Monomer partitioning

For a multimonomer system, the calculation of the concentrations of the monomers in the different phases involves the simultaneous solution of the thermodynamic equilibrium equations and the material balances. Several equilibrium equations may be used, those based on partition coefficients [20] and on the 

Morton-Flory-Huggins equation [21] being the most commonly applied. For a multimonomer system, the parameters of the Morton-Flory-Huggins are not usually available, and it has been sho vn [22] that for solids contents typical of commercial latexes ( 50 wt.%) the use of the Morton-Flory-Huggins equation does not provide significant advantages over the use of partition coefficients. In the latter case, the system of algebraic equations (5) and (6) needs to be solved, where K. is the partition coefficient of monomer i between phase j and the aqueous phase, (fij the volume fraction of monomer i in phase j, rf) the volume fraction of water in the aqueous phase, j) the volume fraction of polymer in the polymer particles, Vy the volume of polymer particles, Vj the volume of monomer droplets, the volume of the aqueous phase, and V, and W are the volumes of monomer i, polymer, and water, respectively. 

During the Intervals 1 and 11 of a batch emulsion polymerisation, monomers are divided, that is, partitioned, over the monomer droplets, the aqueous phase and the polymer particles. The monomer that is consumed by polymerisation in the polymer particles is replaced by monomer that is transferred from the monomer droplets through the aqueous phase into the particle phase. In Interval 111, there are no droplets and the monomer is mosdy located in the polymer particles. In the semi-batch processes, monomers are continuously fed into the reactor, usually under starved conditions, namely, at high instantaneous conversions, for example, polymer/monomer ratios close to 90/10 on weight bases. Under these circumstances, only the newly fed monomer droplets are present in the reactor and the life-time of these droplets is short because the monomers are transferred through the aqueous phase to the polymer particles where they are consumed by polymerisation. 

The concentration of monomer in the polymer particles depends on relative time constants for mass transfer and polymerisatiou Except for poorly emulsified highly water-insoluble monomers, the time constant for mass transfer is negligible with respect to the time constant for polymerisation. Hence the concentrations of the monomers in the different phases are given by the thermodynamic equilibrium  

In this section, the equilibrium of monomer over the different phases is addressed to allow the calculation of the rate of polymerisation, see Equation 4.3 and the instantaneous and cumulative copolymer composition, see Equation 4.2. 

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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. 

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. 

An example of the first approach is the integration of hydrogels into nanostructured silica films by addition of a suitable monomer (e.g., methyl methacrylate, /V-isopropyl acrylamide, etc.) and an initiator for radical polymerization to a solution containing a structure-directing surfactant and a prehydrolyzed silica precursor. During self-assembly, the monomers partition within the hydrophobic core of the surfactant mesophase postsynthesis polymerization (for instance, by UV treatment) followed by solvent washing to remove the surfactant template yields a polymer-silica nanohybrid. 

In an emulsion copolymerization, monomer partitioning between the monomer droplet, polymer particle and aqueous phases plays a key role in determining the rate of copolymerization and the copolymer composition. Two approaches (empirical and thermodynamic) have been proposed to predict the monomer concentrations in the polymer particles in an emulsion copolymerization system. In the emulsion copolymerization of St and MMA, Nomura et al. [45,122,140] first proposed an empirical approach for predicting the saturated concentration of each monomer in the polymer particles as a function of the monomer composition in the monomer droplets, as shown by... 

By combining thermodynamically-based monomer partitioning relationships for saturation [170] and partial swelling [172] with mass balance equations, Noel et al. [174] proposed a model for saturation and a model for partial swelling that could predict the mole fraction of a specific monomer i in the polymer particles. They showed that the batch emulsion copolymerization behavior predicted by the models presented in this article agreed adequately with experimental results for MA-VAc and MA-Inden (Ind) systems. Karlsson et al. [176] studied the monomer swelling kinetics at 80 °C in Interval III of the seeded emulsion polymerization of isoprene with carboxylated PSt latex particles as the seeds. The authors measured the variation of the isoprene sorption rate into the seed polymer particles with the volume fraction of polymer in the latex particles, and discussed the sorption process of isoprene into the seed polymer particles in Interval III in detail from a thermodynamic point of view. 

Tognacci et al. [ 183] discussed various methods for measuring the monomer concentration in the polymer particles. The method proposed by the authors is a direct estimation of the solvent activity by the GC (gas chromatography) measurement of its partial pressure in the gas phase at equilibrium with the polymer particle, monomer droplet (if any) and aqueous phase in the latex. They proposed an original measuring technique and carried out measurements for different monomers (St, MMA, and VAc) and polymeric matrices (PSt and MMA-VAc copolymer), both above and below saturation conditions (corresponding to Intervals II and III). They compared the experimental data with that predicted by the monomer partitioning relationships derived by Maxwell et al. [166,170] and Noel et al. [172]. 

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. 

In the context of utilizing surfactant assemblies for building nanostructured polymeric materials, one other approach that deserves mention is the polymerization of standard monomers partitioned into the hydrophobic regions of surfactant aggregates one in particular that has received a lot of attention is vesicle templating [84]. The basic idea in this approach is to generate vesicles using appropriate surfactants and then to solubilize standard monomers, such as styrene, within the... 

Co, C.C. and Kaler, E.W. (1998) Particle size and monomer partitioning in microemulsion polymerization 2. Online small angle neutron scattering studies. Macromolecules, 31,3203-3210. 

Factors Determining Polymer Growth Monomer Partitioning,... 

Success in vesicle templating depends on control of reaction kinetics, monomer partitioning, membrane and polymer fluidity (Tg vs polymerization temperature), the use of cross-linking monomers, and anchoring polymerizable monomers. In practice, phase separation of the newly forming polymer and the surfactant bilayer has been observed under a variety of conditions. The extent of phase separation appears to follow intuitive guidelines, with the compatibility of the monomer and polymer with the surfactant of central importance. 

On the other hand, when dealing with heterogeneous systems (e.g., suspension or emulsion polymerizations), it is important not to confuse thermodynamic effects of monomer partitioning among phases with variations in reactivity ratios. For the calculation of these, the concentrations of the monomers at the reaction site should be considered (at the particles) instead of global concentrations in the system. 

Dafniotis P, Saldivar E. Modeling emulsion copolymerization reactors. Kinetics and monomer partition [Term Project Che 730 Chemical Reactor Principles. Madison Department of Chemical Engineering, University of Wisconsin May 1990. 

Let us first ignore contributions from monomer partitioning and examine the effects of conversion upon copolymer composition. In most cases, thCTe will be a difference in monomer reactivities (Le. reactivity ratios 1) and a consequent drift in copolymer composition with conversion as the more reactive monomer is consumed preferentially (see Section 1.6.3). Since the total quantity of each monomer is added at the beginning of a batch emulsion polymerization, there is no control over this drift in copolymer composition. Hence, copolymors formed using batch processes can have quite broad composition distributions, the breadth of the distribution for each particular system depending upon the monomer reactivity ratios, the initial comonom composition and monomer partitioning (which is dealt with in Section 7.3.2.2). 

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