Sequence-propagation probability

Digressing for a moment, it should be recognized that the sequence propagation probability, p, in the melt can be related to the comonomer reactivity ratio for addition type copolymerization. Formulating copolymerization kinetics in the classical manner(5), we let Fa represent the fraction of monomer Ma in the increment of copolymer formed at a given stage of the polymerization. Then one can write... 

A major consequence of Eq. (5.26) is the expectation that the melting temperature of a copolymer, where only one type unit is crystallizable, depends only on the sequence propagation probability p and not directly on composition. This result is rather unusual, and is unique to long chain molecules. Considering the major categories of copolymer structure we find in the extremes that... 

With the establishment of some of the unique features of the fusion of random copolymers, their melting temperature-composition relations can now be examined. Copolymers formed by condensation polymerization are usually characterized by a sequence-propagation probability p that is independent of copolymer composition and the extent of conversion. For such systems the quantity p can be... 

The melting temperatures are sensitive to the quantity p, particularly at low comonomer composition. For example, the melting temperatures of two ethylene-butene random-type copolymers prepared by using similar catalysts differ by about 5 °C for 0.5 mol % of side groups and the difference increases to 10 °C with about 3 mol % of side groups [31]. These differences in melting temperature for chemically identical copolymers at the same composition can be attributed to differences in their respective sequence-propagation probabilities. 

The sequence propagation probability, p, is the probability that an A unit is followed by another A unit along a chain. In a truly random copolymer whose comonomer distribution follows zero-order Markovian statistics, p equals X, the mole fraction of A units in the polymer therefore. Equation 11.1 can be rewritten as [10] ... 

The sequence propagation probability p can be related to the comonomer reactivity ratio in a straightforward manner. The problem can be further generalized to the case where p is influenced by the penultimate group. ... 

It is evident that the study of crystalline copolymers presents some very difficult as well as intriguing problems. The theoretical development of equilibrium relations and phase diagrams can be accomplished in principle when it is recognized that one must be concerned with the sequence propagation probability and not the composition. One major difficulty is that although the liquidus of the phase diagram can be determined quite easily, the solidus is extremely difficult to establish in most cases. In addition, it is virtually impossible to establish equilibrium on an experimental basis. As we have enumerated above there is a large number of important contributions to the deviations from equilibrium. The major ones are the finite crystallite size (relative to the equilibrium requirement), possible defected structures within the lattice and most importantly the structure of the interphase. 

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