Multiple-site catalyst

In this work we present hyperbranched polymers as platforms for catalysts that fall into three major classes, according to their topology and binding mode to the polymeric support (Fig. 2) (i) defined multiple site catalysts (ii) dendritic core-shell catalysts (iii) supramolecular catalyst complexes. 

One of the remarkable advantages of metallocene catalysts is their ability to make polyolefins with much more uniform microstructure than the Ziegler-Natta or the Phillips catalysts. Metallocene catalysts are considered to have only one type of active site (single-site catalysts) making polymer chains with the same average properties, while heterogeneous Ziegler-Natta and Phillips catalysts are multiple-site catalyst that makes polyolefins with broad, and sometimes multimodal, microstructural distributions [9]. 

Equation 5.1 is applicable to polyolefins made with single-site catalysts, such as metallocenes, and predicts a polydispersity index of 2.0. It is discussed later how this equation can also be used to model the CLD of polyolefins made with multiple-site catalysts, such as heterogeneous Ziegler-Natta and Phillips catalysts. Despite its simplicity, this equation can be used to predict the complete CLD of single-site polyolefins instantaneously using an easy-to-estimate parameter, t. 

The methods discussed above for single-site catalysts (metallocenes and late transition-metal catalysts) can be extended directly to multiple-site catalysts (Ziegler-Natta and Phillips catalysts) by assuming that each site type behaves essentially as single-site catalysts [87, 88, 99, 100, 101], Therefore, the microstructural distribution of a polymer made with a multiple-site catalyst is treated as a weighted sum of several single-type distributions [102],... 

The reason this relatively weak hypothesis is often made is that the effort required to integrate phenomena taking place from micro- to macroscale in a single model does not necessarily lead to better quantitative predictions when it comes to industrial reactors. Uncertainties in model parameter values, especially for multiple-site catalysts, are... 

The presence of short chain branches, by the addition of one or various comonomers, which could result in intermolecular homogeneous (single-site catalyst) or heterogeneous (multiple-site catalysts) incorporation... 

From a polymer reaction engineering point of view, polyolefins made with metallocene catalysts provide an excellent opportunity for model development because they have well-behaved microstructures. Later it will be shown that models developed for single-site catalysts can also be extended to describe the more complex microstructures of polyolefins made with multiple-site catalysts such as Ziegler-Natta and Phillips catalysts. 

Polymerization kinetics for single- and multiple-site catalysts... 

When catalysts containing more than one type of active sites are used, the conventional approach is simply to repeat the model equations derived for single-site-type catalysts, using distinct kinetic rate constants for each site type. This simply means that the multiple-site catalyst is considered to be a collection of single-site type catalysts. Sometimes, site transformation steps may also be included in the model to permit the conversion of one site type to another, but the polymerization mechanism for each site type remains the one previously described. 

Table 2.10 summarizes the model equations for polymerization with multiple-site catalysts in batch, semibatch and continuous reactors. The moment equations are, as expected, the same as the ones developed for single-site types, but applied for each individual site type, as indicated by the subscript j. Notice that the molar balances for monomer and hydrogen use the concentration of all active site types and that the chain length averages are also calculated using polymer made on all active sites. The new variable n appearing in these equations is the number of active site types in the catalyst. Initial conditions were omitted because they are analogous to the ones shown in Table 2.9, now applied for each site type. 

The method of instantaneous distributions - Flory s most probable distribution for single- and multiple-site catalysts... 

Figure 2.22 introduces the use of Flory s distributions to model the CLD of polymers made with multiple-site catalysts. The approach described here is straightforward if one Flory s distribution describes the CLD of polyolefins made with a single-site catalyst, multiple Flory s distributions will be adequate to represent the CLD of polyolefins made with multiple-site catalysts. Mathematically,... 

Equation 2.87 can be used to represent the CLD of polyolefins made with the combination of two or more metallocenes very well [35, 38]. This is a reasonably easy case, since the individual metallocenes can be tested separately to obtain the values of Flory s T parameter. For multiple-site catalysts, such as heterogeneous Ziegler-Natta and Philips catalysts, the procedure for obtaining r values for each site type is more elaborate and involves the deconvolution of the MWD into several Flory s distributions. This subject will not be covered in this chapter the reader is directed to references 39 and 40 at the end of the chapter for more information on this subject. Suffice to say that MWD deconvolution involves the use of a non-linear least-squares optimization routine to... 

The results of the MWD deconvolution procedure should be interpreted with care. First, make sure that the polymer was produced under spatially uniform and steady-state conditions. Second, ensure that peak broadening during MWD analysis by GPC is negligible. Third, and more importantly, the MWD deconvolution procedure can only retrieve the minimum number of Dory s sites required to represent the measured MWD more sites may be present, but not seen, because of peak superposition. Considerable controversy lingers about the real meaning of the MWD deconvolution procedure. It is, however, important to realize that the use of several Fiery s distributions to describe the MWD of polymer made with multiple-site catalysts is exactly equivalent to using the set of moment equations shown in Table 2.10 they are just different ways of formulating the same problem. One method is not any more valid than the other. 

The models considered earlier were developed for homopolymerization of olefins with single- and multiple-site catalysts. As has aheady been seen, several industrial polyolefins are, however, copolymers of ethylene, propylene and higher a-olefins. Because, for copolymerization, the kinetic rate constants depend on monomer and chain end type (in the terminal model), modeling these systems may seem daunting at first sight, but it will now be shown that, using the concept of pseudo-kinetic constants, the same equations derived for homopolymerization can be applied for copolymerization as well. 

Copolymers made with multiple-site catalysts can be modeled with the same equations derived for homopolymers produced with multiple-site catalysts in Table 2.10. The only modification required is the use of the pseudo-kinetic constants shown in Table 2.12 instead of the actual kinetic constants in the equations presented in Table 2.10. 

Similar to Flory s distribution, Stockmayer s distribution can be applied to non-steady-state solutions and also it can be used to model the CCD of polymer made with multiple-site catalysts [44]. Figure 2.26 shows the CLD x CCD of a model polymer created by superimposing three Stockmayer s distributions. Notice how the trends are similar to the ones measured experimentally using cross-fractionation in Figures 2.5 and 2.12. 

Keywords metallocene catalyst, Ziegler-Natta catalyst, olefin polymerization, polyolefins, homogeneous catalysts, supported catalysts, stereoregularity, molecular weight distribution (MWD), chemical composition distribution, Unipol , Novolen , stereoselectivity, single site catalyst, multiple site catalyst, gas phase process, slurry process, homopolymerization, copolymerization. 

The SEC-FTIR combination, although attractive due to its simplicity, is not able to recover the bivariate distribntion of molecular weight and chemical composition, but can only measure average composition as a function of molecular weight. Consequently, it is not a trne cross-fractionation technique. A method to recover the chemical composition component of the distribntion was proposed for the case of polyolefins made with single and multiple-site catalysts using a... 

Because of the complexity of the fractionation mechanism, not many mathematical models have been proposed to describe separation with Tref. Soares and Hamielec [47] used Stockmayer s distribution (Eq. 7) to simiflate the CCD of Hnear binary copolymers synthesized with miflti-site-type catalysts. Under the assumption that the fractionation process of Tref was controlled only by comonomer composition, the CCD was directly converted into the Tref profile using a calibration curve. For the case of ethylene/1-olefin copolymers made with multiple-site catalysts, the CCD of the whole polymer is described as the weighted summation of the CCDs of the copolymers produced by each active site ... 

Tref has been used for many years in polymer reaction engineering investigations. For instance, Tref was one of the most important analytical techniques to determine the presence of multiple-site catalysts on heterogeneous Ziegler-Natta catalysts used for olefin polymerization, as previously illustrated in Fig. 18. Crystaf, with a much shorter analysis time than Tref, permits the routine determination of the CCD in polymer reaction engineering projects. 

Amer and van Reenen [39] fractionated isotactic polypropylenes by TREE to get fractions with different molar masses but similar tacticities. The DSC results of the fractions indicated that the crystallization behaviour is strongly affected by the configuration (tacticity) and the molar mass of the PP. Soares et al. [40] proposed a new approach for identifying the number of active catalyst sites and the polymer chain microstructural parameters produced at each active site for ethylene/l-olefin copolymers synthesized with multiple-site catalysts. This method is based on the simultaneous deconvolution of bivariate MMD/CCD, which can be obtained by cross-fractionation techniques like SEC/TREE or TREE/SEC. The proposed approach was validated successfully with model ethylene/1-butene and ethylene/ 1-octene copolymers. Alamo and co-workers [41] studied the effects of molar mass and branching distribution on mechanical properties of ethylene/1-hexene copolymer film grade resins produced by a metallocene catalyst Molar mass fractions were obtained by solvent/non-solvent techniques while P-TREE was used for fractionation according to the 1-hexene content. 

Polymerization Kinetics with Multiple-site Catalysts... 

All heterogeneous Ziegler-Natta and Phillips catalysts have two or more active-site types and many soluble Ziegler-Natta and metallocene catalysts may also show multiple-site behavior [36, 37]. In addition, several metallocene catalysts, when supported on organic and inorganic carriers, may behave like multiple-site catalysts even if they behaved as single-site catalysts in solution polymerization. Therefore, several of the catalysts used industrially for polyolefin manufacturing have in fact two or more active-site types. 

The kinetics of polymerization with multiple-site catalysts is generally considered to be the same as with single-site catalysts, as described by Eqs. (1)-(14) for homopolymerization and in Table 8.1 for copolymerization, with different polymerization kinetic parameters assigned to each site type. In some cases, the polymerization mechanism may be extended to include site transformation steps, where sites of one type may change into sites of another type, such as the one described with the reversible reaction in Eq. (23), where D could be a catalyst modifier such as an electron donor, for instance. 

Since these additional site transformation steps may affect the relative ratio of site types present in the reactor but do not influence the general polymerization behavior with multiple-site catalysts, for the sake of simplicity they will not be further considered in this chapter. 

It is usually straightforward to detect the presence of multiple-site types on a coordination catalyst because these catalysts will produce polymer with polydispersity higher than 2 even under invariant polymerization conditions. The simplest way to visualize this phenomenon is to assume that every different site type on a multiple-site catalyst produces polymers that follow a distinct Flory s distribution that is, those with a distinct number-average chain length, [38]. In this way, the chain length distribution for the whole polymer is a combination of distinct Flory s distributions weighted by the mass fraction of polymer made on each site type, mj [Eq. (24)]. 

The graphical representation of Eq. (24) for a coordination catalyst having three distinct site types is shown in Figure 8.24. It is important to remember that the use of Eq. (24) is a direct consequence of assuming that the mechanism of polymerization for multiple-site catalysts is described with the same set of equations, Eqs. (1)-(14), used to describe single-site catalysts. In other words, Flory s distribution is the logical consequence of the mechanism adopted for coordination polymerization. 

For polymers made with multiple-site catalysts, the instantaneous number- and weight-average chain lengths are given by Eqs. (25) and (26). 

Similarly, the bivariate molecular weight and chemical composition distributions of binary copolymers made with multiple-site catalysts can be described as a weighted superposition of Stockmayer s distributions [39]. If we consider only the chemical composition component of the distribution, as described by Eq. (22), the distribution of polymer made with a multiple-site catalyst becomes Eq. (28). 

For the case of multiple-site catalysts, population balances are derived for each catalyst site type, and the chain length-averages for the whole polymer are found by averaging the values calculated for each site type [Eqs. (86) and (87)]. 

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