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The rheological properties of viscoelastic materials like polymer melts aregreatly affected by factors like salinity, temperature, concentration and pH ofthe solution. In this study, the memory of the stress affected by each of thesefactors is shown to be trapped in the order of the fractional derivative of thedynamical equation describing stress and strain in the material. To demonstratethis, the rheological properties of the polymer melt hydrolyzed polyacrylamideHPAM have been modeled using a two element Maxwell model. The model hassuccessfully reproduce existing experimental data on elastic modulus andcomplex viscosity for these stress factors, besides predicting the developmentof creep compliance with shear rate. The work also establishes that it ispossible to tailor a particular rheological property by suitably tuning a pairof properties, complementary conjugates, that offset each others effects on therheology. The study shows that HPAM has at least two pairs of complementaryconjugates in temperature and pH, and concentration and pH. Further it is shownthat the variation of viscosity with shear rate shows a power law behavior foralmost all variations in stress parameters. Our modelling using fractionalcalculus establishes that the fractional order derivative q which is recognizedas a memory index to emergent phenomena, shows an inverse relationship withrespect to the power law exponent a, the higher the memory index q, the smalleris the power-law exponent a.

Memory of rheological stress in polymers using Fractional Calculus