Viscoelastic behaviour at the thermal sol-gel transition of gelatin Shan-hui Hsu* and Alexander M. Jamieson%~ Departments of *Biomedical Engineering and %MacromolecularScience, Case Western Reserve University, Cleveland, OH 44106, USA (Received 15 September 1992) Rheological studies of gelatin solutions in the concentration range 4-14% were performed through the sol-gel transition as a function of concentration, pH and ionic strength. At the gel point, a power-law frequency dependence of the viscoelastic functions G'(e~), G"(~o)and r/*(og) was observed. The power-law exponents n obtained from these dynamic measurements were confirmed by creep experiments and are in agreement with a previous study in a lower concentration range, 1-5%. Under all conditions, the n values fall between 0.64 and 0.72, a range consistent with theoretical treatments of Martin et al. and Muthukumar et al. The critical gel strength, S, increases with concentration approximately as Sac C133 in the concentration range 4-14%. Within experimental error, S is approximately consistent with an empirical relation suggested in the recent literature, S--G~-"~/~, where Ge and r/o are, respectively, the equilibrium modulus of the fully developed gel and the shear viscosity of the initial sol. The implications of these observations with respect to the structure of the critical gel are discussed. (Keywords: viscoelasticity; gelatin; sol-gel transition; critical gel) BACKGROUND strength of the hydrodynamic interaction between the polymer chain segments 6'9'1°. Measurements of the oscillatory shear moduli are Previous experimental studies include those by Winter frequently used to monitor continuously the viscoelastic al 2-4,7,8, properties of crosslinking systems from the sol through et . Muller et al. 5 and Martin et al. 6 on gels the transition to the gel state. According to a traditional formed from covalent polymeric networks. In such suggestion 1, the gel point corresponds to the intersection systems, G' and G" exhibit a power-law dependence with an exponent that depends on the gel stoichiometry 2-5'7's. of the storage and loss moduli, G'(~o) and G"(m), i.e. Values ranging between 0.3 and 0.9 have been reported 7. the point at which tan6=G"/G'= 1. More recently, Lin et al. 11 investigated crystallization-induced gelation experiment 2-7 and theory 6's'9 indicate that, at the gel in the thermoplastic elastomer polypropylene and point, G' and G" exhibit a power-law dependence on the observed power-law scaling of G' and G" with an exponent oscillation frequency, and gelation may occur before or n=0.13. In another recent study, Amis et al. 12"13 after the crossover of G' and G" at a specified frequency, investigated changes in dynamic viscoelasticity during Several theoretical analyses have developed expressions the thermo-reversible gelation of gelatin at concentrations for the frequency dependence of G', G" and the complex ranging from 0.90 to 5.10% (w/w) and at five different viscosity, r/*(og), at the gel point 2 9, using the fractal scaling concept to define the gel network structure. The frequencies over a range from 272 to 9450 Hz using the multiple lumped resonator (m.l.r.) technique. They results of these investigations indicate that at the sol-gel found a power-law frequency dependence of G' and transition point: G". At the gel point, G' and G" exhibited power- G'=A~o" (1) law frequency dependence with frequency exponents G" = Bo~" (2) statistically distributed over a range of values from 0.58 and to 0.77 under a variety of experimental conditions (temperatures and pH). The corresponding frequency- tan f = G"/G' =B/A = tan(nn/2) (3) independent values of tan c5 range from 1.3 to 2.5. The values of n and tan6 are numerically similar to where A and B are related to the material strength factor those obtained for chemically crosslinked gels in non- of the gel, S, by2: stoichiometric systems. The authors note 12'~3 that the S = G'og-"F(1- n)- ~ cos(nn/2) (4) viscoelastic behaviour of gelatin at the gel point can be described by the percolation model of Martin et al. 6, S=(A2+B2)i/2F(n)sin(nn/2) (5) 2/3~<n~<1 in the Rouse limit. The exponent n is determined by the fractal dimension An interesting feature of systems that gel via a of the network, the stoichiometry of the gel 5'7 and the percolation mechanism is that they have tan 6 = 1.732 at the gel point. Thus, they are not physically gel-like and :~To whom correspondence should be addressed exhibit macroscopic flow at and for a considerable 0032 3861/93/1226024)7 © 1993 Butterworth-Heinemann Ltd. 2602 POLYMER, 1993, Volume 34, Number 12