The impact of nanoparticles on the degree of the nematic ordering

Nanodelci dispergirani v nematičnih tekočih kristalih v splošnem deformirajo nematično strukturo. V številnih primerih dispergirani nanodelci vplivajo na tekočekristalno ureditev podobno kot naključno polje. Slednje vsiljuje molekulam tekočih kristalov relativno naključno orientacijsko urejenost, katere verjetnostna porazdelitev je odvisna predvsem od geometrije nanodelcev in jakosti ter vrste sklopitve med nanodelci in obdajajočo tekoče kristalno matriko. Nedavne eksperimentalne meritve nakazujejo, da pri povečevanju koncentracije nanodelcev preide klasična nematična ureditev v fazo, ki spominja na paranematično ureditev. Prehod je postopen in se izvede v relativno ozkem oknu koncentracij nanodelcev pri relativno nizki koncentraciji (okoli 0,1%). Pri nadaljnjem povečevanju se stopnja nematične urejenosti relativno malo spreminja do koncentracij 1%. Slednje obnašanje še ni bilo teoretično obravnavano. V magistrskem delu izdelamo minimalni matematični model, ki kvantitativno in kvalitativno opiše spremembo orientacijskega ureditvenega parametra v prisotnosti nanodelcev, ki vsiljujejo naključno urejenost. Izpeljemo dvodimenzionalni mrežni model v odvisnosti od ureditvenega parametra pri temperaturi absolutne ničle. V približku povprečnega polja numerično rešimo izpeljane enačbe. Rezultati simulacij v dobrem približku reproducirajo modelirane eksperimentalne meritve.Nanoparticles dispersed in nematic liquid crystals generally deform the nematic structure. In numerous examples dispersed nanoparticles affect liquid crystal ordering in a similar way as a random field. The latter enforces a random orientational order on the liquid crystal molecules, whose probability distribution depends mainly on the geometry of the nanoparticles and on the strength and type of coupling between the nanoparticles and the surrounding liquid crystal matrix. Recent experimental measurements indicate, that upon increasing the concentration of nanoparticles, the classical nematic order transitions into a paranematic order like phase. The transition is gradual and appears at a relatively low concetration (around 0,1%) within a relatively narrow range of nanoparticle concentration. Further increasing the concentration of nanoparticles up to 1% has relatively little effect on the degree of nematic ordering. This behaviour has yet to be theoretically studied. In this master thesis we construct a minimal mathematical model, which qualitatively and quantitatively descibes the change of the orientational order parameter due to the presence of nanoparticles, which enforce a random order. We derive a two-dimensional lattice model in terms of the order parameter at absolute zero kelvin. In the mean field approximation we numerically solve the equations of the derived model. The simulation results in a good approximation reproduce the modeled experimantal results

Effects of Nanoparticles on Screw Dislocation Structures in Smectic A phase

V seminarju obravnavamo vpliv nanodelcev na strukturo zvitih dislokacij v smektični A fazi tekočih kristalov. Za opis sistema uvedemo ureditveni parameter, ki ga uporabimo v Landau – de Gennesovem fenomenološkem modelu. Minimizacija proste energije vodi do Euler – Lagrangevih enačb, ki jo rešujemo numerično z Eulerjevo metodo. Z nanodelci induciramo različne robne pogoje znotraj jedra dislokacije. Preučili smo, kako različno površinsko obdelani nanodelci vplivajo na strukturne lastnosti dislokacije.In the seminar we study how nanoparticles effect the screw dislocation structure in smectic A phase of liquid crystals. To describe the system we introduce an order parameter, the which we use in the Landau – de Gennes phenomenological model. We insert the free energy density of the system into the Euler – Lagrange equation, which we solve numerically with the Euler method. Nanoparticles induce different boundary conditions inside the dislocation core. We compare simulation results of the system with and without nanoparticles

The impact of nanoparticles on the degree of the nematic ordering

Nanodelci dispergirani v nematičnih tekočih kristalih v splošnem deformirajo nematično strukturo. V številnih primerih dispergirani nanodelci vplivajo na tekočekristalno ureditev podobno kot naključno polje. Slednje vsiljuje molekulam tekočih kristalov relativno naključno orientacijsko urejenost, katere verjetnostna porazdelitev je odvisna predvsem od geometrije nanodelcev in jakosti ter vrste sklopitve med nanodelci in obdajajočo tekoče kristalno matriko. Nedavne eksperimentalne meritve nakazujejo, da pri povečevanju koncentracije nanodelcev preide klasična nematična ureditev v fazo, ki spominja na paranematično ureditev. Prehod je postopen in se izvede v relativno ozkem oknu koncentracij nanodelcev pri relativno nizki koncentraciji (okoli 0,1%). Pri nadaljnjem povečevanju se stopnja nematične urejenosti relativno malo spreminja do koncentracij 1%. Slednje obnašanje še ni bilo teoretično obravnavano. V magistrskem delu izdelamo minimalni matematični model, ki kvantitativno in kvalitativno opiše spremembo orientacijskega ureditvenega parametra v prisotnosti nanodelcev, ki vsiljujejo naključno urejenost. Izpeljemo dvodimenzionalni mrežni model v odvisnosti od ureditvenega parametra pri temperaturi absolutne ničle. V približku povprečnega polja numerično rešimo izpeljane enačbe. Rezultati simulacij v dobrem približku reproducirajo modelirane eksperimentalne meritve.Nanoparticles dispersed in nematic liquid crystals generally deform the nematic structure. In numerous examples dispersed nanoparticles affect liquid crystal ordering in a similar way as a random field. The latter enforces a random orientational order on the liquid crystal molecules, whose probability distribution depends mainly on the geometry of the nanoparticles and on the strength and type of coupling between the nanoparticles and the surrounding liquid crystal matrix. Recent experimental measurements indicate, that upon increasing the concentration of nanoparticles, the classical nematic order transitions into a paranematic order like phase. The transition is gradual and appears at a relatively low concetration (around 0,1%) within a relatively narrow range of nanoparticle concentration. Further increasing the concentration of nanoparticles up to 1% has relatively little effect on the degree of nematic ordering. This behaviour has yet to be theoretically studied. In this master thesis we construct a minimal mathematical model, which qualitatively and quantitatively descibes the change of the orientational order parameter due to the presence of nanoparticles, which enforce a random order. We derive a two-dimensional lattice model in terms of the order parameter at absolute zero kelvin. In the mean field approximation we numerically solve the equations of the derived model. The simulation results in a good approximation reproduce the modeled experimantal results

Impact of Weak Nanoparticle Induced Disorder on Nematic Ordering

Dilute mixtures of nanoparticles (NPs) and nematic liquid crystals (LCs) are considered. We focus on cases where NPs enforce a relatively weak disorder to the LC host. We use a Lebwohl-Lasher semi-microscopic-type modeling where we assume that NPs effectively act as a spatially-dependent external field on nematic spins. The orientational distribution of locally favoured “easy„ orientations is described by a probabilistic distribution function P. By means of a mean field-type approach, we derive a self-consistent equation for the average degree of nematic uniaxial order parameter S as a function of the concentration p of NPs, NP-LC coupling strength and P. Using a simple step-like probability distribution shape, we obtain the S(p) dependence displaying a crossover behaviour between two different regimes which is in line with recent experimental observations. We also discuss a possible origin of commonly observed non-monotonous variations of the nematic-isotropic phase temperature coexistence width on varying p

Enhanced electrical properties and large electrocaloric effect in lead-free Ba0.8Ca0.2ZrxTi1−xO3 (x = 0 and 0.02) ceramics

The effects of 2% Zr introduction in Ba0.8Ca0.2TiO3 (BCT) system on its electrical and electrocaloric properties was investigated. BCT and Ba0.8Ca0.2Zr0.02Ti0.98O3 (BCZT) ceramics synthesized by solid-state processing were crystallized in a pure perovskite phase with a group space P4mm. After Zr insertion, the enhanced dielectric constant was obtained around the Curie temperature (Tc) in BCZT ceramic (εr = 6330 at Tc = 388 K) compared to BCT ceramic (εr = 5080 at Tc = 388.6 K). Moreover, the large-signal piezoelectric coefficient (d∗33) was improved from 270 to 310 pm/V in BCT and BCZT ceramics, respectively, under a moderate electric field of 25 kV/cm. The electrocaloric effect was determined via indirect and direct methods. In the indirect approach, the electrocaloric temperature change (ΔT) was calculated via Maxwell relation, and the measured ferroelectric polarization P (E, T) extracted from the P–E curves recorded at 24 kV/cm. The maximum values of ΔT = 0.68 K and the electrocaloric responsivity ζ = 0.283 K mm/kV obtained at 385 K in BCZT ceramic were found to be higher than those observed in BCT ceramic (ΔT = 0.37 K and ζ = 0.154 K mm/kV at 387 K). In the direct approach, ΔT was measured utilizing a modified high-resolution calorimeter at 14 kV/cm. As the direct method is more sensitive to the latent heat, it provided larger values for smaller applied field, i.e., ΔT = 0.474 and 0.668 K for BCT and BCZT ceramics, respectively. A significant ζ of 0.477 K mm/kV was obtained in BCZT at 385 K and 14 kV/cm that matches the values found in lead-based materials. These results suggest that BCZT lead-free ceramics could have an excellent potential to be used in solid-state refrigeration applications