  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.
