Solid state degradation model

Figure 1 Solid-state degradation models, a—fraction decomposed. A = Prout-Tompkins, kt = ln(-p ), B = 2 dimensional phase boundary kl = l-(l-a)1 2, C=Avrami-Erofeev, kt — [—ln(l — a)] , w=l, D = Avrami-Erofeev, = 0.5.

The equations for various solid state degradation models, (p) and (q) are fitting parameters related to the mechanism of reaction. a,/2 is the half life of the reaction. 

Argyroponlos, D. S., and Snn, Y, Photochemically induced solid-state degradation, condensation, and rearrangement reactions in lignin model compounds and milled wood iignin, Photochem. andPhotobiol. 64(3), 510-517 (1996). 

DS Argyropoulos and Y Sun. Photochemically Induced Solid-State Degradation, Condensation, and Rearrangement Reactions in Lignin Model Compounds and Milled Wood Lignin. Photochem Phorobiol 64 510-517, 1996. 

Because the radiation in most cases will not penetrate the entire sample, the concentration of the reactant is unlikely to approach zero at infinite time. A plot of remaining concentration vs. time will therefore level off at a value greater than zero. This should be taken into account when selecting the kinetic model for studies of solid-state degradation (Sande, 1996). The solid-state degradation will in some cases appear to consist of a series of consecutive processes with different mechanisms and rates (Carstensen, 1974). Such a stepwise change in reaction rate is most likely caused by an alteration in sample surface and fading of subsequent layers. The concept of reaction order may not be useful for photodecomposition in the solid state (De VUliers et al 1992). 

A descriptor rate constant for solid-state degradation can be obtained once a theoretical rate equation has been derived and the data have been tested to see if they conform to the proposed model. However, for solid-state degradation in which the factors affecting the degradation mechanism have not been elucidated, because of the complexity involved, often an apparent constant (or constants) obtained by fitting the observed degradation curve to an empirical equation or equations is utilized. Such constants and the empirical relationships themselves can sometimes be used for stability prediction purposes. This section first discusses various theoretical equations used to describe the solid-state stability of drugs and introduces an empirical equation that can often describe the data adequately. 

Figure 18. Schematic representation of the Jander model for solid-state degradation.

Solid-state degradation is not straightforward to model and predict as the first step is some sort of disruption of the crystal that has large activation energy. When this is true, although high-temperature studies may show degradation, the rate will decrease rapidly with decreased temperature, perhaps 10-fold per 10°C decrease in temperature. 

Polymer degradation can be observed in solution, in melt or in the solid state. Degradation in solution is principally used vith model compounds for kinetics studies, vhereas degradation in melt is frequently associated vith processing con-... 

Luminescence properties of and phenomena in polymer systems continues to be widely researched in connection with mechanisms of polymer degradation and stabilization, molecular dynamics, solubility, blend miscibility, and solar energy harnessing. A number of interesting reviews have appeared. Molecular dynamics of polymers in solution and in the solid state have been covered, as has excimer formation,photoresponsive polymers,behaviour of polymer gels, and photochromic phenomena. Photoisomerization of enzymes and model compounds has also been discussed in depth, with particular emphasis on proteins and synthetic polymers containing azo-compounds or spirobenzopyrans. ... 

C. Oliyai, J. P. Patel, L. Carr, and R. T. Borchardt, Chemical pathways of peptide degradation. VII. Solid state chemical instability of an aspartyl residue in a model hexapeptide. Pharm. Res. 7/.-901-908 (1994). 

With this collection of short review papers we would like to present a broad overview of research on polyfluorenes and related heteroanalogues over the last two decades. The collection begins with papers on the synthesis of polyfluorenes and related polyheteroarenes, then reports photophysical properties of this class of conjugated polymers both at the ensemble and the single chain level, continues with a discussion of the rich solid state structures of polyfluorenes, and finally switches to device applications (e.g. in OLEDs). In addition, two chapters are devoted to defined oligofluorenes as low molecular weight model systems for polyfluorenes and also to degradation studies. 

To clarify the mechanisms of the clay-reinforced carbonaceous char formation, which may be responsible for the reduced mass loss rates, and hence the lower flammability of the polymer matrices, a number of thermo-physical characteristics of the PE/MMT nanocomposites have been measured in comparison with those of the pristine PE (which, by itself is not a char former) in both inert and oxidizing atmospheres. The evolution of the thermal and thermal-oxidative degradation processes in these systems was followed dynamically with the aid of TGA and FTIR methods. Proper attention was paid also to the effect of oxygen on the thermal-oxidative stability of PE nanocomposites in their solid state, in both the absence as well as in the presence of an antioxidant. Several sets of experimentally acquired TGA data have provided a basis for accomplishing thorough model-based kinetic analyses of thermal and thermal-oxidative degradation of both pristine PE and PE/MMT nanocomposites prepared in this work. 

Wong, H.-S. et al., Modeling of transconductance degradation and extraction of threshold voltage in thin oxide MOSFETs, Solid-State Electron., 30, 953, 1987. 

Kinetic Models Describing Chemical Drug Degradation in the Solid State... 

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