Estimation of flocculation structure in filled polymer composites by dynamic rheological measurements

The frequency and concentration dependences of the storage modulus (G′) for carbon black and short-carbon-fiber-filled polymer composites were investigated by means of dynamic rheological measurements. It was found that G′ at low frequencies and amplitudes could be used as a sensitive experimental parameter for detecting the flocculation structure of the ultra-fine-particle-filled polymer composites. Correlation of electrical resistivity of the composites to the relative storage modulus, G′r(=G′c/ G′p), revealed that the three-dimensional interparticle networks start to construct through the matrix when G′r increases to 7 regardless of the composite systems. Quantitative calculations in order to determine the flocculation structure were carried out by means of the modified Kerner equation. A plot of the calculated value, defined as the floc index A, dependence of electrical resistivity for various systems was found to be a universal curve. Accordingly, we suggest that A might universally correspond to the flocculation structure of the filler, which is independent of the nature of the filler, the molecular weight, the chemical composition of the polymer and the temperature at which the measurement is made. This method is particularly effective for estimating the flocculation structure of ultra-fine-particle-filled polymer composites no matter whether the filler is conductive or not.