Bimodal MWDs

Detailed modifications in the polymerisation procedure have led to continuing developments in the materials available. For example in the 1990s greater understanding of the crystalline nature of isotactic polymers gave rise to developments of enhanced flexural modulus (up to 2300 MPa). Greater control of molecular weight distribution has led to broad MWD polymers produced by use of twin-reactors, and very narrow MWD polymers by use of metallocenes (see below). There is current interest in the production of polymers with a bimodal MWD (for explanations see the Appendix to Chapter 4). 

A conspicuous finding in these studies is that Et2AlCl-based initiator systems lead to bimodal distributions whereas those with EtjAlBr and Et2All lead to mono-modal distributions. Also, the MWD for Et2AlCl was broader ( 1.4 to 5.9) than those for Et2AlBr ( 1.7 to 2.2) and Et2AlI ( 1.9 to 3.0). A possible explanation for the bimodal MWD is given in Section 5. The reason(s) for the relatively narrow MWD s (<2) of LMWF and HMWF remains obscure. 

The assumption that an impurity, probably water, gives rise to bimodal MWD with f-BuX/Et2AlCl system was confirmed directly by experiments. First polymerizations were carried out at —60 °C by using the H20 /Et2AlCl system, i.e., by increasing the moisture content in the enclosure from the usual <30 ppm to 150 ppm. Yields were 30% or less. The GPC trace of these PIB s (Fig. 9) coincides with those... 

Our preliminary results with this model indicate that distinctly bimodal MWD s are formed for some values of the parameters whereas near equality of the average values for each phase leads to a somewhat broadened unimodal MWD for other parameter choices. These results will be presented in detail, and we will explore some refinements to the above described model in a forthcoming publication (18). 

The log Mn vs. count calibration curve is shown on Figure 5. This is a fairly linear calibration curve, but it covers only a relatively narrow molecular weight range of 145,000 to 317,000 g/mole. Although we have sought to prepare higher MW samples for this purpose, we inadvertently obtained polymers with bimodal MWD s and did not use them for this calibration. 

As reported by Spassky et al. [62], aluminum complexes of Schiff bases as initiators exhibit much lower activities than aluminum porphyrins for the ringopening polymerization of epoxides. In fact, the polymerization of PO (500 equiv) using a Schiff base complex (Salphen)AlCl (13) as initiator proceeded extremely slowly at room temperature to attain only 4% conversion in 8 d. Even at 80 °C, the polymerization was slow, and required 6 d for completion, affording a polymer with broad and bimodal MWD (Fig. 32A). 

Figure 3. Symmetrical bimodal MWD using regularization with linear programming. The solid line represents the initial distribution, and the circles represent the computed distribution.

Fig. 4.27 represents the velocity profiles v(r) and degrees of conversion P(r) at the exit of a reactor for different values of Da/Da and constant [A] = 0.7 mol%. At Da = 0.5 (a rather low degree of conversion at the axis of the reactor), a low-viscosity stream flows out (breaks through) into the central zone (Fig. 4.27 b, curves 1 and 2). This means that the end-product leaving the reactor is a mixture consisting of two species (fractions) with very different molecular weights, leading to the appearance of a pronounced bimodal MWD-H, which is not due to the chemical process but is a direct consequence of the hydrodynamic situation in the reactor. 

For bimodal MWDs none of the methods successfully resolved the two peaks for the case where a majority of the molecules were of low molecular weight (Figure 5). However, CONTIN provided the closest solution. For the case where the skewed low molecular weight peak consisted of only one quarter of the total mass, the GEX fit method gave good results. CONTIN showed three peaks, but the agreement can still be considered fair because of the difficulty in discerning two widely separated peaks of this type. As in the unimodal cases, the subdistribution method showed the poorest fits. 

When ionization is weak, a clear bimodal MWD is observed. The concentration of ion pairs equals [C ] = 10 8 mol/L, whereas the concentration of free ions changes from [C + ] = 0.3-10-7, 10-7, and to 310"7 mol/L. This means that the proportion of monomer consumed by free ions increases from 76% to 90% and to 97%, respectively. This is depicted in the relative proportions of the HMW and LMW peaks. 

For example, the polymerization of alkyl vinyl ethers using an HC1/ SnCU (or adduct S/SnCl4) initiating system in methylene chloride is very fast even at - 15° C to give polymers with broad and often bimodal MWDs (Figure 17D) [105], Similar effects of solvent polarity are found in the polymerizations of p-alkoxystyrenes [107], styrene [25], and iV-vinylcar-bazole [108],... 

These salt effects are schematically depicted in Scheme 8. As we will discuss later more in detail (Sections Vl.B.3 and VII.E.3), mechanistically, salts may act in two different ways. In polar solvents they will suppress the free ions and considerably reduce their lifetime. This often converts bimodal MWD to monomodal MWD and provides controlled polymers. However, in polymerization of vinyl ethers initiated by strong Lewis acids such as SnCl4, where only ion pairs are present after addition of a few percent of salts or in nonpolar toluene, control is still very poor (Fig. 17B). Controlled polymers can be obtained only after addition of a more than equimolar amount of tetra-n-butylammonium halides. This implies that the salts change the weakly nucleophilic counterion SnCIs-to the more nucleophilic SnCl62 , which faster converts growing carbo-cations to covalent species. Another effect of added salts is related to... 

In methylene chloride solvent without added salt, the polymerization is not controlled and generates polystyrene with bimodal MWDs (e.g., Figure 23a), which are very similar to those found in nonliving cationic... 

The bimodal MWDs of emulsion-polymerized polyethylenes, which are significantly different from those formed in bulk polymerization, have been reported experimentally [307-309]. An MC simulation was conducted for the experimental conditions reported in [307], and an example is shown in Fig. 20 [310]. 

According to the MC simulation, the high molecular weight, narrow distribution component consists of the largest polymer molecule in each polymer particle, and the bimodal MWD is formed because of the limited space effects. 

Assuming a simple zero-one system during Interval II, a model analysis was conducted to clarify the conditions needed to form bimodal MWD through the effects of limited space [311]. 

Although the kinetic behavior during Interval 111 was not considered in [311], P =0.5 is an important consideration when we look at the possibility of forming bimodal MWDs in emulsion polymerization that involves chain transfer to polymer. 

On the basis of the MC simulation results [270], it is expected that if the amount of divinyl monomer is reduced to the level of, say, several crosslinkers per primary chain, a bimodal MWD (as shown in Fig. 26) may result. 

Fig. 26 MC simulation results that show bimodal MWDs in the emulsion copolymerization of vinyl/divinyl monomers [270]...

CjHjijTiCHjQ-AlCHjClj b ethylene 0 °C, toluene polyethylene and bimodal MWD 2 or more monomodal to lOS)... 

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