Length scales of interactions in magnetic, dielectric, and mechanical nanocomposites

Skomski, Ralph; Balamurugan, Balamurugan; Schubert, Eva; Enders, Axel; Sellmyer, David J.

doi:10.1557/opl.2011.109

Cited by 6 publications

(5 citation statements)

References 46 publications

(61 reference statements)

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“…In Figure 5, we test our theoretical predictions of Equation (4) for ε eff against the three most commonly used mixing rules, the Bruggeman, [ 138–141 ] Lichtenecker, [ 142 ] , and the MG rules. [ 90,94 ] The Bruggeman mixing rule is used in the form

\begin{matrix} true \\ right ε_{normaleff} false(BR false) = \frac{1}{4} (normalΔ ε (() 3 η - 2) + ε_{p} + \sqrt{{[normalΔ ε (() 2 - 3 η) - ε_{p}]}^{2} + 8 ε_{m} ε_{p}}) \end{matrix}

where

Δ ε

ε_{p} - ε_{m}

.…”

Section: Resultsmentioning

confidence: 99%

Theoretical Study of Nanocomposite Permittivity with a Tunable Clustering of Inclusions

Allahyarov

2020

Advcd Theory and Sims

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A new analytical model is proposed for the nanocomposite permittivity eff in mean-field approach using integrated coefficients for the inclusion clustering and matrix reaction effects. Predictions for eff are in a satisfactory agreement with the Lichtenecker and Bruggeman mixing rules, depending on whether the reaction field is ignored or incorporated into the theory. The observed differences between the Maxwell-Garnett, Lichtenecker, and Bruggeman results are interpreted in terms of the fraction of the stored dipolar energy they take into account. A novel analytical expression for the average dipolar field ⟨ ⃗ E ⟩ in the film shows a U-shaped dependence on the filler packing fraction , with an absolute maximum at m = 1/e. New analytical expressions derived for the average dipolar energy u m and dipole-dipole interaction energy u m in the nanocomposite depend on the cluster orientation parameter , and take into account the film boundary effects. It is found that the enhancement of eff at higher is associated with an increase in the inclusion dipole moment p in the oriented clusters resulting from dipole-dipole correlations, which inflate the energy u p stored inside the inclusions.

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\begin{matrix} true \\ right ε_{normaleff} false(BR false) = \frac{1}{4} (normalΔ ε (() 3 η - 2) + ε_{p} + \sqrt{{[normalΔ ε (() 2 - 3 η) - ε_{p}]}^{2} + 8 ε_{m} ε_{p}}) \end{matrix}

where

Δ ε

ε_{p} - ε_{m}

.…”

Section: Resultsmentioning

confidence: 99%

Theoretical Study of Nanocomposite Permittivity with a Tunable Clustering of Inclusions

Allahyarov

2020

Advcd Theory and Sims

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“…Both the MG and BR theories are mean-field theories and do not take into account correlation and exchange effects between dipoles. [73][74][75][76] The physics underlying these mixing rules is given in Appendix A.…”

Section: Dielectric Behavior Of Compositesmentioning

confidence: 99%

“…In general, the original BR equation can be written for any inclusion geometry in the following form 73,74…”

Section: Dielectric Behavior Of Compositesmentioning

confidence: 99%

Dipole correlation effects on the local field and the effective dielectric constant in composite dielectrics containing high-k inclusions

Allahyarov

Löwen

Zhu

2016

Phys. Chem. Chem. Phys.

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Mixing dielectric polymers with high permittivity (high-k) inclusions can affect their electrical properties. In actuation applications of dielectric elastomers, the polarized inclusions generate additional volume polarization-related electrostriction. In energy storage applications, it is possible to store more energy in dielectric composites because of additional polarization of the inclusions and interfaces. However, mixing an electroactive polymer with high-k inclusions also brings several disadvantages. The expulsion of the field from the interior of high-k fillers and the presence of two poles on the filler surface along the applied field direction result in higher local fields EL near the inclusion poles. The resulting field enhancement lowers the breakdown field (Eb) threshold for the material and therefore compromises the actuation and energy storage capabilities of dielectric composites. To mitigate this issue, the dependence of EL on the morphology of inclusion distribution, the field localization effect in chained configurations, and the role of the dipole-dipole correlation effects in the enhancement of the dipolar field of inclusions are analyzed. We show that the dipolar correlation effects are strong in large inclusion composites and their contribution to the inclusion dipole moment μ and to the local fields EL can reach 30-50%. A new method for deriving the composite permittivity from the field EL distribution, based on a caged probe technique, is also presented.

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“…However, this approximate method is used until now, see e.g. [7][8][9][10]. We demonstrate below that that in some cases this classical theory does not behave adequately.…”

Section: Introductionmentioning

confidence: 98%

Effective Medium Theory for the Elastic Properties of Composite Materials with Various Percolation Thresholds

2020

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It is discussed that the classical effective medium theory for the elastic properties of random heterogeneous materials is not congruous with the effective medium theory for the electrical conductivity. In particular, when describing the elastic and electro-conductive properties of a strongly inhomogeneous two-phase composite material, the steep rise of effective parameters occurs at different concentrations. To achieve the logical concordance between the cross-property relations, a modification of the effective medium theory of the elastic properties is introduced. It is shown that the qualitative conclusions of the theory do not change, while a possibility of describing a broader class of composite materials with various percolation thresholds arises. It is determined under what conditions there is an elasticity-theory analogue of the Dykhne formula for the effective conductivity. The theoretical results are supported by known experiments and show improvement over the existing approach. The introduction of the theory with the variable percolation threshold paves the way for describing the magneto-elastic properties of magnetorheological elastomers, as it has been achieved for magneto-dielectric and magnetic properties recently.

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Length scales of interactions in magnetic, dielectric, and mechanical nanocomposites

Cited by 6 publications

References 46 publications

Theoretical Study of Nanocomposite Permittivity with a Tunable Clustering of Inclusions

Theoretical Study of Nanocomposite Permittivity with a Tunable Clustering of Inclusions

Dipole correlation effects on the local field and the effective dielectric constant in composite dielectrics containing high-k inclusions

Effective Medium Theory for the Elastic Properties of Composite Materials with Various Percolation Thresholds

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