Volume fraction determination of microgel composed of interpenetrating polymer networks of PNIPAM and Polyacrylic acid

Interpenetrated polymer network microgels, composed of crosslinked networks of poly(N-isopropylacrylamide) and Polyacrylic acid (PAAc), have been investigated through rheological measurements at four different amounts of Polyacrylic acid. Both PAAc content and crosslinking degree modify particle dimensions, mass and softness, thereby strongly affecting the volume fraction and the system viscosity. Here the volume fraction is derived from the flow curves at low concentrations by fitting the zero-shear viscosity with the Einstein-Batchelor equation which provides a parameter $k$ to shift weight concentration to volume fraction. We find that particles with higher PAAc content and crosslinker, are characterized by a greater value of k and therefore by larger volume fractions when compared to softer particles. The packing fractions obtained from rheological measurements are compared with those from static light scattering for two PAAc contents revealing a good agreement. Moreover, the behaviour of the viscosity as a function of packing fraction, at room temperature, has highlighted an Arrhenius dependence for microgels synthesized with low PAAc content and a Vogel-Fulcher-Tammann dependence for the highest investigated PAAc concentration. A comparison with the hard spheres behaviour indicates a steepest increase of the viscosity with decreasing particles softness. Finally, the volume fraction dependence of the viscosity at a fixed PAAc and at two different temperatures, below and above the volume phase transition, shows a quantitative agreement with the structural relaxation time measured through dynamic light scattering indicating that IPN microgels softness can be tuned with PAAc and temperature and that, depending on particle softness, two different routes are followed.