Sequence lengths, number-average

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. 

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. 

The mole ratio of monomers M] and M2 contained in the copolymer is given by the ratio of the two number-average sequence lengths... 

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 the observed triad concentrations in Table III, the number average sequence lengths for the VCI2 monomer were calculated5 using the equation ... 

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, ... 

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.

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... 

The sequence distribution of monomer residues in copolycondensation reactions of this type has been studied in detail by Peebles (18,39). If all monomers are assumed to have equal reactivity and if the reaction has gone to completion, the number-average sequence length of 3IG residues(g) is given by ... 

Hi number average sequence length of mf-units, i.e. average num-... 

Related to the run number R is the number average sequence length (N.A.S.L.), which is defined for a monomer A in an AB copolymer as the total number of A monomers in the polymer chain divided by the total number of blocks of monomer A (regardless the block length) [5]. Using the notation n(A) for N.A.S.L., the expression for n(A) is the following ... 

Both the run number R and the number average sequence length can be obtained from pyrolysis data. 

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... 

With the development of polymer structural characterizations using spectroscopy, there has been a considerable effort directed to measurements of tacticity, sequence distributions and number average sequence lengths (59 65). Two methods have been traditionally used for microstructure analysis from polymer solutions. Vibrational spectroscopy (infrared) and Nuclear Magnetic Resonance (NMR). Neither of these techniques is absolute. The assignment of absorption bands requires the use of model compounds or standards of known structure. 

The number average sequence length of Mi is then given by 00... 

Figure 8. Effect of soft segment content on point of phase separation during polyurethane polymerization as indicated by discontinuity in DSC reaction profile. Dotted line shows theoretical prediction assuming separation at constant number-average sequence length (1.3) of hard segments ("see text).

The development of the concepts of run number, average sequence lengths and triad distributions would be of little more than academic interest if they could not be usefully applied. The concept of run number is most valuable in a consideration of the effect of comonomer content versus branch length in affecting polyethylene density. The following section utilizes the run number in a correlation with a number of polyethylene physical properties. 

Table III. Number-Average Sequence Lengths of Some Dichlorocarbene Adducts of Cis-Polybutadiene...

The number-average sequence length of monomer Mi, in a way that is completely analogous to the definition of number-average molecular weight, is... 

NASL number average sequence length NIR near infrared... 

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