P. M. SCHWARTZ, R. A. BLAKELEY, AND B. B. ROBINSON
1868
Efficiency of the Electrochemiluminescent Process by P. M. Schwartz, R. A. Blakeley, and B. B. Robinson* R C A Laboratories, Princeton, New Jersey 08640 (Received November 11, 1071) Publication costs assisted by RCA Laboratories
A steady-state analysis is presented for electrochemiluminescence produced by a periodic driving voltage. The light emission efficiency is calculated and the results are compared with measurements made on a system of rubrene-tetra-n-butylammonium perchlorate-benzonitrile. The theory indicates that the losses inherent in cyclic operation should only limit the quantum efficiencyto 82.8% if singlet excited states are created directly and 41.4% if they are created by triplet annihilation. The measured differential quantum efficiency is 8.7%. The observation that the average rubrene molecule emits many photons before it is destroyed indicates that the spurious reactions which limit cell life should not limit cell efficiency. Since the singlet fluorescence of rubrene is very efficientand the triplet states are highly vulnerable to quenching reactions, it is concluded that triplet reactions play a dominant role in the cell process. The observed efficiency is quite competitive with those observed in electroluminescent diodes and indicates that ecl systems would make useful devices if cell lifetimes can be extended.
Introduction
+
A+ 2e- +A(4) The phenomenon of electrochemiluminescence (eel) A+ A- +A* A (5) has been studied experimentally and theoretically by a nA* +nA hv number of u7orkers.l Only a small part of this work has (6) been devoted to the efficiency of the eel process. In A* &--,A Q' (7) addition, all the theoretical analysis has been pertinent Here, A represents a molecule of the active species, A* to the controlled-double-potential-step experiment. represents an excited state of that species, hu repreThe quantum efficiency of the eel cell provides a valsents a photon, and Q represents some excited state uable clue to the basic processes involved and is a paquencher . rameter of central interest to any consideration of the disWe consider a one-dimensional system (see Figure 1) play device potential of ecl. In this paper we present governed by the above reactions and bounded a t the a theoretical analysis of the ecl process for the case of origin by an electrode. If we let A , A+, and A - stand cyclic boundary conditions assuming rapid recombinafor the concentrations of those species, then the betion. These boundary conditions are not only easier to havior of the system is described by the equations achieve experimentally but also the conditions of greatest interest for continuous operation device apdA b -(AvA) = 2RA+Aplications. We also present the results of efficiency at ax measurements on the rubrene-tetra-n-butylammonium perchlorate (TBAP)-benzonitrile (BN) system. The measured efficiencies, 8.7%, compare favorably with those of electroluminescent diodes for device applicawhere vA, vA+, and vA- are the average tions, indicating that ecl systems have excellent device velocities and R is the anion-cation recombination potential if cell lifetimes can be extended. cornparcoefficient; the equations Of momentum transfer ison of the measurements with the theory indicates that the results are consistent with the conclusion, based on dv a vu qa vu kTba -+vu-- E + - + - - = 0 (10) other evidence, of Chang, Hercules, and Roe2that most at dx m T ambx of the excited molecules which take part in the recomwhere a = A , A+,or A - ; and Poisson's equation. The bination are in triplet states which are quite suscepfirst term of the momentum equation is negligible at the tible to quenching processes. low frequencies of interest. The electric fields in the Theory ecl solution are sufficiently small to make the third term The ecl process has often been described by the folsmaller than the last (diffusion-dominated flow). The lowing condensed set of reactiom2 second term is of order va2/l, where 1 is the scaling length A+e--+A(1)
+
+
+
+
+
+
+ eA- +A+ + 2eA 4A+
The Journal of Physical Chemistry, Vol. 76,No. IS, 1972
(2) (3)
(1) A comprehensive list of references is available in A. Zweig, Advan. Photochem., 6,425 (1968). (2) J. Chang, D. M ,Hercules, and D. K. Roe, Electrochim. Acta, 13, 1197 (1968).
EFFICIENCY OF THE ELECTROCHEMILUMINESCENT PROCESS
1869
molecules are destroyed. This provides us with a boundary condition at the electrode.
If we solve the problem by Fourier analysis we find nl = A. - A - A + - A - = 0, where A0 is the original molecular concentration. We solve the problem for a harmonic boundary condition for n2 at the electrode. nz(O,t) = A - - A+ x
0
Figure 1. One-dimensional model of an eel cell with neutral, anion, and cation of fluorescent molecule A in solution.
for the gradients in the system. This is negligible compared to the last term, which is of order vthermai2/Z. We can, therefore, rewrite the momentum transfer equation as vu =
a
- (D/a)(ba/bz)
=
A , A+, or A -
D
=
(11)
(kT/m)r
where D is the diffusion coefficient of molecule A, k is Boltzmann’s constant, T is the temperature, m is the molecular mass, and 7 is thc collision time of the molecule in solution. Equation ii can be used t o convert the equations of particle conservation to
=
AOe-jwt
(16)
Then because the heat conduction equation is linear the solution for any arbitrary boundary condition on n2 can then be found by the proper Fourier construction. Taking
n2 = N(x)e-jWt
(17)
we find
nz
=
A- - A+ =
{
A. exp -
&$
x) sin {cot -
dg
x)
(18)
where the phase has been arbitrarily adjusted. The light is emitted at recombination planes where n2(xo) = 0 (see Figure 2 ) . There are infinite numbers of these located a t xon =
dc
(cot f n r ) ; n = 0, 1,2, . .
.
(19)
The rate of production of photons at each plane is given by
and
Equations 11, 12, and 13 describe the ecl system when they are solved consistent with suitable electrode boundary conditions at the origin. The right-hand sides of eq 12 and 13 make this a difficult nonlinear system of equations which has been solved with the aid of a computer by Feldberg3)4for the case of two-pulse operation and by Cruser and Bard5for continuous operation. In the limit of large R there is negligible coexistence of A+ and A- ions at any position in the cell. I n this limit the only quantities needed to discuss the cell operation are A A + A - and A - - A+, both of which obey the simple heat equation
+ +
(bn/bt) - D(b2n/bx2)
=
0
where 7 is the fraction of recombinations that produce a photon. A simple integration yields the total number of photons produced from the entire cell during one cycle no. of photons cycle
W
The current at the electrode is given by
b
J ( 0 , t ) = eD -(AbX
- A+)/,,o
=
(14)
which can be solved analytically by well-known methods.6 Mow, recombination ceases to be a bulk phenomenon and occurs only at planes separating regions where only A + or A - have nonzero values. I n the basic ecl process there is the assumption that no
(3) S. W. Feldberg, J:Amer. C h m . Soc., 88, 390 (1966). (4) S. W. Feldberg, J . Phys. Chem., 70, 3928 (1966). ( 5 ) S. A. Cruser and A. J. Bard, J . Amer. Chem. SOC.,91, 267 (1969). (6) H. S. Carslaw and J. C. Jaeger, “Conduction of Heat in Solids,” Oxford University Press, London, 1959.
The Journal of Physical Chemistry, Vol. 76, No. IS,1979
1870
P. M. SCHWARTZ, R. A. BLAKELEY, AND B. B. R O B I N ~ O N W t '0
- ,
W
t
3H . 4
Figure 3. Typical ecl cell. Figure 2. Density profiles for the cyclic mode of operation as a function of distance from the electrode for several times during the cycle.
One can integrate eq 22 to obtain the total number of ions leaving the electrode during a cycle no. of ions cycle
=
3.414
4;
T SURFACE ORS
A.
The quantum efficiency is obtained by dividing the total number of photons emitted by the cell (eq 21 gives the number at one electrode) by the number of ions entering the system from one electrode (23); one obtains quantum efficiency = 0.8287 (24) The efficiency found in eq 24 is independent of frequency. Therefore, eq 24 also gives the efficiency for any arbitrary periodic solution. We see from eq 24 that the inherent losses of the periodic mode of operation only limit its potential to an efficiency of 83%. This loss is due to the annihilation of ions which are created and swept back to the electrode during the cycle without experiencing recombination.
Measurements A series of measurements was made on electrochemical cells which contained a solution of 2 X M rubrene and lo-' M tetra-n-butylammonium perchlorate (TBAP) in benzonitrile. The benzonitrile used was JICB Spectroquality that mas stored in a desiccator over phosphorus pentoxide. The TBAP was Polarographic Grade obtained from Southwestern Analytical Chemical. I t was dried in uacuo at -80" and stored in a vacuum desiccator. The rubrene purchased from Aldrich Chemical was purified by liquid chromography on a column of activated alumina using trichloroethylene as the solvent. The rubrene was recovered by evaporating the solvent and then baking in vacuo at 200-250" for several hours. Because of its sensitivity to photoinduced reactions, the processing and storage of the rubrene was done at reduced light The Journal of Phgsical Chemistrg, Vol. 76, N o . 19,2972
Figure 4. Integrating box for light output measurements.
levels. However, once the working solution for the cells was degassed it was stable at normal light levels. A typical cell is shown in Figure 3. The electrodes are platinum, and a stopcock can be fitted to the ground-glass joint so that the cell may be sealed under vacuum. In order to prepare a cell for the light output measurements, the solids were weighed out and placed in the cell along with the appropriate volume of benzonitrile. The cell was then evacuated, and the solution was degassed by several freeze-thaw cycles. The measurements were performed by placing the part of the cell containing the electrodes in an integrating box like that shown in Figure 4. The diffuse reflecting surfaces were formed with Eastman Kodak KO.6080 white reflectance paint. The photocell in the box was standardized against one that had been calibrated by the Yational Bureau of Standards. Avoltage square wave was applied between electrodes no. 1 and 2 . The output of the photocell was measured with an operational amplifier in a current follower circuit, and the average current through the cell during each half of the period was measured by connecting electrode no. 2 to the input of the circuit in Figure 5 , The voltage outputs of the amplifier circuits were measured with a digital voltmeter. The light output as a function of the current through the cell was measured for several different square wave
EFFICIENCY OF THE ELECTROCHEMILUMINESCENT PROCESS
1871
2 20 I
21
- I5 Figure 5. Current follower circuit for measuring current during each half-cycle.
periods. Typical results.for a cell are shown in Figure 6. The slope of the lines in Figure 6 is the differential quantum efficiency (DQE) of the ecl cell. This is the experimental quantity that corresponds to the quantum efficiency calculated in eq 24. The lines in Figure 6 are offset along the abscissa because of the current needed to charge the double-layer capacitors at the electrodes to the oxidation and reduction potentials. The slope of the lines for the larger periods in Figure 6 corresponds to a DQE of 8.7%. For each frequency the excitation of the cell was increased until the light output saturated or decreased. A t the higher frequencies the measured DQE appeared to decrease; however, this could have been caused by uneven charging of the electrodes so that parts of the electrodes had achieved the reaction potentials while other parts had not. This value for the DQE implies that q , the ecl efficiency, is only -0.1.
Discussion Since normal rubrene fluorescence is 83% efficient, we expect q r ~ 0 . 8 3in eq 24 and the efficiency to be -70% if singlet excited states dominate the recombination reaction. On the other hand, it takes four ions to create one photon if triplet states dominate. This would indicate a maximum efficiency for this process of ~ 4 0 % which ~ could be seriously degraded further by the well-established tendency for triplets to experience
Figure 6. Output characteristics of a rubrene ecl cell.
quenching reactions. We conclude that high quantum efficiency is indicative of singlet reactions and low quantum efficiency is indicative of triplet reactions. These theoretical expectations assume that the molecules are not destroyed by some spurious reaction at a rate which is comparable to the rate at which they emit photons. This assumption has been confirmed experimentally by measuring the operating lifetime of a cell. I n this way we have found that the average number of molecules destroyed in the ecl chain is smaller than the number that emit a photon. The measured efficiencies, -9%, are, therefore, consistent with the conclusion of Chang, Hercules, and Roe2 based on other evidence that most of the excited states participating in the recombination process are triplet states. The measured efficiencies compare favorably with those observed in electroluminescent diodes and indicate that ecl systems would make useful devices if cell lifetimes can be significantly extended.
Acknowledgments. We wish to thank Professor J. Turkevich for his advice on some of the experimental work and to acknowledge the advice and encouragement of Dr. M. C. Steele and Dr. R. D. Larrabee.
The Journal of Physical Chemistry,Vol. 76,No. 13, 197g
