Model polymerization reactions

The main objectives in modeling polymerization reactions are to compute polymerization rate and polymer properties for various reaction conditions. These two types of model outputs are not separate but they are usually very closely related. For example, an increase in reaction temperature raises polymerization rate... 

Immobilized CALB has frequently been applied in the literature as a catalyst for polymerization of aliphatic polyesters, polycarbonates, polyurethanes and their copolymers. In the present work on CALB catalyzed polymerization, the ring opening of e-caprolactone to polycaprolactone was selected as the model polymerization reaction (Figure 3.3). This model reaction has been well established in the literature [24-27] as an example of a polymerization reaction that can be successfully catalyzed by immobilized lipases (see also Chapter 4). Polymer synthesis and characterization was performed in four steps (i) polymerization (ii) separation (iii) purification and (iv) characterization. 

The challenge in modeling polymerization reactions is the fact that the structural properties to be modeled (molecular weight distribution, CCD and sequence distribution, as well as the other structural properties described in the preceding) are not only functions of reaction time, but are also distributions of properties. To completely characterize polymer structure, evolution requires extremely complex models. The discussion in the following will serve to introduce some of the simplest models. 

One of the most sensitive tests of the dependence of chemical reactivity on the size of the reacting molecules is the comparison of the rates of reaction for compounds which are members of a homologous series with different chain lengths. Studies by Flory and others on the rates of esterification and saponification of esters were the first investigations conducted to clarify the dependence of reactivity on molecular size. The rate constants for these reactions are observed to converge quite rapidly to a constant value which is independent of molecular size, after an initial dependence on molecular size for small molecules. The effect is reminiscent of the discussion on the uniqueness of end groups in connection with Example 1.1. In the esterification of carboxylic acids, for example, the rate constants are different for acetic, propionic, and butyric acids, but constant for carboxyUc acids with 4-18 carbon atoms. This observation on nonpolymeric compounds has been generalized to apply to polymerization reactions as well. The latter are subject to several complications which are not involved in the study of simple model compounds, but when these complications are properly considered, the independence of reactivity on molecular size has been repeatedly verified. 

In this section we examine some examples of cross-linked step-growth polymers. The systems we shall describe are thermosetting polymers of considerable industrial importance. The chemistry of these polymerization reactions is more complex than the hypothetical AB reactions of our models. We choose to describe these commercial polymers rather than model systems which might conform better to the theoretical developments of the last section both because of the importance of these materials and because the theoretical concepts provide a framework for understanding more complex systems, even if they are not quantitatively successful. 

The Fischer-Tropsch process can be considered as a one-carbon polymerization reaction of a monomer derived from CO. The polymerization affords a distribution of polymer molecular weights that foUows the Anderson-Shulz-Flory model. The distribution is described by a linear relationship between the logarithm of product yield vs carbon number. The objective of much of the development work on the FT synthesis has been to circumvent the theoretical distribution so as to increase the yields of gasoline range hydrocarbons. 

The FTS mechanism could be considered a simple polymerization reaction, the monomer being a Ci species derived from carbon monoxide. This polymerization follows an Anderson-Schulz-Flory distribution of molecular weights. This distribution gives a linear plot of the logarithm of yield of product (in moles) versus carbon number. Under the assumptions of this model, the entire product distribution is determined by one parameter, a, the probability of the addition of a carbon atom to a chain (Figure 4-7). ... 

Kennedy, J. P. and Rengachary, S. Correlation Between Cationic Model and Polymerization Reactions of Olefins. Vol. 14, pp. 1 —48. 

Recently, Kennedy and Rengachary11 studied cationic olefin model and polymerization reactions. Important conclusions of the model study were ... 

The rate of the r-BuX + Me3Al M X > f-BuMe + Me2AlX reaction decreases as X = Cl > Br > I10. This decrease is explained by a decrease in the rate of displacement of MeX by r-BuX, which in turn is determined by the basicity and/or size of the halogen in f-BuX. Since the basicity decreases and size increases as X changes from Cl to Br to I, the rate of displacement, R, decreases. In isobutylene polymerization using f-BuX/Me3Al/MeX and r-BuX/Et2 AlCl/MeX (X = Cl, Br, I), the r-BuX reactivity decreases as f-BuCl > f-BuBr > r-BuI = 0. The similarity between initiator reactivity sequences in model and polymerization reactions indicates that the rate governing event is the same for both, i.e the rate of displacement, R1. 

These values show that from the two possible alternatives of ion formation that one is preferred, which leads to the formation of an anion with the largest number of F-, after which, of Cl-ligands. It is remarkable that ionization in Lewis acid mixtures is favoured versus that in pure Lewis acids in all cases. This could be the reason why the polymerization conversion increases when using Lewis acid mixtures as initiators. However, it should be pointed out here that the quantum chemical reaction energies employed are only then comparable with each other, when they are valid for the same process used for modelling the reactions. 

A mathematical model for this polymerization reaction based on homogeneous, isothermal reaction is inadequate to predict all of these effects, particularly the breadth of the MWD. For this reason a model taking explicit account of the phase separation has been formulated and is currently under investigation. 

Gas phase olefin polymerizations are becoming important as manufacturing processes for high density polyethylene (HOPE) and polypropylene (PP). An understanding of the kinetics of these gas-powder polymerization reactions using a highly active TiCi s catalyst is vital to the careful operation of these processes. Well-proven models for both the hexane slurry process and the bulk process have been published. This article describes an extension of these models to gas phase polymerization in semibatch and continuous backmix reactors. 

The computer model used for this analysis is based on a plug flow tubular reactor operating under restraints of the commonly accepted kinetic mechanism for polymerization reactions ( 5 ) ... 

In addition to solubilization, entrapment of polymers inside reversed micelles can be achieved by performing in situ suitable polymerization reactions. This methodology has some specific peculiarities, such as easy control of the polymerization degree and synthesis of a distinct variety of polymeric structures. The size and shape of polymers could be modulated by the appropriate selection of the reversed micellar system and of synthesis conditions [31,191]. This kind of control of polymerization could model and/or mimic some aspects of that occurring in biological systems. 

From the results discussed so far, it is evident that only CH2 groups have been observed in the very early stages of the ethylene polymerization reaction. Of course, this could be due to formation of metallacycles, but can be also a consequence of the high TOP which makes the observation of the first species troublesome. To better focalize the problem it is useful to present a concise review of the models proposed in the literature for ethylene coordination, initiation, and propagation reactions. 

We have reviewed experiments on two classes of systems, namely small metal particles and atoms on oxide surfaces, and Ziegler-Natta model catalysts. We have shown that metal carbonyls prepared in situ by reaction of deposited metal atoms with CO from the gas phase are suitable probes for the environment of the adsorbed metal atoms and thus for the properties of the nucleation site. In addition, examples of the distinct chemical and physical properties of low coordinated metal atoms as compared to regular metal adsorption sites were demonstrated. For the Ziegler-Natta model catalysts it was demonstrated how combination of different surface science methods can help to gain insight into a variety of microscopic properties of surface sites involved in the polymerization reaction. 

Results obtained with germanes also provide models for the kinds of reactions that may be occurring in the silane polymerization reaction as well. For example, we have succeeded in carrying out the reaction shown in Equation 4 (26). The analogous reactions with triphenylsilane, or triphenylstannane, were not... 

Like many homogeneously catalyzed reactions, the overall cycle (or cycles) in these polymerization reactions probably contains too many steps to be easily analyzed by any single approach. Both kinetics and model compound studies have thrown light on some of the steps. However, as indicated above, many of the model compounds isolated from the reactions of primary silanes with metallocene alkyls and hydrides are too unreactive to explain the polymerization results. 

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... 

Off-line analysis, controller design, and optimization are now performed in the area of dynamics. The largest dynamic simulation has been about 100,000 differential algebraic equations (DAEs) for analysis of control systems. Simulations formulated with process models having over 10,000 DAEs are considered frequently. Also, detailed training simulators have models with over 10,000 DAEs. On-line model predictive control (MPC) and nonlinear MPC using first-principle models are seeing a number of industrial applications, particularly in polymeric reactions and processes. At this point, systems with over 100 DAEs have been implemented for on-line dynamic optimization and control. 

Figure4.74 Optimized structures of (a) thereactantl, (b) the intermediate complex II, and (c) the product III of the model ethylene-polymerization reaction (4.106), with labeled methyl (Cm), proximal (Cp), and distal (Cd) carbon atoms.

Table 4.43. Skeletal geometries and atomic charges of the alternative secondary-Cp (Hsec) andprimary-Cp (IIpri) propylene complexes, as well as of the transition state (IIpri ) and actual product (IIIpri) of the model propylene-polymerization reaction (4.107) cf Figs. 4.79 and4.80...

The TIS and DPF models, introduced in Chapter 19 to describe the residence time distribution (RTD) for nonideal flow, can be adapted as reactor models, once the single parameters of the models, N and Pe, (or DL), respectively, are known. As such, these are macromixing models and are unable to account for nonideal mixing behavior at the microscopic level. For example, the TIS model is based on the assumption that complete backmixing occurs within each tank. If this is not the case, as, perhaps, in a polymerization reaction that produces a viscous product, the model is incomplete. 

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