Vpliv anizotropnih nanodelcev na orientacijsko urejenost tekočih kristalov

Cvetko, Matej

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Title:	Vpliv anizotropnih nanodelcev na orientacijsko urejenost tekočih kristalov
Authors:	ID Cvetko, Matej (Author) ID KRALJ, SAMO (Mentor) More about this mentor... ID Ambrožič, Milan (Comentor)
Files:	DR_Cvetko_Matej_2013.pdf (2,89 MB) MD5: AFBACFA735FC6A7987B87B2DFE04DCCC
Language:	Slovenian
Work type:	Dissertation
Typology:	2.08 - Doctoral Dissertation
Organization:	FNM - Faculty of Natural Sciences and Mathematics
Abstract:	V doktorski disertaciji smo preučevali vpliv naključnega nereda na strukturne lastnosti nematskih tekočih kristalov (NTK). Slednje na semi-mikroskopski skali predstavljamo kot delce anizotropnih oblik cilindrične simetrije. Takšen sistem je primeren za preučevanje temeljnih lastnosti vpliva nereda, doseženega z zlomom zvezne simetrije. Sorodne primere predstavljajo naključni magneti, nečisti superprevodniki oz. superfluidi, mešanice različnih ogljikovih nano-cevk ter številni drugi sistemi kondenzirane materije. Sistemi, ki jih direktno obravnavamo, so najbližji naključno motenim magnetnim spinom. V slednji primerjavi je na semi-mikroskopski skali ena bistvena razlika. Za nematsko ureditveno polje je značilna t.i. »head-to-tail« invariance (neobčutljivost na 180° obrat). Nasprotno so magnetni sistemi občutljivi na spremembo predznaka magnetizacije. Omenjena razlika pomembno vpliva na možno strukturo topoloških defektov v strukturnem polju. Toda makroskopska domenska struktura, ki ji bomo posvetili največ pozornosti, je od tega le šibko odvisna. Omejili smo se na primere, v katerih so izviri naključnega polja »nečistoče« koncentracije ter so anizotropnih oblik. Pri preučevanju smo uporabili Lebwohl-Lasherjev mrežni model, v katerem je kubična mreža zapolnjena z NTK in »nečistočami«. Interakcije v modelu so kratkega dosega (čutijo jih le najbližji sosednji spini). Iskali smo mezoskopske statične rešitve sistema pri temperaturi nič, kar v realnosti pomeni sisteme globoko v nematski fazi. Vektorska polja, ki opisujejo orientacijsko porazdelitev NTK in »nečistoč«, so ponazorjeni s t.i. nematskimi spini oz. spini »nečistoč«. »Head-to-tail invariance« je upoštevana le pri nematskih spinih. Preučevali smo vrsto kvalitativno različnih modelov. Najprej smo preučili t.i. klasični RAF (random anisotropic field) model, v katerem so izviri naključnega polja »nečistoče«, kjer smo slednje delce poimenovali dis-orientacijski centri (DOC). V tem modelu je lahko posamezno mesto v mreži hkrati zasedeno tako z NTK kot DOC. V nadaljevanju smo preučili model, v katerem smo onemogočili hkratno zasedanje posameznega mesta v mreži s prej omenjenimi delci. Ta model smo poimenovali razširjeni RAF model. V obeh modelih so DOC orientacijsko »zamrznjeni« (statični), kjer je njihova orientacijska porazdelitev izotropna. V tretjem primeru smo preučevali model, v katerem obe vrsti spinov (nematski spini ter spini DOC) opišemo z variacijskimi polji. Poudarimo, da v slednjem modelu sistem ni frustriran na lokalnem ali globalnem nivoju. Pri tem smo vsiljevali medsebojno pravokotno postavitev NTK in DOC. V simulacijah smo izhajali iz homogene ali naključne začetne konfiguracije sistema, kar smo poimenovali zgodovina vzorca. Iz izračunane mezoskopsko-stacionarne konfiguracije sistema smo izračunali orientacijsko korelacijsko funkcijo nematskega spinskega polja. Iz korelacijske funkcije lahko sklepamo na vrsto ureditve sistema ter na različne druge makroskopske strukturne lastnosti posameznega sistema. Sistem lahko zavzame ureditev kratkega (SRO), kvazi red dolgega dosega (QLRO) ali red dolgega dosega (LRO). Za razlikovanje med slednjima dvema ureditvama je potrebna analiza končne velikosti. Iz poteka korelacijske funkcije lahko poleg dosega ureditve sistema razberemo še povprečno domensko dolžino, sistema ter razpršenost okrog njene vrednosti preko domenskega disperzijskega parametra. Ključni rezultati naloge so naslednji. Z uporabo klasičnega RAF modela smo pokazali, da je veljavnost Imry-Ma teorema, ki pomeni pomemben temelj statistične mehanike nereda, odvisna od zgodovine vzorca. Dobljeni rezultati namreč kažejo na to, da neskončno majhna naključna motnja uniči LRO in ga nadomesti s SRO le v sistemih z naključno začetno konfiguracijo. Za takšne sisteme smo dokazali, da ustrezajo skalni napovedi Imry-Ma teorema. V sistemih s homogeno začetno konfiguracijo omenjeni teorem ne velja. S temi rezultati lahko razložimo, zakaj različni eksperimenti na navidezno en
Keywords:	Tekoči kristali, nanodelci, Imry-Ma teorem, zodovina sistema, ureditev, domenska struktura, Lebwohl-Lasher model, nered
Place of publishing:	[Maribor
Publisher:	M. Cvetko]
Year of publishing:	2013
PID:	20.500.12556/DKUM-41184
UDC:	539.22(043.3)
COBISS.SI-ID:	20024072
NUK URN:	URN:SI:UM:DK:NRIQAEN8
Publication date in DKUM:	11.09.2013
Views:	2909
Downloads:	147
Metadata:
Categories:	FNM
:	CVETKO, Matej, 2013, Vpliv anizotropnih nanodelcev na orientacijsko urejenost tekočih kristalov [online]. Doctoral dissertation. Maribor : M. Cvetko. [Accessed 22 April 2025]. Retrieved from: https://dk.um.si/IzpisGradiva.php?lang=eng&id=41184 Copy citation

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Secondary language

Language:	English
Title:	Influence of anisotropic nanoparticles in orientational order of liquid crystalsInfluence of anisotropic nanoparticles in orientational order of liquid crystals
Abstract:	We studied the impact of random field-type disorder on structural properties of nematic liquid crystals (LCs). The latter are on the semi-microscopic scale represented by rod-like objects exhibiting cylindrical symmetry. Such configurations are adequate for studying fundamental properties of influence of disorder on systems exhibiting continuous symmetry breaking. Examples of such systems are random magnets, impure superconductors or superfluids, mixtures of different carbon tubes and numerous other condensed matter materials. The closest condensed matter analogs to our study are randomly perturbed magnetic spins. However, on the semi-microscopic scale these configurations exhibit one crucial difference. Namely, nematic orientational field exhibits head-to-tail symmetry while magnetization can be described with an ordinary vector field. This detail strongly influences topological defect gauge field structure; however macroscopic domain-type behavior is weakly affected. We focused on cases where random anisotropic field (RAF) perturbations were imposed by rod-like impurities of different concentration. We used Lebwohl-Lasher type lattice model where LC molecules and impurities occupied lattice cites of a cubic lattice. Interactions within the model are short ranged. We searched static solutions at temperature zero, which represent in reality systems well below the isotropic-nematic phase transition. Vector fields describing orientational distribution of LC molecules and impurities are presented by nematic and impurity spins. In the case of nematic spins head-to-tail invariance is taken into account. We studied several qualitatively different models. In the first case we considered classical RAF-type model, in which impurities act as a local field. At a given site both nematic and impurity spins could be defined, if RAF is present at a site. In the second case we consider cases where sites are occupied either by LC or impurity field. In both cases impurities are orientationally quenched and their orientational distribution is isotropic. Note that in the latter study we do not have any true frustrations at local or global level. In the third case we studied examples where both fields are variational fields. In this case we assumed that LC and impurity fields tend to be perpendicular to each other. In simulations we used two different histories of samples. We either started from random or homogenously aligned initial states. From calculated static configurations we calculated orientational correlation function of the nematic spin field. From it we could infer range of order and its characteristics. In studied cases orientational ordering could be either short ranged (SRO), quasi long ranged (QLRO) or long ranged (LRO). The latter two could be distinguished by finite-size analysis. In the case of SRO we extracted from the correlation function characteristic average domain size and dispersion of domain sizes with distribution parameter. The key results of the thesis are as follows. Using the classical random-field type model we have demonstrated that the Imry-Ma theorem, one of the pivotal stone of statistical mechanics of disorder, is obeyed only for certain histories of samples. Namely, our simulations suggest that infinitesimally weak degree of disorder destroys LRO and replaces it with SRO, if a system is quenched from the isotropic phase. Furthermore, the predicted scaling within Imry-Ma teorem is obeyed. If a system is quenched from a homogeneous initial configuration Imry-Ma scaling is not obeyed. Our results explain why different experiments on seemingly identical samples yield substantially different results. Furthermore, our simulations reveal that in systems of our interest qualitatively different configurations exist which are trapped in potential energy valleys with relatively deep minima. In the case of model, where sites are occupied either with LC or impurity we obtain qualitatively similar results in the regime below percolation threshold. The main quantitative difference is due to the effective change in
Keywords:	Liquid crystals, nanoparticles, Imry-Ma theorem, history of system, order, domain structure, Lebwohl-Lasher model, disorder

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