CURRENT RESEARCH HIGHLIGHTS

Research in Theme C has been primarily concerned with explaining the bulk properties of complex composite materials.  Composites are increasingly important in manufacturing new materials to meet the needs of advanced technologies.  In BICS we use a blend of numerical modelling and analysis to understand the experimental results. Network models are used to simulate the materials (Fig. 1).  From these we understand that the bulk conductivities of these and related physical systems have emergent properties which are a feature of large binary networks and independent of the exact details of the system (Fig. 2).  To treat the problem analytically we investigate the poles and zeroes of the conductance (Fig. 3); looking at their statistical properties (Fig. 4).  From this we can derive formulae for the behaviour of a "typical" sample (Fig. 5).  These are found to fit exceptionally well with the simulations and give great insight into the origin of the emergent response found in many real materials.



Figure 1: A 2D resistor-capacitor representation of a composite material with microstructural features.

Figure 2: The electrical response of many realisations of a 50:50 mix of components assigned randomly.  The upper and lower limits are determined by the existence or absence of percolation paths of either component.  The central emergent power-law region is due to contributions from all components and clusters.

Figure 3: The electrical response (admittance |Y|) of a simple network of components, showing poles and zeroes in the conductivity in complex frequency space.  These collectively determine the response to real frequencies.

 

Figure 4: The distribution of poles for many random realisations.  These are found to have strong statistical regularity and can be used to understand the averaged bulk response of the systems.

 

Figure 5: Curves from analytical formulae are overlayed on network simulations, showing the excellent agreement between numerics and analysis.  The only scaling used are the conductivities of the individual components and the network size, with no other fitting parameters.