Diffusion-kinetic modelling

In theory, one assumes the formation of radicals before the chemical stage begins (see Sect. 2.2.3). These radicals interact with each other to give molecular products, or they may diffuse away to be picked up by a scavenger in a homogeneous reaction to give radical yields. The overlap of the reactive radicals is more on the track of a high-LET particle. Therefore, the molecular yields should increase and the radical yields should decrease with LET. This trend is often observed, and it lends support to the diffusion-kinetic model of radiation-chemical reactions. 

Burns and Curtiss (1972) and Burns et al. (1984) have used the Facsimile program developed at AERE, Harwell to obtain a numerical solution of simultaneous partial differential equations of diffusion kinetics (see Eq. 7.1). In this procedure, the changes in the number of reactant species in concentric shells (spherical or cylindrical) by diffusion and reaction are calculated by a march of steps method. A very similar procedure has been adopted by Pimblott and La Verne (1990 La Verne and Pimblott, 1991). Later, Pimblott et al. (1996) analyzed carefully the relationship between the electron scavenging yield and the time dependence of eh yield through the Laplace transform, an idea first suggested by Balkas et al. (1970). These authors corrected for the artifactual effects of the experiments on eh decay and took into account the more recent data of Chernovitz and Jonah (1988). Their analysis raises the yield of eh at 100 ps to 4.8, in conformity with the value of Sumiyoshi et al. (1985). They also conclude that the time dependence of the eh yield and the yield of electron scavenging conform to each other through Laplace transform, but that neither is predicted correctly by the diffusion-kinetic model of water radiolysis. 

La Verne and Pimblott [19] and Pimblott and La Verne [43] refined Eq. (15) and developed an analytical description of these effects of scavengers using the deterministic diffusion kinetic model outlined in Section 2. For a single scavenger, they showed that the dependence of the amount of scavenging reaction on the concentration of S could be better described by [22] ... 

To address the questions of non-homogeneous/spur kinetics, John Hunt and his group at Toronto developed a sub-nanosecond pulse-radiolysis system.In their stroboscopic pulse radiolysis system, they could observe from about 30 to 350 ps after the pulse with a time resolution of about 10 ps. Their results showed no significant decay of the electron between 30 and 350 ps, which was not consistent with the diffusion-kinetic models of spur decay in radiation chemistry. 

Figure 1. Comparison of the extent of delignificatlon predicted by the homogeneous (first-order, second-order and third-order) models and by the reaction-diffusion kinetic model. The open circles are the measured Klason lignin contents In the residues obtained from methylamine extraction of red spruce at 276 bar, 185 C and 1 g/mln solvent flow rate.

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... 

For near and supercritical conditions, combustion gas-phase data are often used as the point of reference to assess solvent effects. The gas-phase values of kig, available for temperatures 800-2500 K, show the activation energy 90 kJ mol In condensed phase, stabilization of H2O molecules via H-bonding may increase the activation barrier, but on the other hand the reaction can be promoted by the solvent cage effect. Diffusion-kinetic modelling and stochastic simulation of chemical reactions in radiation tracks have shown that the occurrence of reaction (15.19) is consistent with the anomalous increase in H2 yield observed in water radiolysis at temperatures above 523 K, if kig is of the order of 1-2x10 s (4-8x10 s ) at 573 K. Considering the two... 

Burns, W.G. and Reed, C.R.V., Effects of L.E.T. (hnear energy transfer) and temperature in the radiolysis of cyclohexane. 1. Experimental results and comparisons with predictions of diffusion kinetic models, Trans. Faraday Soc., 66, 2159, 1970. 

The traditional unipolar diffusion charging model is based on the kinetic theory of gases i.e., ions are assumed to behave as an ideal gas, the properties of which can described by the kinetic gas theory. According to this theory, the particle-charging rate is a function of the square of the particle size dp, particle charge numbers and mean thermal velocity of tons c,. The relationship between particle charge and time according White s... 

Among the dynamical properties the ones most frequently studied are the lateral diffusion coefficient for water motion parallel to the interface, re-orientational motion near the interface, and the residence time of water molecules near the interface. Occasionally the single particle dynamics is further analyzed on the basis of the spectral densities of motion. Benjamin studied the dynamics of ion transfer across liquid/liquid interfaces and calculated the parameters of a kinetic model for these processes [10]. Reaction rate constants for electron transfer reactions were also derived for electron transfer reactions [11-19]. More recently, systematic studies were performed concerning water and ion transport through cylindrical pores [20-24] and water mobility in disordered polymers [25,26]. 

Torkelson and coworkers [274,275] have developed kinetic models to describe the formation of gels in free-radical pol5nnerization. They have incorporated diffusion limitations into the kinetic coefficient for radical termination and have compared their simulations to experimental results on methyl methacrylate polymerization. A basic kinetic model with initiation, propagation, and termination steps, including the diffusion hmitations, was found to describe the gelation effect, or time for gel formation, of several samples sets of experimental data. 

Small amounts of cyclized products are obtained after the preparation of Grignard reagents from 5-hexenyl bromide.9 This indicates that cyclization of the intermediate radical competes to a small extent with combination of the radical with the metal. Quantitative kinetic models that compare competing processes are consistent with diffusion of the radicals from the surface.10 Alkyl radicals can be trapped with high efficiency by the nitroxide radical TMPO.11 Nevertheless, there remains disagreement about the extent to which the radicals diffuse away from the metal surface.12... 

Raub TJ, CL Barsuhn, LR Williams, DE Decker, GA Sawada, NFH Ho. (1993). Use of a biophysical-kinetic model to understand the roles of protein binding and membrane partitioning on passive diffusion of highly lipophilic molecules across cellular barriers. J Drug Targeting 1 269-286. 

Marcus AH. 1985a. Multicompartment kinetic models for lead I. Bone diffusion models for long-term retention. Environ Res 36 442-458. 

The rigorous kinetic modeling with the incorporation of the diffusion step allows explaining the deactivation of the carbon filament growth and the influence of the affinity for carbon formation on the nucleation of the filamentous carbon. 

A kinetic model based on the Flory principle is referred to as the ideal model. Up to now this model by virtue of its simplicity, has been widely used to treat experimental data and to carry out engineering calculations when designing advanced polymer materials. However, strong experimental evidence for the violation of the Flory principle is currently available from the study of a number of processes of the synthesis and chemical modification of polymers. Possible reasons for such a violation may be connected with either chemical or physical factors. The first has been scrutinized both theoretically and experimentally, but this is not the case for the second among which are thermodynamic and diffusion factors. In this review we by no means pretend to cover all theoretical works in which these factors have been taken into account at the stage of formulating physicochemical models of the process... 

Liquid-liquid multiphasic catalysis with the catalyst present in the ionic liquid phase relies on the transfer of organic substrates into the ionic liquid or reactions must occur at the phase boundary. One important parameter for the development of kinetic models (which are crucial for up-scaling and proper economic evaluation) is the location of the reaction. Does the reaction take place in the bulk of the liquid, in the diffusion layer or immediately at the surface of the ionic liquid droplets ... 

In this paper, the kinetics and polymerization behavior of HEMA and DEGDMA initiated by a combination of DMPA (a conventional initiator) and TED (which produces DTC radicals) have been experimentally studied. Further, a free volume based kinetic model that incorporates diffusion limitations to propagation, termination by carbon-carbon radical combination and termination by carbon-DTC radical reaction has been developed to describe the polymerization behavior in these systems. In the model, all kinetic parameters except those for the carbon-DTC radical termination were experimentally determined. The agreement between the experiment and the model is very good. 

As shown in Example 22-3, for solid particles of the same size in BMF, the form of the reactor model resulting from equation 22.2-13 depends on the kinetics model used for a single particle. For the SCM, this, in turn, depends on particle shape and the relative magnitudes of gas-film mass transfer resistance, ash-layer diffusion resistance and surface reaction rate. In some cases, as illustrated for cylindrical particles in Example 22-3(a) and (b), the reactor model can be expressed in explicit analytical form additional results are given for spherical particles by Levenspiel(1972, pp. 384-5). In other f l cases, it is convenient or even necessary, as in Example 22-3(c), to use a numerical pro-... 

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