Quadrupolar glass freezing in solid hydrogen: Distribution functions for the orientational axial and eccentric order parameters

1993 ◽  
Vol 48 (21) ◽  
pp. 15658-15665 ◽  
Author(s):  
T. K. Kopec´
Keyword(s):  
Solid Hydrogen ◽  
Order Parameters ◽  
Distribution Functions ◽  
Hydrogen Distribution ◽  
Quadrupolar Glass

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.

Calculation of the order parameter of solid hydrogen in the quadrupolar-glass phase

1994 ◽  
Vol 49 (14) ◽  
pp. 9460-9468 ◽  
Author(s):  
K. Walasek ◽  
K. Lukierska-Walasek
Keyword(s):  
Order Parameter ◽  
Glass Phase ◽  
Solid Hydrogen ◽  
Quadrupolar Glass

Orientation Distribution Functions Based upon Both 〈P1〉, 〈P3〉 Order Parameters and upon the Four 〈P1〉 up to 〈P4〉 Values: Application to an Electrically Poled Nonlinear Optical Azopolymer Film

2005 ◽  
Vol 59 (3) ◽  
pp. 322-328 ◽  
Author(s):  
V. Rodriguez ◽  
F. Lagugné-Labarthet ◽  
C. Sourisseau
Keyword(s):  
Thin Film ◽  
Second Harmonic ◽  
Orientation Distribution ◽  
Entropy Method ◽  
Order Parameters ◽  
Distribution Functions ◽  
Optical Elements ◽  
Polar Order ◽  
Relaxation Period ◽  
Nonlinear Properties

The most probable orientational distribution functions of rod-like polar molecules contained in a noncentrosymmetric uniaxial system are established using the first-rank and third-rank Legendre polynomials, 〈 P1(cos θ)〉 and 〈 P3(cos θ)〉 order parameters, and the maximum entropy method. Emphasis is put on the different domains of existence in the (〈 P1〉, 〈 P3〉) plane for the various shapes of the distributions: it is thus shown that, for any positive 〈 P1(cos θ)〉 value and for decreasing 〈 P3(cos θ)〉 values, the distribution function may exhibit either a distorted oblate form with an intense maximum at 0°, or a three-leaved rose curve with maxima at 60°, 180°, and 300°, and finally another markedly oblate shape with a strong maximum at 180°. As an illustrative example, we have considered the azobenzene molecular orientations in an electrically poled p(DR1M) homopolymer thin film after a thermal process and several relaxation periods. We have made use not only of the 〈 P1〉 and 〈 P3〉 parameters determined from polarized second-harmonic generation (SHG) measurements, but also of the 〈 P2〉 values extracted from UV-visible spectra and of the 〈 P4〉 values adjusted according to the information entropy theory. In such a thin film with very large nonlinear properties (d33 coefficients were varying from 437.0 to 117.0 pm/V at 1064 nm) it is evidenced that a strong polar order is maintained even after a long relaxation period of 42 days. So, the distribution functions demonstrate that the poling treatment was quite efficient and they emphasize the importance in the determination of both couples of odd and even order parameters in such uniaxially oriented optical elements.

Evidence for quadrupolar glass phases in solid hydrogen at reduced ortho concentrations

1978 ◽  
Vol 17 (12) ◽  
pp. 5016-5024 ◽  
Author(s):  
N. S. Sullivan ◽  
M. Devoret ◽  
B. P. Cowan ◽  
C. Urbina
Keyword(s):  
Solid Hydrogen ◽  
Quadrupolar Glass

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
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