Paper detail

Memory of rheological stress in polymers using Fractional Calculus

The rheological properties of viscoelastic materials like polymer melts are greatly affected by factors like salinity, temperature, concentration and pH of the solution. In this study, the memory of the stress affected by each of these factors is shown to be trapped in the order of the fractional derivative of the dynamical equation describing stress and strain in the material. To demonstrate this, the rheological properties of the polymer melt hydrolyzed polyacrylamide HPAM have been modeled using a two element Maxwell model. The model has successfully reproduce existing experimental data on elastic modulus and complex viscosity for these stress factors, besides predicting the development of creep compliance with shear rate. The work also establishes that it is possible to tailor a particular rheological property by suitably tuning a pair of properties, complementary conjugates, that offset each others effects on the rheology. The study shows that HPAM has at least two pairs of complementary conjugates in temperature and pH, and concentration and pH. Further it is shown that the variation of viscosity with shear rate shows a power law behavior for almost all variations in stress parameters. Our modelling using fractional calculus establishes that the fractional order derivative q which is recognized as a memory index to emergent phenomena, shows an inverse relationship with respect to the power law exponent a, the higher the memory index q, the smaller is the power-law exponent a.