Although first proposed more than a century ago by Born in the 1910s, ferroelectricity in nematic fluids has not been experimentally realized until recently [1,2], immediately becoming a major topic of soft matter research [3]. These fascinating new materials offer a full new range of potential applications for nematic liquid crystals, beyond the well-established multibillion-euro display market.

The accomplishment of new applications is directly intertwined with our fundamental understanding of the materials and our ability to process, control and fabricate polarization structures. The importance of the results confined in the manuscript “Polarization patterning in ferroelectric nematic liquids via flexoelectric coupling” relies precisely on the latter. We propose a unique approach how to fabricate electric polarization structures in ferroelectric liquids exploiting flexoelectric coupling of the nematic director and the polarization by using photopatterning alignment technology. Alignment techniques widely used for the control of orientation in classical non-polar nematic materials have been shown to be somehow limited in the case of ferroelectric nematic liquids, as in addition to orientational coupling constraints, polar coupling constraints in the boundary surfaces play an important role in the resulting macroscopic structure [4].

In this paper, we investigate the possibilities of using photoalignment technology to create custom polarization structures. It is shown that mm-size uniform ferroelectric domains can be created with a simple uniform pattern. In such domains, some defects can be observed at the edges, provoking a dragonfly-like optical distortion around them, with long wings extending transversally to the defect and sharply ending at the defect-bending tip. It is shown that such optical trace results from a splay distortion of the nematic structure around the defects, evidencing that topological defect lines in the ferroelectric nematic phase, carry in this case an electrical charge (Fig.1).

Figure 1. Dragonfly-like splay deformations due to charged defect lines. POM images at different geometries a) extinction position, b) with full wave plate at 45° and c), d) with the sample rotated in opposite directions e-h) Corresponding dtmm simulations for the structure confined in (i-j). Crossed bidirectional white arrows indicate the direction of the polarizer and analyzer, while the green arrow indicates the orientation of the photopatterned direction. The structure twists across the cell thickness to accommodate the splay around the defect line. This splay director distortion reflects the electric charge of the defect line.

We furthermore created a series of splayed structures, which exploit and experimentally visualize the flexoelectric coupling between polarization and nematic deformations. Similarly, as in piezoelectricity, where strain induces polarization, splay deformations of the orientational director field in nematic materials can result in electric polarization. Such an effect is very weak in the case of non-polar nematic materials. In this paper, it is experimentally demonstrated that in the case of ferroelectric nematics, the flexoelectric coupling between deformation and polarization is indeed strong and we can use it to create custom electric polarization structures. One-dimensional splayed photopatterned structures in the confining cells lead to periodic polarization domains, with elongated areas of opposite polarization. This point is proved by second harmonic generation (SHG) microscopy with incorporated interferometry capabilities, to discern the direction and the sign of the polarization (Fig.2). The structures are investigated via polarizing optical microscopy and the observations are compared with calculated images using diffractive transfer matrix method (DTMM) optical simulations. Such comparison demonstrates that the depolarization field created by bound charges arising from the splay structure causes the escape from the surface splay to a uniform structure in the centre of the confining cell. The stability of the deduced structures has been additionally assessed by a simple model, in which elastic and electrostatic torques are balanced.

Figure 2.  a) SHG interferometry images of the periodic-splay structures Splay-P40A40 and Splay-P40A20, with period 40 µm and maximum splay angle 40° and 20°, respectively. b) SHG interferograms corresponding to the highlighted areas in (a) with matching colours. The SHG phase for two neighbouring splay domains is opposite, i.e., polarization lies in opposite directions for splay regions of opposite signs. c) Calculated charge distribution −∇⋅P across the cell thickness. d, e) Schematic representation of the surface and cell centre planes (d) and 3D sketch (e) showing the flexoelectric coupling between the splay deformation and the polarization direction.

Finally, the potentialities of guiding polarization, through splay-guiding channels, either in a uniform or a bend background are shown for a series of structures, comparing the behaviour between different materials. In addition to the relevance for technological developments, the results in this manuscript are also of interest for the fundamental understanding of polarity in fluids. We observe that the gained control of polarization structures is accompanied by the consecution of periodic arrays of topological defects, as the boundary between regions with opposite polarization does not occur by melting into a nonpolar nematic structure, but through the appearance of a topological defect. 

References

1. Mandle, R. J., Cowling, S. J. & Goodby, J. W. Rational design of rod-like liquid crystals exhibiting two nematic phases.  Eur. J.23, 14554–14562 (2017).
2. Nishikawa, H. et al. A fluid liquid-crystal material with highly polar order.  Mater.29, 1702354 (2017).
3. Sebastián, N., Čopič, M. & Mertelj, A. Ferroelectric nematic liquid-crystalline phases.  Rev. E106, 021001 (2022).
4. Caimi, F. et al. Surface alignment of ferroelectric nematic liquid crystals. Soft Matter, 17, 8130-8139 (2021)