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Register a new userSpatially resolved x-ray studies of liquid crystals with strongly developed bond-orientational order
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We present an x-ray study of freely suspended hexatic films of the liquid crystal 3(10)OBC. Our results reveal spatial inhomogeneities of the bond-orientational (BO) order in the vicinity of the hexatic-smectic phase transition and the formation of large scale hexatic domains at lower temperatures. Deep in the hexatic phase up to 25 successive sixfold BO order parameters have been directly determined by means of angular x-ray cross-correlation analysis (XCCA). Such strongly developed hexatic order allowed us to determine higher order correction terms in the scaling relation predicted by the multicritical scaling theory over a full temperature range of the hexatic phase existence.
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We report on X-ray studies of freely suspended hexatic films of three different liquid crystal compounds. By applying angular X-ray cross-correlation analysis (XCCA) to the measured diffraction patterns the parameters of the bond-orientational (BO) order in the hexatic phase were directly determined. The temperature evolution of the BO order parameters was analyzed on the basis of the multicritical scaling theory (MCST). Our results confirmed the validity of the MCST in the whole temperature range of existence of the hexatic phase for all three compounds. The temperature dependence of the BO order parameters in the vicinity of the hexatic-smectic transition was fitted by a conventional power law with a critical exponent $betaapprox0.1$ of extremely small value. We found that the temperature dependence of higher order harmonics of the BO order scales as the powers of the first harmonic, with exponent equal to harmonic number. This indicates a nonlinear coupling of the BO order parameters of different order. It is shown that compounds of various composition, possessing different phase sequences, display the same thermodynamic behavior in the hexatic phase and in the vicinity of the smectic-hexatic phase transition.
Motivated by experiments on colloidal membranes composed of chiral rod-like viruses, we use Monte Carlo methods to determine the phase diagram for the liquid crystalline order of the rods and the membrane shape. We generalize the Lebwohl-Lasher model for a nematic with a chiral coupling to a curved surface with edge tension and a resistance to bending, and include an energy cost for tilting of the rods relative to the local membrane normal. The membrane is represented by a triangular mesh of hard beads joined by bonds, where each bead is decorated by a director. The beads can move, the bonds can reconnect and the directors can rotate at each Monte Carlo step. When the cost of tilt is small, the membrane tends to be flat, with the rods only twisting near the edge for low chiral coupling, and remaining parallel to the normal in the interior of the membrane. At high chiral coupling, the rods twist everywhere, forming a cholesteric state. When the cost of tilt is large, the emergence of the cholesteric state at high values of the chiral coupling is accompanied by the bending of the membrane into a saddle shape. Increasing the edge tension tends to flatten the membrane. These results illustrate the geometric frustration arising from the inability of a surface normal to have twist.
Optical methods are most convenient to analyze spatially periodic patterns with wavevector $bm q$ in a thin layer of a nematic liquid crystal. In the standard experimental setup a beam of parallel light with a short wavelength $lambda ll 2 pi/q$ passes the nematic layer. Recording the transmitted light the patterns are either directly visualized by shadowgraphy or characterized more indirectly by the diffraction fringes due to the optical grating effects of the pattern. In this work we present a systematic short-wavelength analysis of these methods for the commonly used planar orientation of the optical axis of liquid crystal at the confining surfaces. Our approach covers general 3D experimental geometries with respect to the relative orientation of $bm q$ and of the wavevector $bm k$ of the incident light. In particular the importance of phase grating effects is emphasized, which are not accessible in a pure geometric optics approach. Finally, as a byproduct we present also an optical analysis of convection rolls in Rayleigh-Benard convection, where the refraction index of the fluid is isotropic in contrast to its uniaxial symmetry in nematic liquid crystals. Our analysis is in excellent agreement with an earlier physical optics approach by Trainoff and Cannell [Physics of Fluids {bf 14}, 1340 (2002)], which is restricted to a 2D geometry and technically much more demanding.
We introduce the spatial correlation function $C_Q(r)$ and temporal autocorrelation function $C_Q(t)$ of the local tetrahedral order parameter $Qequiv Q(r,t)$. Using computer simulations of the TIP5P model of water, we investigate $C_Q(r)$ in a broad region of the phase diagram. First we show that $C_Q(r)$ displays anticorrelation at $rapprox 0.32$nm at high temperatures $T>T_Wapprox 250$ K, which changes to positive correlation below the Widom line $T_W$. Further we find that at low temperatures $C_Q(t)$ exhibits a two-step temporal decay similar to the self intermediate scattering function, and that the corresponding correlation time $tau_Q$ displays a dynamic crossover from non-Arrhenius behavior for $T>T_W$ to Arrhenius behavior for $T<T_W$. Finally, we define an orientational entropy $S_Q$ associated with the {it local} orientational order of water molecules, and show that $tau_Q$ can be extracted from $S_Q$ using an analog of the Adam-Gibbs relation.
We have studied the high-frequency dynamics of salol by inelastic x-ray scattering over a wide temperature range between 50 and 450 K, across the glass transition. We find that salol efficiently realizes the mechanism of dynamical arrest described by the mode-coupling theory, as manifested by a cusp singularity in the behaviour of the non-ergodicity parameter and a $Q$ dependence of the critical non-ergodicity parameter that is in phase with the static structure factor. These results confront positively the mode-coupling theory with liquids with local order.
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