Relaxation conformational

Averbukh I Sh, Blumenfeld L A, Kovarsky V A and Perelman N F 1986 A model of the mechanism of enzyme action in terms of protein conformational relaxation Blochim. Blophys. Acta. 873 290-6... 

Blumenfeld L A, Burbajev D S and Davydov R M 1986 Processes of conformational relaxation in enzyme catalysis The Fluctuating Enzyme ed E R Welch (New York Wiley) pp 369-402... 

The randomization stage refers to the equilibration of the nonequilibrium conformations of the chains near the surfaces and in the case of crack healing and processing, the restoration of the molecular weight distribution and random orientation of chain segments near the interface. The conformational relaxation is of particular importance in the strength development at incompatible interfaces and affects molecular connectivity at polymer-solid interfaces. 

Finally, we want to describe two examples of those isolated polymer chains in a sea of solvent molecules. Polymer chains relax considerably faster in a low-molecular-weight solvent than in melts or glasses. Yet it is still almost impossible to study the conformational relaxation of a polymer chain in solvent using atomistic simulations. However, in many cases it is not the polymer dynamics that is of interest but the structure and dynamics of the solvent around the chain. Often, the first and maybe second solvation shells dominate the solvation. Two recent examples of aqueous and non-aqueous polymer solutions should illustrate this poly(ethylene oxide) (PEO) [31]... 

To understand the global mechanical and statistical properties of polymeric systems as well as studying the conformational relaxation of melts and amorphous systems, it is important to go beyond the atomistic level. One of the central questions of the physics of polymer melts and networks throughout the last 20 years or so dealt with the role of chain topology for melt dynamics and the elastic modulus of polymer networks. The fact that the different polymer strands cannot cut through each other in the... 

Later we will describe both oxidation and reduction processes that are in agreement with the electrochemically stimulated conformational relaxation (ESCR) model presented at the end of the chapter. In a neutral state, most of the conducting polymers are an amorphous cross-linked network (Fig. 3). The linear chains between cross-linking points have strong van der Waals intrachain and interchain interactions, giving a compact solid [Fig. 14(a)]. By oxidation of the neutral chains, electrons are extracted from the chains. At the polymer/solution interface, positive radical cations (polarons) accumulate along the polymeric chains. The same density of counter-ions accumulates on the solution side. 

Stimulation of the conformational relaxation movements of the polymeric chains (by repulsion between the nascent positive charges), with the generation of free volume. Local nuclei or general and simultaneous relaxation occur, depending on the initial compaction of the polymer film. 

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. 

According to our initial hypothesis, these anomalous effects are the experimental results occurring under kinetic control of conformational relaxation. Here conformational relaxation is exposed over its entire length to the influence of the electrochemical variables, the temperature, the polymer-polymer interactions, the polymer-solvent interactions, etc. These are the monitors that can be used to validate each new step of theoretical development during our attempt to integrate electrochemistry and polymer science. 

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. 

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... 

Once formed, the columns of an oxidized polymer begin to expand (Fig. 38), this process being controlled by conformational relaxation in the borders between the oxidized and reduced regions. In order to advance the development of our model by the inclusion of this process, the following simplifications and hypotheses were considered ... 

In order to obtain the current consumed during the nucleated relaxation process under a constant potential, we assume that a stationary density of charge (<, ) will be stored in the polymer at the polarization potential E. The storage of these charges is controlled by both conformational relaxation (3r) and diffusion ( processes, so... 

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 ... 

IX. POLYMER-SOLVENT INTERACTIONS FROM THE ELECTROCHEMICALLY STIMULATED CONFORMATIONAL RELAXATION MODEL... 

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-... 

Figure47. Chronoamperometric responses to potential steps carried out using a polypyrrole electrode from -2000 to 300 mV vs. SCE for 50 s, in 0.1 M UCI04 solutions of different solvents. (Reprinted from H.-J. Grande, T. F. Otero, and I. Cantero, Conformational relaxation in conducting polymers Effect of the polymer-solvent interactions. 7. Non-Cryst. Sol. 235-237,619, 1998, Figs. 1-3, Copyright 1998. Reproduced with kind permission of Elsevier Science-NL, Sara Burgerhartstraat 25, 1055 KV Amsterdam, The Netherlands.)...

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. 

Taking into account that the amount of charge consumed during relaxation at a given overpotential under pure conformational relaxation processes is proportional to the relaxation area of the oxidized regions ... 

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. 

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