Ideal copolymers and the second‐order transitions of synthetic rubbers. i. non‐crystalline copolymers

Abstract

Theoretical and practical evidence is put forward to show that copolymers can be treated like solutions of small molecules in the interpretation of packing phenomena, and that ideal volumeadditivity of the repeating units in copolymers is frequently realized. On this basis equations are derived for predicting 0, the second-order transition temperature, of binary copolymers from the two second-order transition temperatures of the pure polymers and their coefficients of expansion in the glassy and rubbery states. Previous mechanistic theories of the second-order transition temperature of such copolymers are thus superseded by a general reduction of the problem to the mechanism of thermal expansion. Practical applications to the choice of monomers in producing synthetic rubbers are outlined, and attention is drawn to the importance of second-order transitions in kinetic measurements on the reactions of polymers. Derivation of theoryMeasurements of density, d, preferably expressed as specific volume, V = Ild, are easy to make and give direct evidence of the packing together of molecules in various states. For ordinary small molecules such measurements are interpreted in terms of partial specific volumes of the components (see Lewis & Randall, 1923)~ and the same treatment has been applied to solutions of polymers in small molecules (Heller & Thompson, 1951). If two liquids mix without change of volume, a plot of V against weight fraction c, is linear and the two partial specific volumes are constant. We extend this treatment to the monomeric units of a polymer and show by theoretical and practical evidence that this linearity, reflecting volume additivity of the units, is common both in the rubbery and in the glassy states. We are thus led to a simple law of ideal copolymers, corresponding to that of ordinary ideal solutions, which postulates a constant rubber volume ~V R and a constant glass volume iVG at each temperature for the ith species of repeating unit in all its ideal rubbery and glassy copolymers, these two constants being equal to the specific volume of the pure polymer in these two states. If, then, we consider a copolymer made up of two components whose pure polymers are both rubbers (at the temperature under consideration) the specific volume of the copolymer containing a fraction c2 of component (2) will be given by:A similar argument applies when both pure polymers are glasses, but the situation is more complex when one (which we shall always denote by i = I) is a rubber above its transition temperature O,, and the other is a glass (i = 2) below its transition temperature Oz. Our postulate implies that the state, rubbery or glassy, of the particular copolymer considered determines whether the rubbery or glassy volumes of both components enter into the specific-volume equation:For any temperature T lying between 0, and 8, there will be a composition at which the copolymer has its transition temperature 8 at T. It is clear from the foregoing that at this point the plot of V against c2 will change slope ...

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