Sequence length determination

Nuclear Magnetic Resonance. The successful study of polymers in solution by high resolution NMR spectroscopy started with the pioneering work on the sequence structure of poly methyl methacrylate in 1960. Since then, an ever-increasing number of investigations have been carried out ranging from the elucidation of the statistics of homopolymer and copolymer structure to the study of conformation, relaxation and adsorption properties of polymers. The aspects of sequence length determination and tacticity have received considerable attention (Klesper 84, for example, reports more than 500 entries). Therefore, a detailed review will not be attempted. (For a detailed description of the NMR Theory and statistics of polymer structure, see Bovey 59, Randall 23, and Klesper 84). 

R.R. Joshi and S.K. Gupta, Microstructure and Sequence Length Determination of Antifouling Polymers (unpublished results). 

Denchev Z, DuChesne A, Stamm M and Fakirov S (1998) Sequence length determination in poly(ethylene terephthalate)-bisphenol-A polycarbonate random copolymers by application of selective degradation, J Appl Polym Sci 68 429-440. 

These terms are subsequently used for the number average sequence length determination. Table 7.24 shows a comparison of Py-GC and NMR values for the number average sequence length calculation of vinylidene chloride/vinyl chloride copolymer samples A-F. The number average sequence lengths for vinyl chloride, N(C), and vinylidene chloride, N (D), of samples C, D, and E are all within 1 unit difference (1.53 versus 1.40,1.7%versus 1.50, and 3.69 3.00 for vinyl chloride,... 

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. 

The measurement procedure is known as the pulse sequence, and always starts with a delay prior to switching on the irradiation pulse. The irradiation pulse only lasts a few microseconds, and its length determines its power. The NMR-active nuclei (here protons) absorb energy from the pulse, generating a signal. 

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,... 

A special kind of random noise, pseudo random noise, has the special property of not being really random. After a certain time interval, a sequence, the same pattern is repeated. The most suitable random input function used in CC is the Pseudo Random Binary Sequence (PRBS). The PRBS is a logical function, that has the combined properties of a true binary random signal and those of a reproducible deterministic signal. The PRBS generator is controlled by an internal clock a PRBS is considered with a sequence length N and a clock period t. It is very important to note that the estimation of the ACF, if computed over an integral number of sequences, is exactly equal to the ACF determined over an infinite time. 

When measuring vinyl polymer tactlclty, one prefers the longest complete n-ad distribution available as well as the translated simplest comonomer distribution, possibly m versus r. An alternative exists to the m versus r distribution In the form of number average or mean sequence lengths. If any vinyl homopolymer Is viewed conceptually as a copolymer of meso and racemic dyads, mean sequence lengths can be determined for continuous runs of both meso and racemic configurations (32), that Is,... 

Although the derivation above involves the steady-state assumption, the copolymerization equation can also be obtained by a statistical approach without invoking steady-state conditions [Farina, 1990 Goldfinger and Kane, 1948 Melville et al., 1947 Tirrell, 1986 Vollmert, 1973]. We proceed to determine the number-average sequence lengths, h and h2, of monomers 1 and 2, respectively. h is the average number of Mj monomer units that follow each other consecutively in a sequence uninterrupted by M2 units but bounded on each end of the sequence by M2 units. h2 is the average number of M2 monomer units in a sequence uninterrupted by Mj units but bounded on each end by Mi units. 

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 ... 

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... 

Carbon-13 nuclear magnetic resonance was used to determine the molecular structure of four copolymers of vinyl chloride and vinylidene chloride. The spectra were used to determine both monomer composition and sequence distribution. Good agreement was found between the chlorine analysis determined from wet analysis and the chlorine analysis determined by the C nmr method. The number average sequence length for vinylidene chloride measured from the spectra fit first order Markovian statistics rather than Bernoullian. The chemical shifts in these copolymers as well as their changes in areas as a function of monomer composition enable these copolymers to serve as model... 

Figure 12.4 The pulse scheme of the three-pulse echo sequence to determine Xe diffusion coefficients in polymers and other porous systems. The shaded areas are magnetic field gradient pulses with amplitude g and length 8. The time between the two gradient pulses A determines the time during which the diffusion path length is...

---