1,720,982 research outputs found
Universal mean-field phase diagram for biaxial nematics
No full textFully attractive and partly repulsive molecular interactions,
characteristic of biaxial liquid crystal molecules,
are described by a class of quadratic Hamiltonians,
originally put forward by Straley.
The partly repulsive interactions require a minimax principle for
the associated mean-field free energy.
By analyzing the different phases in a bifurcation scenario,
we show that the phase diagram described by Sonnet et al. [Phys. Rev. E 67
061701 (2003)] is universal.
Our model predictions are in agreement
with recent observations on both V-shaped and tetrapodal
molecules
Universal features in the nematic uniaxial-to-biaxial transition
No full textRecent experimental findings about new nematogenic molecules have reported thermally driven transitions to biaxial phases, which has revived the interest for macroscopic biaxiality. In particular, the simplified interaction model proposed by Straley for molecules endowed with D_2h symmetry has met renewed interest. In the scenario obtained for phases a unifying character can be captured. There exists a universal feature in the behaviour of one uniaxial order parameter, rebounding at the biaxial-to-uniaxial transition. This finding has been confirmed by means of a Monte-Carlo simulation. Moreover, the phase sequences and the order of the transitions are poorly influenced by one of the interaction parameters
Bifurcation Analysis of a Mean-Field Model for Biaxial Nematics
No full textThe interest for macroscopic biaxiality has been recently revived by the experimental evidence of thermally driven transitions to biaxial phases, promoted by newly synthesized nematogenic molecules. In particular, the interaction model proposed by Straley for molecules endowed with D2h symmetry has been widely reconsidered. We elaborated a mean-field model based on a quadrupolar approximation to the mean torque potential has proven capable of capturing the universal features characterizing all phase diagrams compatible with the interaction model. Moreover, the phase sequences and the order of the transitions are weakly influenced by one of the interaction parameters. Here we show how to we derive the analytical bifurcation equations underlying our numerical analysis, and, subsequently, how these equations are instrumental to the correct resolution of the mean-field model. These bifurcation equations are integrated in a numerical code based on MATCONT, used for bifurcation analysis, which will be made available to the scientific community
Steric Effects in Polar Nematic Liquid Crystals
No full textRecent measurements in a nematic liquid crystal formed by polyester compounds have given evidence of spontaneous macroscopic polar ordering. A mean-field theory for liquid crystals is built combining short-range, repulsive, steric forces with the average electric dipolar energy exchanged between molecules sharing the same excluded region. Such model is capable of identifying both uniaxial and biaxial polar phases. Under the assumption of a spheroidal shape for the molecules, and through a numerical bifurcation analysis, we assess the stability of phases upon two interaction parameters: the degree of intrinsic biaxiality, and the relative orientation of the permanent electric dipoles
Membrane-mediated interactions of rod-like inclusions
No full textInclusions embedded in lipid membranes undergo a mediated force. due to the tendency of the membrane to relax its excess of elastic energy. In this paper we determine the exact shape of a two-dimensional vesicle hosting two different inclusions. and we analyse how the inclusion conformation influences the mediated interaction. We find non-trivial equilibrium configurations for the inclusions along the hosting membrane, and we derive the complete phase diagram of the mediated interaction. In particular, we find a non-vanishing mediated force even when the distance between the inclusions is much greater than their size. Our model can be applied to describe the mediated interactions of parallel, elongated inclusions embedded in three-dimensional membranes
Introduzione alla Meccanica Teorica
No full textIl libro nasce dall’esperienza didattica degli autori nell’insegnamento dei corsi di Fisica Matematica per la Facoltà di Ingegneria dell’Università degli studi di Pavia.
Partendo da considerazioni geometriche elementari, viene proposto un percorso fondato sul formalismo vettoriale e tensoriale, volto a studiare le proprietà di inerzia, la cinematica, la statica e la dinamica di sistemi di punti materiali e di corpi rigidi, fino ad arrivare a introdurre i concetti di base della meccanica lagrangiana dei sistemi olonomi e i suoi risultati principali.
Scopo principale del testo è quello di fornire un supporto didattico per l’apprendimento delle nozioni basilari della meccanica teorica.
Ogni argomento viene presentato e motivato, con alcuni esempi ed applicazioni utili e significativi per la comprensione e l’apprendimento dello studente
Identification of low-symmetry phases in nematic liquid crystals
Full text linkMesophases of nematic liquid crystals (NLC) are traditionally identified by building a second-rank ordering tensor S that efficiently describes the average orientation of nematogenic molecules with respect to a fixed laboratory/reference frame. In general, both in experiments and in simulations, the symmetry group of the molecules is known a-priori, contrary to the symmetry group of the phase; this latter has to be determined by analysing the numerical realisation of S, possibly affected by numerical errors. Furthermore, when a mesophase has a simple symmetric structure, as is the case of uniaxial nematics, the identification of the preferred direction is relatively an easy task. However, this task becomes less straightforward when the symmetry group of a mesophase is more complex. There is no generally accepted procedure to perform this analysis, but we have provided in a previous paper a new algorithm suited to identifying the symmetry group of the phase. We implement here such algorithm which gives a canonical representation of S for each of the classes that can be distinguished with a second-rank ordering tensor, and determines the nearest tensor of the assigned symmetry by group averaging
Calamitic and antinematic orientational order produced by the generalized Straley lattice model
No full textWe consider here a classical model, consisting of D2h-symmetric particles in a three-dimensional simple-cubic lattice; the pair potential is isotropic in orientation space, and restricted to nearest neighbors. The simplest potential model is written in terms of the squares of the scalar products between unit vectors describing the three interacting arms of the molecules, as proposed in previous literature. Two predominant antinematic couplings of equal strength (+1) are perturbed by a comparatively weaker calamitic one, parameterized by a coupling constant −z ranging in [−1,0]. This choice rules out thermodynamically stable phases endowed with macroscopic biaxiality. The antinematic terms favor states with the corresponding molecular axes mutually orthogonal. Although the low-temperature phase of the special case with null calamitic term (PP0) is uniaxial and antinematically ordered, in the general case presented here both Monte Carlo and molecular-field approaches show that, for z close to zero, the models exhibit a low-temperature uniaxial nematic phase, followed by an antinematic one, and finally by the orientationally disordered one. On the other hand, for sufficiently large values of z, we only find evidence of uniaxial calamitic behavior, as expected by following the limiting cases
- …
