Experimental observation of nonuniversal behavior of the conductivity exponent for three-dimensional continuum percolation systems

Tunable Percolation in Semiconducting Binary Polymer Nanoparticle Glasses

Binary polymer nanoparticle glasses provide opportunities to realize the facile assembly of disparate components, with control over nanoscale and mesoscale domains, for the development of functional materials. This work demonstrates that tunable electrical percolation can be achieved through semiconducting/insulating polymer nanoparticle glasses by varying the relative percentages of equal-sized nanoparticle constituents of the binary assembly. Using time-of-flight charge carrier mobility measurements and conducting atomic force microscopy, we show that these systems exhibit power law scaling percolation behavior with percolation thresholds of ∼24-30%. We develop a simple resistor network model, which can reproduce the experimental data, and can be used to predict percolation trends in binary polymer nanoparticle glasses. Finally, we analyze the cluster statistics of simulated binary nanoparticle glasses, and characterize them according to their predominant local motifs as (p(i), p(1-i))-connected networks that can be used as a supramolecular toolbox for rational material design based on polymer nanoparticles.

A scalable and facile synthesis of alumina/exfoliated graphite composites by attrition milling

We present a facile one-pot synthesis of alumina/exfoliated graphite composite having excellent electrical conductivity (>1,000 S m⁻¹), fracture toughness (5.6 MPa m^0.5), and wear resistance, which is enhanced by 7.7 times compared to pure alumina.

Tunneling and Percolation Behavior in Granular Metals

The nature of the percolation process in granular metals is examined for the first time by a computer simulation of a system of metallic grains embedded in an insulating matrix. Assuming that the intergrain conduction is due to quantum mechanical tunneling it is found that a percolation-like critical behavior of the conductivity is obtained, but that a percolation universal behavior will be found only in a very special case. In contrast, the behavior of the electrical noise does not deviate substantially from the universal one. Comparison of these results with recent experimental observations suggests that in the metallic range, both transport properties are controlled by the continuous metallic network rather than by intergrain tunnelin.. We propose that the metallic network resembles the previously studied system of ‘inverted random voids’.

Determination of the percolation threshold in Fe/MgO magnetic granular multilayers

The evolution of the morphology, magnetic and transport properties of Fe(t nm)/MgO(3.0 nm) multilayers with respect to the nominal metallic layer thickness was investigated. A comparison with existing experimental data on discontinuous metal-insulator multilayers, ultrathin epitaxial Fe films on MgO substrates and granular cermet films is made. It is confirmed that the deposition conditions and the material composition play a crucial role in the percolation process. Nominal thicknesses of Fe layers at which an infinite metallic cluster is formed and the conditions for continuous Fe coverage were determined. Different methods of percolation threshold detection were analysed. We show that investigation of the temperature dependence of resistance in nanostructures could lead to an overestimation of the percolation threshold value, while magnetic measurements alone could lead to its underestimation.

Direct measurement of the percolation probability in carbon nanofiber-polyimide nanocomposites

We present the first experimental measurement of the geometric critical exponent beta associated with the percolation probability, the probability a metallic filler belongs to the conducting network, of an electrical composite. The technique employs conducting-tip atomic force microscopy to obtain a conducting areal density, and is demonstrated on polyimide nanocomposites containing different concentrations of carbon nanofibers. We find beta approximately 1 and t (the exponent for bulk conductivity) approximately 3. These values are consistent with the predictions for the Bethe lattice and larger than the values predicted in the 3D lattice percolation model. Hence, this electrical composite likely belongs to the same universality class as the Bethe lattice. The ability to measure geometric and transport critical exponents on the same material is critical to drawing this conclusion.

Control of the electrical conductivity of composites of antimony doped tin oxide (ATO) nanoparticles and acrylate by grafting of 3-methacryloxypropyltrimethoxysilane (MPS)

The effect of the addition of antimony doped tin oxide (ATO) nanoparticles on the electrical conductivity of acrylate films is described. To enable dispersing of ATO in acrylate matrices, 3-methacryloxypropyltrimethoxysilane (MPS) was grafted on the surface of the filler. The amount of MPS used for this surface modification was found to strongly affect the electrical conductivity. Surface modification with a large amount of MPS resulted in colloidally stable dispersions of ATO, leading to a homogeneous distribution. Surface modification with small amounts of MPS led to instable ATO dispersions and aggregation of ATO into a fractal type network, which gives a much higher conductivity especially at low-volume fractions. For composites with a fractal type ATO network a second effect was found. Decreasing the amount of on ATO grafted MPS resulted in an increase of the electrical conduction between the ATO particles.

Modeling of Aqueous Transport in Rigid Porous Matrices near the Percolation Threshold

PURPOSE

To demonstrate control of passive diffusion of small molecules through rigid ceramic matrices via manipulation of matrix porosity near the percolation threshold, and to model such control using percolation scaling relationships on both infinite and finite lattices.

MATERIALS AND METHODS

Rigid alumina disks of controlled porosity were prepared using standard ceramic casting and sintering techniques. Structural void space distributions in sintered disks were measured by dimensional and volume displacement (pycnometry) methods. The impact of void space on transport was determined by tracking the diffusion of ionized benzoic acid across sintered disks mounted in Stokes diffusion cells. Critical percolation thresholds were estimated by fitting structural and transport-dependent results to percolation scaling relationships. Finite-size scaling studies were performed by adding polymer microspheres of known diameter to the disks to generate artificially large pores.

RESULTS

Nonlinear least squares techniques were used to fit both structural and transport-dependent properties of rigid alumina disks to total disk porosity using percolation scaling relationships. The critical percolation threshold determined from structural properties (0.129) was lower than that determined from benzoic acid transport (0.169). The transport-derived percolation threshold exactly matched that expected for a tetrakaidecahedral (14 sided) lattice. Finite-size scaling was demonstrated through a nonzero effective volume fraction for transport at the percolation threshold.

CONCLUSIONS

Manipulation of total disk porosity near the percolation threshold was shown to be a suitable means of controlling the transport rate of a model small molecule, while deliberate enlargement of individual pores was demonstrated to decrease this threshold without increasing total porosity. The lower-than-expected percolation threshold obtained from the structural model was ascribed to limitations of the measurement technique. The threshold determined from the aqueous transport model was concluded to represent the true threshold for this system.

Computer simulation of electrical conductivity of colloidal dispersions during aggregation

The computation approach to the simulation of electrical conductivity of colloidal dispersions during aggregation is considered. We use the two-dimensional diffusion-limited aggregation model with multiple-seed growth. The particles execute a random walk, but lose their mobility after contact with the growing clusters or seeds. The two parameters that control the aggregation are the initial concentration of free particles in the system p and the concentration of seeds psi. The case of psi=1, when all the particles are the immobile seeds, corresponds with the usual random percolation problem. The other limiting case of psi=0, when all the particles walk randomly, corresponds to the dynamical percolation problem. The calculation of electrical conductivity and cluster analysis were done with the help of the algorithms of Frank-Lobb and Hoshen-Kopelman. It is shown that the percolation concentration phi c decreases from 0.5927 at psi=1 to 0 at psi --> 0. Scaling analysis was applied to study exponents of correlation length v and of conductivity t. For all psi>0 this model shows universal behavior of classical 2d random percolation with v approximately t approximately 4/3. The electrical conductivity sigma of the system increases during aggregation reaching up to a maximum at the final stage. The concentration dependence of conductivity sigma(phi) obeys the general effective medium equation with apparent exponent ta(psi) that exceeds t. The kinetics of electrical conductivity changes during the aggregation is discussed. In the range of concentration Pc(phi)<p<0.9527 the time of percolation cluster formation pi c decreases with increasing phi.

Tunneling and nonuniversality in continuum percolation systems

The values obtained experimentally for the conductivity critical exponent in numerous percolation systems, in which the interparticle conduction is by tunneling, were found to be in the range of t0 and about t0 + 10, where t0 is the universal conductivity exponent. These latter values are, however, considerably smaller than those predicted by the available "one-dimensional"-like theory of tunneling percolation. In this Letter, we show that this long-standing discrepancy can be resolved by considering the more realistic "three-dimensional" model and the limited proximity to the percolation threshold in all the many available experimental studies.

Current percolation and anisotropy in polycrystalline MgB(2)

The influence of anisotropy on the transport current in MgB(2) polycrystalline bulk samples and wires is discussed. A model for the critical current density is proposed, which is based on anisotropic London theory, grain boundary pinning, and percolation theory. The calculated currents agree convincingly with experimental data, and the fit parameters, especially the anisotropy, obtained from percolation theory agree with experiment or theoretical predictions.