Partition coefficient, monomer

After phase separation, two sets of equations such as those in Table A-1 describe the polymerization but now the interphase transport terms I, must be included which couples the two sets of equations. We assume that an equilibrium partitioning of the monomers is always maintained. Under these conditions, it is possible, following some work of Kilkson (17) on a simpler interfacial nylon polymerization, to express the transfer rates I in terms of the monomer partition coefficients, and the iJolume fraction X. We assume that no interphase transport of any polymer occurs. Thus, from this coupled set of eighteen equations, we can compute the overall conversions in each phase vs. time. We can then go back to the statistical derived equations in Table 1 and predict the average values of the distribution. The overall average values are the sums of those in each phase. 

Schuller [150] and Guillot [98] both observed that the copolymer compositions obtained from emulsion polymerization reactions did not agree with the Mayo Lewis equation, where the reactivity ratios were obtained from homogeneous polymerization experiments. They concluded that this is due to the fact that the copolymerization equation can be used only for the exact monomer concentrations at the site of polymerization. Therefore, Schuller defined new reactivity ratios, TI and T2, to account for the fact that the monomer concentrations in a latex particle are dependent on the monomer partition coefficients (fCj and K2) and the monomer-to-water ratio (xp) ... 

The Mayo Lewis equation, using reactivity ratios computed from Eq. 18, will give very different results from the homogenous Mayo Lewis equation for mini-or macroemulsion polymerization when one of the comonomers is substantially water-soluble. Guillot [151] observed this behavior experimentally for the common comonomer pairs of styrene/acrylonitrile and butyl acrylate/vinyl acetate. Both acrylonitrile and vinyl acetate are relatively water-soluble (8.5 and 2.5%wt, respectively) whereas styrene and butyl acrylate are relatively water-insoluble (0.1 and 0.14%wt, respectively). However, in spite of the fact that styrene and butyl acrylate are relatively water-insoluble, monomer transport across the aqueous phase is normally fast enough to maintain equilibrium swelling in the growing polymer particle, and so we can use the monomer partition coefficient. 

A high-pressure unit with on-line sampling of the aqueous phase has been developed to measure monomer partition coefficients [19]. Eig. 14.4 shows a schematic set-up of the equipment and a description of the relevant components and features. With this equipment, the partition coefficient m2 given by Eq. (7) can be measured as a function of pressure and temperature. 

Figure 8. Simulated and measured values of the apparent HCB-soil distribution coefficient (K ) as a function of Tween 80 concentration and the HCB-monomer partition coefficient (K. Input parameters CMC = 35 mg/L b = 8.0 L/g = 5.99 g/kg Kj, = 403.4 L/kg = 0.0 Ldcg = 0.09 L/kg.

TABLE 1 The Partitioning Coefficient, K, for Hard Spheres in a Matrix of Chains with m Monomers at Packing Fraction r] ... 

It is also necessary to select the initiator according to the particular monomer(s) and the substrate. Factors to consider in this context, aside from initiator half-lives and decomposition rates, are the partition coefficient ot the initiator between the monomer and polyolefin phases and the reactivity of the monomer vs the polyolefin towards the initiator-derived radicals. 

Obviously, construction of a mathematical model of this process, with our present limited knowledge about some of the critical details of the process, requires good insight and many qualitative judgments to pose a solvable mathematical problem with some claim to realism. For example what dictates the point of phase separation does equilibrium or rate of diffusion govern the monomer partitioning between phase if it is the former what are the partition coefficients for each monomer which polymeric species go to each phase and so on. 

Barrett and Thomas (10)proposed that these effects of differential monomer adsorption could be modeled by correcting homogeneous solution copolymerization reactivity ratios with the monomer s partition coefficient between the particles and the diluent. The partition coefficient is measured by static equilibrium experiments. Barrett s suggested equations are ... 

F = The monomer s partition coefficient between the diluent and the particles... 

Changes of the partition coefficient with monomer consumption in the diluent phase. 

Concentrations in Water and Particles. In order to obtain the rates of reaction, the concentrations of the two monomers and the chain transfer agent in the water and polymer phases were calculated using equilibrium partition coefficients (H). ... 

Partition coefficients between water and an alkanol (e.g., octanol) should be determined in preformulation programs [26]. The partition coefficient of a compound that exists as a monomer in two solvents is given by... 

Fujisawa S, Masuhara E. 1981. Determination of partition coefficients of acrylates, methacrylates, and vinyl monomers using high performance liquid chromatography (HPLC). J Biomed Mater Res 15 787- 793. 

The impact of salt concentration on the formation of micelles has been reported and is in apparent accord with the interfacial tension model discussed in Sect. 4.1, where the CMC is lowered by the addition of simple electrolytes [ 19,65, 280,282]. The existence of a micellar phase in solution is important not only insofar as it describes the behavior of amphipathic organic chemicals in solution, but the existence of a nonpolar pseudophase can enhance the solubility of other hydrophobic chemicals in solution as they partition into the hydrophobic interior of the micelle. A general expression for the solubility enhancement of a solute by surfactants has been given by Kile and Chiou [253] in terms of the concentrations of monomers and micelles and the corresponding solute partition coefficients, giving... 

Monomer concentrations as a function of total surfactant concentration. Experimental CMC s are marked by arrows. At 0.01 o total surfactant levels, the monomer concentrations will be approximately given by the CMC values except for Cj E g whose CMC is 0.06.. Inset shows absorption profile if values of partition coefficient (P) shown apply. From Florence (1982). 

Where ki is the intrinsic partition coefficient for the monomeric species Ci( ) is the concentration of the monomer in the aqueous phase. 

P is a partition coefficient for radicals between two parts of the system - template and surrounding medium. The kinetic scheme of template polymerization is more complicated than that for simple radical polymerization. For many systems (monomer-template-solvent) general kinetic equation was applied ... 

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