Influence of the dimension of a polycrystalline film and the optical anisotropy of crystallites on the effective dielectric constant of the film

The dimension $D$ of a polycrystalline film and the optical anisotropy $m = \varepsilon_{z}/\varepsilon_{x}$ of uniaxial crystallites with the principal components $\varepsilon_{x} = \varepsilon_{y}$ and $\varepsilon_{z}$ of the tensor of the dielectric constant have been shown to produce a strong influence on the effective dielectric constant $\varepsilon_{D}^{*}$ and the effective refractive index $n_{D}^{*}= {(\varepsilon_{D}^{*})}^{1/2}$ of the film in the optical transparency region, as well as on the boundaries of the intervals $B_{Dl}\le \varepsilon_{D}^{*}\le B_{Du}$. The intervals $\Delta_{2}(m)= B_{2l}-B_{2u}$ and $\Delta_{3}(m)=B_{3l}-B_{3u}$ are separated by a gap for m in the range 1 $<m<$ 2, whereas the theoretical dependence $\varepsilon_{2}^{*}(m)$ is separated by a gap from the interval $\Delta_{3}(m)$ for $m$ in the range 1 $<m<$ 4. This is confirmed by a comparison of the experimental $(n_{oP})$ and theoretical $(n_{2}^{*})$ ordinary refractive indices for uniaxial polycrystalline films of the conjugated polymer poly(p-phenylene vinylene) (PPV) with uniaxial crystallites and appropriate values of $m$. In the visible transparency region of the PPV films with a change in $m(\lambda)$ in the range 2 $<m(\lambda)<$ 3 due to the dependence of the components $\varepsilon_{x,z}(\lambda)$ on the light wavelength $\lambda$, the refractive indices $n_{oP}^{2}(\lambda)= \varepsilon_{oP}(\lambda)$ are consistent with the theoretical values of $\varepsilon_{2}^{*}(\lambda)$ and lie outside the interval $\Delta_{3}(m)$. For $m(\lambda)>$ 3 near the electronic absorption band of the crystallites, the values of $\varepsilon_{oP}(\lambda)$ lie in the region of the overlap of the intervals $\Delta_{2}(m)$ and $\Delta_{3}(m)$. The boundaries $m_{c}$ of the range 1 $<m<m_{c}$ are determined, for which the interval $\Delta_{2}(m)$ is separated by a gap from the dependences $\varepsilon_{3}^{*}(m)$ corresponding to the effective medium theory with spherical crystallites and hierarchical models of a polycrystal, as well as from the proposed new dependence $\varepsilon_{3}^{*}(m)$.