Conformational Relaxation Control

We define a nucleation overpotential rjN EN E0 (Fig. 36) required to make the N0 oxidation nuclei appear. The nucleation overpotential is related to the degree of closure (compaction) of the polymeric entanglement ( ), expressed as the fraction of interchain free volume destroyed after polarization at a given potential Ec, compared with the amount of free volume present at Es. 

This equation makes it possible to obtain the dependence between the degree of closure and the cathodic potential at which the polymer is reduced. The probability ( ) of a conformational change that will allow the reduction and compaction of a segment can be expressed as the inverse of the relaxation time. If all the other terms of Eq. (9) are included in P, then 

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. 

By contrast, at large values of tjc the compactness of the structure is so great (t = 1) that the probability of spontaneous conformational 

Thus P is a structural parameter ranging between 0 and 1 that acts at the initial moments of the oxidation process of every segment the higher the degree of closure (v), the lower the probability (P) of any spontaneous conformational changes and the greater the anodic overpotential required to create a relaxation nucleus. Under these conditions both magnitudes are related by 

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Exchange of counter-ions (and solvent) between the polymer and the solution in order to keep the electroneutrality in the film. In a compacted or stressed film, these kinetics are under conformational relaxation control while the structure relaxes. After the initial relaxation, the polymer swells, and conformational changes continue under counter-ion diffusion control in the gel film from the solution. 

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. 

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... 

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 ... 

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-... 

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. 

Thus, at constant temperature and at a constant sweep rate, the influence of the cathodic overpotential (tjc) on the peak overpotential (t]p) of the voltammogram obtained under conformational relaxation control of the polymeric structure is described by... 

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. 

Reversing the previous reasoning, the presence of a conformational relaxation control in voltammetric responses can be detected in a single... 

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... 

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. 

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