Partitioning of monomers

Here Jta(x) denotes the a-th component of the stationary vector x of the Markov chain with transition matrix Q whose elements depend on the monomer mixture composition in microreactor x according to formula (8). To have the set of Eq. (24) closed it is necessary to determine the dependence of x on X in the thermodynamic equilibrium, i.e. to solve the problem of equilibrium partitioning of monomers between microreactors and their environment. This thermodynamic problem has been solved within the framework of the mean-field Flory approximation [48] for copolymerization of any number of monomers and solvents. The dependencies xa=Fa(X)(a=l,...,m) found there in combination with Eqs. (24) constitute a closed set of dynamic equations whose solution permits the determination of the evolution of the composition of macroradical X(Z) with the growth of its length Z, as well as the corresponding change in the monomer mixture composition in the microreactor. 

It was in article [52] where the main reason responsible for the above-mentioned peculiarities was explicitly formulated and substantiated. Its authors related these peculiarities with partitioning of monomer molecules between the bulk of a reaction mixture and the domain of a growing polymer radical. This phenomenon induced by preferential sorption of one of the monomers in such a domain is known as the bootstrap effect. This term was introduced by Harwood [53], because when growing a polymer radical can control under certain conditions its own microenvironment. This original concept enabled him to interpret many interesting features peculiar to this phenomenon. Particularly, he managed to qualitatively explain the similarity of the sequence distribution in copolymerization products of the same composition prepared in different solvents under noticeable discrepancies in composition of monomer mixtures. 

A similar explanation is advanced to explain the urea effect namely the occurrence of increased partitioning of monomer between solution and substrate in the presence of additive. 

It was observed that the NIR-predicted monomer concentration varied greatly during the first 45 minutes after monomer addition but then stabihzed this was attributed to slow solubilization of large monomer droplets into the water phase, and slow partition of monomer between the water phase and the latex phase, leading to large local variations in monomer concentration. This was avoided by allowing a 60-minute soak period after monomer addition, before the temperature was increased to start the polymerization. 

Only possible for some covalent and metal chelate-based processes Phase partitioning of monomers complicates system... 

In this method where two phases are involved, the nature of the organic solvent influences the partition of monomers between the bulk solvent ami the interface. In addition, a good solvent for the diamine would cause division of this monomer into the organic phase, hence disturbing the balance of the two... 

Another practical consideration relates to the use of the semibatch feed policies in emulsion copolymerization. One would need to account for the partitioning of monomers in the different phases as well as the presence of monomer droplets (desired or not) during the particle nucleation and growth stages. 

Complete description of the thermodynamics of partitioning of monomers between the aqueous phase, monomer droplets and latex particles obviously is more complex and requires knowledge of many quantities that are difficult to measure, such as interaction paramet and interfacial tensions [6,7]. As a consequence, there have been essentially two types of approach used to account for... 

German, Maxwell and co-workers also have examined partitioning of monomers in the absence of monomer droplets, i.e. during Interval III of an emulsion polymerization, for which the equilibrium condition is... 

The theoretical developments described in the remainder of this section follow those reported by German, Maxwell and co-workers [20-25], though there are differences in the nomenclature used. In order to eliminate the complicating effects of particle number concentration, the assumptions are made that particle nucleation is complete and that only the partitioning of monomer between the latex particle, aqueous and monomer droplet phases need be considered. To define the thermodynamic conditions for equilibrium, the chemical potential of each monomer in each of these phases is required. The following equations were employed ... 

The solutions to Equation (1) for various experimental conditions involve the statistical analysis of the distribution of free radicals among the particles to give values of n, and the partition of monomer between the two phases to give [M] [3,4,5,6,9]. 

According to Mdller-Plesset " partitioning of monomer Hamiltonian,... 

The SANS technique was further adopted to study the partitioning of monomer between microemulsion droplets and polymer particles for various monomers (ST, w-butyl methacrylate, -butyl methacrylate, and CeMA) (34). It was found that, during microemulsion polymerization, the partitioning of monomer is strongly dependent on the composition of microemulsion, especially on the distance to the phase boundary in the pseudo three-phase diagram of the surfactant/cosurfactant-oil-water system. For example, the monomer partitioning is linear in nature and the concentration of monomer in polymer particles is quite low if the initial microemulsion composition is far away from the phase boundary. In contrast, the monomer partitioning is essentially nonlinear and the... 

Monomer solubility in the continuous phase plays an important role in all of this. The rate at which oligomeric radicals grow depends on the concentration of monomer, while at the same time the solubility of the oligoradicals (which is a direct function of monomer solubility) affects how readily they self-nucleate or are captured. The partition of monomer between the disperse and continuous phases, either monomer-swollen micelles or particles, also depends on the solubility. A so-called "water-insoluble monomer will have a low concentration in the continuous phase and a high concentration in the micelles, with the result that pol3nnerlzation is slow in early stages unless micelles are present. For water-soluble monomers, micelles are unnecessary for rapid particle formation because polymerization can progress readily in the aqueous phase. 

The small-angle neutron scattering technique was further adopted to study the partitioning of monomer between the microemulsion droplets and latex particles for a variety of monomers (styrene, n-butyl methacrylate, r-butyl... 

Partition of monomer between continuous and condensed (microspheres) phases favors the latter one. The concentration of monomer in microspheres is about 10 times higher than that in solution. ... 

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