Thermoreversible Gelation Driven by Coil-to-Helix Transition of Polymers

This paper theoretically studies thermoreversible gelation driven by aggregation of helices formed on the polymer chains. Two fundamentally different cases of (i) multiple association of single helices, and (ii) association by multiple helices with multiplicity k (such as double helices ( k = 2), triple helices ( k = 3), etc.) are treated on the basis of different equations. The helix length distribution on a polymer chain (or assemble of chains for multiple helices) is derived as a function of polymer concentration and temperature. It obeys a power law of the parameter t = 1 − ν/(1 − θ), where θ is the helix content per chain and ν is the average number of helices on a chain divided by the total number n of the repeat units. The sol/gel transition point is found on the temperature−concentration plane. It is found that, in the case of k -ple helices, the condition n θ/ζ = k /( k − 1) is fulfilled at the gel point, where ζ is the average helix length. Hence, the independent measurement of θ and ζ gives the multiplicity k . Theoretical calculation of the total helix content in the solution is compared with experimental data of optical rotation in ι-carrageenan solutions at different polymer concentrations. It is shown that at low temperature there is a sharp transition from network to bundle state (pair, triplet, etc.). This network-to-bundle transition becomes a real phase transition in the limit of infinite chain length.