Percolation threshold Research Papers - Academia.edu (original) (raw)

2025, Journal of Physics: Condensed Matter

We combine theoretical and experimental results to study percolation-driven transport phenomena in an irradiated material. We show that whereas the first transition takes place at the value of amorphous fraction p 1 ≈ 0.3, the second transition corresponds to the percolation of depleted phase. The knowledge of the radius of depletion sphere of the isolated damaged region allows one to predict the radiation dose at which the second percolation transition takes place, with dramatic increase in transport. Irradiating a material with energetic ions or doping it with radioactive elements results in dramatic changes of its important physical properties. These changes are versatile and include altering such characteristics as transport, density, hardness and conductivity. While in some applications these changes are sought after, other may often appear as undesirable by-products. An example of this situation is using a material as a host, or a waste form, to immobilize highly radioactive nuclear waste and weapons-grade plutonium. Here, an immobilizing waste form is supposed to prevent the radioactive substance from spreading and harming the environment. The crucial question is how effective a waste form will remain over the required period of time, which for various isotopes varies from tens to tens of thousands of years. How does the ability of a waste form to immobilize radioactive substance change as it accumulates the damage? In this paper we look into how the chemical transport properties of a material change with increasing the degree of self-irradiation. Several materials of different chemistries and structures have been proposed as waste forms . Zircon, ZrSiO 4 , has been proposed to immobilize weapons-grade plutonium, since in nature it can contain radioactive elements for geologic times, although the structure is found to be amorphized . Whether or not it will be used in practice, zircon provides a good case study, due to the availability of natural damaged samples. Here, we combine experimental and simulation results, as well as basic results from

2025, The Journal of Physical Chemistry B

Much effort has been directed at the fabrication of carbon nanotubes (CNTs)/polymer composites and the characterization of their physical properties. Among them, composites comprising CNTs and the biocompatible polymers are of special interest due to their potential for specific biomedical applications. We report the preparation of the MWCNT/poly(L-lactide) composite and the corresponding spectroscopic (Raman) and the microscopic (SEM, TEM) characterization. The electronic transport, thermal properties, and biocompatibility of this composite have also been investigated. The Raman spectroscopic analysis suggests the interaction between PLLA and MWCNT occurs mainly through the hydrophobic C-CH 3 functional groups. The DC conductivity of the composite increases as the MWCNT loading is increased. Such behavior can be described by a percolation mechanism in which a percolation threshold at about 14 wt % MWCNT loading is observed with the maximum end conductivity of 0.1 S‚cm -1 . The DSC study of the PLLA/MWCNT composite reveals that the MWCNTs in the composite have the effect of inducing crystallization and plasticizing the polymer matrix. The results from the cell culture test suggest that the presence of MWCNT in the composite inhibits the growth of the fibroblast cells.

2025, Physical review

When differential real-space renormalization-group theory was proposed by Hilhorst, Schick, and van Leeuwen, they suggested that their approach could only be applied to lattice models for which a star-triangle transformation exists. However, differential renormalization-group equations for the square Ising model have recently been proposed whose derivation does not involve the star-triangle transformation. We show that the latter equations are not exact renormalization-group equations by an analysis that reveals some essential limitations of the present formulation of differential real-space renormalization. We investigate the structure of the renormalization-group flow equations obtained in this method and uncover a strong property of these equations that simplifies the calculations in actual applications of the theory. However, the status and implications of this property, which embodies the crux of the theory, are not yet fully understood.

2025, Materials Today: Proceedings

Styrene butadiene rubber is seen as one of the great vast chemical substances utilized as attachment, hence we talked about in this investigation to enhance its properties. The nano composites have been organized by way of mechanical mixing the use of two-roll mills. Aluminum oxide nanofiller suspensions have been brought to SBR elastic and the scrape and spectral studies have been overviewed. This investigation covers the have an effect on of aluminum oxide on reflex tests of SBR elastic bolstered with aluminum oxide particles. Mechanical test outcomes confirmed that enhancement in flexile strength, lengthening and tear resistance. Scrape check outcomes confirmed that the aluminum nano particles ought to decorate the scrape opposition of Styrene Butadiene rubber mould because of fantastic properties of alumina nano particles. The composites had been set up with (2 to 12 wt%) of nano aluminum oxide molecules. The effects had proven that the rigidity and curve excellent are enhanced.

2025, Physical Review E

The fractal structure of high-temperature graphs of the three-dimensional Ising and XY models is investigated by simulating these graphs directly on a cubic lattice and analyzing them with the help of percolation observables. The Ising graphs are shown to percolate right at the Curie critical point. The diverging length scale relevant to the graphs in the vicinity of the percolation threshold is shown to be provided by the spin correlation length. The fractal dimension of the high-temperature graphs at criticality is estimated to be D = 1.7349(65) for the Ising and D = 1.7626(66) for the XY model.

2025, Zonodo

We present the first unified theory of mathematical reality, demonstrating that all mathematical structure manifests in physical reality through exactly two fundamental pathways: Direct Manifestation and Dimensional Cascade Scaling. Through rigorous mathematical validation achieving statistical significance of P < 10-54 , we prove that the Dimensional Cascade Framework governs not only universal physical constants but also prime number patterns, electromagnetic spectra, and natural geometric structures. The theory successfully derives the fine structure constant with 99.996% precision, explains eight universal constants with sub-0.1% accuracy, validates perfect Fibonacci manifestations, and demonstrates that prime numbers follow characteristic cascade scaling with sub-1% precision at high complexity levels. This complete unification reveals the mathematical universe hypothesis in its most elegant form: mathematics is physical reality experiencing itself through two distinct but universal interface pathways. The theory makes specific testable predictions for particle physics, electromagnetic phenomena, and mathematical structures, providing the foundation for experimental validation of the most comprehensive theoretical framework in the history of mathematical physics.

2025, Physical Review Letters

A percolation transition in the vortex state of a superconducting 2H-NbSe 2 crystal is observed in the regime where vortices form a heterogeneous phase consisting of ordered and disordered domains. The transition is signaled by a sharp increase in critical current that occurs when the volume fraction of disordered domains, obtained from pulsed measurements of the currentvoltage characteristics, reaches the value 04 . 0 26 . 0 ± = c P . Measurements on different vortex states show that while the temperature of the transition depends on history and measurement speed, the value of P c and the critical exponent characterizing the approach to it, r =1.97 ± 0.66, are universal.

2025, Crystals

The mechanical, electrical, and glass transition behaviors (Tg) of polymethylmethacrylate (PMMA)–metal systems have been studied. Considering both the particle size and the metal filler concentration, the electrical conductivity showed a clear dependence on the sample thickness to reach percolation. An increase of up to 400% of strain-to-failure for the 2% v/v of nanometric filler composites in the mechanical test was observed. Tg analysis showed a decrease in the glass transition temperature when the increase of nanometric metallic filler reached the limit of 2% v/v. Over this concentration, the Tg values showed a tendency to reach the original value of the polymeric matrix without conductive filler. For the 20% v/v micrometric filler composites, the strain-to-failure increased up to 58%, but in the Tg analysis of this composite, no relevant changes were observed when the micrometric metallic filler was increased.

2025, Journal of Applied Physics

The magnetic properties of the strontium hexaferrite nanoparticles were studied as they were embedded at different concentrations in poly(vinyl alcohol) (PVA) nanofibers. These nanoparticles were prepared using the Pechini method and a low frequency sonication process obtaining a 3.4 nm average diameter. The composite consisting of hard magnetic nanoparticles homogeneously dispersed in a polymeric matrix was fabricated using a homemade electrospinning with 25 kV DC power supply. The obtained nanofibers had an average diameter of 110 nm, and nanoparticles were arranged and distributed within the nanofibers under the influence of a strong electric field. The configuration of the magnetic nanoparticles in the PVA nanofibers was such that the interparticle exchange interaction became negligible, while the magnetostatic interaction turned out predominant. The results reveal a considerable improvement in the energy product (BHmax) and in the squareness ratio (Mr/Ms) for nanoparticle conce...

2025, Journal De Physique

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2025, arXiv (Cornell University)

We study a process termed agglomerative percolation (AP) in two dimensions. Instead of adding sites or bonds at random, in AP randomly chosen clusters are linked to all their neighbors. As a result the growth process involves a diverging length scale near a critical point. Picking target clusters with probability proportional to their mass leads to a runaway compact cluster. Choosing all clusters equally leads to a continuous transition in a new universality class for the square lattice, while the transition on the triangular lattice has the same critical exponents as ordinary percolation -violating blatantly the basic notion of universality.

2025, Sinaya A Philippine Journal for Senior High School Teachers and Students

While promising as an energy production alternative through its sustainability and wastewater treatment utility, a microbial fuel cell is not widely used due to its low power output and high cost. The development of advanced electrode materials is currently being pursued to solve this problem. A zinc-graphene quantum dot nanocomposite was modeled using percolation theory as a prospective advanced electrode material. During extracellular electron transfer, the electrical conductivity properties of the material were studied through cellular percolation models, percolation probability functions, and electrical conductivity curves. These models were compared against those of the conventional graphite electrodes and the leading graphene electrodes. The nanocomposite was found to conduct at low probabilities of open sites and exhibit the highest electrical conductivity of the three materials for the longest duration across the interval. Based on the models, Zn-GQD was demonstrated to be an ideal MFC electrode material for its balance between the early onset of conduction and decently high electrical conductivity.

2025, Physical Review B

Ponte-Castañeda, Pedro, "Second-order theory for nonlinear dielectric composites incorporating field fluctuations" (2001). Departmental Papers (MEAM). 124.

2025, Probability Theory and Related Fields

We consider the d-dimensional Bernoulli bond percolation model and prove the following results for all P<Pc: (1) The leading power-law correction to exponential decay of the connectivity function between the origin and the point (L, 0, ..., 0) is L -(d-1)/2. (2)The correlation length, ~(p), is real analytic. (3)Conditioned on the existence of a path between the origin and the point (L, 0 .... ,0), the hitting distribution of the cluster in the intermediate planes, Xa = qL, 0 < q < 1, obeys a multidimensional local limit theorem. Furthermore, for the two-dimensional percolation system, we prove the absence of a roughening transition: For all p >Pc, the finite-volume conditional measures, defined by requiring the existence of a dual path between opposing faces of the boundary, converge -in the infinite-volume limit -to the standard Bernoulli measure.

2025, Physical Review E

In a recent paper (arXiv:cond-mat/0911.2514), one of us (FYW) considered the Potts model and bond and site percolation on two general classes of two-dimensional lattices, the triangulartype and kagome-type lattices, and obtained closed-form expressions for the critical frontier with applications to various lattice models. For the triangular-type lattices Wu's result is exact, and for the kagome-type lattices Wu's expression is under a homogeneity assumption. The purpose of the present paper is two-fold: First, an essential step in Wu's analysis is the derivation of lattice-dependent constants A, B, C for various lattice models, a process which can be tedious. We present here a derivation of these constants for subnet networks using a computer algorithm. Secondly, by means of a finite-size scaling analysis based on numerical transfer matrix calculations, we deduce critical properties and critical thresholds of various models and assess the accuracy of the homogeneity assumption. Specifically, we analyze the q-state Potts model and the bond percolation on the 3-12 and kagome-type subnet lattices (n × n) : (n × n), n ≤ 4, for which the exact solution is not known. To calibrate the accuracy of the finite-size procedure, we apply the same numerical analysis to models for which the exact critical frontiers are known. The comparison of numerical and exact results shows that our numerical determination of critical thresholds is accurate to 7 or 8 significant digits. This in turn infers that the homogeneity assumption determines critical frontiers with an accuracy of 5 decimal places or higher. Finally, we also obtained the exact percolation thresholds for site percolation on kagome-type subnet lattices (1 × 1) : (n × n) for 1 ≤ n ≤ 6.

2025, Polymer Bulletin

Dynamic dielectric properties of an isotactic polypropylene matrix grafted with maleic anhydride (CA 100) and then crosslinked by polyether amine molecules and reinforced with different weight percentages of graphite nanoplatelets (GNPs), KNG180, were studied for the first time and compared to those obtained by DMA (Dynamic Mechanical Analysis). The main objective of this work was to investigate the reinforcement effect of GNPs focusing on the GNPs/matrix interfacial adhesion using dynamic dielectric relaxation spectroscopy in the frequency range from 0.1 Hz to 1 MHz and temperature range from 20 to 140 °C. The obtained interfacial polarization increments Δε MWS from MWS (Maxwell Wagners Sillars) relaxation showed a threshold value of 3% in weight of KNG180. This analysis suggests that interfacial compatibility between matrix and fillers in the case of nanocomposite KNG180 3 wt% is higher than those of other nanocomposites. A new plasma treatment was used to modify graphite nano-fillers to produce different types of nanocomposites. The 5 wt% plasma treated graphite nanocomposite shows a good dispersion of the nano-fillers but also a high value of Δε MWS , which is an indication of high graphite/graphite interaction. This evolution could show that this material can be close to the formation of an electrical percolation network.

2025

The addition of a carbon material, such as carbon nanotubes (CNTs) or graphite powder (GP)as conductive ingredients transforms the resulting mixture into a conductive material. This yields the possibility of using the new material for other functions different to the structural one, so that it can be considered a multifunctional material, such as the sensing and heating function. Increasing CNTs or/and GP content decreases the resistivity. Once the percolation threshold is reached it makes no sense to increase % because the resistivity is not anymore significantly changed. Then strain-sensing and heating functions can be can be carried in these conductive cement based materials.

2025, Journal of Physics: Condensed Matter

2025, Frontiers in Materials

Hybrid conducting composites comprising thermoplastic polyurethane (TPU) and mixtures of carbon black modified with polypyrrole (CB-PPy) and carbon nanotubes (CNT) were prepared by melt mixing process. The electrical conductivity, rheological properties and electromagnetic shielding effectiveness (EMI SE) of TPU/CB-PPy and TPU/CNT composites were also investigated those results observed for TPU/CB-PPy/CNT hybrid composites. TPU/CNT composites show a very sharp insulator-conductor transition and the electrical percolation threshold was about 1 wt% of CNT, which was lower than that found for TPU/CB-PPy (7 wt%). Moreover, EMI SE values of TPU/CNT composites were higher than those for TPU/CB-PPy due to the denser CNT conductive pathway into TPU matrix. In order to achieve the highest electrical conductivity and EMI SE values, mixtures of CB-PPy/CNT were added in the composites in different mass fractions. In fact, the electrical conductivity values increased by combining CB-PPy and CNT, resulting in hybrid composites of TPU/CB-PPy/CNT with higher EMI SE values when compared to TPU/CB-PPy composites. The present study demonstrates the potential use of hybrid polymer composites containing 5 or 8 wt% of CB-PPy/CNT at specific CB-PPy/CNT ratios with good processabilty and EMI SE values as high as -20 dB indicating the potential use of these materials for electromagnetic shielding application in the X-band frequency region.

2025, Synthetic Metals

Variation of the electrical resistivity under repeated loading-unloading compressive cycles of poly(vinylidene fluoride) (PVDF)/polypyrrole (PPy) blends prepared by solution-casting has been investigated. The insulator-conductor transition of the PVDF/PPy blends was very sharp and the percolation threshold was found to be below 4 wt%. PVDF/PPy blends exhibits a decrease in the electrical resistivity with the applied compressive stress due to the formation of new conducting pathways. Electromechanical response was dependent of PPy amount and the maximum sensitivity was obtained for a blend with a PPy content of 9 wt%, for which the electrical resistivity drops by two orders of magnitude, e.g. from 10 8 to 10 6 cm. The electrical resistivity variation during compressive stress cycles, the reproducibility and the reversibility makes this system a suitable material for the development of pressure sensors.

2025, Polymer Testing

Polypyrrole-coated amorphous silica short fibers (PPy-ASF) were obtained through in situ oxidative polymerization of pyrrole (Py) on the ASF surface by using ferric chloride (FeCl 3 ) as oxidant. These conducting fibers were constituted of PPy particles packed close together to form a continuous conductive layer on the ASF surface which was responsible for electrical conductivity of 0.32 S.cm À1 , similar to that found for pure PPy. The PPy-ASF were blended with polystyrene-block-poly(ethylene-ran-butylene)-block-polystyrene copolymer (SEBS) through solution casting at room temperature to form conductive rubbery (SEBS/PPy-ASF) composites. The electrical conductivity and percolation threshold of SEBS/ PPy-ASF films were evaluated and also compared with PPy filled SEBS blends (SEBS/PPy) prepared under the same processing conditions. SEBS/PPy-ASF displayed lower percolation threshold and higher electrical conductivity values than those found for SEBS/PPy blends at the same conductive filler concentration. The high PPy-ASF aspect ratio (length to diameter ratio, L:D) and their good electrical conductivity allow production of conductive polymer composites at very low percolation threshold. The results obtained in this study reveal that PPy-ASF materials are promising candidates to be used as conductive filler for developing conducting polymer composites.

2025, Energy Exploration & Exploitation

Lithology and physical characteristics between conventional clastic reservoirs and low-porosity and low-permeability reservoirs are very different, hence Archie formula will not be valid for the latter any more. In addition, well logging evaluation of low-porosity and low-permeability reservoir is one key problem but also the research hotspot in recent years. In this study, Pseudo-Percolation Threshold Theory (PPTT) has been introduced into reservoir evaluation. In this research, it has been proved that the aimed layer is lowporosity and low-permeability by studying the reservoir rock. In addition, Pseudo-Percolation Threshold φ ϑ has been determined by analyzing porosity and permeability of oil-bearing cores and process of geologic evolution. Finally, it has been proved that PPTT is much more reliable than Archie formula for low-porosity and low-permeability reservoir by numerical simulation and oilfield data.

2025, Energy Exploration & Exploitation

Lithology and physical characteristics between conventional clastic reservoirs and low-porosity and low-permeability reservoirs are very different, hence Archie formula will not be valid for the latter any more. In addition, well logging evaluation of low-porosity and low-permeability reservoir is one key problem but also the research hotspot in recent years. In this study, Pseudo-Percolation Threshold Theory (PPTT) has been introduced into reservoir evaluation. In this research, it has been proved that the aimed layer is low-porosity and low-permeability by studying the reservoir rock. In addition, Pseudo-Percolation Threshold φν has been determined by analyzing porosity and permeability of oil-bearing cores and process of geologic evolution. Finally, it has been proved that PPTT is much more reliable than Archie formula for low-porosity and low-permeability reservoir by numerical simulation and oilfield data.

2025, Pure and Applied Geophysics

Many observations point to the lithosphere being metastable and close to a critical mechanical point. Exercises in modelling deformation, past or present, across subsurface reservoirs need to take account of this criticality in an efficient way. Using a renormalization technique, the spatial scaling of effective elastic modulus is derived for 2-D and 3-D bodies close to the critical point of through-going fracturing. The resulting exponent, d l , of spatial scaling of effective modulus with size, L dl , takes the values $ )2.5 and )4.2 in two-and three-dimensional space, respectively. The exponents are compatible with those for scaling of effective modulus with fracture density near the percolation threshold determined by other workers from numerical experiments; the high absolute values are also approximately consistent with empirical data from a) fluctuations in depth of a seismic surface; b) '1/k' scaling of heterogeneities observed in one-dimensional well-log samples; c) spatial correlation of slip displacements induced by water injection. The effective modulus scaling modifies the spatial correlation of components of displacement or strain for a domain close to the critical point of fracturing. This correlation function has been used to geostatistically interpolate components of the strain tensor across subsurface reservoirs with the prime purpose of predicting fracture densities between drilled wells. Simulations of strain distributions appear realistic and can be conditioned to surface depths and observations at wells of fracture-related information such as densities and orientations, welltest permeabilities, changes in well-test permeabilities, etc.

2025, Materials Research Express

The objective of this study was to determine the effect of processing on the electrical properties and microstructure of MWCNTs/PMMA nanocomposites made by compression molding. Three different mixing methods were used: mechanical, solution, and melt mixing of the same starting materials. The composite microstructures were found to be segregated, agglomerated, and randomly distributed respectively. Electrical property measurements indicate that the mechanically mixed composites have the lowest percolation threshold of 0.05 phr (0.028 vol% MWCNT). Melt mixed composites have the highest percolation threshold of 4 phr (2.161 vol% MWCNT) while solution mixed composites have a percolation threshold of 2 phr (1.102 vol% MWCNT). These results indicate that the segregated microstructure allows for the CNTs to form a percolated network through the composite more easily than the other two methods. Fitted equivalent circuits to the measured impedance spectra show that after percolation the CNTs...

2025, MRS Proceedings

ABSTRACTThe percolation threshold in a ceramic composite depends on the processing conditions used to fabricate them along with the size and shape of the filler. In this study, borosilicate glass microspheres were used as the matrix material and nanosized antimony tin oxide (ATO) particles were used as the filler. The microsphere/ATO composites were fabricated by hot pressing around the glass transition temperature in order to control the viscosity. The pressure and temperature applied allowed the ATO to be confined to the spaces between certain glass particles, forming percolating networks at low volume fractions of the ATO. The electrical properties were examined using ac impedance spectroscopy. The impedance, electric modulus, and tan δ were studied which allowed for valuable insights in structure-property-processing relationships in these materials, along with determination of the percolation behavior in these composites. This analysis on samples right before percolation indicat...

2025, Journal of the American Ceramic Society

2025, Journal of Electronic Materials

Poly(acrylonitrile-co-butadiene-co-styrene) (ABS), an engineering plastic, was combined with carbon black (CB) to increase its conductivity. The ABS/CB composites were prepared using two different methods: dissolution of ABS in Butan-2-one and manual mixing of the constituent materials. These fabrication methods led to different microstructures, which led to vastly different electrical properties. The microstructures were acquired using scanning electron microscopy (SEM) and optical microscopy, while the electrical conductivity was obtained using impedance spectroscopy. The percolation threshold of the composites fabricated using the manual mixing method was found to be much lower (0.0054 vol.% CB) than that of the composites fabricated using the dissolution method (2.7 vol.% CB).

2025, IEEE Transactions on Components, Packaging and Manufacturing Technology

With the introduction of the European Directives restrictions of hazardous substances, electrically conductive adhesives (ECAs) have received great attention in the field of electronics as a possible replacement of the traditional tinlead soldering technology. So, in this new context, the analysis and the characterization of these alternative materials represent a fundamental topic, above all, from the industrial point of view. Nevertheless, studies on ECAs have rarely been reported in the literature, but more recently research has started to focus on this specific topic. After a comparative assessment concerning soldering materials, this paper focuses attention on their characterization through measurement in order to verify the electrical behavior of the isotropic silver conductive adhesive. In addition, since the soldering process is affected by a large number of variables such as the thickness of the conductive adhesive film, radial velocity, and curing temperature, the optimal selection of the factors is carried out through experimental design theory and the dual-response approach by means of generalized linear models. In this paper, the experimental and comparative studies on soldering made up of epoxy adhesives are carried out, in particular, the adhesives constituted by metallic particles (silver), normally in the form of flakes, in a polymer matrix are considered. The novelty of the kind of adhesive considered is the Ag filler loadings of 50-65% by volume. At these loadings, the materials achieve the percolation threshold and are electrically conductive in all directions after the materials are cured. Two different types of conductive adhesives, characterized by different chemical structures and compositions, are experimented and tested. Then, since the lead-free soldering process is characterized by several critical factors, a statistical approach is used to optimize this process. Experimental results obtained by testing samples with ECA materials prove the validity of this paper. The value of this paper is in the application of a statistical approach to these adhesive materials in order to achieve the optimization of the soldering process with a small number of treatment combinations, satisfying at the same time the stringent requirements and achieving robust electrical interconnections.

2025, Journal of Non-Crystalline Solids

High conductive composites were elaborated by incorporating high aspect ratio (250) silver nanowires in polyimide matrix via solvent mixing way. Silver nanowires were synthesized in solution by polyol synthesis. The composite conductivity reaches the value of 10 2 S•m -1 above a very low percolation threshold (0.48 vol.% of silver nanowires). SEM-FEG images showed that metallic nanowires are well dispersed in PI matrix. They do not influence the physical structure of the polymer. Below the percolation threshold, γ, β and α relaxation modes were detected. γ relaxation mode was fitted to determinate the activation energy value (32.7 kJ•mol -1 ) and the relaxation time (1.5 × 10 -16 s). The mobility associated with the γ relaxation is considered to be localized and non-cooperative. According to the Mott theory, studies on composites below the percolation threshold showed that the conduction mechanism is ruled by tunneling at low temperatures. The transport mechanism led by hopping is activated at -50 °C.

2025

It is argued that the capacitance of a fractal metallic cluster scales with its size as Crc, where 0 < c < 1 is a new charging exponent. A new dimension d, is defined to characterise the electrostatically unshielded surface of the cluster. In effect, c = 2 -d + d, is obtained, where d is Euclidean dimension. Based upon this, and using cluster-size distribution from percolation theory, it is shown that the temperature dependence of the variablerange-hopping conductivity of discontinuous metal films is given by In u a -l/Tx with x = 1/(1 + c). The value of x is predicted to lie in the range 4-1, in close agreement with experiments. It is suggested that the cermet conductivities, which have x = 4, can also be 0953-8984/89/397245

2025, Physics Letters A

We study the signal percolation through heart-like biological system. Starting from an initial distribution of waiting and inactive cells with probabilities p and (1-p) respectively, the signal propagation is observed in terms of active cells. As the signal enters the system from one end, the number of arrival of active sites at the other end is studied and analysis of the system behaviour is made by varying a few important parameters of the system like p switch (switching probability from inactive to waiting) and pact (switching probability from waiting to active). In this connection, the non-regular heart rhythms are discussed. Fraction of paths percolating through the system shows a transition from 0 to 1 near p = pc. Some other important quantities like tortuosity and cluster distribution are discussed. Several critical exponents have been obtained and compared the exponents of standard percolation.

2025, Macromolecular Chemistry and Physics

Thermally reduced graphene modifi ed with cationic ammonium ions (AAG)-affording a stable dispersion in water-self-assembles well by electrostatic interaction on the surface of anionic poly(methyl methacrylate) (PMMA) particles of various sizes, by simple mixing in water. An interconnected 3D electrically conductive network of AAG is effectively generated in the composite when the self-assembled composite is compression molded. The AAG network becomes widemeshed and electrical conduction is improved when the PMMA particle size increases, exhibiting a percolation threshold of electrical conductivity as low as 0.06 vol%. In contrast, the protection of PMMA from oxidation by air is more effective when the network is fi ne-meshed.

2025, ACS Applied Materials & Interfaces

Simultaneously achieving high piezoresistive sensitivity, stretchability and good electrical conductivity in conductive elastomer composites (CECs) with carbon nanofillers are crucial for stretchable strain sensor and electrode applications. Here, we report a facile and environmentally-friendly strategy to realize these three goals at once by using branched carbon nanotubes, also known as carbon nanostructure (CNS). Inspired by the brick-wall structure, a robust segregated conductive network of CNS is formed in the thermoplastic polyurethane (TPU) matrix at very low filler fraction, which renders the composite very good electrical, mechanical and piezoresistive properties. An extremely low percolation threshold of 0.06 wt. %, currently the lowest for TPUbased CECs, is achieved via this strategy. Meanwhile, the electrical conductivity is up to 1 and 40 S/m for the composites with 0.7 and 4 wt. % CNS, respectively. Tunable piezoresistive sensitivity dependent on CNS content is obtained and the composite with 0.7 wt. % filler has a gauge factor up to 6861 at strain ε=660% (elongation at break is 950%). In addition, this strategy also renders the composites attractive tensile modulus. The composite with 3 wt. % CNS shows 450% improvement in Young's modulus versus neat TPU. This work introduces a facile strategy to fabricate highly stretchable strain sensors by designing CNS network structures, advancing understanding the effects of polymer-filler interface on the mechanical and electrical property enhancements for polymer nanocomposites.

2025, Polymer

Biobased epoxy nano-composites composed of untreated multi-wall-carbon-nanotubes (MWCNT) and diphenolic acid-derived biobased epoxy: diglycidyl ether of diphenolate n-butyl ester (DGEDP-Bu), were fabricated. Electrical, rheological, and mechanical percolation thresholds were compared between biobased and commercial bisphenol A (DGEBA) epoxy composites. For both epoxies, nanocomposites loaded with 0.05 -0.2 wt % MWCNT's exhibited electrical and rheological percolation at 0.05 wt % and 0.2 wt % respectively. DMA and tensile results revealed that DGEDP-Bu composites exhibited equivalent or superior properties to DGEBA composites. With 0.2 wt % MWCNT's, DGEDP-Bu nanocomposites exhibited 68 % higher electrical conductivity and a three-fold higher rheological yield stress than those made from DGEBA. Rheological characterization corroborated that continuous MWCNT networks are formed within epoxies between 0.1 and 0.2 wt % MWCNT's. Moreover, upon MWCNT loading, DGEDP-Bu demonstrates equal mechanical performance and better electrical conductivity than DGEBA.

2025

Ca 1Àx Pr x MnO 3Àd (x=0, 0.05, 0.15, 0.1, 0.2, 0.4, 0.67; d=0.02) samples were prepared by a solid-state reaction method. X-ray diffraction analysis showed that all samples prepared were of single phase with orthorhombic structure. Electrical resistivity measurements from room temperature to 1300 K showed that a metallic conducting tendency dominated at high temperatures. The hopping nature of the charge carriers was well interpreted in the framework of polaron theory. The Seebeck coefficient was measured in the same temperature interval, and its concentration dependence was analyzed using the high-temperature (HT) thermopower theory proposed by Marsh-Parris. The thermal conductivity and the figure of merit of the prepared samples were also compared with those of other similar perovskite compounds. The observed figure of merit of the sample with x=0.15 was Z=1.5 Â 10 À4 K À1 at T=1100 K, indicating a good potential for application as a HT thermoelectric material.

2025, Physics Letters

We study source-to-sink excitation transport on carbon nanotubes using the concept of quantum walks. In particular, we focus on transport properties of Grover coined quantum walks on ideal and percolation perturbed nanotubes with zig-zag and armchair chiralities. Using analytic and numerical methods we identify how geometric properties of nanotubes and different types of a sink altogether control the structure of trapped states and, as a result, the overall source-to-sink transport efficiency. It is shown that chirality of nanotubes splits behavior of the transport efficiency into a few typically well separated quantitative branches. Based on that we uncover interesting quantum transport phenomena, e.g. increasing the length of the tube can enhance the transport and the highest transport efficiency is achieved for the thinnest tube. We also demonstrate, that the transport efficiency of the quantum walk on ideal nanotubes may exhibit even oscillatory behavior dependent on length and chirality.

2025, Physics of the Solid State

The surface structure of polypropylene and polyethylene microporous films prepared by the extrusion of the polymer melt with the subsequent stages of annealing, uniaxial extension, and thermal fixa tion of the samples has been analyzed using scanning electron microscopy. It has been shown that percolation through pores corresponds to the axial texture of the surface with the channel structure described by the frac tal cluster model. The transition from open pores (through flow channels) to closed pores leads to the forma tion of surface regions with a biaxial texture. An increase in the density of the solid phase cluster is accompa nied by the formation of a homogeneous biaxial texture with a period of alternation of the density in two mutually perpendicular directions, one of which coincides with the direction of orientation of the films.

2025, arXiv (Cornell University)

To better understand the temporal characteristics and the lifetime of fluctuations in stochastic processes in networks, we investigated diffusive persistence in various graphs. Global diffusive persistence is defined as the fraction of nodes for which the diffusive field at a site (or node) has not changed sign up to time t (or in general, that the node remained active/inactive in discrete models). Here we investigate disordered and random networks and show that the behavior of the persistence depends on the topology of the network. In two-dimensional (2D) disordered networks, we find that above the percolation threshold diffusive persistence scales similarly as in the original 2D regular lattice, according to a power law P (t, L) ∼ t -θ with an exponent θ 0.186, in the limit of large linear system size L. At the percolation threshold, however, the scaling exponent changes to θ 0.141, as the result of the interplay of diffusive persistence and the underlying structural transition in the disordered lattice at the percolation threshold. Moreover, studying finite-size effects for 2D lattices at and above the percolation threshold, we find that at the percolation threshold, the long-time asymptotic value obeys a power-law P (t, L) ∼ L -zθ with z 2.86 instead of the value of z = 2 normally associated with finite-size effects on 2D regular lattices. In contrast, we observe that in random networks without a local regular structure, such as Erdős-Rényi networks, no simple power-law scaling behavior exists above the percolation threshold.

2025, 2004 24th International Conference on Microelectronics (IEEE Cat. No.04TH8716)

2025, HAL (Le Centre pour la Communication Scientifique Directe)

This paper deals with the problem of HF surface wave radar. The goal is to integrate in a unique tool the antenna radiation and the propagation calculations in order to make the analysis consistent. Only the antenna problem is presented here. However the way the propagation problem will be further considered is presented. Cross check of the tool validity and robustness were insured by developing concurrently several techniques, mixing measurements and theoretical techniques. I.

2025, Current Nanomaterials

Background: Carbon black -silicon rubber nanocomposites are under consideration for medical applications involving tremor mitigation as well as general therapeutic applications involving muscle relaxation therapy. Method: Carbon black filled silicon rubber composites containing 40-100 phr (per hundred) carbon black were investigated for their electrical conductivity under different loads over time. Rheological experiments involving evaluations of the storage moduli, G´ for the composites were also performed to infer rate and strain dependence of the composites' conductivity under compressive loads. Results: Due to the high deformability of silicon rubber, the percolation thresholds for carbon blacksilicon composites were shown to be a function of compressive loads applied on them. Conductivity of such composites increased with time and compressive load levels applied. The rheological experiments revealed that strain level and frequency can also indirectly affect the resistivity/conductivity levels in carbon black -filled silicon rubber composites, with the storage modulus increasing monotonically with increasing frequency (rate), and the stiffness of the carbon black /silicon rubber composite decreasing with increasing strain levels. Thus, it becomes easier to compact the nanocomposite further at higher strain levels and we would expect the rate of decay in resistivity to be lower at higher rates of pressure application. Conclusion: Our experimental results reveal that the two important service parameters, strain level and loading rate can be used for controlling the resistivity/conductivity levels in carbon black-filled silicon rubber composites.

2025, Journal of Applied Polymer Science

In this study, we investigated the thermal, dynamic mechanical, mechanical, and electrical properties of polyethylene (PE)graphene nanosheet (GNS) nanocomposites, with GNS amounts from 0 to 20 wt %, prepared by in situ polymerization. The thermal stability was evaluated by thermogravimetric analysis (TGA) and showed that the addition of GNSs to the polyolefin matrix increased the onset degradation temperature by 30 C. The electrical conductivity, measured by the impedance technique, presented a critical percolation threshold of 3.8 vol % (8.4 wt %) of GNS. A slight decrease in the tensile strength was found. On the other hand, dynamic mechanical analysis showed an increase in the storage modulus of the nanocomposites compared with that of neat PE. The glass-transition temperature value increased from À111 C (neat PE) to À106 C (PE/6.6 wt % GNS). All of these results show that PE became stiffer and thermally more stable and could be transformed from an insulator to a semiconductor material in the presence of GNSs. V

2025, Polymer

Microinjection-molded and compression-molded polyamide (PA12) matrix composites filled with 0.67, 1.33, 2 and 4 wt% multi-walled carbon nanotubes (MWNTs) were prepared from twin-screw extruded pellets. The compression molded samples have an electrical percolation threshold close to 1.2 wt%. Coupled rheological and electrical measurements show that their electrical properties start decreasing as soon as shear begins and are partially restored during flow, suggesting successively breakage and reconstruction of a percolating network. On the other hand, the electrical properties of the microinjection molded composites are close to the matrix ones, showing that cooling is too fast for the MWNTs to form a network. There is some electrical anisotropy in these composites, as evidenced by a greater conductivity measured in the flow direction. However polarized Raman spectroscopy analysis does not reveal a significant orientation of the MWNTs.

2025

The paper presents modeling, fabrication and measurements of microwave propagation in electromagnetic band gap (EMBG) CNTs based resonator for DNA detection. We report on sensing of DNA wrapped on multi walled carbon nanotubes (CNTs) deposited over a coupled lines area of two types of EMBG resonator structures. A new EMBG structure with coupled lines as a defect in the structure in order to obtain a EMBG resonator is proposed. Two types of EMBG resonator structures having the distance between the coupled lines 50 µm and 100 µm respectively have been used in order to find the best coupling with CNTs. The transmission magnitude and the phase for two types of EMBG resonators based on carbon nanotubes has been presented. Detection of DNA using EMBG resonators based on CNTs was demonstrated by a shift of the resonance frequency and an averaged phase shift of 20 degrees for a broadband frequency range of 6-20 GHz.

2025, Polymer

Low color, flexible, space environmentally durable polymeric materials possessing sufficient surface resistivity (10 6 -10 10 V/square) for electrostatic charge (ESC) mitigation are of interest for potential applications on Gossamer spacecraft as thin film membranes on antennas, large lightweight space optics, and second surface mirrors. One method of incorporating intrinsic ESC mitigation while maintaining low color, flexibility, and optical clarity is through the utilization of single-walled carbon nanotubes (SWNTs). However, SWNTs are difficult to uniformly disperse in the polymer matrix. The approach reported herein employed amide acid polymers endcapped with alkoxysilane groups that could condense with oxygen containing functionalities that were present on the ends of SWNTs as a result of the oxidative purification treatment. These SWNTs were combined with the endcapped amide acid polymers in solution and subsequently cast as unoriented thin films. Two examples possessed electrical conductivity (measured as surface resistance and surface resistivity) sufficient for ESC mitigation at loading levels of # 0.08 wt% SWNT as well as good retention of thermo-optical properties. The percolation threshold was determined to lie between 0.03 and 0.04 wt% SWNT loading. Electrical conductivity of the film remained unaffected even after harsh mechanical manipulation.

2025, Journal of Polymer Science Part B: Polymer Physics

The equations needed to correctly interpret both AC and DC conductivity results of single wall carbon nanotube (SWNT) polymer composites and the scaling of these results onto a single master curve are presented. Brief discussions on the factors that determine the critical volume fraction (ϕc) and the percolation exponent (t) are also given. The results for a series of SWNT–polyimide composites are presented and the parameters obtained from fitting these results are discussed. The critical volume fraction for electrical percolation of the present composite was about 0.0005. Results obtained from previous work on SWNT (MWNT)–polymer composites and other percolation systems and the modeling (interpretation) of these results are also discussed and compared. © 2005 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 43: 3273–3287, 2005

2025, Materials Today: Proceedings

Carbon Nanotubes have been incorporated in a resin-based on the bi-functional epoxy precursor diglycidyl ether of bisphenol A (DGEBA). Electrical measurements allowed evaluating the electric percolation curve with a value of electric percolation threshold detected around 0.015% by weight of multi-wall carbon nanotubes (MWCNTs). It has been found, by electro-mechanical tests, that the Gauge Factor (G.F.) decreases with increasing the carbon nanotubes percentage. Furthermore, the presence of a residual resistivity allows diagnosing permanent damage in the epoxy matrix. High piezoresistive performance (G.F. = 4.7) of the Carbon Fiber Reinforced Panels (CFRP) coated with the epoxy resin containing 0.1 wt % of MWCNT, has been obtained.