Polymerization reaction modeling

One of the key tasks in polymerization reaction modeling is to determine or estimate the model parameters... 

De Thomas etal. [Ill] studied the production of polyurethanes and showed that NIRS can be used successfully to monitor the course of the reaction in real time. Spectral data were obtained with a dispersive instrument, using standard transflectance probes. An MLR model was derived for the quantitative determination of isocyanate concentrations during the urethane polymerization reaction. Model predictions were used to build statistical process control charts and to detect trends along the polymerization reaction. The authors suggested that the integration of NIRS with process control routines could lead to improvements of product quality and consistency, while minimizing reaction time. However, model predictions were not used as feedback information for any sort of correction of the process trajectory. Similar studies were performed by Dallin [112] for prediction of the acid number during the production of polyesters. 

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. 

Chains with uttdesired functionality from termination by combination or disproportionation cannot be totally avoided. Tn attempts to prepare a monofunctional polymer, any termination by combination will give rise to a difunctional impurity. Similarly, when a difunctional polymer is required, termination by disproportionation will yield a monofunctional impurity. The amount of termination by radical-radical reactions can be minimized by using the lowest practical rate of initiation (and of polymerization). Computer modeling has been used as a means of predicting the sources of chain ends during polymerization and examining their dependence on reaction conditions (Section 7.5.612 0 J The main limitations on accuracy are the precision of rate constants which characterize the polymerization. 

Not much effort has been made, except for the Tafel studies, to establish the empirical kinetics and models of interfacial reactions to obtain thick polymeric films (>100 nm) of industrial interest from different monomers. However, this is much more than the few kinetic studies performed until now to understand the mechanism of chemically initiated polymerization. Electrochemical models still have an advantage in obtaining priority in the industrial production of tailored materials. 

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. 

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. 

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