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Muhammad Ali, 2021, doktorska disertacija

Opis: In this thesis, we study the structure and optical transmission properties of the twist-bend nematic liquid crystalline phase, made of bent dimers, confined in thin planar cells. Confinement leads to the formation of a periodic modulated structure, the formation of which is explained as follows. The twist-bend nematic phase is characterized by a heliconical modulation of the molecular long axes. Due to a short pitch of modulation (approximately 10 nm), the twist-bend nematic phase behaves as a pseudo-layered medium. At temperatures below the nematic – twist-bend nematic phase transition, the heliconical pitch and thus the thickness of the pseudo-layers reduces, which leads to a two-dimensional undulation of pseudo-layers in the direction perpendicular to the cell surfaces and along the surfaces. The undulated structure is responsible for a stripe texture observed under a polarizing microscope and acts as a diffraction grating. We constructed theoretical models to predict the pseudo-layer structure of a confined twist-bend nematic phase and to describe the properties of light diffracted on such cells. The free energy of the two-dimensional pseudo-layer structure of the twist-bend nematic phase is expressed in terms of the nematic director field, by which we describe the direction of the heliconical axis, and a complex smectic order parameter, the gradient of which gives the direction of the layer normal. At first, we assume that pseudo-layers are perpendicular to the surfaces (bookshelf geometry) and find a stable structure by assuming an ansatz for the pseudo-layer displacement from the bookshelf geometry and then minimizing the free energy at a very strong and very weak surface anchoring. In this way a threshold condition for the onset of the modulated structure is obtained, as well as the amplitude and period of modulation. Next, we assume that, at the onset of the twist-bend nematic phase, pseudo-layers are formed at some angle (pre-tilt) with respect to the surface. We find that in both cases, the bookshelf and pre-tilted one, the calculated period of modulation far from the phase transition is always approximately twice the cell thickness, which agrees with experimental observations. The properties of light diffracted by the spontaneously formed grating were studied both experimentally and theoretically. We measured the intensity and polarization properties of the first two orders of the diffracted light and the temperature dependence of the polarization of the second order diffraction peaks. To predict the observed properties of the diffracted light and to simplify the description of such gratings, we consider different preliminary models of a one-dimensional spatial variation of the optic axis, the direction of which is given by two angles. A transfer matrix method is used and a good agreement between the experimental and theoretical results is obtained. In a more comprehensive approach, we determine the spatial variation of the optic axis direction from the modeled structure. The electric field in the diffracted light is obtained by using the transfer matrix method and beam propagation method. In the case of a pre-tilt of the pseudo-layers and very strong surface anchoring both methods give good qualitative agreement with experimental results, only in the case of the temperature dependence of the second order diffraction peaks, a more complex beam propagation method is superior to the transfer matrix method. The thesis is divided into three parts. In the first part, we focus on the physical properties of the twist-bend nematic phase and its structure in thin planar cells. In the second part, a continuum model is proposed and finally, the properties of diffracted light are discussed and theoretically predicted by using the beam propagation method and transfer matrix method.
Ključne besede: Bent-dimer liquid crystals, twist-bend nematic phase, undulation of pseudo-layers, polarization, diffraction grating, beam propagation method, transfer matrix method.
Objavljeno v DKUM: 21.10.2021; Ogledov: 1202; Prenosov: 85
.pdf Celotno besedilo (10,65 MB)

Simplified computation of matchings in polygraphs
Ante Graovac, Damir Vukičević, Damir Ježek, Janez Žerovnik, 2005, izvirni znanstveni članek

Opis: Matching polynomial and perfect matchings for fasciagraphs, rotagraphs and twisted rotagraphs are treated in the paper. Classical transfer matrix approach makes it possible to get recursions for matching polynomial and perfect matchings, but the order of the matrix grows exponentially in the number of the linking edges between monographs. Novel transfer matrices are introduced whose order is much lower than that in classical transfer matrices. The virtue of the method introduced is especially pronounced when twoor more linking edges end in the same terminal vertex of a monograph. An example of a polyacene polygraph with extended pairings is given where a novel matrix has only 16 entries as compared to 65536 entries in the classical transfer matrix. However, all pairings are treated here on equal footing, but the method introduced can be applied to selected types of pairings of interest in chemistry.
Ključne besede: polygraphs, matching polynomial, matchings, perfect matchings, Kekulé structures, extended structures, recursive enumeration, transfer matrix method
Objavljeno v DKUM: 05.07.2017; Ogledov: 1483; Prenosov: 87
.pdf Celotno besedilo (102,97 KB)
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