Structural model for the reinforcement of polymethyl methacrylate/carbon nanotube nanocomposites at an ultralow nanofiller content

The structural basis of the anomalously high reinforcement of polymer/carbon nanotube nanocomposites at an ultralow nanofiller content is studied. This effect is shown to be caused by the absence of interaction between carbon nanotubes and the related sharp increase in the interphase adhesion. From the standpoint of a nanofiller structure, the effect disappears when three critical points related to the structure of carbon nanotubes in a polymer matrix are reached. These points are a percolation threshold, an aggregative nanofiller stability threshold, and the beginning of formation of closed circular carbon nanotube structures.     

Comparative Analysis of the Reinforcement of Polymers with 2D-Nanofillers: Organoclay and Boron Nitride

Using the percolation reinforcement model, it has been shown that the main factor governing the degree of reinforcement of polymer/2D-nanofiller composites is the ability of a nanofiller to generate interfacial regions. This parameter is interrelated with two fundamental structural characteristics of a nanocomposite, i.e., the fractal dimension of its structure and the content of polymer matrix/nanofiller interfacial surfaces. The negative effect of high nanofiller anisotropy on the elasticity modulus of a nanocomposite is demonstrated.     

Nonlinear resistance of polymer composites with carbon nanotube additives in the percolation state

The electrical properties of a polymer composite with carbon nanotube additives have been analyzed. The state of the system near the percolation threshold, when charge is transferred along a single percolation path, has been considered. For this state, the current–voltage characteristics of a percolation chain made up of carbon nanotubes have been calculated under the assumption that the contact resistance between neighboring nanotubes is much higher than the intrinsic resistance of the nanotubes. According to recent data, the distance between neighboring (contacting) nanotubes has been assumed to be randomly distributed. It has been shown that, under the given conditions, the current–voltage characteristic is essentially nonlinear. This indicates the nonohmic conductivity of the composites. The dependence of the current–voltage characteristic on the spread of the contact distribution over distances has been discussed.     

The affection on the nature of percolation by concentration of pentagon–heptagon defects in graphene lattice

In this paper the percolation behavior with a specific concentration of the defects was discussed on the twodimensional graphene lattice. The percolation threshold is determined by a numerical method with a high degree of accuracy. This method is also suitable for locating the percolation critical point on other crystalline structures. Through investigating the evolution of the largest cluster size and the cluster sizes distribution, we find that under various lattice sizes and concentrations of pentagon-heptagon defects there is no apparent change for the percolation properties in graphene lattice.     

Quantum versus geometric disorder in a two-dimensional Heisenberg antiferromagnet

We present a numerical study of the spin-1/2 bilayer Heisenberg antiferromagnet with random interlayer dimer dilution. From the temperature dependence of the uniform susceptibility and a scaling analysis of the spin correlation length we deduce the ground state phase diagram as a function of nonmagnetic impurity concentration p and bilayer coupling g. At the site percolation threshold, there exists a multicritical point at small but nonzero bilayer coupling g(m)=0.15(3). The magnetic properties of the single-layer material La(2)Cu(1-p)(Zn,Mg)(p)O4 near the percolation threshold appear to be controlled by the proximity to this new quantum critical point.     

Electrical properties of aluminium island films near the percolation threshold

Electrical properties of Al island films on NaCl substrates are studied. The temperature dependence of the resistance is determined in situ under vacuum conditions for films with various volume fractions q. It has been found that the electrical properties of the film are subject to significant changes near the percolation threshold, when q approaches 0.51. This behaviour is to be attributed to a change in the type of conduction. The temperature coefficient of resistance TCR for the percolation threshold q_c is close to zero. For q<q_c and q>q_c, TCR is smaller than zero or greater than zero, respectively.     

Diffusion of atoms incorporated in the surface layer of the fcc(111) face

The kinetics of the migration of the impurity atom due to the diffusion of vacancies on the fcc(111) face was investigated. The study focused on the dependence of the diffusion coefficient of the impurity on the degree of surface coverage with vacancies. It was shown by molecular dynamics that this dependence is linear in the limit of the vanishingly small concentration of vacancies 1; the results of modeling coincided with the predictions of our analytical theory. The diffusion coefficient increased nonlinearly with and its growth correlated with that of the size of the percolation clusters. After the percolation threshold was overcome, the diffusion coefficient of the impurity quickly tended toward its value for the surface without hindrances.     

Evolution of a Magnetoresonance Line Near to a Limit of Percolation in Dilute Magnetics

In paper the results of numerical modeling of a magnetic resonance in dilute magnetics near to a threshold of a percolation are discussed. The classical equation of motion of magnetic moments is used in view of an exchange interaction such as RKKI and imitation of spin-phonon interaction by Monte-Carlo method. It is shown, that cluster structure of a magnetic and threshold of percolation are determined by critical distance, on which there is a change of a sign of an exchange interaction. In an examination of percolation phase transition the jump change of breadth of a line of a magnetic resonance is set, that can form the basis for experimental definition of a threshold percolation and parameters of an exchange interaction by methods of a radiospectroscopy.     

Effect of polymer-filler interface interactions on percolation conductivity of thermoplastics filled with carbon black

Conductive composites based on PE, PP, PS, PMMA and PA filled with carbon black have been studied. It was found that percolation behavior of the conductivity depended on the degree of polymer-filler interaction. Equations taking into account the polymer-filler interactions were proposed to describe the conductivity of composite above and below the percolation threshold.     

Temperature dependence of the electrical conductivity of vapor grown carbon nanofiber/epoxy composites with different filler dispersion levels

The influence of the dispersion of vapor grown carbon nanofibers (VGCNF) on the electrical properties of VGCNF/epoxy composites has been studied. A homogeneous dispersion of the VGCNF does not imply better electrical properties. The presence of well distributed clusters appears to be a key factor for increasing composite conductivity. It is also shown that the main conduction mechanism has an ionic nature for concentrations below the percolation threshold, while above the percolation threshold it is dominated by hopping between the fillers. Finally, using the granular system theory it is possible to explain the origin of conduction at low temperatures.     

Computer simulation of surface-enhanced Raman scattering in nanostructured metamaterials

The simulation of local field fluctuations and surface-enhanced Raman scattering in percolation systems at the percolation threshold is described. An approximate real-space renormalization group method was used in the simulation. It allows one to radically reduce the computation time compared to an exact calculation and to obtain detailed information about the electromagnetic field. The local fields in real macroscopic systems can be calculated by using this approximation. A computer simulation of the local fields in metal island (percolation) films has been performed by the developed method. The calculation has confirmed the existence of giant local field fluctuations. In turn, the local electric field excites Raman scattering. The local fields of surface-enhanced Raman scattering have been calculated for the first time. The dependence of the Raman scattering enhancement factor on the reference frequency and Stokes shift has been derived. An experimental observation of this dependence could be considered as a confirmation of the electromagnetic nature of the enhancement.     

Percolation transition in an irreversible-surface reaction model

Monte Carlo simulation studies of percolation transition in a surface reaction model describing the oxidation of carbon mono-oxide on a catalytic surface are presented. The percolation transition for adsorbed oxygen atoms occurs below the poisoning transition where carbon mono-oxide completely covers the surface of the catalyst and takes place for an oxygen coverage of about 0.525 which is close to the percolation transition in an Ising lattice gas with nearest-neighbor attractive interactions. In several respects the oxygen clusters near the percolation threshold resemble those of the Ising lattice gas near its critical point.     

The effect of orientational disorder on hopping conductivity in disordered organic semiconductors

The model of variable range hopping is generalized to systems with extended sites. The calculation of the hopping conductivity of a disordered medium with chain structure is reduced to the percolation problem for a system of one-dimensional fragments with random distribution of lengths and orientations. The percolation problem is solved using the Monte Carlo method and the method based on the bonding criterion. The percolation threshold, which determines the dependence of the conductivity on the fragment lengths and degree of their orientational ordering (texture), is calculated. It is shown that the conductivity increases exponentially with fragment lengths and decreases with orientational ordering.     

Effect of melt viscosity and surface tension of polymers on the percolation threshold of conductive-particle-filled polymeric composites

The electrical conductivities of carbon-black-filled low-density polyethylene (LDPE), poly(methyl methacrylate) (PMMA), and poly(vinyl chloride)-vinyl acetate (PVC/ VAc) copolymer were measured as functions of carbon content and melt viscosity of the matrix at the temperatures at which the composites were prepared. Sharp breaks in the relationship between the carbon filler content and the conductivity of composites were observed in all specimens at some content of the carbon filler. The conductivity jumps as much as 10 orders of magnitude at the break point. This phenomenon has been known as the “percolation threshold”. The critical carbon content corresponding to the break point     

Electron transport in the carbon-copper nanocluster structure

The electron transport in hydrogenated amorphous carbon films a-C: H with copper nanocluster inclusions has been investigated. The conditions of cluster formation are derived. It is theoretically demonstrated that the energy band structure of the matrix substantially affects the conditions of cluster formation. The electron transport depends on the cluster structure. It is found that, below the percolation threshold (the case of isolated clusters), the transport current is governed by two components depending on the electric field strength. At low field strengths, the current is caused by electrons in the conduction band of amorphous carbon, which are thermally excited from copper clusters. At high field strengths, the transport current is provided by tunneling electrons from the Fermi level of copper clusters to the conduction band of a-C: H. The difference between the mobility edge of the conduction band of amorphous carbon and the Fermi level in copper clusters is determined from the temperature dependence of the resistance and proves to be equal to 0.48 eV. The temperature dependences of the resistance at low field strengths exhibit a fine structure. It is revealed that, above the percolation threshold, the electrical resistance of clusters is considerably contributed by the residual resistance, which is supposedly associated with the electron scattering by cluster surfaces. The temperature effect on the electron transport is examined using the spin-wave scattering technique at a frequency of 4.0 GHz. It is found that the spin wave in the yttrium iron garnet (YIG) film is predominantly affected by thermally excited electrons located above the mobility edge in the conduction band of a-C: H.     

A self-consistent Ornstein-Zernike approximation for the site-diluted Ising model

We propose a theory for the site-diluted Ising model which is an extension to disordered systems of the self-consistent Ornstein-Zernike approximation of Hoye and Stell. By using the replica method in the context of liquid-state theory, we treat the concentration of impurities as an ordinary thermodynamic variable. This approach is not limited to the weak-disorder regime or to the vicinity of the percolation point. A preliminary analysis using series expansion shows that it can predict accurately the dependence of the critical temperature on dilution and can reproduce the nonuniversal behavior of the effective exponents. The theory also gives a reasonable estimate of the percolation threshold.     

Is superdense fluid hydrogen a molecular metal?

Recent experiments on the compression of liquid hydrogen in reverberating shock waves, which indicate the transition into a metallic state at about nine times the liquid H₂ density [S. T. Weir, A. C. Mitchell, and W. J. Nellis, Phys. Rev. Lett. 76, 1860 (1996)], have been interpreted by a microscopic percolation in a virtual molecular structure with a continuous spectrum of the electron excitations. The scaling dependence of the electron mobility on the energy above the percolation threshold has been used to qualitatively describe the electrical conductivity of fluid molecular hydrogen in the vicinity of the insulator-metal transition point. Zh. éksp. Teor. Fiz. 113, 1094–1100 (March 1998) Published in English in the original Russian journal. Reproduced here with stylistic changes by the Translation Editor.     

Effect of Carbon on the Electrical Properties of Copper Oxide-Based Bulk Composites

The effect of carbon filler on the electrical resistance and the thermopower of copper oxide-based composites produced by ceramic technology by hot pressing has been studied. It is found that the dependences of the electrical resistivity on the filler concentration are characteristic by S-like curves that are typical of percolation systems; in this case, the resistivity decreases more substantially as the carbon content increases as compared to the decrease in thermopower value, which is accompanied by the existence of the maximum of the factor of thermoelectric power near the percolation threshold. The studies of the temperature dependences of the resistivity and the thermopower at low temperatures show that, in the range 240–300 K, the predominant mechanism of the electrotransfer of all the composites under study is the hopping mechanism. At temperatures lower than 240 K, the composites with a nanocrystalline CuO matrix have a hopping conductivity with a variable hopping distance over localized states of the matrix near the Fermi level, which is related to the conductivity over intergrain CuO boundaries. A schematic model of the band structure of nanocrystalline CuO with carbon filler is proposed on the base of the analysis of the found experimental regularities of the electrotransfer.     

Tricritical point in heterogeneous k-core percolation

k-core percolation is an extension of the concept of classical percolation and is particularly relevant to understanding the resilience of complex networks under random damage. A new analytical formalism has been recently proposed to deal with heterogeneous k-cores, where each vertex is assigned a local threshold k(i). In this Letter we identify a binary mixture of heterogeneous k-cores which exhibits a tricritical point. We investigate the new scaling scenario and calculate the relevant critical exponents, by analytical and computational methods, for Erd?s-Rényi networks and 2D square lattices.     

Effect of temperature on the electron field emission from aligned carbon nanofibers and multiwalled carbon nanotubes

Effect of temperature and aspect ratio on the field emission properties of vertically aligned carbon nanofiber and multiwalled carbon nanotube thin films were studied in detail. Carbon nanofibers and multiwalled carbon nanotube have been synthesized on Si substrates via direct current plasma enhanced chemical vapor deposition technique. Surface morphologies of the films have been studied by a scanning electron microscope, transmission electron microscope and an atomic force microscope. It is found that the threshold field and the emission current density are dependent on the ambient temperature as well as on the aspect ratio of the carbon nanostructure. The threshold field for carbon nanofibers was found to decrease from 5.1 to 2.6 V/μm when the temperature was raised from 300 to 650 K, whereas for MWCNTs it was found to decrease from 4.0 to 1.4 V/μm. This dependence was due to the change in work function of the nanofibers and nanotubes with temperature. The field enhancement factor, current density and the dependence of the effective work function with temperature and with aspect ratio were calculated and we have tried to explain the emission mechanism.