Resonant x-ray spectroscopy of columnar liquid crystal phases formed by bent-core molecules

Tekoči kristali so snovi, ki imajo tudi anizotropno tekočinsko fazo. Zgrajeni so iz velikih organskih molekul anizotropnih oblik. V magistrskem delu obravnavamo tekoče kristale iz molekul z ukrivljeno sredico. Zaradi svoje oblike imajo takšne molekule permanentni električni dipol, kadar pa se zlagajo v plasti, so plasti praviloma polarizirane. Molekule z ukrivljeno sredico se učinkovito zlagajo tudi v stolpiče, ki jih tvorijo fragmenti smektičnih plasti. Med stolpičaste tekočekristalne faze iz molekul z ukrivljeno sredico uvrščamo faze B_1, nagnjeno B_1, B_1rev in nagnjeno B_1rev. Razlikujejo se po različni povprečni smeri dolgih in kratkih osi molekul. Za ločevanje med strukturami se uporablja več optičnih, električnih, termičnih in drugih metod, mi pa se omejimo na klasično in resonančno elastično rentgensko spektroskopijo. S klasično rentgensko spektroskopijo merimo razlike v porazdelitvi elektronske gostote, kar nam da sliko prostorske ureditve molekul. Klasično dopolnjuje resonančna rentgenska spektroskopija, ki je občutljiva tudi na orientiranost dolgih in kratkih osi molekul. Oblikovni faktor molekule z ukrivljeno sredico je anizotropna količina, zato ga opišemo s tenzorjem, ki je premo sorazmeren z anizotropnim delom tenzorja dielektričnosti. Izračunamo tenzorske oblikovne faktorje za pet možnih ureditev ukrivljenih molekul v nagnjeni B_1rev fazi. Iz tenzorskega oblikovnega faktorja napovemo intenziteto in polarizacijo interferenčnih vrhov v odvisnosti od polarizacije vpadnega valovanja. S primerjavo lege vrhov, ki so dovoljeni pri klasični rentgenski spektroskopiji, in lege interferenčnih vrhov pri resonančni rentgenski spektroskopiji napovemo, kateri vrhi so čisto resonančni, torej klasično prepovedani. Vrhi, ki jih napovemo pri klasični in resonančni rentgenski spektroskopiji, so lahko resonančno ojačani. S teoretičnim modelom napovemo, da je smer polarizacije linearno polariziranega valovanja, ki se resonančno sipa na vzorcu tekočega kristala iz molekul z ukrivljeno sredico, zmeraj pravokotna na smer polarizacije vpadnega valovanja. Ugotovimo, da lahko med strukturami z različnimi orientacijami molekul najdemo razlike v interferenčnih spektrih pri resonančni rentgenski spektroskopiji, zato je ta metoda ustrezna za razlikovanje med strukturami. Liquid crystals are materials that possess at least one anisotropic liquid phase. Their building blocks are long organic molecules of anisotropic shapes. In the master thesis, we focus on liquid crystals consisting of bent-core molecules. Because of their bent shape, such molecules have a permanent electric dipole, so layered structures are usually polarized. Bent-core molecules are also effectively distributed into columns, which are made up of smectic layer fragments. B_1, tilted B_1, B_1rev and tilted B_1rev are examples of the columnar liquid crystal phases made of bent-core molecules. These phases differ in the average direction of the long and short molecular axes in smectic layer fragments. To differentiate between the phases, several optic, electric, thermic and other methods can be employed. In this work, we limit ourselves to the hard and soft resonant elastic x-ray spectroscopy. With the hard x-ray spectroscopy, we measure the differences in the distribution of the electron density, which in turn gives us information on the spatial distribution of molecules. The hard x-ray spectroscopy is complimented by the soft resonant x-ray spectroscopy, which is sensitive to the orientation of the long and short molecular axes. The form factor of a bent-core molecule is an anisotropic quantity that is described by a tensor, which is proportional to the anisotropic part of the dielectric tensor. We calculate tensorial form factors for five possible packings of bent-core molecules in the tilted B_1rev phase. Then we use the tensorial form factor to predict the intensity and polarization of the interference peaks as a function of the polarization of the incident wave. By comparing the position of the peaks allowed in the hard x-ray spectroscopy with the position of peaks found with the soft resonant x-ray spectroscopy, we predict, which peaks are purely resonant, therefore forbidden in the hard x-ray spectroscopy. Peaks, which are predicted by both the hard and soft resonant x-ray scattering, can be resonantly enhanced. The theoretical model predicts that the direction of the polarization of the scattered wave is perpendicular to the direction of the polarization of the incident wave for all the studied structures of the tilted B_1rev phase. The soft resonant x-ray scattering pattern differs significantly for the studied structures, so we conclude that the method can be used to determine the structure of the tilted B_1rev phase.