Using optical rotation to study the triple helix reversion of gelatin in aqueous solutions demonstrates that the reversion is a combination of first-order and second-order kinetic processes. On the basis of this observation, we propose a new two-step mechanism of triple helix formation in polypeptides, that leads to an expression distinct from the one obtained by Flory and Weaver. The ratelimiting step is formation of a two-stranded nucleus, which can be intramolecular (first order) or intermolecular (second order). The triple helix is formed by subsequent wrapping of a third strand onto this nucleus. We estimate the minimum stable helix length and the size of the loop at the end of an intramolecular helix from our kinetics analysis. The new two-step mechanism of triple helix formation is consistent with all existing literature data and allows prediction of concentration and temperature dependencies of helix formation rate.
A rheo-optical device outfitted with a Peltier temperature control for rapid temperature changes has been constructed that allows simultaneous measurement of the optical rotation of light and the controlled-stress rheology. Optical rotation provides a direct in situ assessment of the extent of triple helix reversion in a gelatin solution undergoing physical gelation in the rheometer. Thermal gelation of gelatin was monitored over a wide range of concentrations and temperatures. Assuming dynamic scaling theory applies, viscosity data below the gel point were used to evaluate the gel point and determine the value of the viscosity exponent. Above the gel point, creep-recovery experiments are used to measure the shear modulus and determine the dynamic scaling elastic modulus exponent. During thermal gelation, the time-dependent optical rotation shows an initial rapid growth region where new helices are formed, followed by a slower growth region involving helix lengthening. For cases where the gel point occurs before the helix reversion slows appreciably, the viscosity and modulus exponents are found to depend on gelatin concentration, but not on temperature. However, anomalous exponents are measured using the same methods at higher temperatures, where the helix reversion slows appreciably before the gel point is reached. These results suggest that extreme caution must be used in evaluating dynamic exponents from any physical gelation process. The observed concentration dependences of the dynamic scaling exponents are discussed in terms of chain overlap and entanglement. For gelatin gelation, the plethora of different, reported percolation exponents in the literature are rationalized.
We report viscosity, recoverable compliance, and molar mass distribution for a series of randomly branched polyester samples with long linear chain sections between branch points. Molecular structure characterization determines tau=2.47+/-0.05 for the exponent controlling the molar mass distribution, so this system belongs to the vulcanization (mean-field) universality class. Consequently, branched polymers of similar size strongly overlap and form interchain entanglements. The viscosity diverges at the gel point with an exponent s=6.1+/-0.3, that is significantly larger than the value of 1.33 predicted by the branched polymer Rouse model (bead-spring model without entanglements). The recoverable compliance diverges at the percolation threshold with an exponent t=3.2+/-0.2. This effect is consistent with the idea that each branched polymer of size equal to the correlation length stores k(B)T of elastic energy. Near the gel point, the complex shear modulus is a power law in frequency with an exponent u=0.33+/-0.05. The measured rheological exponents confirm that the dynamic scaling law u=t/(s+t) holds for the vulcanization class. Since s is larger and u is smaller than the Rouse values observed in systems that belong to the critical percolation universality class, we conclude that entanglements profoundly increase the longest relaxation time. Examination of the literature data reveals clear trends for the exponents s and u as functions of the chain length between branch points. These dependencies, qualitatively explained by hierarchical relaxation models, imply that the dynamic scaling observed in systems that belong to the vulcanization class is nonuniversal.
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