Free radical polymerization kinetic modeling

Here, gt takes into account one interesting feature of the free radical polymerization kinetics the auto acceleration in the rate of reaction (better known as the Trommsdorff or gel effect). The gel effect is taken into account in the model (42) by including the experimental correlation developed in [18] for the termination rate ... 

Comprehensive Models. This class of detailed deterministic models for copolymerization are able to describe the MWD and the CCD as functions of the polymerization rate and the relative rate of addition of the monomers to the propagating chain. Simha and Branson (3) published a very extensive and rather complete treatment of the copolymerization reactions under the usual assumptions of free radical polymerization kinetics, namely, ultimate effects SSH, LCA and the absence of gel effect. They did consider, however, the possible variation of the rate constants with respect to composition. Unfortunately, some of their results are stated in such complex formulations that they are difficult to apply directly (10). Stockmeyer (24) simplified the model proposed by Simha and analyzed some limiting cases. More recently, Ray et al (10) completed the work of Simha and Branson by including chain transfer reactions, a correction factor for the gel effect and proposing an algorithm for the numerical calculation of the equations. Such comprehensive models have not been experimentally verified. 

Strategies for controlling the copolymer composition and MWD of latices based on linear and non-linear copolymers, such as styrene/butyl acrylate copolymers and methyl methacrylate/n-butyl acrylate copolymers, are described. These strategies involve on-line procedures based on calorimetric measurements and open-loop processes employing a mathematical model for determining the trajectories of the manipulated variables, such as monomer feed flow rates and chain transfer agent. 35 refs. (3rd lUPAC-Sponsored International Symposium on Free-Radical Polymerization Kinetics and Mechanism, II Ciocco (Lucca), Tuscany, Italy, 3rd-9th June, 2001)... 

Recently the polymeric network (gel) has become a very attractive research area combining at the same time fundamental and applied topics of great interest. Since the physical properties of polymeric networks strongly depend on the polymerization kinetics, an understanding of the kinetics of network formation is indispensable for designing network structure. Various models have been proposed for the kinetics of network formation since the pioneering work of Flory (1 ) and Stockmayer (2), but their predictions are, quite often unsatisfactory, especially for a free radical polymerization system. These systems are of significant conmercial interest. In order to account for the specific reaction scheme of free radical polymerization, it will be necessary to consider all of the important elementary reactions. 

Our acrylic polymerization model was developed to meet the need for solving these problems. Kinetics used are based on fairly well accepted and standard free radical polymerization mechanisms. 

The accepted kinetic scheme for free radical polymerization reactions (equations 1-M1) has been used as basis for the development of the mathematical equations for the estimation of both, the efficiencies and the rate constants. Induced decomposition reactions (equations 3 and 10) have been Included to generalize the model for initiators such as Benzoyl Peroxide for... 

In this paper, the kinetics and polymerization behavior of HEMA and DEGDMA initiated by a combination of DMPA (a conventional initiator) and TED (which produces DTC radicals) have been experimentally studied. Further, a free volume based kinetic model that incorporates diffusion limitations to propagation, termination by carbon-carbon radical combination and termination by carbon-DTC radical reaction has been developed to describe the polymerization behavior in these systems. In the model, all kinetic parameters except those for the carbon-DTC radical termination were experimentally determined. The agreement between the experiment and the model is very good. 

The above example gives us an idea of the difficulties in stating a rigorous kinetic model for the free-radical polymerization of formulations containing polyfunctional monomers. An example of efforts to introduce a mechanistic analysis for this kind of reaction, is the case of (meth)acrylate polymerizations, where Bowman and Peppas (1991) coupled free-volume derived expressions for diffusion-controlled kp and kt values to expressions describing the time-dependent evolution of the free volume. Further work expanded this initial analysis to take into account different possible elemental steps of the kinetic scheme (Anseth and Bowman, 1992/93 Kurdikar and Peppas, 1994 Scott and Peppas, 1999). The analysis of these mechanistic models is beyond our scope. Instead, one example of models that capture the main concepts of a rigorous description, but include phenomenological equations to account for the variation of specific rate constants with conversion, will be discussed. 

Bamford et al. ( 1 ) have presented the basic kinetics for free-radical polymerization of styrene, and Hamielec et al., (2 ) employing Bamford s nomenclature, developed differential equations that are the starting point for the mathematical model. 

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. 

Table 3 Kinetic model equations for free radical polymerization...

Cure modelling of polyester pultrusion systems was carried out by Ng and Manas Zloczower (1989). A mechanistic model that couples free-radical polymerization and diffusion control (Section 1.2.3) was used for the cure kinetics and is shown here ... 

Kinetics models are useful for designing commercial reactors and for studying the fundamental mechanisms of the important reactions. The free-radical polymerization that takes place in emulsion systems is characterized by three main reactions initiation, propagation, and termination. Various radical transfer reactions can also be important. The rate of polymerization for bulk, solution, and suspension processes can be expressed as shown by Equation 2 ... 

To explain this technique, let us consider as an illustration a simple kinetic model for free radical polymerization, which contains only a subset of the possible reactions in these systems (Table 12.1). The application of the technique to a batch reactor, which is the simplest one, will be used to illustrate the method extension to other reactor types is straightforward. 

Cavin, L., Rouge, A., Meyer, X, Renken, A. Kinetic modeling of free radical polymerization of styrene initiated by the bifunctional initiator 2,5-dimethyl-2,5-bis(2-ethyl hexanoyl peroxy)hexane. Polymer 41(11), 3925-3935 (2000)... 

Krajnc, M., Poljansek, I., Golob, J. Kinetic modeling of methyl methacrylate free-radical polymerization initiated by tetraphenyl biphosphine. Polymer 42(9), 4153 162 (2001)... 

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