Degradation modelling diffusion kinetics

Example 1. Let us consider an example that exemplifies step 3 in the core-box modeling framework. The system to be studied consists of one substance, A, with concentration x = [A]. There are two types of interaction that affect the concentration negatively degradation and diffusion. Both processes are assumed to be irreversible and to follow simple mass action kinetics with rate constants p and P2, respectively. Further, there is a synthesis of A, which increases its concentration. This synthesis is assumed to be independent of x, and its rate is described by the constant parameter p3. Finally, it is possible to measure x, and the measurement noise is denoted d. The system is thus given in state space form by the following equations ... 

First, Fig. 15.2 shows the diffusion profile that does match Fickian diffusion kinetic model. What expected is that the slope should become smaller and smaller with after initial linearity. Fig. 15.2 is just opposite. Fig. 15.3 demonstrates the diffusion index n is far higher than the value n = 0.5. All these facts indicate that polymer degradation is companying with the in vitro water diffusion progressing, which... 

Modeling the behavior of bioerodible polyanhydrides is complicated by the many phenomena contributing to release profiles described in the previous section. The degradation kinetics may be coupled to other processes, such as diffusion and dissolution, and the overall erosion kinetics represent the sum of all of these multiple processes (Goepferich, 1996a). 

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. 

Adsorption has a significant impact on the movement of allelo-chemical substances in soil. Such movement in soil by water is important from the standpoint of mechanism of phytotoxin activity in the receiving species at a site remote from the donor plant. Adsorption reduces the solute concentration in the soil solution and consequently minimizes redistribution in the environment. Solute transport has been described by Pick s second law of diffusion and the kinetic models for adsorption and degradation of reactive solutes (, 44). The contribution of adsorption is measured and expressed as the retardation factor, R. 

The issue of bioavailability is further clouded by the physical characteristics of soil and the role of a possible mass transfer limitation. Soil constituents are not simply flat surfaces with free and equal access to all bacterial species. The formation of aggregates from sand-, silt-, and clay-sized particles results in stable structures which control microbial contact with the substrate (Figure 2.7). Discussion of sorption mechanisms and binding affinities must include the possible impact of intra-aggregate transport of the substrate. If the substrate is physically inaccessible to the microorganism then both desorption from soil constituents and diffusion to an accessible site are necessary. The impact of intra-aggregate diffusion on degradation kinetics has been modeled for y-hexachlorocyclohexane (Rijnaarts et al., 1990) and naphthalene (Mihelcic Luthy, 1991). 

Diffusion of solutions of Cr, Co and Mn ions through a PTFE membrane allows for separation of Cr from the remaining ions. Thermal stability of polymeric materials is a significant consideration in many poly(phosphazene) applications. The kinetics of the thermal degradation of PTFE are best fit with a model requiring a two step initiation for depolymerization. These steps involve formation of defect units, such as =P(0)NH- and =P(0)N(CH2CFj)-, which become active centers for depolymerization. Mixed... 

These linear kinetic models and diffusion models of skin absorption kinetics have a number of features in common they are subject to similar constraints and have a similar theoretical basis. The kinetic models, however, are more versatile and are potentially powerful predictive tools used to simulate various aspects of percutaneous absorption. Techniques for simulating multiple-dose behavior evaporation, cutaneous metabolism, microbial degradation, and other surface-loss processes dermal risk assessment transdermal drug delivery and vehicle effects have all been described. Recently, more sophisticated approaches involving physiologically relevant perfusion-limited models for simulating skin absorption pharmacokinetics have been described. These advanced models provide the conceptual framework from which experiments may be designed to simultaneously assess the role of the cutaneous vasculature and cutaneous metabolism in percutaneous absorption. 

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. 

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