Reaction-diffusion degradation model

Small polymer chains produced from the hydrolysis reaction during degradation are diffusible. The diffusion mechanism of small polymer chains in solute aud the corresponding diffusion coefQcient are of great interest in the area of polymer degradation. A BD model for simulating the diffusion of small polymer chains and calculating the diffusion coefficient is introduced in this section. 

The broadest class of models, phenomenological models, account explicitly for individual phenomena such as swelling, diffusion, and degradation by incorporation of the requisite transport, continuity, and reaction equations. This class of models is useful only if it can be accurately parameterized. As phenomena are added to the model, the number of parameters increases, hopefully improving the model s accuracy, but also requiring additional experiments to determine the additional parameters. These models are also typically characterized by implicit mean-field approximations in most cases, and model equations are usually formulated such that explicit solutions may be obtained. Examples from the literature are briefly outlined below. 

A model for the SSP of PET under typical industrial processing conditions has been developed by Ravindrath and Mashelkar [15]. Their calculations are also based on experimental data reported in the literature. The results allow the rough conclusion that the reaction rate decreases by a factor of 6 for the temperature range between 285 and 220 °C, accompanied by a decrease of the thermal degradation by a factor of 40. The fact that suitable SSP conditions can be found to warrant a fast reaction rate and minimal degradation makes this process industrially important. These same authors also state that at an early stage of the reaction the kinetics have a predominant influence, whereas diffusivity plays a major part at a later stage of the reaction. 

The kinetic aspect common to all the topics discussed in this chapter is the pyrolysis reactions. The same kinetic approach and similar lumping techniques are conveniently applied moving from the simpler system of ethane dehydrogenation to produce ethylene, up to the coke formation in delayed coking processes or to soot formation in combustion environments. The principles of reliable kinetic models are then presented to simulate pyrolysis of hydrocarbon mixtures in gas and condensed phase. The thermal degradation of plastics is a further example of these kinetic schemes. Furthermore, mechanistic models are also available for the formation and progressive evolution of both carbon deposits in pyrolysis units and soot particles in diffusion flames. 

Taking this as a reasonable approximation for PE and PE-n-MMT, the fits with the aid of nonlinear regression were attempted by the model (5), where an one-dimensional diffusion type reaction was used for the first step and the nth-order (Fn) reaction - for the two subsequent steps of the overall thermal degradation process (Figure 6, Table 1). 

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