A Simple Model of Random Tetrafunctional Networks with Defects: Fid-Bau Portal

A Simple Model of Random Tetrafunctional Networks with Defects

Ziabicki, Andrzej / Walasek, Janusz

Abstract Real crosslinked systems include a wide variety of structures. Crosslinks can be connected in many ways, including connection by multiple chains, intramolecular loops, etc. A simple topological model of random tetrafunctional crosslinked systems has been described. A system produced by crosslinking consists of uncrosslinked polymer chains and/or unused crosslinking agent, a low-crosslinked set of aggregates (sol) and (beyond some critical point) also a densely crosslinked network (gel). In a tetrafunctional system one can distinguish seven ‘topological elements’ connected to a crosslink: single- and multiple-connected chains, free-end chains, loops and voids (unsaturated functionalities). These elements can appear at a crosslink (junction) in 34 different combinations. First-order topological structure of the system is described by fractions of the 34 junction types. All macroscopic characteristics, such as gel point, modulus of elasticity, swelling equilibrium and sol—gel ratio, can be expressed as functions of the junction type distribution. The distribution of junction types has been derived from the assumption of randomness, and expressed as an explicit function of the number of the seven topological elements. These, in turn, can be estimated from basic information about crosslinking kinetics, and from an additional model assumption related to conformational properties of the polymer chains. In this way, complex structure of a crosslinked system and its physical properties can be described in terms of a few parameters which can be determined experimentally.