Bimodal composition 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. 

Bimodal composition distribution, which applies only to copolymers, can produce resins having different concentrations of copolymer, i.e. different melting points in polymer chains that are the same length. 

In order to avoid the use of lead compounds on environmental grounds, lithium fluoride (liF) has been chosen to obtain super-rate burning of nitramine composite propellants.P7281 Typical chemical compositions of HMX composite propellants-with and without liF are shown in Table 7.4. The non-catalyzed HMX propellant is used as a reference pyrolant to evaluate the effect of super-rate burning. The HMX particles are of finely divided, crystalline (3-HMX with a bimodal size distribution. Hydroxy-terminated polyether (HTPE) is used as a binder, the OH groups of which are cured with isophorone diisocyanate. The chemical properties of the HTPE binder are summarized in Table 7.5. 

The conditions of the existence of such bimodal distributions are well-known for the binary copolymerization [169-171], since in this case the differential equation proposed by Skeist [12] for the determination of the composition distribution has an explicit solution. Indeed when m = 2, the only one independent equation of the two equations (5.2) has a simple solution [169, 170, 172] ... 

The binary systems have two possible qualitatively different forms of the composition distribution of the products of the complete conversion (p = 1) shown in Fig. 4. The bimodal distribution is realized when the initial system composition x° is inside the basin of the stable SP corresponding to the homopolymer of the monomer Ms and the reactivity ratio of the corresponding radical rs < 0.5. In the opposite case when 0.5 < rs < 1 the composition distribution is unimodal. These conclusions derived at first [169-170] from the expressions (5.4) can also be obtained as a particular care from the general results [6, 134] of the analysis of the trajectory behavior near SP for the copolymerization of any number m of monomers. 

Description The CX process uses two polymerization reactors in series. The products have bimodal molecular-weight distribution (MWD), where MWD and composition distribution is freely and easily controlled by adjusting the operating conditions of two reactors without changing the catalyst. 

Computer simulations have also been used to model the properties of composites for specific particle distributions and geometry, e.g. spherical particles with either a bimodal size distribution (Fu et ai, 1999) or an... 

Particle Shape. The delineation of two families of materials on the basis of particle shape is very clear from the electron microscope evidence. That the families are xx, lx and xl, 11 points directly to the presence or absence of crosslinking in the PBMA as a source of particle shape differentiation. Overall concentration of the PBMA precursors is not a strong factor, since the irregular particles were observed in all three of the xx compositions, but an examination of the effect of crosslinker concentration alone was not carried out. In related work on an epoxy-butyl acrylate system in which component polymerization rates and the simultaneity of the reactions were matched, it was reported (3) that, prior to gelation of the matrix, irregular particles of crosslinked acrylate were formed but spherical particles were found in the absence of crosslinker. Together with the observation of an apparent bimodal size distribution, our results are similar, even though our system and conditions are markedly different from those in the earlier study. 

Figure 6.2. Compositional distribution of A 32 complete retroviral genomes and B the corresponding LTRs Numbers of A and B are plotted against % GC. Each bar in the histograms has a width corresponding to a 2% GC interval. (From Zoubak at al., 1992). The recent addition (not shown) of 13 additional genomes (Tsyba et al., 2004) has confirmed the bimodal pattern.

When we studied the compositional distribution of six genes (or small multigene families) and one family of transposable elements, Tntl, in DNA fractions from tobacco Nicotiana tabacum) separated according to base composition, we could show that gene distribution is bimodal and that such bimodality is due to the different base composition of the two parental genomes of tobacco N. sylvestris and N. tomentosiformis) and to the different parental origin of the genes tested (Matassi et al., 1991). 

The CCD curve shown in Fig. 15 contains all the information on composition distribution and it is a common practice to compare the CCD curves of the different resins to be evaluated In addition to the CCD curve, it is convenient to work with some easy-to-use average parameters. In the case of multiple peaks (like those shown in Fig. 15), integration of the peaks is most appropriate. In bimodal LLDPE, the most important parameters to measure are the homopolymer (linear) and soluble fraction percentages. Calculation of moments similar to... 

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