Number-average sequence length calculation

Table TV, the resulting calculation of VCl number average sequence length calculated using the first order Markov agrees very well with the observed sequence lengths.

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,... 

Calculation of the N.A.S.L. (Number Average Sequence Length) can be performed, according to the definition given by Randall, given the model probabilities. Generation of the coefficients used in the equation required for this option, however, has not been automated. 

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... 

The observed number average sequence lengths deviate from those predicted from Bernoullian statistics, i.e., n = 1/[VC1], However, corresponding calculations based on first order Markovian statistics are in excellent agreement. 

To calculate the number average sequence length using first order Markovian statistics, it is necessary to estimate p, ... 

The number of triads in a copolymer of AB type can provide information to calculate the number average sequence length n(A) (see rel. 2.3.34). The total number of A monomers can be expressed in triad terms as Naaa + Naab + Nbaa + Nbab. where Naaa is the total number of triads containing A found in the polymer microstructure, Naab is the number of triads containing AAB, etc. The total number of blocks can be expressed... 

In this way, the number average sequence length of A sequences is calculated from the mass fractions, and Wb, and the molar masses, Mp, and Mb, of the monomeric units, together with the fraction of all AB and BA... 

The probability of forming a sequence from two identical monomeric units is therefore given by the product of the individual probabilities Pii for the addition of a second monomer and pi2 for the probability of ending this sequence (see the analogous calculation of the molecular weight in poly condensations. Chapter 17). Thus, the number-average sequence length is... 

Wang and Smith [101] used PGC to carry out compositional and structural studies of these copolymers. Composition and number average sequence lengths (which reflects monomer arrangements) in the copolymers were calculated using formulae that incorporate pure trimer and hybrid trimer peak intensities. 

A triad distribution is useful because it gives the relative concentrations of each of the possible connecting sequences. With this information, the comonomer concentrations, number average sequence lengths and the run number can be calculated as follows ... 

Number-average sequence lengths for both the dichlorocyclo-propane and the cis-butadiene units can be calculated from the C data using the assignments in Figure 2 and standard equations. 

Benzene, chlorobenzene, dichlorobenzene and trichlorobenzene are four major products formed in the pyrolysis of vinylidene chloride/vinyl chloride copolymer. To make the composition calculation, the first assumption is that all trimer peak intensities generated from the Py-GC after correction for pyrolysis efficiency and detection efficiency accurately represent the triad distribution of the vinylidene chloride/vinyl chloride copolymer. If a close relationship exists between the triad distribution in the polymer chain and the production of trimers in pyrolysis, the composition and number average sequence length can be calculated on the basis of the trimer production in the pyrolysis. Results were in good agreement with those obtained by H-NMR (Table 4.11). Copolymers containing 11 wt% and 5 wt% vinyl chloride and 5% and 89% vinylidene chloride were successfully analysed. 

Where and njj are the number average sequence lengths of monomers C and D. NCCC, NCCD + OCC, NDCD, NCDC, DDC and NDDD are the experimentally derived triad molar fractions or numbers of molecules. From the formulae above, if all six triad molar fractions or numbers of molecules can be generated, then the number average sequence lengths of monomers C and D can be calculated. 

Brar and Sunita [58] described a method for the analysis of acrylonitrile-butyl acrylate (A/B) copolymers of different monomer compositions. Copolymer compositions were determined by elemental analyses and comonomers reactivity ratios were determined using a non-linear least squares errors-in-variables model. Terminal and penultimate reactivity ratios were calculated using the observed distribution determined from C( H)-NMR spectra. The triad sequence distribution was used to calculate diad concentrations, conditional probability parameters, number-average sequence lengths and block character of the copolymers. The observed triad sequence concentrations determined from C( H)-NMR spectra agreed well with those calculated from reactivity ratios. 

Wang and co-workers [90] showed that pyrolysis - gas chromatography of styrene- butyl acrylate can be used to obtain the number average sequence length which can be further used to calculate the percentage of monomer in these copolymers. 

By means of the statistical parameters, the number-average sequence lengths can be calculated ... 

Cheng-Yu Wang et af applied pyrolysis gas chromatography to the determination of the structure of styrene-n-butyl acrylate copolymers. The number average sequence length which reflects monomer arrangement was calculated using formulae that incorporate pure trimer peak intensities and hybrid trimer peak intensities. 

If triads are being measured, the number-average sequence length can be calculated by using... 

As a test of our measurements on the model copolymer, you might like to calculate the number average sequence lengths using the triad information... 

Of course, if tetrads or higher -ads are measured, corresponding relationships can be derived for calculating the number-average sequence lengths. 

Pyrolysis products such as benzene, toluene, styrene, and naphthalene were observed. The amount of these aromatic compounds formed directly reflects the concentration of chlorine atoms and their distribution in the CPE. The composition and structure calculations were based on those degraded trimer peak intensities obtained by Py-GC. This Py-GC method can be used to quantitatively determine the chlorine content in CPE. The same method can also explore the microstructure through number-average sequence length (NASL) of ethylene and vinyl chloride monomers. Other structure-related terms, such as the percentage of grouped vinyl chloride monomers, i.e., the percentage of chlorine atoms structured as polyvinyl chloride (PVC)-like structures, can also be calculated. 

Polymeric structure determination does not have to be limited by the copolymer system. Other polymers that are produced by other methods may be treated as a copolymer system consisting of two different types of monomers. Chlorinated polyethylene is a good example [35]. In some circumstances, a chlorinated polyethylene system can be considered as a copolymer system of vinyl chloride and 1,2-dichloroethylene. By examining the appropriate fragments that correspond to the trimer combination of vinyl chloride and 1,2-dichloroethylene, one can utilise a statistical formula to calculate the number-average sequence length and composition. One can also explore the chlorine content as well as the arrangement of chlorine atoms in the polyethylene chain. 

Figure 7.15 shows the pyrogram of the trimer area for five different mole compositions of STY/n-BA. The number-average sequence lengths were calculated for all five polymers. The peak areas were normalised on the basis of the summation of and... 

Nbasba eqnalling 1. All normalised peak areas were then used to calculate the number-average sequence length for both styrene and -butyl acrylate (Table 7.7). 

Kapur and Brar [179] prepared acrylonitrile-ethyl methacrylate (A/E) copolymers of different monomer concentrations in bulk by free radical initiation. Copolymer composition was determined by nitrogen analysis and the comonomer reactivity ratios were determined by the method of Kelen-Tiidos. C-NMR spectra of several A/E copolymers are discussed in terms of their triad monomer sequence and cotacticity. Terminal and penultimate reactivity ratios were calculated using the observed monomer triad sequence distribution determined from C-NMR spectroscopy for individual samples. Triad sequence distribution was used to calculate dyad concentrations, probability parameters, number average sequence lengths, and the comonomer mole fractions in the copolymers. The configurational sequence distributions in terms of all the 10 A-centred and 10 E-centred triad cotactic sequences have been determined and found to be in excellent agreement with those obtained using various cotactic probability parameters. 

Brar and Sunita [184] have reported the reactivity ratios (r) for the acrylonitrile]A)-methyl acrylate (M) monomer pair using the errors in variables model (EVM) [185, 186] with the use of a computer program written by O Driscoll and co-workers [187]. The primary structure factors monomer composition, diad/triad sequence distribution, conditional probabilities, and number-average sequence lengths of acrylonitrile-methyl acrylate copolymers were determined on the basis of C H -NMR analyses and compared with those calculated from reactivity ratios as determined from EVM program. The diad sequence calculated from C H)-NMR (proton decoupled C-NMR) spectra was correlated with the Tg of A/M copolymers. 

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