Modeling of Decomposition

Arrhenius kinetics is widely accepted for the modeling of the decomposition process. Considering the decomposition process as a one-stage chemical reaction, the rate of decomposition is determined by the temperature, T, and the quantity of reactants as follows  

During TGA tests, a constant heating rate is used  

From Eq. (2.19), the decomposition degree can be determined as a function of the temperature T, and compared with the experimental measurements from TGA, if the involved kinetic parameters are identified. The modeling performance will be evaluated through a comparison to TGA results in Chapter 4. 

Kinetic theory was formulated to model the conversion degree of a material from one state to another. At each temperature, a FRP material can be considered as a mixture of materials in different states, with changing mechanical properties. The content of each state varies with temperature, thus the composite material shows temperature-dependent properties. If the quantity of material in each state is known and a probabilistic distribution function accounting the contribution from each material state to the effective properties of the mixture is available, the mechanical properties of the mixture can be estimated over the whole temperature range. 

This concept is applied in Chapters 4 and 5 that describe the temperature-dependent thermophysical and mechanical properties of FRP composite materials subjected to elevated temperature and fire. In Chapter 3, however, the estimation of the effective properties of a material mixture through a distribution function of its individual components (in different material states) is introduced first. 

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Fig. 1.30 Arrhenius plots for dehydrogenation of MgH (Tego Magnan ) nulled for 20 h and catalyzed by 5 wt% Ni (tests were done in the temperature range 275-375°C using a nonactivated powder). Arrhenius plots were obtained using various models of decomposition process (Table 1.6)...

Gholz H. L., Wedin D. A., Smitherman S. M., Harmon M. E., and Parton W. J. (2000) Long-term dynamics of pine and hardwood litter in contrasting environments toward a global model of decomposition. Global Change Biol. 6(7), 751-765. 

Smith, O.L. Soil Microbiology A Model of Decomposition and Recycling CRC Press Boca Raton, FL, 1982 Chapter 12. 

In the system of equations (1), we took into account that the oxygen precipitates serves as sinks for oxygen atoms and vacancies and as sources of interstitial silicon atoms. At the same time, the carbon precipitates, in turn, also serve as sinks for carbon atoms and interstitial silicon atoms and as sources for vacancies. Kinetic model of decomposition of... 

Figure 2. Two models of decomposition. The one on the left is the standard subprocedure model where control is tranrferred to the subroutine and then returned when the subroutine completes. The one on the right is the more powerful model of communicating sequential processes. The main procedure spawn a co-routine with which it communicates when necessary while allowing parallel activity. The concurrent model is critical for interface specification. ...

Bunnell, F.L. and Tait, D.E.N. (1974). Mathematical simulation models of decomposition processes. In Soil Organisms and Decomposition in Tundra, pp. 207-225 (A.J. Holding, O.W. Heal, S.R. Maclean, and P.W. Flanagan, eds.). Tundra Biome Steering Committee, Stockholm. 

Criado et al. [CRI 90] calculated the expressions of the CRTA curves a (7) for the one-process models of decomposition gathered by Sharp [SHA 66] (see section 10.2.2). The obtained functions made it possible to differentiate between the various one-process models concerned. 

The first classical trajectory study of iinimoleciilar decomposition and intramolecular motion for realistic anhannonic molecular Hamiltonians was perfonned by Bunker [12,13], Both intrinsic RRKM and non-RRKM dynamics was observed in these studies. Since this pioneering work, there have been numerous additional studies [9,k7,30,M,M, ai d from which two distinct types of intramolecular motion, chaotic and quasiperiodic [14], have been identified. Both are depicted in figure A3,12,7. Chaotic vibrational motion is not regular as predicted by tire nonnal-mode model and, instead, there is energy transfer between the modes. If all the modes of the molecule participate in the chaotic motion and energy flow is sufficiently rapid, an initial microcanonical ensemble is maintained as the molecule dissociates and RRKM behaviour is observed [9], For non-random excitation initial apparent non-RRKM behaviour is observed, but at longer times a microcanonical ensemble of states is fonned and the probability of decomposition becomes that of RRKM theory. 

Model based on the variation of the number of active" coordination sites at the catalyst surface. The growth of tubules during the decomposition of acetylene can be explained in three steps, which are the decomposition of acetylene, the initiation reaction and the propagation reaction. This is illustrated in Fig. 14 by the model of a (5,5) tubule growing on a catalyst particle ... 

Figure 9. Schematic model of the film-formation mechanism on/in graphite (a) the situation before reaction (b) formation of ternary lithiated graphite Lir(solv)vC , (c) film formation due to decomposition of Li t(solv)v. Prepared with data from Ref. [155],...

For the catalyst system WCU-CsHbAICIs-CzHsOH, Calderon et al. (3, 22, 46) also proposed a kinetic scheme in which one metal atom, as the active center, is involved. According to this scheme, which was applied by Calderon to both acyclic and cyclic alkenes, the product molecules do not leave the complex in pairs. Rather, after each transalkylidenation step an exchange step occurs, in which one coordinated double bond is exchanged for the double bond of an incoming molecule. In this model the decomposition of the complex that is formed in the transalkylidenation step is specified, whereas in the models discussed earlier it is assumed that the decom-plexation steps, or the desorption steps, are kinetically not significant. 

The approach taken in the development of an analytical model for the combustion of double-base propellants has been based on the decomposition behavior of the two principal propellant ingredients, nitrocellulose and nitroglycerin. The results of several studies reviewed by Huggett (HI2) and Adams (Al) show that nitrocellulose undergoes exothermic decomposition between 90° and 175°C. In this temperature range, the rate of decomposition follows the simple first-order expression... 

Kinetic expressions for appropriate models of nucleation and diffusion-controlled growth processes can be developed by the methods described in Sect. 3.1, with the necessary modification that, here, interface advance obeys the parabolic law [i.e. is proportional to (Dt),/2]. (This contrasts with the linear rate of interface advance characteristic of decomposition reactions.) Such an analysis has been provided by Hulbert [77], who considers the possibilities that nucleation is (i) instantaneous (0 = 0), (ii) constant (0 = 1) and (iii) deceleratory (0 < 0 < 1), for nuclei which grow in one, two or three dimensions (X = 1, 2 or 3, respectively). All expressions found are of the general form... 

It is appropriate to start with BaN6 since this compound has been studied particularly intensively and has been regarded as a model in the development of the theory of kinetics of decompositions of solids. The sigmoid a—time curves for BaN6 pyrolyses, Fig. 15, are typical examples of solid state autocatalytic behaviour. 

The solid product, BaO, was apparently amorphous and porous. Decomposition rate measurements were made between the phase transformation at 1422 K and 1550 K (the salt melts at 1620 K). The enthalpy and entropy of activation at 1500 K (575 13 kJ mole-1 and 200 8 J K"1 mole-1) are very similar to the standard enthalpy and entropy of decomposition at the same temperature (588 7 kJ and 257 5 J K-1, respectively, referred to 1 mole of BaS04). The simplest mechanistic explanation of the observations is that all steps in the reaction are in equilibrium except for desorption of the gaseous products, S02 and 02. Desorption occurs over an area equivalent to about 1.4% of the total exposed crystal surface. Other possible models are discussed. 

The effects that changes in vegetation have on soil carbon pools and nutrient availability are also difficult to evaluate. However, several models have been successful in predicting vegetation-soil nutrient relationships because they assume that such changes occur as a result of different rates of decomposition and nutrient release from leaf litter of different taxa 50, 60), Such predictions could be tested and the models refined or parameterized for new taxa by measuring soil nutrient availability and respiration in stands of different species on the same soil type. For example, fifty years ago the U.S. Civilian Conservation Corps (CCC) established such stands as species trial plots measurements in some indicate large differences in soil nutrient availability (48), Further measurements in these stands would now occur at the same time-scale at which we expect the feedback between species replacement and soil processes to occur. 

The UASB tractor was modeled by the dispensed plug flow model, considering decomposition reactions for VFA componaits, axial dispersion of liquid and hydrodynamics. The difierential mass balance equations based on the dispersed plug flow model are described for multiple VFA substrate components considaed... 

C15-0141. In your own words, describe the induced-fit model of enz Tne specificity. Illustrate with diagrams, using a h q)othetical enz Tne that catalyzes the decomposition of a square but cannot catalyze the decomposition of a triangle ... 

Figure 5. Cartoon models of the reaction of methanol with oxygen on Cu(llO). 1 A methanol molecule arrives from the gas phase onto the surface with islands of p(2xl) CuO (the open circles represent oxygen, cross-hatched are Cu). 2,3 Methanol diffuses on the surface in a weakly bound molecular state and reacts with a terminal oxygen atom, which deprotonates the molecule in 4 to form a terminal hydroxy group and a methoxy group. Another molecule can react with this to produce water, which desorbs (5-7). Panel 8 shows decomposition of the methoxy to produce a hydrogen atom (small filled circle) and formaldehyde (large filled circle), which desorbs in panel 9. The active site lost in panel 6 is proposed to be regenerated by the diffusion of the terminal Cu atom away from the island in panel 7.

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