Clausius mosotti equation
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The Clausius–Mossotti relation expresses the dielectric constant (relative permittivity, εr) of a material in terms of the atomic polarizibility, α, of the material's constituent atoms and/or molecules, or a homogeneous mixture thereof. It is named after Ottaviano-Fabrizio Mossotti and Rudolf Clausius. It is equivalent to the Lorentz–Lorenz equation. It may be expressed as:[1][2]
{\displaystyle {\frac {\epsilon _{\mathrm {r} }-1}{\epsilon _{\mathrm {r} }+2}}={\frac {N\alpha }{3\epsilon _{0}}}}
where
{\displaystyle \epsilon _{r}=\epsilon /\epsilon _{0}} is the dielectric constant of the material
{\displaystyle \epsilon _{0}} is the permittivity of free space
{\displaystyle N} is the number density of the molecules (number per cubic meter), and
{\displaystyle \alpha } is the molecular polarizability in SI-units (C·m2/V).
In the case that the material consists of a mixture of two or more species, the right hand side of the above equation would consist of the sum of the molecular polarizability contribution from each species, indexed by iin the following form: (see Lorrain and Corson - Electromagnetic Field and Waves, 1962, 2nd Edition, page 116)
{\displaystyle {\frac {\epsilon _{\mathrm {r} }-1}{\epsilon _{\mathrm {r} }+2}}=\sum _{i}{\frac {N_{i}\alpha _{i}}{3\epsilon _{0}}}}
In the CGS system of units the Clausius–Mossotti relation is typically rewritten to show the molecular polarizability volume {\displaystyle \alpha '=\alpha /(4\pi \varepsilon _{0})} which has units of volume (m3).[2] Confusion may arise from the practice of using the shorter name "molecular polarizability" for both {\displaystyle \alpha } and {\displaystyle \alpha '} within literature intended for the respective unit system.
{\displaystyle {\frac {\epsilon _{\mathrm {r} }-1}{\epsilon _{\mathrm {r} }+2}}={\frac {N\alpha }{3\epsilon _{0}}}}
where
{\displaystyle \epsilon _{r}=\epsilon /\epsilon _{0}} is the dielectric constant of the material
{\displaystyle \epsilon _{0}} is the permittivity of free space
{\displaystyle N} is the number density of the molecules (number per cubic meter), and
{\displaystyle \alpha } is the molecular polarizability in SI-units (C·m2/V).
In the case that the material consists of a mixture of two or more species, the right hand side of the above equation would consist of the sum of the molecular polarizability contribution from each species, indexed by iin the following form: (see Lorrain and Corson - Electromagnetic Field and Waves, 1962, 2nd Edition, page 116)
{\displaystyle {\frac {\epsilon _{\mathrm {r} }-1}{\epsilon _{\mathrm {r} }+2}}=\sum _{i}{\frac {N_{i}\alpha _{i}}{3\epsilon _{0}}}}
In the CGS system of units the Clausius–Mossotti relation is typically rewritten to show the molecular polarizability volume {\displaystyle \alpha '=\alpha /(4\pi \varepsilon _{0})} which has units of volume (m3).[2] Confusion may arise from the practice of using the shorter name "molecular polarizability" for both {\displaystyle \alpha } and {\displaystyle \alpha '} within literature intended for the respective unit system.
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