Copolymer sequence-length distribution

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. 

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.

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... 

Using an Ising model for rotational isomeric states the unperturbed dimensions, 0 / nl2, are evaluated for copolymers of propylene and pentene-1. Chemical composition, tacticity, and sequence length distribution are varied. It is found that only for atactic copolymers 0 I n 2 depends linear on the chemical composition. Deviations from linearity cannot be attributed... 

However, in some cases, additional effects on (dn/dc)copo must be considered. Due to cooperative interactions between the monomer units in the polymer chain, copolymer refractive index increments may deviate from the summation scheme. As a result of different sequence length distributions, different values of (dn/dc)copo can be obtained for the same gross composition. Copolymer (dn/dc)copo values can be obtained by multiple detection SEC providing the chemical composition at each slice of the elution curve. 

Copolymer properties are known to be a function of the molecular weight distribution (MWD), the copolymer composition distribution (CCD) and in some cases the sequence length distribution (SLD). The optimal design, operation and control of reactors to produce high quality copolymers with efficient production rates requires ... 

Problem 7.13 Consider an alternating copolymerization with = V2 = 0.1 and fi = 0.5. What percentage of the alternating copolymer structure is made of M1M2 sequence Compare the sequence length distribution with that for the ideal copolymer in Problem 7.12(a) which has the identical overall composition. 

The distributions of the various lengths of the Mi and M2 sequences are called the sequence length distributions, which define the microstructure of a copolymer. The probabilities of forming Mi and M2 sequences of x units, that is, their respective mole fractions n cCMi) and nxiM.2), are given by (see Problem 7.1 for derivation),... 

Solvent effects on the optical densities of alternating and random copolymers of styrene and methyl methacrylate can explain the variation in hypochromism at 269.5 nm (see Figure 1 and Table II). Actually, the hypochromism seems to depend on specific interactions between methyl methacrylate mers and styrene mers. Good correlations between hypochromism and chemical structure of the copolymers can be deduced on the basis of the sequence length distribution. 

Pn P i — Pii = Pi = 0.50. Although the most plentiful sequence is Mi at 50%, there are considerable amounts of other sequences 25%, 12.5%, 6.25%, 3.13%, 1.56%, and 0.78%, respectively, of dyad, triad, tetrad, pentad, hexad, and heptad sequences. The distribution of M2 sequences is exactly the same as for Mi sequences. For a feed composition other than equimolar, the distribution becomes narrower for the monomer present in lower amount and broader for the monomer in larger amount—a general phenomenon observed for all sequence length distributions. It is clear that the copolymer, with an overall composition of Fi = F2 — 0.50, has a microstructure that is very different from that of a perfectly alternating copolymer. 

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