Percolation Structure Research Articles

Critical path analysis of conductance fluid invasion and rupture

Critical path analysis (CPA)is very useful tool in treating transport properties of strongly heterogeneous conducting materials. In this work we show how the range of applicability of CPA is extended to percolating behavior induced by diverse dynamical processes. We illustrate this through useful applications in the context of conductance of random resistor networks, fluid invasion of a porous matrix and tough rupture of disordered materials. For random conducting systems it is reviewed that there is a formal analogy between transport on fractal (percolating) structures and transport in strongly heterogeneous networks. For invasion percolation, we show that CPA holds exactly for all dimensions and distributions of disorder. Finally, for toughness tests it is shown that the strength of an undiluted system is identical to that of the toughest directed percolation backbone. A common thread is laid among these problems by posing them in terms of scale-invariant relations of system properties on hierarchical lattices.

LOCALIZATION OF FRACTONS, RANDOM WALKS AND LINEAR POLYMERS IN PERCOLATION

We review analytical and numerical results for the vibrational amplitudes of localized excitations, the probability distribution of random walks and the distribution of linear polymers (modeled by self-avoiding walks of N steps) on percolation structures at criticality. Our numerical results show that the fluctuations of these quantities, at fixed shortest-path distance (“chemical length”) l from the center of localization, are considerably smaller than at fixed Euclidean distance r from the center. Using this fact, we derive via convolutional integrals explicit expressions for the averaged functions in r-space, and show analytically and numerically that three different localization regimes occur. In the short-distance regime, remarkably, the averages show a universal spatial decay behavior, with the same exponent for both fractons and random walks, while in the asymptotic regime, the averages depend explicitly on the number of configurations considered.

Universality of the Network and Bubble Topology in Cosmological Gravitational Simulations

Using percolation statistics we, for the first time, demonstrate the universal character of a network pattern in the real space, mass distributions resulting from nonlinear gravitational instability of initial Gaussian fluctuations. Percolation analysis of five stages of the nonlinear evolution of five power law models reveals that all models show a shift toward a network topology if seen with high enough resolution. However, quantitatively, the shift is significantly different in different models: the smaller the spectral index ,n, the stronger the shift. On the contrary, the shift toward the bubble topology is characteristic only for the n <= -1 models. We find that the mean density of the percolating structures in the nonlinear density distributions generally is very different from the density threshold used to identify them and corresponds much better to a visual impression. We also find that the maximum of the number of structures (connected regions above or below a specified density threshold) in the evolved, nonlinear distributions is always smaller than in Gaussian fields with the same spectrum, and is determined by the effective slope at the cutoff frequency.

Phase transition in metallic plasmas

An estimate is made for the energy of a virtual atomic structure on the metallic side of the metal-nonmetal transition in a dense plasma. On the assumption of a nearly uniform valence electron density, the interatomic interaction is treated as a Madelung energy, which is found to be approximately one-third of that for the one-component plasma model. Our estimate is verified by solving numerically the pseudowave equation for the valence electrons in ellipsoidal atomic cells which are compatible with the percolation structure of overlapping classically accessible spheres. The critical value of the Coulomb coupling parameter has been shown to agree with experiment at the liquid-gas critical points of cesium and rubidium, which can be identified with the plasma-phase-transition critical points.

ELECTRON TRANSPORT PROPERTIES IN FINE-PARTICLE FILMS OF Au EVAPORATED ONTO Si NATIVE OXIDE: THERMAL ANNEALING EFFECTS

We investigated electron transport in fine-particle films of Au prepared onto Si native oxide. Electron transport measurements and TEM observations were carried out for as-deposited and after thermal treatment of the films in air. We observed the anomalous resistance increases in as-deposited fine-particle films of Au and obtained α T =4.5. After 150°C thermal treatment in air, however, these anomalous resistance increases in the Au films disappeared and its topography appeared on the TEM images drastically changed into percolative structure. We found that the size of the Au fine particles causes anomalous resistance increase at low temperature.

Slow Nonequilibrium Dynamical Rearrangement of the Lateral Structure of a Lipid Membrane

The lipid bilayer of the biological membrane is a multicomponent molecular mixture capable of exhibiting compositional and structural heterogeneity. Using Fourier transform infrared spectroscopy and Monte Carlo computer simulation techniques, we report here for the first time the existence of a long-lived nonequilibrium heterogeneous lateral membrane structure composed of gel and fluid domains in a binary dipalmitoylphosphatidylcholine−dibehenoylphosphatidylcholine (DC16 PC−DC22 PC) lipid membrane. The nonequilibrium dynamic ordering process of coexisting phases following a thermal quench from the fluid state into the gel−fluid phase coexistence region is characterized by a relaxation time on the order of hours. This slow process leads to a long-lived compartmentalized percolative lateral membrane structure with a dynamic network of interfacial regions having properties different from the coexisting gel and fluid bulk phases.

Ac Response of Heterogeneous Materials: A Numerical Study

ABSTRACTThe ac and dc electrical properties of composite materials are studied using hierarchical lattices. First we show that the hierarchical model can correctly account for the main scaling properties of critical percolative structures. Then we study the effect of potential disorder by assuming that the microscopic conductances are distributed according to a power law distribution function. We find that in the limit of strong disorder, the predictions are in qualitative agreement with reported experimental measurements.

Temperature-, electric field- and solute-induced percolation in water-in-oil microemulsions

We report investigations on the percolation of the aqueous phase in water-in-oil microemulsions, comparing systems stabilized by ionic AOT and non-ionic Igepal amphiphiles. First, we briefly review the opposite effect of temperature on the two systems and compare electric conductivity with viscosity data. In the second part, we show that percolation can be induced by high electric fields resulting in a shift of the percolation curve. The electric field measurements allow to investigate the dynamics of clustering of the water droplets to form a network of percolating channels. We examine the slow build-up and the fast decay of the percolating structure, monitoring simultaneously electric conductivity and electric birefringence. In the third part we discuss the effect of some solutes on the percolation curve, especially of small molecules which act as protein denaturants and of native and denatured proteins like methemoglobin, chymotrypsin and gelatin. The spectroscopic determination of the dimerization of hemin, released from denatured hemoglobin, reflects the incorporation of the hemin monomers in the surfactant monolayer. In the gelatin system time resolved electric birefringence shows that even at low concentrations it is the macromolecule which determines the structure of the aqueous domain. In the appendix, a simple estimate of the intrinsic Kerr-constant is given for microemulsion droplets deformed in an electric field.

Non-equilibrium effects of core-cooling and time-dependent internal heating on mantle flush events

Abstract. We have examined the non-equilibrium effects of core-cooling and time-dependent internal-heating on the thermal evolution of the Earth's mantle and on mantle flush events caused by the two major phase transitions. Both two- and three-dimensional models have been employed. The mantle viscosity responds to the secular cooling through changes in the averaged temperature field. A viscosity which decreases algebraically with the average temperature has been considered. The time-dependent internal-heating is prescribed to decrease exponentially with a single decay time. We have studied the thermal histories with initial Rayleigh numbers between 2 x 107 and 108 . Flush events, driven by the non-equilibrium forcings, are much more dramatic than those produced by the equilibrium boundary conditions and constant internal heating. Multiple flush events are found under non-equilibrium conditions in which there is very little internal heating or very fast decay rates of internal-heating. Otherwise, the flush events take place in a relatively continuous fashion. Prior to massive flush events small-scale percolative structures appear in the 3D temperature fields. Time-dependent signatures, such as the surface heat flux, also exhibits high frequency oscillatory patterns prior to massive flush events. These two observations suggest that the flush event may be a self-organized critical phenomenon. The Nusselt number as a function of the time-varying Ra does not follow the Nusselt vs. Rayleigh number power-law relationship based on equilibrium (constant temperature) boundary conditions. Instead Nu(t) may vary non-monotonically with time because of the mantle flush events. Convective processes in the mantle operate quite differently under non-equilibrium conditions from its behaviour under the usual equilibrium situations.

Structure Development of a Polybutadiene/Polyisoprene Blend during Spinodal Decomposition. Comparison between Light Scattering and Optical Microscopy

The typical interconnected bicontinuous percolation structure of a critical 50/50 wt % polybutadiene (PB)/polyisoprene (PI) mixture was characterized in detail by the structure function of a light scattering experiment and by statistical image processing of optical microscope images. The time development of the interdomain distance and the local radius of the curved interface in the late stage of the spinodal decomposition are obtained for the first time for the same system by both methods and are found to be in good agreement. PB/PI blends are systems with a lower critical solution temperature (LCST). The critical point was varied within a wide temperature range by changing the 1,2 content of the PB. For optical microscopy, the structure was fixed by photo-cross-linking and the optical contrast was achieved in a second step by selective staining of the PI phase by exposing the sample to iodine vapor.

Fractal properties of percolating film structures

We simulate nucleation and growth processes of thin films on the basis of the so-called rate equation approach allowing “atoms” to diffuse and rearrange whereby enhancing their co-ordination number. The resulting percolating structures are different from those obtained by the “pure” percolation model where “atomic diffusion” is not taken into account. However, the fractal properties for p = p c are the same as for the percolation model with the fractal dimension of d f = 1.896 and for random walks of d w = 2.87. Moreover, d f and d w are independent on the diffusion time we choose for our simulations.

Percolation structure model in the smearing region†

The model of the percolation structure on the percolation threshold in the smearing region is developed and is actually the generalization of a weak link model (WLM). On the basis of the above, the local joule overheats are calculated in percolation systems with a wide distribution spectra of conductances.

Computer Simulation of Percolation Structure in Composites

Two-dimensional computer simulations were conducted on percolative structure in which second phases of various aspect ratios were arranged in a matrix phase. The second phases were randomly arranged in an array with two different computational programs; one prohibiting an overlap among second phases and the other allowing the overlap. From the simulation prohibiting the overlap, it was predicted that a continuous path was formed at less amounts of the second phase with higher aspect ratios. In the simulation allowing the overlap, a continuous path throughout the array was formed by arranging the second phase of an aspect ratio of 100 with less than 4% in the array. These results agreed well with the conduction path formation in hotpressed ceramic composites consisting of an insulator matrix and electrically conductive whisker additives.

Polymerization-induced spinodal decomposition of [formula omitted] methacrylate mixture and the influence of incorporating poly(vinyl acetate) macromonomer

The structural development during radical polymerization of a mixture of methyl methacrylate (MMA) and poly(ethylene- co-vinyl acetate) (EVA) was investigated by light scattering and optical microscopy. In the early stage of polymerization, the mixture of MMA/EVA was a single phase. As the polymerization of MMA proceeded, phase separation took place via spinodal decomposition (SD). This was supported by the characteristic change in light-scattering profile with reaction time. Analysis by the linearized and scaling theories showed that the reaction-induced phase separation behaviour was different from the familiar thermally induced SD during isothermal annealing after temperature jump. The scaling analysis showed that the final phase-separated structure may be formed by the interruption of a co-continuous percolation structure. Moreover, to investigate the effect of graft copolymer on SD, a poly(vinyl acetate) (PVAc) macromonomer with a methacrylate end-group was added to the MMA/EVA mixture to yield PMMA-PVAc graft copolymer during the polymerization. The incorporation of PVAc macromonomer increased the dominant wavenumber of the final frozen phase-separated structure (smaller periodic distance). The reasons seem to be that the concentration fluctuation growth is suppressed until the system reaches a deep quench depth at which the fluctuation should have a large wavenumber, and that the coarsening is retarded at the late stage by the graft copolymer formed in situ.

Local heating, resonant pinning and anisotropic interactions in anionic layered conductors

Our percolative model of high-temperature superconductivity (HTS) in the layered cuprates explains correlations between Meissner volume fractions, the superconductive transition temperature T c, and internal friction losses which we ascribe to resonant pinning centers located between, not in, metallic cuprate planes. The bistable nature of such dopant centers leads to correlations between the bistable activation energy E A and T c. The electron-boson coupling strength λ can be estimated from the relaxation time τ 0 of such centers, and one finds that λ≳1, so that HTS can be the result of strong electron-boson coupling at such centers. The electron-boson coupling through bistable bosons is much stronger than that through phonons, as is shown by the dependence of phonon softening at T c on phonon polarizations, which is largest for q and E perpendicular to the cuprate planes. Explicit equations for T c and the superconductive energy gas E g are proposed with a characteristically percolative structure, and these equations agree well with experiment in the case of the most studied HTS for which values of E A are available.

Percolation and pore structure in mortars and concrete

The cement paste in concrete and mortar has been shown to have a pore size distribution different than that of plain paste hydrated without aggregate. For mortar and concrete, additional porosity occurs in pore sizes larger than the plain paste's threshold diameter as measured by mercury intrusion. Based on the assumption that these larger pores are essentially present only in the interfacial zones surrounding each aggregate, an experimental program was designed in which the volume fraction of sand in a mortar was varied in a systematic fashion and the resultant pore system probed using mercury intrusion porosimetry. The intrusion characteristics were observed to change drastically at a critical sand content. Similar results are observed for a series of mortar specimens in which the cement paste contains 10% silica fume. To better interpret the experimental results, a hard core/soft shell computer model has been developed to examine the percolation characteristics of these interfacial zone pores. Using the model, interfacial zone percolation in concretes is also examined. Finally, the implications of interfacial zone percolation for transport properties and durability of mortar and concrete are discussed.

A reply to a discussion by S. Chatterji of the paper “Percolation and pore structure in mortars and concrete”

A reply to a discussion by S. Chatterji of the paper “Percolation and pore structure in mortars and concrete”

A discussion of the paper “Percolation and pore structure in mortars and concrete” by D.N. Winslow, M.D. Cohen, D.P. Bentz, K.A. Snyder and E.J. Garboczi

A discussion of the paper “Percolation and pore structure in mortars and concrete” by D.N. Winslow, M.D. Cohen, D.P. Bentz, K.A. Snyder and E.J. Garboczi

Observing the Percolation Effect in Thick Film Superconductors

A thick film superconductor paste has been produced to determine the properties of granulated superconductor materials and to observe the percolation effect. The base of the paste was chosen to be of the BiSrCaCuO system because of its high Tc and advantageous current density properties. For contacts, a conventional Ag/Pt paste was used. The critical temperature was between 110 K and 115 K depending on the printed layer thickness. The critical current density was between 200 and 300 A/cm2. The R‐T and U‐l functions were measured with different parameters (Imeasuring. Bexternal. Number of layers, T). The measurement results confirmed the conducting mechanism theory in the material. A percolation structure model was built and is described. Finally, some fundamental advantages and problems of the process are discussed and the high‐frequency electric field sensor realised is described.

Random and cooperative sequential adsorption

Irreversible random sequential adsorption (RSA) on lattices, and continuum "car parking" analogues, have long received attention as models for reactions on polymer chains, chemisorption on single-crystal surfaces, adsorption in colloidal systems, and solid state transformations. Cooperative generalizations of these models (CSA) are sometimes more appropriate, and can exhibit richer kinetics and spatial structure, e.g., autocatalysis and clustering. The distribution of filled or transformed sites in RSA and CSA is not described by an equilibrium Gibbs measure. This is the case even for the saturation "jammed" state of models where the lattice or space cannot fill completely. However exact analysis is often possible in one dimension, and a variety of powerful analytic methods have been developed for higher dimensional models. Here we review the detailed understanding of asymptotic kinetics, spatial correlations, percolative structure, etc., which is emerging for these far-from-equilibrium processes.