Second-Order Transitions and Mesh Distribution Functions of Cross-Linked Polystyrenes

Abstract

To the definition of the state of ``liquid with thermally fixed structure'' is added that of ``liquid with chemically fixed structure.'' Polystyrene is combined with increasing proportions of divinylbenzene. The resulting space network is represented analytically by means of the definition of a mesh width. The second‐order transition temperatures of these copolymers are determined from V—T curves. They obey a function where the constant 586[Me·T] characterizes the stiffening of the polystyrene by the addition of divinylbenzene. These polystyrene space networks are capable of being thermally activated up to a critical mesh width of 4 C atoms. The mesh widths are of varying sizes, the distribution is called the ``polydictiality.'' The mesh distribution function can be obtained from the V—T curves. The capacity of the space network to be thermally activated ceases fairly suddenly. This can be understood from a function of the capacity to be activated. The experimentally determined mesh distribution functions are expressed by means of a Gauss error curve. The width of this curve, about 1.7, is in surprising agreement for all copolymers. This means that approximately 50 percent of all meshes lie around the average mesh width with a variation of ±2 meshes. The method can be applied to all cross‐linked high polymers.