Particle kinetic behavior

Focusing on the shorter time-scale component, the characteristic recovery time shows a strong dependence on the pump-laser power or, equivalently, the number of electrons injected The higher the power, the shorter the recovery time. Similar behavior has been noted by Ford et al. [40]. If 1>app is plotted versus the number of electrons injected per particle (Fig. 4), a linear correlation is obtained. In other words, the reaction appears to be first order in electrons (and first order in the oxidized dye). What does this mean mechanistically The simplest interpretation—sketched in Scheme 1—is that the injected electrons are free to return to any available dye molecule, not just the molecule from which they originated. This would be the case if injected electrons avoided surface states (at least at these shorter times) and remained in the conduction band. (Notably, the power-dependent kinetic behavior persists in a rigid glass matrix. Consequently, possible... 

Atoms taking part in diffusive transport perform more or less random thermal motions superposed on a drift resulting from field forces (V//,-, Vrj VT, etc.). Since these forces are small on the atomic length scale, kinetic parameters established under equilibrium conditions (i.e., vanishing forces) can be used to describe the atomic drift and transport, The movements of atomic particles under equilibrium conditions are Brownian motions. We can measure them by mean square displacements of tagged atoms (often radioactive isotopes) which are chemically identical but different in mass. If this difference is relatively small, the kinetic behavior is... 

Our final goal in the present paper is to devise an optimal type of the first stage reactor and its operation method which will maximize the number of polymer particles produced in continuous emulsion polymerization. For this purpose, we need a mathematical reaction model which explains particle formation and other kinetic behavior of continuous emulsion polymerization of styrene. 

Comparison between Experimental Results and Model Predictions. As will be shown later, the important parameter e which represents the mechanism of radical entry into the micelles and particles in the water phase does not affect the steady-state values of monomer conversion and the number of polymer particles when the first reactor is operated at comparatively shorter or longer mean residence times, while the transient kinetic behavior at the start of polymerization or the steady-state values of monomer conversion and particle number at intermediate value of mean residence time depend on the form of e. However, the form of e influences significantly the polydispersity index M /M of the polymers produced at steady state. It is, therefore, preferable to determine the form of e from the examination of the experimental values of Mw/Mn The effect of radical capture mechanism on the value of M /M can be predicted theoretically as shown in Table II, provided that the polymers produced by chain transfer reaction to monomer molecules can be neglected compared to those formed by mutual termination. Degraff and Poehlein(2) reported that experimental values of M /M were between 2 and 3, rather close to 2, as shown in Figure 2. Comparing their experimental values with the theoretical values in Table II, it seems that the radicals in the water phase are not captured in proportion to the surface area of a micelle and a particle but are captured rather in proportion to the first power of the diameters of a micelle and a particle or less than the first power. This indicates that the form of e would be Case A or Case B. In this discussion, therefore, Case A will be used as the form of e for simplicity. 

The reason why the experimental values of particle number are somewhat lower than the theoretical values seems to be that the time where the number of polymer particles was measured is not at infinite but at only 1 hour after the start of polymerization. Figure 9 shows that the number of polymer particles increases with reaction time. The solid lines represent the theoretical values predicted by the Nomura and Harada model. However, since Nt= 0 when Mq= 0, there would be an optimum value of MQ where the number of polymer particles formed becomes maximum. Unfortunately, it is difficult at present to predict the optimum value of MQ theoretically because any reaction model cannot yet explain perfectly the kinetic behavior at high monomer-conversion range. Therefore, one cannot help determining, at present, the optimum value of MQ experimentally. Figures 7 and 8 also show that Eq.(40) roughly satisfies the experimental results. 

Simulate the kinetic behavior by combining the P (t) probability functions for the pseudocompartments to obtain the state probabilities P ( ) of a particle belonging to the phenomenological compartments at time t. That is defined by means of appropriate matrices Bi and E 2 with indicator variables, i.e., 0 s or l s ... 

Changing activation energies are, however, not always indicative for the presence of limitations. The approach of thermodynamic equilibrium in the case of exothermal reactions can cause this phenomenon, as for hydrogenation reactions [44]. Also, changes in rate determining steps and catalyst deactivation might be causes. The same holds for reaction orders. Table 3 gives the various observations that can be made when mass transfer affects the isothermal kinetic behavior of catalyst particles. 

As is clear from Eq. l,the rate of particle growth (R /Nr) is proportional to the monomer concentration, [M]p and the average number of radicals per particle, n, respectively. Thus, n is one of the basic parameters that characterize the kinetic behavior of particle growth in an emulsion polymerization system. Early researchers devoted their efforts to deriving a quantitative description of n by solving Eq. 3 for n defined by Eq. 2 [4,119,120]. 

In this case, the kinetic behavior is quite similar to that of suspension polymerization, except that the polymer particles are supphed with free radicals from the external water phase. When the polymerization proceeds according to Eq. 48, the system is sometimes referred to as obeying pseudo-bulk kinetics. 

Therefore, they showed both theoretically and experimentally that the kinetic behavior of the emulsion polymerization of St initiated by AIBN is basically similar to that initiated by KPS, and concluded that this similarity is mainly due to the radicals produced from the water-soluble fraction of the initiator, because the radicals produced pair-wise inside the small volume of a monomer-swoUen latex particle or a monomer-swollen micelle are very hkely to recombine. 

Oscillations in the number of polymer particles, the monomer conversion, and the molecular weight of the polymers produced, which are mainly observed in a CSTR, have attracted considerable interest. Therefore, many experimental and theoretical studies dealing with these oscillations have been published [328]. Recently,Nomura et al. [340] conducted an extensive experimental study on the oscillatory behavior of the continuous emulsion polymerization of VAc in a single CSTR. Several researchers have proposed mathematical models that quantitatively describe complete kinetics, including oscillatory behavior [341-343]. Tauer and Muller [344] proposed a simple mathematical model for the continuous emulsion polymerization of VCl to explain the sustained oscillations observed. Their numerical analysis showed that the oscillations depend on the rates of particle growth and coalescence. However, it still seems to be difficult to quantitatively describe the kinetic behavior (including oscillations) of the continuous emulsion polymerization of monomers, especially those with relatively high solubility in water. This is mainly because the kinetics and mech-... 

This can be explained by the fact that the flow in the CCTVFR became closer to plug flow as the Taylor number was dropped closer to. Therefore, the steady-state particle number and the steady-state monomer conversion could be arbitrarily varied by simply varying the rotational speed of the inner cylinder. Moreover, no oscillations were observed, and the rotational speed of the inner cylinder could be kept low, so that the possibility of shear-induced coagulation could be decreased. Therefore, a CCTVFR with these characteristics is considered to be highly suitable as a pre-reactor for a continuous emulsion polymerization process. In the case of the continuous emulsion polymerization of VAc carried out with the same CCTVFR, however, the situation was quite different [365]. Oscillations in monomer conversion were observed, and almost no appreciable increase in steady-state monomer conversion occurred even when the rotational speed of the inner cylinder was decreased to a value close to. Why the kinetic behavior with VAc is so different to that with St cannot be explained at present. 

Situations with an excess of ion exchanger occur if,. for example, a given ionic species has to be removed from the solution by a batch operation. An excess of particles with ion exchange properties is usually also present when the sorption of trace ions by soils or soil components (clay minerals, oxides, humic substances) is investigated. Especially in this latter case the particles will be invariably polydisperse. This anomalous kinetic behavior will, of course, only be observed experimentally if the concentration of ions A in the solution and in the various fractions of the ion-ex-changer particles in the mixture are measured continuously. 

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