Polymer conformational relaxation

The factor in the outer brackets accounts for the influence of polymer conformational relaxation on the equilibrium rates, and has values typically ranging from 0.01 to 0.5, depending on the depth of the binding potential When [Pg.460]

Oxidation processes have not yet been considered, since they are complicated by polymer conformational relaxation processes and the low electronic conductivity of the starting fully reduced state. Other workers have considered ionic diffusion through the thickness of a PPy.C104 film during oxidation [50], but these results cannot be directly compared with Smela et al. because in one case the anion is dominant and in the other case the cation is dominant. 

Differential Flory Huggins interaction parameter for the polymer ( Conformational relaxation (second step of dilution) (23)... 

Quantum well interface roughness Carrier or doping density Electron temperature Rotational relaxation times Viscosity Relative quantity Molecular weight Polymer conformation Radiative efficiency Surface damage Excited state lifetime Impurity or defect concentration... 

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. 

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... 

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... 

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. 

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. 

The polycarbonate membranes are stretch-oriented during fabrication in order to improve their mechanical properties. If the membrane is subsequently heated above its glass-transition temperature ( 150°C), the polymer chains relax to their unstretched conformation and the membrane shrinks. This shrinking of the membrane around the Au nanowires in the pores causes the junction between the nanowire and the pore wall to be sealed. This is illustrated in Fig. 5, which shows voltammograms for tri-methylaminomethylferrocene (TMAFc+) before (Fig. 5A) and after (Fig. 

C.J. Farrell, A. Keller, M.J. Miles, and D.P. Pope, Conformational relaxation time in polymer solutions by elongational flow experiments 1. Determination of exten-sional relaxation time and its molecular weight dependence, Polymer, 21,1292 (1980). 

A frequency dependence of complex dielectric permittivity of polar polymer reveals two sets or two branches of relaxation processes (Adachi and Kotaka 1993), which correspond to the two branches of conformational relaxation, described in Section 4.2.4. The available empirical data on the molecular-weight dependencies are consistent with formulae (4.41) and (4.42). It was revealed for undiluted polyisoprene and poly(d, /-lactic acid) that the terminal (slow) dielectric relaxation time depends strongly on molecular weight of polymers (Adachi and Kotaka 1993 Ren et al. 2003). Two relaxation branches were discovered for i.s-polyisoprene melts in experiments by Imanishi et al. (1988) and Fodor and Hill (1994). The fast relaxation times do not depend on the length of the macromolecule, while the slow relaxation times do. For the latter, Imanishi et al. (1988) have found... 

This is exactly the molecular-weight dependence of conformational relaxation times of polymer in non-entangled state and for the region of diffusive mobility (see equation (4.41), weakly-entangled system). 

Electrochemically stimulated conformational relaxation model (ESCR model) — This model [i, ii] describes the relaxation phenomena occurring during the charging and discharging of -> conducting polymers. It assumes that applying an anodic -> overpotential to a neutral conjugated polymer, as a first step, an expansion of the closed polymeric structure occurs. In this way, partial oxidation takes place and counter ions from the solution enter the solid polymer under the influence of an electrical field at those points of the polymer/electrolyte... 

Since the appearance of the redox [ii, iii] and conducting [iv] polymer-modified electrodes much effort has been made concerning the development and characterization of electrodes modified with electroactive polymeric materials, as well as their application in various fields such as -> sensors, actuators, ion exchangers, -> batteries, -> supercapacitors, -> photovoltaic devices, -> corrosion protection, -> electrocatalysis, -> elec-trochromic devices, electroluminescent devices (- electroluminescence) [i, v-viii]. See also -> electrochemically stimulated conformational relaxation (ESCR) model, and -> surface-modified electrodes. 

If all we had to worry about was transitions between two different bond conformational states, say trans and gauche (so that there would be more trans conformations as the chain was stretched out), and if the rotations of all the bonds were independent of one another, then the conformational relaxation process we have described here could be described in terms of a single relaxation time t1 (top of Figure 13-84). But in real polymer materials there is a whole range or spectrum of time-dependent rearrangements. 

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