Symmetry and chirality in crystals

Chirality in Liquid Crystals

Symmetry and Chirality: Continuous Measures

Folding Applying a set of inverse symmetry operations on a set of points. This procedure is one of the main steps in the folding unfolding method for evaluating the CSM of a set of points. Folding unfolding method A visual and computational procedure for evaluating the CSM of a set of points. Fuzzy subset A set whose elements have a range of values corresponding to the degree of membership in t...

Chlorophylls, Symmetry, Chirality, and Photosynthesis

Chlorophylls are a fundamental class of tetrapyrroles and function as the central reaction center, accessory and photoprotective pigments in photosynthesis. Their unique individual photochemical properties are a consequence of the tetrapyrrole macrocycle, the structural chemistry and coordination behavior of the phytochlorin system, and specific substituent pattern. They achieve their full pote...

Chirality and biaxiality in cholesteric liquid crystals.

We investigate the statistical mechanics of chirality and biaxiality in liquid crystals through a variety of theoretical approaches, including Monte Carlo simulations, lattice mean-field theory, and Landau theory. All of these calculations show that there is an important interaction between cholesteric twist and biaxial order: The twist acts as a field on the biaxial order, and conversely, the ...

Symmetry in crystals

Matter is usually classified into three states: gaseous, liquid, and solid. Gases are composed of almost isolated particles, except for occasional collisions; they tend to occupy all the available volume, which is subject to variation following changes in pressure. In liquids the attraction between nearest-neighbour particles is high enough to keep the particles almost in contact. As a conseque...