Fluctuation Mediated Interaction and Phase Separation of Nanoparticles in a Liquid Crystal Solvent

Water-in-oil microemulsions of nanodroplets in the isotropic phase of a thermotropic liquid crystal exhibit, with decreasing temperature and in anticipation of a demixing transition, enhanced correlation in fluctuations of both molecular orientation and droplet concentration. Mean field modeling of this pretransition behavior, on the basis of a lattice in which the nanodroplets are introduced as holes, shows that the observed interdroplet attractive interaction is produced by the disordering effect of the droplets on the liquid crystal and mediated solely by paranematic fluctuations.

Figure 1

Experimentally determined phase diagram of $5\mathrm{D}\mathrm{H}\mu \mathrm{e}\mathrm{m}$ as a function of temperature $(T)$ and micellar concentration $(\varphi )$. Continuous lines indicate the phase boundaries of the isotropic phase (light grey) and of nematic phase (dark grey) enclosing the (white) demixing region. Experiments performed at $\varphi =0.15$ and $\varphi =0.075$ (along the vertical arrows) enable determining the divergence $T$ for the fluctuation in nematic order [squares, connected through the dotted line $T^{*}(\varphi )$] and for the micellar osmotic compressibility [diamonds, laying on the spinodal dashed curve $T_M^{*}(\varphi )$]. The meaning of $T^{*}$ and $T_M^{*}$ is sketched in the isometric projection plane on the right, where the behavior of the relevant susceptibilities ($\chi$, from Figs. 2, 3) is shown.

Figure 2

(a) Intensity autocorrelation function $g(\tau )$ vs retardation time $\tau$ for polarized (open dots) and depolarized (full dots) scattered light. Shadows highlight the two different components. (b) Depolarized scattered intensity $I_{\mathrm{V}\mathrm{H}}$ vs $T$ for bulk 5CB (crosses), $5\mathrm{D}\mathrm{H}\mu \mathrm{e}\mathrm{m}$ with $\varphi =0.075$ (full dots) and with $\varphi =0.15$ (empty dots). Lines indicate $1/[T-T^{*}(\varphi )]$ fitting curves, diverging at the $T^{*}$ marked by the vertical lines. (c) Correlation time for paranematic fluctuations ${\tau }_{\mathrm{L}\mathrm{C}}(T)$ scaled with viscosity $\eta (T)$ and fitted to $1/[T-T^{*}(\varphi )]$. Symbols as in (b). (d) Comparison of static ($I_{\mathrm{V}\mathrm{H}}$) and dynamic (${\tau }_{\mathrm{L}\mathrm{C}}/\eta$) behavior showing collapse of the $5\mathrm{D}\mathrm{H}\mu \mathrm{e}\mathrm{m}$ data on bulk.

Figure 3

Static (main figure) and dynamic (inset) behavior of the light scattered by the $5\mathrm{D}\mathrm{H}\mu \mathrm{e}\mathrm{m}$ droplets for $\varphi =0.075$ (full dots) and $\varphi =0.15$ (empty dots). The micellar osmotic compressibility (proportional to $I_M$) vs $T$ has been fitted to $1/[T-T_M^{*}(\varphi )]$ and diverge where marked by the vertical lines. Inset: micellar collective diffusion coefficient $D$ vs $T$ (dots) for $\varphi =0.075$; the line indicates the expected behavior of $D_{\mathrm{H}\mathrm{S}}(T)$ for hard spheres suspended in 5CB having $R=20\AA$.

Figure 4

Phase diagram obtained from the mean field analysis of the diluted Lebwhol-Lasher model in Eq. (1). Continuous lines indicate the phase boundaries of the isotropic (light grey) and nematic (dark grey) phases enclosing the (white) demixing region. The dashed line is the spinodal curve $T_M^{*}(\varphi )$, where the micellar osmotic compressibility $\partial \varphi /\partial \Pi$ diverges. The dotted line is the divergence temperature $T^{*}(\varphi )$ for the nematic correlation length and for the mean square amplitude of nematic order fluctuations $(⟨Q_{zz}^2⟩)$. The predicted divergence of two such susceptibilities along the line indicated by the arrow is plotted in the inset.