MOLECULAR THEORY OF THE YIELD BEHAVIOR OF A POLYMER GEL - APPLICATIONTO GELATIN

A microscopic model for the endopoint separation dependent scission ra te of a polymer connection in a network is developed. The predicted di ssociation rate is proportional to the exponential of the bond force, which is in line with experiments. This atomistic description is there upon incorporated in a mesoscopic theory to describe strain hardening and failure of physical gels. The resulting theory has been analyzed b y a new numerical algorithm, which is some 100 to 1000 times faster th an the algorithm described in the literature. We applied this theory t o gelatin. To arrive at the correct nonlinear rheologic behavior of th e gel, the non-Gaussian nature of the polymer endpoint distribution ha s to be taken into account. There are four important physical quantiti es that, describe the nonlinear rheology of gelatin. For relatively sm all shear strain (0<gamma<1), stress increases nonlinearly with strain when a gel is deformed (strain hardening). The strain at which the ge l ruptures (the yield strain gamma(y)) increases quite slowly with she ar rate: gamma(y) proportional to gamma.(0.05). When experiemnts are c arried out at different hear rate, we find a linear correlation betwee n yield stress and yield strain. Finally it is observed that the yield strain decreases with increasing strain hardening. These four observa tions are all covered by the theory up to quantitative accuracy. The i nterpretation that comes forward from this work is that the nonlineari ty of the stress-strain curve for gamma<1 is correlated to the strain at which the gel yields. The reason for this correlation is that both effects are dominated by a non-Hookean force-distance relationship of the polymer connections. On the one hand side, this function directly causes the upturn of the stress-strain curve. On the other hand, thr r ate by which polymer connections break is proportional to the exponent ial of this force. Therefore a nonlinear force-distance relationship l eads both to a nonlinear stress-strain relation and to an early and su dden yield behavior. (C) 1996 American Institute of Physics.