On the origin of transport non-universality and piezoresistivity in segregated conductor-insulator composites and application to thick-film resistors

In this thesis we address the description of electrical transport properties of disordered conductor-insulator composites, mostly by numerical Monte Carlo simulations and analytical study of realistic tunnelling-percolation models. Such composites are basically constituted by conducting particles dispersed in an insulating matrix and present a conductor-insulator phase transition, with critical exponent t, as the volume concentration of the conducting phase x is decreased towards a critical concentration xc. Percolation theory shows that close to this phase transition the conductivity Σ of the composite follows a simple power-law Σ = Σ0(x - xc)t        (1) with a universal transport exponent t = t0 ≃ 2, independent of the detailed characteristics of the system. Two representative examples of such composite materials are conducting polymers, used for example for anti-static purposes, electromagnetic interference shielding or current-limiting switches and thick-film resistors (TFRs) used as resistors in electronic applications where high thermal, chemical, mechanical and aging stability are needed and as sensing elements for force and pressure sensors. This work focuses mostly on TFRs, composed of a glassy phase embedding small conducting grains, which are, from our point of view, ideal model systems. They present a complex microstructure, due to segregation of the conducting phase in the spaces left over in between the large glassy regions, unusually large piezoresitive responses and are an important class among the composite materials presenting universality-breakdown of the critical transport exponent, showing values of t > t0, and as large as 10. Experimentally, non-universal transport exponents have been repeatedly observed, but we lack a theory accounting satisfactorily for this phenomenon. A better understanding of this transport non-universality is the main issue addressed in this thesis. We formulate a lattice and a continuum model, aimed at describing the transport properties of disordered conductor-insulator composites, presenting or not a segregated microstructure. Our main assumptions are that the transport properties, close to the phase transition, are governed by the formation of a percolating cluster of conducting particles and that the electrical transport between the conducting particles is mainly governed by simple tunnelling. We also introduce segregation in the continuum model, which is the main interaction between the conducting and insulating phases considered in this work. In this framework, we present a complete study of segregation and its influence on the critical concentration xc. We show how the relative size of the conducting and insulating particles changes the effectiveness of segregation. Moreover we show that the critical concentration xc is not a monotonically decreasing function of segregation, but presents a minimum, well before maximal segregation is reached, which is a result of broad technological interest. Now, the main outcome of this work is a new interpretation of the experimentally observed non-universality of the direct current transport exponent. We show that realistic tunnelling-percolation models, although not presenting true non-universality of transport, lead to a transport exponent t strongly depending on the concentration of the conducting phase x, so that the conductivity does, indeed, not follow a simple power-law. As t is experimentally extracted by fitting the concentration dependence of the conductivity with the simple power law of equation 1, apparent non-universal transport exponents will be obtained. This is what we call apparent non-universality, which might be experimentally very difficult to distinguish from true non-universality. We propose an analytical formula, containing only few parameters of our model, replacing the power-law of equation (1), which fits very nicely some experimental measurements of the conductivity of conductor-insulator composites. Our models also account for the large increase of the piezoresistivity experimentally observed in conductor-insulator composites close to the percolation threshold. But contrary to classical tunnelling-percolation predictions, we show that more realistic models lead to a saturation of the piezoresistivity close enough to the percolation threshold. This feature has not been observed yet, but would be a direct confirmation of the scenario proposed in this work for the appearance of transport non-universality

Piezoresistive properties of low-firing temperature thick-films on steel sensors

Thick-film materials are very advantageous for piezoresistive pressure and force sensors because of ease of processing, reliability and low cost. The standard substrate material used with thick-film technology for sensing is alumina, but its elastic modulus is high and its strength rather low. Steels offer better mechanical properties and permit assembly without an elastomer seal, which is required for pressure sensing in severe conditions. In order to use the steel as substrate, the standard firing temperature of thick-films has been decreased. In previous studies, we have developed and characterized 2 low-firing thick-film systems (dielectrics, resistors and conductors) compatible with austenitic and ferritic materials. We have formulated these systems to achieve to chemical and thermal expansion compatibility. Other parameters like adherence, soldering properties and process, have been optimized too in order to be adapted on high-performance sensors. In this work, we will present the characterization of 2 steel sensors based on low fired thick-film technology: a high-performance pressure sensor based on high-strength steel substrate chemically similar to the ferritic steel, and a force sensor used in surgical operation of total knee arthroplasty (TKA) based on a medical alloy comparable to the austenitic steel. Key words: thick film system, high strength steel, pressure sensors, low-temperature firing

Optimisation of a Thick-Film 10...400 N Force Sensor

Abstract: The ring-on-ring bending principle allows the fabrication of simple, low-cost thick-film piezoresistive sensors for compressive forces in the 10 to 400 N range. However some imperfections are encountered in its basic embodiment, such as relatively high force-signal hysteresis and nonrepeatability (up to ca. 5%). These shortcoming were studied in this work, and major improvements achieved. Hysteresis was found to be mainly due to friction at the outer support ring, and considerably reduced by inserting a compliant silicone glue ring. The same glue ring was used to permanently bond the sensor to a rigid base, thereby giving well-defined and constant boundary conditions and also considerably improving the repeatability of the sensitivity. Overall, hysteresis and repeatability error were reduced down to a level of ca. 1%

LTCC ultra high isostatic pressure sensors

Piezoresistive pressure sensors using classical deformable structures such as membranes progressively run into difficulties at very high pressures (above 1 to 2 kbar), due to the decreasing ratio between the available sensing strain on the outer membrane surface and the maximal materials strain experienced on the pressurised side. Therefore, a novel "isostatic" pressure sensor concept, whereby the sensing element is immersed in the pressure fluid, has been developed. This method in principle allows the measurement of very high pressures, because materials stresses within the sensing beam are all compressive. LTCC (Low-Temperature Cofired Ceramic) beams with hermetically embedded thick-film piezoresistor bridges have been fabricated, packaged and characterised as sensor elements. The observed sensitivity is comparable to the response expected from the LTCC and piezoresistor materials properties. Key words: piezoresistivity, thick-film, LTCC, high pressure sensor

Optimisation of a Thick-Film 10...400 N Force Sensor

Abstract: The ring-on-ring bending principle allows the fabrication of simple, low-cost thick-film piezoresistive sensors for compressive forces in the 10 to 400 N range. However some imperfections are encountered in its basic embodiment, such as relatively high force-signal hysteresis and nonrepeatability (up to ca. 5%). These shortcoming were studied in this work, and major improvements achieved. Hysteresis was found to be mainly due to friction at the outer support ring, and considerably reduced by inserting a compliant silicone glue ring. The same glue ring was used to permanently bond the sensor to a rigid base, thereby giving well-defined and constant boundary conditions and also considerably improving the repeatability of the sensitivity. Overall, hysteresis and repeatability error were reduced down to a level of ca. 1%

Calcium regulates acid-sensing ion channel 3 activation by competing with protons in the channel pore and at an allosteric binding site

The extracellular Ca2+ concentration changes locally under certain physiological and pathological conditions. Such variations affect the function of ion channels of the nervous system, and consequently also neuronal signalling. We investigated here the mechanisms by which Ca2+ controls the activity of acid-sensing ion channel (ASIC) 3. ASICs are neuronal, H+-gated Na+ channels involved in several physiological and pathological processes, including the expression of fear, learning, pain sensation and neurodegeneration after ischemic stroke. It was previously shown that Ca2+ negatively modulates the ASIC pH dependence. While protons are default activators of ASIC3, this channel can also be activated at pH7.4 by removal of the extracellular Ca2+. Two previous studies concluded that low pH opens ASIC3 by displacing Ca2+ ions that block the channel pore at physiological pH. We show here that an acidic residue, distant from the pore, controls, together with pore residues, the modulation of ASIC3 by Ca2+. Our study identifies a new regulatory site in ASIC3 and demonstrates that ASIC3 activation involves an allosteric mechanism together with Ca2+ unbinding from the channel pore. We provide a molecular analysis of a regulatory mechanism found in many ion channels

Optimal Percolation of Disordered Segregated Composites

We evaluate the percolation threshold values for a realistic model of continuum segregated systems, where random spherical inclusions forbid the percolating objects, modellized by hard-core spherical particles surrounded by penetrable shells, to occupy large regions inside the composite. We find that the percolation threshold is generally a non-monotonous function of segregation, and that an optimal (i. e., minimum) critical concentration exists well before maximum segregation is reached. We interpret this feature as originating from a competition between reduced available volume effects and enhanced concentrations needed to ensure percolation in the highly segregated regime. The relevance with existing segregated materials is discussed.Comment: 5 pages, 4 figure

Percolative properties of hard oblate ellipsoids of revolution with a soft shell

We present an in-depth analysis of the geometrical percolation behavior in the continuum of random assemblies of hard oblate ellipsoids of revolution. Simulations where carried out by considering a broad range of aspect-ratios, from spheres up to aspect-ratio 100 plate-like objects, and with various limiting two particle interaction distances, from 0.05 times the major axis up to 4.0 times the major axis. We confirm the widely reported trend of a consistent lowering of the hard particle critical volume fraction with the increase of the aspect-ratio. Moreover, assimilating the limiting interaction distance to a shell of constant thickness surrounding the ellipsoids, we propose a simple relation based on the total excluded volume of these objects which allows to estimate the critical concentration from a quantity which is quasi-invariant over a large spectrum of limiting interaction distances. Excluded volume and volume quantities are derived explicitly.Comment: 11 pages, 8 figure