Macroscopic Conductivity Research Articles

Global and local conductivity in percolating crosslinked carbon black/epoxy\u2013amine composites

Conductive particle-filled polymer composites are promising materials for applications where both the merits of polymer and conductivity are required. The electrical properties of such composites are controlled by the particle percolation network present in the polymeric matrix. In this study, the electrical properties of crosslinked carbon black–epoxy–amine (CB-EA) composites with various CB concentrations are studied at room temperature as a function of the AC frequency f. A transition at critical frequency fc from the DC plateau σDC to a frequency-dependent part was observed. Conductivity mechanisms for f > fc and f < fc were investigated. By considering the fractal nature, conduction for f > fc was verified to be intra-cluster charge diffusion. For f < fc, with the assistance of conductive atomic force microscopy (C-AFM), the conduction behavior of individual clusters can be observed, revealing both linear and nonlinear I–V characteristics. By combining microtoming and C-AFM measurements, 3D reconstructed images offer direct evidence that the percolating network of these materials consists of both a low-conductivity part, in which the charge transports through tunneling, and a high-conductivity part, which shows ohmic electrical properties. Nevertheless, for these CB-EA composites, the presence of these non-ohmic contacts still leads to Arrhenius-type behavior for the macroscopic conductivity.

Homogenization of transport properties of composites based on stochastic dynamics

A new stochastic dynamic homogenization method (SDHM) for the homogenization of transport properties of composites is introduced. The method is based on a stochastic dynamic description of the transport process. It exploits the formal correspondence between stochastic differential equations (SDE) and Fokker-Planck equations (FPE). Generalized homogenized conductivities are obtained from the flux of trajectories of a stochastic process that is the exact microscopic counterpart of the macroscopic conduction process through the composite. The method is meshless, does not require a spatial discretization of the governing equations, and is particularly well suited to the homogenization of random heterogeneous materials.

A Deep Neural Network Model of Particle Thermal Radiation in Packed Bed

Prediction of particle radiative heat transfer flux is an important task in the large discrete granular systems, such as pebble bed in power plants and industrial fluidized beds. For particle motion and packing, discrete element method (DEM) now is widely accepted as the excellent Lagrangian approach. For thermal radiation, traditional methods focus on calculating the obstructed view factor directly by numerical algorithms. The major challenge for the simulation is that the method is proven to be time-consuming and not feasible to be applied in the practical cases. In this work, we propose an analytical model to calculate macroscopic effective conductivity from particle packing structures Then, we develop a deep neural network (DNN) model used as a predictor of the complex view factor function. The DNN model is trained by a large dataset and the computational speed is greatly improved with good accuracy. It is feasible to perform real-time simulation with DNN model for radiative heat transfer in large pebble bed. The trained model also can be coupled with DEM and used to analyze efficiently the directional radiative conductivity, anisotropic factor and wall effect of the particle thermal radiation.

Macroscopic conductivity of aqueous electrolyte solutions scales with ultrafast microscopic ion motions

Despite the widespread use of aqueous electrolytes as conductors, the molecular mechanism of ionic conductivity at moderate to high electrolyte concentrations remains largely unresolved. Using a combination of dielectric spectroscopy and molecular dynamics simulations, we show that the absorption of electrolytes at ~0.3 THz sensitively reports on the local environment of ions. The magnitude of these high-frequency ionic motions scales linearly with conductivity for a wide range of ions and concentrations. This scaling is rationalized within a harmonic oscillator model based on the potential of mean force extracted from simulations. Our results thus suggest that long-ranged ionic transport is intimately related to the local energy landscape and to the friction for short-ranged ion dynamics: a high macroscopic electrolyte conductivity is thereby shown to be related to large-amplitude motions at a molecular scale.

Charge percolation in metal-organic framework (HKUST-1)‒graphene nanocomposites

Modulating the conductivity of microporous metal-organic frameworks (MOFs) through formulation of composites with graphene (G), as the conductive element, is demonstrated, without being limited to a particular MOF composition or topology. The synthesis allows for varying G content within the composite systematically, resulting in highly electrically conductive composites beyond 30 wt% G. The charge percolation model can effectively be utilized to describe the macroscopic electrical conductivity of the synthesized composites. Starting from a non-conductive MOF (HKUST-1, σ = 2*10−8 S m−1), enhanced conductivity can be accessed through increasing the G wt%, reaching more than nine orders of magnitude increase in conductivity up to 23.3 S m−1 for the composite containing 59.4 wt% G. A charge percolation threshold of 30 wt% G was observed, where sufficient G-G contacts were established within the composite. The ab initio DFT calculations on Cu-paddlewheel@G model indicated several non-covalent interactions, including OH⋯π and π‒π interactions, governing the deposition of the MOF on top of G (range of ‒101.3 kJ/mol to −113.8 kJ/mol). This approach is potentially transferable to the vast majority of MOFs, as surface functionalization of the conductive filler is not a prerequisite for the attainment of bottom-up assembly of the MOF@G.

Improved space charge transport model in bi‐layer dielectrics—considering carrier dynamic equilibrium

The Maxwell–Wagner model and bipolar charge transport model both aim at describing the charge transport behaviours in dielectrics. The Maxwell–Wagner model performs well in calculating the polarisation current and electric field distribution, but it is too macroscopic to describe the microscopic behaviours of space charges. The bipolar charge transport model can well simulate the space charge accumulation, but it cannot quantitatively relate the microscopic transport behaviours with the macroscopic conductivities of dielectrics. Considering the shortages of the above two models, an improved charge transport model, named carrier dynamic equilibrium model, was proposed in this study to simulate the polarisation process of the low-density polyethylene/ethylene propylene diene monomer bi-layer dielectric by introducing a source term of carrier dynamic equilibrium. Effects of carrier mobility and non-equilibrium carrier lifetime on the simulation results were explored, and a comparison among the results of measurement and different models was also made. Compared with the Maxwell–Wagner model and bipolar charge transport model, the improved model has the best coincidence with measurements, which can provide an accurate reference for the design of high-voltage direct current insulation systems.

Graphical Representation and Explanation of the Conductivity Tensor of Anisotropic Media

Electrical anisotropy is a property of the Earth materials that can be studied through electromagnetic geophysical methods, such as magnetotellurics. It consists of the electrical conductivity changing with the orientation and being mathematically characterized by the conductivity tensor. In order to better understand the conductivity tensor and provide more effective tools for quantitatively analyzing the conductivity tensor of anisotropic structures, three graphical representations for symmetric tensors using ellipsoids, Mohr circles and geometric forms are presented. The ellipsoid representation can be applied to indicate the strength of the anisotropy in different directions. The Mohr circle provides a graphic representation of a tensor as a function of the rotation of the coordinate system. For the geometric forms, one-dimensional (1-D), two-dimensional (2-D) and three-dimensional (3-D) sheet models with given parameters (sizes and resistivities of the constituent prisms), the macroscopic anisotropic conductivity may be calculated using the closed-form mathematical formulas. These three graphical representations have different abilities for revealing information on the conductivity tensor. Four synthetic examples involving uniaxial or biaxial anisotropic conductivity structures are examined in the principal axis coordinate system to investigate the advantages and disadvantages of the graphical displays.

Effects of percolation on the effective conductivity of irregular composite porous media

We develop a phenomenological model for the effective conductivity of porous media that consist of two distinct materials characterized by different values of hydraulic conductivity. Our focus is two-fold: first, to relate the terms and parameters of macroscale conductivity to the spatial variability of local flow and conductivity observed in computational experiments, and second to develop a reduced order model for effective conductivity based on those observations. Darcys law is assumed to hold at local (mesoscopic) and large (macroscopic) scales. At the mesoscale a composite medium is a configuration of irregular subdomains consisting of two different materials. The resulting heterogeneities force fluid to flow along irregular paths, and this produces spatial variability in the magnitude and the orientation of the Darcy flux. This variability, along with the macroscopic effective conductivity, depends on the proportion of the total volume allocated to each material, the ratio of the two conductivity values, and the spatial connectivity of material subvolumes. Computational experiments indicate that the effects of heterogeneity are most pronounced when the two conductivity values are very different, and when the volume fraction of the more conductive material is near a percolation threshold. The percolation threshold is the critical volume fraction of the more conductive material at which the medium is no longer traversed by connected paths through that material. The percolation threshold determines the existence of three regimes in effective conductivity, two where the effective conductivity obeys power laws and is dominated by one of the materials, and a third intermediate regime that interpolates between the power laws.

The effect of temperature and graphene concentration on the electrical conductivity and dielectric permittivity of graphene–polymer nanocomposites

Several recent experiments have revealed the remarkable influence of temperature and graphene concentration on the effective electrical properties of graphene–polymer nanocomposites, but no theory seems to exist at present to quantify such dependence. In this work, we develop a novel micromechanics-based homogenization scheme to connect the microstructural features of constituent phases to the temperature-dependent macroscopic conductivity and permittivity for the nanocomposites. The key microstructural features include the graphene volume concentration, temperature-dependent electrical properties of constituent phases, percolation threshold, imperfect mechanical bonding effect with temperature-degraded interlayer, and the temperature-dependent electron tunneling and Maxwell–Wagner–Sillars polarization. We consider the activation of free electrons and polarization of molecules to write the constitutive equations of polymer, and the collision and vibration probabilities to write those of graphene. We highlight the developed theory with a direct comparison to the experimental data of rGO/epoxy nanocomposites over the temperature range from 293 to 353 K. It shows that before the percolation threshold, the effective electrical conductivity and dielectric permittivity markedly increase with temperature, but after the percolation threshold, the influence of temperature diminishes significantly. In the latter case, the effective permittivity increases only slightly, while the conductivity exhibits an opposite trend.

Nanoscale percolation in doped BaZrO3 for high proton mobility

Acceptor-doped barium zirconate is a promising proton-conducting oxide for various applications, for example, electrolysers, fuel cells or methane-conversion cells. Despite many experimental and theoretical investigations there is, however, only a limited understanding as to how to connect the complex microscopic proton motion and the macroscopic proton conductivity for the full range of acceptor levels, from diluted acceptors to concentrated solid solutions. Here we show that a combination of density functional theory calculations and kinetic Monte Carlo simulations enables this connection. At low concentrations, acceptors trap protons, which results in a decrease of the average proton mobility. With increasing concentration, however, acceptors form nanoscale percolation pathways with low proton migration energies, which leads to a strong increase of the proton mobility and conductivity. Comparing our simulated proton conductivities with experimental values for yttrium-doped barium zirconate yields excellent agreement. We then predict that ordered dopant structures would not only strongly enhance the proton conductivities, but would also enable one- or two-dimensional proton conduction in barium zirconate. Finally, we show how the properties of other dopants influence the proton conductivity.

Modeling Depolarization Delay, Sodium Currents, and Electrical Potentials in Cardiac Transverse Tubules

T-tubules are invaginations of the lateral membrane of striated muscle cells that provide a large surface for ion channels and signaling proteins, thereby supporting excitation–contraction coupling. T-tubules are often remodeled in heart failure. To better understand the electrical behavior of T-tubules of cardiac cells in health and disease, this study addresses two largely unanswered questions regarding their electrical properties: (1) the delay of T-tubular membrane depolarization and (2) the effects of T-tubular sodium current on T-tubular potentials. Here, we present an elementary computational model to determine the delay in depolarization of deep T-tubular membrane segments as the narrow T-tubular lumen provides resistance against the extracellular current. We compare healthy tubules to tubules with constrictions and diseased tubules from mouse and human, and conclude that constrictions greatly delay T-tubular depolarization, while diseased T-tubules depolarize faster than healthy ones due to tubule widening. Increasing the tubule length non-linearly delays the depolarization. We moreover model the effect of T-tubular sodium current on intraluminal T-tubular potentials. We observe that extracellular potentials become negative during the sodium current transient (up to −40 mV in constricted T-tubules), which feedbacks on sodium channel function (self-attenuation) in a manner resembling ephaptic effects that have been described for intercalated discs where opposing membranes are very close together. The intraluminal potential and sodium current self-attenuation however greatly depend on sodium current conductance. These results show that (1) the changes in passive electrical properties of remodeled T-tubules cannot explain the excitation–contraction coupling defects in diseased cells; and (2) the sodium current may modulate intraluminal potentials. Such extracellular potentials might also affect excitation–contraction coupling and macroscopic conduction.

Linking Macroscopic and Nanoscopic Ionic Conductivity: A Semiempirical Framework for Characterizing Grain Boundary Conductivity in Polycrystalline Ceramics.

Understanding the chemical and charge transport properties of grain boundaries (GBs) with high point defect concentrations (beyond the dilute solution limit) in polycrystalline materials is critical for developing ion-conducting solids for electrochemical energy conversion and storage. Elucidation and optimization of GBs are hindered by large variations in atomic structure, composition, and chemistry within nanometers or Ångstroms of the GB interface, which limits a fundamental understanding of electrical transport across and along GBs. Here we employ a novel correlated approach that is generally applicable to polycrystalline materials whose properties are affected by GB composition or chemistry. We demonstrate the connection between the nanoscopic chemical and transport properties of individual boundaries and the macroscopic ionic conductivity in oxygen-conducting Pr0.04Gd0.11Ce0.85O2-δ. The key finding is that GBs with higher solute concentration have lower activation energy for cross-GB ion conduction through a polycrystalline conductor. The resultant semiempirical framework presented here provides a tool for understanding, designing and optimizing polycrystalline ionic conductors.

Apprehending the effects of mechanical deformations in cardiac electrophysiology: A homogenization approach

We follow a formal homogenization approach to investigate the effects of mechanical deformations in electrophysiology models relying on a bidomain description of ionic motion at the microscopic level. To that purpose, we extend these microscopic equations to take into account the mechanical deformations, and proceed by recasting the problem in the framework of classical two-scale homogenization in periodic media, and identifying the equations satisfied by the first coefficients in the formal expansions. The homogenized equations reveal some interesting effects related to the microstructure — and associated with a specific cell problem to be solved to obtain the macroscopic conductivity tensors — in which mechanical deformations play a nontrivial role, i.e. they do not simply lead to a standard bidomain problem posed in the deformed configuration. We then present detailed numerical illustrations of the homogenized model with coupled cardiac electrical–mechanical simulations — all the way to ECG simulations — albeit without taking into account the abundantly-investigated effect of mechanical deformations in ionic models, in order to focus here on other effects. And in fact our numerical results indicate that these other effects are numerically of a comparable order, and therefore cannot be disregarded.

Effects of land-use/cover change on soil hydraulic properties and pore characteristics in a semi-arid region of central Iran

The semi-arid regions of central Iran have vastly undergone the manipulation and conversion of rangelands to dry farmlands. Soil hydraulic properties and pore characteristics may differ in various land-use/cover types. This study evaluated the effects of good and poor rangeland, dry farmland and abandoned farmland on the soil hydraulic properties and pore characteristics in a semi-arid region of central Iran. A completely randomized design was used to analyze the effects of land-use/cover on soil hydraulic properties and pore characteristics. Water infiltration into the soil at inlet matric suction (h) values of 2, 5, 10 and 15 cm was measured using a tension infiltrometer in different land-use/cover types with 18 replications. Wooding's analytical method was used to model the infiltration data and the best-fit values for Gardner’s parameters of macroscopic capillary length (λc) and saturated hydraulic conductivity (Ks) were estimated. Pore characteristics were also estimated using the Watson and Luxmoore method. The results indicated that saturated and near-saturated hydraulic conductivity values [Kh] and λc were significantly influenced by the land-use/cover type. For h < 5 cm, good rangeland and dry farmland had the highest and lowest means of hydraulic conductivity, steady-state flux and sorptivity, respectively. The K values at h lower than 5 cm were found to be as follows: good rangeland > poor rangeland > abandoned farmland > dry farmland. Good rangeland had a greater number of large pore-size class (i.e., > 0.06 cm) and total porosity. Dry farmland and good rangeland had the lowest and highest proportions of large pore-size class (> 0.06 cm), respectively. Inappropriate management practices such as over-grazing of poor rangeland, cultivation and harvesting machinery stress and soil organic carbon decomposition in the dry farmland decreased the frequency of very large pore-size classes (i.e., > 0.15 cm). Although very large and large pores contributed to less than 1% of the soil volume, more than 50% of the total water flow would happen through these pore-size classes. Preserving rangelands in good condition can maintain soil structure and stability and would enhance water infiltration into the soil. These findings can be used by decision makers and land managers for holistic management in ecosystems of semi-arid areas.

A Mechanics Based Surface Image Interpretation Method for Multifunctional Nanocomposites.

Graphene nanosheets and thicker graphite nanoplatelets are being used as reinforcement in polymeric materials to improve the material properties or induce new functional properties. By improving dispersion, de-agglomerating the particles, and ensuring the desired orientation of the nano-structures in the matrix, the microstructure can be tailored to obtain specific material properties. A novel surface image assisted modeling framework is proposed to understand functional properties of the graphene enhanced polymer. The effective thermal and mechanical responses are assessed based on computational homogenization. For the mechanical response, the 2-D nanoplatelets are modeled as internal interfaces that store energy for membrane actions. The effective thermal response is obtained similarly, where 2-D nanoplatelets are represented using regions of high conductivity. Using the homogenization simulation, macroscopic stiffness properties and thermal conductivity properties are modeled and then compared to the experimental data. The proposed surface image assisted modeling yields reasonable effective mechanical and thermal properties, where the Kapitza effect plays an important part in effective thermal properties.

Effective medium approximation for conductivity of coated-inclusion composites with anisotropic coating

Effective medium approximations are constructed in this paper to estimate the macroscopic conductivity of coated-inclusion composites with thin anisotropic coating. The two-phase coated-inclusion are substituted by equivalent one-phase inclusion, using the multi-coated spheres assemblage and the differential substitution approaches. Then, the usual effective medium approximation schemes are applied to the equivalent medium to estimate the conductivity of original three-phase composites. The results obtained were compared with the numerical simulation by finite element method in 2D show the effectiveness of the methods.

Fast Electrochemical Netting of Composite Chains for Transferable Highly Conductive Polymeric Nanofilms.

Broad applications of electropolymerized conducting polymers (CPs) often prefer thinner soft electrodes to comply with downscaling of the fabrication resolution. However, high conductivity of existing CP films vanishes as thickness decreases to the nanoscale (i.e., below 100 nm), with an unclear mechanism so far. In this study, with an unprecedented family of polypyrrole (PPy) nanofilms that can be easily transferred in a fast and contamination-free manner, we are able to trace the initial development of electrical conductance along with chains' arrangement starting from the very early electrochemical deposition. Our results evidence that the classical nodular polymeric aggregation fundamentally accounts for the persistent losses of interchain connectivity and macroscopic conductivity at a limited thickness. Surprisingly, this seemingly disadvantageous structure can be altered into a large conjugated network to robustly restore the conductivity back to over 80 S cm-1 even below 100 nm, while the controllable formation, growth, and collapse of such networks radically vary the conductivity over a range of 3 orders of magnitude (0.8-129 S cm-1). These observations depict the first physical picture detailing how the long-range conductivity builds up in a growing conjugated network, which opens a route to fast synthesis and diverse applications of such highly conductive CP nanofilms.

Thermal properties of thin films made from MoS2 nanoflakes and probed via statistical optothermal Raman method

A deep understanding of the thermal properties of 2D materials is crucial to their implementation in electronic and optoelectronic devices. In this study, we investigated the macroscopic in-plane thermal conductivity (κ) and thermal interface conductance (g) of large-area (mm2) thin film made from MoS2 nanoflakes via liquid exfoliation and deposited on Si/SiO2 substrate. We found κ and g to be 1.5 W/mK and 0.23 MW/m2K, respectively. These values are much lower than those of single flakes. This difference shows the effects of interconnections between individual flakes on macroscopic thin film parameters. The properties of a Gaussian laser beam and statistical optothermal Raman mapping were used to obtain sample parameters and significantly improve measurement accuracy. This work demonstrates how to address crucial stability issues in light-sensitive materials and can be used to understand heat management in MoS2 and other 2D flake-based thin films.

Thermal Conductivity of Polyamide-6,6/Carbon Nanotube Composites: Effects of Tube Diameter and Polymer Linkage between Tubes.

Reverse nonequilibrium molecular dynamics simulations were done to quantify the effect of the inclusion of carbon nanotubes (CNTs) in the Polyamide-6,6 matrix on the enhancement in the thermal conductivity of polymer. Two types of systems were simulated; systems in which polymer chains were in contact with a single CNT, and those in which polymer chains were in contact with four CNTs, linked together via polymer linkers at different linkage fractions. In both cases, heat transfer in both perpendicular and parallel (to the CNT axis) directions were studied. To examine the effect of surface curvature (area) on the heat transfer between CNT and polymer, systems containing CNTs of various diameters were simulated. We found a large interfacial thermal resistance at the CNT-polymer boundary. The interfacial thermal resistance depends on the surface area of the CNT (lower resistances were seen at the interface of flatter CNTs) and is reduced by linking CNTs together via polymer chains, with the magnitude of the reduction depending on the linkage fraction. The thermal conductivity of polymer in the perpendicular direction depends on the surface proximity; it is lower at closer distances to the CNT surface and converges to the bulk value at distances as large as 2 nm. The chains at the interface of CNT conduct heat more in the parallel than in the perpendicular directions. The magnitude of this thermal conductivity anisotropy reduces with decreasing the CNT diameter and increasing the linkage fraction. Finally, microscopic parameters obtained from simulations were used to investigate macroscopic thermal conductivities of polymer nanocomposites within the framework of effective medium approximation.

(Invited) Effect of Junction Resistance on the Percolation Conductivity of Metal Nanowire Networks for Transparent Conductors

Random networks of one-dimensional (1D) nanoelements, such as carbon nanotubes, graphene nanoribbons, and metal nanowires, have attracted significant research interest recently for next-generation transparent conductors. As a result, these networks can be used in many device applications, such as touch screens, flat panel displays, solar cells, light-emitting diodes (LEDs), and wearable flexible electronics. Among these nanomaterials, metal nanowire networks, such as silver and copper, exhibit high optical transmittance, low sheet resistance, mechanical flexibility, and solution-based fast deposition. These unique properties make metal nanowire networks promising candidates to replace indium tin oxide (ITO), which suffers from brittleness, scarcity, high cost, and slow deposition. At high optical transmittance values required for transparent conductors, the conductivity of metal nanowire networks is governed by percolation transport, which deals with the formation of long-range connectivity in random networks. As a result, Monte Carlo simulations need to be employed to theoretically calculate, predict, and optimize the conductivity of metal nanowire networks [1,2]. Two types of resistance contributions determine the overall conductivity of the nanowire network. The first is the nanowire-nanowire junction resistance and the second is the resistance of the nanowire itself. In most Monte Carlo simulations, it is assumed that the nanowire-nanowire junction resistance is much larger than the nanowire resistance, resulting in a junction resistance-dominated network [2-4]. Although this is the case for carbon nanotube networks, recent experiments have shown that, for metal nanowire networks, the junction resistance can be significantly lowered by post-deposition treatments, such as thermal annealing, plasmonic welding, joule heating, and mechanical pressing. In such cases, the nanowire resistance becomes comparable to the junction resistance and it can no longer be ignored. When the junction resistance becomes much lower than the nanowire resistance, the network becomes nanowire resistance-dominated, which is the lowest resistance limit for a given set of nanowire and device parameters. Despite the significant role the junction resistance plays in determining the percolation conductivity of metal nanowire networks, a systematic study of the effect of nanowire-nanowire junction resistance on the network conductivity as a function of other nanowire and device parameters is currently lacking. In this work, we perform systematic Monte Carlo simulations to study the effect of the nanowire-nanowire junction resistance on the conductivity and percolation critical exponents of metal nanowire networks. We define a parameter called the resistance ratio, which is the ratio of the nanowire-nanowire junction resistance to the nanowire resistance per unit length. We perform Monte Carlo simulations of the nanowire network conductivity by varying the resistance ratio over a span of six orders of magnitude, ranging all the way from a junction resistance-dominated to a nanowire resistance-dominated network. First, we study the effect of the resistance ratio on the nanowire network conductivity at different values of the other nanowire and device parameters, such as nanowire density, nanowire length, device length, device width, nanowire alignment, and nanowire curviness. Next, we study the effect of the resistance ratio on the percolation critical exponents. Approaching the percolation threshold, conductivity exhibits a power law dependence on nanowire and device parameters, which is characterized by percolation critical exponents. We first extract the critical nanowire density, nanowire length, device width, and alignment angle at the percolation threshold by calculating the percolation probability as a function of each variable. Then, we extract the critical exponents as a function of the resistance ratio for nanowire density, nanowire length, device width, nanowire alignment, and nanowire curviness. We find that the resistance ratio plays a crucial role in determining both the conductivity and the percolation critical exponents of metal nanowire networks. This study illustrates how the junction resistance affects the macroscopic conductivity of transparent, conductive metal nanowire networks. It also shows that Monte Carlo simulations are an essential predictive tool for providing insights into percolation transport and optimizing the electronic properties of these networks. These results are not limited to metal nanowire networks, but can be extended to any two-dimensional (2D) or quasi-2D network, film, or nanocomposite consisting of 1D nanoelements.