Mathematical model for characterization of temperature-responsive polymers: A study on the rheological behavior of gelatin and poly(N-isopropylacrylamide)

This study introduces a mathematical model for detailed characterization of temperature-responsive polymers, focusing on critical temperature, viscosity, storage modulus, their rate of change in the transition region, flow behavior, and potential hysteresis. Applied to gelatin (GEL) and poly(N-isopropylacrylamide) (pNIPAm), the model analyzes their rheological responses across various temperatures. It was observed that gel's critical temperature is slightly above its polymer's lower critical solution temperature, and vice versa for upper critical solution temperature polymers. The critical temperature for GEL was 28 °C, as opposed to 37 °C for pNIPAm. While concentration changes affected these values, the contribution of tetramethylethylenediamine (typically used in combination with various initiators to start the polymerization reaction) was found to be insignificant. GEL exhibited significant hysteresis, unlike pNIPAm's rapid transition. Their storage modulus and viscosity showed a linear correlation with concentration, with deviations at high pNIPAm concentrations suggesting the influence of polymer interactions and crosslinking. These findings offer valuable insights for applications requiring temperature sensitivity.