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Heat conduction plays a vital role in the performance and durability of any component. A wide range of applications are available that demand a good heat conduction ability. The property used to understand the heat conduction behaviour in a solid is called effective thermal conductivity (Keff). It is recommended to reinforce an adequate amount of filler material in the matrix to increase the Keff of the composite. The current study used carbon black (CB) particulates, a by-product of waste tyre pyrolysis, as the reinforcing agent in the epoxy resin. The composites are prepared by solution casting method with different volume % of filler. To study the thermal behaviour of samples, effective thermal conductivity, glass transition temperature (Tg) and co-efficient thermal expansion (CTE) are measured as a function of vol.% of filler. After plotting the experimental results, it is noticed that the Keff and Tg are increased and CTE is decreased with an increase in vol.% of CB. The percolation threshold is also calculated from the Keffvs. vol.% curve. Various mathematical models are incorporated to verify the experimental results of effective thermal conductivity. A finite element method (FEM) based numerical model is also developed to study the thermal conductivity behaviour of composites. ANSYS MECHANICIAL APDL is used for the FEM analysis. The FEM results showed a marginal variation from experimental data at 0.99 vol.% of CB. The reason behind this is the formation of voids during sample making, the effect of which is not taken in FEM. [ABSTRACT FROM AUTHOR]

In this study, the effect of the polymer matrix structure on the rheological and electrical percolation threshold of polymer/carbon black (CB) conductive polymer composites (CPCs) was investigated. Poly(lactic acid) (PLA) and high‐density polyethylene (HDPE) were used as polymer matrices. Through rheological analyses, an increase in complex viscosity was observed with increasing CB concentration, accompanied by a reduction in the Newtonian plateau. Additionally, an increase in the solid‐like behavior was observed, suggesting the formation of a percolated network. The rheological percolation threshold was found to be 5.13% CB mass fraction for the PLA/CB composite and 10.72% for the HDPE/CB composite. Electrical conductivity results were fitted to the sigmoidal Boltzmann model, and its derivative was used to identify the electrical percolation threshold. For PLA/CB, this threshold was reached at 5.39% CB mass fraction, while for HDPE/CB, it occurred at 5.75%. Morphology analysis by scanning electron microscopy and atomic force microscopy indicated that the polymer matrix structure affected the distribution/dispersion of the CB particles within the polymer matrix. Highlights: The effect of polymer matrix structure on polymer/CB CPCs was investigated.The crystallinity of the polymer matrix affected the percolation threshold.PLA/CB showed higher conductivity than HDPE/CB CPCs. [ABSTRACT FROM AUTHOR]

Some models have been proposed for the electrical conductivity of graphene-filled nanocomposites, but they have not reflected the characteristics of an imperfect interphase surrounding the graphene nanosheets. In this article, the size and conductivity of an imperfect interphase are used to develop a model for conductivity of the graphene/polymer system. Also, “Y,” the degree of conduction transfer through an imperfect interphase, is expressed as graphene dimensions and interphase conductivity to define the effective converse aspect ratio and effective filler portion in the samples. The developed model for nanocomposite conductivity is examined by the experimental data of some samples. Furthermore, the influences of various factors on “Y,” percolation onset, and nanocomposite conductivity are investigated. Thin and large nanosheets, poor filler conductivity, and high interphase conductivity produce a high “Y.” Likewise, “Y” and graphene volume portion (φf)({\varphi }_{\text{f}}) significantly govern the conductivity of samples. Y = 9 and φf{\varphi }_{\text{f}} = 0.03 yield the highest nanocomposite conductivity of 16 S/m, while Y < 2 or φf{\varphi }_{\text{f}} < 0.022 cannot improve the conductivity of samples.

This paper presents the results of an experimental study of the percolation behavior of the complex dielectric constant of ceramic matrix composites (CMC). Samples of piezoactive CMC were obtained by joint sintering of synthesized PZT piezoceramic powder (matrix) and crushed particles of sintered PZT piezoceramics (filler) of different compositions. The experimental dependencies of real and imaginary parts of the complex dielectric constant of CMC on the porosity of piezoceramic matrix and volume content of ceramic filler particles were measured and analyzed. It was shown that the additional porosity of the ceramic matrix resulting from sintering of the CMC masks the dielectric percolation transition, that actually occurs at the volume concentration of ceramic filler close to percolation threshold (V ∼ 1/3). [ABSTRACT FROM AUTHOR]

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.

The behavior and evolution trajectory of hydrofracture, which show a close relationship with the hydrothermal mineralization process, is greatly influenced by fluid flow and fluid pressure. However, further investigation is needed to achieve an in-depth understanding of the formation and evolution mechanisms behind the link between the rate of fluid pressure development and the occurrence of induced hydrofracture and mineralization process. We considered different fluid pressure development rates as the initial data for a cellular automaton model. With the increase in the fluid pressure increase rates, the corresponding hydrofracture became more focused, changing in scale from a large number of small-scale hydrofractures to a small number of large-scale hydrofractures. Episodes of fluid pressure fluctuation induced by either low or high fluid pressure increase rates were shown to trigger mineral precipitation and further contribute to the generation of strong spatially structured and enriched geochemical patterns. Moreover, the correlation length at the percolation threshold, which is of great significance to the degree and scale of mineralization, increased with the increasing fluid pressure increase rates. It was concluded that computational grids with high fluid pressure increase rates are much more prone to produce enriched geochemical patterns with strong spatial structures than grids with low fluid pressure increase rates owing to a larger correlation length at the percolation threshold. These results suggest that the way of fluid pressure development is a key factor for quantifying the behavior of hydrofracture and mineralization process. [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]

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. [ABSTRACT FROM AUTHOR]

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]

Soil aggregates are clumps of soil particles bound to each other through organic matter. Soil with aggregates has favorable features for crop cultivation, such as adequate water retention and filtration. This feature was clarified from the perspective of the network formed by pores. The connectivity of pore networks in soil was investigated in this study using virtually generated porous media with and without aggregates. The connectivity for drainability was evaluated using the percolation probability (PP), which is represented as a curve of the ratio of the largest subnetwork formed by pores that are larger than a certain value as the value decreases from the maximum to the minimum pore size. Compared with the PP of porous media without aggregates, PP with aggregates has a smaller percolation threshold, which is the point at which PP rises sharply, indicating that soil with aggregates has high drainability. Furthermore, PP without aggregates asymptotically approached the diagonal, whereas PP with aggregates left the diagonal halfway and approached again. This demonstrates that the aggregates contain loosely isolated subnetworks and that the water retained in the aggregates is difficult to drain once the aggregates are filled with water. These findings enhanced our understanding of the water retention property of soils with aggregates. [ABSTRACT FROM AUTHOR]

Abstract Pharmaceutical controlled-release formulations are systems developed by a set of unit operations to achieve a satisfactory combination between a drug and excipients to allow its gradual release. These devices must simultaneously meet criteria for stability, biocompatibility, safety, efficacy, scalability at industrial volumes, and technological efficiency for drug release. Controlled-release systems (CRSs) must release drugs in a way that maintains an adequate concentration in the organism, a requirement that is challenging to meet in practice. Even though novel CRSs may be designed with new materials as excipients, new drugs, or emerging manufacturing technologies, the mechanisms for drug release continue to be governed by a set of similar physicochemical phenomena such as diffusion, swelling, or erosion. These phenomena are too complex to be analyzed by numerical methods; however, they are relatively accessible by probabilistic models especially the Monte Carlo simulation. In this review, we discuss key findings related to the use of this probabilistic method for analyzing the drug-controlled release process in different pharmaceutical devices. Based on this evidence, we propose their potential application in the characterization of new drug-controlled release systems, synergy with other computational methods, and their capability to be adapted for in vivo or in vitro kinetic analysis.

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.

This paper presents the results of an experimental study of the percolation behavior of the complex dielectric constant of ceramic matrix composites (CMC). Samples of piezoactive CMC were obtained by joint sintering of synthesized PZT piezoceramic powder (matrix) and crushed particles of sintered PZT piezoceramics (filler) of different compositions. The experimental dependencies of real and imaginary parts of the complex dielectric constant of CMC on the porosity of piezoceramic matrix and volume content of ceramic filler particles were measured and analyzed. It was shown that the additional porosity of the ceramic matrix resulting from sintering of the CMC masks the dielectric percolation transition, that actually occurs at the volume concentration of ceramic filler close to percolation threshold (V ∼ 1/3).

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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 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 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 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]

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.

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]

Conductive polymer composites (CPCs) are promising alternatives to metal conductive materials due to their light-weight and low-cost. This work investigates the effect of the crystallization behavior of the matrix on the electrical property of CPCs, where semi-crystalline polypropylene (PP) and amorphous styrene-butadiene-styrene tri-block copolymer (SBS) are selected as a matrix, respectively, and conductive carbon black (CB) particles are introduced into matrixes by melting blending. Based on the electrical properties of CPCs with various CB contents and percolation theory, the percolation threshold of 1.8 vol% in PP matrix composites is obtained, much lower than that of SBS matrix composites (5.4 vol%). The analysis with a polarizing microscope and differential scanning calorimeter confirms that such a significant difference in percolation threshold between two composites is due to the crystallization behavior while the crystallization induced segregated structure is proposed. Finally, the rheology behaviors and mechanical properties are characterized for microstructures and applications, respectively. [ABSTRACT FROM AUTHOR]

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]

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 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]

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]

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.

[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]

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 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]

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]

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]