The structure and properties of molecular trees and networks

Abstract

The gel point is a well-understood critical point in polymer science (Flory, Stockmayer). A summary is given of the resolution of those aspects which may seem paradoxical at first sight. The relevant equations for the basic paradigm of f-functional polycondensation are very simple. Special attention is paid to the critically branched state of materials not far from the gel point. The quasi-invariance principle is explained according to which all solution properties appear ultimately to level off as the critical conversion is approached from below. The ‘Malthusian’ packing paradox is resolved by a proper treatment of the ring-chain competition situation, which also disposes of the spurious divergence of the rate of cyclization predicted by a more naive theory. Network theories not based on extinction probability (Charlesby) are not worth considering. The proper definition of an elastically active network chain (EANC) was based on this concept by Scanlan and by Case in 1960, and it greatly simplifies the graph-like-state theories of network structure (usually called ‘network topology’). It allows classical rubber elasticity theory to be applied near the gel point. The point is characterised by a fifth-order Ehrenfest transition due to the contribution of long-range correlations to the configurational free energy. Though directly relevant data on reversible gelation are not available, data on isothermal crosslinking of very diverse systems support this analysis. Except possibly for some highly crosslinked systems, the parameter Mc (mean chain length between ‘crosslinks’) is an undesirable ingredient of elasticity or swelling theories. Chain-end corrections are quite undesirable (and usually done incorrectly). Everything is correctly and more simply formulated in terms of Scanlan-Case EANCs. The proper understanding of the gel point as a critical point allows the construction of reduced plots, illustrated with temperature superposition of experimental modulus-conversion plots (by M. Judd) for aqueous gelatin jellies. These fit reasonably to the basic model involving triple-helix junction zones, essentially without adjusting arbitrary parameters. Such reduced-variable treatments for critically branched materials eliminate the otherwise inescapable difficulties of characterization, purity, electrolyte content, etc., from gelatin research. © 1975, Walter de Gruyter. All rights reserved.