Polymer phase homogeneous model

The homogeneous models assttme three phases, i.e., metal, polymer film arrd an electrolyte solutiott. Electrorric, tttixed electrorric (electron or polaron) and iotric charge trarrsport processes are cotrsidered in the metal, within the polymer film and in the solutiott, respectively. The polymer phase itself consists of a polymer matrix with incorporated ions arrd solvent molecrrles. A one-dimensional model is used, i.e., the spatial changes of all qttantities (concerrtrations, potential) within the film are described as a function of a single coordirrate x, which is a good approach when an electrode of usual size is used. The metal Ipolymer and the polymer solution interfacial boundaries are taken as planes. Two intetfacial poterttial differences are considered at the two interfaces, and a potential drop inside the film when crrrrerrt flows. The thicknesses of the electric double layers at the irrterfaces are small in... 

Fig. 3.10a,b Schematics of the two models for polymer-modified electrodes, a Homogeneous model Zjf j/f, interfacial impedances (s f soIution fiIm f s film substrate), Zb impedance of the bulk phase, R -. solution resistance b porous (heterogeneous) model Z the impedance per unit length of the transport channel in the polymer phase, Z2 the impedance per unit length of the transport channel in the pores, Z3 the specific impedance at the iimer interface, which corresponds to charge transfer and charging processes, solution resistance. (From [68], reproduced with the permission of Elsevier Ltd.)... 

Some of these studies focused on the analysis of equilibrium-limited reactions, namely those in which the conditions of the respective conversion could be enhanced relatively to the value obtained in a conventional reactor, the so-called thermodynamic equilibrium conversion.i i The developed models considered generic equilibrium-limited reactions carried on in membrane reactors with perfectly mixed or plug-flow pattems. In all these studies, the main assumptions considered consisted in isothermal and steady-state operation, Fickian transport across a non-porous membrane with a homogeneously distributed nanosized catalyst with constant diffusion coefficients, Henry s law for describing the equilibrium condition at the interfaces membrane/gas, and equality of local concentrations at the interface polymer phase/catalyst surface. 

A detailed description of AA, BB, CC step-growth copolymerization with phase separation is an involved task. Generally, the system we are attempting to model is a polymerization which proceeds homogeneously until some critical point when phase separation occurs into what we will call hard and soft domains. Each chemical species present is assumed to distribute itself between the two phases at the instant of phase separation as dictated by equilibrium thermodynamics. The polymerization proceeds now in the separate domains, perhaps at differen-rates. The monomers continue to distribute themselves between the phases, according to thermodynamic dictates, insofar as the time scales of diffusion and reaction will allow. Newly-formed polymer goes to one or the other phase, also dictated by the thermodynamic preference of its built-in chain micro — architecture. 

On the basis of the concept described above, we propose a model for the homogeneous crystallization mechanism of one component polymers, which is schematically shown in Fig. 31. When the crystallization temperature is in the coexistence region above the binodal temperature Tb, crystal nucleation occurs directly from the melt, which is the well-known mechanism of polymer crystal nucleation. However, the rate of crystallization from the coexistence region is considered to be extremely slow, resulting in single crystals in the melt matrix. Crystallization at a greater rate always involves phase separation the quench below Tb causes phase separations. The most popular case... 

In the photochemical conversion model (Fig. 3), the most serious problem is the undesired and energy-consuming back electron transfer (shown as dotted arrows) as well as side electron transfer, e.g., the electron transfer from (Q) to (T2)ox. It is almost impossible to prevent these undesired electron transfers, if the reactions are carried out in a homogeneous solution where all the components encounter with each other freely. In order to overcome this problem, the use of heterogeneous conversion systems such as molecular assemblies or polymers has attracted many researchers. The arrangement of the components on a carrier, or the separation of the Tj—Q sites from the T2—C2 ones in a heterogeneous phase must prevent the side reactions of electron transfer. 

In order to account for the well known sorption and swelling properties of polymer ion exchangers, Helfferich s model [427] is frequently used for liquid phase reactions. According to this, the pore liquid of the resin, where the reaction occurs, is treated as a homogeneous system and the reactant is assumed to be distributed according to a distribution coefficient... 

We now consider some models of polymer structure and ascertain their usefulness as representative volume elements. The Takayanagi48) series and parallel models are widely used as descriptive devices for viscoelastic behaviour but it is not correct to use them as RVE s for the following reasons. First, they assume homogeneous stress and displacement throughout each phase. Second, they are one-dimensional only, which means that the modulus derived from them depends upon the directions of the surface tractions. If we want to make up models such as the Takayanagi ones in three dimensions then we shall have a composite brick wall with two or more elements in each of which the stress is non-uniform. 

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