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J. Phys. Chem. 1983, 87,3166-3171
(NH3)6-,]3-nion. If Velo is evaluated in such a way, we obtain the following values: 50.7, 30.6, 13.9,0, and -15.6 cm3 mol-' for n = 0, 1, 2, 3, and 4, respectively. The negative value of Velo for anionic complex ion [Co(NOz)4(NH3)2]-is obviously unacceptable on the ground of the physical significance of Velo. To liberate us from this apparent contradiction we must return to the starting point of our discussion and reject the assumption that for the nonelectrolytic complex solute [CO(NO,),(NH~),]~ the term Velo is neglected. Consequently the value of Pint of [CO(NO,),(NH,),]~evaluated just above should be larger to some extent. On the other hand, the variation of V20 and ?-Stokes with the degree of ligand substituion as given in Table I11 indicates the decrease of electrostriction with increasing number of NOz- in the complex while the hydrodynamic dimension of the complex ions remains the same. X-ray studies21,22have shown that the bond distance between the central metal cobalt(II1) and the nitrogen atom is nearly the same for Co-N02 and Co-NH, bonds. The Co-N core of the complex ion does not change with the replacement of the ligand from NH, to NO2-. Therefore, the observed variation of Vzo and i$Kso with the number of the ligand NO2- in the complex ions, as shown in Table I11 and Figure 4, can be interpreted from the point of the variation of the degree of interactions between complex ion [Co(N0,),(NH3),J3-" and the solvent water. The non-Coulombic interactions of ligands with outershell water molecules do work, but their role may be less significant than the Coulombic ones. In the following discussion, emphasis will be placed on the Coulombic charge effects in analyzing our experimental results. In this study, the charge of the complex ion varies successively from 3+ to 1-. However, the positive or negative charge is not situated on the central cobalt atom, which always has 3+ charge. The positive charge of the cobalt atom is neutralized by the electron pair of the nitrogen atom of the ligand NH, and/or NOz-, and the resulting charge of the complex as a whole is distributed on the surface of the complex. For example, each hydrogen atom in the [Co-
Acknowledgment. We are pleased to thank Professor Yutaka Miyahara of our university for his encouragement to carry out this work. Registry No. [Co(NH3)&13,10534-89-1;[CoN02(NH3),]C1, 13782-02-0;tr~ns-[Co(NO2)2(NH3)4]Cl, 10534-83-5;Co(NOJ,(NH3)3, 13600-88-9;K[CO(NO.J~(NH,)~], 14285-97-3.
(21) Tanito, Y.; Saito, Y.; Kuroya, H. Bull. Chem. SOC.Jpn. 1952,25, 188. (22) Komiyama, Y. Bull. Chem. SOC.Jpn. 1956, 29,300.
(23) Pauling, L."The Nature of the Chemical Bond", 3rd ed.; Cornell University Press: Ithaca, NY, 1960. (24) For example: Passinski, A. Acta Physicochim. URSS 1938,8,385.
(NH3)6]3+ion has '/6+ charge,a while '/rcharge is allotted to one oxygen atom of the ligand NO2-. It has long been assumed that the ions themselves do not contribute to the measured compressibilities of solutions and this assumption is the principle employed to determine the hydration number of ions by the compressibility measurement^.'^^^^^ Hence, the values of dKB0reflect the compressibility of the water molecules around the solute. Water molecules around negatively charged solute are generally less firmly attached to the solute than for the case of water molecules around positively charged solute. The increase of the number of ligand NOz- in place of NH, results in the changes in the charge distribution on the surface of the complex, namely, from positively charged surface to partly positively and partly negatively charged surface. Solutewater interactions reflected in V20and i$&O are dominated by this kind of local charge distribution on the solute surface. This interpretation is in accordance with the fact that VZoand i$Kso vary linearly from [CO(NO,),(NH,)~]+ to [CO(NO,)~(NH,),]-and that as mentioned above the If term Velocannot be set to zero for [CO(NO~),(NH,),]~. the electrostriction is assumed to be arising from the influence of the charge distributed on the surface of the coordinated ligand on the surrounding water molecules, the electrostriction should be expected to occur even for the neutral-type complex [CO(NO~),(NH,),]~. In conclusion, this work has shown that, in aqueous solutions of nitroamminecobalt(II1) complex salts, solutesolute interactions are approximately represented in terms of DH theory but the interactions of complex ions with water molecules can only be explainable after taking account of the charge distribution on the surface of the complex.
Photooxidation of Thiacyanine Dyes at ZnO Single-Crystal Electrodes C. Kavassalls and M. T. Spltler' Deparlment of Chemistry, Carr Laboratory, Mount Hoiyoks College, South Hadley, Massachusetts 0 1075 (Received: October 4, 1982; In Final Form: January 24, 1983)
The photooxidation of a series of thiacyanine dyes has been studied at the (1010) face of ZnO single-crystal electrodes by using a total internal reflection technique. These dyes, a thia-n-carbocyanine series where n = 0, 1,2,3, were found to produce a photocurrent with an efficiency, aP,of Dye aggregate formation and increasing surface coverage of the electrode by the dye also influence aP,causing it, in general, to decline. These data are discussed in the context of a model for dye-sensitized photocurrent.
Introduction When adsorbed a t an electrode surface, organic dyes serve as sensitive probes of the energetic and 'kinetic-requiremen& for transfer"-3 This is a 'Onsequence
of the charge transfer that can be initiated between dye and substrate when the electrode is illuminated with ra(2) Gerischer, H.; Spitler, M.; Willig, F. In "Electrode Processes 1979"; Bruckenstein, S., Ed.; Electrochemical Society: Princeton, NJ, 1980; p 115.
(1) Gerischer, H.; Willig, F. In "Topics in Current Chemistry";Davison, A., Ed.; Springer: New York, 1976; Vol. 61, p 31. 0022-3654/83/2087-3166$01.50/0
(3) Muller, N.; Papier, G.; CharlC, K.-P.; Willig, F. Ber. Bunsenges. Phys. Chem. 1979, 83, 130.
@ 1983 American Chemical Society
The Journal of Physical Chemistry, Vol. 87, No. 16, 1983 3107
Photooxidation of Thiacyanine Dyes
diation actinic for the dye. The rate and extent of this transfer are primarily dependent on the oxidation and reduction potentials of the excited dye. These potentials of the dye are under control of the experimentalist through a judicious selection of the molecule's excitation energy and its ground-state redox properties. In addition, one has the control over initiation and termination of the reaction that is inherent in a photoreaction. A simple electron exchange between an excited, adsorbed dye and an electrode must occur within the lifetime of the excited state of the dye. This provides a nanosecond window in which to investigate electrontransfer reactions at solids. Models for the ideal behavior of excited molecules at electrode surfaces have been described in detail for insul a t o r ~ , ~metal^,^,^ -~ and semiconductors1~"7as substrates. In the case of insulating organic electrodes, experimental results correlate very well with the predictions of models. At metal electrodes few photoreactions of adsorbed dyes are expected because of rapid quenching of the excited state, and very few have been found. For the photooxidation of dyes at semiconductor electrodes, however, consistent agreement between theory and experiment has not been as good. In an exoergic photooxidation of a dye, the electron transfer from the excited molecule to the conduction band of a semiconductor electrode should result in a quantum efficiency for photocurrent production, GP,approaching unity: where @, is defined as the number of electrons measured as current per photon absorbed by the dye. Values of 0 between 0.5 and 1.0 have been reported for the photooxidtion of dyes at polycrystalline semiconductor electrode^.^^^ However, at well-defined faces of single-crystal electrodes, @ has been found to remain in the range 10-3-10-2.1@14 the models for photoreactions cannot explain the @ values at these best characterized of surfaces, the crystahographic faces of single crystals, then there cannot be great confidence in their application at electrode surfaces less welldefined. There is evidence15that the high values of @, at polycrystalline electrodes fall quickly to the range of 10-2-10-3 upon aging of the electrode in aqueous solutions. Evidently there is a time-dependent modification of the surface of these electrodes which has an effect upon a, that has not been observed at single-crystal surfaces. The intent of this and subsequent work is to explore the grounds for this discrepancy between theory and experiment at single-crystal surfaces. In this inquiry, we also wish to demonstrate the use of a sensitive total internal reflection technique.13 It has been utilized in these experiments to determine aPfor a series of thiacyanine dyes at zrto single-crystal electrodes as a function of the oxidation potential of their excited states. These dyes, thia-n-carbocyanine, where n = 0, 1,2, 3, vary systematically in their ground- and excited-state oxidation poten-
ff
(4) Gerischer, H. In 'Faraday Discussions"; The Chemical Society: London, 1974; Vol. 58. (5) Gerischer, H. Photochem. Photobiol. 1972, 16, 243. (6) Gerischer, H. In 'Physical Chemistry, An Advanced Treatise"; Eying, H., Ed.; Academic Press: New York, 1970; Vol. IXA. (7) Memming, R. Photochem. Photobiol. 1972,16,325. (8) Arden, W.; Fromherz, P. J. Electrochem. SOC.1980, 127, 370. (9) Hada, H.; Yonezawa, Y.; Inaba, H. Ber. Bumenges. Phys. Chem. 1981, 85, 425. (IO)Spitler, M. T.; Calvin, M. J. Chem. Phys. 1977, 66, 4294. (11) Spitler, M.; Calvin, M. J. Chem. Phys. 1977, 67, 5193. (12) Schumaker, R.; Wilson, R. H.; Harris, L. A. J.Electrochem. SOC. 1980, 127, 96. (13) Spitler, M.; Lubke, M.; Gerischer, H. Ber. Bumenges. Phys. Chem. 1979,83, 663. (14) Tributach, H.; Calvin, M. Photochem. Photobiol. 1971, 14, 95. (15) Bressel, B. Ph.D. Dissertation, Technische Universitat, West Berlin, 1982.
4; 'yHxL
DYE/
/
-+---e--
EOS
ELECTROLYTE
,
ZnO
I
i
I
i
I
by-?,
LENS
I
COMPUTER
RECORDER
Figure 1. Experimentalarrangement for laser internal reflection studies is depicted here. A dye laser and an Ar ion laser provide light modulated by an electrooptlc shutter (EOS) to be internally reflected wlthln a ZnO single crystal polished in the form of an internal reflection element. A beam splitter (S) is used to divert a portion of the Incoming light to one of two photodiodes @) to provide a reference signal agalnst which the Intensity of the internally reflected beam may be compared by an ampllfler (A). An external signal generator (0) provides the control potential for a potentiostat (POT) which amplifles the current ( 1 ) produced by the laser pulses and yields an input ( V , ) to a mlcrocomputer which controls the experiment.
tiale over a 0.7-eV range. They also tend to aggregate at low concentrations in aqueous solutions. It will be shown how this aggregation influences @, and how the degree of surface aggregation may be controlled so that the dependence of @, on the dyes' excited-state oxidation potential can be determined. The results will be interpreted in the light of a modeF8 proposed for the photooxidation of dyes at semiconductor surfaces.
Experimental Section Standard photoelectrochemical techniques were employed to obtain photocurrent action spectra and photocurrent voltage curves for these dyes. A three-electrode electrochemical system was used with a ZnO working electrode, a Ag/AgCl reference electrode, and a Pt counterelectrode. The system was potentiostatically controlled with input control potential supplied by a PAR 175 universal programmer. Flat-band potentials were determined through impedance measurements using the lock-in technique. An Oriel 150-W Xe lamp and a Bausch and Lomb high-intensity monochromator enabled illumination of the electrode surface with monochromatic radiation. This light was reflected onto the ZnO surface through a Pyrex window. Before entering the cell the beam was chopped by a PAR 192 variable chopper at frequencies ranging from 15 to 25 Hz. The modulated currents produced at the electrode were measured with a PAR 5204 lock-in analyzer and recorded on an X-Y recorder. The action spectra presented in this work have been corrected for spectral variations in lamp output and monochromator throughput. A computer-controlled total internal reflection system was constructed in order to measure simultaneously photocurrent and absorption of light by the dye adsorbed to the semiconductor surface. The electrochemical cell and
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The Journal of Physical Chemistty, Vol. 87, No. 16, 1983
experimental apparatus for this system are shown in Figure 1. The electrochemical portion of this system functions in a manner similar to the three-electrode system just described except that a flow cell has been used to allow introduction of reagents to the electrolyte at will. A pulsed beam of light is used to excite dye molecules adsorbed to the surface of a ZnO electrode; photocurrent produced at the semiconductor-electrolyte interface is amplified and recorded as a function of time. A t the same time the absorption of light by the adsorbed dye can be monitored through internal reflection spectroscopy (IRS). In the measurement of this absorption, a Lexel 95-4 argon ion laser and a Coherent 599 dye laser were used as light sources. A home-built 350-V pulse generator, triggered by the computer, drove a Lasermetrics Model 3031 electrooptic shutter. This electronically coordinated shutter produced light pulses of duration ranging from 40 ps to minutes. Neutral density filters decreased the intensity of the laser light before it reached the electrode. A fraction of the modulated beam was deflected to a photodiode to serve as a reference measure of beam intensity. The remaining light was then internally reflected by the ZnO electrode and exited onto a second photodiode. The signals from both photodiodes were fed into a differential amplifier and then into an Ithaca Model 1201 low-noise preamplifier. By rotation of a circular neutral density wedge placed in front of the second photodiode, the difference between the signals could be nulled. This was done with only electrolyte in the cell before each experiment. Any subsequent decrease in light intensity detected when dye solution is added to the cell represented the portion of the incoming light absorbed by the dye. That absorption signal could then be monitored by a Biomation 2805 transient recorder and stored by the computer. Concurrently the photocurrent produced was drawn off through a contact at the rear of the electrode. This current was detected with the potentiostat and amplified by a PAR 113 low-noise preamplifier. The resultant signal was fed into a second input channel of a transient recorder or a computer. In this way the time dependence of the photocurrent and absorption could be observed simultaneously. An example of the data from this system is seen in Figure 2. If the light intensity is known, 9, can be calculated from these data by dividing the current pulse by the absorption pulse. Single crystals of ZnO were provided by Dr. R. Helbig of the University of Erlangen-Nurnberg in the form of hexagonal needles grown by vapor deposition. In addition to undoped specimens, crystals lightly doped with indium were also used in these experiments. For use in the standard three-electrode electrochemical cell, the ZnO was cut perpendicular to the C axis. The crystals, 4 mm long and 2-3 mm wide in cross section, were then embedded with RTV silicon rubber glue in cylindrical shells made of Teflon. The electrical contact was made with silver paint. For use in the internal reflection system, the singlecrystal needles were cut to a length of about 5 mm and then ground at the ends at a 45' angle to a final surface polish of 1wm. Since the smoothness of the (1010) prismatic faces was better than X/2, dye sensitization could be studied at these surfaces in a pristine condition. In these experiments crystals with up to three reflections were used at a light intensity of about 1 mW focused to a 0.5 mm diameter spot on the electrode surface. It was found that the tendency of the dyes to aggregate and the a, for these aggregates declined with increasing
Kavassalis and Spltler
3.0
-
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v
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--
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1
500 psec--N
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Flgwe 2. Example of the data produced by the experimental apparatus of Figure 1 is shown here for 3,3'diethyithiacarbocyanine excited by the 528.7-nm line of the argon laser. The absorption of light by the adsorbed dye is shown at the top wlth the resultant current underneath.
use of these electrodes, indicating the need for a reproducible and clean electrode surface. Unfortunately, cleaning of ZnO electrodes with acids or bases etches the surface severely, making the electrode useless for internal reflection studies. Consequently, the electrodes were only used for about a dozen experiments before being discarded. The thiacyanine dyes were made available to us by Prof. Alan Waggoner of the Carnegie Mellon University. These cationic and planar dyes are water soluble but will form aggregates at relatively low solution concentrations. Before use of the dyes as sensitizing agents, their purity was examined by using thin-layer chromatography. Using silica gel and a solvent system of 79.96% CH2C12,19.99% CH30H, and 0.05% CH3COOH,we observed only one spot for each dye. The notation used for the dyes in these experiments is as follows: Disc2(l), 3,3'-diethylthiacyanine; DiSC2(3),3,3'-diethylthiacarbocyanine; DiSC2(5), 3,3'-diethylthiadicarbocyanine;DiSC2(7), 3,3'-diethylthiatricarbocyanine. Dye solutions were prepared by diluting ethanolic stock solutions to the desired concentration using 0.1 M KC1 with the ratio of alcohol to salt solution being about 1:25. However, for 10" M solutions, 20% alcohol was employed to minimize aggregation. Some solutions were prepared with methanol and 0.1 M LiCl as the electrolyte to further minimize aggregation. The final solutions were purged with nitrogen prior to use in the electrochemical cell. Results The photocurrent action spectrum for DiSC2(1)is shown in Figure 3a, where current from only the monomeric form of the adsorbed dye is evident. The red shift of the action
The Journal of Physical Chemistry, Vol. 87, No. 16, 1983 3169
Photooxidation of Thiacyanine Dyes
(0)
400
4 50
SO0
,
550
600
650
1
"E
x
-
t6.I
.4
o-o-o-o-o_6~~~0 ABSORPTION (YJ
Flgure 3. (a) Photocurrent action spectra and solution absorption spectra are shown for DiSC,(l) and DiSC2(3). The action spectrum of DiSCA1) (II), taken at a solution concentration of 3.5 X lo-' M, is red shifted from the dye's absorption spectrum (I). The absorption spectrum of DiSC,(3) (111) is contrasted with action spectra at concentrations of (IV) 1.6 X (V) 6.0 X lo-', and (VI) 6.5 X lo-' M. Concentrations of I and I11 are 1 X and 5 X lo-' M. The structure of this thia-n-carbocyanine series is given in part a, where DiSCAl) is n = 0. (b) a,, data from the laser IRS system are plotted here as a function of absorption of the adsorbed dye for DISC2(1) and DISCA3) at several wavelengths. These wavelengths are indicated in the action spectra of part a.
spectrum relative to the solution spectrum results from a corresponding shift in the absorption spectrum of the adsorbed dye.'JOJ' Using the IRS cell, we determined 9, as the dye adsorbed onto the surface. In this experiment the concentration of the dye in the electrolyte can be increased slowly so that aPcan be determined as the amount of adsorbed dye increases. The resultant data are plotted in Figure 3b as a function of the absorption of the adsorbed dye layer. These results are from a single experiment which was found typical of this dye's behavior. Throughout these experiments the electrode was biased at a potential of +0.25 V vs. SCE where a plateau in current was attained in the photocurrent voltage curve. For DiSC2(3) the dimer form appears to play a significant role in the action spectra as the solution concentration of the dye increases. This is depicted in Figure 3a, where the dimer peak at 530 nm can attain importance equal to the monomer at 575 nm. The IRS data in Figure 3b show that a, at the monomer wavelength remains relatively constant with increasing surface coverage whereas the dimer at 530 nm declines by a factor of three. With Disc&) in the electrolyte, aggregation can become the predominate feature in the action spectra. This is seen in Figure 4a, where low concentrations of dye result in a monomeric action spectrum, but higher dye concentrations result in H-band absorption and photocurrent from aggregates of the adsorbed dye at 575 nm. The transition between the two extremes is a gradual and monotonic function of the DiSC,(5) solution concentration. In Figure
2
I
DtSC, ( 7 )
I
3
4 ABSORPTION (Yd
6
Figure 4. (a) Photocurrent action spectra and solution absorption spectra are ghren for DiSCA5) and DiSC,(7). The absorption spectrum of DISC#) (I) is compared with action spectra for this dye at (11) 5 X lo-', (111) 9 X lo-', and (IV) 2 X M. The action spectrum (VI) at a concentration of 5 X 10" M of DiSC,(7) is shown red shifted from the electrolyte spectrum (V) of the dye. Concentration of I is 3 X lo-' M. (b) data from the laser IRS system are plotted here as a function of absorption of the adsorbed dye for DiSC,(5) and DiSCA7) at several wavelengths. The wavelengths are indicated in part a.
aP
TABLE I: @ p at the Lowest Absorption Value for Each of the Thiacyanine Dyes DiSC, (1) DiSC, ( 3 )
a,,%
DiSC, ( 5 )
1 . 2 t 0.1 1.1 t 0.1 0.40
t
0.05
DiSC, ( 7 )
0 . 2 5 t 0.03
4b the IRS measurements show that aPdeclines slightly for both the H-band aggregate and the monomer as the amount of adsorbed dye increases. Experimentation with DiSC,(7) was more difficult as solutions of the dye bleached upon standing; therefore, solutions were deoxygenated by bubbling argon through them as they were used. The action spectra for this dye are shown in Figure 4a. Little of the aggregation evident in the absorption spectrum of the electrolyte in this figure is reflected in the action spectrum. Figure 4b shows that 9, for this dye falls much more quickly with increasing absorption than the other dyes. The steepness of this decline may be attributed to the low extinction of the dye monomer at this wavelength. In Table I are listed estimates of aPfor the monomer forms of each of these dyes. This range of 0.2-1.270 has been taken from Figure 3b and 4b at the lowest recorded absorption. Given the tendency of these dyes to aggregate on the electrode surface, this limit is the best estimate that can be made for the b, of the monomer dye because the monochromatic photometry of the laser does not provide sufficient information for an unambiguous determination of the degree of aggregation of the dye on the surface or the extent of its surface coverage of the electrode. Discussion Observed Behavior of Sensitized Photocurrent. All of
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The Journal of Physical Chemistry, Vol. 87, No. 16, 1983
the dyes in this vinylogous series produce anodic photocurrents when adsorbed at the ZnO surface. This is not unexpected as they all meet the criterion for oxidation that their excited-state energy levels have a potential more negative than that of the ZnO conduction band. These energy levels for the electron in the excited state of the dye as monomer can be calculated if its oxidation potential, excitation energy, and rearrangement energy are known.’~lS Taking a rearrangement energy for these dyes of 0.3 eV,2*3this level, EoDedon, vs. Ag/AgCl is -1.5 V for DiSC2(1),-1.0 V for DiSC2(3),-0.9 V for Disc2@),and -0.8 V for DiSC2(7). From impedance measurements an estimate for the energy of the ZnO conduction band of -0.6 V was obtained at pH 6 which places it at an energy able to accept electrons from all of these dyes. The action spectra of Figures 3 and 4 show that the aggregate forms of the dye can also sensitize photocurrent. The photocurrent peak blue shifted from the monomer is indicative of the absorption of an H-band aggregate. This form of the dye is composed of a parallel stack of dye molecules with their centers aligned perpendicular to the plane of the dye molecule; this whole unit is adsorbed with the long side of each molecule in contact with the surface.16 H-band aggregates will have an excited donor level with a potential negative of the monomer if there is no significant difference between the oxidation potential of the monomer and aggregate forms of the dye. The extent of this aggregate sensitization can be controlled by increasing the solution concentration of the dye or the KC1 electrolyte, either of which determines the amount of dye adsorption at the surface.1° The effect of increasing dye aggregation or adsorption on 9,is variable as the data of Figure 3b and 4b show. A fall in 9,is evident for DiSC2(7)at 630 nm at a wavelength where the aggregate in solution is known to absorb, indicating that the aggregate adsorbs readily but does not sensitize photocurrent. The cause of such declines in 9 is unclear and probably complex in nature. For DiSC2(7y it is likely that multilayers of dye are formed which would greatly decrease the probability of a successful charge transfer to the electrode from a dye on the outer layer. This behavior contrasts with DiSC2(5)where the H-band aggregate sensitizes photocurrent with an efficiency near that of the monomer. For DiSC2(3) at the monomer peak of 570 nm, 9, remains constant as more dye adsorbs, implying that all adsorbed dye molecules have the same Yet in Figure 2 the decline in current for a dye is unaccompanied by a corresponding fall in absorption, showing that this is not the case; the adsorbed dye molecules do have different values for a,, as has been previously noted.13J4 These data are compatible only in the circumstance in which the majority of the adsorbed dye functions as an antenna which absorbs the light and transfers excitation to molecules with the highest With time these molecules are oxidized and the observed declines. The role of energy transfer in this photooxidation could be more closely examined if the molecules were adsorbed more than 50 distant from one another. For DiSC2(5)this would correspond to a surface coverage of less than 0.3%, which is just out of the range of these experiments and is a subject for more sensitive experiments with these systems. Aggregation appears to play an important role in the sensitization of photocurrent by these cyanine dyes. Their further study will require experimental apparatus capable of a more complete spectral characterization of the ad-
+,
(16) James, T. H., Ed.“The Theory of the Photographic Process” 4th ed.; Macmillan: New York, 1977 and references therein.
K.tT
ZnO -1
0
+I
+2
semlconductor
Flgure 5. Model for dye-sensitized electron transfer at semiconductors is presented here where the electron in the dye’s excited state Eo,,.& is captured with a rate constant k , by an intermediate state in the gray energy region depicted here. From this state it may be drawn off as current with a rate constant k , or return to the oxidized dye at energy level EoD+with rate constant k,.
sorbed dye. This capability has been developed, and work is in progress using Ti02 and SrTi03 electrodes in an internal reflection arrangement. Models for Dye Sensitized Photocurrent. As is seen in Table I, excitation of the monomer forms of these dyes results in photocurrent with efficiencies that range between 0.2 % and 1.2 % . Competing reactions must therefore divert 99% of the excited electrons away from photocurrent production. There are two possible candidates for this competition both of which can be assumed to be faster than internal relaxation of the excited dye. First, an excited dye may be quenched by energy transfer to some species on the surface which cannot induce photocurrent. Given the energy transfer among the adsorbed dye molecule^?'^ it would be possible for the excitation to migrate on the surface until it reached a quenching site. The second possibility involves a back-reaction in which the injected electron returns to the oxidized dye molecule.2*8This would be possible only if the electron were trapped at some intermediate state in the surface region before it is drawn off into the electrode bulk as current. This scheme is depicted in Figure 5 where it is indicated how the electron can return from the intermediate state to the dye and short-circuit the photocurrent. An electron with energy EoDb in the ground state of the dye is elevated by a photon of energy hv to a level EoDedm where it can be captured by an intermediate state with a rate constant ket. The electron can either return to the oxidized dye at energy EoD+(k,) or be drawn off as current (kinj). With this scheme aPcan be written2 as kinj ket[tl 9, = (1) ket[tl + kfl + kq kinj + krev where kinjis the rate constant for electron injection into the semiconductor, [t] is the concentration of these surface traps, kfl = rate constant of fluorescence, and kq = com(17) Miyasaka, T.; Watanabe, T.; Fujishima, A.; Honda, K. Nature (London) 1979,277,638.
J. Phys. Chem. 1983,87,3171-3173
3171
b i n d rate constant for all other relaxation pathways. This is no fortuitous, complementary variation of the rate of expression can be seen as the product of the quantum energy-transfer quenching and concentration of surface efficiencies for electron transfer from the excited dye to traps to give this 99% figure for all four dyes. If the back-reaction is responsible for any significant fraction of the surface trap and for electron injection from this trap into the bulk. This back-reaction model attributes low this quenching, this result would imply that the product values of aP to a large k,,, in this back-reaction. In conk,,[t] in eq 1 remains constant over the 0.7-eV range that trast, high values for aptsuch as those reported for fresh the excited states of these dyes span. With these oxidations all being exoergic, k,, can be expected to stay conpolycrystalline substrates, would imply that k,,, is insignificant and that the role of surface states is minimal. stant, implying that the concentration of surface traps is This mechanism is analogous to one found in photothe same over 0.7 eV in energy. This is not impossible behavior for a surface state, but, at the least, it would be graphic systems for the dye sensitization of silver halides. There an intermediate trapping state plays a significant very unu~ual.'~ role in latent image formation and is more clearly defmed.16 These two alternatives could be distinguished with a fast The Ag+ ion functions as an irreversible trap which results spectroscopic analysis of the adsorbed dye layer following pulsed excitation. Energy-transfer quenching should not in a quantum efficiency for latent image formation that lead to production of transient radical intermediates often approaches unity.le In the photocurrent case, however, its identity is unknown and its existence has been whereas a back-reaction mechanism would. The appropostulated to explain, among other observations, low values priate internal reflection experiments are now being deof aPobserved at single-crystal semiconductor s u r f a c e ~ . ~ ~ ~ signed J~ to resolve this question. The concentration of these traps need not be large. With Acknowledgment. For support of this work we are inthe fast energy transfer between dye molecules at an debted to the Mount Holyoke College Department of electrode surface the excitation should be able to travel Chemistry, a William and Flora Hewlett Foundation Grant among the molecules until such a trap is encountered and of the Research Corp. for instrumentation, the National recombination can occur. Science Foundation 69A Program for an instrumentation The data of these experiments are not unequivocal in grant, the Department of Energy, Office of Basic Energy assigning the relative roles of these two quenching mechSciences, and NATO for travjl funds. We thank Dr. anisms. However, they do provide sufficient information Helbig for the donation of the ZnO single crystals and Dr. to draw conclusions about the energetic distribution of Waggoner for the dyes. surface traps involved in the back-reaction mechanism. It is clear that current production is quenched with an efRegistry No. 1, 20766-55-6; 3, 18403-49-1; 5, 7187-55-5; 7, ficiency of 99% for these dyes; one can assume that there 23178-68-9; ZnO, 1314-13-2. (18)Spitler, M. In 'Photoelectrochemistry: Fundamental Processes and Measurement Techniques"; Wallace, W., Nozik, A,, Deb, S.,Eds.; Electrochemical Society: Princeton, NJ, 1982;p 282.
(19)Morrison, S. R. 'Electrochemistry at Semiconductor and Oxidized Metal Electrodes": Plenum Press: New York, 1980.
Mean Field Theory of Fused Salts Robert B. McBroom and Donald A. McQuarrle' Department of Chemlstry, Unlverslty of Callfornia, Davls, Callfornk, 956 16 (Recelved: October 7, 1982; In Final Form: January 10, 1983)
The mean field theory of fluids of Longuet-Higginsand Widom is applied to fused salts and compared to Monte Carlo data and molecular dynamics data.
In many ways the study of fused salts is easier than that of aqueous electrolytes, because water, which is difficult to model, is not present. In the past, the only method for the study of Coulombic fluids was Debye-Huckel the0ry.l While the theory is physically intuitive, it is applicable only to very dilute solutions.2 The advent of the integral equation method in modern liquid theory has improved the situation to the point where the thermodynamic properties of Coulombic systems ranging from very dilute -~ up to fused salt concentrations can be ~ b t a i n e d . ~The
simplest of these theories, the mean spherical approxim a t i ~ nhas , ~ the ~ advantage of being analytic and gives fairly good results for fused salts.8 Some of the other integral equation theories, such as the extended mean spherical approximation9 and the hypernetted chain approximation?l0 give very good results but must be solved numerically. This can be time-consuming and expensive. Experimental evidence has shown that simple liquids have structures that are similar to the structure of a hypothetical hard-sphere liquid, l1 that is, a collection of hard
(1) P. Debye and F. Hackel, Phys. Z., 24, 185 (1923). (2) J. G.Kirkwood and J. C. Poirier, J.Phys. Chem., 68,591(1954). (3)M.J. Gillan, Phys. Chem. Liq., 8, 121 (1978). (4)D. A. McQuarrie, "Statistical Mechanics", Harper and Row, New York, 1975. (5)J. P. Hansen and I. R. McDonald, "Theory of Simple Liquids", Academic Press, London, 1976.
(6)E. Waisman and J. L. Lebowitz, J. Chem. Phys., 56, 3086 (1972). (7)E. Waisman and J. L. Lebowitz, J. Chem. Phys., 56, 3093 (1972). (8)M. C. Abramo, C. Caccamo, and G. Pizzimenti, Phys. Chem. Liq., 6,167 (1977). (9)M. Medina-Noyola and D. A. McQuarrie,J. Chem. Phys., 74,3025 (1981). (IO) B. Larsen, J. Chem. Phys., 68,4511 (1978).
0022-365418312087-3171$01.50/0
0 1983 American Chemical Society
