Liquid crystals are a broad class of soft materials with a wide range of interest across different fields. Their common fundamental feature is the combination of order and fluidity. On the one hand, this is a basic requirement for self-organization and structure formation in living systems and indeed the physics of liquid crystals has emerged as a flourishing new research frontier in cell biology. On the other hand, this characteristic makes them sensitive and responsive to a large variety of stimuli such as light, electric and magnetic fields, mechanic forces and thermal gradients, with consequent technological interest in photonics, optofluidics, organic electronics and biosensing. In all cases, the elasticity of liquid crystalline phases, i.e. their mechanical response to distortions of their ordered state, is paramount since their behavior at the micro- and meso-scale is the result of the competition between internal elastic forces, geometric constraints and external fields. The common thread of this thesis is the elasticity of nematics - i.e. of liquid crystals with pure orientational order. The topic is approached from a microscopic and theoretical perspective, and three major open questions are addressed. Stimulated by the need to clarify the role of the saddle-splay elastic constant, K24, in recent controversial experiments, in Part I we develop a consistent formulation in which the surface-like elastic constants (K24 and K13) are treated on the very same footing of the bulk ones (K11, K22 and K33). The application of the method to the simple paradigmatic system of hard achiral rods uncovered a novel mechanism leading to spontaneous mirror symmetry breaking, with potential implications on a broad range of experimentally relevant systems. In Part II we present a microscopic approach, denominated non-local, that overcomes the classical assumptions of nemato-elasticity theories (effective-rod treatment of any particle type) and that accounts for the coupling between the specific particle morphology and the geometry of the director distortions. This interplay, manifesting tangibly in the onset of new types of orientational order among specifically shaped nematogens in response to certain deformations, is crucial for the formation of novel modulated liquid crystal phases that are attracting considerable attention. Lastly, in Part III, we extend the non-local microscopic model to the more general case of particles endowed with flexibility in order to describe the elasticity of nematic polymers, which constitutes a long standing issue in the field. We set up a theoretical-computational methodology that fully accounts for the interplay between the director field and both the orientational and the conformational degrees of freedom of polymer chains, without resorting to the decoupling approximation which is generally adopted in existing theories. Calculations for model systems in the semiflexible regime show distinct effects on the bulk elastic constants, with a special sensitivity of K33, which dramatically decreases with increasing flexibility. This is a promising step towards understanding and controlling the mechanical properties of biopolymeric liquid crystalline materials.
I cristalli liquidi sono una vasta classe di materiali soffici con un'ampia gamma di campi d'interesse. La caratteristica fondamentale che li accomuna è la combinazione di ordine e fluidità. Da un lato, questa combinazione è uno dei requisiti di base per l'auto-organizzazione e la formazione di strutture nei sistemi viventi, e infatti la fisica dei cristalli liquidi sta emergendo come una delle nuove frontiere nella ricerca in biologia cellulare. Dall'altro, tale caratteristica rende i cristalli liquidi sensibili a una grande varietà di stimoli come luce, campi elettrici e magnetici, forze meccaniche e gradienti termici, con conseguente rilevanza per applicazioni in fotonica, optofluidica, elettronica organica e bio-sensoristica. In tutti questi casi, l'elasticità delle fasi liquido cristalline, cioè la loro risposta meccanica a distorsioni dello stato ordinato, è cruciale dal momento che il loro comportamento alla micro- e mesoscala è il risultato della competizione fra forze elastiche interne, vincoli geometrici e campi esterni. Il filo conduttore di questa tesi è lo studio dell'elasticità dei nematici, ovvero di cristalli liquidi con puro ordine orientazionale. L'argomento viene trattato da una prospettiva microscopica e teorica, e in particolare vengono affrontate tre questioni aperte principali. Stimolati dal bisogno di chiarificare il ruolo della costante elastica detta di saddle-splay, K24, in recenti esperimenti controversi, nella Parte I sviluppiamo un formalismo in cui le costanti elastiche di superficie (K24 e K13) sono trattate allo stesso modo di quelle di bulk (K11, K22 e K33). L'applicazione del metodo ad un sistema semplice e paradigmatico, gli hard rod non chirali, svela un nuovo meccanismo che porta alla rottura spontanea della simmetria di riflessione, con potenziali implicazioni in un'ampia classe di sistemi rilevanti dal punto di vista sperimentale. Nella Parte II presentiamo un approccio microscopico, detto non-locale, che oltrepassa le classiche assunzioni delle teorie per la nemato-elasticità (trattamento di ogni particella come un rod efficace) e che rende conto dell'accoppiamento fra la specifica morfologia di una particella e la geometria delle deformazioni del direttore. Questa mutua interazione, che si manifesta tangibilmente in nuovi tipi di ordine orientazionale in nematogeni con specifiche forme in risposta a certe distorsioni, è cruciale per la formazione delle nuove fasi liquido cristalline modulate che recentemente stanno attraendo particolare attenzione. Infine, nella Parte III, applichiamo il modello microscopico non-locale al caso più generale di particelle flessibili, con l'obiettivo di modellizzare l'elasticità dei nematici polimerici, la quale rappresenta un problema aperto da diverso tempo. Mettiamo a punto una metodologia teorico-computazionale in particolare senza ricorrere alla approssimazione di disaccoppiamento che invece viene tipicamente utilizzata nelle teorie esistenti. I risultati per sistemi modello nel regime semiflessibile mostrano effetti distinti sulle costanti elastiche, con una speciale sensibilità della K33 che decresce drasticamente al crescere della flessibilità. Questo rappresenta un passo promettente verso la comprensione e il controllo delle proprietà meccaniche dei materiali liquido cristallini bio-polimerici.
Curvatura, flessibilità e fluttuazioni orientazionali: come le caratteristiche molecolari controllano le proprietà elastiche e la struttura mesoscopica nei nematici / Revignas, Davide. - (2023 Jun 16).
Curvatura, flessibilità e fluttuazioni orientazionali: come le caratteristiche molecolari controllano le proprietà elastiche e la struttura mesoscopica nei nematici
REVIGNAS, DAVIDE
2023
Abstract
Liquid crystals are a broad class of soft materials with a wide range of interest across different fields. Their common fundamental feature is the combination of order and fluidity. On the one hand, this is a basic requirement for self-organization and structure formation in living systems and indeed the physics of liquid crystals has emerged as a flourishing new research frontier in cell biology. On the other hand, this characteristic makes them sensitive and responsive to a large variety of stimuli such as light, electric and magnetic fields, mechanic forces and thermal gradients, with consequent technological interest in photonics, optofluidics, organic electronics and biosensing. In all cases, the elasticity of liquid crystalline phases, i.e. their mechanical response to distortions of their ordered state, is paramount since their behavior at the micro- and meso-scale is the result of the competition between internal elastic forces, geometric constraints and external fields. The common thread of this thesis is the elasticity of nematics - i.e. of liquid crystals with pure orientational order. The topic is approached from a microscopic and theoretical perspective, and three major open questions are addressed. Stimulated by the need to clarify the role of the saddle-splay elastic constant, K24, in recent controversial experiments, in Part I we develop a consistent formulation in which the surface-like elastic constants (K24 and K13) are treated on the very same footing of the bulk ones (K11, K22 and K33). The application of the method to the simple paradigmatic system of hard achiral rods uncovered a novel mechanism leading to spontaneous mirror symmetry breaking, with potential implications on a broad range of experimentally relevant systems. In Part II we present a microscopic approach, denominated non-local, that overcomes the classical assumptions of nemato-elasticity theories (effective-rod treatment of any particle type) and that accounts for the coupling between the specific particle morphology and the geometry of the director distortions. This interplay, manifesting tangibly in the onset of new types of orientational order among specifically shaped nematogens in response to certain deformations, is crucial for the formation of novel modulated liquid crystal phases that are attracting considerable attention. Lastly, in Part III, we extend the non-local microscopic model to the more general case of particles endowed with flexibility in order to describe the elasticity of nematic polymers, which constitutes a long standing issue in the field. We set up a theoretical-computational methodology that fully accounts for the interplay between the director field and both the orientational and the conformational degrees of freedom of polymer chains, without resorting to the decoupling approximation which is generally adopted in existing theories. Calculations for model systems in the semiflexible regime show distinct effects on the bulk elastic constants, with a special sensitivity of K33, which dramatically decreases with increasing flexibility. This is a promising step towards understanding and controlling the mechanical properties of biopolymeric liquid crystalline materials.File | Dimensione | Formato | |
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tesi_Davide_Revignas.pdf
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