A. Schönhofer

Computer simulation of chiral liquid crystal phases. I. The polymorphism of the chiral Gay-Berne fluid

Abstract We report the results of computer simulation studies for a bulk system composed of chiral particles interacting via the Gay-Berne potential and an additive chiral potential. Using Monte Carlo (MC) simulations in the NVT ensemble, the chirality-temperature plane of the phase diagram was studied at different points by a variation of the chirality parameter c describing the strength of the chiral potential. Additionally to the well-known isotropic, nematic and smectic phases of the Gay-Berne fluid, we localized regions of cholesteric phase. For large values of the chirality parameter we also observed blue phases. Furthermore, when starting from a cholesteric phase and decreasing the temperature at constant c, we obtained a phase region showing characteristics of the recently discovered helical smectic A∗ phase. All phases have been characterized by correlation functions, order parameters, and visual representations of selected configurations. All results of the simulation are limited by the small sy...

Optical activity of oriented molecules: II. Theoretical description of the optical activity

Abstract The theory of the optical activity of oriented molecules is developed starting from an expression given by Gō. In order to describe the experiments, a tensioral rotational strength RT = gkl33KNKkl is introduced. The orientational distribution coefficients gkl33 determine the influence of the type and magnitude of the orientation to RT. The tensor of rotation RNKkl is a function of magnetic dipole, electric dipole and electric quadrupole transition moments. Not all the coordinates of the tensor can be determined experimentally at present. It is shown however, that for molecules of a sufficiently high symmetry e.g. D2-symmetry the tensor will have a very simple form. For two unsaturated keto steroids the magnitude of the coordinates RNK11, RNK 22 and RNK33 is estimated from experimental results.

Optical activity of oriented molecules. IX. Phenomenological Mueller matrix description of thick samples and of optical elements

Abstract The Mueller matrix of a non-depolarizing, homogeneous but anisotropic medium is calculated in a closed form from the “differential matrix”, i.e. from the Mueller matrix of a thin layer of the same medium. The implications of certain symmetry properties of the sample on its Mueller matrix are discussed as well as some properties and a possible geometric visualisation of the latter originating from its relationship to a Lorentz transformation. There results a decomposition into a product of a general retarder and a general polarizer matrix. Three examples of application of the general formulas are given: (1) A suitable equation for constructing the Mueller matrices of optical elements, (2) a criticism of a CD measurement by means of a non-ideal modulator, and (3) by slight generalization to an inhomogeneous medium, a model for absorbing cholesteric phases.

Symmetry properties of the Mueller matrix

Abstract The transmission of polarized light through a sample is considered which may also be in an external electric or magnetic field. The transformation properties of the Mueller matrix on application of certain spatial symmetry operations, partially combined with reversal of motion, to the sample (including the fields) can be given explicitly. Their bearing on the behaviour of the Mueller matrix under arbitrary rotations and rotation-reflections is investigated. Among other applications, the optical properties of a (non-depolarizing) liquid are discussed as depending on the direction of a homogeneous external field.

Optical activity of oriented molecules III. The absorption process and the vibrational coupling effects for the tensor of rotation

Abstract Equations for the rotation and the ellipticity of samples exhibiting linear and circular birefringence and dichroism (i.e. for small elliptical birefringence and dichroism) are given. By this a second presentation of the frequency dependence for linear and circular birefringence of anisotropic solutions is developed. The absorption coefficients of anisotropic solutions for linearly polarized light are calculated from the H-matrix of Gō. For a special type of orientational distribution function the absorption behaviour is analysed. Within the adiabatic approximation and by neglecting the variation of the electronic transition moments with the nuclear distances, the structure of a circular dichroism band is independent of the orientational distribution function. Empirically, this is not the case for α, β-unsaturated keto steroids. By including this variation in the adiabatic approximation the coordinates of the tensor of rotation RNnKkij are altered by different amounts due to the coupling by vibrations of the involved states with other electronic states of the system (Herzberg-Teller method). As a consequence of this coupling electric dipole and magnetic dipole/electric quadrupole transition moments not belonging to the observed transition |K0> ← |N0> are added to the zeroth order tensor of rotation RNKij. Le., first order tensor of rotation RLM/PRij = 1 4 LM|ekli PR + eklj PR}, multiplied by a mixing parameter depending on the type of vibration have to be added to RNKij. As a consequence, the structure of the CD band will depend on the orientational distribution function. The model developed is demonstrated for molecules with symmetry D2.

Computer simulation of chiral liquid crystal phases. IV. Intermolecular chirality transfer to rotamers in a cholesteric phase

Abstract Intermolecular chirality transfer was studied by investigating the conformational distribution of rotamers in a cholesteric guest-host phase using Monte Carlo (MC) simulations in the NVT ensemble. The guest-host system under investigation was given by N c = 238 rigid, chiral Gay-Berne atropisomers as host molecules and N a = 18 flexible Gay-Berne rotamers as guest molecules. The rigid, chiral Gay-Berne atropisomers of point symmetry group D2 were defined by joining two Gay-Berne particles through a bond with a suitable fixed dihedral angle. The possibility of internal rotation about the bond axis without a rotational barrier was introduced as an internal degree of freedom for the guest molecules, for convenience denoted as Gay-Berne rotamers. Starting from an isotropic configuration, cholesteric phases were obtained on equilibrating the guest-host systems, whereby left-handed and right-handed cholesterics were formed depending on the M- and P-helicity of the atropisomers, respectively. Analysing ...

Helical twisting power of chiral mono- and bis-aminoanthraquinones. Intramolecular and intermolecular chirality transfer in liquid-crystal phases

The helical twisting power (HTP) of mono- and bis-aminoanthraquinones with chiral substituents depends strongly on the position of substitution. It is shown that the Intramolecular chirality transfer yields, for each compound, several conformers which are different for the 1-cyclohexylethyl, 1-phenylethyl and 1-naphthalen-1-ylethyl substituents. Each conformer contributes differently to the HIP of a compound. Furthermore, the HIP of a bis-substituted compound is approximately the sum of the HIP values of the corresponding mono-substituted compounds if the orientation of the substituents with respect to the orientation axis (principal axis of the order tensor belonging to the largest eigenvalue) is the same in each case. This means that the contribution of a ‘chiral area’, induced around an asymmetric carbon atom by Intramolecular chirality transfer, to the HTP depends on its orientation with respect to the orientation axis. A variation of this orientation can cause even a change of sign of the HIP in spite of the fact that the dependence of the HIP on the order parameters, S* and D*, is small.

Circular dichroism of oriented molecules. Electric dipole/magnetic dipole and electric dipole/electric quadrupole contribution for cholest-4-en-3-one

Abstract Three independent molecular quantities Δe * ii have been determined for 2,2,4,6,6-d 5 -cholest-4-en-3-one ( 1 ) by the circular dichroism of isotropic (CD) and anisotropic (ACD) samples using order parameters evaluated from 2 H NMR spectra. The orientation axis depends on temperature which may originate from a conformational change of 1 . A refined analysis of the ACD measurements is given and applied to 1 because all coordinates of the order tensor are known. The order of the molecules as calculated from 2 H NMR spectra is higher than that obtained by UV and IR spectroscopy. The estimated electric dipole/electric quadrupole contribution to the ACD is in the order of magnitude of the electric dipole/magnetic dipole contribution.

Optical activity of oriented molecules. α,β-unsaturated steroid ketones and their sector rules

Abstract Polarized spectroscopy is applied to the nπ* transition of α,β-unsaturated ketosteroids. The anisotropy of the CD of the oriented molecules (ACD) is shown to be strong for all compounds analyzed. Two different vibrational band progressions, namely an “allowed” and a “forbidden” one, determine most of the absorption of this transition. The CD of the “allowed” progression is positive whereas that of the “forbidden” one is negative. In general, for these compounds the CD of the isotropic solution Δϵ is determined by the “forbidden” progression. The variation of the intensity of the “allowed” and “forbidden” CD contributions by substitution in the vicinity of the enone chromophore may provide an explanation of a failure of the helicity rule for the enone system. As an example for such a failure the behaviour of some substituted α,β-unsaturated ketosteroids is discussed where the CD of the “allowed” progression determines the sign of Δϵ. Herewith, it is suggested - which is also plausible from the theoretical point of view - that helicity or sector rules can be applied only in such cases where the CD of the compound to be analyzed belongs to the same transition |Nn〉 → |Kk〉, e.g. the same vibronic transitions n, k in N and K as the CD of the compounds from which the rule is derived, a fact which is not always taken into account in literature.

Orientational distribution coefficients for oriented systems, e.g., a liquid crystal matrix☆

Abstract For a class of measurements, UV and CD, e.g., the measurable quantities are represented by M kl = g ijkl X ij , where the X ij describe a symmetric or antisymmetric tensorial property of the molecule. The g ijkl are the orientational distribution coefficients which represent a generalized form of the Saupe order matrix. For an optically biaxial (uniaxial) system there are thirty-four(eight) independent orientational distribution coefficients which bear information about the orientational distribution function. The conditions for the determination of these g -values via independent measurable quantities M kl are analysed. Some problems introduced by an incomplete knowledge of the molecular tensor X ij are discussed.