Resistor Network Approach Research Articles

The Resistor Network Approach to Modeling Screen-Printed Silver Ink Under Uniaxial Stretch

Abstract Flexible electronic devices are used in a wide variety of applications that utilize their unique ability to stretch, bend, and twist. Experimental methods were developed for evaluating the piezoresistive behavior of printed conductive inks under uniaxial strain. DuPont 5025 screen-printed silver ink on Kapton and Melinex substrates was stretched until substrate failure. Kapton samples were found to rupture at around 60% strain and have a relative resistance, R/R0, of about 30–40 at substrate rupture. On Melinex substrates, the ink was found to electrically fail before the substrate ruptured but could be stretched to strains exceeding 130% or higher before failing. The relative resistance values for these high strains in the Melinex samples were erratic and could exceed 1000 and in one case more than 30,000. The ink strain to failure exhibited a dependence on conductor width with narrower conductors failing before wider ones. Finally, a 2.5D RVE model that accounts for ink filler volume fraction, particle size distribution, contact resistance, and electron tunneling was developed that accurately predicts the piezoresistive behavior of 5025 ink up to 60% axial strain. An initial parametric study found that increasing the volume fraction of the RVE results in improved electrical performance.

Active regulation schemes to enhance the performance of thin film boiling using nanoporous membranes

With the help of the micro/nano-porous membranes, synergistic flows of supply water and departing vapor can be realized, which considerably enhances boiling heat transfer. Ultrahigh heat flux of 1230 W/cm2 was reported in the thin film boiling experiments, of which the sample was fabricated by depositing nanosized platinum (Pt) layer on the surface of a nanoporous membrane. As an indispensable component, the nanoporous membrane plays an essential role by functioning as both the distributor of liquid fluid and the substrate of heating surface. However, there is still a lack of comprehensive understanding of the impacts of the nanoporous membrane. In this work, the resistor network approach developed in our former study was extended to analyze the influence of the nanoporous membrane on the performance of the unique thin film boiling. What's more, two active regulation schemes were proposed for nanoporous membrane to achieve better manipulation and enhanced performance. It was found that for a nonuniform nanoporous membrane, the critical heat flux was lower than that of a uniform membrane, and any further increase of electric power after reaching CHF would result in river-shaped crack of melted Pt resistors. For the nonuniform AAO membrane, the both active regulation schemes would effectively cope with the voltage fluctuation that could have led to the melt of the Pt layer. Therefore, better performance could be achieved by applying the active regulation schemes. Hopefully, the explorative studies on the active regulation schemes could provide operation guidance for future application of the thin film boiling.

Modeling the Influence of Particle Shape on Mechanical Compression and Effective Transport Properties in Granular Lithium‐Ion Battery Electrodes

The calendering step during manufacturing of lithium‐ion batteries is an essential process in the production, as it significantly influences the microstructure of electrodes and, therefore, the performance of the battery. Within this context, this article investigates the influence of particle shapes on the micromechanical responses during calendering and, in turn, their impact on the effective transport properties of battery electrodes. The electrodes are modeled using discrete elements. For this reason, a novel algorithm for the generation of random stress‐free particle assemblies consisting of superellipsoids is presented. The effective conductivities of solid and pore phase are calculated with a resistor network approach. In this context, a new analytical formula for calculating the individual resistance between two mechanically deformed ellipsoidal particles is presented. Furthermore, a geometrical approach is chosen for the pore phase for calculating individual resistances of pore throats in superellipsoidal particle assemblies. With the theoretical fundamentals, the effective conductivities of solid and pore phases of uniaxially compressed ellipsoidal particle assemblies are investigated. The mechanical response and its influence on the evolution of the effective conductivities are discussed. The deeper insight into the interplay between the calendering process and electrode microstructure can be a helpful information regarding a specific electrode design.

Modeling and Analysis of Porous Platinum Nanolayer Used in Thin Film Boiling by Resistor Network Approach

Utilizing nanoporous membranes can realize a new thin film boiling regime with ultrahigh heat flux of over 1 kW/cm2. In thin film boiling experiments, a nanoscaled platinum (Pt) layer coating serves as both heater and temperature sensor and therefore plays a fundamentally important role. However, river-shaped micro cracks were discovered in the Pt layer after experiments, of which the origin and the influence are still unclear. In this paper, based on the microscopic observation, the porous Pt layer was abstracted as a resistor network. A comprehensive model was set up to quantitatively analyze the Pt layer by obtaining the resistance and temperature of all the resistors in the network. With this model, the formation of the river-shaped cracks was successfully simulated and the influence of the thickness uniformity of Pt layer was analyzed in detail. It was found that the river-shaped cracks were formed by the successive melting of resistors, which started from the thinner or thicker resistor and its adjacent resistors that achieved critical heat flux (CHF) earlier than the rest resistors, and then spread to the other part of the Pt layer in a way similar to a chain reaction. For ideal Pt layer with uniform thickness, it could eliminate the river-shaped cracks, achieve higher CHF and endure a wider voltage variation. The in-depth modeling on Pt layer may not only help the fundamental study of the thin film phase change heat transfer, but also contribute to the research of other nanoscaled conductive layers.

Self-assembly of carbon nanotubes in polymer melts: simulation of structural and electrical behaviour by hybrid particle-field molecular dynamics.

Self-assembly processes of carbon nanotubes (CNTs) dispersed in different polymer phases have been investigated using a hybrid particle-field molecular dynamics technique (MD-SCF). This efficient computational method allowed simulations of large-scale systems (up to ∼1 500 000 particles) of flexible rod-like particles in different matrices made of bead spring chains on the millisecond time scale. The equilibrium morphologies obtained for longer CNTs are in good agreement with those proposed by several experimental studies that hypothesized a two level "multiscale" organization of CNT assemblies. In addition, the electrical properties of the assembled structures have been calculated using a resistor network approach. The calculated behaviour of the conductivities for longer CNTs is consistent with the power laws obtained by numerous experiments. In particular, according to the interpretation established by the systematic studies of Bauhofer and Kovacs, systems close to "statistical percolation" show exponents t ∼ 2 for the power law dependence of the electrical conductivity on the CNT fraction, and systems in which the CNTs reach equilibrium aggregation show exponents t close to 1.7 ("kinetic percolation"). The confinement effects on the assembled structures and their corresponding conductivity behaviour in a non-homogeneous matrix, such as the phase separating block copolymer melt, have also been simulated using different starting configurations. The simulations reported herein contribute to a microscopic interpretation of the literature results, and the proposed modelling procedure may contribute meaningfully to the rational design of strategies aimed at optimizing nanomaterials for improved electrical properties.

A micromechanical model for effective conductivity in granular electrode structures

Optimization of composition and microstructure is important to enhance performance of solid oxide fuel cells (SOFC) and lithium-ion batteries (LIB). For this, the porous electrode structures of both SOFC and LIB are modeled as a binary mixture of electronic and ionic conducting particles to estimate effective transport properties. Particle packings of 10 000 spherical, binary sized and randomly positioned particles are created numerically and densified considering the different manufacturing processes in SOFC and LIB: the sintering of SOFC electrodes is approximated geometrically, whereas the calendering process and volume change due to intercalation in LIB are modeled physically by a discrete element approach. A combination of a tracking algorithm and a resistor network approach is developed to predict the connectivity and effective conductivity for the various densified structures. For SOFC, a systematic study of the influence of morphology on connectivity and conductivity is performed on a large number of assemblies with different compositions and particle size ratios between 1 and 10. In comparison to percolation theory, an enlarged percolation area is found, especially for large size ratios. It is shown that in contrast to former studies the percolation threshold correlates to varying coordination numbers. The effective conductivity shows not only an increase with volume fraction as expected but also with size ratio. For LIB, a general increase of conductivity during the intercalation process was observed in correlation with increasing contact forces. The positive influence of calendering on the percolation threshold and the effective conductivity of carbon black is shown. The anisotropy caused by the calendering process does not influence the carbon black phase.

Two-component Coulomb glass in insulators with a local attraction

Motivated by evidence of local electron-electron attraction in experiments on disordered insulating films, we propose a new two-component Coulomb glass model that combines strong disorder and long-range Coulomb repulsion with the additional possibility of local pockets of a short-range inter-electron attraction. This model hosts a variety of interesting phenomena, in particular a crucial modification of the Coulomb gap previously believed to be universal. Tuning the short-range interaction to be repulsive, we find non-monotonic humps in the density of states within the Coulomb gap. We further study variable-range hopping transport in such systems by extending the standard resistor network approach to include the motion of both single electrons and local pairs. In certain parameter regimes the competition between these two types of carriers results in a distinct peak in resistance as a function of the local attraction strength, which can be tuned by a magnetic field.

Random resistivity network calculations for cuprate superconductors with an electronic phase separation transition

The resistivity as a function of temperature for high temperature superconductors is very unusual and, despite its importance, lacks a unified theoretical explanation. It is linear with the temperature for overdoped compounds but it falls more quickly as the doping level decreases. The resistivity of underdoped cuprates increases like that of an insulator below a characteristic temperature where it shows a minimum. We show that this overall behavior can be explained by calculations using an electronic phase segregation into two main component phases with low and high electronic densities. The total resistance is calculated from the various contributions through several processes of random picking of the local resistivities and using a common statistical random resistor network approach.

Mesoscale models of conductivity in polymeric electrolytes—A comparative study

The studies of conductivity behavior of composite polymeric electrolytes (CPE) have been widely realized for about 15 years. There is, however, a lack of a versatile and efficient model of conductivity in these systems. The effective medium approach was introduced to predict the conductivity of systems according to some previously defined mixing rules. The main limitation of this method, however, is the fact that each new composite microstructure forces a new mixing rule development. This paper presents the random resistor network approach as an alternative method to the effective medium theory based approach. The presented comparison of both methods is based on both dc and ac simulated conductivity data. Some experimental data are introduced to compare the models with the conductivity values obtained for real samples.

Random Resistor Network Approach to Modeling of Conductivity in Composite Polymeric Electrolytes.

There is lack of a versatile and efficient model of conductivity for composite polymeric electrolytes. The main limitation of the already applied Effective Medium Theory approach is the fact that each new composite microstructure forces a new mixing rule development. This paper deals with a more elaborate and versatile approach based on the Random Resistor Network method. The introduced model yields simulated conductivity values for composites of any possible microstructure. It is based on current iteration procedure for a randomly generated three dimensional resistor network constituting a digital image of the sample studied. Both the d.c. conductivity value and bulk a.c response of the composite can be calculated. For a.c. studies, the resistors in the network nodes are exchanged for parallel RC or R(CPE) (constant phase element) connections. Additionally, the temperature dependence of the conductivity of the composite can be predicted on basis of the experimentally determined conductivities of the particular phases.

Distribution of return intervals of extreme events

The distribution of return intervals of extreme events is studied in time series characterized by finite-term correlations with non-exponential decay. Precisely, it has been analyzed the statistics of the return intervals of extreme values of the resistance fluctuations displayed by resistors with granular structure in nonequilibrium stationary states. The resistance fluctuations are calculated by Monte Carlo simulations using a resistor network approach. It has been found that for highly disordered networks, when the auto-correlation function displays a non-exponential and non-power-law decay, the distribution of return intervals of the extreme values is a stretched exponential, with exponent independent of the threshold.

Random Resistor Network Approach to Modeling of Conductivity in Composite Polymeric Electrolytes.

not Available.

Conductivity studies of composite polymeric electrolytes—from experiment to computer modeling

The composite polymeric electrolytes (CPE) are well known systems in which improvement in the electrical conductivity of the polymer is achieved by the addition of a nonconductive additive (ceramic powders, immiscible polymers). The filler forms small grains (characterized by the average radius R) randomly distributed in the polymer matrix in a uniform way. The currently widely accepted mechanism of enhanced conductivity was previously discussed in the literature and is based on the assumption of the formation of amorphous highly conductive grain shells of a particular thickness ( t) on the polymer–filler interface due to the inhibition of the polymer crystallization process on the grain surface. The system is complicated and multiphase, thus very difficult for theoretical studies. In this paper a conductivity model based on the application of the Random Resistor Network approach is employed to study CPE. The first stage of the simulation is based on the generation of a virtual composite sample and its transformation into a three-dimensional resistor network. Two different algorithms were developed to find the electrical properties of the resulting network. One is leading to the calculation of the number of percolation paths in the sample and the other is giving directly the conductivity value. The dependency of conductivity on the grain filler concentration was studied for varying grain sizes, changing t / R ratio and for different statistical distributions of the t / R parameter. The obtained results of the simulation are in general agreement with the experimental data.

Random resistor network application to modelling of d.c. ionic conductivity in composite polymeric electrolytes

A new class of conductivity models based on the application of the random resistor network approach is developed to study composite polymeric electrolytes. The simulation is based on virtual composite sample generation and its transformation into the form of a three-dimensional resistor network. Average grain diameter and its statistical distribution, shell thickness and different dependencies of local shell conductivity on the distance from the grain surface can act as variables. The use of the modified iteration procedure based on the Kirkpatrick approach leads to direct current resistivity value. The results were obtained for the matrix size 100 × 100 × 100 units (with assumption 1 unit = 1 μm). The dependency of conductivity on the grain filler concentration was studied for varying grain sizes, changing shell thickness and for different statistical distributions of these parameters. The obtained results of simulation are in general agreement with the experimental data.

Structure and Thermal Conductivity of Silica Aerogels from Computer Simulations

ABSTRACTAerogels are of current interest in the aerospace community due to their light weight and low thermal conductivity, making them suitable for a variety of applications, notably cryotank insulation.These gels typically exhibit a complex structure; the smallest feature is a “primary” particle of amorphous silica, typically 2-5nm in diameter. The primary particles aggregate to form “secondary” particles, typically an order of magnitude larger, and these, in turn, form pearl-necklace structures whose details depend on the density. The gels appear to exhibit fractal dimensionality, at least over a small range of length scales.In this work, we investigate the relationship between the structure of the gels, their dimensionality and density, and their thermal conductivity. We model the secondary-particle aggregate structure using a modified Diffusion Limited Cluster Aggregation (DLCA) model. The model produces qualitatively different structures at low and high densities that are consistent with experimental observation. At lower densities, we find evidence for a transition from fractal behavior at small length scales to approximately compact behavior at larger lengths.We model the thermal conductivity using a variant of the random resistor network approach that has been used to describe, e.g. hopping electrical conduction in doped semiconductors. In our model, each secondary particle is assigned an effective thermal conductance that depends on the particle's size, and on the details of its contacts with neighboring particles; the conductivity of the gel network is obtained using standard numerical techniques. The scaling of the thermal conductivity with density and fractal dimension is discussed.

Formation of a percolating cluster in films prepared by cathodic electrodeposition of a mixture of lower and higher molecular weight epoxy–amine adducts

The electrodeposition behavior of blends of primary dispersions of a lower and a higher molecular weight epoxy–amine adduct has been investigated. The throwing power of the above-mentioned blends showed a voltage-dependent critical composition at which the throwing power dropped to a much lower value. This was assigned to the formation of an infinite conducting cluster, the extension of which is dependent on the rate of the electrocoagulation process at the cathode boundary. The random resistor network approach of Stauffer (RRNS) and the random resistor network approach of Miller and Abrahams (RRNMA) were applied to the experimental data with high correlations ( r 2=0.9314 and 0.9699). The percolating cluster formed within the film, however, gave a critical exponent of conductivity equal to 1.1028, much less than expected from a classical three-dimensional lattice (i.e., 1.5–2.0). This discrepancy was explained in terms of the changed behavior of the film resulting from the bubbles formed near the cathode and its effect on the infinite conducting cluster.

Modelling of ambipolar transport properties of composite mixed ionic-electronic conductors

The ability to transport both ionic and electronic species is one of the most important properties of a mixed ionic-electronic conductor for electrosynthesis, gas separation, and electrode applications. In this paper, resistor network approach is used to predict the effective conductivities of a composite mixed conductor consisting of any number of randomly-distributed phases. The model is further used to predict the effective ionic, electronic, and ambipolar transport behavior of two-phase and three-phase composite mixed conductors as a function of the volume fraction of each randomly-distributed constituent phase. Results indicate that the optimum ambipolar conductivity occurs only within certain volume fractions of the constituent phases, depending on their relative ionic and electronic conductivities.

粉末プロセスの制御と製品評価 Ｉ 分散系の比粘度の関するランダム抵抗網モデル

The Random Resistor Network Approach is applied to a modeling of the relative viscosity of disperse systems. A suspension that solid particles are dispersed in a liquid is represented by occupied or empty sites of cubic lattice. The resistivity of the heterogeneous system is equivalent to the viscosity of suspension according to the excitation-response theory. Monte Carlo simulation of zero-shear viscosity was conducted for the varied solids loading and solid/liquid bond resistance. The calculation results exhibit a good agreement with the experimental data obtained before. Bond Resistance and bond probability of particles introduced into the model enables the modeling of the dynamic viscous behavior of suspensions.

Resistor-network approach to growth probability for dielectric-breakdown models at a surface.

For the dielectric-breakdown model a general method is presented for calculation of the growth probability on the growing-perimeter sites of the aggregate at a surface. The growth probability is given by solving the electrostatic problem for a superconducting aggregate in the semi-infinite normal-resistor network. The electric field at the perimeter site is obtained by solving the resistor-network problem with the lattice bond-bond Green's function. The fractal dimension D is found from the scaling assumption for the cluster-top occupancy probability.