Radical generation rates

The entry rate was calculated using radical generation rate, thermal entry rate, reentry rate, and initiator efficiency. The method for calculating initiator efficiency will be discussed later. 

Rate of Formation of Primary Precursors. A steady state radical balance was used to calculate the concentration of the copolymer oligomer radicals in the aqueous phase. This balance equated the radical generation rate with the sum of the rates of radical termination and of radical entry into the particles and precursors. The calculation of the entry rate coefficients was based on the hypothesis that radical entry is governed by mass transfer through a surface film in parallel with bulk diffusion/electrostatic attraction/repulsion of an oligomer with a latex particle but in series with a limiting rate determining step (Richards, J. R. et al. J. AppI. Polv. Sci.. in press). Initiator efficiency was... 

The rates of propagation and termination in the aqueous phase were also calculated. The radical entry rate, radical generation rate, and aqueous propagation rate were then used to develop an algebraic equation for the rate of formation of primary precursors. This equation is an extension to copolymers of the homogeneous nucleation equation derived by Hansen and Ugelstad (7.) for a homopolymer. 

The research on the processes of mechanical destruction in deformed polypropylene (PP) melts was conducted with the aid of stable radical (tripentachlorphenylmethyl) consumption. There was defined the dependence of radical generation rate on shear rate. At low values y it is approximate to linear. 

The contribution of mechanical priming to the dependence of radical generation rate... 

The temperature dependence of radical generation rate in the Arrhenius coordinates at... 

Radicals are consumed during the reaction by bimolecular chain termination steps such as eq. (5). Replacement radicals are produced by chain branching reactions such as eq. (4). The new radicals (e. g., alkoxy radicals see below) can abstract hydrogen to start new chains. At steady state, the radical generation rate is essentially equal to the radical consumption rate. There have been lively debates in the literature on the sources of the original radicals this question is essentially unresolved [8, 10, 14]. 

Figure 1. Computed time dependencies of the concentration of the transient (R ) and the persistent radicals (Y ) for [Y]o = [R]o = 0, a common radical generation rate r = 10 6 Ms1, Ayr = kc= 109 M 1 s 1, and different ratios k,y/ ktr in a log—log representation. The log—log representation enhances the visualization of the different time regimes.

In the homogeneous MMA polymerization with 1-32 (Y = CH3)/CuBr/L-9 (R = n-Pen), the rate increased in the order xylene < DMB < DPE,179 probably due to the differences in the dielectric constant and coordination ability of the solvents. With the homogeneous Ru-1 catalyst, the polymerization of MMA was faster in a polar solvent such as CPI2C12 than in toluene.159 A more detailed analysis on solvent effects was carried out by end-capping a polymer radical with hydroxyl-TEMPO, where the radical intermediate was generated from bromide macroinitiators via CuBr/L-4 catalyst.242 A polar solvent such as butyl acetate increases the radical-generation rate from poly(acrylate)s but not from polystyrene. On the other hand, no rate increase was found for both macroinitiators in DMF, which is... 

Simplified model based on Rayleigh-Plesset equation and chemical kinetics to predict OH radicals generation rate and the effect of parameters such as reactant concentration, temperature, etc. 

One should note that this ratio should be controlled at the desired level regardless of the magnitude of the total radical concentration, and hence impurities which affect the radical concentration will have no effect on copolymer composition control. The on-line measurement of heat generation rate can thus be used to set the appropriate monomer feed rate. If polymerization is too slow because of radical scavengers, one can increase the radical generation rate to compensate, and, in parallel, increase the monomer inflow rate to maintain the ratio constant (or, vice versa to compensate for a possible auto-acceleration operating point). Additional discussion is provided in Dub6 etal. [56]. 

Equations 6.57 and 6.58 show that PSD is the result of the competition between nuc-leation, particle growth and coagulation. Particle growth broadens the PSD because of the higher number of radicals in large particles. This is an intrinsic feature of the system and there is little that the operator can do to modify it. Particle nucleation depends mainly on the availability of the emulsifier, but it is also affected by the radical generation rate, the water-solubility of the monomers and the number of particles already... 

The overall radical generation rate is then given by... 

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