Stepwise heat-capacity change at an orientation transition in liquid crystals

During a phase transition in a bulk material, heat is exchanged with matter to balance the changes in the internal energy and the entropy of the system. Here we report on the thermal detection of a surface-mediated anchoring transition, a spontaneous and discontinuous orientation change between planar (P) and homeotropic (H) alignments within a single nematic phase by changing temperature. In this case a stepwise change in the heat flow, similar to a glass transition, is observed by means of high-resolution differential scanning calorimetry. We found that the jump in the specific heat does not depend on the sample volume, although the contribution of molecules in the vicinity of surfaces, which trigger the transition, becomes less with increasing the sample volume. This means that different molecular orientations, H and P, with respect to surfaces have different thermodynamic free energies. We also address why the anchoring transition occurs by means of grazing-incidence x-ray diffraction measurements, which clearly reveal the formation of quasismectic layers parallel to surfaces in the nematic phase.

Figure 1

Anchoring transition observed in the N phase of CCN47 in a cell with CYTOP surfaces. (a) Texture evolution on cooling in a CYTOP cell. The labeled numbers stand for the temperature difference from the Iso-N phase-transition temperature. First, the P state emerges as typical schlieren textures with two and four brushes (three in the right). At $T_{\mathrm{ATr}}$, the domains of the H state are observed as dark spots (second left). In the SmA and N${}_{\mathrm{H}}$ temperature windows, a dark image persists (left), signifying that the molecules point to the surface's normal direction (parallel to the viewing direction). (b) HR-DSC charts in a 25-$\mu$m-thick CYTOP cell upon both cooling and heating. The result in a 25-$\mu$m-thick AL1254 cell upon cooling is also shown. The base lines of three HR-DSC charts are properly shifted.A double-arrowed scale bar corresponds to 1 mW/g. Dashed lines are drawn to emphasize that the heat flow in the H state is smaller than that in both the N${}_{\mathrm{P}}$ and Iso phases in the CYTOP cell. (c) The nucleation of Iso domains in the N phase for both AL1254 and CYTOP surfaces. Clearly, AL1254 has a greater ability to create nuclei, i.e., a strongly wettable surface.

Figure 2

(a) Detailed DSC chart around $T_{\mathrm{ATr}}$ for cells with various thicknesses on heating. Despite the unchanged $T_{\mathrm{ATr}}$, the magnitude of the jump in heat flow is nearly independent of the cell thickness, but increases slightly with decreasing cell thickness. Since $\frac{dQ}{dt}$ is scaled (a double-arrowed scale bar: 1 mW/g) by each sample volume, it is equivalent to a specific heat capacity. The baselines are properly shifted. (b) Total heat flow change upon ATr in each sample as a function of cell thickness. (c) Variation of heat flow with time upon both cooling (closed circles, slow growth) and heating (open circles, fast growth). (d) Schematic Gibbs free energy ($G$) vs temperature ($T$) and molecular tilt angle ($\theta$), and the accompanying ATr processes in a CYTOP cell. Because the CYTOP surface reduces the distinction between two states, P and H, both free-energy curves can intersect, unlike normal surfaces that prefer only one alignment. In low- and high-temperature regions far from ATr, the stability of the H and P states is quite different, leading to a preferential alignment, whereas a metastable (superheated or supercooled) region appears due to the energy barrier between the two states, resulting in bistability.

Figure 3

GI-XRD measurements in two sample geometries; (a) In the minidroplet geometry, the incident angle ($\theta$) of the x ray is fixed at 0.1${}^{\circ }$ to ensure the total reflection condition on the alignment surface. All the data were taken on cooling. For the CYTOP surface, a ring pattern in the Iso phase reflects the isotropic orientation of the LC molecules. Sharp SAX signals, indicating well-aligned surface-layer structures, can be confirmed immediately when cooling down to the N phase. The orthogonal splitting directions of the SAX [wave vector, $q_{\mathrm{s}}$ ($\parallel q_z)=0.302$ ${\AA }^{-1}$) and WAX [$q_{\mathrm{w}}$ ($\parallel q_x)=1.202$ ${\AA }^{-1}$] signals indicate a SmA-like structure. The existence of a layer structure parallel to the surfaces indicates the formation of SmA-like layers parallel to the surfaces. The intensity and sharpness increase with decreasing temperature, implying the development of the surface-induced quasi-SmA structure. In contrast, both SAX and WAX patterns exhibit rings and no observable surface Sm-like structure can be found on the AL1254, even in the lower temperature range of the N phase. (b) Similar XRD results as those in the microdroplet geometry were found for the in situ cell geometry. The SAX signals locate at the poles, indicating the SmA-like layer running parallel to the surface.