scholarly journals Orientational distribution functions and order parameters in “de Vries”-type smectics: A simulation study

2016 ◽  
Vol 145 (13) ◽  
pp. 134901 ◽  
Author(s):  
Frank Jenz ◽  
Mikhail A. Osipov ◽  
Stefan Jagiella ◽  
Frank Giesselmann
Keyword(s):  
Simulation Study ◽  
Order Parameters ◽  
Distribution Functions ◽  
De Vries ◽  
Orientational Distribution

scholarly journals Order Parameters, Orientational Distribution Functions and Heliconical Tilt Angles of Oligomeric Liquid Crystals

2019 ◽  
Author(s):  
Richard Mandle ◽  
John W. Goodby
Keyword(s):  
Phase Transition ◽  
Liquid Crystals ◽  
Tilt Angle ◽  
Order Parameter ◽  
Nematic Phase ◽  
Liquid Crystalline ◽  
Thermal Evolution ◽  
Order Parameters ◽  
Distribution Functions ◽  
Orientational Distribution

We compare the order parameters, orientational distribution functions (ODF) and heliconical tilt angles of the TB phase exhibited by a liquid-crystalline dimer (CB7CB) to a tetramer (O47) and hexamer (O67) by SAXS/WAXS. Following the N-TB phase transition we find that all order parameters decrease, and while 〈P2 〉 remains positive 〈P4 〉 becomes negative. For all three materials the order parameter 〈P6 〉 is near zero in both phases. The ODF is sugarloaf-like in the nematic phase and volcano-like in the TB phase, allowing us to estimate the heliconical tilt angle of each material and its thermal evolution. The heliconical tilt angle appears to be largely independent of the material studied despite the differing number of mesogenic units.

scholarly journals On the orientational distribution functions in de Vries-type smectic liquid crystals

2018 ◽  
Vol 45 (13-15) ◽  
pp. 2097-2108 ◽  
Author(s):  
Per Rudquist ◽  
Mikhail A. Osipov ◽  
Frank Giesselmann
Keyword(s):  
Liquid Crystals ◽  
Distribution Functions ◽  
Smectic Liquid Crystals ◽  
De Vries ◽  
Orientational Distribution

scholarly journals Order parameters, orientational distribution functions and heliconical tilt angles of oligomeric liquid crystals

2019 ◽  
Vol 21 (13) ◽  
pp. 6839-6843 ◽  
Author(s):  
Richard J. Mandle ◽  
John W. Goodby
Keyword(s):  
Liquid Crystals ◽  
Orientational Order ◽  
Helical Structure ◽  
Order Parameters ◽  
Distribution Functions ◽  
X Ray ◽  
X Ray Scattering ◽  
Orientational Distribution ◽  
Pitch Length ◽  
Ray Scattering

Twist-bend (TB) phases possess a local helical structure with a pitch length of a few nanometers. X-ray scattering experiments on aligned samples of dimeric and oligomeric materials allows the orientational order parameters, orientational distribution functions and heliconical tilt angles to be calculated.

scholarly journals Order Parameters, Orientational Distribution Functions and Heliconical Tilt Angles of Oligomeric Liquid Crystals

2019 ◽  
Author(s):  
Richard Mandle ◽  
John W. Goodby
Keyword(s):  
Phase Transition ◽  
Liquid Crystals ◽  
Tilt Angle ◽  
Order Parameter ◽  
Nematic Phase ◽  
Liquid Crystalline ◽  
Thermal Evolution ◽  
Order Parameters ◽  
Distribution Functions ◽  
Orientational Distribution

We compare the order parameters, orientational distribution functions (ODF) and heliconical tilt angles of the TB phase exhibited by a liquid-crystalline dimer (CB7CB) to a tetramer (O47) and hexamer (O67) by SAXS/WAXS. Following the N-TB phase transition we find that all order parameters decrease, and while 〈P2 〉 remains positive 〈P4 〉 becomes negative. For all three materials the order parameter 〈P6 〉 is near zero in both phases. The ODF is sugarloaf-like in the nematic phase and volcano-like in the TB phase, allowing us to estimate the heliconical tilt angle of each material and its thermal evolution. The heliconical tilt angle appears to be largely independent of the material studied despite the differing number of mesogenic units.

Explicit Flow-Aligned Orientational Distribution Functions for Dilute Nematic Polymers in Weak Shear

2002 ◽  
Author(s):  
M. Gregory Forest ◽  
Ruhai Zhou ◽  
Qi Wang
Keyword(s):  
Kinetic Theory ◽  
Mean Field ◽  
Distribution Functions ◽  
Small Molecular Weight ◽  
Exact Probability ◽  
Exact Probability Distribution ◽  
Orientational Distribution ◽  
Alignment Angle ◽  
Nematic Polymers ◽  
Leslie Angle

Flow-alignment of sheared nematic polymers occurs in various flow-concentration regimes. Analytical descriptions of shear-aligned nematic monodomains have a long history across continuum, mesoscopic and mean-field kinetic models, sacrificing precision at each finer scale. Continuum Leslie-Ericksen theory applies to highly concentrated, weak flows of small molecular weight polymers, giving an explicit macroscopic alignment angle formula dependent only on Miesowicz viscosities. Mesoscopic tensor models apply at all concentrations and shear rates, but explicit “Leslie angle” formulas exist only in the weak shear limit (Cocchini et. al, 90; Bhave et. al, 93; Wang, 97; Rienacker and Hess, 99; Maffettone et. al, 00; Forest and Wang, 02; Forest et. al, 02c; Grecov and Rey, 02), with distinct behavior in dilute versus concentrated regimes. Exact probability distribution functions (pdf’s) of kinetic theory do not exist for highly concentrated nematic states, even without flow, although appealing flow-aligned approximations have been derived (Kuzuu and Doi, 83; Kuzuu and Doi, 84; Semenov, 83; Semenov, 86; Archer and Larson, 95; Kroger and Seller, 95), which offer a molecular theory basis for the Leslie alignment angle. A simpler problem concerns the dilute concentration regime where the unique quiescent equilibrium is isotropic, corresponding to a constant pdf, and whose weak shear deformation is robust to mesoscopic closure approximation (Forest and Wang, 02; Forest et. al, 02c): steady, flow-aligning, weakly anisotropic, and biaxial. The purpose of this paper is to explicitly construct the weakly anisotropic branch of stationary pdf’s by a weak-shear asymptotic expansion of kinetic theory. A second-moment pdf projection confirms mesoscopic model predictions, and further yields explicit Leslie angle and degree of alignment formulas in terms of molecular parameters and normalized shear rate.

On the Overall Properties of Composites Reinforced by Fibers With Prescribed Orientations

2015 ◽  
Author(s):  
Yana Morenko ◽  
Pavlo Krokhmal ◽  
Olesya I. Zhupanska
Keyword(s):  
Uniform Distribution ◽  
Elastic Properties ◽  
Optimization Problem ◽  
Distribution Functions ◽  
Fiber Reinforced Composites ◽  
Semidefinite Optimization ◽  
Reinforced Composites ◽  
Fiber Reinforced ◽  
Positive Semidefinite Matrices ◽  
Orientational Distribution

This study is concerned with development of bounds on the elastic properties of fiber reinforced composites with arbitrary orientational distribution of fibers. Generalization of the Mori-Tanaka model [1] and Hashin-Schtrikman variational bounds [2] to the cases of non-aligned composite phases are examined. Orientation distribution functions (ODF) are used to describe orientation probability density. It is shown that the Mori-Tanaka scheme applied to the non-aligned fiber reinforced composites violates symmetry of the effective elastic moduli tensor. The study of the literature also reveals that there are no known bounds derived for the composites with orientational distribution (except for the random uniform distribution) of phases. To overcome this issue we propose to formulate a problem of finding tightest bounds for the composites with non-aligned phases as a nonlinear semidefinite optimization problem, i.e., an optimization problem where the optimization variables are represented by symmetric positive semidefinite matrices. Such a formulation guarantees that any solution of the optimization problem represents a valid tensor of elastic material properties. The optimization problem then is solved by an interior point method to produce optimal bounds for the overall elastic properties of two-phase composite with uniform distribution of carbon nanotubes in a polymer matrix.

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