The critically branched state in a covalent synthetic system and in the reversible gelation of gelatin

Abstract

The critically branched state of matter (close to a gel point) is further explored theoretically and experimentally. Fluctuations and effects due to cutting the high molecular weight tail of the distribution are examined in terms of asymptotic formulae derived from the Flory-Stockmayer distribution for random ƒ-functional condensates. “Tail-cutting” can arise from preparative and instrumental limitations, or from statistics alone when systems of relatively small size are involved. A law of quasi-invariance is deduced, according to which random critically branched materials will appear to have constant weight average molecular weight M_w, irrespective of their real (higher)M_w, if the molecular weight distribution is always cut at a fixed size-limit. Model polycondensates of decamethylene glycol/benzene 1 : 3 : 5 triacetic acid (DMG/BTA) are further studied near the gel point. The relation η∝M_w for the bulk viscosity η has been confirmed and serves to locate the gel point. The relative conversion α/α_c can be determined to a few parts in ten thousand. Light scattering and intrinsic viscosities have been measured on sol fractions extracted from three post-gel samples containing about 1 to 5 % gel. The statistical inference that the newly-formed gel must be practically ring-free (“tree-like”) is confirmed, since highly branched sol molecules up to size 10⁸ are extractable with high efficiency. The evolution in time of Young's modulus E(300–2000 dyn cm^–2) of jellies prepared by isothermal gelation of aqueous gelatin has been followed in a micro-sphere rheometer. A classical gelation process by random cross-linking is postulated, each cross-link consisting of a rapidly formed helical section comprising n primary chains, locally twisted together. With a “front-factor”g around ½, the classical rubber elasticity equation E= 3gN_eRT/V is reasonably fitted to the measurements without adjustment of parameters, for n= 3 but not n= 2.