The degradation equation

The existence of four independent degradation mechanisms prompts the formulation of a degradation equation . The incremental degradation dD, of a plastic due to the action of microbes B, macro-organisms M, photons P, and chemical C, behaves as follows  

Despite the mathematical shallowness of this equation, the reader should appreciate that the degradation of a plastic may have four independent contributions (partial terms in brackets) which combine and interact with each other. Global concepts of definitions and standards tend to address the partial components of this equation, e.g. biodegradation tests, dD = are 

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It was further shown that such equations could be extended to a wide variety of amides and related compounds and even allowed the prediction of the degradation products of agrochemicals of the benzoylphenylurea type [13]... 

This reaction also plays a role in the degradation of polysulftdes. A back-biting mechanism as shown in equation 6 results in formation of the cycHc disulfide (5). Steam distillation of polysulftdes results in continuous gradual collection of (5). There is an equiUbrium between the linear polysulftde polymer and the cycHc disulfide. Although the linear polymer is favored and only small amounts of the cycHc compound are normally present, conditions such as steam distillation, which remove (5), drive the equiUbrium process toward depolymerization. 

When the polymers are exposed to ultraviolet radiation, the activated ketone functionahties can fragment by two different mechanisms, known as Norrish types I and II. The degradation of polymers with the carbonyl functionahty in the backbone of the polymer results in chain cleavage by both mechanisms, but when the carbonyl is in the polymer side chain, only Norrish type II degradation produces main-chain scission (37,49). A Norrish type I reaction for backbone carbonyl functionahty is shown by equation 5, and a Norrish type II reaction for backbone carbonyl functionahty is equation 6. 

Methylene chloride is one of the more stable of the chlorinated hydrocarbon solvents. Its initial thermal degradation temperature is 120°C in dry air (1). This temperature decreases as the moisture content increases. The reaction produces mainly HCl with trace amounts of phosgene. Decomposition under these conditions can be inhibited by the addition of small quantities (0.0001—1.0%) of phenoHc compounds, eg, phenol, hydroquinone, -cresol, resorcinol, thymol, and 1-naphthol (2). Stabilization may also be effected by the addition of small amounts of amines (3) or a mixture of nitromethane and 1,4-dioxane. The latter diminishes attack on aluminum and inhibits kon-catalyzed reactions of methylene chloride (4). The addition of small amounts of epoxides can also inhibit aluminum reactions catalyzed by iron (5). On prolonged contact with water, methylene chloride hydrolyzes very slowly, forming HCl as the primary product. On prolonged heating with water in a sealed vessel at 140—170°C, methylene chloride yields formaldehyde and hydrochloric acid as shown by the following equation (6). 

The equations and performance parameters for all the major components of a power train must be corrected for ambient conditions and certain parameters must be further corrected to design conditions to accurately compute the degradation. Therefore, to fully compute the performance, and degradation of the plant and all its components, the actual, corrected, and transposed to reference conditions of critical parameters must be computed. 

Estimate the concentration of a discharged chemical at the intake point by 1) simple dilution, or by a simplified degradation equation with dilution. 

Starting with the results of GPC analysis, two approaches have been successfully applied to the problem of polymer degradation, using either the differential or the integral expression of the kinetics equations a) in the first technique, a number of GPC traces are recorded at successive degradation times or degradation yields. Each MWD is divided in a number of... 

In flow-induced degradation, K is strongly dependent on the chain length and on the fluid strain-rate (e). According to the rate theory of molecular fracture (Eqs. 70 and 73), the scission rate constant K can be described by the following equation [155]... 

By using the kinetic equations developed in Sect. 5.2, the degradation yield as a function of strain rate and temperature can be calculated. The results, with different values of the temperature and preexponential factor, are reported in Fig. 51 where it can be seen that increasing the reaction temperature from 280 K to 413 K merely shifts the critical strain rate for chain scission by <6%. 

Solutions containing the nucleophiles and/or HS dissolve elemental sulfur by reactions according to the following equations (nucleophilic degradation) ... 

The rate equations for the degradation reaction mechanism shown in Equations (i) to (iii) are as follows (1) ... 

Studies of chlorophyll degradation in heated broccoli juices over the 80 to 120°C range revealed that chlorophylls degrade first to their respective pheophytins and then to other degradation products in what can therefore be described as a two-step process. Both chlorophyll and pheophytin conversions followed a first-order kinetics, but chlorophyll a was more heat sensitive and degraded at a rate approximately twice that of chlorophyll This feature had been observed by other authors. Temperature dependence of the degradation rate could adequately be described by the Arrhenius equation. ... 

If the equation for this decomposition is known, the enthalpy of formation of the product is subtracted from the sum of the enthalpies of formation of the degradation products. 

This reasoning is used systematically in the most complex cases by looking for the most energetic compounds that are likely to be formed. It leads to the descending order of priority of the degradation substances this is taken into account in the writing of the equation. 

Thermal Stress. The Arrhenius equation states that a 10°C increase in the temperature doubles the rate of most chemical reactions. However, this approach is generally only useful to predict a product s shelf life if the instability of the emulsion is due to a chemical degradation process. Furthermore, this degradation must be identical in mechanism but different in rate at the investigated temperatures. Thus, the instability of... 

The aerobic degradation of formaldehyde in wastewater has been studied by different authors in both continuous22 and batch experiments.23 25 The degradation can occur by two possible paths (see Equations 19.10 and 19.11) ... 

When microorganisms use an organic compound as a sole carbon source, their specific growth rate is a function of chemical concentration and can be described by the Monod kinetic equation. This equation includes a number of empirical constants that depend on the characteristics of the microbes, pH, temperature, and nutrients.54 Depending on the relationship between substrate concentration and rate of bacterial growth, the Monod equation can be reduced to forms in which the rate of degradation is zero order with substrate concentration and first order with cell concentration, or second order with concentration and cell concentration.144... 

This is useful, albeit basic, information for an ES working in the domain of sick cars. If you are employed as a car mechanic, you are not likely to benefit from, or even be interested in, the presence within the knowledge base of details about how lead sulfate batteries degrade with age and how any diminution in concentration of the active materials in the battery can be related through the Nernst equation to a reduction in its voltage. In the context of car repair, all that you need to know is that the battery is dead and the car will not start, so it will need replacing or recharging. 

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