This equation is valid for composite systems having
only spherical rigid particles in very low concentrations.
In actual situations, morphology of the dispersed
phase may deviate from the ideal case.
Therefore, the theoretical value of kE may be inappropriate
in such cases. In this study, the value of kE
is determined from experimental data based on the
Einstein equation from the slope of Eb=Er versus /p.
As Einstein’s equation is valid for a very low concentration,
kE is extracted from a set of blends with
low concentrations of PH, namely up to 3 vol %. kE
values obtained in this way are 6.16 and 8.4 for
SBR/PH with 2 and 7 phr sulfur, respectively, and
6.24 and 8.36 for NBR/PH with 2 and 7 phr sulfur,
respectively. In all cases, regression coefficient is so
close to one, namely greater than 0.99, indicating the
linearity of the curve in this range of PH concentration.
It is observed that the empirical values of kE
are higher than that of the theoretical one. This probably
could be due to agglomeration of the resin particles
within the rubber matrix. It has also been
reported that the agglomeration of particles as well
as state of agglomeration increase the suspension
viscosity and Einstein’s coefficient in comparison
with the completely dispersed systems.33 For a suspension
viscosity including agglomeration of particle
with random packing, a value of 6.76 has been
reported for kE.35 It is also found that the values of
kE are the same for both SBR and NBR compounds
at the same sulfur content; however, it increases by
increasing the sulfur content from around 6.3 to 8.3.
It seems that the sulfur content increases the affinity
of the particles to form more agglomeration, which
could be a consequence of decreasing the surface
energy of the rubber phase. Such an observation has
been addressed in the literature for blend of ethylene–
propylene–diene rubber/propylene that a reduction
in surface energy has been observed at high
extent of crosslinking density.36 This has been attributed
to the reduction of the flexibility of both
induced and permanent dipoles attached to the rubber
segments within the vulcanized network