Degradation modelling rate equation

Based on this model, the following rate equations relating the hydrolytic degradation of pesticides from sediment water suspensions can be written dC... 

A critical component to any mathematical model of pyrolysis, ignition, or even flame spread is the modeling of small-scale thermal degradation. Traditionally, thermal degradation processes in solids are considered to be analogous to chemical reactions in gases and liquids and are modeled in terms of sets of kinetic rate equations, typically of the form... 

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. 

Most degradation processes are temperature-activated, and they are best represented by the classic Arrhenius reaction rate equation. The application of such a model is shown in Figure 2.13. The short-term points are obtained by selecting the life criterion (for example a 50% drop in toughness) and then ageing the material at several elevated temperatures until the desired extent of degradation is achieved. Four such points are recommended. A linear extrapolation on a log(criterion) versus 1/T plot allows prediction of the life at... 

In a previous study [8], a model based on a first-order rate equation was derived to acconnt for the effect of irradiance on the degradation rate of dye concentration in the flnorescent vinyl film. This model was snbsequently modified to account for the impact of temperature by including an Arrhenins factor ... 

A kinetic analysis based on the Coats-Redfern method applied nonisothermal TGA data to evaluate the stability of the polymer during the degradation experiment. Of the different methods, the Coats-Redfern method has been shown to offer the most precise results because gives a linear fitting for the kinetic model function [97]. This method is the most frequent in the estimation of the kinetic function. It is based on assumptions that only one reaction mechanism operates at a time, that the calculated E value relates specifically to this mechanism and that the rate of degradation, can be expressed as the basic rate equation (Eq. 5.3). This method is an integral method that assumes various... 

Degradation rates were determined for the reported data using a nonlinear regression of conventional first-order kinetic equations. The software used for this fitting procedure was Model Manager, Version 1.0 (Cherwell Scientific, 1999). 

The CAT model estimates not only the extent of drug absorption, but also the rate of drug absorption that makes it possible to couple the CAT model to pharmacokinetic models to estimate plasma concentration profiles. The CAT model has been used to estimate the rate of absorption for saturable and region-depen-dent drugs, such as cefatrizine [67], In this case, the model simultaneously considers passive diffusion, saturable absorption, GI degradation, and transit. The mass balance equation, Eq. (51), needs to be rewritten to include all these processes ... 

The simplest scenario to simulate is a homopolymerization during which the monomer concentration is held constant. We assume a constant reaction volume in order to simplify the system of equations. Conversion of monomer to polymer, Xp defined as the mass ratio of polymer to free monomer, is used as an independent variable. Use of this variable simplifies the model by combining several variables, such as catalyst load, turnover frequency, and degradation rate, into a single value. Also, by using conversion instead of time as an independent variable, the model only requires three dimensionless kinetics parameters. 

The critical value to test for equality on slopes is F0,25j-i,n-2i = Eo.25,2,15 = 152. Since / (slope) < / 0.25,2,15, hypothesis (47) for equal degradation rate cannot be rejected at the 0.25 level of significance. It is concluded that there is no significant difference among the slopes of model (14), that is, the model represented by Equation (14) reduces to model (29). 

Hammett s equation was also established for substituted phenols from the elementary hydroxyl radical rate constants. The Hammett resonance constant was used to derive a QSAR model for substituted phenols. The simple Hammett equation has been shown to fail in the presence of electron-withdrawing or electron-donating substituents, such as an -OH group (Hansch and Leo, 1995). For this reason, the derived resonance constants such as o°, cr, and o+ were tested in different cases. In the case of multiple substituents, the resonance constants were summed. Figure 5.24 demonstrates a Hammett correlation for substituted phenols. The least-substituted compound, phenol, was used as a reference compound. Figure 5.24 shows the effects of different substituents on the degradation rates of phenols. Nitrophenol reacted the fastest, while methoxyphenol and hydroxyphenol reacted at a slower rate. This Hammett correlation can be used to predict degradation rate constants for compounds similar in structure. 

Figure 9.19 shows the Hammett s equation for degradation rates of substituted nitrobenzenes from experimental data. Photocatalytic degradation of the nitro aromatic compounds by UV/Ti02 from the experimental data reported by Dillert et al. (1995) are used to construct the model. The degradation of nitrobenzenes can be described according to the number of nitro substituents nitrobenzene > dinitrobenzene > 1,3,5-trinitrobenzene (Dillert et al., 1995). 

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