Average sequence length

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 ... 

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 sequence identity averaged over the whole length of the molecule is generally low among different P-type ion transport ATPases, the conserved sequences around the phosphate acceptor aspartyl group and in the ATP binding domain are well preserved [30,32,46]. Structure predictions based on the hydropathy plots... 

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,. ... 

The detector response ratio is elevated with respect to the homopolymer line but very near parallel to it less than = 0.74,or number average styrene sequence lengths less... 

The number and weight average sequence lengths accumulated with conversion are calculated from ... 

Instantaneous number average styrene sequence length Number average styrene sequence length... 

Weight average styrene sequence length Polynier chain length Reactivity ratios... 

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,... 

Mean sequence lengths can also be used to write average configurational structures, that is. 

The sequence distributions are clearly non-Bernoulllan in this case although they could satisfy conformity to Markovian behavior as indicated by equations 11-13. The following average structure is suggested by these observed mean sequence lengths. 

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... 

Table 5.8 Statistical probabilities and average and sequence lengths for template, T, and non-template, N, systems. [Reprinted from H. L. Frisch and Qihua Xu, Macromolecules, 25, 5145 (1992), with kind permission from ACS]...

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