The research is concerned with· exploration of the utility of fractal methods for
characterising the mixing treatment applied to a rubber compound and also for
characterising the microstructure developed during mixing (filler dispersion). Fractal
analysis is also used for characterisation of the fracture surfaces generated during
tensile testing of vulcanised samples. For these purposes, Maximum Entropy Method
and Box Counting Method are developed and they are applied to analyse the mixing
treatment and the filler dispersion, respectively. These methods are effectively used and
it is found that fractal dimensions of mixer-power-traces and fracture surfaces of
vulcanised rubber decrease with the evolution of mixing time while the fractal
dimension of the state-of-mix (filler dispersion) also decreases.
The relationship of the fractal dimensions thus determined with conventional
properties, such as viscosity, tensile strength and heat transfer coefficient are then
explored For example, a series of thennal measurements are carried out during
vulcanisation process and the data are analysed for determining the heat transfer
coefficient Nuclear Magnetic Resonance is used to obtain the properties of bound
rubber and a quantitative analysis is also carried out and possible mechanisms for the
relationships between the parameters are discussed based on existing interpretations.
Fmally, the utility of the fractal methods for establishing mixing-microstructureproperty
relationships is compared with more conventional and well established
methods. For this purpose, the fractal dimension of the state-of-mix is compared to
conventional methods such as the Payne Effect, electrical conductivity and carbon
black dispersion (ASTM D2663 Method C). It is found that the characterisation by
the fractal concept agrees with the conclusions from these conventional methods. In
addition, it becomes possible to interpret the relationships between these conventional
methods with the help of the fractal concept.
A Doctoral Thesis. Submitted in partial fulfilment of the requirements for the award of Doctor of Philosophy at Loughborough University.