Vinyl polymerization model free-radical

Polyacrylamides are produced commercially in an aqueous environment by free radical polymerization, which follows the classical vinyl polymerization model with initiation, propagation, and termination processes. In this model, the propagation/termination ratio kjk/ and chain transfer to monomer, polymer, initiator, and other small molecules impact the molecular weight of the formed polymer. High-molecular-weight polyacrylamides are possible because of the high ratio for acrylamide and the low chain-... 

The zero-one-two model accurately describes systems wherein n (the average number of free radicals per particle) does not exceed 0.7 it is thus applicable to small-particle styrene (Hawtett et al., 1980), vinyl acetate lUgelstad and Hansen, 1976), and vinyl chloride (Phis and Hamielec, 1975) emulsion polymerizations. In tbe Interval II steady state, the analytic solutions to the various functions involved in the MWD ohiained by Lichti et a . 1980) are as follows in these expressions, the dependence on suppressed since a steady state is assumed... 

In addition polymerization, a free radical transfers from one vinyl monomer to another, leaving behind a trail of chemical bonds (Fig. 6.6). The distinction of addition polymerization, compared with condensation polymerization, is the high correlation of the formed bonds along the path of a free radical. Certain monomers (with two double bonds, such as divinylbenzene) can be visited twice by free radicals and become crosslinks (black circles in Fig. 6.6). As the neighbouring trails of formed bonds begin to overlap, the system approaches its gel point. The model describing... 

In general, a polymerization process model consists of material balances (component rate equations), energy balances, and additional set of equations to calculate polymer properties (e.g., molecular weight moment equations). The kinetic equations for a typical linear addition polymerization process include initiation or catalytic site activation, chain propagation, chain termination, and chain transfer reactions. The typical reactions that occur in a homogeneous free radical polymerization of vinyl monomers and coordination polymerization of olefins are illustrated in Table 2. 

Kinetic models determine the state of cure by predicting the concentration of reacting species from the solution of differential equations for each reacting species. Mikos et al. (1986) and Tobita and Hamielec (1989) have developed kinetic models for vinyl and free-radical network systems. Chain-growth polymerization has also been modelled through kinetic simulations by Okay (1994). 

The reaction engineering aspects of these polymerizations are similar. Good heat transfer to a comparatively inviscid phase makes them suitable for vinyl addition polymerizations. Free-radical catalysis is mostly used, but cationic catalysis is used for nonaqueous dispersion polymerization (e.g., of isobutene). High conversions are generally possible, and the resulting polymer, either as a latex or as beads is directly suitable for some applications (e.g., paints, gel permeation chromatography beads, expanded polystyrene). Suspension polymerizations are run in the batch model. Continuous emulsion polymerization is common. 

Simultaneous polymerization of two monomers by chain initiation usually results in a copolymer whose composition is different from that of the feed. This shows that different monomers have different tendencies to undergo copolymerization. These tendencies often have little or no resemblance to their behavior in homopolymerization. For example, vinyl acetate polymerizes about twenty times as fast as styrene in a free-radical reaction, but the product obtained by free-radical polymerization of a mixture of vinyl acetate and styrene is found to be almost pure polystyrene with hardly any content of vinyl acetate. By contrast, maleic anhydride, which has very little or no tendency to undergo homopolymerization with radical initiation, readily copolymerizes with styrene forming one-to-one copolymers. The composition of a copolymeir thus cannot be predicted simply from a knowledge of the polymerization rates of the different monomers individually. The simple copolymer model described below accounts for the copolymerization behavior of monomer pairs. It enables one to calculate the distribution of sequences of each monomer in the macromolecule and the drift of copolymer composition with the extent of conversion of monomers to polymer. 

Case Study 2 Comparison of Mathematical Models FOR Free Radical Homopolymerization of Vinyl Monomers in scCOj In this case study, a comparison of performance of the different kinetic models proposed in the literature for dispersion polymerization of styrene and MMA in SCCO2 is presented. The models used by Quintero-Ortega et al. [43] (models 1 and 2) and those presented by the groups of Kiparissides [47] (model 3) and Morbidelli... 

The free radical polymerization of vinyl monomers should benefit from the excellent heat transfer and mixing speed of micro-reactors. When Hessel et al. [15] investigated, for the first time, the use of a micro-reactor in a free radical polymerization, they modeled the outcome of a solution polymerization of styrene as a monomer and azobisisobutylonitrile (AIBN) as an initiator for three different micro-reactor types [16], the aim being to compare the effects of micro-reactor... 

Another convenient and effective scheme for the approximate solution of a mathematical description of the polymerization reaction replaces the discrete variable of infinite range, polymer chain length, by a continuous variable. The difference-differential equations become partial differential equations. Barn-ford and coworkers [16,27,28] used this procedure in their analysis of vinyl (radical chain growth) polymerization. Zeman and Amundson [18,19] used it extensively to study batch and continuous polymerizations. Recently, Coyle et al. [4] have applied it to analysis of high conversion free radical polymerizations while Taylor et al. [3] used it in their modelling efforts oriented to control of high conversion polymerization of methyl methacrylate. A rather extensive review of the numerical techniques and approximations has been presented by Amundson and Luss [29] and later by Tirrell et al. [30]. 

The expressions are an outcome of the terminal model theory with several steady-state assumptions related to free-radical fiux (14,23). Based on copolymerization studies and reactivity ratios, chloroprene monomer is much more reactive than most vinyl and diene monomers (Table 1). 2,3-Dichloro-l,3-butadiene is the only commercially important monomer that is competitive with chloroprene in the free-radical copolymerization rate. 2,3-Dichlorobutadiene or ACR is used commercially to give crystallization resistance to the finished raw polymer or polymer vulcanizates. a-Cyanoprene (1-cyano-l,3-butadiene) and /3-cyanoprene (2-cyano-1,3-butadiene) are also effective in copolymerization with chloroprene but are difficult to manage safely on a commercial scale. Acrylonitrile and methacrylic acid comonomers have been used in limited commercial quantities. Chloroprene-isoprene and chloroprene-styrene copolymers were marketed in low volumes during the 1950s and 1960s. Methyl methacrylate has been utilized in graft polymerization particularly for vinyl adhesive applications. A myriad of other comonomers have been studied in chloroprene copolymerizations but those copolymers have not been used with much commercial success. 

Free radical propagation is poorly stereocontrolled, with nearly equal proportion of meso and racemic dyads in polymerization of monosubstituted alkenes and a preference for syndiotactic placement for disubstituted monomers such as methacrylates (rr = 0.62, mm = 0.04). The sequence distrihution follows a first-order Markov model with a slight deviation from Bernoulian statistics. However, for very bulky substituents, as in polymerization of triphenylmethyl methacrylate, the preference for isotacticity was observed (mm = 0.64, rr = 0.12). Recently, complexation with Lewis acids and acidic solvents enabled to enhance stereocontrol in polymerization of vinyl esters and acrylamides, and to a smaller degree in polymerization of methacrylates (127-129). 

The Smith-Ewart model describes satisfactorily the polymerization of styrene, isoprene, and methyl methacrylate for these systems, it can be used to predict the size of the latex particles and the corresponding molar masses. In contrast, it is unsuited for the case of monomers partially water-soluble or polymers insoluble in their monomer—that is, polymerization of vinyl chloride and vinyl acetate. It accounts neither for the fact that styrene can be polymerized in absence of surfactant nor for the fact that free radicals (RM ) can equally penetrate into a micelle or in an already formed particle during the initial phase. 

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