Percolation threshold

By varying the concentration of surfactant in reverse micelle system, Ag particles from 10 to 200 nm in average diameter were synthesized, which have been characterized by X-ray diffraction and transmission electron microscopy. Isotropical conductive adhesives (ICAs) were prepared by using Ag particles as conductive fillers. It was found that the percolation threshold of ICAs depends on the filler size, which reaches to 63 wt.% when the filler average particle diameter is 50 nm. Results obtained by theoretical calculation are in good agreement with the experimental results.

The fracture of the target and projectile during normal penetration is described using a model of chaotic disintegration modifying the theory of chaotic disintegration of liquids. The radius of the locally smallest fragment is calculated equating its kinetic energy of deformation with its surface energy of fracture. The probability of lacunae opening in the target and projectile materials increases near the target/projectile interface. The percolation threshold for this probability determines the boundary of the fractured zone. When this fractured zone reaches the rear surface of the target the fragments can leave it. Mass distribution of the fragments was calculated with the help of percolation theory. Then, the shape of the debris cloud and the direction, velocity and range of its propagation are calculated to estimate vulnerability behind the perforated target.The calculations were compared with results of normal impact experiments performed with tungsten sinter alloy rods (D=20 mm, L/D=6) against 40 and 70 mm rolled homogeneous armor (RHA) at an impact velocity of 1700 m/s  and . For observation of the bulging, breakup and fragmentation of the bulge as well as debris cloud formation and expansion, flash X-ray and laser stroboscope techniques have been applied. From the X-ray photographs and soft recovery tests the shape of the debris cloud and velocity field of the fragments as well as the fragment number and mass distributions have been determined, respectively. The calculations predict well the experimental data.

It is increasingly acknowledged that we are on the verge of the next technological revolution and the fourth industrial revolution, driven by the digitization and interconnection of all physical elements and infrastructure under the control of advanced intelligent systems. Therefore, there will be a new era of automation that should result in enhanced productivity. However, such productivity enhancements
have been anticipated before, particularly during the third industrial revolution commonly known as the ‘information age’, and have failed to materialize. Were the productivity increases observed following the first and second industrial revolutions a one-time aberration that will not be repeated in the new digital age? In this paper, we attempt to address
this question by a semi-quantitative analysis of the prior productivity jumps and their physical technological origins, and extend this analysis to the latent set of analogous digital technologies. Using this approach, we project that there will indeed be a second productivity jump in the United States that will occur in the 2028–2033 timeframe when the
aggregate of the of constituent technologies reaches the tipping point at 51 percent penetration.

The present doctoral thesis is based on experimental data obtained mostly using the structure of two research units: the “Laboratório de Reciclagem de Polímeros” at “Universidade Federal de Uberlândia”, Brazil, and “Laboratoire Génie des Procédés Papetiers” at “Université Grenoble Alpes”, France. This study was performed from 2014 to 2017 within the joint doctoral program between Universidade Federal de Uberlândia and Université Grenoble Alpes established in the agreement for cotutelle of doctoral thesis signed by these two institutions.
This manuscript is organized in three chapters. Chapter I is the literature review. This section was designed to provide most of information required to understanding of context of the research work developed in the following chapters. Through the analysis and comparison of selected publications, this chapter covers topics such as: cellulose
structure and its features, cellulose polymorphs, mercerization and regeneration process, cellulose nanocrystals, its production, properties and applications. Chapter II presents a comprehensive study of cellulose I and II nanocrystals prepared by sulfuric acid hydrolysis focusing basically on morphological and molecular structure. Chapter III is a
research work on mechanical properties of natural rubber nanocomposites reinforced using high aspect ratio cellulose nanocrystals isolated from soy hulls, with emphasis on the mechanical, thermal and morphological properties of the nanocomposites obtained. This manuscript is the original work of the author.

Ionic groups incorporated into a polymer have a decided effect on its physical properties. A number of ionomers and polyelectrolytes have been widely applied. In particular, sulfonated bisphenol-A polysulfone (SPSF) has been used as a composite or single-component membrane for the desalination of water. In this article, the synthesis and physical characteristics of sulfonated polysulfone are addressed. A detailed synthesis route is provided and methods that yield determinable levels of sulfonation are described. These ion-containing polymers retain an excessive amount of residual salts, which, of course, are impurities to the system. Therefore, before any analyses were made the polymers were subjected to a thorough soxhlet extraction process with boiling water, which appeared to be quite effective. The degree of sulfonation was assessed by several methods such as 1H NMR and FT-IR. A new 1H NMR method was derived because the method cited in the literature proved to be too inconsistent for our work. The new 1H NMR method used a quaternary ammonium counterion [N(CH3)4]. These methyl protons are easily measured and may be ratioed against the isopropylidene protons in the polymer backbone that act as an internal standard. Characterization of the physical properties of SPSF consisted of water uptake, differential scanning calorimetry (DSC), thermomechanical analysis (TMA), and solubility studies. Its physical appearance and mechanical behavior were improved by the solution procedure. Also addressed were the effects of different counterions (Na+ & Mg++) with SPSFs of low levels of sulfonation. The variation in physical properties between the divalent and monovalent counterions is dramatic, especially when observed by TMA in the rubber plateau above the apparent glass temperature.

The PZT/polyvinyl chloride (PVC) composites are prepared by hot-pressing technique using a novel nanocrystalline PVC. The d33 value observed in this work for the 0.5PZT/0.5PVC composite is close to the 0.5PZT/0.5PVDF composite reported in the literature, but PVC is much cheaper than PVDF. The three-phase fgC/0.5PZT/(0.5 − fg)PVC composites are obtained by adding a small content of graphite particles to the 0.5PZT/0.5PVC composite. The measured dielectric properties demonstrate that a percolation transition occurs in the three-phase composites as in normal two-phase metal–insulator continuum media. An optimum piezoelectric property is obtained by adding fg = 0.005 before the percolation threshold in the fgC/0.5PZT/(0.5 − fg)PVC composites, which is 50% higher than that of the 0.5PZT/0.5PVC composite. X-ray powder diffraction (XRD) patterns show domain rotation is easy in this three-phase composite, and P–E hysteresis loops conform that a small amount of graphite particles adding in the composite break the polymer seclusion, and considerably decrease coercive field of the composite.

This report describes the results of a theoretical investigation into the nonlinear optical response of granular composites. In particular, we have investigated the degree to which the cubic nonlinear response can be enhanced in such composites, relative to the same response in pure materials. Cubic nonlinear response is potentially of great practical importance in developing novel materials with a strongly intensity-dependent transmission coefficient, index of refraction, etc. We find that there are many types of composite geometries which give rise to such strong enhancements. These include composites near the percolation threshold, composites in which one of the components is arranged in the form of a fractal cluster, and nonlinear coatings (such as dyes) adsorbed onto the surface of particles which have a resonant optical response at an appropriate frequency. We have carried out this investigation using both analytical approximations and a variety of approximate numerical techniques, including large-scale computer simulations. Finally, we briefly describe some work in progress, in which a composite composed of materials with a purely guardratic response can exhibit an enhanced curbic response.

In this work, we highlight the links between fractals and scaling in cells and explore the kinetic consequences for biochemical reactions operating in fractal media. Based on the proposal that the cytoskeletal architecture is organized as a percolation lattice, with clusters emerging as fractal forms, the analysis of kinetics in percolation clusters is especially emphasized. A key consequence of this spatiotemporal cytoplasmic organization is that enzyme reactions following Michaelis-Menten or allosteric type kinetics exhibit higher rates in fractal media (for short times and at lower substrate concentrations) at the percolation threshold than in Euclidean media. As a result, considerably faster and higher amplification of enzymatic activity is obtained. Finally, we describe some of the properties bestowed by cytoskeletal organization and dynamics on metabolic networks.

Percolation on two-dimensional small-world networks has been proposed as a model for the spread of plant diseases. In this paper we give an analytic solution of this model using a combination of generating function methods and high-order series expansion. Our solution gives accurate predictions for quantities such as the position of the percolation threshold and the typical size of disease outbreaks as a function of the density of "shortcuts" in the small-world network. Our results agree with scaling hypotheses and numerical simulations for the same model.

La criticalidad auto-organizada (SOC) fue propuesta a mediados de la década de 1990 por el dinamarqués Per Bak [1948-2002] para modelar procesos complejos de transiciones de fase. El concepto arroja luz sobre procesos de naturaleza fractal y distribuciones independientes de escala en la cultura, el arte y la sociedad. Aunque la técnica gozó de sus momentos de fama, en los últimos años su impulso parece haberse agotado; habrá que examinar por qué.

En esta misma presentación se analizan otras teorías de dinámica no lineal subyacentes a diversos procesos de la naturaleza y la cultura: epidemiología, percolación, umbrales críticos, ruptura de simetría, morfogénesis.

The electrical conductivity of polymer/multi-walled carbon nanotubes (MWCNTs) composites in a powder and in a hot-pressed compacted state, prepared by mechanical mixing, was studied. The semicrystalline ultrahigh molecular weight polyethylene (UHMWPE) was used as a polymer matrix. The data clearly evidence the presence of a percolation threshold φc at a very small volume fraction of the MWCNTs φ in a polymer matrix, φc ≈ 0.0004–0.0007. The ultralow percolation threshold in UHMWPE/MWCNTs thermoplastic composites was explained by high aspect ratio of the nanotubes and their segregated distribution inside the polymer matrix. The method of composite preparation effects the values of percolation threshold concentration φc and critical exponent t. A noticeable positive temperature coefficient of resistivity (PTC effect) was observed in the region of temperatures higher than melting point. It was explained by influence of thermal expansion of the polymer matrix and independence from the melting process that is a result of specific structure of conductive phase.