Extended Flory principle

In this case the role of kinetically independent elements in accordance with the extended Flory principle is performed by monomeric units of different kinds S0,...,Sf, while here the rate constants of the elementary reactions of condensation ky(z, =0,...,f-l) between functional groups belonging to units S and S act as the parameters of the FSSE model. It has been suggested [76] to characterize every molecule by vector 1 with components /0,...,/(,...,Zf equal to the numbers of units of types S0,...,S ,...,Sf that this molecule is comprised of. Kinetic schemes of the reactions between monomeric units as well as between molecules may be written down as follows ... 

Among the first of them are the so-called substitution effects due to steric, induction, catalytic, or some other types of influence of the reacted active centers on the reactivity of neighboring unreacted centers. In order to take account of such short-range effects it has been suggested (Kuchanov, 1978) to use under mathematical modeling an extended Flory principle. In line with this principle, the reactivity of any active center of a molecule is supposed to be controlled exclusively by local chemical structure of the... 

This closure property is also inherent to a set of differential equations for arbitrary sequences Uk in macromolecules of linear copolymers as well as for analogous fragments in branched polymers. Hence, in principle, the kinetic method enables the determination of statistical characteristics of the chemical structure of noncyclic polymers, provided the Flory principle holds for all the chemical reactions involved in their synthesis. It is essential here that the Flory principle is meant not in its original version but in the extended one [2]. Hence under mathematical modeling the employment of the kinetic models of macro-molecular reactions where the violation of ideality is connected only with the short-range effects will not create new fundamental problems as compared with ideal models. 

This is the simplest of the models where violation of the Flory principle is permitted. The assumption behind this model stipulates that the reactivity of a polymer radical is predetermined by the type of bothjts ultimate and penultimate units [23]. Here, the pairs of terminal units MaM act, along with monomers M, as kinetically independent elements, so that there are m3 constants of the rate of elementary reactions of chain propagation ka ]r The stochastic process of conventional movement along macromolecules formed at fixed x will be Markovian, provided that monomeric units are differentiated by the type of preceding unit. In this case the number of transient states Sa of the extended Markov chain is m2 in accordance with the number of pairs of monomeric units. No special problems presents writing down the elements of the matrix of the transitions Q of such a chain [ 1,10,34,39] and deriving by means of the mathematical apparatus of the Markov chains the expressions for the instantaneous statistical characteristics of copolymers. By way of illustration this matrix will be presented for the case of binary copolymerization ... 

In this section the theory of phase equilibria of polymer solutions is discussed as it is a simple practical illustration of the Flory-Huggins theory and can be extended to explain the principles behind the fractionation techniques which are used with polymer solutions. Finally the technique of gel-permeation chromatography, which is now widely used in polymer laboratories, is described in detail. 

---