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The interest in ECL was so strong that in the 1970s several investigators decided this might be a way to create light in a usable way. An electrochemical cell can be built with two electrodes separated by a narrow space filled with solution in which both A an D are located.  A and D could be two different chemicals or one in the case of diphenylanthracene (DPA). You independently control the potential of the two electrodes using a potentiostat so that at the anode you generate the cation radical form of A at a diffusion-controlled rate.  At the cathode you generate the radical anion form of the species  D at a diffusion controlled rate. These molecules will diffuse away from the electrode at which they are produced into the solution volume between the electrodes. Where they meet at the center of the device the electron transfer reaction between the donor and the acceptor will occur and there will be an emissive state. This is heroic science because it’s very hard to produce.
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==Solution Electrogenerated Chemiluminescence Example Molecules==
[[Image:OLED2 ECL.PNG|thumb|300px]]
The following examples will focus on Diphenylanthracene since so much is known about its electrogenerated chemiluminescence ([[ECL]]). Diphenylanthracene (DPA), Di-iosamyl quinacridone, and Rubrene  have the following characteristics:
*Absorbance spectra in solution with vibronic fine structure
*A small Stokes shifts
*Luminescence spectra with corresponding vibronic  fine structure
 
<br clear="all">
 
==Prototype Emissive Devices==
[[Image:OLED2 prototype.JPG|thumb|400px|Solution electrogenerated chemiluminesence.
]]
Interest in ECL was so strong that in the 1970s several investigators decided it might be a usable way to create light. <ref>Keszthelyi CP, Laser D, Bard AJ. 1975. Journal of the Electrochemical Society 122: 1642-1642</ref>
<ref>Laser D, Bard AJ. 1975. J. Electrochem. Soc. 122: 632-640</ref>
<ref>Brilmyer GH, Bard AJ. 1980. Journal of the Electrochemical Society 127: 104-110</ref> An electrochemical cell can be built with two electrodes separated by a narrow space filled with solution in which both acceptors (A) and donors (D) are located.  A and D could be two different chemicals, or the same (as with [[diphenylanthracene]]). By independently controlling the potential of the two electrodes using a potentiostat, the cation radical form of A<sup>+.</sup> is generated at the anode at a diffusion-controlled rate.  At the cathode you generate the radical anion form of D<sup>-.</sup> at a diffusion controlled rate. These molecules will diffuse away from the electrode at which they are produced into the solution between the electrodes. Where they meet at the center of the device the electron transfer reaction between the donor and the acceptor occurs, causing an emissive state to occur.
 
*Layers must be very thin so they can be filled electrochemically in a very short period of time.
*The possibility of interaction for the two molecules must be high.
*The cation and anion radicals of the molecule must have long lifetimes, and must be carefully purified.
*One of these electrodes must allow light to leave the system, otherwise there is no display.
 
[[image:OLED2_energetics.JPG|thumb|400px|Characterization of the Energetics of Charge Recombination<ref>“Light Emitting Electrochemical Processes,” 
N.R. Armstrong, R.M. Wightman, E.M. Gross;
Annu. Rev. Phys. Chem. 52, 391-422, (2001)</ref>]]
The solution ECL experiment is simple to construct. A flowing solution containing both D and A is passed in front of a Pt or Au microelectrode surrounded by a reference and counter electrode in a small solution cavity.  The potential of the Au or Pt electrode is alternatively pulsed positive (to generate A<sup>+.</sup>) and negative (to generate D<sup>-.</sup>) with a typical frequency of several KHz.  The products of these heterogeneous electron transfer reactions diffuse away from the electrode, where they are likely to encounter each other (on the time scale of microseconds).  The resultant recombination reactions generate the emissive state of one pair of these molecules. The light from that emission event is coupled out to a multi-channel detector spectrophotometer which records the emission spectrum.
 
One example is this non-display application used by Neal Armstrong (University of Arizona) and Mark Wightman (University of North Carolina) to study the dynamics of electron transfer and light emission. The setup has a very small solvent-containing cavity. A window in the center is positioned opposite a photomultiplier tube or some photodetector. There are three electrodes. A 5-50 micron diameter working electrode is positioned in the center, typically a small microband or microdisc electrode. The counter and reference electrodes are poised on either side. The solution cavity is able to flow in fresh solution periodically.
 
See Keszthelyi 1975<ref>Keszthelyi CP, Laser D, Bard AJ. 1975. Journal of the Electrochemical Society 122: 1642-1642</ref>
 
See Laser 1975 <ref>Laser D, Bard AJ. 1975. J. Electrochem. Soc. 122: 632-640</ref>
 
See Brilmyer 19080<ref>Brilmyer GH, Bard AJ. 1980. Journal of the Electrochemical Society 127: 104-110</ref>
 
See Armstrong 2001 <ref>“Light Emitting Electrochemical Processes,”  N.R. Armstrong, R.M. Wightman, E.M. Gross; Annu. Rev. Phys. Chem. 52, 391-422, (2001)</ref>
 
 
 
<br clear="all">
 
==Characterization of the Energetics of Charge Recombination==
The potential of the working electrode is modulated with respect to the reference electrode between two extremes. At one extreme it generates the cation radical (A<sup>+.</sup>) and at the other extreme it generates the anion radical (D<sup>-.</sup>).
The potential of the these two extremes is cycled at frequencies of a kilohertz or more. By quickly flipping the potential back and forth, both species are generated in the diffusion layer volume next to the electrode surface, where they can interact and give off a photon which is counted with the detector. Wightman was able to monitor single photons and single electron transfer events with this system. Further studies of the light emitting process can be conducted using spectroscopy to compare with results from the device.
 


Layers must be very thin so they can be filled elecrochemically in a very short period of time
==Cross Reactions==
The possibility of interaction for the two molecules to be high.
[[Image:Dpa_voltammogram.png|thumb|400px|Voltammogram for reduction and oxidation of DPA]]
You need molecules that have long lifetimes for the both the cation radical and the anion radical space so that means some careful purification has to be done.
This an example of a [[Cyclic voltammetry |voltammogram]] obtained at the microelectrode for Diphenylanthracene (DPA) in a low dielectric constant solvent. The negative scan shows the microelectrode response for a one-electron reduction of DPA to its radical anion.  The positive scan shows the one-electron oxidation of DPA to its radical cation form.  The difference between the midpoint potentials is called the halfway potential. This shows the energy difference of the two forms, and hints at the amount of excess free energy that will be generated by the redox reaction that follows.  In this reaction there is more than 3 electron volts of excess free energy. DPA's excited state easily forms and re-emits with a peak wavelength of about 450 nm. If you calculate the energy, this corresponds to 3-3.1 eV. So the electro-chemical event generated more than enough excess free energy to create the excited singlet state of DPA.


One of these electrodes has to allow you get light out of the system otherwise there is no display.
Now compare the yield of the DPA excited states while systematically changing the redox event that occursFirst generating the DPA anion with one pulse and the DPA cation with another pulse, the &Delta;E<sub>1/2</sub> is about 3.33 electron voltsThis forms the excited singlet state known as the “S-route” .
The solution ECL experiment is simple to construct – a flowing solution containing both D and A is passed in front of a Pt or Au microelectrode surrounded by a reference and counter electrode in a small solution cavityThe potential of the Au or Pt electrode is alternatively pulsed positive (to generate A+.) and negative (to generate D-.) with a frequency typically up to a few KHz. The products of these heterogeneous electron transfer reactions diffuse away from the electrode, where they are likely to encounter each other (on the time scale of microseconds)The resultant recombination reactions generate the emissive state of one pair of these molecules, the light from that emission event is coupled out to a multi-channel detector spectrophotometer and the emission spectrum recorded.


Consider the non- display application which was used to look at the dynamics of electron transfer and light emission. This system was used by Neal Armstrong  and Mark Wightman and the UNC , a group that had the world’s expertise in this area at the time.
Next, add a second species of Methoxybenzophonone, which reduces at a slightly less negative potential. It generates an anion radical at 3.24 electron volts. Spectroscopy shows that the DPA excited state is still formed, but slightly less efficiently. It is still an S-route process.
This involves a very small cavity with solvent in it. A window in the center positioned opposite a photomultiplier tube or some photodetector.


There are three electrodes. The center one is the working electrode, typically a small microband or microdisc electrode with a diameter of 5-50 microns. The counter and reference electrodes are poised on either side. The solution cavity is able to flow in fresh solution periodically, this is important.  
With Benzophonone, it has a less negative potential with an excess free energy of 3.15 volts, and is still an S-route.


You modulate the potential of the working electrode with respect to the reference electrode between two extremes. At one extreme it generates the cation radical of A and at the other extreme it generates the anion radical of D.
<embed_document width="55%" height="400">http://depts.washington.edu/cmditr/media/OLED2_ecl_redoxpairs.pdf</embed_document>
You cycle the potential of the these two extremes at frequencies of a kilohertz or more. By flipping the potential back and forth so fast you generate both species in the diffusion layer volume next to the electrode surface where they can interact and give off a photon which is counted with the detector. Wightman was able to monitor single photons and single electron transfer events with this system. The results can be further studied with spectroscopy of the light emitting process to confirm that the results match or differ  from what you see in a device.


This an example of a voltamogram of the obtained at the micro electrode for DPA in a low dielectric constant solvent. When you scan negatively you the microelctrode response for a one electron reduction of the DPA to its radical anion. When you scan positively this give the one electron oxidation of the DPA to its radical cation form. The different between the midpoint  potentials are called the halfway potentials. This give an indication of the energy difference of the two forms and a clue to the amount of excess free energy that will be generated by the redox reaction that follows.  In this reaction there is more than 3 electron volts of excess free energy. DPA exciting state easily forms and re-emits with a peak wavelength of about 450 nm. If you calculate the energy this is 3-3.1 eV. So the electo chemical event generated more than enough excess free energy to create the excited singlet state of DPA.
See Wightman 1995,1997 <ref>Wightman et.al.: JACS, 119 (1997) 11920. </ref><ref>JEAC, 396 (1995) 85.</ref>


Now you compare the yield the DPA excited states as you systematically change the redox event that occurs.  First generating the DPA anion with one pulse and the DPA cation with another pulse the ΔE_(½ ) is about 3.33 electron volts.  This forms the excited singlet state known as the “S-route” .
See [[wikipedia:Cyclic_voltammetry]]


Next you put a second species Methoxybenzophonone which reduced at a slightly less negative potential, generating its anion radical at 3.24 electron volts. When you do spectroscopy you see that you are still forming the DPA exciting state and its slightly less efficient. It is still an S-route process.
==Marcus Theory for Electron Transfer==
<embed_document width="55%" height="400">http://depts.washington.edu/cmditr/media/OLED2_marcustheory.pdf</embed_document>


Using Benzophonone it has a less negative potential with an excess free energy of 3.15 volts and still is an S-route.
The Marcus Theory for electron transfer provides some predictability to describe both probability of light emission from an ECL cross reaction, and the probability of light emission in an OLED at the interface between two dissimilar charge transporting layers.   
The Marcus theory for electron transfer provides some of the needed predictability to describe both probability of light emission from an ECL cross reaction, and the probability of light emission in an OLED at the interface between two dissimilar charge transporting layers.   


All electron transfer reactions proceed through a transition state whose energy is defined primarily by the “reorganization energy” (λT).  This energy can be divided into an “internal reorganization” energy (λi -- the energy needed to reorganize the internal molecular environment in going from the initial to the final state), and the “external reorganization energy (λo – the energy needed to reorganize the solvent or condensed phase environment surrounding the molecule in proceeding from the initial to the final state).
:<math>k_{et}\quad \propto \quad exp\bigg[\frac{-(\Delta G-\lambda)^2}{4 \lambda k_BT}\bigg]\,\!</math>
In general as the excess Gibbs free energy (ΔE  α  ΔG) in the system is increased (Points a, b, c) so that ΔE  (ΔG) is close to or exceeds λT = λi + λo in magnitude, the reaction rate accelerates exponentially.  For light-emitting electrochemical processes this reaction rate enhancement leads directly to greater production of emissive states, i.e. the output of the ECL process is controlled by controlling the difference in reduction and oxidation potentials of the two reacting components.  
 
where
:<math>\lambda\,\!</math> is the reorganization energy
:<math>\Delta G\,\!</math> is the Gibbs free energy
 
 
All electron transfer reactions proceed through a transition state whose energy is defined primarily by the “reorganization energy” (λ<sub>T</sub>).  This energy can be divided into an “internal reorganization” energy (λ<sub>i</sub> -- the energy needed to reorganize the internal molecular environment in going from the initial to the final state), and the “external reorganization energy" (λ<sub>o</sub> – the energy needed to reorganize the solvent or condensed phase environment surrounding the molecule in proceeding from the initial to the final state).
 
In general as the excess Gibbs free energy (ΔE  α  ΔG) in the system is increased (Points a, b, c in the slides above) so that ΔE  (ΔG) is close to or exceeds λ<sub>T</sub> = λ<sub>i</sub> + λ<sub>o</sub> in magnitude, the reaction rate accelerates exponentially.  For light-emitting electrochemical processes this reaction rate enhancement leads directly to greater production of emissive states. The output of the ECL process is controlled by the difference in reduction and oxidation potentials of the two reacting components.  
   
   
This provides some guidance in the design of two-layer OLEDs (see below), where it is clear that you want to maximize the excess free energy in the critical charge recombination process.
This provides some guidance in the design of two-layer OLEDs when trying to maximize the excess free energy in the critical charge recombination process.


You go  from a situation where you maximized the free energy at point C. Then by changing the identity of the two pairs of the redox reaction you go to less free energy at point B and then finally point A. You still generate the excited state but with lower overall rate.  
First, we maximize free energy at point C. Then by changing the identity of the two pairs of the redox reaction we see less free energy at point B, and then finally point A. The excited state is generated at a lower overall rate.  


The rate is proportional to the number of photons you get out of the experiment.
The rate at which the excited state occurs is proportional to the output of photons. This gives an underlying principal for the design of OLED systems. The goal is to maximize the free energy and minimize the reorganization energies for those redox events. By maximizing the rate of electron transfer, we maximize the rate of light output.
This gives an underlying principal for the design of OLED systems.
The idea is maximize the free energy and minimize the reorganization energies for those redox events. Maximize the rate of electron transfer and therefore maximize the rate of light output. You want to me at position C rather position A in the design of the systems.  


Unfortunately the design is never that simple.  
Unfortunately the design is never that simple.  


The DPA+ + BP- system is results in point A.
*The DPA<sup>+</sup> + BP<sup>-</sup> is shown in point A.


The DPA+ + MOPA- puts us at point B
*The DPA<sup>+</sup> + MOPA<sup>-</sup> is shown in point B


The DPA+ + DPA- system is results in point C.
*The DPA<sup>+</sup> + DPA<sup>-</sup> system is shown in point C.


You have changed which species gets reduced and as a consequence changed the excess free energy in the redox reaction.
By changing which species gets reduced, the excess free energy in the redox reaction is also changed.
It is possible to create an excess free energy which exceeds the reorganization energy (point d) in which case you enter the “inverted region” and reaction rate decreases.  A few examples of this phenomenon have been observed in solutions and glasses, but it has not been, to date, reported in OLEDs.
It is possible to create an excess free energy which exceeds the reorganization energy (point D). In this case the reaction enters the “inverted region” and the reaction rate decreases.  A few examples of this phenomenon have been observed in solutions and glasses, but it has not yet been reported in OLEDs.
   
   
It would be possible to go too far and get into what’s called “Marcus inverted region” where the excess free energy larger by far than the reorganization energy. In this case you might see the rate of reaction come down. To date we have not seen examples of this in OLEDs. It may have occurred but it difficult to prove.  It’s really a question if the excess free energy is much less than the reorganization energy, comparable or greater than the reorganization energy.
In the “Marcus inverted region”, the excess free energy is much larger than the reorganization energy. In this case the rate of reaction may decrease. To date this has not been discovered in OLEDs. It may have occurred but it is difficult to prove.
 
See Marcus 1965 <ref>Marcus, R. A. J. Chem. Phys. 1965, 43, 2654-2657.</ref>
   
See Marcus 1970 <ref>Marcus, R. A. J. Chem. Phys. 1970, 52, 2803-2804.</ref>
 
See Sutin 1982 <ref>Sutin, N. Acc. Chem. Res. 1982, 15, 275-282.</ref>
 
== References ==
<references/>
 
[[category:organic LED]]
 
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Latest revision as of 14:20, 8 November 2010

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Solution Electrogenerated Chemiluminescence Example Molecules

OLED2 ECL.PNG

The following examples will focus on Diphenylanthracene since so much is known about its electrogenerated chemiluminescence (ECL). Diphenylanthracene (DPA), Di-iosamyl quinacridone, and Rubrene have the following characteristics:

  • Absorbance spectra in solution with vibronic fine structure
  • A small Stokes shifts
  • Luminescence spectra with corresponding vibronic fine structure


Prototype Emissive Devices

Solution electrogenerated chemiluminesence.

Interest in ECL was so strong that in the 1970s several investigators decided it might be a usable way to create light. [1] [2] [3] An electrochemical cell can be built with two electrodes separated by a narrow space filled with solution in which both acceptors (A) and donors (D) are located. A and D could be two different chemicals, or the same (as with diphenylanthracene). By independently controlling the potential of the two electrodes using a potentiostat, the cation radical form of A+. is generated at the anode at a diffusion-controlled rate. At the cathode you generate the radical anion form of D-. at a diffusion controlled rate. These molecules will diffuse away from the electrode at which they are produced into the solution between the electrodes. Where they meet at the center of the device the electron transfer reaction between the donor and the acceptor occurs, causing an emissive state to occur.

  • Layers must be very thin so they can be filled electrochemically in a very short period of time.
  • The possibility of interaction for the two molecules must be high.
  • The cation and anion radicals of the molecule must have long lifetimes, and must be carefully purified.
  • One of these electrodes must allow light to leave the system, otherwise there is no display.
Characterization of the Energetics of Charge Recombination[4]

The solution ECL experiment is simple to construct. A flowing solution containing both D and A is passed in front of a Pt or Au microelectrode surrounded by a reference and counter electrode in a small solution cavity. The potential of the Au or Pt electrode is alternatively pulsed positive (to generate A+.) and negative (to generate D-.) with a typical frequency of several KHz. The products of these heterogeneous electron transfer reactions diffuse away from the electrode, where they are likely to encounter each other (on the time scale of microseconds). The resultant recombination reactions generate the emissive state of one pair of these molecules. The light from that emission event is coupled out to a multi-channel detector spectrophotometer which records the emission spectrum.

One example is this non-display application used by Neal Armstrong (University of Arizona) and Mark Wightman (University of North Carolina) to study the dynamics of electron transfer and light emission. The setup has a very small solvent-containing cavity. A window in the center is positioned opposite a photomultiplier tube or some photodetector. There are three electrodes. A 5-50 micron diameter working electrode is positioned in the center, typically a small microband or microdisc electrode. The counter and reference electrodes are poised on either side. The solution cavity is able to flow in fresh solution periodically.

See Keszthelyi 1975[5]

See Laser 1975 [6]

See Brilmyer 19080[7]

See Armstrong 2001 [8]



Characterization of the Energetics of Charge Recombination

The potential of the working electrode is modulated with respect to the reference electrode between two extremes. At one extreme it generates the cation radical (A+.) and at the other extreme it generates the anion radical (D-.). The potential of the these two extremes is cycled at frequencies of a kilohertz or more. By quickly flipping the potential back and forth, both species are generated in the diffusion layer volume next to the electrode surface, where they can interact and give off a photon which is counted with the detector. Wightman was able to monitor single photons and single electron transfer events with this system. Further studies of the light emitting process can be conducted using spectroscopy to compare with results from the device.


Cross Reactions

Voltammogram for reduction and oxidation of DPA

This an example of a voltammogram obtained at the microelectrode for Diphenylanthracene (DPA) in a low dielectric constant solvent. The negative scan shows the microelectrode response for a one-electron reduction of DPA to its radical anion. The positive scan shows the one-electron oxidation of DPA to its radical cation form. The difference between the midpoint potentials is called the halfway potential. This shows the energy difference of the two forms, and hints at the amount of excess free energy that will be generated by the redox reaction that follows. In this reaction there is more than 3 electron volts of excess free energy. DPA's excited state easily forms and re-emits with a peak wavelength of about 450 nm. If you calculate the energy, this corresponds to 3-3.1 eV. So the electro-chemical event generated more than enough excess free energy to create the excited singlet state of DPA.

Now compare the yield of the DPA excited states while systematically changing the redox event that occurs. First generating the DPA anion with one pulse and the DPA cation with another pulse, the ΔE1/2 is about 3.33 electron volts. This forms the excited singlet state known as the “S-route” .

Next, add a second species of Methoxybenzophonone, which reduces at a slightly less negative potential. It generates an anion radical at 3.24 electron volts. Spectroscopy shows that the DPA excited state is still formed, but slightly less efficiently. It is still an S-route process.

With Benzophonone, it has a less negative potential with an excess free energy of 3.15 volts, and is still an S-route.

<embed_document width="55%" height="400">http://depts.washington.edu/cmditr/media/OLED2_ecl_redoxpairs.pdf</embed_document>

See Wightman 1995,1997 [9][10]

See wikipedia:Cyclic_voltammetry

Marcus Theory for Electron Transfer

<embed_document width="55%" height="400">http://depts.washington.edu/cmditr/media/OLED2_marcustheory.pdf</embed_document>

The Marcus Theory for electron transfer provides some predictability to describe both probability of light emission from an ECL cross reaction, and the probability of light emission in an OLED at the interface between two dissimilar charge transporting layers.

<math>k_{et}\quad \propto \quad exp\bigg[\frac{-(\Delta G-\lambda)^2}{4 \lambda k_BT}\bigg]\,\!</math>

where

<math>\lambda\,\!</math> is the reorganization energy
<math>\Delta G\,\!</math> is the Gibbs free energy


All electron transfer reactions proceed through a transition state whose energy is defined primarily by the “reorganization energy” (λT). This energy can be divided into an “internal reorganization” energy (λi -- the energy needed to reorganize the internal molecular environment in going from the initial to the final state), and the “external reorganization energy" (λo – the energy needed to reorganize the solvent or condensed phase environment surrounding the molecule in proceeding from the initial to the final state).

In general as the excess Gibbs free energy (ΔE α ΔG) in the system is increased (Points a, b, c in the slides above) so that ΔE (ΔG) is close to or exceeds λT = λi + λo in magnitude, the reaction rate accelerates exponentially. For light-emitting electrochemical processes this reaction rate enhancement leads directly to greater production of emissive states. The output of the ECL process is controlled by the difference in reduction and oxidation potentials of the two reacting components.

This provides some guidance in the design of two-layer OLEDs when trying to maximize the excess free energy in the critical charge recombination process.

First, we maximize free energy at point C. Then by changing the identity of the two pairs of the redox reaction we see less free energy at point B, and then finally point A. The excited state is generated at a lower overall rate.

The rate at which the excited state occurs is proportional to the output of photons. This gives an underlying principal for the design of OLED systems. The goal is to maximize the free energy and minimize the reorganization energies for those redox events. By maximizing the rate of electron transfer, we maximize the rate of light output.

Unfortunately the design is never that simple.

  • The DPA+ + BP- is shown in point A.
  • The DPA+ + MOPA- is shown in point B
  • The DPA+ + DPA- system is shown in point C.

By changing which species gets reduced, the excess free energy in the redox reaction is also changed. It is possible to create an excess free energy which exceeds the reorganization energy (point D). In this case the reaction enters the “inverted region” and the reaction rate decreases. A few examples of this phenomenon have been observed in solutions and glasses, but it has not yet been reported in OLEDs.

In the “Marcus inverted region”, the excess free energy is much larger than the reorganization energy. In this case the rate of reaction may decrease. To date this has not been discovered in OLEDs. It may have occurred but it is difficult to prove.

See Marcus 1965 [11]

See Marcus 1970 [12]

See Sutin 1982 [13]

References

  1. Keszthelyi CP, Laser D, Bard AJ. 1975. Journal of the Electrochemical Society 122: 1642-1642
  2. Laser D, Bard AJ. 1975. J. Electrochem. Soc. 122: 632-640
  3. Brilmyer GH, Bard AJ. 1980. Journal of the Electrochemical Society 127: 104-110
  4. “Light Emitting Electrochemical Processes,” N.R. Armstrong, R.M. Wightman, E.M. Gross; Annu. Rev. Phys. Chem. 52, 391-422, (2001)
  5. Keszthelyi CP, Laser D, Bard AJ. 1975. Journal of the Electrochemical Society 122: 1642-1642
  6. Laser D, Bard AJ. 1975. J. Electrochem. Soc. 122: 632-640
  7. Brilmyer GH, Bard AJ. 1980. Journal of the Electrochemical Society 127: 104-110
  8. “Light Emitting Electrochemical Processes,” N.R. Armstrong, R.M. Wightman, E.M. Gross; Annu. Rev. Phys. Chem. 52, 391-422, (2001)
  9. Wightman et.al.: JACS, 119 (1997) 11920.
  10. JEAC, 396 (1995) 85.
  11. Marcus, R. A. J. Chem. Phys. 1965, 43, 2654-2657.
  12. Marcus, R. A. J. Chem. Phys. 1970, 52, 2803-2804.
  13. Sutin, N. Acc. Chem. Res. 1982, 15, 275-282.
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