Sequence length copolymers

Item (2) requires that each event in the addition process be independent of all others. We have consistently assumed this throughout this chapter, beginning with the copolymer composition equation. Until now we have said nothing about testing this assumption. Consideration of copolymer sequence lengths offers this possibility. 

As a last example of the application of HPTMC, we calculate the phase behavior of block copolymers and random copolymers. Again, lattice models are used in these calculations. For block copolymers, we study the influence of the number of blocks on the phase behavior for random copolymers, we examine the effect of sequence length. We use a one-dimensional Ising model to represent the random copolymer. Sequence length is statistically determined by the temperature of the one-dimensional Ising model. When this temperature approaches infinity, the sequence of the copolymer is completely random when the temperature approaches zero, the random copolymer becomes a diblock copolymer. For all calculations, the chain length isn = 1000. 

As expected, fig increases and fi decreases with increasing extent of reaction. For the samples prepared using aqueous NaOH, the observed sequence lengths are in reasonable agreement with those expected for a random copolymer displaying Bernoullian statistics (Table III) (2). The random copolymer sequence lengths were calculated using Equation 6, where Pg is the mole fraction of dichlorocyclopropane units. 

This technique can be used to measure chain molecular structure, copolymer composition, and copolymer sequence lengths. It can also deduce isotactic/atactic ratios and other structure variations, as shown, for example, in Ref. 17. Mass spectrometry and NMR are currently not in routine on-line process use, but can be used to calibrate other on-line methods. 

In the context of monitoring polymerization reactions, IR spectroscopy has a long history, with early reports of its use related to polymerization reaction monitoring stretching back to at least the 1950s [46,47], with a subsequent report of continuous IR measurements at 805 cm" to monitor ethacrylate polymerization in toluene [48]. IR methods have been extended to offline copolymer sequence length analysis [49, 50], curing reactions [51], picosecond time-resolved studies of initiation events [52], and other aspects of polymer characterization. 

While mass balance modeling will result in the values of scalar properties (monomer concentration, etc.), properties of a polymerization system such as molecular weight, copolymer composition, and copolymer sequence length are, due to the nature of the polymerization processes, distributions of properties. Thus, for example, there will be a distribution of molecular weights within the product of most polymerization reactors. In these cases, population balances, rather than species balances must be written for these properties. Three examples are given in the following. More complete treatments of the technique can be found elsewhere [3,4]. 

Equations (7.40) and (7.41) suggest a second method, in addition to the copolymer composition equation, for the experimental determination of reactivity ratios. If the average sequence length can be determined for a feedstock of known composition, then rj and r2 can be evaluated. We shall return to this possibility in the next section. In anticipation of applying this idea, let us review the assumptions and limitation to which Eqs. (7.40) and (7.41) are subject ... 

Using proton NMR of solutions, the composition of polymers can be analyzed.47 Carbon-13 NMR spectroscopy is a useful tool for studying the sequence length of segments in copolymers and thereby determining the blockiness of the copolymer. With solid-state NMR, the mobility of chain segments can be studied and the crystallinity determined. 

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. 

With regards to the copolymerization, a recent kineuc study by Gruber and KneU (10 has indicated that styrene n-butyl methacrylate obeys the cla ical kinetic theory with regards to composition and sequence length to complete conversion. This theory is applied to high conversion to charau terize copolymer samples for GPC analysis. 

B. Measurement of Property Distributions for Copolymers. Figure 12 shows chromatograms of typical products in the copolymerization study (Column Code B2). Since the detector is responding to concentration, composition, and periiaps sequence length, the direct single detector interpretation as described for PMMA is not immediately applicable here. Tacticity variation is yet another consideration but ]s assumed of sa ond order importance for th samples (22). 

V. Copolvmerization Kinetics. Qassical copolymerization kinetics commonly provides equations for instantaneous property distributions (e.g. sequence length) and sometimes for accumulated instantaneous (i.e. for high conversion samples) as well (e.g. copolymer composition). These can serve as the basis upon whkh to derive nations which would reflect detector response for a GPC separation based upon properties other than molecular weight. The distributions can then serve as c bration standards analagous to the use of molecular weight standards. 

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.

A few reviews have dealt with the identification of synthetic polymers by Py-GC/MS [76]. In addition to compositional studies, applications of pyrolysis to synthetic polymers include sequence length characterization in copolymers [77] and tacticity measurements in stereoregular homopolymers [78]. 

Recently, Kroeze et al. prepared polymeric iniferter 34 including poly(BD) segments in the main chain [152]. They successfully synthesized poly(BD)-block-poly(SAN), which was characterized by gel permeation chromatography, elemental analysis, thermogravimetric analysis, NMR, dynamic mechanical thermal analysis, and transmission electron microscopy. By varying the polymerization time and iniferter concentration, the composition and the sequence length were controlled. The analysis confirmed the chain microphase separation in the multiblock copolymers. 

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