## 3 Experimental Results  
### Sample Preparation and Experimental Setup  
The LC chosen is 8 CB. It was purchased from Synthon (Germany) and used without further purification. I measured the nematic-to-smectic A transition temperature \(T_{\mathrm{NA}}=33.8\,^{\circ}\mathrm{C}\) and the nematic-to-isotropic transition temperature \(T_{\mathrm{NI}}=40.75\,^{\circ}\mathrm{C}\). All the samples were prepared between two ITO (Indium Tin Oxide)-coated glass plates. A thin band of ITO was removed on the sides of the plates and the metallic wires used to measure the capacitance were soldered on the ITO surface with an ultrasonic soldering system in order to decrease the parasitic capacitances. Nickel wires were used as a spacer to fix the sample thickness and a slow-cure epoxy glue was used to bond them together. To reduce the uncertainties, thin samples (\(d\approx 7.5\,\upmu\)m) with large surface area (\(S\approx 2.5\,\upmu\)m) were used to measure the dielectric constants, while a thick sample (\(d\approx 50\,\upmu\)m) was used to measure \(V_{c}\). In all samples, a special care was taken to ensure the parallelism between the two glass plates, always better than \(5\times 10^{-5}\) rad. The thickness of the empty cells was measured with an Ocean Optics USB2000 spectrometer. The dielectric constant \(\varepsilon_{\perp}\) was measured using homeotropic samples. In that case, the glass plates were treated with the polyimide Nissan SE-4811. The polyimide was deposited by spin-coating and the plates were then baked at 180 \({}^{\circ}\)C for 30 min. The measurements of \(\varepsilon_{\parallel}\) and \(L\) were performed using planar samples. The unidirectional planar anchoring was achieved by photoalignment using a commercial azo-dye, Brilliant Yellow, sold by Sigma. The dye was dissolved in DMS (0.3% by weight) and then deposited by spin-coating at 2000 rpm during 30 s. Before that, the plates were cleaned with sulfochromic acid, flushed with distilled water and dried at 100 \({}^{\circ}\)C during 15 min. Once the dye was deposited, the plates were baked at 95 \({}^{\circ}\)C for 30 min. The unidirectional planar anchoring was obtained by illuminating the plates during 30 min under normal incidence with the linearly polarized parallel light beam of a mercury vapor lamp equipped with a filter at \(\lambda=436\) nm. The power of the light beam was 1.1 mW/cm\({}^{2}\), so the exposure dose was close to 2 J/cm\({}^{2}\). The relative humidity in the room, which is another important parameter according to [PERSON] et al. [29], was close to 40% during all the steps of preparation of the sample. With this protocole a strong planar anchoring was obtained, with no pretilt angle. All the capacitance measurements were performed at 5 kHz in the dielectric regime of the LC (I measured a charge relaxation frequency close to 500 Hz in 8 CB) with a HP 4284A LCR meter, initially calibrated with standard capacitors. All the cells were filled by capillarity in the isotropic phase. Finally, the samples were placed into a home-made oven regulated to within \(\pm 2\) mK thanks to an ATNE ATSR 100 PID controller. Measurement of the Dielectric Constants \(\varepsilon_{\parallel}\) and \(\varepsilon_{\perp}\)  
I first measured the two dielectric constants. In usual experiments, \(\varepsilon_{\perp}\) is obtained by measuring the capacitance \(C_{\perp}\) of a planar sample below the onset of Freedericksz instability and \(\varepsilon_{\parallel}\) is deduced from an extrapolation to 0 of the capacitance curve \(C(1/V)\) by assuming that \(L/d\ll 1\). This requires the use of very thick samples (except if the anchoring is very strong, which we do not know _a priori_) and, in that case, the capacitance measurements are less precise. To avoid this difficulty, I directly measured \(\varepsilon_{\parallel}\) using a thin homeotropic sample of thickness \(d=7.5\)\(\upmu\)m. Measurements were performed between 0.1 and 20 Vrms by step of 0.1 Vrms and 2 s per step.