scholarly journals Impact of Weak Nanoparticle Induced Disorder on Nematic Ordering

Crystals ◽  
2019 ◽  
Vol 9 (3) ◽  
pp. 171 ◽  
Author(s):  
Dejvid Črešnar ◽  
Christina Kyrou ◽  
Ioannis Lelidis ◽  
Aleksandra Drozd-Rzoska ◽  
Szymon Starzonek ◽  
...  
Keyword(s):  
Mean Field ◽  
Isotropic Phase ◽  
Weak Disorder ◽  
Nematic Ordering ◽  
Probabilistic Distribution ◽  
Distribution Shape ◽  
Simple Step ◽  
Orientational Distribution ◽  
Phase Temperature ◽  
Consistent Equation

Dilute mixtures of nanoparticles (NPs) and nematic liquid crystals (LCs) are considered. We focus on cases where NPs enforce a relatively weak disorder to the LC host. We use a Lebwohl-Lasher semi-microscopic-type modeling where we assume that NPs effectively act as a spatially-dependent external field on nematic spins. The orientational distribution of locally favoured “easy” orientations is described by a probabilistic distribution function P. By means of a mean field-type approach, we derive a self-consistent equation for the average degree of nematic uniaxial order parameter S as a function of the concentration p of NPs, NP-LC coupling strength and P. Using a simple step-like probability distribution shape, we obtain the S(p) dependence displaying a crossover behaviour between two different regimes which is in line with recent experimental observations. We also discuss a possible origin of commonly observed non-monotonous variations of the nematic-isotropic phase temperature coexistence width on varying p.

scholarly journals Effect of weak disorder on the BCS–BEC crossover in a two-dimensional Fermi gas

2017 ◽  
Vol 31 (09) ◽  
pp. 1750066
Author(s):  
Ayan Khan ◽  
B. Tanatar
Keyword(s):  
Field Theory ◽  
Mean Field Theory ◽  
Mean Field ◽  
Fermi Gas ◽  
Ultracold Fermi Gas ◽  
Condensate Fraction ◽  
Two Dimensional ◽  
Weak Disorder ◽  
Unique Nature

In this paper, we study the two-dimensional (2D) ultracold Fermi gas with weak impurity in the framework of mean-field theory where the impurity is introduced through Gaussian fluctuations. We have investigated the role of the impurity by studying the experimentally accessible quantities such as condensate fraction and equation of state of the ultracold systems. Our analysis reveals that at the crossover, the disorder enhances superfluidity, which we attribute to the unique nature of the unitary region and to the dimensional effect.

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.

Particle Orientational Properties and Viscosity of a Dense Colloidal Dispersion Composed of Ferromagnetic Spherocylinder Particles: Analysis by Means of Mean Field Approximation for a Simple Shear

2005 ◽  
Author(s):  
Akira Satoh
Keyword(s):  
Magnetic Field ◽  
Applied Magnetic Field ◽  
Mean Field ◽  
Magnetic Interaction ◽  
Colloidal Dispersion ◽  
Field Approximation ◽  
Magnetic Interactions ◽  
Mean Field Approximation ◽  
Particle Interactions ◽  
Orientational Distribution

We have theoretically investigated the particle orientational distribution and viscosity of a dense colloidal dispersion composed of ferromagnetic spherocylinder particles under circumstances of an applied magnetic field. The mean field approximation has been applied to take into account the magnetic interactions of the particle of interest with the other ones which belong to the neighboring clusters, besides its own cluster. The basic equation of the orientational distribution function, which is an integro-differential equation, has approximately been solved by Galerkin’s method and the method of successive approximation. Even when the magnetic interaction between particles is of the order of the thermal energy, the effect of particle-particle interactions on the orientational distribution comes to appear more significantly with increasing the volumetric fraction of particles. This effect comes to appear more significantly when the influence of the applied magnetic field is not relatively so strong compared with magnetic particle-particle interactions.

Transitions de phase dans une couche monomoléculaire sur un substrat liquide adhésif

1975 ◽  
Vol 53 (21) ◽  
pp. 2369-2374 ◽  
Author(s):  
Alain Caillé ◽  
Göran Ågren
Keyword(s):  
Field Theory ◽  
Nematic Phase ◽  
Short Range ◽  
Mean Field Theory ◽  
Mean Field ◽  
Isotropic Phase ◽  
Minimum Length ◽  
Monomolecular Layer ◽  
Short Range Repulsion ◽  
Breadth Ratio

We use a lattice model to characterize the state of a monomolecular layer of long and rigid molecules. The solutions are obtained using a mean field theory with only short range repulsion forces. The basic results are: (1) a stable nematic phase for a region of density above a minimum length to breadth ratio; (2) the transition between the nematic phase and the isotropic phase is found to be second order. The results are in excellent agreement with those obtained with a mercury subphase.

scholarly journals Non-equilibrium evolution of Bose-Einstein condensate deformation in temporally controlled weak disorder

2021 ◽  
Vol 10 (1) ◽  
Author(s):  
Milan Radonjic ◽  
Axel Pelster
Keyword(s):  
Mean Field ◽  
Einstein Condensate ◽  
Weak Disorder ◽  
Field Approach ◽  
Bose Einstein Condensate ◽  
Adiabatic Switching ◽  
Long Time ◽  
Disorder Potential ◽  
Bose Einstein ◽  
Non Equilibrium

We consider a time-dependent extension of a perturbative mean-field approach to the homogeneous dirty boson problem by considering how switching on and off a weak disorder potential affects the stationary state of an initially {equilibrated} Bose-Einstein condensate by the emergence of a disorder-induced condensate deformation. We find that in the switch on scenario the stationary condensate deformation turns out to be a sum of an equilibrium part{, that actually corresponds to adiabatic switching on the disorder,} and a dynamically-induced part, where the latter depends on the particular driving protocol. If the disorder is switched off afterwards, the resulting condensate deformation acquires an additional dynamically-induced part in the long-time limit, while the equilibrium part vanishes. {We also present an appropriate generalization to inhomogeneous trapped condensates.} Our results demonstrate that the condensate deformation represents an indicator of the generically non-equilibrium nature of steady states of a Bose gas in a temporally controlled weak disorder.

Influences of Magnetic Particle-Particle Interactions on Orientational Distributions and Rheological Properties of a Semi-Dense Colloidal Dispersion Composed of Rod-Like Hematite Particles: Analysis by Means of Mean Field Approximation for an External Magnetic Field Parallel to the Angular Velocity Vector of a Simple Shear Flow

2007 ◽  
Author(s):  
Ryo Hayasaka ◽  
Masayuki Aoshima ◽  
Toshinori Suzuki ◽  
Akira Satoh
Keyword(s):  
Magnetic Field ◽  
Magnetic Moment ◽  
Mean Field ◽  
Field Approximation ◽  
Field Direction ◽  
Magnetic Interactions ◽  
Mean Field Approximation ◽  
Magnetic Field Direction ◽  
Orientational Distribution ◽  
The Magnetic Field

We have investigated mainly the influences of magnetic particle-particle interactions on orientational distributions and viscosity of a semi-dense dispersion, which is composed of rod-like particles with a magnetic moment magnetized normal to the particle axis. In addition, the influences of the magnetic field strength, shear rate, and random forces on the orientational distribution and rheological properties have been clarified. The mean field approximation has been applied to take into account magnetic interactions between rod-like particles. The basic equation of the orientational distribution function has been derived from the balance of torques and solved by the numerical analysis method. The results obtained here are summarized as follows. For a strong magnetic field, the rotational motion of the rod-like particle is restricted in a plane normal to the shearing plane because the magnetic moment of the particle is restricted in the magnetic field direction. Under circumstances of a very strong magnetic interaction between particles, the magnetic moment is strongly restricted in the magnetic field direction, so that the particle has a tendency to incline in the flow direction with the magnetic moment pointing to the magnetic field direction. For a strong shear flow, a directional characteristic of rod-like particles is enhanced, and this leads to a more significant one-peak-type distribution of the orientational distribution function. Magnetic interactions between particles do not contribute to the viscosity because the mean-field vector has only a component along the magnetic field direction.

scholarly journals Symmetry breaking and structure of a mixture of nematic liquid crystals and anisotropic nanoparticles

2010 ◽  
Vol 6 ◽  
Author(s):  
Marjan Krasna ◽  
Matej Cvetko ◽  
Milan Ambrožič
Keyword(s):  
Random Fields ◽  
Short Range ◽  
Liquid Crystalline ◽  
Short Range Order ◽  
Isotropic Phase ◽  
Nematic Ordering ◽  
Domain Type ◽  
Elastic Forces ◽  
Orientational Ordering ◽  
The Impact

Orientational ordering of a homogeneous mixture of uniaxial liquid crystalline (LC) molecules and magnetic nanoparticles (NPs) is studied using the Lebwohl–Lasher lattice model. We consider cases where NPs tend to be oriented perpendicularly to LC molecules due to elastic forces. We study domain-type configurations of ensembles, which are quenched from the isotropic phase. We show that for large enough concentrations of NPs the long range uniaxial nematic ordering is replaced by short range order exhibiting strong biaxiality. This suggests that the impact of NPs on orientational ordering of LCs for appropriate concentrations of NPs is reminiscent to the influence of quenched random fields which locally enforce a biaxial ordering.

FINITE TEMPERATURE PROPERTIES OF OPTICAL LATTICES

2005 ◽  
Vol 19 (31) ◽  
pp. 4567-4586
Author(s):  
FUXIANG HAN ◽  
YONGMEI ZHANG
Keyword(s):  
Temperature Dependence ◽  
Optical Lattice ◽  
Order Parameter ◽  
Optical Lattices ◽  
Mean Field ◽  
Mott Insulator ◽  
Superfluid Phase ◽  
Self Consistent ◽  
The One ◽  
Consistent Equation

Within a mean-field treatment of the Bose–Hubbard model for an optical lattice, we have derived a self-consistent equation for the order parameter of possible phases in the optical lattice at finite temperatures. From the solutions to the self-consistent equation, we have inferred the temperature dependence of the order parameter and transition temperatures of Mott-insulator and superfluid phases into the normal phase. The condensation fraction in the superfluid phase has been deduced from the one-body density matrix and its temperature dependence has been given. In terms of the normalized correlation function of quasiparticles, strong coherence in the superfluid phase and its loss in Mott-insulator phases are demonstrated.

A TWO-PARTICLE CLUSTER THEORY OF THE TRANSFORMED CHIRAL SYSTEM FOR LIQUID CRYSTALS

2000 ◽  
Vol 14 (05) ◽  
pp. 475-483
Author(s):  
ZHANG ZHIDONG ◽  
LIU JINWEI ◽  
ZHANG WU
Keyword(s):  
Liquid Crystals ◽  
Mean Field Theory ◽  
Mean Field ◽  
Present Theory ◽  
Particle Cluster ◽  
Cluster Theory ◽  
Chiral Nematic ◽  
Temperature Dependences ◽  
Orientational Distribution ◽  
Chiral System

The chiral molecules are confined to the sites of a simple cubic lattice with their long axes in the XY-plane and the helix axis along the Z direction. The intermolecular interaction takes the form proposed by van der Meer et al. which is the simplest possible for chiral nematic liquid crystals. The chiral potential can thus be transformed to that for an achiral system but with different interactions between molecules in the same layer and those in neighboring layers. We have presented a generalized two-particle cluster theory which is suited for treating the model system with different neighboring intermolecular interactions. Such a theory has been used to study the transformed chiral system. The equation for the equilibrium distribution is solved by an iterative method. The temperature dependences of the order parameters T2and T4and of the internal energy per particle are calculated. The single orientational distribution function is shown at the scaled temperature t=2.3, i.e. near the phase transition in the simulation. The present theory, taking into account the short range correlations between molecules, yields improved results compared with the mean field theory.

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