid not only for CdS. Band-edge movement under illumination and in the presence of different redox couples has also been found for many different n- and p-type semiconductors.I2 Indeed, a somewhat similar model has been formulated very recently for RuSZ.13 Further investigations concerning other materials are under way. Registry No. Fe(CN),'-, 13408-62-3; Co(sep)'+, 72496-77-6; Co(NH,),3+, 14695-95-5; Fe(EDTA)'+, 114059-37-9; CdS, 1306-23-6; 02, 7782-44-7; H202, 7722-84-1; Fe, 7439-89-6; V, 7440-62-2; Cr, 744047-3; Pt, 7440-06-4; Cd, 7440-43-9. (12) (a) Nakato, Y.; Tsumura, A,; Tsubomura, H. J . Electrochem. SOC. 1980, 127, 1502; 1981, 128: 1300. (b) Nakato, Y.; Tsumura, A,; Tsubomura,
H. Photoeffects at Semiconductor-Electrolyte Interfaces; Nozik, A. J., Ed.; ACS Symposium Series; American Chemical Society: Washington, DC, 1981: p 9. (c) Kelly, J. J.; Memming, R. J. Electrochem. SOC.1982, 129, 730. (d) Kelly, J. J.; Notten, P. H. L. J. Electrochem. Sac. 1983, 130, 2452. (e) Fornarini, L.; Nozik, A. J.; Parkinson, B. A. J . Phys. Chem. 1984, 88, 3238. (f) Jaegermann, W. J . Phys. Chem. 1984, 88, 5309. (9) Ennaoui, A.; Tributsch, H. Sol. Energy Mater. 1986, 14,461. (h) Tubbesing, K.; Meissner, D.; Memming, R.; Kastening, B. J . Electroanal. Chem. 1986, 214, 685. (13) Kiihne, H. M.; Tributsch, H. J . Electroanal. Chem. 1986, 201, 263.
Coexistence of Small Micelles with Large Micelles Noriaki Funasaki,* Sakae Hada, and Saburo Neya Kyoto Pharmaceutical University, Misasagi, Yamashina, Kyoto 607, Japan (Received: May 6.1987; In Final Form: September I , 1987)
The aggregation properties of hexaoxyethylene glycol dodecyl ether (DE6) at 25 'C were investigated by gel filtration chromatography (GFC), and computer simulations of the GFC data revealed that a large micelle formed at high concentrations is the dimer of small micelles at low concentrations. Centroid volumes of frontal elution in the leading boundary were analyzed by an asymptotic theory, and the aggregation number and equilibrium constant for secondary aggregation of small micelles were determined. A plate theory, which assumes rapid equilibria for micellization and solute partition between the stationary phase and the mobile phase, predicted centroid volumes very close to the observed ones. The derivative of the frontal elution curve in the trailing boundary has a monomer peak and a micellar peak. The micellar peak normalized by the micellar concentration shifted toward the smaller elution volume side with increasing concentration and became broad at intermediate concentrations. These results could be computer simulated and provided strong evidence for the coexistence of small micelles with large micelles. Furthermore, these results are consistent with static light scattering, membrane osmometry, sedimentation velocity, fluorescence decay, and GFC data by other researchers.
Introduction The molecular weight M of a surfactant micelle formed at the critical micellization concentration (cmc) can be determined through extrapolation from higher concentrations by static light scattering, membrane osmometry, ultracentrifugation, and other methods. Above the cmc, however, an exact value of M cannot be determined unless the intermicellar interaction is taken into consideration quantitatively. Owing to difficulties involved in estimating the intermicellar interaction, it is still a matter of controversy if micellar growth occurs or not above the cmc.1-20 (1) Balmbra, R. R.; Clunie, J. S.; Corkill, J. M.; Goodman, J. F. Trans. Faraday SOC.1962, 58, 1661. (2) Attwood, D.; Elworthy, P. H.; Kayne, S. B. J . Phys. Chem. 1970, 74, 3529.
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For instance, static light scattering is the most extensively used method for determination of M . By this method it was early (3) Corti, M.; Degiorgio, V. J . Phys. Chem. 1981, 85, 1442. (4) Degiorgio, V. In Physics of Amphiphiles: Micelles, Vesicles and Microemulsions; Degiorgio, V., Corti, M., Eds.; North-Holland: Amsterdam, 1985; p-303. (5) Okawauchi, M.; Shinozaki, M.; Ikawa, Y . ;Tanaka, M. J . Phys. Chem. 1987, 91, 109. (6) Brown, W.; Johnsen, R.; Stilbs, P.; Lindman, B. J . Phys. Chem. 1983, 87, 4548. (7) Kato, T.;Seimiya, T. J . Phys. Chem. 1986, 90, 3159. (8) Ottewill, R. H.; Storer, C. C.; Walker, T. Trans. Faraday SOC.1967, 63, 2796. (9) Lofroth, J. E.: Almgren, M. In Surfactants in Solufion; Mittal, K. L.; Lindman, B., Eds.; Plenum: New York, 1984; p 627. (10) Zana, R.; Weil, C. J . Phys. Lett. 1985, 46, L953.
0 1988 American Chemical Society
