Percolation Regime Research Articles

Wavelength dependence of the second harmonic generation of percolating gold thin films

We study the spectral dependence of the second harmonic generation (SHG) emitted by gold thin films around percolation. Previous studies found that the SHG peaks sharply at the percolation regime, i.e., at the critical layer thickness where the static permittivity of the film diverges. Another important characteristic is the very large field enhancement obtained in the regime of almost touching particles, while the thin film does not behave as a metal yet. Here, we show that these properties and, in particular, the amount of SHG extracted are wavelength-dependent. We investigate experimentally the evolution of the SHG as a function of the critical thickness of the film for four different applied fundamental wavelengths. A spectral dependence of the SHG is found, and a simple model is presented that qualitatively reproduces the variations of the measured SHG. We find that the local field enhancement at the fundamental wavelength dominates the signal and also that external factors play a role, such as the film absorbance. These results are particularly interesting for applications requiring an optimization of the SHG.

Electrical Conductivity and Structural Evolution of Polymer-Derived SiC Ceramics Pyrolyzed From 1200 °C to 1800 °C

Abstract Room temperature (RT) electrical conductivity and microstructure of polymer-derived SiC pyrolyzed at temperatures ranging from 1200 °C to 1800 °C were studied. We have shown that both free carbon content and pyrolysis temperature have significant effects on the DC conductivity of polymer derived ceramic (PDC) SiC. The RT DC conductivity of the PDC SiC increased gradually with increasing pyrolysis temperature, and it drastically increases 3 orders of magnitude after 1500 °C. This high electrical conductivity occurs due to the formation of a network of turbostratic carbon (percolative network). Below the percolation regime, hopping enables the electron movement from one carbon cluster site to another. Microstructural investigation with X-ray diffraction (XRD), Raman, and transmission electron microscopy (TEM) analysis showed that the crystal size of SiC increases with increasing pyrolysis temperature, and carbon clusters act as an inhibitor for grain growth at lower pyrolysis temperature. Upon dissociation of clusters, accelerated grain growth occurs and graphitization of carbon occurs along the grains.

In situ observation of the percolation threshold in multiphase magma analogues

Magmas vesiculate during ascent, producing complex interconnected pore networks, which can act as outgassing pathways and then deflate or compact to volcanic plugs. Similarly, in-conduit fragmentation events during dome-forming eruptions create open systems transiently, before welding causes pore sealing. The percolation threshold is the first-order transition between closed- and open-system degassing dynamics. Here, we use time-resolved, synchrotron-source X-ray tomography to image synthetic magmas that go through cycles of opening and closing, to constrain the percolation threshold ΦC at a range of melt crystallinity, viscosity and overpressure pertinent to shallow magma ascent. During vesiculation, we observed different percolative regimes for the same initial bulk crystallinity depending on melt viscosity and gas overpressure. At high viscosity (> 106 Pa s) and high overpressure (~ 1–4 MPa), we found that a brittle-viscous regime dominates in which brittle rupture allows system-spanning coalescence at a low percolation threshold (ΦC~0.17) via the formation of fracture-like bubble chains. Percolation was followed by outgassing and bubble collapse causing densification and isolation of the bubble network, resulting in a hysteresis in the evolution of connectivity with porosity. At low melt viscosity and overpressure, we observed a viscous regime with much higher percolation threshold (ΦC > 0.37) due to spherical bubble growth and lower degree of crystal connection. Finally, our results also show that sintering of crystal-free and crystal-bearing magma analogues is characterised by low percolation thresholds (ΦC = 0.04 – 0.10). We conclude that the presence of crystals lowers the percolation threshold during vesiculation and may promote outgassing in shallow, crystal-rich magma at initial stages of Vulcanian and Strombolian eruptions.

Critical scaling for an anisotropic percolation system on $\Z ^2$

In this article, we consider an anisotropic finite-range bond percolation model on $\mathbb {Z}^2$. On each horizontal layer $\{ (x,i)\colon x \in \mathbb {Z}\}$ we have edges $\langle (x,i),(y,i)\rangle $ for $1 \le |x-y|\le N$. There are also vertical edges connecting two nearest neighbor vertices on distinct layers $\langle (x,i),(x,i+1)\rangle $ for $x,i \in \mathbb {Z}$. On this graph we consider the following anisotropic independent percolation model: horizontal edges are open with probability $1/(2N)$, while vertical edges are open with probability $\epsilon $ to be suitably tuned as $N$ grows to infinity. The main result tells that if $\epsilon = \kappa N^{-2/5}$, we see a phase transition in $\kappa $: positive and finite constants $C_1, C_2$ exist so that there is no percolation if $\kappa <C_1$ while percolation occurs for $\kappa >C_2$. The question is motivated by a result on the analogous layered ferromagnetic Ising model at mean field critical temperature [11, J. Stat. Phys. 161, (2015), 91–123] for which the authors showed the existence of multiple Gibbs measures for a fixed value of the vertical interaction and conjectured a change of behavior in $\kappa $ when the vertical interaction suitably vanishes as $\kappa \gamma ^{b}$, where $1/\gamma $ is the range of the horizontal interaction. For the product percolation model we have a value of $b$ that differs from what was conjectured in that paper. The proof relies on the analysis of the scaling limit of the critical branching random walk that dominates the growth process restricted to each horizontal layer and a careful analysis of the true horizontal growth process, which is interesting by itself. This is inspired by works on the long range contact process [17, Probab. Th. Rel. Fields 102, (1995), 519–545]. A renormalization scheme is used for the percolative regime.

Entropic repulsion for the Gaussian free field conditioned on disconnection by level-sets

We investigate level-set percolation of the discrete Gaussian free field on $\mathbb{Z}^d$, $d\geq 3$, in the strongly percolative regime. We consider the event that the level-set of the Gaussian free field below a level $\alpha$ disconnects the discrete blow-up of a compact set $A$ from the boundary of an enclosing box. We derive asymptotic large deviation upper bounds on the probability that the local averages of the Gaussian free field deviate from a specific multiple of the harmonic potential of $A$, when disconnection occurs. These bounds, combined with the findings of the recent article [12], show that conditionally on disconnection, the Gaussian free field experiences an entropic push-down proportional to the harmonic potential of $A$. In particular, due to the slow decay of correlations, the disconnection event affects the field on the whole lattice. Furthermore, we provide a certain 'profile' description for the field in the presence of disconnection. We show that while on a macroscopic scale the field is pinned around a level proportional to the harmonic potential of $A$, it locally retains the structure of a Gaussian free field shifted by a constant value. Our proofs rely crucially on the 'solidification estimates' developed in arXiv:1706.07229 by A.-S. Sznitman and the second author.

Contour loop analysis of multi-affine nanostructure AZO rough surfaces

Morphology of multi-affine aluminum-doped zinc oxide (AZO) thin films during spray pyrolysis growth process is characterized by contour loop analysis. The results show that the fractal dimension of each contour loop, Df, is different for various level cuts (in contrast to monofractal structures). Averaging it on all levels leads to a value Df = 1.13 ± 0.02, which remains constant during the growth process. Furthermore, there is a crossover to percolation regime with the exponent . Fractal dimension d of all contour loops, calculated by the box-counting method, decreases with the thickness, while the decreasing behavior is not as the monofractal structures ( ) and is influenced by the whole values of h(q) spectrum. To find the distribution of crystalline grains in the AZO rough surfaces during the growth process, the area cumulative distribution of loops was investigated. The results indicate that the exponent, μ, decreases with enhancement of thickness during the growth process. The loops radius is linearly proportional to the grain size of deposited thin films, which could be introduced as a new numerical parameter for determining this experimental measure.

On macroscopic holes in some supercritical strongly dependent percolation models

We consider $Z^d$, with d bigger or equal to three. We investigate the vacant set of random interlacements in the strongly percolative regime, the vacant set of the simple random walk, and the excursion set above a given level of the Gaussian free field in the strongly percolative regime. We derive asymptotic upper and lower exponential bounds for the large deviation probability that the adequately thickened component of the boundary of a large box centered at the origin in the respective vacant sets or excursion set leaves in the box a macroscopic volume in its complement. We also derive geometric information on the shape of the left-out volume. It is plausible, but open at the moment, that certain critical levels coincide, both in the case of random interlacements and of the Gaussian free field. If this holds true, the asymptotic upper and lower bounds that we obtain are matching in principal order for all three models, and the macroscopic holes are nearly spherical. We heavily rely on the recent work arXiv:1706.07229 by Maximilian Nitzschner and the author for the coarse graining procedure, which we employ in the derivation of the upper bounds.

Graphene nanoplatelets as an effective additive to tune the microstructures and piezoresistive properties of cement-based composites

Abstract Piezoresistive cement-based composites, as a type of self-sensing materials, are urgently needed for developing smart buildings. Herein the effect of graphene nanoplatelets (GNPs) on the pore structure, microstructure, mechanical and piezoresistive properties of cement mortar was investigated. A four-probe method was used to quantitatively assess the piezoresistive properties of the GNP-modified cement mortars under cyclic compressions. Results show that appropriate incorporations of GNPs in cement mortars can densify the microstructure and enhance the mechanical properties. The changes in electric conductivity against GNP content follow a percolation regime. The extents and rates of piezoresistive reactions have no simple correlations with GNP contents and loading levels. The mechanisms of piezoresistive reaction are associated with the elastic deformation and interfacial conductance between GNPs and material matrix. However, the interfacial conductance only works in moderate GNP contents. The results and findings of this study may pave a wide path for the uses of cement-based piezoresistive composites in developing self-health monitoring buildings and infrastructures in the future.

Scaling laws under quantum Hall effect for a smooth disorder potential

We carried out the analysis of discovered experimental values of the critical parameter κ for the quantum Hall plateau-plateau transitions in modulation-doped GaAs/AlGaAs heterostructures. It turned out that these values are in the main concentrated at the range of 0.5–0.7. We argue that within the theoretical concepts for the large-scale disorder potential, it corresponds to a borderland between quantum tunnelling processes and classical percolation regime. Just, the critical exponent value for the bandwidth of delocalized states, κ = 0.54 ± 0.01, obtained by us for HgTe-based heterostructure with inverted band spectrum, can be associated with a smooth character of impurity potential in our system.

Interplay between synthetic conditions and micromorphology in poly(3,4-ethylenedioxythiophene):tosylate (PEDOT:Tos): an atomistic investigation.

Micromorphology of conjugated polymers is expected to play a crucial role in both heat and charge transport properties. In this perspective, the details of the polymerization mechanism acquire a fundamental relevance, providing the link between the basic chemical reaction paths and the resulting molecular structure and arrangement. For PEDOT, the role played by the Brønsted bases (proton scavengers) and their impact on the distribution of polymer chain lengths are still a matter of debate. In the present work, we have systematically analyzed several reaction paths leading to PEDOT polymerization. By means of atomistic simulations, we identified the thermodynamically preferred reaction path, proving that tosylate anions rule proton scavenging. PEDOT chain length was computed to be ∼12-13 monomeric units. We could also demonstrate how the proton scavengers set at once the chain lengths and the sample crystallinity. Furthermore, we found that tosylate gives rise to a sharper multimodal distribution of chain length, a feature that supports hypotheses regarding the occurrence of a percolative transport regime mediated by tie chains bridging paracrystalline regions.

Decoupling inequalities and supercritical percolation for the vacant set of random walk loop soup

It has been recently understood [9, 24, 30] that for a general class of percolation models on $\mathbb{Z} ^{d}$ satisfying suitable decoupling inequalities, which includes i.a. Bernoulli percolation, random interlacements and level sets of the Gaussian free field, large scale geometry of the unique infinite cluster in strongly percolative regime is qualitatively the same; in particular, the random walk on the infinite cluster satisfies the quenched invariance principle, Gaussian heat-kernel bounds and local CLT. In this paper we consider the random walk loop soup on $\mathbb{Z} ^{d}$ in dimensions $d\geq 3$. An interesting aspect of this model is that despite its similarity and connections to random interlacements and the Gaussian free field, it does not fall into the above mentioned general class of percolation models, since the required decoupling inequalities are not valid. We identify weaker (and more natural) decoupling inequalities and prove that (a) they do hold for the random walk loop soup and (b) all the results about the large scale geometry of the infinite percolation cluster proved for the above mentioned class of models hold also for models that satisfy the weaker decoupling inequalities. Particularly, all these results are new for the vacant set of the random walk loop soup. (The range of the random walk loop soup has been addressed by Chang [6] by a model specific approximation method, which does not apply to the vacant set.) Finally, we prove that the strongly supercritical regime for the vacant set of the random walk loop soup is non-trivial. It is expected, but open at the moment, that the strongly supercritical regime coincides with the whole supercritical regime.

Continuum percolation for Cox point processes

We investigate continuum percolation for Cox point processes, that is, Poisson point processes driven by random intensity measures. First, we derive sufficient conditions for the existence of non-trivial sub- and super-critical percolation regimes based on the notion of stabilization. Second, we give asymptotic expressions for the percolation probability in large-radius, high-density and coupled regimes. In some regimes, we find universality, whereas in others, a sensitive dependence on the underlying random intensity measure survives.

Effect of Lime and Organic Binders on Clay Gold-Bearing Ores Filterability

The present work relates to hydrometallurgy, in particular, to gold-bearing clay ores leaching processes. The initial and agglomerated material filterability was studied. Filterability varies in different agglomeration conditions. Influence of cement, lignosulfonate, plastizer (Cemmix CemPlast), lime consumption was investigated. The negative effect of organic reagents additives, such as plasticizer (Cemmix CemPlast) and lignosulfonate, on the filtration process was established. Colmatation of agglomerated ore minimizes at CaO and Ca (OH)2 using as a modifier of the system, also phase separation in the percolation regime and under pressure proceeds without difficulty. Lime and cement joint use in the optimum proportion at clay ore agglomeration under the studied conditions reduces the filtration duration from a few hours to 2-5 minutes.

Coarsening and percolation in the kinetic 2d Ising model with spin exchange updates and the voter model

We study the early time dynamics of bimodal spin systems on 2d lattices evolving with different microscopic stochastic updates. We treat the ferromagnetic Ising model with a locally conserved order parameter (Kawasaki dynamics), the same model with a globally conserved order parameter (non-local spin exchanges), and the voter model. As already observed for non-conserved order parameter dynamics (Glauber dynamics), in all the cases in which the stochastic dynamics satisfy detailed balance, the critical percolation state persists over a long period of time before usual coarsening of domains takes over and eventually takes the system to equilibrium. By studying the geometrical and statistical properties of time-evolving spin clusters we are able to identify a characteristic length , different from the usual length that describes the late time coarsening, which is involved in all scaling relations in the approach to the critical percolation regime. We find that this characteristic length depends on the particular microscopic dynamics and the lattice geometry. In the case of the voter model, we observe that the system briefly passes through a critical percolation state, to later approach a dynamical regime in which the scaling behaviour of the geometrical properties of the ordered domains can be ascribed to a different criticality.

Towards fractional-order capacitors with broad tunable constant phase angles: multi-walled carbon nanotube-polymer composite as a case study

In this study, multi-walled carbon nanotube (MWCNT) filled polyevinelidenefluoride-trifluoroethylene-chlorofluoroethylene composites are used to realize fractional-order capacitors (FOCs). A solution-mixing and drop-casting approach is used to fabricate the composite. Due to the high aspect ratio of MWCNTs, percolation regime starts at a small weight percentage (wt%), 1.00%.The distributed MWCNTs inside the polymer act as an electrical network of micro-capacitors and micro-resistors, which, in effect, behaves like a FOC. The resulting FOCs’ constant phase angle (CPA) can be tuned from to by changing the wt% of the MWCNTs. This is the largest dynamic range reported so far at the frequency range from 150 kHz to 2 MHz for an FOC. Furthermore, the CPA and pseudo-capacitance are shown to be practically stable (with less than 1% variation) when the applied voltage is, changed between 500 µV and 5 V. For a fixed value of CPA, the pseudo-capacitance can be tuned by changing the thickness of the composite, which can be done in a straightforward manner via the solution-mixing and drop-casting fabrication approach. Finally, it is shown that the frequency of a Hartley oscillator built using an FOC is almost 15 times higher than that of a Hartley oscillator built using a conventional capacitor.

Ionic transport in AgI‐HgS‐As2S3 glasses: Critical percolation and modifier‐controlled domains

AbstractElectrical measurements, dc and ac, show that (AgI)x(HgS)0.5‐x/2(As2S3)0.5‐x/2 glasses, 0.0 ≤ x ≤ 0.6, exhibit drastic changes in ionic conductivity σi with silver iodide additions. The ionic transport increases by 13 orders of magnitude with increasing silver content from ~0.002 to ~23 at.%, and the activation energy decreases from 1.05 to 0.35 eV. Two distinctly different ion transport regimes above the percolation threshold concentration, xc ≈ 30 ppm, were distinguished. The critical percolation regime at low silver content (≤ 2‐5 at.% Ag) is characterized by a random distribution of silver‐related entities and obeys a power‐law composition dependence of σi. The ion transport parameters depend on the host network connectivity, represented by the average coordination number &lt;n0&gt;, via the critical fictive temperature T0; the calculated T0 value is comparable to the glass transition temperature for the glassy (HgS)0.5(As2S3)0.5 host matrix. In contrast, in the modifier‐controlled domain, the silver‐related entities are nonrandomly distributed. The high Ag+ ionic mobility results from interconnected tetrahedral (AgI2/2S2/2)n chains in the silver iodide content range 0.2 &lt; x ≤ 0.5, and from 2D layers (Ag3/3I3/3)n or 3D mixed tetrahedral subnetwork (AgI3/3S1/2) in the range x &gt; 0.5.

Disconnection by level sets of the discrete Gaussian free field and entropic repulsion

We derive asymptotic upper and lower bounds on the large deviation probability that the level set of the Gaussian free field on $Z^d$, d bigger or equal to three, below a given level disconnects the discrete blow-up of a compact set A from the boundary of the discrete blow-up of a box that contains A, when the level set of the Gaussian free field above this level is in a strongly percolative regime. These bounds substantially strengthen the results of arXiv:1412.3960, where A was a box and the convexity of A played an important role in the proof. We also derive an asymptotic upper bound on the probability that the average of the Gaussian free field well inside the discrete blow-up of A is above a certain level when disconnection occurs. The derivation of the upper bounds uses the solidification estimates for porous interfaces that were derived in the work arXiv:1706.07229 of A.-S. Sznitman and the author to treat a similar disconnection problem for the vacant set of random interlacements. If certain critical levels for the Gaussian free field coincide, an open question at the moment, the asymptotic upper and lower bounds that we obtain for the disconnection probability match in principal order, and conditioning on disconnection lowers the average of the Gaussian free field well inside the discrete blow-up of A, which can be understood as entropic repulsion.

The Widom–Rowlinson model under spin flip: Immediate loss and sharp recovery of quasilocality

We consider the continuum Widom–Rowlinson model under independent spin-flip dynamics and investigate whether and when the time-evolved point process has an (almost) quasilocal specification (Gibbs-property of the time-evolved measure). Our study provides a first analysis of a Gibbs–non-Gibbs transition for point particles in Euclidean space. We find a picture of loss and recovery, in which even more regularity is lost faster than it is for time-evolved spin models on lattices. We show immediate loss of quasilocality in the percolation regime, with full measure of discontinuity points for any specification. For the color-asymmetric percolating model, there is a transition from this non-almost-sure quasilocal regime back to an everywhere Gibbsian regime. At the sharp reentrance time $t_{G}>0$, the model is a.s. quasilocal. For the color-symmetric model, there is no reentrance. On the constructive side, for all $t>t_{G}$, we provide everywhere quasilocal specifications for the time-evolved measures and give precise exponential estimates on the influence of boundary condition.

Partial inertia induces additional phase transition in the majority vote model.

Explosive (i.e., discontinuous) transitions have aroused great interest by manifesting in distinct systems, such as synchronization in coupled oscillators, percolation regime, absorbing phase transitions, and more recently, the majority-vote model with inertia. In the latter, the model rules are slightly modified by the inclusion of a term depending on the local spin (an inertial term). In such a case, Chen etal. [Phys Rev. E 95, 042304 (2017)2470-004510.1103/PhysRevE.95.042304] have found that relevant inertia changes the nature of the phase transition in complex networks, from continuous to discontinuous. Here we give a further step by embedding inertia only in vertices with degree larger than a threshold value 〈k〉k^{*}, 〈k〉 being the mean system degree and k^{*} the fraction restriction. Our results, from mean-field analysis and extensive numerical simulations, reveal that an explosive transition is presented in both homogeneous and heterogeneous structures for small and intermediate k^{*}'s. Otherwise, a large restriction can sustain a discontinuous transition only in the heterogeneous case. This shares some similarities with recent results for the Kuramoto model [Phys. Rev. E 91, 022818 (2015)PLEEE81539-375510.1103/PhysRevE.91.022818]. Surprisingly, intermediate restriction and large inertia are responsible for the emergence of an extra phase, in which the system is partially synchronized and the classification of phase transition depends on the inertia and the lattice topology. In this case, the system exhibits two phase transitions.

Preparation and cold welding of silver nanowire based transparent electrodes with optical transmittances >90% and sheet resistances

In this article, silver nanowires (AgNWs) with aspect ratios of 1000 and lengths up to 200 μm are obtained by a modified polyol approach. These very long AgNWs are then utilized to prepare transparent electrodes (TEs) displaying a transmittance of 91.3% at a sheet resistance of 8.6 ohm/sq without any post-treatment. Furthermore, we also demonstrate a process for the cold welding of Ag NWs by simply dipping the AgNWs films into CTAB solutions, resulting in a further improvement for the optoelectronic performance. After the post-treatment, the AgNW-based TEs can achieve a transmittance of 93% at a sheet resistance of 9.5 ohm/sq. In addition, the electric behaviors of AgNW-based TEs are investigated. In the bulk-like regime, for the as-prepared AgNW-based TEs, the Figure of merit (FOM), DC to optical conductivity ratio reaches up to 566.8. After the cold welding process, the DC to optical conductivity ratio can reach even higher values (631.6). In the percolative regime, the as-prepared and welded AgNW-based TEs can achieve Π (FOM with percolative-like behavior) values of 166.8 and 242.1, respectively.