ISSN:
0449-2978
Keywords:
Physics
;
Polymer and Materials Science
Source:
Wiley InterScience Backfile Collection 1832-2000
Topics:
Chemistry and Pharmacology
,
Physics
Notes:
It was previously shown that for a stationary random copolymer of A, B, and C, we have in general p(AB) + p(AC) = p(BA) + p(CA), etc., in place of p(AB) = p(BA) which is valid for a stationary binary copolymer. Here, p(AB) for example, is the probability that a randomly picked pair of consecutive comonomers in the polymer consists of an A followed by a B. For a stationary ternary copolymer produced by a first-order Markovian addition mechanism, we show that PABPBCPCA/PACPCBPBA = k, where k is a constant characteristic of a particular set of three monomers but independent of its composition. Here, PAB is the conditional probability of finding a monomer of B given that its immediate predecessor is an A. We further show that if the individual rate constants of the monomer additions involved take a special form such as used in the Alfrey-Price Q-e scheme, then we have k = 1 irrespective of the kinds of monomers, and in addition we have p(AB) = p(BA), p(AC) = p(CA), etc. Thus, although these latter results were previously proposed by Ham as an alternative basis to supplant the Q-e scheme, they may rather be regarded as mathematical consequences of special assumptions adopted for the form of the individual rate constants. For a stationary random copolymer of four components A, B, C, and D, we have p(AB) + p(AC) + p(AD) = p(BA) + p(CA) + p(DA), etc., in general. For a first-order Markovian four-component copolymer, we show that there are seven different combinations of the conditional probabilities that are constants (k1, k2,…, k1) independent of the monomer composition. Again, if we assume the same special form for the rate constants involved, we find that all the seven constants k1, k2, …, k7 reduce to unity and p(XY) = p(YX) for X,Y, = A, B, C, D.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1002/pol.1971.160090401
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