Surface-induced orientational order in stretched nanoscale-sized polymer dispersed liquid-crystal droplets

We investigate orientational ordering in stretched polymer-dispersed liquid-crystal (PDLC) droplets using deuterium nuclear magnetic resonance, in the nematic and isotropic phases. In the latter case, we estimate the surface order parameter $S_0$ and the thickness of the interfacial layer from the temperature-independent surface ordering model for an elliptical cavity with a varying aspect ratio. A simple phenomenological model well describes the quadrupole splitting frequency of NMR spectra in the isotropic phase. The strain dependence of $S_0$ suggests that stretching-induced changes in the orientation of polymer chains in the PDLC matrix noticeably affect liquid-crystal surface anchoring. Experimental results are supported by simulated NMR spectra obtained as output from Monte Carlo simulations of paranematic ordering in ellipsoidal droplets based on the Lebwohl-Lasher lattice model.

Figure 1

SEM photographs of PDLC films: (a) before stretching, (b) 400% strain. The average initial diameter of undeformed droplets is $(92\pm 16)\mathrm{nm}$. Arrows indicate the major and minor axes for one of the stretched droplets. The average axis lengths in the sample with 400% strain are estimated as $(460\pm 80)\mathrm{nm}$ and $(41\pm 7)\mathrm{nm}$ for the major and minor axes, respectively. The corresponding aspect ratio (measured from more than 100 droplets in several pictures) is $11\pm 2$.

Figure 2

The schematic diagram of the coordinate system of NMR measurement.

Figure 3

The NMR spectra of $5\mathrm{CB}\text{−}\alpha d_2$ in an unstretched PDLC film with (a) the magnetic field applied along the $Z$ axis and (b) $Y$ axis, and (c) in a bulk sample aligned parallel to the magnetic field. (d) Schematic depiction of droplet organization: bipolar axes not aligned.

Figure 4

The NMR spectra of $5\mathrm{CB}\text{−}\alpha d_2$ in a 100% stretched PDLC film: (a) magnetic field along the $Z$ axis, (b) magnetic field along the $Y$ axis, (c) magnetic field along the $X$ axis. (d) Schematic depiction of droplet organization: bipolar axes aligned.

Figure 5

The NMR spectra of $5\mathrm{CB}\text{−}\alpha d_2$ in (a) 5%, (b) 20%, (c) 100%, and (d) 400% stretched PDLC films. The magnetic field is applied along the $X$ axis.

Figure 6

Schematic diagram of the elliptical geometry: (a) cylindrical coordinate system for elliptical geometry, (b) surface molecule alignment with respect to the elliptical surface and the applied magnetic field.

Figure 7

The molecular orientational order parameter profile in an elliptical cavity at different $z$. The dashed line illustrates the surface of the elliptical cavity.

Figure 8

${}^2\mathrm{H}$-NMR spectra for $5\mathrm{CB}\text{−}\alpha d_2$ of 100% and 400% stretched PDLC films in the isotropic phase. The magnetic field is parallel to the tensile axis ($X$ axis).

Figure 9

Temperature dependence of the degree of surface-induced nematic order: (a) $S_{00}$ calculated from Eq. (16) and (b) $S_0$ calculated from Eq. (17), with ${\xi }_0=0.65\mathrm{nm}$, $T^{*}=300.9\mathrm{K}$, and $l_0=1.0\mathrm{nm}$, both for 400% strain.

Figure 10

Temperature dependence of the quadrupole splitting frequency $⟨\delta \nu ⟩$ of 5%, 20%, 100% and 400% stretched PDLC in isotropic phase. Solid curves are the best fits for the temperature-independent model given by Eq. (17).

Figure 11

Strain dependence of $S_0$.

Figure 12

Bipolar droplet with 20% strain at $\mathcal{T}=1.20$: simulated director field (a) and nematic order parameter map (b) (half and whole $XY$ cross section through the droplet center, respectively), calculated by diagonalizing the MC-time-averaged local ordering matrix $\mathbf{Q}\left(i\right)=\frac{1}{2}(3⟨{\mathbf{u}}_i\otimes {\mathbf{u}}_i⟩-I)$ [40].

Figure 13

Temperature scans of order parameter profiles plotted through the droplet center along the $Y$ axis: (a) 5% strain, (b) 400% strain; temperature range $\mathcal{T}=1.12–1.20$ (curves top to bottom, step size 0.01). The subsurface degree of order $S_0$ shows no major temperature dependence and thus supports the temperature-independent model, Eq. (17).

Figure 14

Strained bipolar droplets: ${}^2\mathrm{H}$-NMR spectra; (a) 5% strain, (b) 400% strain. The quadrupole splitting decreases with temperature and increases with strain.

Figure 15

Strained bipolar droplets: temperature dependence of the simulated quadrupolar splitting. Top to bottom: 400%, 100%, 20%, 5% strain. Experimental (left) vs simulated data (right). Bulk NI transition temperature for 5CB is $\sim 302\mathrm{K}$.

Figure 16

Strained bipolar droplets: surface roughness dependence of the simulated quadrupolar splitting. Top to bottom: 400%, 100%, 20%, 5% strain, and no strain (for comparison only). On the abscissa the degree of surface-imposed order $S_s$ is plotted. $\mathcal{T}=1.16$ $(\sim 312\mathrm{K})$ in all cases.