Reaction-limited growth

For reaction-limited growth of a sphere the preceding equation gives... 

The mass-transfer-lLmited growth time is much shorter than the reaction-limited growth time, and the reaction should therefore be nearly reaction controlled with a reaction time of 2.77 min. If we heated the reactor to increase k , then the limiting time if k —> oo may be the mass-transfer-limited rate of < 1 sec. 

Transport-Limited Growth 285 Aerosol Phase, Reaction-Limited Growth 286 Dynamics Of Growth Continuity Relation in v Space 288... 

In the model, two limits are considered a reaction-limited growth, which is characterized by a strong size dependence of the growth rate, and diffusion-limited growth, with much weaker size dependence. These limits refer only to the bonding between a particle and a monomer the overall rate is still governed by the hydrolysis. 

In the experimental part the relations between equations 3 and 6 were tested the data were best described with a reaction-limited growth (in the presence of a rate-limiting hydrolysis of the monomers). The increase in... 

A noteworthy exception to the preceding generalizations is reaction-limited growth in which hydrolysis of the monomer is incomplete [4]. In such a scenario, the unhydrolyzed sites are poisoned, or nonreactive, because of the presence of large alkoxy ligands, thereby leading to a more ramified structure. 

The conditions of reaction-limited growth and diffusion-limited growth are summarized in Fig. 1. Also presented are the characteristic morphologies of the evolving particles. 

R (fcpc/fch) diffusion-limited growth (8.3) R (fcpc/fch) reaction-limited growth (8.4)... 

Wirth CT, Zhang C, Zhong G, Hofmann S, Robertson J. Diffusion—and reaction— limited growth of carbon nanotube forests. ACS Nano 2009 3 3560-6. 

Much work has been done on the incorporation of castor oil into polyurethane formulations, including flexible foams [64], rigid foams [65], and elastomers [66]. Castor oil derivatives have also been investigated, by the isolation of methyl ricinoleate from castor oil, in a fashion similar to that used for the preparation of biodiesel. The methyl ricinoleate is then transesterified to a synthetic triol, and the chain simultaneously extended by homo-polymerization to provide polyols of 1,000, 000 molecular weight. Polyurethane elastomers were then prepared by reaction with MDl. It was determined that lower hardness and tensile/elongation properties could be related to the formation of cyclization products that are common to polyester polyols, or could be due to monomer dehydration, which is a known side reaction of ricinoleic acid [67]. Both side reactions limit the growth of polyol molecular weight. 

In spite of these theoretical results, dendritic-type forms for solid-state precipitation processes are the exception rather than the rule. This may happen because the theory is for pure diffusion-limited growth. Interface-limited growth tends to be stabilizing because the composition gradient close to a growing precipitate is less steep when the reaction is partly interface-limited. Thus, G is smaller, and Eq. 20.73 shows that this is a stabilizing effect. This and several other possible explanations for the paucity of observations for unstable growth forms in solid-state... 

The key feature of the model of Nicollian and Reisman (73) is that the surface-reaction-limited oxidation process has viscous oxide flow as the rate-limiting mechanism. During oxidation, volume expansion occurs when silicon is oxidized, and the viscous flow of oxide accompanies this expansion. The rate of growth at the interface is given by... 

Figure 5.6 A discrete, reaction-limited dissolution process interpreted with the population growth model of dissolution.

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