Relaxation-Controlled Oxidation

The relaxation charge consumed is obtained by integration along the polarization time  

These two equations quantify the evolution of the relaxation current and the relaxation charge as a function of the polarization time when the conducting polymer is submitted to a potential step from Ec to E. They are the relaxation chronoamperogram and the relaxation chronocoulogram, 

Therefore these equations, even though the relaxation charge represents only a small fraction of the overall charge consumed during the complete oxidation, fulfill all the requirements for simulating the point in time at which the chronoamperograms attain the maximum current as a function of the different variables  

For chronoamperograms obtained by potential steps from the same cathodic potential to different anodic potentials  

When the potential step starts from different cathodic potentials to the same anodic potential, Eq. (24) becomes 

---

If h is the height of every cylinder (i.e., the thickness of the polymer film), the expansion of which follows Eq. (12), the current associated with the relaxation-controlled oxidation, V( 0. in the borders of the cylinder can be stated as... 

By differentiation of Eq. (57), an expression of the current flowing across the film during the relaxation-controlled oxidation process is obtained ... 

Theoretical models available in the literature consider the electron loss, the counter-ion diffusion, or the nucleation process as the rate-limiting steps they follow traditional electrochemical models and avoid any structural treatment of the electrode. Our approach relies on the electro-chemically stimulated conformational relaxation control of the process. Although these conformational movements179 are present at any moment of the oxidation process (as proved by the experimental determination of the volume change or the continuous movements of artificial muscles), in order to be able to quantify them, we need to isolate them from either the electrons transfers, the counter-ion diffusion, or the solvent interchange we need electrochemical experiments in which the kinetics are under conformational relaxation control. Once the electrochemistry of these structural effects is quantified, we can again include the other components of the electrochemical reaction to obtain a complete description of electrochemical oxidation. 

I .irtial oxidation under amformation.il relaxation control... 

After polarization to more anodic potentials than E the subsequent polymeric oxidation is not yet controlled by the conformational relaxa-tion-nucleation, and a uniform and flat oxidation front, under diffusion control, advances from the polymer/solution interface to the polymer/metal interface by polarization at potentials more anodic than o-A polarization to any more cathodic potential than Es promotes a closing and compaction of the polymeric structure in such a magnitude that extra energy is now required to open the structure (AHe is the energy needed to relax 1 mol of segments), before the oxidation can be completed by penetration of counter-ions from the solution the electrochemical reaction starts under conformational relaxation control. So AHC is the energy required to compact 1 mol of the polymeric structure by cathodic polarization. Taking... 

Figure 37. Lateral section of a polymeric film during the nucleation and growth of the conducting zones after a potential step. (Reprinted from T. F. Otero, H.-J. Grande, and J. Rodriguez, A new model for electrochemical oxidation of polypyrrole under conformational relaxation control. /. Electroanal. Chem. 394, 211, 1995, Figs. 2-5. Copyright 1995. Reprinted with permission from Elsevier Science.)...

This is the relaxation time of the polymer oxidation under electro-chemically stimulated conformational relaxation control. So features concerning both electrochemistry and polymer science are integrated in a single equation defining a temporal magnitude for electrochemical oxidation as a function of the energetic terms acting on this oxidation. A theoretical development similar to the one performed for the Butler-Volmer equation yields... 

When a polymer relaxes at a constant anodic potential, the relaxation and partial opening of the polymeric structure involve a partial oxidation of the polymer. Once relaxed, the oxidation and swelling of the relaxed polymer goes on until total oxidation is reached this is controlled by the diffusion of the counter-ions through the film from the solution. This hypothesis seems to be confirmed by the current decay after the chronoam-perometric maximum is reached. We will focus now on the diffusion control. 

Equations (37) and (38), along with Eqs. (29) and (30), define the electrochemical oxidation process of a conducting polymer film controlled by conformational relaxation and diffusion processes in the polymeric structure. It must be remarked that if the initial potential is more anodic than Es, then the term depending on the cathodic overpotential vanishes and the oxidation process becomes only diffusion controlled. So the most usual oxidation processes studied in conducting polymers, which are controlled by diffusion of counter-ions in the polymer, can be considered as a particular case of a more general model of oxidation under conformational relaxation control. The addition of relaxation and diffusion components provides a complete description of the shapes of chronocoulograms and chronoamperograms in any experimental condition ... 

These equations describe the full oxidation of a conducting polymer Submitted to a potential step under electrochemically stimulated confer-mational relaxation control as a function of electrochemical and structural variables. The initial term of /(f) includes the evolution of the current consumed to relax the structure. The second term indicates an interdependence between counter-ion diffusion and conformational changes, which are responsible for the overall oxidation and swelling of the polymer under diffusion control. 

The influence of the solvent on the oxidation of film under conformational relaxation control is illustrated in Fig. 47, which shows chronoamperograms obtained by steps from -2000 to 300 mV vs. SCE at room temperature (25°C) over 50 s in 0.1 M LiC104 solutions of different solvents acetonitrile, acetone, propylene carbonate, (PC), dimethyl sulfoxide (DMSO), and sulfolane. Films were reduced over 120 s in the corresponding background solution. Despite the large differences observed in the relative shape of the curves obtained in different solvents, shifts in the times for the current maxima (/max) are not important. This fact points to a low influence of the solvent on the rate at which confor-... 

When rfc = 0, the polymeric structure is considered to be open enough (i = 0) that any subsequent oxidation will not occur under conformational relaxation control, hence P = 1. Every polymeric chain at the poly-mer/solution interface acts as a nucleus a planar oxidation front is formed that advances from the solution interface toward the metal/polymer interface at the diffusion rate. 

Equations (57) and (58) describe the electrochemical oxidation of conducting polymers during the anodic potential sweep voltammograms (/f vs. q) or coulovoltagrams (Qr vs. tj) under conformational relaxation control of the polymeric entanglement initiated by nucleation in the reduced film. They include electrochemical variables and structural and geometric magnitudes related to the polymer. 

So a linear dependence between the potential of the voltammetric peak and the increasing cathodic initial potential for the voltammograms (Fig. 57) points to an oxidation process occurring under conformational relaxation control of the electrode structure. 

Taking into account the variation in the oxidized area as a function of the overpotential, and the counter-ion flows, the charge consumed during the potential sweep in those regions where the structure was previously opened under conformational relaxation control, is given by... 

As in chronoamperograms, the fraction of the overall oxidation charge involved in relaxation processes is quite small in the absence of any external stress. The share of the overall current at every potential between electrochemical processes occurring under relaxation control and those driven by swelling-diffusion control can be observed in Fig. 66. I(r) has... 

When the oxidation of an electrochromic film is produced under conformational relaxation control, and the current is stopped before the coalescence between blue nuclei is produced, the elec-trodic potential remains constant but the expansion of the nucleus goes on, at the expense of a decrease in the degree of oxidation inside the nucleus until a uniform composition is achieved, with uniform darkening of the film. 

T.F. Otero and I. Boyano, Potentiostatic oxidation of polyaniline under conformational relaxation control Experimental and theoretical study. J. Phys. Chem. B, 107,4269 (2003). 

Otero, T.E, H. Grande, and J. Rodriguez. 1995. A new model for electrochemical oxidation of polypyrrole under conformational relaxation control. J Electroanal Chem 394 211. 

A catalytic oxidation system may cost 150 per car, but the catalyst cost is estimated to be 30, less than 1% of the cost of an automobile (2). In a few years, the gross sale of automotive catalysts in dollars may exceed the combined sale of catalysts to the chemical and petroleum industries (3). On the other hand, if the emission laws are relaxed or if the automotive engineers succeed in developing a more economical and reliable non-catalytic solution to emission control, automotive catalysis may turn out to be a short boom. Automotive catalysis is still in its infancy, with tremendous potential for improvement. The innovations of catalytic scientists and engineers in the future will determine whether catalysis is the long term solution to automotive emissions. 

Steps 1 and 2 of polymer oxidation described in the previous section can be considered as a relaxation step. Then the oxidation is completed by swelling184 186 under diffusional control. The electrochemically stimulated conformational relaxation, swelling, and oxidation of a conducting polymer is shown in Fig. 35. 

---