Propagation controlled

List of Steps in the Selection of a DDA or Other Flame Propagation Control Method... 

In the selection of an appropriate DDA or other flame propagation control method consideration must he given to a nnmher of factors which affect the choice. Presented helow is a list of items to he considered in a logical sequence. 

The termination kinetic constant exhibits a somewhat more complex behavior. From the onset of reaction, termination is diffusion controlled (segmental diffusion controlled). The diffusion of the macroradicals is the controlling step and the primary means of free radical termination. At some later conversion, the termination mechanism changes from segmental to reaction diffusion control. In this region, a plateau in k, occurs. Reaction diffusion is a propagation controlled... 

Polymerization with propagation controlled by asymmetric groups to be introduced in the monomer before the polymerization and to be cleaved after the polymerization. 

It would be naive to even consider the principles of propagation controlled by ion pairs and free ions as being clarified. Nevertheless, a lot has been done, and the mosaic is being filled in, step by step. Important findings were also recorded with polymerizations of other monomers. 

One of the most important parameters in the S-E theory is the rate coefficient for radical entry. When a water-soluble initiator such as potassium persulfate (KPS) is used in emulsion polymerization, the initiating free radicals are generated entirely in the aqueous phase. Since the polymerization proceeds exclusively inside the polymer particles, the free radical activity must be transferred from the aqueous phase into the interiors of the polymer particles, which are the major loci of polymerization. Radical entry is defined as the transfer of free radical activity from the aqueous phase into the interiors of the polymer particles, whatever the mechanism is. It is beheved that the radical entry event consists of several chemical and physical steps. In order for an initiator-derived radical to enter a particle, it must first become hydrophobic by the addition of several monomer units in the aqueous phase. The hydrophobic ohgomer radical produced in this way arrives at the surface of a polymer particle by molecular diffusion. It can then diffuse (enter) into the polymer particle, or its radical activity can be transferred into the polymer particle via a propagation reaction at its penetrated active site with monomer in the particle surface layer, while it stays adsorbed on the particle surface. A number of entry models have been proposed (1) the surfactant displacement model (2) the colhsional model (3) the diffusion-controlled model (4) the colloidal entry model, and (5) the propagation-controlled model. The dependence of each entry model on particle diameter is shown in Table 1 [12]. 

Two major entry models - the diffusion-controlled and propagation-controlled models - are widely used at present. However, Liotta et al. [28] claim that the collision entry is more probable. They developed a dynamic competitive growth model to understand the particle growth process and used it to simulate the growth of two monodisperse polystyrene populations (bidisperse system) at 50 °C. Validation of the model with on-line density and on-line particle diameter measurements demonstrated that radical entry into polymer particles is more likely to occur by a collision mechanism than by either a propagation or diffusion mechanism. 

P. Fife. Propagator-controller systems and chemical patterns. In C. Vidal and A. Pacault, editors, Non-equilibrium dynamics in chemical systems, pages 76-88. Springer-Verlag, Berlin, 1984. 

Fife, P. Propagator-Controller Systems and Chemical Patterns in Nonequilibrium Dynamics in Chemical Systems Vidal, C. Pacault, A., Ed. Springer-Verlag Berlin, 1984 pp 76-88. 

This reaction is fundamentally different than Equation 3.27 in several aspects. It is an addition rather than a transfer reaction, so that the rate is dependent on the number of unsaturated chain-ends rather than the number of repeat imits in the chains, with importance relative to propagation controlled by the ratio... 

Fife refers to a set of partial differential equations like eqs. (6.28) as a propagator—controller system, for reasons that will become clear later. We recall that the small parameter e 1 makes u change much more rapidly than v. It also makes the time scale of the chemical change much shorter than that of the diffusion that is, the diffusion terms are small compared with the chemical rates of change. Note that all the chemistry is in the functions / and g, which are constructed so that neither concentration can grow to infinity. We will want to consider either a one-dimensional geometry (spatial variable x) or a radially symmetric two-dimensional system, like a Petri dish. 

Marek and coworkers simulated the experiments using an abstract two-variable propagator-controller model (Sevcikova and Marek, 1986). To include electric field effects, they added another term to the reaction-diffusion equation ... 

Figure 10.9 Assumed action of fibres in crack propagation control according to RBM theory, after Romualdi and Batson (1963) ...

Crack initiation and crack propagation are two clearly different phenomena in the mechanics of thin layers on substrates . The experiments on the ITO layer indicate that not the crack initiation but the crack propagation dominates the critical failure strain of the ITO layers. The fact that the poor quality of the ITO edge of the uniformly coated sample does not affect the failure strain clearly supports the propagation-controlled mechanism. A well-defined crack propagation threshold leads to a high Weibull modulus (m 20). The level of this threshold is determined by layer properties, like internal stress, layer thickness and adhesion to the substrate. 

In the present set of experiments, with 0.75 mm wide ITO lines, the sudden increase in resistance and the well-defined, propagation controlled critical failure strain is obtained. In many applications in electronics industry significantly smaller details are present. For active matrix addressed displays, for instance, transistors and connection lines significantly smaller than 100 pm are applied. When the size of the cracks, initiated for instance around a defect, have a stable size, comparable to the size of the component, crack initiation-controlled mechanisms and not the propagation control may govern the resistance of the lines. 

Springer-Verlag, Berlin, 1984, pp. 76-88. Propagator-Controller Systems and Chemical Patterns. 

Tezuka Y, Aoki K (1989) Direct demonstration of the propagation theory of a conductive zone in a polypyrrole film by observing temporal and spatial variations of potentials at addressable microband array electrodes. J Electroanal Chem 273 161-168 Tezuka Y, Aoki K, Ishii T (1999) Alternation of conducting zone from propagation-control to diffusion-control at polythiophene films by solvent substitution. Electrochim Acta 44 1871-1877... 

A (chemical) propagator-controller (PC) system is a reacting and diffusing system which supports chemical wave fronts in some chemical species (the propagator species), the velocity and wave forms of these fronts being modulated by the concentrations of other species (the controller species). The dynamics of the controller species may in turn be influenced by the concentrations of the propagator species. 

A number of models dealing with absorption of free radicals by the latex particles were proposed. They are (a) the collision-controlled model [1,17,18], (b) the diffusion-controlled model [19], (c) the surfactant displacement model [20], (d) the colloidal model [21], and (e) the propagation-controlled model [22, 23]. The dependence of the rate constant for absorption of free radicals by the latex particles on the particle diameter d ) predicted by these models is summarized in Table 4.1 [24]. At present, the most widely accepted models... 

Development of the propagation-controlled model for the absorption of the initiator-derived free radicals is based on the following major assumptions [22] ... 

As mentioned above, the two most popular reaction mechanisms involved in the absorption of free radicals by the monomer-swoUen micelles and polymer particles are the diffusion- and propagation-controlled models. Nevertheless, liotta et al. [39] were inclined to support the colUsion-controlled model. A dynamic competitive particle growth model was developed to study the emulsion polymerization of styrene in the presence of two distinct populations of latex particles (i.e., bimodal particle size distribution). Comparing the on-line density and particle size data with model predictions suggests that absorption of free radicals by the latex particles follows the collision-controlled mechanism. 

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