Polymers, kinetic modeling from ideality

A kinetic model based on the Flory principle is referred to as the ideal model. Up to now this model by virtue of its simplicity, has been widely used to treat experimental data and to carry out engineering calculations when designing advanced polymer materials. However, strong experimental evidence for the violation of the Flory principle is currently available from the study of a number of processes of the synthesis and chemical modification of polymers. Possible reasons for such a violation may be connected with either chemical or physical factors. The first has been scrutinized both theoretically and experimentally, but this is not the case for the second among which are thermodynamic and diffusion factors. In this review we by no means pretend to cover all theoretical works in which these factors have been taken into account at the stage of formulating physicochemical models of the process... 

The above-described "labeling-erasing" procedure is in common use in statistical chemistry of polymers (Kuchanov, 2000). It gives a chance to obtain a number of important theoretical results under kinetic modeling of polymerization and polycondensation processes, where the deviation from their description in terms of the ideal kinetic model is due to the short-range effects. 

The basic biofilm model149,150 idealizes a biofilm as a homogeneous matrix of bacteria and the extracellular polymers that bind the bacteria together and to the surface. A Monod equation describes substrate use molecular diffusion within the biofilm is described by Fick s second law and mass transfer from the solution to the biofilm surface is modeled with a solute-diffusion layer. Six kinetic parameters (several of which can be estimated from theoretical considerations and others of which must be derived empirically) and the biofilm thickness must be known to calculate the movement of substrate into the biofilm. 

The model of the ideal gas ignores intermolecular interactions. Given some intermolecular interactions, statistical mechanics must be employed to obtain the equation of state of the real fluid. For fluids of high density, approximations are necessary, but these naturally evolve from the formal, general statistical mechanical framework. For polymers in bulk, the present theories are of the kinetic theory variety since they do not, in principle, relate all macroscopic properties to the constituent molecular properties. In approaching a statistical mechanical theory of polymers in bulk, we can first ask if we can learn from these successes in the statistical mechanics of gases. One way to accomplish this is to consider a bulk polymer situation whicli simulates as closely as possible ideal gas situations. This model illustrates the following ... 

Deviations from this model can be interpreted in terms of a voltage dependent loss of charge separation yield due to either lower electron injection yields or kinetic competition between charge recombination (equation 10.8 and 10.9) and equation 10.10. The first two terms on the right of equation 10.11 compose the usual non-ideal one diode current-voltage characteristic of a solar cell. The final term in equation 10.11 is a light-dependent recombination current, and is required to describe adequately the observed behavior for the cells assembled with the polymer electrolyte with and without plasticizer. 

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