Copolymerization chemical control model

In evaluating the kinetics of copolymerization according to the chemical control model, it is assumed that the termination rate constants k,AA and A,Br are known from studies on homopolymerization. The only unknown in the above expression is the rate constant for cross termination (AtAB)- The rate constant for this reaction in relation to klAA and kmB is given by the parameter . 

Values of 0 required to fit the rate of copolymerization by the chemical control model were typically in the range 5-50 though values <1 are also known. In the case of S-MMA copolymerization, the model requires 0 to be in the range 5-14 depending on the monomer feed ratio. This "chemical control" model generally fell from favor wfith the recognition that chain diffusion should be the rate determining step in termination. 

Equations (7.58) and (7.68) yield the rate of copolymerization, and may be taken from previous studies of the chemical control model, or from an empirical correlation between this parameter and the r T2 product [27] which is based on the fact that cross-termination over homo-termination. Direct measurements of have been obtained [26] by measuring the absolute values of the rates of propagation and termination in pure monomers and in mixtures of various compositions. In the case of styrene-/7-metho)q styrene, = 1, indicating that no polar or other influences favor cross-termination. In most cases, however, cross-termination is... 

The kinetics of diffusion-controlled termination in copolymerization is difficult to study. The original interpretation of low-conversion rate data was based on a chemically controlled model utilizing a cross-termination factor ... 

Equations (7.46) and (7.56) yield the rate of copolymerization, and

previous studies of the chemical control model. 

Chemical Control Model For copolymerization, Eq. (7.52) for chemical control model is conveniently written (Rudin, 1982) as... 

The rate of copolymerization, unlike the copolymer composition, depends on the initiation and termination steps as well as on the propagation steps. In the usual case both monomers combine efficiently with the initiator radicals and the initiation rate is independent of the feed composition. Two different models, based on whether termination is diffusion-controlled, have been used to derive expressions for the rate of copolymerization. The chemical-controlled termination model assumed that termination proceeds with chemical control, that is, termination is not diffusion-controlled [Walling, 1949]. But this model is of only historical interest since it is well established that termination in radical polymerization is generally diffusion-controlled [Atherton and North, 1962 Barb, 1953 Braun and Czerwinski, 1987 North, 1963 O Driscoll et al., 1967 Prochazka and Kratochvil, 1983] (Sec. 3-10b). 

The basic reaction scheme for free-radical bulk/solution styrene homopolymerization is described below. A complete description of copolymerization kinetics involving styrene is not given here however, the homopolymerization kinetic scheme can be easily extended to describe copolymerization using the pseudo-kinetic rate constant method [6]. Such practice has been used by many research groups [7-10] and has been used extensively for modelling of copolymerization involving styrene by Gao and Penlidis [11]. In this section, all rate constants are defined as chemically controlled, i.e. they are only a function of temperature. 

Problem 7.16 Bulk polymerization of styrene in the presence of 1 g/L of AIBN initiator at 60°C gave a measured polymerization rate of 5.92 mol/L-s. Predict the rate of copolymerization at 60°C of a mixture of styrene (Mi) and methyl methacrylate (M2) with 0.579 mole fraction styrene and the same initial concentration of the initiator as in the homopolymerization case. Compare the rates predicted from chemical control, diffusion control, and combined models with the experimental value of 4.8x10 mol/L-s [25]. Use relevant kp and kt values for homopolymerization from Table 6.7 and assume 0 = 15. [Other data ri = 0.52, T2 = 0.46 monomer density = 0.90 g/cm .]... 

In multimonomer polymerizations, the number of possible reactions increases rapidly with the number of monomers. For example, for the copolymerization of two monomers under the assumption of terminal model kinetics, four propagation steps must be considered (see Eq. 6.1). Similarly, for the termination step (chemically controlled), three reactions are possible ... 

Tip 13 (related to Tip 12) Copolymerization, copolymer composition, composition drift, azeotropy, semibatch reactor, and copolymer composition control. Most batch copolymerizations exhibit considerable drift in monomer composition because of different reactivities (reactivity ratios) of the two monomers (same ideas apply to ter-polymerizations and multicomponent cases). This leads to copolymers with broad chemical composition distribution. The magnirnde of the composition drift can be appreciated by the vertical distance between two items on the plot of the instantaneous copolymer composition (ICC) or Mayo-Lewis (model) equation item 1, the ICC curve (ICC or mole fraction of Mj incorporated in the copolymer chains, F, vs mole fraction of unreacted Mi,/j) and item 2, the 45° line in the plot of versus/j. 

The spectra obtain by NIR are typically broad and difficult to assign to specific chemical functional groups. It is thus important to have multivariate calibration techniques to extract the desired chemical information. Beyers [24] describes the in-line monitoring of controlled radical copolymerization reactions using NIR. This is a good case study that describes how a calibration model was built to resolve the issue of similar spectral characteristics for methacrylate and acrylamide monomers. 

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