Particle phase, discrete

Microemulsion and miniemulsion polymerization processes differ from emulsion polymerization in that the particle sizes are smaller (10-30 and 30-100 nm respectively vs 50-300 ran)77 and there is no discrete monomer droplet phase. All monomer is in solution or in the particle phase. Initiation usually takes place by the same process as conventional emulsion polymerization. As particle sizes reduce, the probability of particle entry is lowered and so is the probability of radical-radical termination. This knowledge has been used to advantage in designing living polymerizations based on reversible chain transfer (e.g. RAFT, Section 9.5.2)." 2... 

Successful NMP in emulsion requires use of conditions where there is no discrete monomer droplet phase and a mechanism to remove any excess nitroxide formed in the particle phase as a consequence of the persistent radical effect. Szkurhan and Georges"18 precipitated an acetone solution of a low molecular weight TEMPO-tcrminated PS into an aqueous solution of PVA to form emulsion particles. These were swollen with monomer and polymerized at 135 °C to yield very low dispersity PS and a stable latex. Nicolas et at.219 performed emulsion NMP of BA at 90 °C making use of the water-soluble alkoxyamine 110 or the corresponding sodium salt both of which are based on the open-chain nitroxide 89. They obtained PBA with narrow molecular weight distribution as a stable latex at a relatively high solids level (26%). A low dispersity PBA-WocA-PS was also prepared,... 

Emulsion polymerization has proved more difficult. N " Many of the issues discussed under NMP (Section 9.3.6.6) also apply to ATRP in emulsion. The system is made more complex by both activation and deactivation steps being bimolecular. There is both an activator (Mtn) and a deactivator (ML 1) that may partition into the aqueous phase, although the deactivator is generally more water-soluble than the activator because of its higher oxidation state. Like NMP, successful emulsion ATRP requires conditions where there is no discrete monomer droplet phase and a mechanism to remove excess deactivator built up in the particle phase as a consequence of the persistent radical effect.210 214 Reverse ATRP (Section 9.4,1,2) with water soluble dialky 1 diazcncs is the preferred initiation method/87,28 ... 

The partial differential equations describing the catalyst particle are discretized with central finite difference formulae with respect to the spatial coordinate [50]. Typically, around 10-20 discretization points are enough for the particle. The ordinary differential equations (ODEs) created are solved with respect to time together with the ODEs of the bulk phase. Since the system is stiff, the computer code of Hindmarsh [51] is used as the ODE solver. In general, the simulations progressed without numerical problems. The final values of the rate constants, along with their temperature dependencies, can be obtained with nonlinear regression analysis. The differential equations were solved in situ with the backward... 

Overall, the relatively brittle polyurethane resin matrix was transformed by the incorporation of a discrete rubber particle phase into a semiductile material... 

In the Lagrangian approach, the elemental control volume is considered to be moving with the fluid as a whole. In the Eulerian approach, in contrast, the control volume is assumed fixed in the space, the fluid is assumed to flow through and pass the control volume. The particle-phase equations are formulated in Lagrangian form, and the coupling between the two phases is introduced through particle sources in the Eulerian gas-phase equations. The standard k-e turbulence model, finite rate chemistry, and DTRM (discrete transfer radiation model) radiation model are used. 

TFM. And the particle phase motion is solved by tracking discrete parcels, each representing a number of particles with the same properties and following the Newton s law of motion. In the MP-PIC method, the coUisional interaction between particles is replaced by using the normal stress of solids (Snider, 2001), which is calculated on the grid points for gas phase and interpolated to the positions of parcels. The gas continuity equation is the same as Eq. (16), whereas the gas momentum equation reads... 

Discrete particle modeling (DPM) is an advanced computational technique for particulate systems (in this case, fluidized beds) that has already been presented in Chapter 7 of Volume 3, Modem Drying TechnoU. DPM combines continuous (Eulerian) CFD for the gas phase with a discrete (Lagrangian) consideration of the particle phase by means of a discrete element method (DEM), and is therefore often also denoted as DEM-CFD. Its appHcation enables the resolution of not only interactions between the gas and the particle phase, but also of particle-particle and particle-wall interactions, in the sense of a four-way coupling (compare also with Chapter 5 in Volume 1, Modem Drying Technology). 

To analyze the individual heat transfer kinetics of droplet clusters within the spray of twin-fluid atomizers, the local correlations between the droplet concentration and the heat and flow conditions are evaluated. Numerical simulations of the spray flow analyzed in this paper have been carried out with Large-Eddy-Simulation (LES) models with Lagrangian particle tracking (discrete particle method) for the droplet motion. A synthetic perturbation generator [30] for the inflow conditions for the gas flow and simple perturbations are added to the dispersed phase to induce realistic vortex patterns at the nozzle and in the consequent spray. 

In the first coarse-grained approach, the discrete phase is treated as an Eulerian continuum, interpenetrating with the real continuous phase. The particle-particle interactions are then captured by an effective particle phase rheology obtained from kinetic theory of granular flows. These so-called two-fluid (Euler-Euler) models have been very successful at predicting the dynamic properties of, e.g., gas-solid fluidized beds (see Van derHoefet al, 2008 Verma et al, 2013). Despite their success, two-fluid models also have their limitations they are usually limited to idealized cases ofmonodisperse hard sphere particles, while extensions to polydisperse mixtures (e.g., in size or in contact properties) are difficult to make. Also, because no particles are explicitly tracked, it is difficult to include particle properties which may vary from particle to particle, such as particle temperature, surface moisture concentration, or chemical surface species concentrations. 

Impact polystyrene contains polybutadiene added to reduce brittleness. The polybutadiene is usually dispersed as a discrete phase in a continuous polystyrene matrix. Polystyrene can be grafted onto rubber particles, which assures good adhesion between the phases. 

If a linear mbber is used as a feedstock for the mass process (85), the mbber becomes insoluble in the mixture of monomers and SAN polymer which is formed in the reactors, and discrete mbber particles are formed. This is referred to as phase inversion since the continuous phase shifts from mbber to SAN. Grafting of some of the SAN onto the mbber particles occurs as in the emulsion process. Typically, the mass-produced mbber particles are larger (0.5 to 5 llm) than those of emulsion-based ABS (0.1 to 1 llm) and contain much larger internal occlusions of SAN polymer. The reaction recipe can include polymerization initiators, chain-transfer agents, and other additives. Diluents are sometimes used to reduce the viscosity of the monomer and polymer mixture to faciUtate processing at high conversion. The product from the reactor system is devolatilized to remove the unreacted monomers and is then pelletized. Equipment used for devolatilization includes single- and twin-screw extmders, and flash and thin film evaporators. Unreacted monomers are recovered for recycle to the reactors to improve the process yield. 

In the absence of a suitable soHd phase for deposition and in supersaturated solutions of pH values from 7 to 10, monosilicic acid polymerizes to form discrete particles. Electrostatic repulsion of the particles prevents aggregation if the concentration of electrolyte is below ca 0.2 N. The particle size that can be attained is dependent on the temperature. Particle size increases significantly with increasing temperature. For example, particles of 4—8 nm in diameter are obtained at 50—100°C, whereas particles of up to 150 nm in diameter are formed at 350°C in an autoclave. However, the size of the particles obtained in an autoclave is limited by the conversion of amorphous siUca to quartz at high temperatures. Particle size influences the stabiUty of the sol because particles <7 nm in diameter tend to grow spontaneously in storage, which may affect the sol properties. However, sols can be stabilized by the addition of sufficient alkaU (1,33). 

Production of net-shape siUca (qv) components serves as an example of sol—gel processing methods. A siUca gel may be formed by network growth from an array of discrete coUoidal particles (method 1) or by formation of an intercoimected three-dimensional network by the simultaneous hydrolysis and polycondensation of a chemical precursor (methods 2 and 3). When the pore Hquid is removed as a gas phase from the intercoimected soHd gel network under supercritical conditions (critical-point drying, method 2), the soHd network does not coUapse and a low density aerogel is produced. Aerogels can have pore volumes as large as 98% and densities as low as 80 kg/m (12,19). 

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