Acoustically driven oscillations of freely suspended liquid crystal filaments

Abstract

Some liquid crystalline phases of bent-core mesogens are known to form stable freely-suspended filaments with length to diameter ratios of 1000 and larger. These structures can behave like thin liquid chords. We study filament oscillations excited with harmonic sound waves. From amplitudes of the filament motion and phase shifts respective to the harmonic excitation signal we develop a model for the filament dynamics. Like in solid chords, the resonance frequency f 0 is inversely proportional to their length. The dependence of f 0 upon the filament radius allows one to draw conclusions on the nature of the filament tension. For thin filaments, this tension can be largely attributed to surface tension, while for thick filaments there must be other, bulk contributions in addition. The decay time of the filament oscillations is proportional to the filament length. This can be explained by the assumption that dissipation is restricted to the two filament ends. An important observation is that thick filaments often deviate significantly from cylindrical shape.

Physics of liquid crystals of bent-shaped molecules

“…Magdeburg, Germany (Biscari and Calderer 2005;Bauman and Phillips 2009) and Kent, Ohio(Antal Jákli, Krüerke, and Nair 2003;T. Ostapenko et al 2014;Salili, Ostapenko, et al 2016) providing information on filament tensions and damping processes (Martin W. Schroder Gerhard Pelzl, and Wolfgang Weissflog 2004;Yao, Spiegelberg, and McKinley 2000;Stannarius, Nemeş, and Eremin 2005;Nemeş 2008;Nemeş et al 2006;Nemes, Eremin, and Stannarius 2006;Petzold et al 2009;Antal Jákli, Krüerke, and Nair 2003;Coleman et al 2003). A transition between the disc-shaped and cone-shaped configurations gives rise to a new relaxation soft mode, where the direction of the cone tip oscillates.…”

Tension of freely suspended fluid filaments

“…Earlier mechanical and electrical studies explored the dynamical properties of such filaments [6,7,12]. However, still very little is known about their mechanical characteristics.…”

“…Later, mechanical resonances were studied under continuous excitation with sound waves [12]. If one neglects contributions of the internal filament structure, a plausible assumption is to set Σ equal to the specific surface energy per filament length [3,4], 2πrσ (radius r, surface tension σ).…”

“…Freely suspended fluid filaments are among the most exotic structures formed by liquid crystalline materials [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18]. Most of these unique structures are found in some mesophases of bent-core smectogens.…”

“…6 are slightly elliptical in the cross section. We take the perimeter of an ellipse and make a correction that takes the corrugations of the filament surface [12] into account. When the bundle consists of much smaller, cylindrical fibrils, then its surface can be considered as an array of parallel cylinders.…”