 [page 81↓] 
As reported in chapter 3, ECL was produced by applying a series of triple potential steps to the electrode immersed in the electrochemical solution containing the organic compound (Og). The generation of luminescence in the electrochemical environment involves the following reactions:
At the positive potential step and during t_{f}
(a) 
At the negative potential step and during t_{r}
(b) 

(c) 

(d) 
where Og refers to the aromatic precursor of the luminescent moiety Og*, Og^{+.} and Og¯^{.} are the positive and negative radical ions produced by the electrochemical oxidation and reduction of Og, and k_{ex} is the rate constant for the bimolecular annihilation reaction (c). Here the luminescence is produced during the negative potential step and is referred to as cathodic ECL. (It can be the other way around where first the negative radicals are produced followed by the production of positive radicals, resulting in the generation of anodic ECL). The luminescence process, represented by equation (d), is faster in the time scale of the experiment, irrespective of the mode of production of the excited state (i.e., through direct singlet formation or by triplettriplet annihilation reaction). Hence, the kinetics of the ECL process is defined by the annihilation reaction (c), which, in turn, depends on the transport of the radical cations and anions. Thus, the shape of the ECL transient, corresponding to the decay of the luminescence intensity with time, depends on the rate constant of the annihilation reaction (c) as well as on the rate parameters of the electrochemical reactions (a) and (b).
 [page 82↓] 
The simulation of the ECL transient is of interest since it serves as a tool to study the kinetics of both the ECL and electrochemical reactions [85] (see the scheme of reactions above). The following points are considered in the simulation:
1. Initially the electrochemical solution consists of a uniform concentration of the neutral organic molecule (e.g., DPA) of concentration C° (in the supporting electrolyte solution). The electrode potential was chosen for the reactant to stay in the neutral state.
2. In the first potential step of duration t_{f} to a positive value, the organic molecule was oxidized. Since it is a potential step experiment, the magnitude of the potential step was increased to a higher positive value (E°' + 250 mV) to ensure the kinetic feasibility of the electrode reaction (a). Therefore, the current in this step is controlled by the diffusion of the Og towards the electrode and Og^{+.} away from the electrode which can be described by Fick's second law:
(4.1.1a) 
and
(4.1.1b) 
where D_{Og} and D_{Og+}. are the diffusion coefficients, C_{Og} and C_{Og+.} are the concentrations of the neutral and oxidised species, respectively and x is the distance. As the orders of the diffusion coefficients D_{Og} and D_{Og+}. do not differ much [86], it is a common practice to use a single diffusion coefficient D to describe the transport. Concentration profiles of, say, the neutral species can be obtained by solving the linear equation (4.1.1a).
(4.1.1c) 
The concentration distribution of the radical cation can then be calculated by applying the condition .
3. When the potential was stepped to a negative value (E°'  250 mV) of duration t_{r}, there will be the formation of radical anion Og¯· (b). Now the [page 83↓]diffusion of Og and Og^{+.}will take place towards the electrode and Og¯· away from the electrode. When both Og¯· and Og^{+.} meet with each other, there will be the bimolecular annihilation reaction (c) giving rise to luminescence. The luminescence process is considered to be instantaneous in the time scale of the experiment. Eq.(c) becomes modified as
Therefore, the following equations have to be solved to describe the kinetics and concentration profiles in the second potential step (b):
(4.1.1d) 
(4.1.1e) 
(4.1.1f) 
Fig. 4.1.2a: Equivalent circuit representation of the electrochemical processes.  

The electrochemical system behaves as a resistance and capacitance (RC) circuit. When the electrode is subjected to a potential step, the ions from the supporting electrolyte build up near the electrode trying to counteract the charge on the metal. Thus, the electrode/solution interface behaves as a capacitor, of [page 84↓]capacitance C_{dl}, although the ions do not strictly confine to a single layer on the solution side. Initially the current corresponding to charging of this double layer flows through the circuit, the magnitude of which is determined by the resistance of the electrochemical solution (R_{u}). For a detailed discussion see sections 2.1.2ii and 2.1.2iii. The product R_{u}*C_{dl} = τ is termed as the time constant; it determines the time for the decay of the charging current and the onset of conditions for faradaic reactions. Hence, consideration of the double layer charging process becomes important in ECL experiment, the generation of which, in turn, depends on the electrochemical production of the radical ions [57].
It is difficult to solve the diffusionreaction equation (Eqs.(4.1.1df)) by analytical methods. Hence, the technique of digital simulation was followed. The point model was considered. In the point model, the concentration of each species is represented as a twodimensional array of time and distance; the array of time starts from the time of application of the potential step, and the array of distance starts from the electrode surface. The points on the time axis are uniformly separated by an interval Δt, and those on the distance axis are equally separated by the diffusional length Δx. As an example, the concentration is denoted in general terms 'C'; it can be described in the point model as follows:
 [page 85↓] 
Fig. 4.1.3a Representation of concentration array in point model.  

The partial differential equations (Eqs.(4.1.1df)) are expressed in finite difference forms by selecting very small values for Δx and Δt. The electrode potential fixes the concentration at the point zero. The concentration at each point on the distance axis, starting from the first point to the point i_{max} corresponding to the diffusion layer thickness can be calculated from the finite difference equations:
(4.1.3a) 
(4.1.3b) 
(4.1.3c) 
Another important consideration is the dependence of the diffusion layer thickness on the duration of the potential step, which is crucial for experiments done under transient conditions. The diffusion layer thickness (κ) is connected [page 86↓]to the duration of the experiment by the equation,
(4.1.3d) 
The simulation of the concentration, current and luminescence profiles are obtained by the methodology described below:
Time is denoted by the vector 'k' ( ) and distance by 'i' ( ). The diffusion coefficient was converted to the dimensionless parameter D_{M }(). The value of D_{M} should be ≤ 0.45 for the simulation to be consistent [86]. Initially the electrochemical solution consists of a uniform concentration of the neutral organic molecule Og. The point k = 0 represents the time from the point of application of the first potential step (in our case the positive potential step) until the time prior to the application of the second one. The concentrations of the species Og^{+.} and Og are obtained by using the error functions (cf. Eq.(4.1.1c)). The concentration of the negative species, Og¯· is zero during this interval. The maximum value of the 'i' vector is calculated using the expression i_{max }= (2 D_{M }k_{max})^{1/2}. The concentration array is constructed until i > i_{max}.
The point k = 1 represents the time of the application of the second potential step, i.e., k = 1 implies t_{r }> 0 where t_{r} denotes the duration of the second potential step. The concentrations of the different species at the electrode surface (i = 0) are fixed by the Nernst equation:
(4.1.4a) 
The concentrations for i > 0 are assumed to have the same values fixed in the earlier time, i.e., the concentrations calculated using error function at k=0.
The diffusionreaction process is allowed to occur from k = 1 to until k_{max}, and for each value of k, the value of i_{max} is calculated as described earlier. This simulation yields the profiles of concentration with time and distance profiles.
 [page 87↓] 
Since the luminescence decay is assumed to be instantaneous, the concentrationtime profile of 0.5 C_{Og }can represent the luminescence transient.
The current transient is calculated as follows:
(4.1.4b) 
Where 'j_{F}' represents the faradaic current density, F is the faraday's constant, J is the flux of the species, and z is the charge of the same; 'n' denotes the number of electroactive species. Since the iteration is done for the second potential step, the faradaic reaction of interest, in the present case is the conversion of Og^{+} to Og¯· and Og to Og¯·. Hence, the current density can be represented as follows:
(4.1.4c) 
For the system under consideration, the flux balance equation can be written as J_{Og }+J_{Og+ }+ J_{Og}¯·= 0. By making use of this condition and Fick's first law, the final expression for the current density is obtained as follows:
(4.1.4d) 
Due to the charging process of the electrochemical interface (metal/polymer) during the initial stages of the potential step (few milliseconds), the applied potential does not reach its final value at the same time as that of its application, but after a certain time lag, which can be represented as follows:
(4.1.5a) 
 [page 88↓] 
The effective electrode potential at a time t + Δt can be calculated from its value at the previous time t by the empirical relationship,
(4.1.5b) 
The double layer charging current can be calculated by the following relationship,
(4.1.5c) 
Thus Eq. (4.1.5b) can be rewritten as follows:
(4.1.6d) 
The simulation was done by following the procedures discussed in the earlier sections. The parameter diffusion coefficient D, uncompensated solution resistance R_{u} and double layer capacitance C_{dl} were evaluated as discussed in section 3.1.3.The value of D_{M} was fixed as 0.4; knowing the value of D for DPA from the Cottrel plot, Δx was calculated from the relationship . The simulation was repeated until the calculated current agreed with the experimental current in magnitude and experimental and simulated ECL transients were of the same shape. The value of k_{ex}, corresponding to the coincidence of experimental and simulated transients, is taken as the one for the annihilation reaction (d). Following are the results of simulation of the cathodic and anodic ECL transients of DPA in 0.1 M TBAClO_{4}.
 [page 89↓] 
Fig. 4.1.6 a. Simulation of the anodic transient (potential step between 2.05 V and 1.6V, duration 50ms each) with C° = 1×10^{6 }mol cm^{3} k_{ex }=3x10^{10} lmol^{1}s^{1}, D = 5x10^{6} cm^{2} s^{1}, R_{u}= 109 Ω and C_{dl}= 1.5μ F.  

Fig. 4.1.6 b. Simulation of the cathodic transient (potential step between 1.6 V and 2.05V, duration 50ms each) with C°=1×10^{6 }mol cm^{3} k_{ex }=1x10^{10} lmol^{1}s^{1}, D = 5x10^{6} cm^{2} s^{1}, R_{u}= 109 Ω and C_{dl}= 1.5μ F.  

The anodic and cathodic ECL transients were found to be having almost equal values of the rate constants 3x10^{10} lmol^{1}s^{1}and 1x10^{10} lmol^{1}s^{1}, respectively. The order of the rate constant agrees with the ones reported in the literature [page 90↓][57, 66]. This shows the validity of the present theoretical simulation procedure. The effect of double layer charging on the effective potential felt by the electrochemical reaction, is shown in the following figures during anodic and cathodic ECL experimental conditions. The potential takes time approximately of 0.5 ms to reach its final value.
Fig. 4.1.6c: Effect of double layer charging on the potential step from 2.05 V to 1.6 V.  

Fig. 4.1.6 d: Effect of double layer charging on the potential step from 1.6 V to 2.05 V.  

 [page 91↓] 
It has been reported that the ECL intensity and kinetics are different for different sequences of potential steps for their generation. This concept was discussed in detail in section 3.1.4. Since the speculation and earlier analyses on this effect point to the adsorption of some species other than the electroactive species on the electrode, this concept is beyond the scope of the present theoretical analysis.
Unlike the solution phase ECL, the ECL producing species, the conducting polymer (CP) was coated on the electrode and then dipped in the solution of the electrolyte with the solvent. As explained in the experimental section, care was taken for the CP to remain chemically and physically intact on the electrode by the appropriate choice of the solvent. ECL was produced by applying a series of triple potential steps to the CP coated electrode kept in the electrolytic solution. The kinetics can be explained on similar grounds as that of solution phase ECL:
At the positive potential step and during t_{f}
(A) 
At the negative potential step and during t_{r}
(B) 

(C) 

(D) 
where Pr refers to the oxidizable/reducible unit of the neutral polymer, Pr* is the excited polaron, Pr^{+.} and Pr¯· are the positive and negative polarons produced by the electrochemical oxidation and reduction of Pr, respectively, and k_{ex} is the rate constant for the bimolecular annihilation reaction (C). The cathodic ECL is considered. As with the case of solution ECL, the kinetics of the ECL process is defined by the annihilation reaction (C), since the luminescence process represented by equation (D) is faster in the time scale of the experiment.
 [page 92↓] 
The annihilation reaction and the rate of formation of the positive (A) and negative polarons (B) defers from the corresponding processes in the solution phase due to the unique mode of charge transport in polymers in electrochemical environment. In the solution phase the neutral species (Og) and the positive and negative radical ions (Og^{+.} and Og¯·) move freely to take part in the electron transfer reaction with the electrode or among them. But in the case of polymers this is not possible, since the oxidizable/reducible units (Pr) and the corresponding charged species (Pr^{+.}/Pr¯·) are indeed a part of the big conducting polymer network. They cannot break away from the polymer backbone for the electron transfer reactions. Instead, the electrons (or holes) themselves move towards or away from these units (Pr, Pr^{+.} and Pr¯·) along the conjugated bonds during electron transfer reactions. On the other hand, the electrochemical environment needs to be electrically neutral. Hence, the ions of the supporting electrolyte move in and out of the polymer, depending on the charge requirement during the electron transfer reactions. This counterionic movement controls the local electroneutrality within the conducting polymer [87]. This concept is represented in the following figures:
Fig. 4.2.1a. Representation of double layer charging in the electrode/polymer/solution system: situation prior to charge transfer.  

 [page 93↓] 
Fig. 4.2.1b. State of the polymer during charge transfer and transport maintaining bulk electroneutrality.  

Fig. 4.2.1b. State of the polymer during charge transfer and transport maintaining bulk electroneutrality.  

Since the transport of charges in the conducting polymer is different from that in the solution phase, the flux equations are also different, with the added term, due to the electric field [88]. Thus, the ECL reaction in the polymer phase will have the following set of equations with the flux term modified to account for the migration of the charged species under the influence of the electric field in the polymer:
(4.2.1a) 

(4.2.1b) 
(4.2.1c) 
(4.2.1d) 
(4.2.1e) 
J are the fluxes, z are the charges, C are the concentrations, D are the diffusion coefficients, x is the distance, is the potential gradient, + and  stand for positive and negative counterions respectively; other terms have the conventional meanings. Note that the flux of the neutral polymer site, Pr, does not have the electric field term, as its movement is not influenced by the field.
Thus, we have three Eqs.(4.2.1ac) to describe the transport of electrons (or holes) in the polymer, and the Eqs.(4.2.1de) for the counterionic transport. Besides these five equations, an equation for the potential gradient has also to be solved by iteration considering the unknown parameters: the local concentrations of the five transporting species, the diffusion coefficients of the individual species, the rate constant of the annihilation reaction and current.
The complexity of the system would render an exact solution of this diffusionmigrationreaction problem difficult. Starting from 1965, a few efforts were made to account for this migration of charges in polymers. The first one, in 1965, being that by Cohen and Cooley, who considered the migration of 'noninteracting' cations and anions in a nonconductive polymer phase under the conditions of a current step [89]. The other notable work in 1983 is by Yap et al., who did the simulations for potential step experiments [90]. Later T.R. Brumleve and R.P. Buck improved the model by considering the electroneutrality conditions in defining the concentration of different species in the polymer and expressing the potential gradient inside the polymer film by Poisson's equation [91]. All these works were done by an implicit iterative procedure. Explicit [page 95↓]definition of the potential drop inside the film is not possible as it depends on the concentration distribution of all the charged species inside the polymer, which makes this problem quite complicated. Hence, solving for the current, which in turn depends on the electric field in the polymer, cannot be accomplished reliably in the explicit method.
However, in 1988, the simulation of the experimental result, considering the concept of diffusionmigration was done by R. Lange and K. Doblhofer, by an iterative procedure [92,93]. The iterative procedure was used to analyze a system in which only two charged species were mobile, i.e., the reduction of Fe(CN)_{6} ^{3 }redox ions in a polymer containing fixed positive charges to Fe(CN)_{6} ^{4 }was considered. The local electroneutrality was maintained by these two negative ions and the immobile positive fixed charge of the polyvinylpyridinium polymer, as long as the concentration of the supporting electrolyte in the solution did not exceed 0.1 M. Thus, the complications due to counterion transport from the supporting electrolyte were avoided. Thus, the system is simpler than the one we have. In Fig. 4.2.1c [has been reproduced from 92] the current vs time^{1/2} plot was simulated for two cases, (1) by considering diffusionmigration transport of these two ions in the polymer, (2) by considering just pure diffusion of these ions (Cottrell plot). It was found that the current holds the same dependence on t^{1/2}, irrespective of the mode of transport process.
Fig. 4.2.1c: Plot of current density against t^{1/2} under diffusionmigration conditions for the electrode reaction entity="Objekt118" label="88#28"/>. The pure diffusion case (Cottrell) was included for comparison.  

 [page 96↓] 
However, despite the fact that the value of the diffusion coefficient remains the same, the slopes of these plots differ from each other. Thus, charge transport inside the polymer can be approximately described by the diffusion process, but one must keep in mind that the diffusion coefficient derived from the simulations will also be approximate values.
In fact, in 1988, C.P. Andrieux and J.M. Savéant derived equations for the diffusionmigration in conducting polymers considering an electronhopping mode of charge transport and reported that the Cottrell condition obeyed even in this case. They related the observed diffusion coefficient D_{ap} ^{}to the electron hopping diffusion coefficient D_{E} by the following equation:
(4.2.1f) 
where Ψ is a function which depends on the charge transfer parameters, diffusion coefficient of the mobile counterion, its charge and the number of electrons participating per electron hopping [94].
While the bulk electric field in the polymer phase is disregarded, the electric field created by the ions accelerates the slower moving charge and decelerates the faster one. Eventually both of them move at the same speed and the situation becomes the diffusion of a neutral entity. This kind of transport is termed as ambipolar diffusion in the literature [95]. For the movement of a negative polaron along the polymer coupled with that of the positive counterion from the supporting electrolyte, the observed diffusion coefficient is expressed as
(4.2.1g) 
When the diffusivities of these two species differ considerably, the observed diffusion coefficient becomes that of the slowest moving species, in general that of the counterions. Thus, the simulation of the polymer system was conducted essentially in a way similar to the ECL in the solution phase system:
 [page 97↓] 
With these concepts in mind, it was considered that a procedure for analyzing the ECL potential step experiments should basically rely on a t^{1/2} behavior. The underlying assumptions is that the polarons are coupled to counterions by the condition of electroneutrality, i.e., they are moving as neutral ion pairs and follow as such the diffusion laws.
1. Initially the conducting polymer is in the neutral state with concentration of the active sites (Pr) as C°.
2. In the first potential step of duration t_{f} to a positive value, oxidation of Pr to Pr^{+.} takes place. Since it is a potential step experiment, the magnitude of the potential step was increased to a higher positive value (E°' + 250 mV) to ensure the kinetic feasibility of the electrode reaction (A). Therefore, the current in this step is controlled by the transport of the Pr towards the electrode and Pr^{+.} away from the electrode which can be described by Fick's second law.
(4.2.1h) 
and
(4.2.1i) 
where D are the diffusion coefficients, C_{Pr} and C_{Pr+.} are the concentrations of the neutral and oxidized species, respectively, and x is the distance. Concentration profiles of, e.g., the neutral species can be obtained by solving the linear Eq. (4.2.1h).
(4.2.1j) 
The concentration distribution of the positive polaron can then be calculated by applying the condition .
3. When the potential was stepped to a negative value (E°'  250 mV)of duration t_{r}, there will be the formation of the negative polaron Pr¯·. (b). Now Pr and Pr^{+.} will be transported towards the electrode and Pr¯· away from the electrode. When both Pr¯· and Pr^{+.} meet with each other, there will be the bimolecular annihilation reaction (C) giving rise to luminescence. since the luminescence [page 98↓]process is considered to be instantaneous in the time scale of the experiment, i.e., Eq.(C) will be modified as
Therefore, the following equations have to be solved to describe the kinetics and concentration profiles in the second potential step (B).
(4.2.1k) 
(4.2.1l) 
(4.2.1m) 
The double layer charging phenomena in the electrode/polymer/solution system is considered on the same grounds as in the case of solution ECL. The difference lies in the larger value for the time constant R_{u}*C_{dl} = τ, since the polymer network generally offers a larger resistance for the transport of ions through it, which are necessary for charging the double layer at the electrode/polymer interface.
The point model was considered for the simulation of the ECL transient, which was discussed in detail in section 4.1.3 while dealing with the solution ECL. The partial differential Eqs.(4.2.1km) are expressed in the finite difference forms as discussed there.
 [page 99↓] 
Time is denoted by the vector 'k' ( ) and distance by 'i' ( ). Initially the conducting polymer consists of the active sites Pr in the neutral state. The point k = 0 represents the time from the point of application of the first potential step (in our case the positive potential step) until the time prior to the application of the second one. The concentrations of the species Pr^{+.} and Pr are obtained by using the error functions (see Eq.(4.2.1j)). The concentration of the negative species, Pr¯· is zero during this interval. The maximum value of the 'i' vector is calculated using the expression i_{max }= (2 D_{M} k_{max})^{1/2}. The concentration array is constructed until i > i_{max}.
The point k =1 represents the time of the application of the second potential step, i.e., k =1 implies t_{r }> 0 where t_{r} denotes the duration of the second potential step. The concentrations of the different species at the electrode surface (i = 0) are fixed by the Nernst equation.
(4.2.4a) 
The concentrations for i > 0 are assumed to have the same values fixed in the earlier time, i.e., the concentrations calculated using the error function at k = 0.
The transportreaction process is allowed to occur from k =1 to k_{max}, and for each value of k, the value of i_{max} is calculated as described earlier. This simulation yields the profiles of concentrationtime and concentrationdistance.
Since the luminescence decay is assumed to be instantaneous, the concentrationtime profile of 0.5 C_{Pr} can represent the luminescence transient. The current transient is calculated as follows:
(4.2.4b) 
where 'j_{F}' represents the faradaic current density, F is the Faraday's constant, J is the flux of the species, z is the charge of the same, 'n' denotes the number of electroactive species. Since the simulation is done for the second potential step, the faradaic reaction of interest, in the present case, is the conversion of Pr^{+} to Pr^{} and Pr to Pr¯·. Hence, the current density can be represented as follows:
 [page 100↓] 
(4.2.4c) 
For the system under consideration, the flux balance equation can be written as J_{Pr} + J_{Pr+ } + J_{PR } = 0. By making use of this condition and Fick's first law, the final expression for the current density is obtained as follows:
(4.2.4d) 
Due to the charging process of the electrochemical interface (metal/polymer) during the initial stages of the potential step (few milliseconds), the applied potential does not reach its final value at the same time as that of its application, but after a certain time lag, which can be represented as follows:
(4.2.5a) 
The effective electrode potential at a time t + Δt can be calculated from its value at the previous time t by the empirical relationship,
(4.2.5b) 
The double layer charging current can be calculated by the following relationship,
(4.2.5c) 
Thus, Eq.(4.2.5b) can be rewritten as follows:
(4.2.6d) 
The parameters apparent diffusion coefficient D_{ap}, uncompensated solution [page 101↓]resistance R_{u} and double layer capacitance C_{dl} were evaluated as discussed in chapter 3.2. The concentration C° was calculated from the molecular weight and dry thickness of the polymer. The value of Δx was calculated after fixing D_{M} as 0.45 and by using the relationship . The simulation was repeated until the calculated current agreed with the experimental current in magnitude, and experimental and simulated ECL transients were of the same shape. The value of k_{ex} corresponding to the coincidence of experimental and simulated transients was taken as the one for the annihilation reaction (D) between the positive and negative polarons. Following are the results of simulation of the cathodic and anodic ECL transients of MEHPPV in 0.1 M TEAClO_{4} and 0.1 M TEAPF_{6}.
Fig 4.2.6a. Simulation of the anodic transient (for a potential step between 1.75 V and 1.45 V, SE  0.1M TEABF_{4}) with C° = 5.8×10^{4 }mol cm^{3}, k_{ex }=1x10^{3} lmol^{1}s^{1}, D_{ap} = 3.2x10^{12}cm^{2 }s^{1}, R_{u}= 1x10^{4}Ω and C_{dl}=1 μF.  

 [page 102↓] 
Fig 4.2.6b. Simulation of the cathodic transient (for a potential step between 1.45 V and 1.75 V, SE  0.1M TEABF_{4}) with C° = 5.8×10^{4 }mol cm^{3}, k_{ex}=3x10^{3} lmol^{1}s^{1}, D_{ap} = 8x10^{13} cm^{2} s^{1}, R_{u }= 1x10^{4 }Ω and C_{dl }=2 μF.  

Fig. 4.2.6c. Simulation of the anodic transient (for a potential step between 1.85 V and 1.35 V, SE  0.1M TEAPF_{6}) with C° = 5.8×10^{4 }molcm^{3}, k_{ex }= 6x10^{3} lmol^{1}s^{1}, D_{ap} = 0.5x10^{12 }cm^{2 }s^{1}, R_{u}= 1x10^{4}Ω and C_{dl}= 5μF.  

 [page 103↓] 
Fig 4.2.6d. Simulation of the cathodic transient (for a potential step between 1.35 V and 1.85 V, SE  0.1M TEAPF_{6}) with C° = 5.8×10^{4 }molcm^{3} k_{ex }= 5x10^{3} lmol^{1}s^{1}, D_{ap} = 1.5x10^{13} cm^{2 }s^{1}, R_{u }= 1x10^{4 }Ω and C_{dl }= 6 μF.  

When the values of the diffusion coefficients are compared between the ECL transients with 0.1 M TEABF_{4} and 0.1 M TEAPF_{6}, they are slightly lower with the latter. This could be due to the larger size of the PF_{6} ^{} than that of the BF_{4} ^{}. Though the difference is not very appreciable, the difference could be attributed to the difficulty for transportation of the PF_{6} ^{} ion inside the polymer. This is based on the experimental result (CV) that MEHPPV cannot be reduced in 0.1 M TBABF_{4} due to the larger size of the TBA^{+} ions that are required for the reduction reaction (section 3.2.2). The value of rate constant k_{ex} is of the order of 10^{4} l mol^{1}s^{1} in all the cases except with the anodic ECL in 0.1 M TEABF_{4} that is 10^{1} lmol^{1}s^{1}, the reason of which is hard to speculate. Nevertheless, the magnitudes are lower than that in the solution phase, cf. DPA, which is on the order of 10^{10} lmol^{1}s^{1}. This could be due to the larger internuclear separation between the electron transfer sites in the polymer, which can be inferred from the following equation proposed by Marcus for electron transfer reaction kinetics [96]:
(4.2.5a) 
 [page 104↓] 
Where k_{ex} stands for the electron transfer rate constant, A is the pre exponential factor, ε_{°} is the permittivity of the free space, a is the distance between the edges of the reactant species, R_{h} is the inter nuclear separation, ε_{op} and ε_{s} are the optical and static dielectric constants of the solvent, and other terms have their conventional meanings. The larger the sizes of the reactant species, a will be smaller and R_{h} will be larger, which will lead to a lower magnitude of k_{ex}. Thus, the lower magnitude of the rate constant for the annihilation reaction in the polymers can be understood.
The discussion for the theoretical analysis of the electrogenerated chemiluminescence for DBPPV is the same as that of MEHPPV. The results are presented below.
Fig. 4.3a. Simulation of the anodic ECL transient (for a potential step between 1.9 V and 1.3 V, SE  0.1M TBABF_{4}) with C° = 6.1×10^{4 }molcm^{3}, k_{ex }= 3x10^{4} lmol^{1}s^{1}, D_{ap} = 6x10^{11} cm^{2} s^{1}, R_{u}= 1200 Ω and C_{dl}= 1 μF.  

 [page 105↓] 
Fig. 4.3b. Simulation of the cathodic ECL transient (for a potential step between 1.3 V and 1.8 V, SE  0.1M TBABF_{4}) with C° = 6.1×10^{4 }molcm^{3}, k_{ex }=1x10^{4} lmol^{1}s^{1}, D_{ap} = 1x10^{11} cm^{2} s^{1}, R_{u}= 1200 Ω and C_{dl}= 3μ F.  

The slow rise in the transients could not be explained by the concept of double layer charging alone. However, the progressive dissolution of polymer DBPPV was not considered in the present simulation, as its exact mode is unknown. This could cause variation in the shape of the ECL transients due to the unequal and variable concentrations of the polarons. Also the kinetics of the transport and the annihilation reaction can change due to the disorders introduced by the dissolution. However, the values of the rate constants were calculated to be on the order 10 ^{4} lmol ^{1} s ^{1} . This is again lower than the annihilation rate constant in the solution phase. This is in accordance with the expectation for a disordered system such as a polymer phase in which the polarons are separated farther apart. (cf. discussion based on Marcus theory for electron transfer, section 4.2.5). The low magnitudes of the apparent diffusion coefficients (10 ^{11} cm ^{2} s ^{1} ) suggests that the transport is dominated by the counterion movement, as with the case of MEHPPV. Thus the present theoretical simulation can explain the kinetics of ECL satisfactorily.
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