Polymer particle balances

Polymer Particle Balances (PEEK In the case of multiconponent emulsion polymerization, a multivariate distribution of pjarticle propierties in terms of multiple internal coordinates is required in this work, the polymer volume in the piarticle, v (continuous coordinate), and the number of active chains of any type, ni,n2,. .,r n (discrete coordinates), are considered. Therefore... 

Elnulsifler Magg Balance. The overall emulsifier concentration in the system, Cgt. is constant however, it is distributed among the aqueous liiase (Cg ), the polymer particles and the monomer droplets intertaces (Cga) and the micellar aggregates (Cgm), according to the sinple balance ... 

In [53], segregated catalyst and polymer particles act as micro reactors where the polymerization process takes place. Each particle is an individual reactor with its own energy and material balance. During polymerization, the catalyst particles undergo a change in volume by a factor of 10 -10, thereby generating the corresponding polymer particles. The particle size distributions of catalyst and polymer are the same. 

Material Balances. The material (mass) balances for the ingredients of an emulsion recipe are of the general form (Accumulation) = (Input) - (Output) + (Production) -(Loss), and their development is quite straightforward. Appendix I contains these equations together with the oligomeric radical concentration balance, which is required in deriving an expression for the net polymer particle generation (nucleation) rate, f(t). 

Combining then a balance for the rate of change of the free (unpolymerized) monomer concentration Mmon(0 with one for the total concentration of monomer units Mxoi(t) (bounded and unbounded), assuming that the rate of polymerization in the polymer particles is dominant and differentiating equation (1-6), one obtains ... 

For bioadhesive applications, anionic polymers appear to provide the most effective balance between adhesiveness and toxicity, with carboxylic materials preferred over sulfonic polymers [400]. Polyfacrylic acid) microparticles have been identified as particularly effective bioadhesive materials [402]. Studies with poly(acrylic acid) microparticles have indicated that, while water-swollen particles exhibit good bioadhesion, dry polymer particles give no adhesion at all. In addition, adhesive strength increases as the degree of ionization of the polymer is increased [402]. Thus the expanded nature of the polymer network is important to mucoadhesion, probably via polymer interdiffusion and entanglement with mucin [403],... 

Nomura and Harada already reported an experimental and theoretical study on the effect of lowering the amount of monomer initially charged on the number of polymer particles formed in a batch reactor(14). Under usual conditions in batch operation, micelles disappear and the formation of particles terminates before the disappearance of monomer droplets in the water phase. However, if the initial monomer concentration is extremely low, micelles would exist even after the disappearance of monomer droplets and hence, particle formation will continue until all emulsifier molecules are adsorbed on the surfaces of polymer particles. This condition is quantitatively expressed by the following emulsifier balance equation., ... 

Kiparissides, et al. (8) developed mathematical models of two levels of sophistication for the vinyl acetate system a comprehensive model that solved for the age distribution function of polymer particles and a simplified model which solved a series of differential equations assuming discrete periods of particle nucleation. In practice, the simplified model adequately describes the physical process in that particle generation generally occurs in discrete intervals of time and these generation periods are short in duration when compared with operation time of the system. The simplified model is expanded here for a series of m reactors. The total property balances for number of particles, polymer volume, conversion, and area of particles, are written as ... 

The desorption (exit) of free radicals from polymer particles into the aqueous phase is an important kinetic process in emulsion polymerization. Smith and Ewart [4] included the desorption rate terms into the balance equation for N particles, defining the rate of radical desorption from the polymer particles containing n free radicals in Eq. 3 as kftiN . However, they did not give any... 

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. 

The stirred-tank reactor and the tubular reactor are two basic reactors used for continuous processes, so much of the experimental and theoretical studies pubhshed to date on continuous emulsion polymerization have been conducted using these reactors. The most important elements in the theory of continuous emulsion polymerization in a stirred-tank reactor or in stirred-tank reactor trains were presented by Gershberg and Longfleld [330]. They started with the S-E theory for particle formation (Case B), employing the same assumptions as stated in Sect. 3.3, and proposed the balance equation describing the steady-state number of polymer particles produced as ... 

Observation (i) above can be understood in terms of droplet nucleation and the lack of competition between nucleation and growth. A mechanistic understanding of observation (ii) above was provided by Samer and Schork [64]. Nomura and Harada [136] quantified the differences in particle nucleation behavior for macroemulsion polymerization between a CSTR and a batch reactor. They started with the rate of particle formation in a CSTR and included an expression for the rate of particle nucleation based on Smith Ewart theory. In macroemulsion, a surfactant balance is used to constrain the micelle concentration, given the surfactant concentration and surface area of existing particles. Therefore, they found a relation between the number of polymer particles and the residence time (reactor volume divided by volumetric flowrate). They compared this relation to a similar equation for particle formation in a batch reactor, and concluded that a CSTR will produce no more than 57% of the number of particles produced in a batch reactor. This is due mainly to the fact that particle formation and growth occur simultaneously in a CSTR, as suggested earlier. 

The number of particles is a function of emulsifier type and concentration and initiator level, although for monomers that obey Case 1 kinetics such as vinyl chloride and vinyl acetate, is almost independent of initiator level (Ugelstad et al, 1969 Friis and Nyhagen, 1973). The calculation of iVp for various reactor operations will he discussed later. The monomer concentration in the polymer particle [Mp] can he obtained using a simple mass balance. Assuming the monomer and pdymer volumes are additive, one obtains the following relationship for the conversion interval,... 

The fourth factor determining polymerization rate is the monomer concentration in the particles. For some monomers the ratio of monomer to polymer in the particles is about constant during part of the polymerization. Smith (57) suggested that this results from a balance between the eflFect on the monomer activity of the dissolved polymer and the eflFect of interfacial tension of the very small particles. This equilibrium was put in a quantitative form by Morton, Kaizerman, and Altier (44), who derived the following equation by combining an expression for the interfacial free energy of the particle with the Flory-Huggins equation for the activity of the solvent (monomer) in the monomer-polymer particle. 

Considering a polymerizing emulsion system at its distribution balance, the three phases must show the same monomer activity the monomer-polymer particles, the micellar phase, and the water phase. Both monomer-polymer particles and the organic part of the micelles are lipophilic, and, therefore, compete for monomer. It does not seem plausible to assume that equal monomer activities in these two phases belong to monomer concentrations which differ by several orders of magnitude. Therefore it is likely that new particles are formed also after the disappearance of the pure monomer phase, provided there is a micellar phase, and enough monomer in the monomer-polymer particles as well. 

Extensions of the early model employed mass balances across all components.i The model agreed well with experimental data for the production of polystyrene. However, as in most traditional models it was a particle number model, based on all particles being identical. These models helped analyze polymerization in terms of the number concentration of polymer particles containing actively polymerizing radicals of number, Ai(t). As a result, they contained no particle size... 

In addition to a proper choice of ligand hydrophobicity, the surfactant used is also critical. In general, non-ionic surfactants were found to be efficient for colloidal stabilization of the polymer particles [221]. This is to be expected, as, owing to the ionic nature of the catalyst, and the corresponding ionic strength, electrostatic stabilization is likely to be poor. Adequate hydrophilic/lipophilic balance (HLB) [222] is also a necessary criterion to ensure latex stability in ATR emulsion polymerization [223]. 

The colloidal characteristics of A -alkylacrylamide- or Af-alkylmethacrylamide-based particles are temperature related. In fact, the swelling ability, charge density, charge distribution, hydrophilic-hydrophobic balance, hydration and dehydration properties, particle size, surface polarity, colloidal stability, water content, turbidity, and electrokinetic and rheological properties are indis-cemibly temperature dependent. Such polymer particles can be used as a stimuli-responsive model for the investigation of colloidal properties and for theoretical studies. 

Values for the propagation rate constant can be determined from bulk or solution experiments. Values of k have been published for a wide variety of monomers as a function of temperature. With standard emulsion polymerization recipes the value of [M]p is determined from equilibrium swelling measurements if a free monomer phase is present and by a mass balance if all the monomer is in the polymer particles. One normally assumes that [M] is not dependent on particle size in latexes comprised of different-sized particles. This assumption will be questionable in some systems, especially those involving high-swelling particles. 

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