Molecular Bimodal

Using both condensation-cured and addition-cured model systems, it has been shown that the modulus depends on the molecular weight of the polymer and that the modulus at mpture increases with increased junction functionahty (259). However, if a bimodal distribution of chain lengths is employed, an anomalously high modulus at high extensions is observed. Finite extensibihty of the short chains has been proposed as the origin of this upturn in the stress—strain curve. 

When the catalyst is expensive, the inaccessible internal surface is a liabihty, and in every case it makes for a larger reactor size. A more or less uniform pore diameter is desirable, but this is practically reahz-able only with molecular sieves. Those pellets that are extrudates of compacted masses of smaller particles have bimodal pore size distributions, between the particles and inside them. Micropores have diameters of 10 to 100 A, macropores of 1,000 to 10,000 A. The macropores provide rapid mass transfer into the interstices that lead to the micropores where the reaction takes place. 

One further point might be made here. Although the example illustrates the difference between the two types of molecular weight average, the weight average molecular weight in this example cannot be said to be truly representative, an essential requirement of any measure of central tendency. In such circumstances where there is a bimodal, i.e. two-peaked, distribution additional data should be provided such as the modal values (100 and 100000 in this case) of the two peaks. 

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). 

The narrow molecular weight distribution means that the melts are more Newtonian (see Section 8.2.5) and therefore have a higher melt viscosity at high shear rates than a more pseudoplastic material of similar molecular dimensions. In turn this may require more powerful extruders. They are also more subject to melt irregularities such as sharkskin and melt fracture. This is one of the factors that has led to current interest in metallocene-polymerised polypropylenes with a bimodal molecular weight distribution. 

Zorbax PSM Bimodal and Trimodal columns are packed with mixed pore-size packing to achieve linear size separations over a broad molecular weight range (Table 3.3). Zorbax PSM Bimodal columns are packed with PSM 60 and PSM 1000 particles, and Trimodal columns contain PSM 60, PSM 300, and PSM 3000 particles (Fig. 3.4). Carefully selecting and mixing different pore-size particles in columns provide much better linearity than coupling columns that are each packed with single pore-size particles. 

FIGURE 23.3 A solution of a bimodal mixture of low molecular weight components (black) and high weight components (white) in contact with a porous medium (a) Low and (b) high concentrations. 

We have prepared a copolymer-bearing amino side group and used it either alone or in combination with BP to initiate the photopolymerization of MM A [89]. The gel permeation chromatography (GPC) plot of PMMA initiated by the former system showed a bimodal distribution of molecular weight because both the radicals produced initiate polymerization as follows ... 

Note (1) Polymer D was made up of blending A and C (50 50) in the latex stage. The result was a bimodal molecular weight distribution having an average value close to B (2) All compounds used the same formulation. 

Saito et w/.217 -19 have examined the polymerization of multimethacrylates prepared from p-cyelodextrin. Polymerization using ATRP conditions gave a bimodal molecular weight distribution for the derived PMMA composed predominantly of oligomers of 7 or 14 units indicating that there was little intcrmolccular reaction... 

Polymerization of t-butyl methacrylate initiated by lithium compounds in toluene yields 100% isotactic polymers 64,65), and significantly, of a nearly uniform molecular-weight, while the isotactic polymethyl methacrylate formed under these conditions has a bimodal distribution. Significantly, the propagation of the lithium pairs of the t-Bu ester carbanion, is faster in toluene than in THF. In hydrocarbon solvents the monomers seem to interact strongly with the Li+ cations in the transition state of the addition, while the conventional direct monomer interaction with carbanions, that requires partial dissociation of ion-pair in the transition state of propagation, governs the addition in ethereal solvents. 

In a further study, Rill et al. [325] developed a model of gel permeation chromatography that included a bimodal pore stracture. The smallest mode in the pore-size distribution represents the basic background polyacrylamide pore structure of about 1-mn mean radius, and the second mode was around 5 nm, i.e., in the range of size of the molecular templates. The introduction of this second pore structure was found to substantially improve the peak resolution for molecules with molecular sizes in the range of the pore size. 

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. 

Molecular weights of polysilane polymers depend upon the exact method of synthesis, as well as the purity of the dichlorosilane starting materials. Bimodal molecular weight distributions are commonly reported, as shown in Figure 1, but under some conditions... 

PhMeSi)n(Me2Si)m copolymer, m=n, showing bimodal molecular... 

Our initial studies (23) were performed in toluene, and Table I shows the results from the polymerization of a number of representative monomers. The data reported in Table I are for direct addition of the monomer to the sodium dispersion. Inverse addition often leads to higher molecular weights, although the overall polymer yields are usually lower (15,23). The results in Table I show that, under these reaction conditions, a bimodal molecular molecular weight distribution is normally obtained. Furthermore, it is obvious that the crude polymer yields drop precipitously as the steric hindrance in the monomer increases. 

In some cases, two or more catalysts are present during polymerization. Inevitably, the catalysts exhibit different polymerization kinetics, which results in different populations of molecules. In such cases, we produce polymers with a bimodal molecular weight distribution. 

By using two or more polymerization catalysts simultaneously, polymer chemists can produce copolymers tvith a bimodal composition distribution. This is made possible by the fact that no two catalysts incorporate monomers at exactly the same rate. The net result is that short chain branches may be preferentially incorporated into either the higher or lower molecular weight fractions. Polymer manufacturers can obtain a similar result by operating two polymerization reactors in series. Each reactor produces a resin with a different copolymer distribution, which are combined to form a bimodal product. Copolymers with a bimodal composition distribution provide enhanced toughness when extruded into films. 

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