  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.
