Stress-dependent electrical transport and its universal scaling in granular materials

We experimentally and numerically examine stress-dependent electrical transport in granular materials to elucidate the origins of their universal dielectric response. The ac responses of granular systems under varied compressive loadings consistently exhibit a transition from a resistive plateau at low frequencies to a state of nearly constant loss at high frequencies. By using characteristic frequencies corresponding to the onset of conductance dispersion and measured direct-current resistance as scaling parameters to normalize the measured impedance, results of the spectra under different stress states collapse onto a single master curve, revealing well-defined stress-independent universality. In order to model this electrical transport, a contact network is constructed on the basis of prescribed packing structures, which is then used to establish a resistor-capacitor network by considering interactions between individual particles. In this model the frequency-dependent network response meaningfully reproduces the experimentally observed master curve exhibited by granular materials under various normal stress levels indicating this universal scaling behaviour is found to be governed by i) interfacial properties between grains and ii) the network configuration. The findings suggest the necessity of considering contact morphologies and packing structures in modelling electrical responses using network-based approaches.Comment: 12 pages, 4 figure

Interfacial electro-mechanical behaviour at rough surfaces

International audienceIn a range of energy systems, interfacial characteristics at the finest length scales strongly impact overall system performance, including cycle life, electrical power loss, and storage capacity. In this letter, we experimentally investigate the influence of surface topology on interfacial electro-mechanical properties, including contact stiffness and electrical conductance at rough surfaces under varying compressive stresses. We consider different rough surfaces modified through polishing and/or sand blasting. The measured normal contact stiffness, obtained through nanoindentation employing a partial unloading method, is shown to exhibit power law scaling with normal pressure, with the exponent of this relationship closely correlated to the fractal dimension of the surfaces. The electrical contact resistance at interfaces, measured using a controlled current method, revealed that the measured resistance is affected by testing current, mechanical loading, and surface topology. At a constant applied current, the electrical resistance as a function of applied normal stress is found to follow a power law within a certain range, the exponent of which is closely linked to surface topology. The correlation between stress-dependent electrical contact and normal contact stiffness is discussed based on simple scaling arguments. This study provides a first-order investigation connecting interfacial mechanical and electrical behaviour, applicable to studies of multiple components in energy systems

Stress-dependent electrical conduction in granular materials

This dissertation is focused on electrical conduction behaviour in granular systems with the purpose of acquiring a fundamental understanding towards applications of granular materials. Performance in a range of engineering systems can be largely influenced by complex multi-physics interactions arising from microstructures of granular materials. The bulk of this dissertation is built on six published or submitted papers. After project background and related previous work introduced in Chapters 1 and 2, respectively, Chapters 3 and 4 deal primarily with the contact properties between rough surfaces. The obtained information at the interfacial scale serves as an experimental and numerical basis for modelling inter-particle contacts in granular media. Chapter 5 with the fifth paper presents the effects of network configuration on macroscopic network responses focussing on the dielectric universal scaling behaviour. In Chapter 6, the final paper shows a physical picture illustrating experimentally observed alternating-current universal scaling in conductive granular systems under different stress states. An effective numerical approach incorporating inter-particle interaction has been provided to simulate electrical responses of granular materials. The combination of the studies from macro-scale phenomena, network topologies, and inter-particle properties is presented leading to new physics-based constitutive models that contain lower scale information. This dissertation presents a new comprehensive understanding of conduction behaviour in granular materials by means of a physics-based framework combining features containing both experimental and numerical information obtained across various length scales, guiding design and optimisation of various granular materials

Universality of the emergent scaling in finite random binary percolation networks.

In this paper we apply lattice models of finite binary percolation networks to examine the effects of network configuration on macroscopic network responses. We consider both square and rectangular lattice structures in which bonds between nodes are randomly assigned to be either resistors or capacitors. Results show that for given network geometries, the overall normalised frequency-dependent electrical conductivities for different capacitor proportions are found to converge at a characteristic frequency. Networks with sufficiently large size tend to share the same convergence point uninfluenced by the boundary and electrode conditions, can be then regarded as homogeneous media. For these networks, the span of the emergent scaling region is found to be primarily determined by the smaller network dimension (width or length). This study identifies the applicability of power-law scaling in random two phase systems of different topological configurations. This understanding has implications in the design and testing of disordered systems in diverse applications

Electrical transport in granular metals

In this paper, we studied the frequency-dependent AC conductance of randomly packed stainless steel spheres by means of impedance spectroscopy. Two types of power-law behaviour have been observed: (a) at low frequencies, the dependence of the measured impedance on the applied load; (b) at high frequencies, the dependence of the impedance modulus on frequency. Under different loading conditions, the imaginary parts of the measured conductances exhibit respective peaks at critical frequencies, corresponding to the onset of conductance dispersion. Using these critical points as scaling parameters to normalize the measured conductance, results in the spectra from different loading levels collapsing onto a single master curve. Both the electron tunnelling and capacitive paths among particles contribute to the conduction in granular metallic media, resulting in well-characterized universal behaviour

Electrical transport in granular metals

In this paper, we studied the frequency-dependent AC conductance of randomly packed stainless steel spheres by means of impedance spectroscopy. Two types of power-law behaviour have been observed: (a) at low frequencies, the dependence of the measured impedance on the applied load; (b) at high frequencies, the dependence of the impedance modulus on frequency. Under different loading conditions, the imaginary parts of the measured conductances exhibit respective peaks at critical frequencies, corresponding to the onset of conductance dispersion. Using these critical points as scaling parameters to normalize the measured conductance, results in the spectra from different loading levels collapsing onto a single master curve. Both the electron tunnelling and capacitive paths among particles contribute to the conduction in granular metallic media, resulting in well-characterized universal behaviour

Mapping of the standard deviation of normalised characteristic admittance values.

<p>For varying capacitor proportions from 0.1 to 1.0, different-sized square networks (from 5 × 5 to 600 × 600) were considered. For a given network size and capacitor proportion, ten RC networks were generated and used in the simulations to obtain the averaged normalised characteristic admittance, represented by the black dot. The STD of these points are used for mapping with the colour indicating the STD values, as detailed in the legend.</p