A complete graph effective medium approximation for lattice and continuum percolation

Grimaldi, Claudio

doi:10.1209/0295-5075/96/36004

Cited by 10 publications

(21 citation statements)

References 37 publications

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“…For slender rods (a ≪ 1) and unless the rods are perfectly aligned [52], we can set a = 0 in Eq. (46). For S = 0, we find exactly R(0, 0) = 4/e ≃ 1.47, where e is the Neper number, which reproduces approximately the g * /g * 0 results shown in the inset of Fig.…”

Section: Effect Of Orientational Alignmentsupporting

confidence: 82%

“…For S = 0, we calculate numerically the angle averages in Eq. (46) to find that R(S, 0) increases monotonically as S increases, as shown in the inset of Fig. 6 (dashed line).…”

Section: Effect Of Orientational Alignmentmentioning

confidence: 75%

“…where R(0, a) ≃ 4/e is given by the S = 0 limit of Eq. (46). In terms of volume fraction, Equation (53) applies when φ φ * , where…”

Section: Effect Of Attraction Between the Rodsmentioning

confidence: 99%

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Impact of tunneling anisotropy on the conductivity of nanorod dispersions

Nigro

Grimaldi

2014

Phys. Rev. B

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While the tunneling conductance between two spherical-like conducting particles depends on the relative inter-particle distance, the wave function overlap between states of two rod-like particles, and so the tunneling conductance, depends also on the relative orientation of the rod axes. Modeling slender rod-like particles as cylindrical quantum wells of diameter D and length L ≫ D, we calculate the matrix element of the tunneling between two rods for arbitrary relative orientations of the rod axes. We show that tunneling between two parallel rods is about L/ √ Dξ times larger than the tunneling matrix element for perpendicular rods, where ξ is the tunneling decay length. By considering the full dependence of the tunneling conductance on the angle between rod axes, we calculate within an effective medium theory the conductivity of dispersions of rods with different degrees of alignment. We find that for isotropically oriented rods, the effect of orientation in the tunneling processes is marginal for all rod concentrations. On the contrary, for systems of strongly aligned rods, the enhanced tunneling between nearly parallel rods increases significantly the system conductivity in a relatively large concentration range. Next, we consider systems in which shortrange attraction between rods is added, as in dispersions of rods with depletion interaction. We find that the strongly anisotropic attraction promotes enhanced tunneling between neighboring parallel rods, increasing the effective medium conductivity by several orders of magnitude compared to the case in which the angular dependence of tunneling is ignored, even for relatively weak attractions.

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Section: Effect Of Orientational Alignmentsupporting

confidence: 82%

“…For S = 0, we calculate numerically the angle averages in Eq. (46) to find that R(S, 0) increases monotonically as S increases, as shown in the inset of Fig. 6 (dashed line).…”

Section: Effect Of Orientational Alignmentmentioning

confidence: 75%

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Impact of tunneling anisotropy on the conductivity of nanorod dispersions

Nigro

Grimaldi

2014

Phys. Rev. B

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“…43, and apply Eqs. (22) and (23) to find φ c from the critical density η c . The resulting critical volume fraction compares relatively well with the numerical calculations for λ 0.5, as seen in Fig.…”

Section: Ema Cherry-pit Modelmentioning

confidence: 99%

Theory of percolation and tunneling regimes in nanogranular metal films

Grimaldi

2014

Phys. Rev. B

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Nanogranular metal composites, consisting of immiscible metallic and insulating phases deposited on a substrate, are characterized by two distinct electronic transport regimes depending on the relative amount of the metallic phase. At sufficiently large metallic loadings, granular metals behave as percolating systems with a well-defined critical concentration above which macroscopic clusters of physically connected conductive particles span the entire sample. Below the critical loading, granular metal films are in the dielectric regime, where current can flow throughout the composite only via hopping or tunneling processes between isolated nanosized particles or clusters. In this case transport is intrinsically non-percolative in the sense that no critical concentration can be identified for the onset of transport. It is shown here that, although being very different in nature, these two regimes can be described by treating percolation and hopping on equal footing. By considering general features of the microstructure and of the electrical connectedness, the concentration dependence of the dc conductivity of several nanogranular metal films is reproduced to high accuracy within an effective medium approach. In particular, fits to published experimental data enable us to extract the values of microscopic parameters that govern the percolation and tunneling regimes, explaining thus the transport properties observed in nanogranular metal films.

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“…EMA and MC All these dependencies, and in particular the relationship between the spatial particle arrangements and the global transport properties, can be made explicit by employing the EMA formulation developed in Refs. [13,18], which is a generalization to complete tunneling resistor networks of the classical EMA approach [10,19,20]. The original tunneling network is thus replaced by an effective one where all bond conductances are equal toḡ, whose value is found by requiring that the effective network has the same average resistance as the original.…”

Section: Segregation In the Continuummentioning

confidence: 99%

Tunneling and percolation transport regimes in segregated composites

2012

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We consider the problem of electron transport in segregated conductor-insulator composites in which the conducting particles are connected to all others via tunneling conductances thus forming a global tunneling connected resistor network. Segregation is induced by the presence of large insulating particles which forbid the much smaller conducting fillers to occupy uniformly the three dimensional volume of the composite. By considering both colloidal-like and granular-like dispersions of the conducting phase, modeled respectively by dispersions in the continuum and in the lattice, we evaluate by Monte Carlo simulations the effect of segregation on the composite conductivity σ, and show that an effective medium theory applied to the tunneling network reproduces accurately the Monte Carlo results. The theory clarifies that the main effect of segregation in the continuum is that of reducing the mean inter-particle distances, leading to a strong enhancement of the conductivity. In the lattice segregation case the conductivity enhancement is instead given by the lowering of the percolation thresholds for first and beyond-first nearest neighbors. Our results generalize to segregated composites the tunneling-based description of both the percolation and hopping regimes introduced previously for homogeneous disordered systems.

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A complete graph effective medium approximation for lattice and continuum percolation

Cited by 10 publications

References 37 publications

Impact of tunneling anisotropy on the conductivity of nanorod dispersions

Impact of tunneling anisotropy on the conductivity of nanorod dispersions

Theory of percolation and tunneling regimes in nanogranular metal films

Tunneling and percolation transport regimes in segregated composites

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