Entry rate

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. 

Radical Entry Rate. The rate of transport of the active oligomers from the aqueous phase to the particles have been... 

The entry rate of glucose into red blood cells is far greater than would be calculated for simple diffusion. Rather, it is an example of facilitated diffiision (Chapter 41). The specific protein involved in this process is called the glucose transporter or glucose permease. Some of its properties are summarized in Table 52-3-The process of entry of glucose into red blood cells is of major importance because it is the major fuel supply for these cells. About seven different but related glucose transporters have been isolated from various tissues unlike the red cell transporter, some of these are insidin-dependent (eg, in muscle and adipose tissue). There is considerable interest in the latter types of transporter because defects in their recruitment from intracellular sites to the surface of skeletal muscle cells may help explain the insulin resistance displayed by patients with type 2 diabetes mellitus. 

Table 14.3. Relative rate = (rate in actual entry/rate in first entry) 100...

The input function is the product of amount in the central compartment Aj and the entry rate constant the output function is given by the amount in the effect compartment Ae and... 

DiMasi JA, Paquette C. The economics of follow-on drug development trends in entry rates and the timing of development. PharmacoEcon 2004 22 1-14. 

We shall indicate by (ra -f- rt) the sum of the entry rates of ethyl groups into the polymeric chains, during the polymerization, and by C the amount of conventional active centers (in mols), involved in the polymerization within the interval of time 0, t. 

Palmquist, D. L., Davis, C. L., Brown, R. E. and Sachan, D. S. 1969. Availability and metabolism of various substrates in ruminants. V. Entry rate into the body and incorporation into milk fat of D(-)/3-hydroxybutyrate. J. Dairy Sci. 52, 633-639. 

It is accepted that the radical entry rate coefficient for miniemulsion droplets is substantially lower than for the monomer-swollen particles. This is attributed to a barrier to radical entry into monomer droplets which exists because of the formation of an interface complex of the emulsifier/coemulsifier at the surface of the monomer droplets [24]. The increased radical capture efficiency of particles over monomer droplets is attributed to weakening or elimination of the barrier to radical entry or to monomer diffusion by the presence of polymer. The polymer modifies the particle interface and influences the solubility of emulsifier and coemulsifier in the monomer/polymer phase and the close packing of emulsifier and co emulsifier at the particle surface. Under such conditions the residence time of entered radical increases as well as its propagation efficiency with monomer prior to exit. This increases the rate entry of radicals into particles. 

Guo et al. [29] have estimated the entry rate coefficient, k a, of radicals into micelles (microemulsion droplets) to be 7xl05 cm3 mol-1 s 1, which is several orders of magnitude smaller than ka, the entry rate coefficient into the polymer particles. This was ascribed to the difference of the surface area of microemulsion droplets and polymer particles. The condensed interface layer or the possibly high zeta-potential of the surface of the microemulsion droplets may hinder the entry of radicals. 

The higher the hydrophilicity of macromonomer, the lower the final conversion. This may be attributed to the formation of hydrophilic or surface active oligomer radicals and the low or high radical entry rate. In the system with hydrophilic C1-(EO)17-MA, the limiting conversion was ca. 60%. Thus the low rate of polymerization at ca. 50 or 60% conversion may be discussed in terms of the solution polymerization, a strong bimolecular termination and the low radical entry rate. 

Table 1 Dependence of entry rate coefficient on models [12] particle diameter, as predicted by different...

Maxwell et al. [ 11 ] proposed a radical entry model for the initiator-derived radicals on the basis of the following scheme and assumptions. The major assumptions made in this model are as follows An aqueous-phase free radical will irreversibly enter a polymer particle only when it adds a critical number z of monomer units. The entrance rate is so rapid that the z-mer radicals can survive the termination reaction with any other free radicals in the aqueous phase, and so the generation of z-mer radicals from (z-l)-mer radicals by the propagation reaction is the rate-controlling step for radical entry. Therefore, based on the generation rate of z-mer radicals from (z-l)-mer radicals by propagation reaction in the aqueous phase, they considered that the radical entry rate per polymer particle, p p=pJNp) is given by... 

Another important problem that has been debated for a long time is whether or not the electric charges and the emulsifier layers on the surfaces of the polymer particles affect the radical entry rate of a charged radical (p). It is now con-... 

On the other hand, several reports have been published that point out that when a polymeric surfactant acting as an electrosteric stabilizer is used, the rate of radical entry into a polymer particle should decrease due to a diffusion barrier of the hairy layer built up by the polymeric surfactant adsorbed on the surface of the polymer particles [34-36]. Coen et al. [34] found that in the seeded emulsion polymerization of St using a PSt seed latex stabilized elec-trosterically by a copolymer of acrylic acid (AA) and St, the electrosteric stabilizer greatly reduced the radical entry rate p compared to the same seed latex... 

In our illustrative calculated results, chain transfer reactions are neglected in order to highlight unique characteristics of emulsion polymerization. However, the radical entry rate into a polymer particle is often much smaller than the chain transfer frequency in emulsion polymerization usually. In such cases, dead polymer chain formation is dominated by chain transfer reactions, and the instantaneous weight fraction distribution is given by the following most probable distribution ... 

It is evident from Eq. 85 that the condition =l/(kp[M]pFe) < Cm is needed to apply the CLD method to emulsion polymerization. Note that the radical entry rate may be increased through the radical exit. Even when these conditions are satisfied, a higher polymer concentration than for the corresponding bulk polymerization may result in more occurrences of the polymer transfer reaction. 

One characteristic of the above alkane activation process is the occurrence of a muUiple exchange parameter M greater than unity (M 1.3 - 2) (Note that M = the initial entry rate of D into the alkane divided by the initial rate of H hydrocarbon disappearance). Therefore, each time an alkane is bound to a platinum atom, it suffers several exchanges before being released into the solution. The following scheme has been proposed in the literature to explain the results [31. 

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