Biaxiality-driven twist-bend to splay-bend nematic phase transition induced by an electric field

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Science Advances  02 Sep 2020:
Vol. 6, no. 36, eabb8212
DOI: 10.1126/sciadv.abb8212
  • Fig. 1 Schematic views of the structure of the modulated nematic phases formed by achiral bent-shaped molecules.

    (A) In the splay-bend nematic phase, the director oscillates in a plane, chosen here to be the YZ plane of the laboratory frame XYZ. (B) In the twist-bend nematic phase, the director is arranged on a conical helix with doubly degenerate chirality. The helix axis, h, is parallel to the Z axis of the laboratory frame.

  • Fig. 2 Cell and setup for the electro-optical measurements.

    (A) The two plates of the cell are covered with a PVA layer (shaded in blue), rubbed along the direction r; the in-plane field Er is applied across the two ITO electrodes placed on the bottom plate (shaded in red). (B) Schematic view of the electric field lines in a cross section of the cell. For clarity, the vertical scale is expanded. Close to the electrodes, the field direction and strength vary rapidly because of the edge effects; farther from the ITO stripes, the field is homogeneous and parallel to the substrates and to the rubbing direction r. (C) Setup for the measurement of the phase shift of the light transmitted by the cell. (D) Typical curve of the transmitted intensity as a function of the tilt angle 2i of the Berek compensator; the fit of the data points with a parabola improves significantly the precision of the measurement. The red arrow shows the fitted value of the minimum of the parabola. a.u., arbitrary units.

  • Fig. 3 Textures and phase transitions at varying field and temperature.

    Scale bar, 100 μm. In (A) the field is switched off and in (B to L) a square waveform field is applied, E = 8 V/mm,10 kHz. (A) In the N phase, at E = 0, the director n is parallel to the rubbing direction r. The dashed lines delimit the AR between the electrodes. In the corner, the contrast is saturated to show the slightly larger birefringence in the AR. (B) Subject to the field, n is parallel to r in the AR, but is tilted outside of it. (C and D) On cooling, the NTB phase first appears outside of the AR, meaning that the N-NTB transition is shifted. (E and F) The N-NY phase transition takes place in the AR. To reveal the small birefringence jump at the transition, (F) was recorded with a Berek compensator (γ shows its slow axis). (G to L) Upon further cooling, no other phase transition occurs but, in the region subject to the field, the texture becomes progressively less homogeneous: First very weak, stripe instabilities appear (G and H), then they become more contrasted (I and J), and finally the electrode edges are decorated by focal conics (K and L). For (J) and (L), the Berek compensator was introduced again.

  • Fig. 4 Birefringence of CB7CB measured as a function of temperature in different phases.

    The open red symbols show the data measured in the present study subject to the field E = 8 V/μm in the nematic and NY (now identified as the NSB phase) phases. The blue symbols show the data from (21) measured without applied field in the N and NTB phases of the same mesogen in a thin (1.6-μm) cell. The open symbols show the birefringence measured in the N phase or in large monochiral, uniform domains of the NTB phase. The full squares show the birefringence data measured in the defect wall with an NSB structure, which separates these monochiral domains (the line connecting them is a guide to the eye and does not have any physical meaning). The good agreement of those NSB data with our present results obtained under a field identifies the NY phase with the NSB phase. The continuous black line shows the birefringence expected in the nematic phase (obtained by extrapolation of the Haller function). Its temperature dependence is different from that of the NY phase, which confirms that the field-induced phase is not the usual uniform nematic but a distinct state. It is also of interest that, in the field experiment, the birefringence exhibits a clear jump at the NSB-N transition, which would be consistent with the first-order nature of the transition. Subsequently, the birefringence passes through a weak maximum before decreasing essentially in a linear manner in keeping with that in the defect walls.

  • Fig. 5 Definitions and mutual orientations of the molecular, director, and laboratory frames.

    The blue dashed lines show the trajectory of the director n. (A) The averaged conformer of the dimer is taken to be planar with C2v symmetry. The 2-axis of the molecular frame 123 is chosen to be along the C2 symmetry axis. The highly polarizable rigid cores of the monomers (shown as cylinders) lie in the 23-plane. The axis 3 is parallel to the main axis of the conformer, and its average orientation defines the director n. The z axis of the director frame xyz is parallel to n. The N phase is uniaxial and the orientation of the y axis is arbitrary. In the MN phases, the uniaxial symmetry is broken because of the strong bend of the director, and we choose the y axis parallel to the bend vector, b = n × ( ∇ × n). The biphenyl cores of the monomers are oriented preferentially parallel to the local director at their position, resulting in average orientation of the dimer with 3z and 2y. As the molecular polarizability, α, is due mainly to the biphenyl groups, and because the dielectric tensor, ε = εb, is related to the average of α, we expect εbxx < εbyy < εbzz in the MN phases. (B) In the NTB phase, the laboratory frame XYZ is defined by Z parallel to E (and to the helix axis h) and arbitrary orientation of Y. As yb and bZ, the Z axis lies in the xz plane, tilted at a fixed angle θtb with respect to z. (C) In the NSB phase, the Y axis is no longer arbitrary and is chosen to lie in the yz plane of the director frame. Therefore, the Z axis also lies in that plane and is periodic with respect to the z axis by a position-dependent angle θsb(Z).

  • Fig. 6 N-NTB-NSB phase diagram in the presence of a field.

    The phase diagram is represented as function of the ratios R1 and R3(T) of the elastic constants (A to C) and as a function of the field E and the ratio R1 at a fixed temperature T (D). (A) At E = 0, the N-MN second-order phase transition takes place at R3c(T) = 0, i.e., at T = T* and K33 = 0. The first-order NTB-NSB transition is temperature independent and occurs at R1c ≈ 2. (B) In the presence of a field and if the biaxiality of the MN phases is not taken into account, the N-MN transition is shifted to lower temperature by a field-dependent value. The NTB-NSB transition remains field independent and again takes place at R1c ≈ 2. (C) When the biaxiality of the MN phases is taken into account, the NTB-NSB transition is shifted to higher K11 /K22 values, which are a function of the field and the biaxiality of the dielectric tensor in the MN phases. The shift of the N-MN phase transition remains the same as in the uniaxial case. (D) Phase diagram as a function of the field at a constant temperature T < T*. Up to the critical field Ec(T), the modulated phases remain stable. The biaxial dielectric coupling favors the NSB, and the NTB-NSB transition is shifted to higher K11/K22 values. The shift, ΔR1c(E) = R1c(E) − R1c(0), increases quadratically with the field.

Supplementary Materials

  • Supplementary Materials

    Biaxiality-driven twist-bend to splay-bend nematic phase transition induced by an electric field

    Claire Meyer, Christophe Blanc, Geoffrey R. Luckhurst, Patrick Davidson, Ivan Dozov

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