Impact of $\mathrm{BaTi}{\mathrm{O}}_3$ nanoparticles on pretransitional effects in liquid crystalline dodecylcyanobiphenyl

The pretransitional behavior of dodecylcyanobiphenyl (12CB) (isotropic–smectic-$A$–solid mesomorphism) with $d=50\mathrm{nm}\mathrm{BaTi}{\mathrm{O}}_3$ nanoparticles (NPs) linked to the cubic phase was monitored via temperature studies of dielectric constant. Tests were carried out in the isotropic, liquid crystal mesomorphic, and solid phases. For each phase transition the same value of the critical exponent $\alpha \sim 0.5$ was obtained, including nanocolloids. All phase transitions show the weakly discontinuous nature. The temperature metric of the discontinuity $\mathrm{\Delta }T$ notably decreases when adding nanoparticles. The addition of nanoparticles first decreases the dielectric constant by approximately $50\%$ in comparison with pure 12CB, but already for a concentration $\sim x=0.4\%$ NP an increase over $50\%$ takes place. It is notable that for the latter concentration unique hallmarks of the pretransitional effect emerge also for the solid-mesophase transition. All these indicate the important impact of nanoparticles on multimolecular mesoscale fluctuations.

Figure 1

Temperature changes of the dielectric constant in 12CB and its colloids with $\mathrm{BaTi}{\mathrm{O}}_3$ nanoparticles. Their concentrations are given in percent mass fraction. The solid arrows indicate the isotropic-mesophase transitions (clearing temperatures $T_C$), which are approximately the same for all concentrations. Dashed arrows are for mesophase-solid transitions, related to different concentrations of NPs. Red curves show the experimental data according to Eqs. (1) and (3), with the parameters collected in Table 1. Closed stars are for the extrapolated temperature of the hypothetical isotropic to mesophase continuous phase transition and open stars are the same for the mesophase to isotropic transition.

Figure 2

Temperature changes of the dielectric constant in the isotropic liquid state of 12CB and its colloids with $\mathrm{BaTi}{\mathrm{O}}_3$ nanoparticles in normalized scales referred to as the hypothetical continuous phase transition $({\varepsilon }^{*},T^{*})$. Solid red curves are described by Eq. (1) with the parameters from Table 1. Vertical arrows indicate clearing temperatures. The distances between vertical arrows and the red star indicate values of discontinuities of isotropic-mesophase transitions $\mathrm{\Delta }{T}^{*}$.

Figure 3

Temperature derivative of experimental $\varepsilon \left(T\right)$ data for liquid crystalline 12CB and its colloids with nanoparticles $\mathrm{BaTi}{\mathrm{O}}_3$, given in Fig. 1. Red curves show Eqs. (4) and (5). Dotted arrows indicate the isotropic mesophase transitions (clearing temperature). The solid arrow is for the mesophase-solid transition.

Figure 4

Concentration dependence of ${\mathrm{BaTiO}}_3$ nanoparticles [mass weight fraction MWF $\times 100\%$] of the dielectric constant in the isotropic phase at the clearing temperature $\varepsilon \left(T_C\right)$ (open circles, left scale) and jumps of the dielectric constants $\mathrm{\Delta }\varepsilon$ (closed circles, right scale) at the SmA-I (closed circles, right scale) and SmA-S (triangles, right scale) phase transitions. The $M$ is for the LC mesophase, $I$ is for the isotropic liquid and S is for the solid phase.