To define mathematically the concept of copolymer "randomness", we introduce a new quantity s, which we propose to call "informational entropy". It is defined as the ratio between the natural logarithm of the number of ways of disposing the homosequences of a copolymer and the number of monomeric units contained in the copolymer; it is calculated by applying the methods of information theory.
Informational entropy provides a criterion to judge the displacement of a copolymer from complete randomness; in fact, the description "random" is generally applied not only to "completely" random copolymers (i.e. having rlr~. = i), but also to copolymers which are "slightly displaced" from complete randomness. Numerical calculation of informational entropy shows that, at any given composition, it has its maximum value for rlrz = 1 and decreases very slowly with rtr~.; the definition of random copolymer may be extended, therefore, to copolymers for which the products of reactivity ratios vary over a very wide range. * To whom requests for reprints should be addressed. I" Each group of successive mt units in the copolymer, bound on both sides to mo units, is designated as a homosequence of ml units.
** As shown later in this paper, "informational entropy" is quite distinct from "thermodynamic entropy"; an alternative name might be "informational multiplicity".