Distribution sequence length

It is basically a fractionation process that depends not only on molecular size, but also on chemical composition, stereo-configuration, branching, and crosslinking. For multicomponent systems, fractionation with different ion polymolecularity, chemical heterogeneity and sequence length distribution, solubility or elution fractionation is of primary importance. Therefore, gel permeation chromatography or size exclusion chromatography is used as an important tool for the characterization of PBAs. 

Sequence length distributions are occasionally important. They measure the occurrences of structures like YXY, YXXY, and YXXXY in a random copolymer. These can be calculated from the reactivity ratios and the polymer composition. See, for example. Ham. ... 

Monomer sequence length distribution and penultimate effect in ethylenc-cycloolefln copolymers synthesized over homogeneous metallocene catalysts... 

Gel Permeation Chromatography (CPC) is often the source of molecular wei t averages used in polymerization kinetic modelling Q.,2). Kinetic models also r uire measurement of molecular weight distribution, conversion to polymer, composition of monomers in a copolymerization rea tion mixture, copolymer composition distribution, and sequence length distribution. The GPC chromatogram often reflects these properties (3,. ... 

In analysis of homopolymers the critical interpretation problems are calibration of retention time for molecular weight and allowance for the imperfect re >lution of the GPC. In copolymer analysis these interpretation problems remain but are ven added dimensions by the simultaneous presence of molecular weight distribution, copolymer composition distribution and monomer sequence length distribution. Since, the GPC usu y separates on the basis of "molecular size" in solution and not on the basB of any one of these particular properties, this means that at any retention time there can be distributions of all three. The usual GPC chromatogram then represents a r onse to the concentration of some avera of e h of these properties at each retention time. 

Furthermore, in the more general case we are concerned with a variation of composition and sequence length distribution not only as a function of retention volume but within each chromatogram area segment (or "slice ) at each retention volume. A significant polydispcrsity of one of these properties within a chromatogram slice can easily invalidate the polymer analysis described above. 

The previous sections in this chapter have tried to stress upon the significance of distribution of sequence lengths in polyethylene-based copolymers. The sequence length of interest in a system of ethylene-octene copolymers would be the number of methylene units before a hexyl branch point. As was discussed, this parameter has a greater impact on the crystallization behavior of these polymers than any other structural feature like branch content, or the comonomer fraction. The importance of sequence length distributions is not just limited to crystallization behavior, but also determines the conformational,... 

In some very recent work by Karssenberg et al. [130], attempts have been made to improve the analytical ability of a technique like NMR spectroscopy to effectively predict the distribution of sequence lengths in polyethylene-alkene copolymers. They analyzed the entire [ C-NMR spectrum for homogeneous ethylene-propene copolymers. They used quantitative methods based on Markov statistics to obtain sequence length distributions as shown in Figure 22 [130]. The... 

Figure 22 Sequence length distributions for ethylene-propene copolymers (Karssenberg et al. [130]). Top normalized ethylene sequence length distribution bottom normalized propylene sequence length distribution. Reproduced from Karssenberg et al. [130]. Copyright 2006, John Wiley Sons, Inc. Reprinted with permission of Wiley-Liss, Inc., a subsidiary of John Wiley Sons, Inc.

Among the main molecular structural variables in EPDMs that are stipulated by catalyst systems and that affect the vulcanizate tensile properties we may mention molecular weight (MW) and MWD, degree of unsaturation (LG=C 1) and its distribution in the polymer, composition (C S) and monomer sequence length distribution along molecular chains, and long-chain branching if present. Effect of... 

A study of the difference in monomer sequence length distribution and hence of the possibility of strain-induced crystallization and other structural parameters,including long-chain branching, of samples prepared with the above-mentioned various catalyst systems is under way and constitutes the subject of a subsequent paper. 

Fig. 6-8 Sequence length distribution for an ideal copolymerization with ri = r2 = 1 and/i =/2. After Vollmert (transl. Immergut) [1973] (by permission of Springer-Verlag New York, Inc., New York).

The sequence length distribution for an ideal copolymerization with r = 5, r2 = 0.2 for an equimolar feed composition is shown in Fig. 6-9. This copolymerization has pn — p2 0.8333 andp 2— p22 — 0.1667. Both M and M propagating centers have a 5 1 tendency to add Mi over M2, but Mi pentad sequences are not the most plentiful, although they are among the most plentiful. The most plentiful sequence is Mi at 16.7% with 14.0%, 11.6%, 9.7%, 8.1%, 6.7%, 5.6%, and 4.7%, respectively, of dyad, triad, tetrad, pentad, hexad, heptad, and octad Mi sequences. There are smaller amounts of longer sequences 3.2% of... 

Fig. 6-10 Sequence length distribution for an alternating copolymerization with r 0.1 and...

High-resolution nuclear magnetic resonance spectroscopy, especially 13C NMR, is a powerful tool for analysis of copolymer microstructure [Bailey and Henrichs, 1978 Bovey, 1972 Cheng, 1995, 1997a Randall, 1977, 1989 Randall and Ruff, 1988], The predicted sequence length distributions have been verihed in a number of comonomer systems. Copolymer microstructure also gives an alternate method for evaluation of monomer reactivity ratios [Randall, 1977]. The method follows that described in Sec. 8-16 for stereochemical microstructure. For example, for the terminal model, the mathematical equations from Sec. 8-16a-2 apply except that Pmm, Pmr, Pm and Prr are replaced by p, pi2, p2j, and p22. 

Generally, the molecular weight and the molecular-weight distribution are determined by two side reactions. Moreover, the end groups and in case of copolymers, their sequence length distribution are determined by the following two side reactions ... 

Figure 2 Property distributions in a linear copolymer composition distribution, molecular weight distribution and sequence length distribution of poly styrene-co-n-butyl methacrylate). (Styrene units are represented by "A and n-butyl methacrylate units by B".)...

Copolymers are readily prepared by conducting polymerizations of a mixture of monomers. However, to obtain a product having any reasonable, structural homogeneity, it is necessary to take the reaction mechanism into account, and to perform the experiment under conditions consistent with classical, copolymerization theory. With properly controlled experiments, it is possible to determine the relative reactivities of the monomers, and the range of compositions and mer sequence-length distributions in any copolymer produced.81,82... 

It should be emphasized that copolymerizations that conform to the premises of binary-copolymerization theory produce copolymers of well defined structure. The kinetics of the competitive propagation-reactions determine not only the copolymer composition but also the sequence distribution. The mathematical procedures needed for calculating number-average sequence-lengths of mers, and sequence length-distributions of mers, are well known and have been... 

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