Method for calculating dielectric constant of particle-dispersed composite materials and method for evaluating dispersibility
Abstract:
A method for calculating the dielectric constant of particle-dispersed composite materials that enables an easy evaluation of dispersibility. The composite material is assumed as a cell combination 10 in which unit cells 1 having a length a are combined together in an x-axis, a y-axis, and a z-axis direction and which has a length 1 in the x-axis direction, a length m in the y-axis direction, and a length n in the z-axis direction, the cell combination 10 is created in which a particle element or a medium element is assigned to each of the unit cells 1 Layers have a thickness d in the z-axis direction are combined and layered in the z-axis direction and assigning a capacitance CLayer,h of each of the layers represented by Formula 1 below to Formula 2 to determine a relative dielectric constant εTotal. C Layer , h = { ∑ j = 1 ⌊ m / a ⌋ ⁢ ∑ i = 1 ⌊ l / a ⌋ ⁢ ( ∑ k = 1 ⌊ d / a ⌋ ⁢ 1 ɛ ijk ⁢ ɛ 0 ⁢ a ) - 1 } - 1 Formula ⁢ ⁢ 1 ε0: dielectric constant of vacuum (F/m) ɛ Total = 1 ɛ 0 · n lm · ( ∑ h = 1 ⌊ n / d ⌋ ⁢ C Layer , h ) - 1 Formula ⁢ ⁢ 2
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