A fractal approach to mixing-microstructure-property relationship for rubber compounds

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.