1,721,053 research outputs found
Hysteresis in two-dimensional liquid crystal models
No full textWe make a numerical study of hysteresis loop shapes within a generalized two-dimensional Random Anisotropy Nematic (RAN) model at zero temperature. The hysteresis loops appear on cycling a static external ordering field. Ordering in these systems is history dependent and involves interplay between the internal coupling constant J, the anisotropy random field D, and the ordering external field H. Here the external field is represented by a traceless tensor, analogous to extension-type fields in continuum mechanics. The calculations use both a mean field approach and full lattice simulations. Our analysis suggests the existence of two qualitatively different solutions, which we denote as symmetric and symmetry breaking. For the set of parameters explored, only the symmetric solutions are stable. Both approaches yield qualitatively similar hysteresis curves, which are manifested either by single or double loops. But the quantitative differences indicate that mean field estimates are only of limited predictive value.</p
Domain patterns in homogeneous and random perturbed nematic liquid crystals: A simulation study
No full textWe have simulated lattice models of homogenous and randomly perturbed systems exhibiting continuous symmetry breaking, concentrating on domain sizes and configuration character. The system consists of rod-like objects within a cubic lattice interacting via a Lebwohl-Lasher-type interaction at temperature T, but including impurities at concentration p imposing a random anisotropy field-type disorder, coupled with anchoring strength W to neighboring host director molecules. An example of such systems represents nematic LC or nanotubes. We study molecular domain patterns as a function of p, W, T, and sample history. Histories are defined either by a temperature-quenched history (TQH), a field-quenched history (FQH) or from an annealed history (AH). Finite size-scaling is used to determine the nature of the orientational ordering correlations. We distinguish three different kinds of phase. Short ranged order (SRO) implies exponential decay of orientational correlations. Quasi-long-range order (QLRO) sustains algebraic decay of orientational correlations. True long-range order (LRO) implies a non-zero order parameter in the thermodynamic limit in the absence of an external field. In the TQH case for particular values of p and W, we find SRO or QLRO, with possible LRO at very low W and p. For FQH, in the limit of very low W and p, we observe LRO, which gives way to an SRO regime with increasing p and W. Comparing FQH and TQH histories at particular values of T, we saw QLRO and SRO respectively. The crossover between regimes depends on history, but in general, the FQH yields a more ordered phase than the AH, which in turn yields a more ordered phase than the TQH. In phases in which SRO occurs, the orientational correlation length in the weak-disorder limit obeys universal Imry-Ma scaling ξd ~ W- 2/(4-d).</p
Defect unbinding on a toroidal nematic shell
No full textWe study nematic liquid crystal textures exhibiting topological defects (TDs) on a two-dimensional (2D) toroidal shell. For the toroidal topology the total topological charge of TDs is equal to zero. We use a mesoscopic Landau-de Gennes approach which features a 2D nematic order tensor Q. We show that fat tori unbind TDs. If no extrinsic free energy couples Q with the Weingarten tensor of the torus, then defects and antidefects are assembled along the innermost and the outermost circles of the torus, respectively. In this case, we estimate the critical condition for the onset of TDs using an electrostatic analogy. If, on the other hand, an extrinsic free energy is present, then defects are repelled from these regions
Curvature control of valence on nematic shells
No full textWithin a two-dimensional Landau–de Gennes tensorial formalism we study the equilibrium
configurations of nematic shells, thin films of nematic liquid crystal deposited on the boundary of
colloidal particles of arbitrary shape enforcing a degenerate tangential anchoring on the nematic
molecules. In this formalism, defects appear wherever a scalar order parameter vanishes. Their total
number is the colloidal valence, as this is the number of molecular bridges that can bind every colloid to
its peers. We show how the defect organization on a colloidal particle is affected by the Gaussian
curvature of the colloidal boundary, to the point of changing its valence
Stability and metastability in nematic glasses: a computational study
No full textThe influence of randomly distributed impurities on liquid crystal (LC) orientational ordering is studied using a simple Lebwohl-Lasher type lattice model in two (d=2) and three (d=3) dimensions. The impurities of concentration p impose a random anisotropy field-type of disorder of strength w to the LC nematic phase. Orientational correlations can be well presented by a single coherence length for a weak enough w. We show that the Imry-Ma scaling prediction w holds true if the LC configuration is initially quenched from the isotropic phase. For other initial configurations the scaling is in general not obeye
Hysteretic behaviour of Lebwohl-Lasher rotors
No full textV nalogi preučujemo sklopitev med nanodelci in termotropnimi nematičnimi tekočimi kristali (NTK). Slednje obravnavamo kot cilindrično simetrične objekte, ki jih v literaturi pogosto imenujejo kot rotorji. V prvem delu naloge preučujemo vpliv NTK na urejanje dispergiranih ogljikovih nanocevk (ON). Uporabili smo mezoskopski model, v katerem smo NTK opisali z Landau-de Gennesovo teorijo z enoosnim ureditvenim parametrom. Prisotnost ON smo upošteval z Doi-ovo prosto energiji, s katero smo modelirali liotropni značaj ON. Slednja interakcija upošteva t. i. sklopitev izključitvenega volumna. Obravnavali smo primer bi-disperzne porazdelitve ON v limiti šibke sklopitve NTK-ON. V tej limiti na sklopitev dominantno vpliva anizotropija površinske napetosti, medtem ko je interakcija z nematično orientacijsko urejenostjo relativno zanemarljiva. Glede na jakost ON-NTK interakcije smo zasledil dva kvalitativno različna režima obnašanja. V prvem režimu dispergirane ON posedujejo nezvezni prehod iz izotropne v orientacijsko urejeno fazo. V drugem nadkritičnem režimu pa je prehod med fazama postopen. NTK močno vsiljujejo ON stopnjo urejenosti, medtem ko je povratni urejevalni vpliv zanemarljiv. Tako je nematični ureditveni parameter NTK odvisen predvsem od temperature in le šibko od koncentracije ON. V nematični fazi urejenosti daljše ON izkazujejo močnejšo orientacijsko urejenost.
V drugem delu naloge smo preučeval histerezno obnašanje NTK pri cikličnem spreminjanju zunanjega urejevalnega polja. Pri tem smo predpostavili, da relativno homogeno dispergirani nanodelci v NTK delujejo kot orientacijsko naključno polje. Takšne primere npr. zasledimo v mešanicah NTK in aerosilnih nanodelcev. Osredotočili smo se na določitev režimov s kvalitativno različnim histereznim odzivom. Pri tem smo spreminjali jakost nematične sklopitve in jakost naključnega polja. Večino raziskav smo izvedli v dveh prostorskih dimenzijah. V teoretični analizi smo uporabili dva različna pristopa. Sistem smo najprej analizirali v približku povprečnega molekularnega polja. V prvem koraku smo analogno s klasično izpeljavo v magnetizmu vpeljali efektivno polje, ki deluje na lokalno nematično urejenost. Slednjo smo opisali s tenzorskim ureditvenim parametrom. V efektivnem polju smo upoštevali prisotnost »povprečnih« sosedov. Predpostavili smo, da sta lastna okvirja tenzorskega efektivnega polja in nematične urejenosti vzporedna in na ta način dobili samo-usklajevalno enačbo. V slednji smo vpeljali povprečenje po orientacijski neurejenosti nanodelcev. V drugem pristopu smo numerično preučevali nematično urejenost za dane vrednosti interakcij v sistemu in nato iz dobljene konfiguracije izračunali povprečni globalni nematični ureditveni parameter. V obeh pristopih smo enačbe reševali numerično pri temperaturi nič. Pri spreminjanju jakosti značilnih interakcij sistema smo dobili kvalitativno različne histerezne zanke in določili področja stabilnosti kvalitativno različnih zank. V obeh pristopih smo dobili kvalitativno podobno obnašanje in pojavile so se samo razlike v kvantitativnem obnašanju. Torej približek molekularnega polja predstavlja v tem primeru relativno zanesljivo in preprosto orodje.
Rezultati naloge so potencialno zanimivi za številne aplikacije v nanotehnologiji, ki so osnovane na interakcijah med nematičnimi tekočimi kristali in različnimi nanodelci. V primeru ON bi NTK komponento lahko izkoristili za kontrolirano orientacijsko manipulacijo dispergiranih ON. Tako bi lahko npr. kreirali različne prilagodljive in odzivne vzorce ON s specifičnim makroskopskim obnašanjem. Pri tem bi izkoriščali »mehkobo« NTK komponente in njeno odzivnost na zunanja urejevalna polja in na ograjevalno geometrijo. Po drugi strani bi lahko specifično histerezno obnašanje NTK v cikličnih urejevalnih poljih v prisotnosti nanodelčno generiranega nereda uporabili za različne »mehke« spominske elemente.In the thesis we have examined the coupling of nanoparticles and thermotropic nematic liquid crystals (NLC). The latter are regarded as cylindrically symmetrical objects, often referred to in scientific literature as rotors. In the first part of the thesis we examined the effect of NLC on the ordering of dispersed carbon nanotubes (CN). A mesoscopic model was used, in which NLC were described with the Landau-de Gennes theory with a uniaxial order parameter. Presence of CN was considered with Dois free energy, with which the lyotropic character of CN was modelled. The latter interaction considers the so-called coupling of excluded volume. A case of bi-dispersed distribution of CN was addressed in the weak anchoring limit of NLC-CN. In this limit the anisotropy of surface tension has a dominant effect on the coupling, whereas the interaction with nematic orientation ordering is relatively negligible. Depending on the strength of the NCL-CN interaction two qualitatively different behavioural regimes were detected. In the first regime, the dispersed CN have a discontinuous transition from isotropic to the orientationally ordered phase. In the second supercritical regime, the transition from one phase to the other is gradual. NCL strongly force the degree of ordering to CN, whereas the reverse ordering effect is negligible. It follows that the nematic order parameter of NCL is mostly dependant on temperature and only slightly on the concentration of CN. In the nematic ordering phase the longer CN exhibit a stronger orientation ordering.
In the second part of the thesis we examined the hysteretic behaviour of NCL when cyclically changing the external ordering field. We assumed that the relatively homogeneously dispersed nanoparticles in NCL work as an orientationally random field. Such cases can be found for instance in the mixtures of NCL and aerosil nanoparticles. We focused on the determination of regimes with the qualitatively different hysteretic response. This was achieved with the changing of the strength of the nematic coupling and the strength of the random field. Most of the research was conducted in two spatial dimensions. In the theoretic analysis two different approaches were used. In the beginning the system was analysed in the mean field approximation. In the first step, we analogically introduced with a classical derivation in magnetism an effective field, which affects the local nematic ordering. We described the latter with a tension order parameter. In the effective field the "mean" neighbour presence was considered. We assumed that the inherent frames of the tension effective field and nematic ordering are parallel, which produced a self-adapting equation. In the latter, the averaging was introduced on the orientational disorder of nanoparticles. In the second approach, we numerically researched the nematic ordering from the given value of interactions in the system and then calculated the mean global nematic order parameter from the obtained configuration. In both approaches the equations were numerically solved at zero temperature. With the changing of the strength of characteristic interactions of the system we obtained qualitatively different hysteresis loops and determined the areas of stability of qualitatively different loops. In both approaches we obtained qualitatively similar behaviour, differences were evident only in the quantitative behaviour. Thus, the mean field approximation represents, in this case, a relatively reliable and simple tool.
Results of the thesis are potentially interesting for numerous applications in nanotechnology, which are based on interactions between nematic liquid crystals and various nanoparticles. In the case of CN, the NCL component could be used for a controlled orientational manipulation of dispersed CN. Thusly different adaptable and responsive patterns of CN could be created with specific macroscopic behaviour
Temperature induced phase transition of nematic liquid crystals
Full text linkV diplomskem seminarju obravnavamo dogajanje ob temperaturno induciranem faznem prehodu tekočega kristala med nematično ter izotropno fazo. V ta namen smo sintetizirali tekoči kristal MBBA ter z invertnim polarizacijskim mikroskopom opazovali dogajanje ob faznem prehodu. Vzorec smo izpostavili hitri ter počasni temperaturni spremembi ter opazovali fazni prehod ter rast domenskih struktur pri prehodu. Pri hitri podhladitvi smo izmerili korelacijske dolžine domenskih struktur ter hitrost naraščanja le-teh. Dogajanje ob prehodu smo opisali z Landau – de Gennesovim fenomenološkim modelom.In this thesis we study the Isotropic – Nematic phase transition. For this purpose we have synthesized the liquid crystal MBBA. The phase transition in the MBBA cell was observed under a polarizing microscope. We have studied the development of the domain pattern at the Isotropic – Nematic phase transition in the case of slow and fast continuous temperature reduction. In the case of a fast temperature reduction we measured the correlation length of the domain patterns and their expansion speed. The phase transition is described by the Landau – de Gennes phenomenological model
Measurement of β-decay energy spectrum - designing an experiment
Full text linkRadioaktivnost je ena izmed večno aktualnih tematik, tako z znanstvenega, kot tudi polito-sociološkega ter naravovarstvenega vidika. Ob teoretičnem znanju, ki ga študentje pridobijo tekom študija, pa jim eksperimentalno delo omogoča boljši vpogled v to tematiko. Namen pričujoče diplomske naloge je izdelava nove eksperimentalne vaje, pri kateri študentje merijo emisijski spekter sevanih elektronov pri β- razpadu. Vaja temelji na gibanju nabitega delca v magnetnem polju, saj se meritve energij sevanih elektronov izvajajo s pomočjo magnetnega spektrometra. Ob danem konstantnem polmeru gibanja, se s spreminjanjem vrednosti gostote magnetnega polja, spreminjajo tudi energije elektronov, ki prispejo do detektorja. Iz zveze med energijo elektrona in gostote magnetnega polja, ki smo jo izpeljali na podlagi gibanja relativističnih elektronov v magnetnem polju, lahko iz meritev sklepamo na obliko energijskega spektra. Na osnovi dobljenih rezultatov se študentje prepričajo o zvezni naravi β razpada ter se poglobijo v fizikalne zakonitosti opaženega pojava.Radioactivity is one of the main burning issues throughout history, whether from scientific, political, social or environmentalist aspect. Apart from theoretical knowledge students gain during their study it is the experimental work that offers a better insight into the topic. The purpose of this thesis is designing a new experiment where student measure emission spectrum of emitted electrons during β-decay. The experiment is based on the motion of a charged particle in a magnetic field, for the measurements are being carried out via magnetic spectrometer. Given a fixed radius of motion and while changing the value of magnetic field, energies of the electrons that reach the detector change as well. From the relation between the electron’s energy and magnetic field, derived from the principles that govern the motion of relativistic electrons in a magnetic field, the relation between the electron’s energy and the magnetic field can lead to a conclusion about the shape and the form of the energy spectrum. Based on the measurements, students can realize the continuous nature of the spectrum and are deepening their knowledge of the laws that govern the observed phenomenon
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