Application of X-ray resonant diffraction to structural studies of liquid crystals

Abstract

Abstract. Liquid crystals are soft materials that combine the fluidity of disordered liquids and the long range orientational or positional order of crystalline solids along one or two directions of space. X-ray scattering is widely and generally successfully used to investigate and characterize the microscopic structure of most liquid crystals. In many cases however, the Bragg reflections are forbidden by special symmetries of the unit cell and the low dimensional structure of the liquid crystalline phases are out of reach of conventional X-ray experiments. We show in this paper that this problem can be overcome by resonant scattering of X-rays as it reveals the anisotropy of the tensor structure factor. We review various examples in which the restored forbidden reflections reveal unambiguously the hidden structure of liquid crystalline phases. Moreover, we show that in some cases, a fine analysis of the polarization of the Bragg reflections enables one to discriminate between different structural models. These studies solved long standing questions about biaxial liquid crystal structures and provided new insights into physical phenomena such as supercritical behaviour or commensurate-incommensurate transitions.

Chirality of Liquid Crystals Formed from Achiral Molecules Revealed by Resonant X‐Ray Scattering

“…Special attention will be paid to resonant X-ray scattering (RXS), toward deducing the chiral structure of certain classes of LCs and the unique information that this method can provide, compared to other techniques. Because several review articles are available, related to chiral LCs [12][13][14][15][16][17][18][19][20] as well as to resonant X-ray of smectic phases made of rod-like [21][22][23][24] and bent-core [23] molecules, we focus here on recent RXS studies of structures without positional order (modulated nematic phases), bent-core modulated smectic phases and on LC materials with chiral morphologies. We conclude with the analysis of the recent progress in chirality control and transfer in LC materials and their nanocomposites.…”

Chiral Incommensurate Helical Phase in a Smectic of Achiral Bent-Core Mesogens

“…Since the period of such superlayer structures, p, can be as short as two layers, the structural study of such phases requires the effective probing of molecular orientation at the nanoscale. This can be achieved using resonant X-ray scattering, a technique sensitive to atomic environment [9][10][11][12][13][14][15][16][17][18][19] that has previously enabled the discovery and definitive characterization of superlayer organization in several SmC* phases and sub-phases, employing the Kedge resonance of atoms incorporated in the liquid crystal molecule [9,11].…”

“…Below 99 • C, the incommensurate peak broadens dramatically and moves to higher q, indicating the presence of short-ranged, Sm2-like helical fluctuations persisting in the Sm3 phase, and disappears at the transition to the Sm4 phase at 83 • C. The Sm4 phase exhibits only the bilayer RSoXS reflection at q B . The RSoXS scattering from a single layer can be analyzed, following Levelut and Pansu, in terms of a monoclinic second-rank tensor with a principal axis tilted from and then azimuthally rotated about the layer normal [10,13,14]. Scattering from a stack of such layers is calculated by summing over the contributions of the individual layers at different z. Resonant scattering peaks from azimuthally periodic arrangements are found at wavevectors along z, q(l, m) = l…”

Experimental evidence of soft mode in the smectic C*α phase of chiral ferroelectric liquid crystals

“…This mode also extends to the whole range of the phase SmC * a . Within that phase, it is accompanied by yet another mode with an amplitude of the same order of magnitude (10)(11)(12)(13)(14)(15)(16)(17)(18)(19)(20), but with a longer relaxation time. It is identied as a phase-type Goldstone mode describing the dynamics of the ferroelectric phase SmC*.…”

“…According to the theoretical predictions of the generalised Landau model, 15 the relaxation time s of the phase-type Goldstone mode is proportional to the square of the helix pitch p. The expected pitch in the helical structure of the SmC * a phase, expressed in terms of the number of smectic layers with a thickness of about 4 nm each, ranges from a few to several dozens. [16][17][18] This means that the quantity p in that phase should fall within the range of 10-100 nm. On the other hand, the average values of the parameter p in the SmC* phases are comprised within the range of several hundred to several thousand nm and are 10 to 100 times longer.…”