Effect of nanoparticle chain formation on dielectric anisotropy of nematic composites

A general theory of the dielectric constant of nematic liquid crystal mixtures is presented including the particular case of nematics doped with polar nanoparticles. The results are used to estimate the contribution of chains of polar nanoparticles to the static dielectric anisotropy and birefringence of the nematic composite taking into account contributions from chains of different lengths. The dependence of the dielectric anisotropy on the dipolar interaction strength is considered in detail and it is shown that formation of polar chains of nanoparticles enables one to explain a significant increase of the dielectric constant of the composite as observed experimentally.

Figure 1

The effect of chain formation on the birefringence of the nematic composite: dependencies of the factor ${\delta }_{\eta }$ given by Eq. (54) on the NP coupling strength for the NP density ${\rho }^{*}=0.1,0.01$, and $0.001$ as indicated on the lines.

Figure 2

The effect of chain formation on the birefringence of the composite: dependencies of the factor ${\rho }^{*}{\delta }_{\eta }$ in Eq. (53) on the NP concentration for the coupling strength $\lambda$ varying from 2 to 10 as indicated on the lines.

Figure 3

Anisotropy of the low-frequency composite dielectric susceptibility as a function of NP coupling strength for NP densities ${\rho }^{*}=0.001$ (a) and ${\rho }^{*}=0.01$ (b). Solid lines $1\text{–}6$ depict results of partial summation in Eq. (56) neglecting chains with $m$ higher than $1\text{–}6$ correspondingly. Solid line 7 represents the dependence (58), and the dashed line shows the anisotropy in the absence of chain formation.

Figure 4

Anisotropy of the low-frequency composite dielectric susceptibility as a function of the NP concentration for the NP interaction strength $\lambda$ varying from 2 to 10 as indicated on the lines.