.T. Photochem. Photobiol. A: Chem., 64 (1992) 211-223 211

Kinetic study of photo-induced electron transfer reactions sensitized by colloidal CdS

Alison Green and Andrew Mills Depariment of Chemkq, University College of Swansea, Singleton Park, Swanseu, SA2 8PP WW

(Received September 30, 1991; accepted October 24, 1991)

Abstract

The kinetics of the recovery of the photoinduced transient bleaching of colloidal CdS in the presence of different electron acceptors are examined. In the presence of the zwitterionic viologen, N,N’-dipropyl-2,2’-bipyridinium disulphonate, excitation of colloidal CdS at dif- ferent flash intensities generates a series of decay profiles which are superimposed when normalized. The shape of the decay curves are as predicted by a first-order activation- controlled model for a log-normal distribution of particles sizes. In contrast, the variation in flash intensity in the presence of a second viologen, N,N’-dipropyl-4,4’-bipyridinium sulphonate, generates normalized decay traces which broaden with increasing flash intensity. This behaviour is predicted by a zero-order diffusion-controlled model for a log-normal distribution of particle radii. The photoreduction of a number of other oxidants sensitized by colloidal CdS is examined and the shape of the decay kinetics interpreted via either the first- or zero-order kinetics models. The rate constants and activation energies derived using these models are consistent with the values expected for an activation- or diffusion- controlled reaction.

1. Introduction

The study of photoinduced electron transfer reactions across the semiconduc- tor-solution interface is important in obtaining a better understanding of the role of semiconductor particles in a wide range of photo-oxidation and photoreduction reactions [l]. Colloidal dispersions of semiconductor materials provide an ideal medium for studying electron transfer reactions; the optically transparent nature of the solutions facilitates the ready detection of reaction intermediates and products by fast time- resolved techniques such as flash photolysis [2-S] and pulse radiolysis [2].

On photoflash excitation, several semiconductors (e.g. CdS [5-g], PbS [9], CdSe [lo] and In& [ll]) undergo reversible changes in their corresponding absorption spectra; these transient bleachings and absorbances have been attributed to photo- generated charge carriers trapped on the particles. Whilst there have been numerous qualitative studies of the transient bleachings (and/or absorbances) associated with these electrons or holes, the kinetics of such processes often appear complex and little attempt has been made at a quantitative interpretation of the kinetics.

Colloidal dispersions will often contain a discrete range of particle sizes with a distribution reasonably described by the log-normal (log-gaussian) distribution law. The non-exponential kinetics observed in colloidal TiOz and CdS photosystems, and associated with electron transfer across the semiconductor-solution interface, have

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212

been rationalized using two related kinetic models, i.e. the first-order and zero-order kinetic models, based on the common assumption of a range of rate constants arising from a log-normal distribution of particle sizes [5, 6, 12-141. If the reaction between the photogenerated electrons and an excess of quencher is governed by an activation- controlled electron transfer step, the kinetics can be described by what we have termed the first-order model. In addition to a log-normal distribution in particle size, the first- order model assumes that the reaction is first order with respect to the concentration of photogenerated electrons and that, for particles of radius r, the pseudo-first-order rate constant is directly dependent upon the surface area and therefore on f* [6, 12, 141.

The second of these two models, the zero-order model, can be used to interpret the very different kinetics observed when the reaction between the photogenerated trapped electrons on the CdS particles and the electron acceptor is limited by the rate of diffusion of the quencher to the colloidal particles. In addition to a log-normal distribution in particle size, the zero-order model assumes that the rate of reaction will be zero order with respect to the photogenerated electrons on the semiconductor particle (i.e. that the number of trapped electrons per particle is much greater than 1) and, for particles of radius r, that the rate constant depends directly upon particle size, Le. r [6, 141.

In this paper the two kinetic models are used to analyse the observed kinetics of the transient bleaching recoveq in the absorption spectrum of colloidal Cd!3 in the presence of a number of different oxidants. The reaction of the two neutral viologens, N,N’-dipropyl-2,2’-bipyridinium disulphonate (DQS) [IS] and N,N’-dipropyl-4,4’-bi- pyridinium sulphate (PVS) [16] with the trapped conduction band electrons is used to highlight salient features of the two dissimilar but related models.

2. Materials

A stable yellow colloid was prepared by rapid addition of 2.5 cm3 of Cd(NO& solution (2X lo-* mol dmM3) to 95 cm3 of a hexametaphosphate stabilizer (1 x lo-* mol dme3) plus 2.5 cm3 of Na2S solution (2x lo-* mol dm-3). In order to obtain consistent results the colloid was left to “age” under ambient conditions for 24 h prior to addition of electron donor, which was either ascorbic acid (lo-’ mol dme3; pH 4.5) or, in all studies involving viologens, cysteine (lo-’ mol dmm3; pH 7.0). The colloidal dispersion had an average particle radius of 8 nm, as determined by electron microscopy_

The zwitterionic viologens PVS and DQS were purchased from Sigma, methyl viologen dichloride (M?+) from Aldrich and ail other materials were obtained from B.D.H. in their purest form available.

3. Methods

Flash photolysis was carried out using a standard Applied Photophysics 2005 instrument (pulse duration, 10 p); the output of the flash lamps was filtered with a Kodak B gelatin filter to remove light of A < 410 nm. The solutions were purged with NZ for at least 20 min prior to flashing. The transient decay data were recorded on a Gould digital storage oscilloscope (054020) and transferred to a BBC microcomputer for storage and processing. All solutions were flashed in a 10 cm cell, with the exception

213

of the temperature-controlled outer water jacket was used.

4. Theory

experiments in which an 8 cm3 cell with a thermostatted

Photoflash excitation of an aqueous colloidal dispersion of CdS (5X 10s4 mol dme3) induces a transient bleaching in the absorption spectrum of CdS; this bleaching has been attributed to photogenerated electrons trapped on the particles [5].

It is assumed that the observed transient bleaching signal provides a direct reflection of the concentration of photogenerated electrons via Beer’s law and, from previous work, it appears that the magnitude of the bleaching in absorbance depends directly upon the square of the flash intensity, i.e. AAm1,‘/2 at t=O [14].

In both the zero- and first-order models the polydispersivity of the colloidal sol is described by the log-normal (log-gaussian) distribution law

n =ri exp( -x2) (1)

where n is the number of particles of radius r, rS is the number of particles with number average radius f, and p is a measure of the distribution width of the colloid dispersion.

For the first-order kinetic model, it can be shown 1141 that the ratio of the total concentration of electrons at time t to the total concentration directly after the flash (i.e. t =0) is given by

C,(total) X-W = C

C,_&total) X- -m exp(3pX) exp( -x2) exp[ - r exp(2px)J

/ x-0

C expCJf-4 exp(--X2) x--ca

(3)

where

r = k,,4#L [Q]t (4)

and where k,, is the rate constant for transfer of the electron across the Helmholtz layer to the quencher [Q], and L is Avogadro’s number.

As stated previously, it is assumed that the observed signal is directly proportional to the concentration of photogenerated electrons and, since T and “real time” t are directly related, it follows that

AA, _ CAtotal) C,(total)

M*-0 C,_c(totat) = C,_o(total) (5)

Thus a measure of the distribution width of the colloid can be determined by matching a plot of the experimental data LUJAA r_~ OS. in f, to a theoretical plot of C,(total)/ C&total) vs. In 7 calculated using eqn. (3) of the first-order kinetic model and a value of p which provides a theoretical curve of optimum fit to the experimental data. Once superimposed, the numerical difference between the values of the x coordinated axes of the theoretical and experimental curves (=ln r-ln t) yields a value for R,, the quenching rate constant for the number average particles, since

214

In J& = ln(k,,47r?[Q]L) = In T- In f (6)

From a value for & the heterogeneous rate constant Whet can be calculated, since I;het is given by

According to the zero-order diffusion-controlled model [14], the ratio of the total electron concentration is given by

CT(tota1) Jp ag = c

&_e(total) *- -- exp(3px) exp( -x’)[l - T exp( - 2&l

/ J-e

C exp(3k=) exp(-x2) x--m

where

T 4wD[Q]t = PKJJ1~ (9)

and where D is the sum of the diffusion coefficients for the CdS particle and quencher Q, Kt is a proportionality constant and I,, the incident flash intensity.

In an analogous manner to the first-order model, a p value for the colloid can be found by matching a theoretical CT(total)/C T_a(total) ‘us. In T plot (calculated using eqn. (8) of the zero-order kinetic model and a p value which provides the optimum fit) to the experimental AAJMI_,, vs. In r profile. Once again the number average rate constant Roe is calculated from the difference between In T and In t, i.e.

=ln T-ln t 00)

The gradient of a plot of /& US. [Q] when multiplied by the average number iV,( =K110’nf3L) of electrons per particle, previously estimated to be about 181 [14], provides an estimate of R,i, the number-averaged diffusion-controlled rate constant.

A comparison of eqn. (4) of the first-order model with eqn. (9) of the zero-order model suggests that the kinetics described by the two different models will exhibit contrasting behaviour with respect to the initial intensity of the flash used. Thus, if the first-order model is applicable, a series of transient bleaching recovery profiles generated using different flash intensities will superimpose upon one another when normalized (i.e. when plotted in the form of AAJAA,,, vs. t). In contrast, a parallel series of recovery curves obtained in the presence of a “zero-order quencher” will produce a series of normalized decay curves (M&4,_, W.S. t) which broaden with increasing flash intensity and therefore do not superimpose. However, if the same data are plotted in the form of AAJAA,,, ~5. In t, the curves will all appear identical in shape, i.e. they will be superimposable.

5. Results and discussion

The decay of the photoinduced transient bleaching of colloidal CdS (5 x lop4 mol dmW3) was studied as a function of flash intensity (flash energy, %I@; range studied

215

28-190 J; flash intensity a flash energy) in the presence of the neutral viologen DQS (5X 10m5 mol dmd3). The resulting data when plotted in the form of -ln(AA,/AA,_O) vs. t are illustrated in Fig. 1 and all superimpose upon one another and are identical in shape with a first-order (activation-controlled) plot (fnll curve in Fig. 1) of C,(total)l C,_,,(total) vs. 7 calculated for a p value of 0.9 using eqn. (3) of the first-order kinetic model.

In one set of experiments involving flash photolysis of the CdS colloid at a fixed flash intensity (72 J), the concentration of DQS was varied over the range 5.0~ 10-‘-3,67x 10e5 mol dms3. The resultant normalized decay curves (i.e. data plotted in the form AA,lAA,_O vs. In t) were well matched in shape to a first-order theoretical plot of C,(total)/C,_O(total) VS. In r, calculated using eqn. (3) for p= 1.0. From this work, a series of Lo values as a function of [DQS] were calculated from the experimental data using eqn. (6). The plot of f, ‘us. [DQS] is illustrated in Fig. 2 and is a good straight line (six points; r= 0.9979; m= (6.63 kO.2) X 105 mol-’ dm3 s -‘; c = 4.2Sf0.4 SK’) and, from the gradient fihct= 6.63 X lo5 mol-’ dm3 s-l. This value for I& is well below that expected for a diffusion-controlled reaction involving particles of average radius 8 nm; in the latter case, & is expected to be 6.1 x 10” mol-’ dm3 s-l [17].

In another set of experiments, k. was studied as a function of temperature over the range 15-55 “C using [DQS] =3.34x lo-’ mol dmP3. The Arrhenius plot of the data is illustrated in Fig. 3 and is a good straight line (six points; t=0.9986; m = - (3.67 & 0.1) x 103; c = 14.9& 0.3); from the gradient of this plot an activation

0

0.5

1.0

1.5

2.0

2.5 4 6

Urns

Fig. 1. Transient decay curves obtained on flashing a CdS colloid (5X10-’ mol drn-q with DQS as a quencher (5 x lo-’ mol &n-j>, where the flash energies are 8 J (O), 11.5 J (0), 15 J (A), 17.25 J (A) and 19.5 J (I) and the data are illustrated as -In(AA,lAA,_,) 11s. t: -, plot of - ln[C,(total)/C,_,(total)] WS. 7, calculated using eqn. (3) of the first-order model for p=O.9 and r=1 (ms)/28.

216

30

25

20

my” 15

10

5

0 0 1 2 3 4

[DC!Sl/lO~” mof dm’

Fig. 2. A plot of ko (the number-averaged quenching rate constant) 2)s. [DQS] (5~10~~ to

3.67 X 10m5 mol dmm3) obtained using a CdS colloid (5 x 10m4 mol dmB3) and cysteine (IO-’ mol dme3) as the electron donor, where the quenching process is described by the first-order model with p= 1.0.

Fig. 3. An Arrhenius plot of In io W. T-* (where [DQS] = 3.34 X 10F5 mol dm-‘). The gradient of this graph yields an activation energy of 30.5 kJ mol-‘.

energy of 30.5 kJ moi- ’ was calculated, which is significantly higher than the value of 19 kJ mol-l predicted for a diffusion-controlled process [17], and again consistent with the first-order model assumption of an activation-controlled reaction.

In a parallel series of experiments to those initially described above for DQS, a solution of the second zwitterionic viologen PVS (3.3X 10W6 mol dmv3) was subjected to flash excitation over the flash energy range 28-200 J; the resultant normalized experimental data are illustrated in Fig. 4(a). In contrast with the findings for DQS, for PVS the decay curves do not superimpose but rather broaden out with increasing flash intensity. In addition, the same data when plotted in the form M,/M,_, vs. lnt produce a series of curves all of the same shape, although each curve must be shifted along the x axis to different extents in order to superimpose on each other and with a theoretical zero-order plot of C~total)/CT_O(total) ZIS. In T for p= 1.0 (full curve in Fig. 4(b)). All these findings are indicative of a zero-order diffusion-controlled reaction.

217

(b) InT or (x+lnt)

Fig. 4. (a) Transient decay data obtained on excitation of a CdS colloid (5 X 10e4 mol dm-‘), using cysteine (lo-’ mol dmv3) as the electron donor, at Aash energies of 7.75 J (O), 11.5 J (O), 14.25 J (A), 17.5 J (A) and 20 J (I), with PVS as an electron acceptor. The decay traces are plotted as -ln(AA,/hA,,,~ w.s. t (ms). (b) The same data as illustrated in (a), but now plotted in the form AAl/L4,+, ‘L)s. (x+lnt): -, plot of C~total)/C,_,(total) vs. In T calculated using eqn. (8) of the zero-order model, where p = 1.0.

The quantity “x”, i.e. the distance that each experimental curve must be shifted along the x axis in order to coincide with the zero order theoretical curve of the same shape, is given by the expression

Thus a plot of 3” US. lnf(flash energy)lR] should give a straight line of unity gradient; the plot of this experimental data for PVS is illustrated in Fig. 5 (five points; r= - 0.9971; m = - 0.98 Jt 0.04; c = 5.1& 0.01) and the value of the gradient m = - 0.98 is in excellent agreement with the value of - 1 predicted by the zero-order model.

In another set of experiments at constant flash intensity (72 J), the concentration of PVS was varied over the range (0-5)X lo-’ mol dmm3, and the shapes of the decay profiles were found to be in close agreement to a theoretical plot of Cr(total)/C,_,(total) vs. In T calculated using eqn. (8) of the zero-order model for p= 1.0. The gradient of a plot of & vs. [PVSj illustrated in Fig. 6 (five points: r= 0.9993; m = (1.01 f 0.02) X lo9 mol-’ dm3 s-*; c = (5.78 f 0.64) x 102 s-l) when multiplied by the average number N, (= 181) of electrons per number average particle is 1.84X 1O1l mol dm3 s-l and is equal to kdie< This calculated value of kdi* is slightly higher than the value expected

3.4

3.2

3.0

x

2.9

2.6

2.4 1.7 1.9 2.1 23

In (flash energy)“’ 2.5 2.7

Fig. 5. A plot of “x” W_ In[(flash energy)‘“] from the data illustrated in Fig. 4(b).

0’ I 0 1 2 3 4 5

LPVSI/lO’ mol dm.3

Fig. 6. A graph of Lo., the number-averaged rate constant, ws. [PVS] ([CdS] =5x lo-’ mol dmT3), over the range [PVS]= (0-5)~10-~ mol dmm3, obtained for a zero-order diffusion- controlled quenching process with a p value of 1.0.

219

for a diffusion-controlled process involving particles of average radius 8 nm, i.e. R*i, c- 6.1~10” mol-’ dm3 s-l [17].

In another set of experiments L o’ was studied as a function of temperature over the range 16.5-61.5 “C, using [PVS] =5 x lop6 mol dme3. An Arrhenius plot of the data is illustrated in Fig. 7; it shows a good straight line (six points; r= - 0.9952; m = - (2.15 f 0.09) X Id; c = 15.7 f 0.3) and from the gradient a value of 17.8 kJ mol-t for the activation energy was calculated which is close to that expected for a diffusion- controlled reaction, i.e. about I9 kJ mol-’ [17].

The photosensitized reduction of a number of other electron acceptors by colloidal CdS was also investigated using a similar procedure to that described for DQS and PVS. Thus, by varying the incident flash intensity for a fixed quencher concentration, it was possible, given the contrasting kinetics exhibited by first-order and zero-order quenchers as a function of flash intensity, to distinguish which of the two related log- gaussian kinetic schemes was applicable for the analysis of the observed transient bleaching recovery curves for the quencher under examination, With the appropriate kinetic model identified, the kinetics of electron transfer were fitted to a model-derived theoretical C,,dtotal)/C ,,_,(total) vs. ln(G’) curve (the distribution width p of the colloid used in this work was always found to lie in the range 0.9-1.0 [6]), and the quenching rate constants and activation energies were obtained using the same procedure as that described above for the two zwitterionic viologens above, DQS and PVS. The results of this work are collected in Table 1 together with the standard redox potentials for the quenchers used.

The slow rate of electron transfer between colloidal CdS and the quencher DQS is most probably due to the very negative reduction potential of the DQS-DQS’- couple. The redox potential of a photogenerated electron trapped on a CdS particle is unlikely to be more reducing than the electrons in the conduction band of CdS. Since E.=+ (CDS)= -0.66 V with respect to a normal hydrogen electrode, it appears likely that electron transfer to DQS is thermodynamically non-spontaneous and therefore, if it occurs, that it is likely to be via an activation-controlled rather than a diffusion- controlled reaction. In comparison with DQS, the reduction potentials of PVS, w+ and methyl orange are sufficiently less negative than electron transfer is thermo- dynamically spontaneous. It appears that with these three quenchers an over-potential

E

8.6 -

6.4 -

2.9 3.0 3.1 3.2 3.3 3.4 3.5 l/T (10%‘)

Fig. 7. An Arrhenius plot of In J&. vs. T-’ ([CdS] = 5 X low4 mol dm-‘; [PVS] =5 X 10e6 mol dms3); the gradient provides an activation energy of 17.8 W mol-‘.

TABLE 1

Quenching rate constants and activation energies derived from A-4,&4,,, vx In t curves

Quencher Redox &ct potential (mol-’ dm3 s-*)

kiiff (mol-l dm3 s-l)

E

(lZ mol-‘)

02 Cd’+ Ni2+ DQS PVS MV+ Methyl orange

‘From ref. 15. bFrom ref. 16. SFrom ref. 14. dFrom ref. 18.

0.97 3.8 x 104 82 - 0.40 7.4 x 16 37 - 0.25 1.06x 104 35 - 0.75” 6.63 x 16 31 - 0.41b 1.84 x 10” 18 - 0.44 3.4x10”= 21 - O.Old 6.95 x 10” 17

of more than 200 mV is sufficient to make the electron transfer reaction diffusion controlled, thus indicating that k,, is very high for each of these three quenchers.

For the remaining quenchers, despite similar or substantially more favourable overpotentials for electron transfer than PVS, h4Vzc and methyl orange, all the reactions appear to be activation controlled, implying that in each case kel is substantially lower in comparison with PVS, MS@+ and methyl orange. It is worth noting that, although O2 appears, on an overpotential argument, to be a likely candidate for diffnsion- controlled quenching, it is well known that the O,H,O couple acts as a highly irreversible couple on most materials; therefore k,, is likely to be exceedingly small and thus the reaction could very easily be activation controlled as appears to be the case from the results of this work.

6. Conclusions

At a fixed concentration of the zwitterionic viologen DQS, flash excitation of a CdS colloid at different energies gives rise to transient bleaching decay curves which obey the first-order kinetic model and, in accordance with the model, the normalized data curves all superimpose. In contrast, in the presence of the zwitterionic viologen PVS, a variation in flash intensity generates a series of decay profiles which when normalized do not superimpose; in this case the kinetics of the reaction are described by the zero-order kinetic model.

The variation in transient bleaching recovery kinetics as a function of flash intensity was found to provide a simple method of establishing which of the two log-normal kinetic models it was appropriate to apply in the analysis of the kinetic data. The CdS-sensitized photoreduction of 02, Ni’+ and Cd’+ was found to obey the first- order model, and the reduction of methyl orange and IvW+ the zero-order model.

The values for the rate constants derived from the experimental data agree well with those predicted by the two kinetic schemes and provide evidence to support the initial categorization of the transient recovery kinetics into either an activation- or a difhrsion-controlled process. From this work it appears that the two related log-normal

221

models can be used to rationalize the complex non-exponential kinetics of photoinduced electron transfer between colloidal CdS particles and a number of different oxidants in solution.

Acknowledgment

We thank the Science and Engineering Research Council for supporting this work.

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