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In this study, the impact of three different principles of surface activation techniques for polyamide fibers on the formation of conductive percolation during the subsequent electroless copper deposition process was investigated. The techniques used are (1) polyamide complexation using a solution mixture of calcium chloride, ethanol and water, (2) atmospheric plasma surface treatment and (3) grafting of 2‐hydroxyethylmethacrylate by radical induced polymerization. As a result, the percolation threshold was shifted to lower copper contents. The copper content required to form conductive structures was reduced ranged between 59% and 89%, depending on the activation techniques. Furthermore, the deposition time was reduced by 37%–57%, resulting in a faster build‐up of the percolation on the fabric. Changes in wetting behavior and substrate surface topography were identified to be the main reasons for these observations. While all applied surface activation techniques led to higher copper contents compared to unmodified reference, the atmospheric plasma modification led to the highest copper contents during the deposition process and a more uniform appearance of the metallised layer. Highlights: Three different fiber surface activation methods are evaluated.Fiber surface activation increases wetting and polymer‐metal adhesion.Activated polymer surface leads to faster copper deposition and percolation.Atmospheric plasma modification is the most efficient technique. [ABSTRACT FROM AUTHOR]

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Background and Objectives: Nanostructured dispersed semiconductor structures are of some interest as functional materials for modern chemoresistive sensing and photocatalytic chemistry. Among the promising semiconductor materials for such applications is, in particular, titanium dioxide in the modification of anatase. Despite a significant number of experimental and theoretical works devoted to the consideration of electrophysical properties of anatase nanophase and various structures based on it, the features of degradation of electrical conductivity of such systems with time are not fully investigated. The aim of this work was to analyze the behavior of the fluctuation component of the voltage drop on partially conducting systems of interelectrode bridges made of anatase nanoparticles under conditions of direct current flow in the quasi-stationary regime (with a slow increase in the voltage drop) and as it approaches the threshold of flow, characterized by a rapid increase in the voltage drop. Materials and Methods: Experimental studies of the charge transfer fluctuations in disperse structures near the percolation threshold were carried out using specially prepared samples consisting of densely packed titanium oxide nanoparticles (TiO2). The technique is based on the registration of time dependences of the voltage drop across the structures when a constant current flows through the system of anatase bridges. The behavior of fluctuation components during the measurement cycles was analyzed using moving estimates of the Hurst exponent of sample structural functions of intensity fluctuations. In addition to the sample values of the Hurst exponent, the sample normalized autocorrelation functions of the fluctuation component were calculated. To interpret the observed features, we propose a qualitative phenomenologicalmodel that considers the influence of random sequences of acts of blocking and soft breakdown of local conduction channels in the studied structures on the degradation of the effective ohmic conductivity of the structures. Results: It has been established that when approaching the threshold of percolation due to the depletion of the ensemble of free charge carriers (electrons) in bridges, there are qualitative changes in the dynamics of voltage drop fluctuations on bridge systems (in particular, a significant increase in the Hurst exponent of structural functions of voltage drop fluctuations, correlating with a sharp decline in the effective ohmic conductivity of the structures under study). “Soft” breakdowns of previously blocked local conduction channels may be due to the Poole – Frenkel effect, leading to the escape of trapped electrons into the conduction zone due to thermal fluctuations when the depth of traps decreases under the influence of an external electric field. Conclusion: The results obtained are of some interest from the point of view of further development of fundamental ideas about charge transfer mechanisms in dispersed semiconductor materials used in chemoresistive sensing and catalytic chemistry.

Pressure sensors based on advanced materials have gained high attention for their potential applications in various fields, including sports training. This study focuses on the development of poly(vinylidene fluoride-trifluoroethylene) (P(VDF-TrFE))/graphene composite films as high-performance pressure sensors. The composite films were fabricated using a casting method, and their morphological, structural, thermal, mechanical, and electrical properties were comprehensively characterized. The incorporation of graphene nanoplatelets (GnPs) into the P(VDF-TrFE) matrix led to the formation of a percolated conductive network, resulting in enhanced electrical conductivity and pressure sensitivity. The composite film containing 5 wt% GnP exhibited remarkable sensing capabilities, boasting an elevated sensitivity of 0.85 kPa−1, a rapid response time of 50 ms, and exceptional resilience over 1000 loading-unloading cycles. Moreover, the incorporation of GnP substantially augmented the mechanical properties, with a 65 % enhancement in tensile strength and a 92 % surge in Young's modulus when juxtaposed against pristine P(VDF-TrFE) films. The superior property of these P(VDF-TrFE)/graphene composite pressure sensors, along with their excellent mechanical properties, make them promising candidates for sports training applications, enabling the monitoring and analysis of various biomechanical parameters to optimize athletic performance and prevent injuries.

Polydimethylsiloxane (PDMS) with multiwalled carbon nanotubes (MWCNT) fillers is a piezoresistive nanocomposite which is conformable, printable, and biocompatible. It is widely employed as a sensing layer in flexible pressure sensors, electronic skin (e-skin) of humanoid robots and as wearable sensors. Piezoresistive nanocomposites show significant increase in their electrical conductivity above a certain percolation threshold. In this work, PDMS + MWCNT-based sensing layers with different nanofiller MWCNT concentrations (2, 4 and 7 wt.%) are screen-printed and their electrical, mechanical, and percolation threshold responses are verified. The static I–V characteristics of the samples for a biasing DC voltage of 0-6 V are studied. The tensile test confirms maximum elongation of more than 50 mm. The change in resistance was minimal for 2 wt.% sample as the MWCNT's are sparsely distributed and no conducting channels are formed; for the 7 wt.% sensing layer, negligible change in resistance was observed as the conducting channels are broken. The highest change in resistance of 2.4 MΩ was observed after the percolation threshold value of 4 wt.% of the nanofiller concentration was reached. Overall, the 4 wt.% screen-printed piezoresistive nanocomposite layer showed highest sensitivity with a gauge factor of 4.76 and a linear response suitable for industrial applications. [ABSTRACT FROM AUTHOR]

In-situ methods are highly desirable for the development of segregated conductive composites. We demonstrate a benign and simple method for developing segregated conductive poly (methyl methacrylate)/reduced graphene oxide composites by incorporating two-step in-situ reduction of graphene oxide (GO) with poly(methyl methacrylate) (PMMA) microspheres. First, a one-pot method is demonstrated that involves the synthesis of positively charged PMMA latex followed by in-situ hydrazine reduction of negatively charged GO. In the second step, thermal reduction at 150 °C is used to increase the reduction level of GO. As a result of two-step reduction of GO, the obtained composite exhibits good correlation between their structural, morphological, thermal, and electrical properties. Compared to PMMA matrix, 4 wt % composites formed after in-situ reduction using hydrazine (PMMA-rGO-H) and two-step method (PMMA-rGO-HT) exhibit approximately 108 and 109 fold increases in electrical conductivity, respectively. Further, the percolation threshold for conduction is 1 wt%, indicating the generation of segregated conductive networks. [ABSTRACT FROM AUTHOR]

The physical properties as well as thermal and electrical stability of copper particles can be improved by surface protection, which mainly depends on the coating material. Our study was, therefore, focused on the rheological, thermal, mechanical and electrical characterization of polymer composites by comparing uncoated (Cu), silver-coated (Cu@Ag) and silica-coated (Cu@Si) copper flakes in low-density polyethylene at various volume concentrations (up to 40%). Interactions among particles were investigated by rheological properties, as these indicate network formation (geometrical entanglement), which is important for mechanical reinforcement as well as establishing an electric pathway (electrical percolation). The results showed that geometrical and electrical percolation were the same for Cu and Cu@Si, ~15%, while, surprisingly, Cu@Ag exhibited much lower percolation, ~7.5%, indicating the fusion of the Ag coating material, which also decreased crystal growth (degree of crystallinity). Furthermore, the magnitude of the rheological and mechanical response remained the same for all investigated materials, indicating that the coating materials do not provide any load transfer capabilities. However, they profoundly affect electron transfer, in that, Cu@Ag exhibited superior conductivity (74.4 S/m) compared to Cu (1.7 × 10−4 S/m) and Cu@Si (1.5 × 10−10 S/m). The results obtained are important for the design of advanced polymer composites for various applications, particularly in electronics where enhanced electrical conductivity is desired. [ABSTRACT FROM AUTHOR]

The correlations between the electrical behavior and microstructural properties of samples consisting of particle composites fabricated from SiC particles embedded in a silicone matrix, were investigated using X-ray computed tomography. In the voltage field range 200-1000 V/mm, the measured conductivity as a function of SiC volume fraction exhibits two distinct gaps. Upon further investigations, we attribute these observations to percolation thresholds at the microscale. The first gap, corresponding to interconnections between SiC particles that were originally disconnected, is more significant at higher voltage; while the second one, resulting from shortening conductivity pathways between the external surfaces of the samples with the increase of SiC volume fraction, seems more sensitive to lower voltages and is correlated with a decrease of the tortuosity of the percolated SiC network. [ABSTRACT FROM AUTHOR]

The electrical properties of Con(CoO)100 –n composite thin films obtained by ion-beam sputtering of a composite target in an argon atmosphere and a mixed atmosphere of argon and oxygen (98% Ar + 2% O2) have been studied. It has been established that if oxygen is introduced into the deposition chamber, the position of the percolation threshold shifts towards lower concentrations of the metal phase. It is associated with the special morphology of the films, when small metal Co nanoparticles are located along the boundaries of larger CoO particles, as well as a decrease in the size of inclusions of the metal phase. Studies of the temperature dependences of the electrical resistivity of synthesized Con(CoO)100 –n films have shown that when the metal phase content is up to the percolation threshold the dominant mechanism of charge transfer in the temperature range of 80−140 K is the variable range hopping mechanism of conduction through localized states near the Fermi level, replaced by the nearest neighbors conductivity in the temperature range of 140–300 K. For beyond the percolation threshold Con(CoO)100 –n thin films, the conductivity is determined by a network of metal granules and is characterized by a positive temperature coefficient of electrical resistance. [ABSTRACT FROM AUTHOR]

For a polycrystalline material with a hexagonal close-packed lattice, a model is proposed that allows estimating the yield strength at a given texture. The plasticity properties of an individual grain are described by the generalized von Mises criterion. The most widespread averaging approaches are considered to determine the yield strength of a polycrystal. An original averaging method for a heterogeneous medium under plastic deformation conditions is proposed that takes into account the presence of undeformed grains whose share is determined by means of the percolation theory. Using each approach, the problem about tension/compression of a homogeneous rod of square cross-section is solved for two limiting cases: no texture and rigid basis texture. The calculation results are juxtaposed with the available literature data. The effect of the texture on the yield strength is considered. A qualitative explanation of generating a texture is given. [ABSTRACT FROM AUTHOR]

A systematic study of the effects of the binder matrix on the microwave absorption properties of functional carbon nanoparticle-impregnated rubber composites is reported herein. Flexible rubber composites were fabricated by loading of conductive carbon black (CB) in three different elastomeric binder host matrices: silicone rubber, acrylonitrile butadiene rubber (NBR) and ethylene propylene diene monomer (EPDM) rubber. The DC conductivity, morphology and complex dielectric permittivity were investigated using the four-point probe contact method, scanning electron microscopy and vector network analyzer instrumentation, respectively. The percolation threshold was found to be lowest for CB-silicone rubber composites, i.e. 6 wt.% loading of CB, followed by 12 wt.% for CB-NBR composites and 16 wt.% for CB-EPDM composites. The rheological behavior of these composites was also studied, and their correlation with the observed percolation threshold (DC conductivity) of composites is discussed. The microwave absorption properties (reflection loss [RL]) were calculated based on the measured electromagnetic parameters over a frequency range of 6–18 GHz for each composite system. The significant microwave absorption (RL > −10 dB) properties can be tuned by varying the thickness in the range of 1.7–3.0 mm in these composites. The studies presented in the paper provide a basic framework for selection of an appropriate binder matrix for the development of stealth composites, according to the desired area of application. [ABSTRACT FROM AUTHOR]

Conductive polymer composites (CPC) are gaining increasing popularity due to their unique characteristics, which include light weight and the ability to conduct electricity. In this work, CPC were prepared by blending the polylactic acid (PLA) with a conductive filler, graphene nanoplatelets (GNP), at dosages ranging from 1 to 12 wt % using an internal mixer. The hot press machine was used to compress the CPC into thin sheet, and subsequently characterized for tensile, thermal, and electrical properties. The results showed that the addition of GNP at 7 wt % (percolation threshold) successfully transformed the PLA into an electrically conductive material. The tensile modulus increased with added GNP, but elongation at break and tensile strength exhibited an opposite trend. The incorporation of GNP also enhanced the composite's thermal stability. [ABSTRACT FROM AUTHOR]

Electrical distribution systems (EDS) face the major issue of complete interruption of power when the supply end of the electrical grid encounters extreme events. The integration of distributed energy resources (DERs) at the residential level has opened the path to building energy resilience within these systems, enabling them to withstand such incidents at the load end. To further enhance energy resilience, peer-to-peer (P2P) energy trading networks could be established at the community level. While several researchers have developed models to implement energy trading in the P2P network with DERs, enabling prosumers to benefit from cost savings, the impact of both DERs and P2P energy trading on the system’s resilience has not been evaluated with a quantifiable measure. In this work, we propose a methodology introducing a quantifiable measure for evaluating energy resilience in electrical distribution systems with DERs and P2P energy trading by calculating the percolation threshold (PT) using complex networks for both univariate and multivariate data. We employ cooperative game theory to model P2P energy trading, ensuring that all prosumers participate rationally. We consider the formation of microgrids in a standard IEEE-123 node test feeder system integrated with renewable energy sources. The improvement in energy resilience with trading of energy in the P2P network is analyzed for the most resilient microgrid in the distribution system. The results demonstrate a 67.91% total cost benefit and a 25.07% improvement in the resilience of the microgrid due to the integration of DERs and P2P energy trading for a period of one year.

Background and Objectives: Electrically conductive layers of densely packed semiconductor nanoparticles are a promising material platform for creating, in particular, multisensor chemoresistive systems. A significant disadvantage of multielement chemoresistive sensors of this type is the long-term instability of the parameters of individual elements and large values of response and relaxation times to the initial state. Such a process can be considered as a transition “semiconductor – insulator” in dispersed disordered systems, and the dynamics of the transition can be described in the framework of the percolation theory. The aim of this work was experimental studies and statistical modeling of the effect of degradation of ohmic conductivity of low-dimensional layers of densely packed indium oxide (In2O3) nanoparticles under long-term DC current flow. Dispersed nanostructured layers of indium oxide were chosen as an object of study due to the specific electrophysical properties of this indirect-gap n-type semiconductor. Materials and Methods: Experimental studies of the effect of degradation of ohmic conductivity of dispersed semiconductor structures under long-term exposure to direct current were carried out using specially prepared samples consisting of densely packed indium oxide nanoparticles (In2O3). The effect of structure thickness on the percolation threshold as well as the critical index of the conductivity function was numerically investigated. A cubic resistor network was considered for numerical analysis of the conductivity of a two-phase percolation structure. The network was uniformly and randomly filled with conducting and insulating nodes. Results: One of the main observed features of electron transfer in bridge disordered ensembles of nanoparticles of the studied systems is the achievement of percolation threshold at long-term exposure to direct current and extremely low rate of recovery of deteriorated conductivity after removal of exposure. The established value of the critical conductivity index for the studied structures has an intermediate value between theoretical estimates for three-dimensional and two-dimensional percolation systems, which allows us to consider the studied structures as transitional between two-dimensional and three-dimensional systems. Conclusion: The obtained results can be used as a physical basis for the development of new approaches to the creation of thin structures with limited conductivity.

In order to further expand the understanding of the pore-throat structure of sandstone, a new method is proposed in this paper to reconstruct three-dimensional (3D) virtual sandstone and replicate the natural sandstone pore-throat structure. While reconstructing 3D virtual sandstone, a particle distribution factor M and a dilation filter D were introduced into the site percolation model. The function of M was to control the initial size of the solid particle while ensuring the randomness of the shape of the solid particle, whereas D gave acceptable deformation of the pore-throat structure while changing the porosity (P) of the 3D virtual sandstone. It was found that the virtual sandstone with high similarity to the real sandstone could be reconstructed by changing the combination of M and D regardless of the P, tortuosity, and pore coordination number of the real sandstone. The percolation thresholds of 3D virtual sandstone generated under different M and D were obtained, and the pore connectivity and permeability changes with M, D, and P were also investigated. The proposed method for virtual sandstone generation in this paper provides a novel approach for assessing and predicting the connectivity and permeability of sandstone reservoirs in oil and gas exploration. [ABSTRACT FROM AUTHOR]

The authors replies to the comment made by Yang and Zhou (2024 J. Phys. A: Math. Theor.) on his 2015 paper entitled 'Critical points of Potts and O(N) models from eigenvalue identities in periodic Temperley–Lieb algebras' (Jacobsen 2015 J. Phys. A: Math. Theor. 48 454003). [ABSTRACT FROM AUTHOR]

[Display omitted] Expanded graphite–polyimide composites for fuel cells containing from 0 to 23 wt% expanded graphite were produced by direct compression molding after pre-mixing the binder and filler. The percolation threshold in this system was determined to be 2.5%, while the corrosion current was 3 × 10−2 μA cm−2, and the composites were thermally stable up to 400 °C. [ABSTRACT FROM AUTHOR]

This study investigates the dielectric properties, including dielectric constant (ɛ′), dielectric loss (ɛ″), tangent delta (tan δ), and AC conductivity (σac), of PVA/Y2O3 polymer nanocomposites (PNCs). The dielectric behavior of the PNCs was examined as a function of frequency and temperature. The results revealed that the addition of Y2O3 nanoparticles to the PVA matrix influenced the dielectric properties of the composites. In contrast to pure PVA, the PVA/Y2O3 PNCs with a 15 wt% Y2O3 loading exhibited high values of ɛ′, ɛ″, tan δ and σac are 647.49, 1607.48, 9.70 and 1.024 × 10−5, respectively, at low frequency and at particular temperature. Furthermore, the electrical properties of PVA/Y2O3 PNCs were also investigated using the Cole-Cole plots. These plots provide valuable insights into the complex impedance behavior and allow for comprehensive understanding of the electrical response of the nanocomposites. [ABSTRACT FROM AUTHOR]

Previous work demonstrated that roller compaction of a 40%w/w theophylline–loaded formulation resulted in granulate consisting of un-compacted fractions which were shown to constitute between 34 and 48%v/v of the granulate dependent on processing conditions. The active pharmaceutical ingredient (API) primary particle size within the un-compacted fraction was also shown to have undergone notable size reduction. The aim of the current work was to test the hypothesis that the observations may be more indicative of the relative compactability of the API due to the formulation being above the percolation threshold. This was done by assessing the impact of varied API loads in the formulation on the non-granulated fraction of the final granulate and the extent of attrition of API particles within the non-granulated fraction. The influence of processing conditions for all formulations was also investigated. The results verify that the observations, both of this study and the previous work, are not a consequence of exceeding the percolation threshold. The volume of un-compacted material within the granulate samples was observed to range between 34.7 and 65.5% depending on the API load and roll pressure, whilst the API attrition was equivalent across all conditions. [ABSTRACT FROM AUTHOR]

In this study, an in-depth analysis of the percolation phenomenon for square matrices with dimensions from L = 50 to 600 for a sample number of 5 × 104 was performed using Monte Carlo computer simulations. The percolation threshold value was defined as the number of conductive nodes remaining in the matrix before drawing the node interrupting the last percolation channel, in connection with the overall count of nodes within the matrix. The distributions of percolation threshold values were found to be normal distributions. The dependencies of the expected value (mean) of the percolation threshold and the standard deviation of the dimensions of the matrix were determined. It was established that the standard deviation decreased with the increase in matrix dimensions, ranging from 0.0262253 for a matrix with L = 50 to 0.0044160 for L = 600, which is almost six-fold lower. The mean value of the percolation threshold was practically constant and amounted to approximately 0.5927. The analysis involved not only the spatial distributions of nodes interrupting the percolation channels but also the overall patterns of node interruption in the matrix. The distributions revealed an edge phenomenon within the matrices, characterized by the maximum concentration of nodes interrupting the final percolation channel occurring at the center of the matrix. As they approached the edge of the matrix, their concentration decreased. It was established that increasing the dimensions of the matrix slowed down the rate of decrease in the number of nodes towards the edge. In doing so, the area in which values close to the maximum occurred was expanded. Based on the approximation of the experimental results, formulas were determined describing the spatial distributions of the nodes interrupting the last percolation channel and the values of the standard deviation from the matrix dimensions. The relationships obtained showed that with increasing matrix dimensions, the edge phenomenon should gradually disappear, and the percolation threshold standard deviation values caused by it will tend towards zero. [ABSTRACT FROM AUTHOR]

The charge transport on the electrically charged surface of polytetrafluoroethylene (PTFE) films in the presence of the adsorption of an electrically conductive phase has been studied. The attenuation of the rate of displacement of the potential drop over the film surface, which limits the area of its expansion, has been found. An estimate has been made for the critical index of the correlation length of a percolation cluster that forms on an electrified PTFE surface at high humidity. It has been experimentally established that the leak of charge from an electrically charged surface is determined by percolation processes. [ABSTRACT FROM AUTHOR]

The detection and quantification of metal sulfides in host rocks by electrical measurements have been priorities for field and laboratory studies, motivated by mineral prospecting and fundamental interest in the mantle structure or core/mantle differentiation, among other reasons. Here, we reanalyze electrical data for a dunite host with added FeS or Fe-S-Ni (Saxena et al. 2021), and report additional experimental runs along with electron microprobe analyses. The applied pressure was 2 GPa; impedance spectra were acquired while annealing at 1023 K (below the metal-sulfide solidus), and while varying temperature from 570 to 1650 K. Addition of 6.5 or 18 vol% FeS strongly enhances conductivity of the bulk sample compared with that of the dunite host, though values are 100–100 000 times less than those of pure FeS. These results indicate that most metal sulfide content is not part of a viable conductive path, even for the 18 vol% quantity. Nevertheless, the relatively high conductivity and weak temperature dependence of the 18 vol% sample reveal that contiguous paths of solid or molten FeS span the electrodes. The sample with 6.5 vol% sulfide also exceeds the percolation threshold for temperatures as low as ~100 K below the eutectic melting point, likely because FeS softens. Conductivity is nearly unchanged upon crossing the eutectic temperature, however a decline over 1400–1500 K reveals that the 6.5 vol% molten FeS forms a fragile electrical network in dunite. Samples with Fe50S40Ni10 or Fe40S40Ni20 (at%) are less conductive than pure dunite at temperatures below ~1450 K. This surprising result, likely caused by a reducing influence of Fe or Ni metal, does not support the use of FeS as an analog for compositions with nickel or excess metal. Our findings suggest that probing the electrical network of metal sulfides as solids complements other studies focused on connectivity of molten metal sulfides. [ABSTRACT FROM AUTHOR]

In this study, the phenomenon of node percolation was tested using the Monte Carlo computer simulation method for square matrices with dimensions L = 55, 101 and 151. The number of samples for each matrix was 5 × 106. The spatial distributions of the coordinates of the nodes creating the percolation channel were determined, and maps of the density distribution of these nodes were created. It has been established that in matrices with finite dimensions, an edge phenomenon occurs, consisting of a decrease in the concentration of nodes creating a percolation channel as one approaches the edge of the matrix. As the matrix dimensions increase, the intensity of this phenomenon decreases. This expands the area in which values close to the maximum occur. The length distributions of the left and right clusters of non-conducting nodes were determined for the situation when the next randomly selected node connects them and thus reaches the percolation threshold. It was found that clusters whose dimensions are close to half of the matrix dimensions are most likely to occur. The research shows that both the values of the standard deviation of the percolation threshold and the intensity of the edge phenomenon are clearly related to the dimensions of the matrices and decrease as they increase. [ABSTRACT FROM AUTHOR]

Silver (Ag) thin films have garnered significant attention due to their unique optical properties. This paper systematically investigates the optical characteristics of Ag films prepared using the electron beam evaporation method. The investigation was conducted using spectroscopic ellipsometry and covers a broad wavelength range of 1679 nm to 36 µm (0.738–0.034 eV), spanning from near-infrared to far-infrared regions. Optical and dispersion models were developed to analyze the impacts of Ag nanostructures on the complex refractive indices, dielectric functions, and reflectance. The results indicate that Ag particles and coalescence films exhibit non-metallic and low absorption properties, while Ag percolation and continuous films present a typical Drude model. The reflectance of Ag films increases as the film coverage ratio increases, and it can reach close to 100% in continuous film. Additionally, a non-destructive, non-contact, and vacuum-free means of confirming the percolation threshold of Ag films was proposed based on the slope of the imaginary part curve. This work is useful to guide simulations and provide a basis for the applications of Ag films in different fields. [ABSTRACT FROM AUTHOR]

The physical properties as well as thermal and electrical stability of copper particles can be improved by surface protection, which mainly depends on the coating material. Our study was, therefore, focused on the rheological, thermal, mechanical and electrical characterization of polymer composites by comparing uncoated (Cu), silver-coated (Cu@Ag) and silica-coated (Cu@Si) copper flakes in low-density polyethylene at various volume concentrations (up to 40%). Interactions among particles were investigated by rheological properties, as these indicate network formation (geometrical entanglement), which is important for mechanical reinforcement as well as establishing an electric pathway (electrical percolation). The results showed that geometrical and electrical percolation were the same for Cu and Cu@Si, ~15%, while, surprisingly, Cu@Ag exhibited much lower percolation, ~7.5%, indicating the fusion of the Ag coating material, which also decreased crystal growth (degree of crystallinity). Furthermore, the magnitude of the rheological and mechanical response remained the same for all investigated materials, indicating that the coating materials do not provide any load transfer capabilities. However, they profoundly affect electron transfer, in that, Cu@Ag exhibited superior conductivity (74.4 S/m) compared to Cu (1.7 × 10−4 S/m) and Cu@Si (1.5 × 10−10 S/m). The results obtained are important for the design of advanced polymer composites for various applications, particularly in electronics where enhanced electrical conductivity is desired.

Abstract Al2O3/nickel (Ni) composites were fabricated via hot-press sintering at 1400 °C to investigate the effects of microstructure on their mechanical and electrical properties. For this purpose, various amounts of Ni metal particles (5–20 vol%) were dispersed in Al2O3 ceramics. All the composites were highly densified, with a theoretical density of over 97%, and microstructural observations revealed elongated Ni phases and strong Al2O3/Ni interfaces. The Young’s moduli of the composites with 5–15 vol% Ni content were higher than that of the pure Al2O3 matrix. Additionally, all the composites showed higher fracture toughness than the pure Al2O3 ceramic matrix, owing to toughening mechanisms such as crack deflection and bridging between Al2O3 grains. This microstructural evolution also affected the formation of continuous conductive pathways connecting the elongated Ni particles. As a result, the electrical resistivity of the composite dramatically decreased to 3.6 × 103 Ωcm at 15 vol% Ni and was further reduced to 1.1 × 102 Ωcm when the volume fraction of Ni was increased to 20 vol%. These results suggest that controlling the amount of Ni, which greatly affects the microstructural evolution, can simultaneously enhance the mechanical and electrical properties of Al2O3/Ni composites.

In this paper, data mining is performed based on the directed percolation theory influence mining algorithm, analyzing the maximum influence node mining proportion threshold and calculating the maximum eigenvalue of the non-return matrix. The convergence conditions of the iterative process of immobile points are analyzed to obtain the percolation threshold of the information dissemination process of directed percolation, and the initial vector is selected among the node-associated features to form the iterative formula to mine the maximum percolation theoretical influence. According to the results, students' focus on craftsmanship has risen significantly, and the percentage of students who consider persistent concentration spirit important has increased to 75%. The directed percolation theory's craftsmanship spirit is crucial for developing students' vocational skills and comprehensive literacy.

The paper presents studies of the site percolation phenomenon for square matrixes with dimensions L = 55, 101 and 151 using the Monte Carlo computer simulation method. The number of iterations for each matrix was 5 × 106. An in-depth analysis of the test results using the metrological approach consisting of determining the uncertainty of estimating the results of iterations with statistical methods was performed. It was established that the statistical distribution of the percolation threshold value is a normal distribution. The coefficients of determination for the simulation results in approximations of the percolation threshold using the normal distribution for the number of iterations 5 × 106 are 0.9984, 0.9990 and 0.9993 for matrixes with dimensions 55, 101 and 151, respectively. The average value of the percolation threshold for relatively small numbers of iterations varies in a small range. For large numbers of iterations, this value stabilises and practically does not depend on the dimensions of the matrix. The value of the standard deviation of the percolation threshold for small numbers of iterations also fluctuates to a small extent. For a large number of iterations, the standard deviation values reach a steady state. Along with the increase in the dimensions of the matrix, there is a clear decrease in the value of the standard deviation. Its value is about 0.0243, about 0.01 and about 0.012 for matrixes with dimensions 55, 101 and 151 for the number of iterations 5 × 106. The mean values of the percolation threshold and the uncertainty of its determination are (0.5927046 ± 1.1 × 10−5), (0.5927072 ± 7.13 × 10−6) and (0.5927135 ± 5.33 × 10−6), respectively. It was found that the application of the metrological approach to the analysis of the percolation phenomenon simulation results allowed for the development of a new method of optimizing the determination and reducing the uncertainty of the percolation threshold estimation. It consists in selecting the dimensions of the matrix and the number of iterations in order to obtain the assumed uncertainty in determining the percolation threshold. Such a procedure can be used to simulate the percolation phenomenon and to estimate the value of the percolation threshold and its uncertainty in matrices with other matrix shapes than square ones. [ABSTRACT FROM AUTHOR]

A computer simulation method was firstly used to determine the theoretical percolation threshold of the conductive filler/polymer composites. Firstly, the model by mixing two-phase graphene/ polyurethane composite in a certain proportions was set up, Secondly, effective medium theory is used for the computer simulation calculation to obtain the theoretical percolation threshold of the two-phase graphene/ polyurethane electrothermal material. The simulation results show that the electrothermal composite reaches the theoretical percolation in a graphene addition amount of 3.4 wt%. Based on the above simulation results, a graphene/polyurethane composite aqueous solution was successfully prepared by the solution blending method. Experimental results show that the electrothermal composite material reaches the percolation threshold by the use of 3.7 wt% graphene content. Finally, the mesh electrothermal material was prepared by coating the graphene/polyurethane slurry, and electrothermal temperature of the mesh is 50 °C at 24 V. [ABSTRACT FROM AUTHOR]

Smart concrete is capable of self-assessing its state of stress and strain. It is produced by tailoring the electrical conductivity of concrete with the addition of conductive materials such as carbon fiber. This paper aims at determining the electrical conductivity of smart concrete materials with randomly dispersed carbon fibers. It unravels the conduction mechanism and establishes a theoretical basis of the percolation threshold for conduction. A numerical model for concrete with carbon fiber is developed. The electrical conduction through the concrete is calculated by solving the governing equations based on Kirchhoff's reformulation of Ohm's Law. More than ten thousand cases with varying fiber topologies, fiber fraction ratios and aspect ratios have been generated to account for the randomness of distribution and their electrical properties are evaluated. By analyzing those results, the mechanism behind the percolation threshold is explained. Finally, an algebraic relationship is posited to determine the percolation threshold has been evaluated. The relationship has been validated with experimental results. The results are extremely valuable for the design of self-sensing smart concrete. [ABSTRACT FROM AUTHOR]

Electrical Distribution Systems (EDS) are extensively penetrated with Distributed Energy Resources (DERs) to cater the energy demands with the general perception that it enhances the system's resilience. However, integration of DERs may adversely affect the grid operation and affect the system resilience due to various factors like their intermittent availability, dynamics of weather conditions, non-linearity, complexity, number of malicious threats, and improved reliability requirements of consumers. This paper proposes a methodology to evaluate the planning and operational resilience of power distribution systems under extreme events and determines the withstand capability of the electrical network. The proposed framework is developed by effectively employing the complex network theory. Correlated networks for undesirable configurations are developed from the time-series data of active power monitored at nodes of the electrical network. For these correlated networks, compute the network parameters such as clustering coefficient, assortative coefficient, average degree, and power law exponent for the anticipation; and percolation threshold for the determination of the network's withstand capability under extreme conditions. The proposed methodology is also suitable for identifying the hosting capacity of solar panels in the system while maintaining resilience under different unfavorable conditions and identifying the most critical nodes of the system that could drive the system into non-resilience. This framework is demonstrated on IEEE 123 node test feeder by generating active power time-series data for a variety of electrical conditions using the simulation software, GridLAB-D. The percolation threshold resulted as an effective metric for the determination of the planning and operational resilience of the power distribution system. [ABSTRACT FROM AUTHOR]

The AC electrical properties of EVA- and NBR-based composites filled with different conductive fillers were investigated. Result shows several magnitudes of increment in AC electrical conductivity and dielectric permittivity after the addition of these conductive fillers, indicating that these materials can be used as supercapacitors. The magnitude of increment was varied according to polymer and filler types. Herein, we also have tested the applicability of different sigmoidal models to find out the percolation threshold value of permittivity for these binary polymer composite systems. It is observed that except sigmoidal–Boltzmann and sigmoidal–dose–response models, other sigmoidal models exhibit different values of percolation threshold when considered for any particular polymer composite system. The paper discusses the variation in results of percolation threshold with an emphasis on the advantages, disadvantages and limitations of these models. We also have applied the classical percolation theory to predict the percolation threshold of permittivity and compared with all the reported sigmoidal models. To judge the unanimous acceptability of these models, they tested vis-à-vis the permittivity results of various polymer composites reported in published literature. To comprehend, all the models except the sigmoidal–logistic-1 model were successfully applicable for predicting the percolation threshold of permittivity for polymer composites. [ABSTRACT FROM AUTHOR]

The study suggests that GB-CNT/PA6 multiscale hybrid composite can be used to create a network structure with controllable electrical conductivity, making it a promising material for various practical applications. The paper introduces a new method for controlling electrical conductivity of composite materials by creating a segregated network morphology (SNM) using a glass bubble (GB)-carbon nanotube (CNT)/polyamide 6 (PA6) multiscale hybrid composite. Instead of relying solely on CNTs, the addition of GB allows for a more economical process by reducing the required CNT concentration to achieve the desired electrical conductivity. The paper also analyzes the effects of varying GB and CNT content on electrical conductivity based on percolation theory. The results demonstrate an 18.8 times increase in electrical conductivity with the SNM approach. The study proposes that this approach could be used to create composite materials with controllable electrical conductivity, making them suitable for various applications.

Polyvinyl alcohol is the most commercially water-soluble biodegradable polymer, and it is in use for a wide range of applications. It shows good compatibility with most inorganic/organic fillers, and enhanced composites may be prepared without the need to introduce coupling agents and interfacial modifiers. The patented high amorphous polyvinyl alcohol (HAVOH), commercialized with the trade name G-Polymer, can be easily dispersed in water and melt processed. HAVOH is particularly suitable for extrusion and can be used as a matrix to disperse nanocomposites with different properties. In this work, the optimization of the synthesis and characterization of HAVOH/reduced graphene oxide (rGO) nanocomposite obtained by the solution blending process of HAVOH and Graphene Oxide (GO) water solutions and 'in situ' reduction of GO is studied. The produced nanocomposite presents a low percolation threshold (~1.7 wt%) and high electrical conductivity (up to 11 S/m) due to the uniform dispersion in the polymer matrix as a result of the solution blending process and the good reduction level of GO. In consideration of HAVOH processability, the conductivity obtained by using rGO as filler, and the low percolation threshold, the nanocomposite presented here is a good candidate for the 3D printing of a conductive structure. [ABSTRACT FROM AUTHOR]

The aim of this work is a comprehensive study of the effect of variable atomic composition and structural-phase state of (CoFeZr)x(MgF2)100−x nanocomposites (NCs) on their nonlinear electronic and magnetic/magneto-optical properties. Micrometer-thick nanocomposite layers on the glass substrates were obtained by ion-beam sputtering of a composite target in the argon atmosphere in a wide range of compositions x = 9–51 at·%. The value of the resistive percolation threshold, xper = 34 at·%, determined from the concentration dependencies of the electrical resistance of NCs, coincides with the beginning of nucleation of metallic nanocrystals CoFeZr in MgF2 dielectric matrix. The absolute value of maximum magnetoresistance of NCs is 2.4% in a magnetic field of 5.5 kG at x = 25 at·%, up to the percolation threshold. Two maxima appear in the concentration dependencies of magneto-optical transversal Kerr effect, one of which, at x = 34 at·%, corresponds to the formation of CoFeZr alloy nanocrystals of a hexagonal structure, and the second one at x = 45 at·% corresponds to the phase transition of nanocrystals from a hexagonal to a cubic body-centered structure. The magnetic percolation threshold in (CoFeZr)x(MgF2)100−x system at xfm = 34 at·%, with the appearance of a hysteresis loop and a coercive force of Hc ≈ 8 Oe, coincides with the resistive percolation threshold xper = 34 at·%. Concentration dependence of the coercive force showed that at low contents of metallic alloy x < 30 at·%, NCs are superparamagnetic (Hc = 0). With an increase of the alloy content, in the region of magnetic and resistive percolation thresholds, NCs exhibit a magnetically soft ferromagnetic character and do not change it far beyond the percolation threshold, with the maximum value of the coercive force Hc < 30 Oe. [ABSTRACT FROM AUTHOR]

The paper presents the results from studies of the electrical and magnetic properties of an inhomogeneous percolated medium based on the theory of percolation. The application of this theory has a wide and varied range. Examples include hopping conductivity in semiconductors, properties of porous materials, etc. It was found that, with approaching the percolation threshold pc = 0.35, the resistivity decreases, and the electrical conductivity increases accordingly. An increasing number of individual ferromagnetic nanogranules in (p)–Fe2O3–(1–p) (MBT) composites merge with the formation of individual Fe2O3 clusters in the bentonite matrix, which combine to form a continuous network of clusters. This is due to the fact that the resistivity ρ of the composite is mainly determined by the magnetic component of the latter. [ABSTRACT FROM AUTHOR]

• The effective permeability (EP) affected by network percolation is investigated. • A bimodal distribution of EP for isotropic network is found and analyzed. • Effects of fracture density, fracture–matrix permeability contrast are studied. • Finite-size effect of EP is revealed and studied. • Different EP characteristics of percolating and non-percolating samples are studied. This study investigates the effective permeability of fractured porous media with fracture density near the percolation threshold. A new equivalent matrix-fracture network (EMFN) model was introduced, the code was used to efficiently deal with the huge number of modeling works for steady state flow in fractured porous media. The numerical model was verified by comparing with two previous seepage methods. We conducted a series of Monte Carlo simulations to explore the relationship between permeability discontinuity and three factors, namely fracture density, contrast between fracture and matrix permeability, and the scale of research domain. It was found that the effective permeability presents a bimodal distribution with specified fracture density in the transition regime. Each bimodal function can be subdivided into two well-fitting log-normal functions according to the percolation state to obtain analyzable average permeabilities. The results revealed significant differences between percolating and non-percolating configurations in the response to the change of each of the three factors mentioned above. More importantly, the finite-size effect plays an important role when fracture density is lower than or close to the percolation threshold; but this effect disappears gradually as the increase of fracture density. A stereoscopic approach is introduced to rationalize the scale effect. [ABSTRACT FROM AUTHOR]

The results of experimental studies of ohmic conductivity degradation in the ensembles of nanostructured anatase bridges under a long-term effect of direct current are presented. Stochastic sets of partially conducting inter-electrode bridges consisting of close-packed anatase nanoparticles were formed by means of the seeding particles from drying aqueous suspensions on the surfaces of silica substrates with interdigital platinum electrodes. Multiple-run experiments conducted at room temperature have shown that ohmic conductivity degradation in these systems is irreversible. It is presumably due to the accumulated capture of conduction electrons by deep traps in anatase nanoparticles. The scaling analysis of voltage drops across the samples at the final stage of degradation gives a critical exponent for ohmic conductivity as ≈1.597. This value satisfactorily agrees with the reported model data for percolation systems. At an early stage of degradation, the spectral density of conduction current fluctuations observed within the frequency range of 0.01–1 Hz decreases approximately as 1 / ω , while near the percolation threshold, the decreasing trend changes to ≈ 1 / ω 2 . This transition is interpreted in terms of the increasing contribution of blockages and subsequent avalanche-like breakdowns of part of the local conduction channels in the bridges into electron transport near the percolation threshold. [ABSTRACT FROM AUTHOR]

The effect of SDS in NRL/GNP–SDS composites.

3 mol% yttria tetragonal zirconia polycrystal (3YTZP) composites with orthotropic or isotropic microstructures were obtained incorporating few layer graphene (FLG) or exfoliated graphene nanoplatelets (e-GNP) as fillers. Electrical conductivity was studied in a wide range of contents in two configurations: perpendicular (σ ꓕ) and parallel (σ //) to the pressing axis during spark plasma sintering (SPS). Isotropic e-GNP composites presented excellent electrical conductivity for high e-GNP contents (σ ꓕ ∼ 3200 S/m and σ // ∼ 1900 S/m for 20 vol% e-GNP), consequence of their misoriented distribution throughout the matrix. Optimum electrical performance was achieved in the highly anisotropic FLG composites, with high electrical conductivity for low contents (σ ꓕ ∼ 680 S/m for 5 vol%), percolation threshold below 2.5 vol% FLG and outstanding electrical conductivity for high contents (σ ꓕ ∼ 4000 S/m for 20 vol%), result of the high aspect ratio and low thickness of FLG. • Significantly different electrical performance of orthotropic/isotropic composites. • Significantly higher σ// for e-GNP vs FLG composites for 10 and 20 GBN vol%. • Highest values of σ⊥ and lowest percolation threshold in anisotropic FLG composites. • Excellent electrical performance for isotropic composites with 10 and 20 e-GNP vol%. • GBN aspect ratio, thickness and defects determine composite electrical conductivity. [ABSTRACT FROM AUTHOR]