Diffusion terminated

Another unique attribute of polymerizations of multifunctional monomers is the dominance of reaction diffusion as a termination mechanism [134,136, 143-146]. Reaction diffusion involves the mobility of radicals by propagation through unreacted functional groups. This termination mechanism is physically different from translation and segmental diffusion termination mechanisms which involve the diffusion of polymer macroradicals and chain segments to bring radicals within a reaction zone before terminating. Whereas normal termination mechanisms are related to the diffusion coefficient of the polymer, reaction diffusion must be considered differently. In essence, reaction diffusion is... 

Fatkullin NF, Kimmich R, Kroutieva M (2000) The twice-renormalised Rouse formalism of polymer dynamics Segment diffusion, terminal relaxation, and nuclear spin-lattice relaxation. J Exp Theor Phys 91(1) 150-166 Ferry JD (1980) Viscoelastic properties of polymers, 3rd edn. Wiley, London Ferry JD (1990) Some reflections on the early development of polymer dynamics Viscoelasticity, dielectric dispersion, and self-diffusion. Macromolecules 24 5237-5245 Ferry JD, Landel RF, Williams ML (1955) Extensions of the Rouse theory of viscoelastic properties to undilute linear polymers. J Appl Phys 26 359-362 Fikhman VD, Radushkevich BV, Vinogradov GV (1970) Reological properties of polymers under extension at constant deformation rate and at constant extension rate. In Vinogradov GV (ed) Uspekhi reologii polimerov (Advances in polymer rheology, in Russian). Khimija, Moscow, pp 9-23... 

If diffusion terminates the velocity bias, then S is the distance a molecule is carried downstream in the average time tD necessary to diffuse into a nearby flow channel having a different velocity. Specifically... 

We see, then, two distinct kinds of plate height terms for the mobile phase a term HD proportional to flow velocity v, valid when diffusion terminates a molecule s velocity bias, and a velocity-independent term Hfy valid when flow terminates the bias. The question yet unanswered is how HD and Hf combine in contributing to the overall experimental plate height. Plate heights are usually additive because variances (for independent processes) are additive it is tempting to apply the additive rule here. However, additivity does not apply to HD and Hf. We see this in simple physical terms by looking at two extremes of flowrate. 

It should be noted that to date one more question related to the kinetics of the chain termination reaction in radical polymerization has not yet been conclusively solved. The diffusive nature of termination presupposes a quite definite, non-random distribution of radicals the number of radicals located close to one another must be smaller than that which corresponds to the random law of particle distribution in space. The initiation reaction, i.e., that of the formation of radicals, does not depend on their location in space. This reaction will, therefore, distort the distribution of radicals in space that corresponds to the diffusive termination and will tend to make... 

Some of the voluminous literature on the oxidation and corrosion of aluminum and its alloys has a direct bearing on DMO. Pure aluminum is normally covered by an amorphous native oxide film which is partially converted to 7-alumina at the interface between the parent metal and the amorphous oxide when heated to 450°C in dry air [7-9]. This unusual behavior is explained by growth of the amorphous phase, through outward cation migration, while thickening of the 7-alumina is by epitaxial growth on the parent metal, controlled by inward oxygen diffusion. Termination... 

The plateau region was the most sensitive to polymerization temperature [17]. At higher temperatures, the mobilities of the reacting species increase and the onset of the reaction diffusion dominance over the segmental diffusion termination is delayed. The enhanced mobility and increased propagation rate coefficient retard the initial drop of which enables to reach higher values at the plateau region. 

Now encounters between molecules, or between a molecule and the wall are accompanied by momentuin transfer. Thus if the wall acts as a diffuse reflector, molecules colliding wlch it lose all their axial momentum on average, so such encounters directly change the axial momentum of each species. In an intermolecuLar collision there is a lateral transfer of momentum to a different location in the cross-section, but there is also a net change in total momentum for species r if the molecule encountered belongs to a different species. Furthermore, chough the total momentum of a particular species is conserved in collisions between pairs of molecules of this same species, the successive lateral transfers of momentum associated with a sequence of collisions may terminate in momentum transfer to the wall. Thus there are three mechanisms by which a given species may lose momentum in the axial direction ... 

The assumption that k values are constant over the entire duration of the reaction breaks down for termination reactions in bulk polymerizations. Here, as in Sec. 5.2, we can consider the termination process—whether by combination or disproportionation to depend on the rates at which polymer molecules can diffuse into (characterized by kj) or out of (characterized by k ) the same solvent cage and the rate at which chemical reaction between them (characterized by kj.) occurs in that cage. In Chap. 5 we saw that two limiting cases of Eq. (5.8) could be readily identified ... 

This situation is expected to apply to radical termination, especially by combination, because of the high reactivity of the trapped radicals. Only one constant appears which depends on the diffusion of the polymer radicals, so it cannot cancel out and may be the source of a dependence of the rate constant on the extent of reaction or degree of polymerization. 

Bulk Polymerization. This is the method of choice for the manufacture of poly(methyl methacrylate) sheets, rods, and tubes, and molding and extmsion compounds. In methyl methacrylate bulk polymerization, an auto acceleration is observed beginning at 20—50% conversion. At this point, there is also a corresponding increase in the molecular weight of the polymer formed. This acceleration, which continues up to high conversion, is known as the Trommsdorff effect, and is attributed to the increase in viscosity of the mixture to such an extent that the diffusion rate, and therefore the termination reaction of the growing radicals, is reduced. This reduced termination rate ultimately results in a polymerization rate that is limited only by the diffusion rate of the monomer. Detailed kinetic data on the bulk polymerization of methyl methacrylate can be found in Reference 42. 

Polymerization Processes. Free-radical polymerization is carried out in a variety of ways. One of the practical problems that must be dealt with is mnaway reactions which can result from auto acceleration, an increase in rate of polymerization caused by diffusion-limited termination (reduced... 

The completion stage is identified by the fact that all the monomer has diffused into the growing polymer particles (disappearance of the monomer droplet) and reaction rate drops off precipitously. Because the free radicals that now initiate polymerization in the monomer-swollen latex particle can more readily attack unsaturation of polymer chains, the onset of gel is also characteristic of this third stage. To maintain desirable physical properties of the polymer formed, emulsion SBR is usually terminated just before or at the onset of this stage. 

Emulsion Polymerization. Emulsion polymerization takes place in a soap micelle where a small amount of monomer dissolves in the micelle. The initiator is water-soluble. Polymerization takes place when the radical enters the monomer-swollen micelle (91,92). Additional monomer is supphed by diffusion through the water phase. Termination takes place in the growing micelle by the usual radical-radical interactions. A theory for tme emulsion polymerization postulates that the rate is proportional to the number of particles [N. N depends on the 0.6 power of the soap concentration [S] and the 0.4 power of initiator concentration [i] the average number of radicals per particle is 0.5 (93). 

Termination. The conversion of peroxy and alkyl radicals to nonradical species terminates the propagation reactions, thus decreasing the kinetic chain length. Termination reactions (eqs. 7 and 8) are significant when the oxygen concentration is very low, as in polymers with thick cross-sections where the oxidation rate is controlled by the diffusion of oxygen, or in a closed extmder. The combination of alkyl radicals (eq. 7) leads to cross-linking, which causes an undesirable increase in melt viscosity. 

Inhibitors as well as substrates bind in this crevice between the domains. From the numerous studies of different inhibitors bound to serine pro-teinases we have chosen as an illustration the binding of a small peptide inhibitor, Ac-Pro-Ala-Pro-Tyr-COOH to a bacterial chymotrypsin (Figure 11.9). The enzyme-peptide complex was formed by adding a large excess of the substrate Ac-Pro-Ala-Pro-Tyr-CO-NHz to crystals of the enzyme. The enzyme molecules within the crystals catalyze cleavage of the terminal amide group to produce the products Ac-Pro-Ala-Pro-Tyr-COOH and NHs. The ammonium ions diffuse away, but the peptide product remains bound as an inhibitor to the active site of the enzyme. 

Monomer molecules, which have a low but finite solubility in water, diffuse through the water and drift into the soap micelles and swell them. The initiator decomposes into free radicals which also find their way into the micelles and activate polymerisation of a chain within the micelle. Chain growth proceeds until a second radical enters the micelle and starts the growth of a second chain. From kinetic considerations it can be shown that two growing radicals can survive in the same micelle for a few thousandths of a second only before mutual termination occurs. The micelles then remain inactive until a third radical enters the micelle, initiating growth of another chain which continues until a fourth radical comes into the micelle. It is thus seen that statistically the micelle is active for half the time, and as a corollary, at any one time half the micelles contain growing chains. 

Diffuser jet throw, L, is a parameter commonly used in air diffuser sizing defined as the distance from the diffuser face to the jet cross-section where the centerline velocity equals a terminal velocity (v is often assumed to be 0.25 rn/s). Therefore, the throw (L) can be determined by velocity decay equations with v. equal to the terminal velocity ... 

Air diffusion The process of air distribution into a space by means of an air terminal unit. The components of air diffusion are... 

Displacement air diffusion Air diffusion where the mixing of supply air and room air external to the air terminal device is at a minimum. See also Air diffusion and Air terminal devices. 

Linear air diffuser An air terminal device with single or multiple slots, each of which has an aspect ratio not less than 10 1. Each slot may consist of a number of separate elements and may or may not have an adjustable member, W hich allows the directions of the air delivered to the treated space to be varied. 

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