Full Percolation Research Articles

Cocontinuous Nanostructures by Microphase Separation of Statistically Cross-Linked Polystyrene/Poly(2-vinylpyridine) Networks.

Cocontinuous polymeric nanostructures have drawn considerable attention due to their ability to combine distinct, percolation-dependent properties of two different polymer domains. Randomly end-linked copolymer networks (RECNs) have previously been shown to support the formation of disordered cocontinuous nanostructures across wide composition windows in a robust way. However, achieving highly efficient linking of telechelic polymers with excellent end-group fidelity often requires complex synthetic routes. As an alternative, we study here statistically cross-linked copolymer networks (SCCNs) composed of polystyrene and poly(2-vinylpyridine) (PS and P2VP) with cross-linkable allyl pendent groups that are conveniently synthesized by controlled radical copolymerization. Via selective extraction of P2VP, coupled with gravimetry, small-angle X-ray scattering, and electron microscopy, we find disordered cocontinuous phases across wide composition ranges (up to ≈ 35 wt %), approaching values previously determined for RECNs. Remarkably, even for samples that appear to exhibit full percolation, a substantial fraction of P2VP (≈ 20-30 wt %) cannot be removed, which we ascribe to short strands between nearby cross-linkers that are physically embedded within PS domains. The resulting PS porous monoliths with residual surface P2VP layers enable facile surface modification to resist protein adsorption and templating of porous gold nanostructures.

Bootstrap percolation in random geometric graphs

AbstractFollowing Bradonjić and Saniee, we study a model of bootstrap percolation on the Gilbert random geometric graph on the 2-dimensional torus. In this model, the expected number of vertices of the graph is n, and the expected degree of a vertex is $a\log n$ for some fixed $a>1$ . Each vertex is added with probability p to a set $A_0$ of initially infected vertices. Vertices subsequently become infected if they have at least $ \theta a \log n $ infected neighbours. Here $p, \theta \in [0,1]$ are taken to be fixed constants.We show that if $\theta < (1+p)/2$ , then a sufficiently large local outbreak leads with high probability to the infection spreading globally, with all but o(n) vertices eventually becoming infected. On the other hand, for $ \theta > (1+p)/2$ , even if one adversarially infects every vertex inside a ball of radius $O(\sqrt{\log n} )$ , with high probability the infection will spread to only o(n) vertices beyond those that were initially infected.In addition we give some bounds on the $(a, p, \theta)$ regions ensuring the emergence of large local outbreaks or the existence of islands of vertices that never become infected. We also give a complete picture of the (surprisingly complex) behaviour of the analogous 1-dimensional bootstrap percolation model on the circle. Finally we raise a number of problems, and in particular make a conjecture on an ‘almost no percolation or almost full percolation’ dichotomy which may be of independent interest.

Numerical study on TPB density and percolation properties of microstructure reconstruction of nickel/yttria stabilized zirconia cermet anode based on discrete element method

Microstructure is essential for electrochemistry and transport in Ni/YSZ cermet anodes. Targeting the complexity and irregularity of porous networks, the percolation theory is widely used to model electrode microstructures in representative element (RE) scale based on an ideal prototype of particle units. With the pros of simplicity and generality, however, the idealized particle model deviates somehow the true state of particle clusters. Modeling connections between a lot of particles, the discrete element method (DEM) provides a more realistic state, meanwhile brings high computation cost. This paper provides a combined approach which starts from a DEM-based model for compaction and evolution between particle arrays, then analyzes the statistical properties, e.g. density of triple phase boundary (TPB) and percolations of particles. With consideration of multiple-particle overlaps, the DEM-fitted relationship of percolation probability vs. coordination number presents a smaller percolation threshold and a slower growing rate before reaching a full percolation, compared with some published formulae based on the percolation theory. Simulations at different temperatures are employed to study the effects of sintering. This work has significance of understanding the evolution and optimization of the electrode microstructure, not limited to Ni/YSZ system, and is helpful for more accurate solid oxide fuel cell modeling.

Double-Mesoscopic Hole-Transport-Material-Free Perovskite Solar Cells: Overcoming Charge-Transport Limitation by Sputtered Ultrathin Al2O3 Isolating Layer.

The electrically insulating space layer takes a fundamental role in monolithic carbon-graphite based perovskite solar cells (PSCs) and it has been established to prevent the charge recombination of electrons at the mp-TiO2/carbon-graphite (CG) interface. Thick 1 μm printed layers are commonly used for this purpose in the established triple-mesoscopic structures to avoid ohmic shunts and to achieve a high open circuit voltage. In this work, we have developed a reproducible large-area procedure to replace this thick space layer with an ultra-thin dense 40 nm sputtered Al2O3 which acts as a highly electrically insulating layer preventing ohmic shunts. Herewith, transport limitations related so far to the hole diffusion path length inside the thick mesoporous space layer have been omitted by concept. This will pave the way toward the development of next generation double-mesoscopic carbon-graphite-based PSCs with highest efficiencies. Scanning electron microscope, energy dispersive X-ray analysis, and atomic force microscopy measurements show the presence of a fully oxidized sputtered Al2O3 layer forming a pseudo-porous covering of the underlying mesoporous layer. The thickness has been finely tuned to achieve both electrical isolation and optimal infiltration of the perovskite solution allowing full percolation and crystallization. Photo voltage decay, light-dependent, and time-dependent photoluminescence measurements showed that the optimal 40 nm thick Al2O3 not only prevents ohmic shunts but also efficiently reduces the charge recombination at the mp-TiO2/CG interface and, at the same time, allows efficient hole diffusion through the perovskite crystals embedded in its pseudo-pores. Thus, a stable VOC of 1 V using CH3NH3PbI3 perovskite has been achieved under full sun AM 1.5 G with a stabilized device performance of 12.1%.

Properties of basalt fiber sulfo-aluminate modified cement binders

The present paper considers the influence of basalt fiber method of addicting in to self-stressing concrete, modified by sulfoaluminate type expansive additive, on main properties of concrete. The use of basalt fiber and expansive additive together allows to obtain a composite with optimal structure and high-quality properties. The combined application allows to achieve several effects such as filling effect, pozzolanic effect and dispersed reinforcement effect (due to chaotic fiber distribution in the concrete composite structure and needle-shaped crystal of ettringite micro reinforcement). Use of even small amount of basalt fiber due to disintegration on a great amount of monofilaments with a great specific surface leads to an increase in concrete composite tensile strength due to spatial dispersed reinforcement effect and changing fracture toughness There is also an effect of simultaneous expansion due to adding an expansive additive and strengthening achieved by binding effect of basalt fiber as a dispersion-reinforcing element. The maximum amount of basalt fiber in the research is limited by 4% to prevent full percolation effect, but at the same time to provide the formation of filament spatial skeleton in the concrete structure. In this study are considered the changes of properties of the concrete composite with different degrees of expansion and self-stressing (varied by energy-activity and amount of sulfo-aluminate expansive additive). In the article the most optimal basalt fiber addicting method in the concrete mix is proposed, preferences and influence degree of this method on strength properties are determined. The integral use of the modifying expansive agent makes it possible to predict an increase in impermeability due to chemical-mechanical reinforcement of the structure, which results in durability of this type of concrete. This predetermines a perspective range of their applications in various kinds of structures including those with high serviceability.

Boundary between hadron and quark-gluon structure of nuclei

We show that the boundary between quark-dominated and hadron-dominated regions of nuclear structure may be blurred by multi-nucleon quark clusters arising from color percolation. Recent experiments supporting partial percolation in cold nuclei and full percolation in hot/dense nuclear matter include: deep inelastic lepton-nucleus scattering, relativistic heavy-ion collisions and the binding energy in $^5 He_{\Lambda}$.

Analytical Cell-Based Model for the Breakdown Statistics of Multilayer Insulator Stacks

A fully analytical cell-based model is proposed to describe the breakdown (BD) statistics of multiple-layer insulator stacks. The model is shown to be completely equivalent to the full percolation model by comparing with recently published kinetic Monte Carlo simulations. The role of an initial density of native defects in the as-grown oxide and the time-dependent generation of inert defects are successfully addressed. The effect of the generation of interface states on the stack BD statistics is also incorporated into the model.

Formation of superconducting regions of MgB 2 by implantation of magnesium ions into boron substrate followed by intense pulsed plasma treatment

Mg ion implantation into boron substrates followed by pulsed Ar plasma treatment was used to form MgB 2 compound. Rutherford Backscattering (RBS) analysis of the best samples revealed that the ratio of atomic concentration of Mg to B atoms could be close to the stoichiometry of MgB 2 in the range of about 100 nm beneath the surface. Results of magnetically modulated microwave absorption (MMMA), magnetic moment and electrical conductivity measurements indicate the presence of superconductive grains with critical temperature T c = 25 K. A gradual onset of microscopic percolation is inferred starting from 15 K although no full percolation has been reached.

Deposition and mechanical properties of Ti–Si–N coated layer on WC–Co by RF inductively coupled plasma-enhanced chemical vapor deposition

Coatings of Ti–Si–N on WC–Co substrates were deposited by an r.f. inductively coupled (RFI) PECVD technique. Ti–Si–N coating layers were grown with fairly high deposition rates, and had a maximum hardness value of 38–40 GPa when deposited at 500–600 °C with a Si content of approximately 10 at.%. The film microstructure of maximum hardness was revealed to be a nanocomposite of nano-sized TiN crystallites embedded in amorphous silicon nitride phase by high resolution transmission electron microscopy (HRTEM). The increase of Si content above 10 at.% caused thickening of amorphous silicon nitride phase and an appearance of free Si, although increasing Si also induced finer and more isotropic TiN crystallites with full percolation by amorphous phase. The deposition behaviors of Ti–Si–N, their microstructures, and mechanical property by an RFI-PECVD method were systematically investigated in this work.

Flow in porous media: The "backbone" fractal at the percolation threshold

We show that for all Euclidean dimensions $d \stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{\ensuremath{\zeta}}={\overline{d}}_{w}\ensuremath{-}{\overline{d}}_{f}$, where ${L}_{R}\ensuremath{\sim}{\ensuremath{\xi}}^{\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{\ensuremath{\zeta}}}$ is the effective resistance between two points separated by a distance comparable with the correlation length $\ensuremath{\xi},{\overline{d}}_{f}$ is the fractal dimension of the backbone, and ${\overline{d}}_{w}$ is the fractal dimension of a random walk on the same backbone. We also find a relation between the backbone and the full percolation cluster, ${\overline{d}}_{w}\ensuremath{-}{\overline{d}}_{f}={d}_{w}\ensuremath{-}{d}_{f}$. Thus the Alexander-Orbach conjecture ($\frac{{d}_{f}}{{d}_{w}}=\frac{2}{3}$ for $dg~2$) fails numerically for the backbone.