Dynamic Percolation Theory Research Articles

Transparent nanocomposites with enhanced performances from poly(propylene carbonate) and silica

AbstractIn this study, silica nanoparticles with a refractive index matching PPC and a diameter smaller than the visible light wavelength were chosen to prepare enhanced PPC/silica nanocomposites by a simple melt compounding method. The result exhibited all the nanocomposites possessed excellent transparency (about 90%), even in the nanocomposite with a silica content of 10 wt%. For PPC/silica nanocomposites, the percolation threshold was determined to be 7.5 wt% based on the dynamic rheological behavior and percolation theory. Moreover, the overall performance of the PPC‐based nanocomposite with a silica content of 7.5% is the best. The optimal nanocomposite showed a Young's modulus of 3792 MPa, a yield strength of 46.5 MPa, a storage modulus of 3812 MPa and a highest temperature at maximum weight‐loss rate (Tmax, 309°C). These characteristics are very important for potential commodity applications of PPC.

Robustness Analysis of Interdependent Urban Critical Infrastructure Networks Against Cascade Failures

This paper presents the robustness analysis of the interdependencies between urban critical infrastructures (CI) against cascade failures. An analytical approach based on the dynamic percolation theory was introduced to investigate the multilayer interactional CI networks and to predict the urban calamity spreading as illustrate with example of China. The synergetic effect of the functional and geographical interdependencies between the networks on cascade failures of CI was studied by comparing four relevance patterns: no interdependency, the functional interdependency, the geographical interdependency, and the functional with geographical interdependency, where three different attack strategies were simultaneously considered. The results indicate that the geographical interdependency has a remarkable influence on the robustness of networks compared with functional interdependency. Moreover, excavating the scope and extent of the impact of these interdependencies, one can also find that the power network basically governs the cascade failures of global systems in contrast with water or gas network.

An Experimental Strategy with Zwitterionic Pendants Groups on Poly (poly (ethylene glycol) Methacrylate) to Know the Role of Ion Clusters in the Fast Ionic Conductivity of on Ppegma / LiPF6

In this work propose an experimental strategy to explain the fast ion transport of pPEGMA /LiPF6 electrolytes at high salt concentration with the presence of ion clusters. In this study it has demonstrate the ability to functionalize the lateral chains of pPEGMA with zwitterionic groups without altering the morphology of pPEGMA. This work show a successful functionalization of pPEGMA (pMPS8-co-PEGDMA) able to dissociate salt completely. The analysis of TG, DSC, XRD and IES show that in pPEGMA/LiPF6 at low salt concentration the ionic conductivity is coupled with the mobility of chains, the transport mechanism occur through dynamic percolation theory where the translational dynamics of the ions depends of segmental dynamics and by renewal of hopping probabilities. The monotonic increase of ionic conductions with increasing of ion clusters, is due that the ion motion is complete decoupled of relaxation chains. Tg values increase from -49 to -32 oC, enough to obtain a rigid polymer electrolyte in which the cation transport occur through a static ion clusters way by percolation theory. The ion conduction of the polyether pPEGMA show that it morphology reach a certain rigidity as a rubbery electrolyte when the system change to polymer in salt. Therefore pPEGMA is an ideal polymer to use in the next generation of advanced polymer electrolyte. Figure 1

Theory and Simulation of Attractive Nanoparticle Transport in Polymer Melts

We theoretically study the diffusion of a single attractive nanoparticle (NP) in unentangled and entangled polymer melts based on combining microscopic “core–shell” and “vehicle” mechanisms in a dynamic bond percolation theory framework. A physical picture is constructed which addresses the role of chain length (N), degree of entanglement, nanoparticle size, and NP–polymer attraction strength. The nanoparticle diffusion constant is predicted to initially decrease with N due to the dominance of the core–shell mechanism, then to cross over to the vehicle diffusion regime with a weaker N dependence, and eventually plateau at large enough N. This behavior corresponds to decoupling of NP diffusivity from the macroscopic melt viscosity, which is reminiscent of repulsive NPs in entangled melts, but here it occurs for a distinct physical reason. Specifically, it reflects a crossover to a transport mechanism whereby nanoparticles adsorb on polymer chains and diffuse using them as “vehicles” over a characteristic d...

Polymer electrolytes through functionalization of poly (poly (ethylene glycol) methacrylate) with zwitterionic pendant groups: The role of ion clusters upon conductivity

The present study proposes a complete (pMPS8) and partial (pMPS8-co-PEGDMA) functionalization of poly(poly(ethyleneglycol) methyl ether methacrylate (pPEGMA) with zwitterionic pendant groups to improve the mobility of polymer chains and ion-ion associations during Li+ conduction (weak electrolyte). Structural, thermal and electrochemical characterizations of the polymer electrolytes are conducted to analyze the dependence of conductivity on LiPF6 concentration. The ionic conductivity of pMPS8 (3.22 × 10−5 S cm−1 at 25 °C) in the presence of LiPF6 is due to the incorporation of the zwitterionic pendant groups into the pPEGMA. In pMPS8, a more significant interaction of Li+ with the sulfobetaine group at low LiPF6 concentrations, decreases its ion movement. While at higher salt concentrations, the saturation of sulfonate groups with Li+ makes possible its interaction with ethoxy sites, thus, increasing ionic conductivity. pMPS8 is less sensitive (i.e. ionic conductivities remain constant) to the increases of salt concentration compared to the pMPS8-co-PEGDMA (larger number of ethoxy sites per pendant groups) due to its complete functionalization (short range mobility). The ionic conductivity for pMPS8-co-PEGDMA polymer starts to be significant at molar ratios higher than 1.0: 1.0, suggesting that above this stoichiometry the interactions between zwitterion pendant groups and lithium salt become suppressed, enabling its use at higher LiPF6 concentrations. The analysis of TGA, DSC, XRD and EIS exhibit that ionic conductivity is coupled with the mobility of chains, hence the transport mechanism occurs through dynamic percolation theory where the translational dynamics of the ions depends on segmental dynamics and by renewal of hopping probabilities.

Functionality and performance evaluation of directly compressible co-processed excipients based on dynamic compaction analysis and percolation theory

In the present work functional properties of new, co-processed excipients, Pharmaburst® 500, Parteck® ODT, Ludiflash® and Disintequik™ ODT, intended for direct compression of orally disintegrating tablets (ODTs), were investigated based on dynamic compaction analysis and percolation theory. Tablet disintegration time and mechanical properties have been recognized as critical quality attributes (CQAs) which should be optimized through pharmaceutical development. According to the obtained results, in order to achieve adequate mechanical resistance, excipients exhibiting high compactibility and tabletability are required, while, on the contrary, high porosity excipients with higher extent of elastic deformations, average tabletability and compactibility are necessary to obtain fast tablet disintegration. The results obtained in this study indicate that the most important excipient properties affecting tablet CQAs are porosity, mechanism of consolidation, compactibility and tabletability. Pharmaburst® 500, excipient with the highest elastic recovery, the lowest relative density, average compactibility and tabletability, and remarkably high dilution capacity (69.6% w/w of caffeine or 49.1% w/w of ibuprofen) exhibited favourable performance for ODT direct compression. Dynamic compaction analysis and percolation theory proved to be useful tools which can contribute to identification of the most important excipient functional properties influencing critical quality attributes of the prepared ODTs.

Invulnerability of grown Peer-to-Peer networks under progressive targeted attacks

Security issues of Peer-to-Peer (P2P) networks have attracted more and more research in recent years. In this paper, using complex features of P2P networks, we shift the focus to the study of invulnerability of grown P2P networks under progressive targeted attacks. Based on dynamic process and reverse percolation theory, we present several mechanisms that attacked P2P networks can adopt to minimize the disasters aftermath progressive targeted attacks. In this process, we proposed: (i) the dynamics of grown P2P networks under targeted attacks can make sure an attacked P2P network restore a power-law (PL) characteristic to a normal level; (ii) a global degree restoring process from the aftermath of progressive targeted attacks can restore the status of set of high degree peers to normal; (iii) a reverse percolation process glues the fragmented small connected component of a destroyed grown P2P network into a giant connected component (GCC). Experimental results show that an attacked grown P2P network can restore the key characteristics, such as power-law characteristic of original P2P network, the set of high degree peers and the giant connected component, to a regular status. In this way, we can illustrate the invulnerability of progressive targeted attacks on grown P2P networks which is particularly useful in designing complex P2P networks.

High Ionic Conductivity of Transparent Film of Hydroxyapatite and Poly(vinyl alcohol) Nanocomposite

AbstractSummary: Hydroxyapatite (HAp)‐polyvinyl alcohol (PVA) nanocomposite film containing Li+ was designed as a solid polymer electrolyte. A composite was prepared by reacting Ca(OH)2 with H3PO4 in the presence of PVA which is denatured in order to have the carboxyl group, and a LiN(CF3SO2)2 was added. HAp particles were commonly formed in the shape of spindles (long axis ca. 80 nm and short axis ca. 25 nm). The obtained nanocomposite film, in which HAp particles were dispersed uniformly, is transparent, flexible and drawable. Its ionic conductivity is about 10−3 S/m at room temperature. This value is very large. This high ionic conductivity is considerable on the basis of the dynamic percolation theory.

Ion diffusion in a polymer network: Monte Carlo studies and the dynamic percolation approach

An athermal lattice model for diffusion of tracer particles through a network of polymer chains with variable length is studied (i) by Monte Carlo simulation and (ii) by a more coarse-grained description in terms of dynamic percolation (DP) theory. A recently developed fluctuation site-bond Monte Carlo algorithm is used that allows us to investigate systems with high monomer density. In the high-density regime we find that the tracer correlation factor becomes much smaller than unity, and the time-dependent diffusion coefficient of tracer particles develops power-law behavior. DP-results for diffusion, which require much less computational effort, compare favorably with the full simulations up to moderate densities. Limitations of the DP-concept for high densities are demonstrated.

Temperature-induced percolation behavior of AOT reverse micelles affected by poly(ethylene glycol)s

The influence of poly(ethylene glycol)s additives viz. mono- (EG), di- (DEG), tri- (TEG), tetra- (TeEG) and poly(ethylene glycol)-400 (PEG-400) on temperature-induced electrical percolation of water/AOT/isooctane microemulsion system has been investigated. The composition of microemulsion systems has been kept constant to ω = 22 and [additive] = 0.1 M w.r.t. dispersion medium. The effect of increase in the non-polar continuum ( S= [Oil]/[AOT]) is indicated by increase in the percolation threshold, θ c . The findings have been elaborated in terms of validity of scaling laws in the light of the dynamic percolation theory. The activation energy of the process, Δ E p , has been estimated from Arrhenius plots. Pseudophase concept of the micellar aggregation has been utilized to assess the thermodynamics of clustering of the nanodroplets. The state of trapped water in the micellar core and the corresponding interactions with the AOT head group has been visualized through 1H NMR and FTIR analysis. Results show that at higher ω (>16.0), encapsulated water behaves like free or the bulk water.

Percolating Microemulsions of Nonionic Surfactants Probed by Dielectric Spectroscopy

Charge exchange in aggregated micelles: Percolation phenomena in microemulsions of nonionic surfactants were studied by dielec. spectroscopy. For the studied 10-3 M KCl(aq.)/n-octane/C12E5 system the cond. and Cole-Cole parameter follow the predictions of the dynamic percolation theory, whereas the relaxation time and the dispersion amplitude of the characteristic relaxation are specific to the sample compn.

On the Temperature Percolation in a w/o Microemulsion in the Presence of Organic Derivatives of Chalcogens

The course of temperature percolation in a w/o microemulsion system comprising water/bis(2-ethylhexyl) sulfosuccinate sodium, AOT/isooctane affected by the presence of additives has been investigated. Additives, viz., organic derivatives of chalcogens including dipyridyl diselenide (Py2Se2), diphenyl diselenide (Ph2Se2), and dipyridyl ditelluride (Py2Te2), have been assimilated in the reverse micellar system. Formulations have been studied in terms of (i) the concentration variation of additives, (ii) the change in omega (= [H2O]/[AOT]), and (iii) the change in the nonpolar continuum, S (= [oil]/[AOT]). Phenyl derivatives hinder the percolation, whereas the pyridyl derivative in moderate amounts favors the phenomenon. The estimated values of the critical exponents are lower than those predicted by the dynamic percolation theory. The association model has been implemented to access the thermodynamic parameters of droplet clustering. Pyridyl compounds are expected to alter the rigidity of the surfactant monolayer, which could help to promote the attractive interdroplet interaction. FT-IR spectroscopy has been used to elucidate the changes occurring in the core water in the presence of organic derivatives of chalcogens as the droplet size is increased. Results have been rationalized in terms of the alteration in the physicochemical behavior of the water/AOT/isooctane microemulsion in the presence of additives.

Dynamic percolation theory for particle diffusion in a polymer network

Tracer-diffusion of small molecules through dense systems of chain polymers is studied within an athermal lattice model, where hard-core interactions are taken into account by means of the site exclusion principle. An approximate mapping of this problem onto dynamic percolation theory is proposed. This method is shown to yield quantitative results for the tracer correlation factor of the molecules as a function of density and chain length provided the non-Poisson character of temporal renewals in the disorder configurations is properly taken into account.

Percolation concepts in solid state ionics

Structural disorder is an inherent property of solid materials, which can support a macroscopic ionic current. Many transport phenomena in these solid ionic conductors appear to be related to concepts from percolation theory. We demonstrate this for three classes of materials, namely (i) dispersed ionic conductors, which show conductance properties that can be related to random electrical networks, (ii) ion-doped network glasses, whose concentration-dependent diffusion properties are accessible by critical path analysis, and (iii) polymer ionic conductors. For the latter we discuss Monte Carlo simulations which indicate the applicability of dynamic bond percolation theory.

Broad-Band Conductive Spectra of Polypropylene Oxide Complexed with LiClO4

Broad-band conductive spectroscopy covering a 10 mHz–1 GHz frequency range has been employed to examine the ionic motions in polypropylene oxide (PPO) complexed with 0–1% LiClO4 at temperatures from -60 °C to 100 °C. The dc conduction appears as a plateau of the conductive spectra in their medium frequency range. As the frequency is lowered, the dc conduction is suppressed by the electrode polarization and results in a Cole-Cole conductive relaxation. At high frequencies, the conductive spectra are overtaken by the dielectric relaxations due to dipolar motions associated with the segmental- and normal-mode processes of PPO molecules. In addition, a new relaxation process was found, which is attributable to the ionic motion because the relaxation strength increases with LiClO4 concentration in parallel with an increase of dc conductivity. This finding suggests that the dissociated ions undergo local fluctuational motion (ionic relaxation) prior to starting long-range diffusion (dc conduction). Analysis based on a dynamic bond percolation theory shows that this ionic relaxation occurs in harmony with segmental-mode motion while the dc conduction is associated with the normal-mode process through a renewal of local hopping probabilities.

Stochastic modeling of boiling-site interaction.

A stochastic model is proposed and kinetic equations are derived to describe the boiling process on a solid surface. The model considers bubble growth at discrete nucleation sites and accounts for interactions between adjacent sites. The model is valid for initial stages of nucleate boiling when vigorous surface boiling has not yet commenced. The interactions considered are the seeding with vapor of inactive sites by bubbles at neighboring active sites, and the deactivation of active sites by thermal interference from neighboring sites. The stochastic model is applied in Monte Carlo simulation, employing parameters obtained from experimental results, to predict bubble emission rates and heat fluxes from the surface. The numerical results predict the presence of many permanently inactive sites, the formation of active-site clusters, and the rise in the density of active sites with increase in overall heat flux. The description of the homogeneous nucleate boiling process in terms of dynamic percolation theory is presented.

Mechanical properties of dynamically disordered networks

Ionic motion in polymeric ionic conductors has been recently described in the framework of dynamic percolation theory (DPT) or, more generally, dynamic disorder hopping (DDH). In these models the polymer network above the glass transition is modelled as a random bond network in which the random bond distribution evolves in time with rate characteristic to the polymer motion. The present paper deals with the mechanical properties of such networks. We present a simple analysis of the viscosity of such dynamically disordered networks, thus relating a characteristic network relaxation time to the local (microscopic) viscosity of the polymer. If the same time is assumed to govern ionic transport, we obtain a relation between the ionic diffusion rate and the polymer viscosity. Estimates of the ionic diffusion based on this model are consistent with experimental observations.

Dynamic bond percolation theory for diffusion of interacting particles: Tracer diffusion in a binary mixture lattice gas

Dynamic percolation theory is used to obtain the tracer diffusion coefficient in binary mixtures of ‘‘noninteracting’’ lattice gas (with only the blocking interactions, i.e., double occupancy of a lattice site is forbidden) within the effective medium approximation (EMA). Our approach is based on regarding the background particles as a changing random environment. The result is expressed in terms of two fluctuation time parameters which we attempt to determine self-consistently. We compare two possible choices for these parameters which are consistent with our former results for the single component system. The resulting tracer diffusion coefficient for both choices compares well with numerical simulations whenever single bond EMA is expected to be reliable. Comparison is also made with the theoretical results of Sato and Kikuchi [Phys. Rev. B 28, 648 (1983)] and discrepancies between both theories are discussed.

Tracer diffusion of interacting particles on incomplete lattices: Effective medium approximation

Dynamic percolation theory is adapted to obtain diffusion coefficients for particles with blocking interactions on incomplete lattices, within an effective medium approximation (EMA). The substrate lattices have static bond disorder. The motion of a tracer particle among identical background particles is regarded as particle motion in a fluctuating random environment superimposed on the statically disordered lattice; the fluctuations results from the motion of the background particles. Several schemes for incorporating the effect of the background particles are discussed, all relating their motion in different ways to the macroscopic diffusion. Comparisons with Monte Carlo simulations are performed for two-dimensional simple square and three-dimensional simple cubic lattices. In the range where single bond EMA is thought to be reliable, good agreement with the simulation is achieved.

Dynamic percolation theory for diffusion of interacting particles

The recently developed dynamic percolation theory is used to solve the problem of diffusion of interacting particles in lattice-gas models within an effective medium approximation. The approach is based on the observation that the motion of a tracer particle in a system of (similar or different) particles can be viewed as particle motion in a changing random environment. This makes it possible to use effective medium theory (EMT) solutions to the latter problem. The main conceptual problem of this approach is to relate the characteristic microscopic times for the evolution of the disordered background to the macroscopic diffusion. We discuss and compare several possible ansatzs for this relation and conclude that relating these times to the chemical diffusion rate is the most reasonable simple choice. Using this ansatz, we obtain EMT approximations for the tracer diffusion coefficient in the noninteracting lattice-gas (NILG, blocking interactions only) model and an approximate EMT relation between the chemical and the tracer diffusion coefficients in a lattice gas with nearest-neighbor interactions. Agreement with available simulation results is good whenever single bond EMT is expected to be reliable.