Universality and cluster structures in continuum models of percolation with two different radius distributions

Lorenz, B.; Orgzall, I.; Heuer, H.-O.

doi:10.1088/0305-4470/26/18/032

Cited by 72 publications

(52 citation statements)

References 27 publications

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“…The concentration where the composite behaves as a conductor (and the ac conductivity is loss free) is estimated to be roughly φ′ 0.33 %. The threshold 0.33 is consistent with the percolation threshold in three-dimensional continuous network [15,16,17].…”

supporting

confidence: 74%

Dynamics of electric charge transport and determination of the percolation insulator-to-metal transition in polyvinyl-pyrrolidone/nano-graphene platelet composites

Lampadaris

Sakellis

Papathanassiou

2017

Applied Physics Letters

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Polyvinyl-pyrrolidone (PVP) loaded with different fractions of dispersed nanographene platelets (NGP) were studied by Broadband Dielectric Spectroscopy in the frequency range from 1 mHz to 1 MHz. Complex permittivity and dynamic ac conductivity as a function of frequency, temperature and composition were explored. The concentration-dependent insulator-to-conductor transition was traced through dependence of the dc conductivity and the onset of the dispersive ac ac conductivity. The temperature evolution of the dielectric spectra, below and above the fractional threshold exhibits different dynamics and signs the critical percolation threshold. Percolation is dictated by quantum penetration of the effective potential barrier set by the polymer matrix operating in parallel with conduction along physical contact of NGP, in accordance with predictions for systems consisting of a semi-conducting matrix and dispersed conducting inclusions.* Corresponding author; e-mail address: antpapa@phys.uoa.gr 2 Functional polymers with dispersed nano-structures exhibit properties of significant technological importance, broad applicability and low production cost. Polyvinyl-pyrrolidone (PVP) is a polymer wide known for its pharmaceutical applications. It can be used as binder, coating and disintegrate for tablets stabilizer [1]. PVP is easily dissolved in water; both PVP and water are non-toxic, environmentally friendly and bio-compatible materials. Graphene is an excellent conductor of electricity and can be dispersed into water. Nano-graphene platelets combine the advantageous properties of graphene and the low production cost (e.g., in relation with single layered graphene). Thus, controlling the PVP/NGP composition, one can tune the properties of the composite, respectively, and achieve the desired optimum properties respectively. In this way, novel ambitious devices can be innovated. For example, water solutions PVP/ NGP composite can be used as bio-compatible link between electrodes and skin or tissues. As a result, various coated functional polymers with graphene [2, 3] have been prepared in order to analyse the mechanisms of charge transfer [4], to find the critical nanoparticle concentration to achieve percolation of electric charge carriers along the volume of the composite [5,6,7] and generally to inspect the electrical properties for those various matrices.Lastly, PVA (polyvinyl-alcohol) is a relevant material with polyvinyl-pyrrolidone that has been studied significantly [8]. In such studies, the dc conductivity vs composition is examined to find the percolation threshold. Standard percolation theories [9] assume that the host matrix is a perfect insulator, which is an abrupt assumption in many real systems. Recent progresses on percolation phenomena in systems with matrixes that can be penetrated by electron quantum mechanical tunneling [10] describe better PVP/NGP composites.Aqueous polymer solutions were formed by dissolving PVP K30 (ASG SCIENTIFICCAS 9003-39-8) in de-ionized doubly distilled water and aque...

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supporting

confidence: 74%

Dynamics of electric charge transport and determination of the percolation insulator-to-metal transition in polyvinyl-pyrrolidone/nano-graphene platelet composites

Lampadaris

Sakellis

Papathanassiou

2017

Applied Physics Letters

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“…In contrast, the volume of proteins scales linearly with the surface areas of proteins (Fig 2b). This linear relationship is also what is observed in models for disordered materials [17, 18]. …”

Section: Scaling Behaviorsupporting

confidence: 81%

“…For randomly packed spheres, when the packing density p d is greater than a threshold density p c , clusters become connected to each other, and the size of the largest cluster approaches the size of the whole system [17, 19]. At this percolation threshold p c , the volume V of a cluster of random spheres scale with the length R of the cluster as V ∝ R D , with a characteristic exponent D = 2.5 in three-dimensional space [17, 18].…”

Section: Scaling Behaviormentioning

confidence: 99%

Geometry of protein shape and its evolutionary pattern for function prediction and characterization

Liang

2009

2009 Annual International Conference of the IEEE Engineering in Medicine and Biology Society

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Proteins contain thousands or more atoms and have complex shapes. We discuss here the computation of protein packing defects, in the form of voids and pockets, from experimentally resolved protein structures, and the nature of their distribution and scaling behavior, as well as their origin. We further discuss how evolutionary selection pressure due to biological function unaltered by selection pressure due to constraints from folding and stability can be isolated and estimated, and how such information can be used to predict protein function and characterize binding properties of enzymes.

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“…Detailed studies have revealed that when void-size distribution, [2][3][4][5][6] that is related to the distribution of width, is introduced to this model, the threshold p c depends on this void-size distribution. The universality of this model could be violated, although statistical errors involved in previous calculations did not allow the full confirmation of this phenomenon.…”

Section: Introductionmentioning

confidence: 99%

Conductivity Percolation on a Square Lattice with Two Different Sizes of Particles

et al. 2009

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Electric conductance of percolation clusters is calculated by means of the random circuit approximation, under a binary distribution in the size of the conducting particles. Although we have already investigated the same size distribution model in terms of the percolation threshold, the electric transport conductance of this model is never reported before. The size distribution of conducting particles induces a clear difference in the ensemble of random circuit. However, the observed critical behavior and critical exponents are closely matched to those reported for monodisperse cases.

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Universality and cluster structures in continuum models of percolation with two different radius distributions

Cited by 72 publications

References 27 publications

Dynamics of electric charge transport and determination of the percolation insulator-to-metal transition in polyvinyl-pyrrolidone/nano-graphene platelet composites

Dynamics of electric charge transport and determination of the percolation insulator-to-metal transition in polyvinyl-pyrrolidone/nano-graphene platelet composites

Geometry of protein shape and its evolutionary pattern for function prediction and characterization

Conductivity Percolation on a Square Lattice with Two Different Sizes of Particles

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