Tunable mechanical metamaterials in soft and biological matter

Marinčič, Matevž (avtor), Ravnik, Miha (mentor), Humar, Matjaž (komentor)

This thesis numerically explores the mechanics of complex soft and biological materials along two lines of research. The first focuses on investigating the topological structures in blue phase liquid crystals (BP), stabilized by highly chiral anisotropic elasticity, and the second on using whispering gallery mode (WGM)-supporting microspheres as biosensors for probing local mechanical properties in soft elastic and biological materials. The first part of the thesis is devoted to the study and visualization of half-skyrmions and skyrmion filaments, also known as double-twist cylinders, in blue phases of chiral liquid crystals. Using a combination of Landau–de Gennes theory and surface anchoring, we investigate the effects of confinement to an experimentally relevant planar cell, focusing particularly on the less-studied blue phase III. Using advanced visualization techniques, the 3D structure of BPIII emerges as an amorphous tangle of quarter-skyrmions, stabilized by a connected network of topological defects. This structure transitions into an amorphous quasi-2D array of half-skyrmions bound by vertical disclination lines when confined to layers thinner than approximately half the chiral pitch. The full phase diagram of chiral structures is numerically calculated. Cubic BPI and BPII are also investigated, particularly the effect of stabilization by one-dimensional boundary patterns that impose specific orientations and monocrystallinity. The second part of the thesis introduces the theory and numerical simulations for a novel methodology for local measurement of mechanical properties in soft and biological materials, motivated as a minimally invasive technique with promising biomedical applications. We develop WGM-spectroscopy that utilizes WGM-resonances in dye-doped liquid droplets for high-precision spectral fitting to determine refractive indices, droplet size, and shape. Additionally, we develop finite element simulations to determine the deformation of a liquid inclusion in a soft elastic material, where elastocapillary effects influence the mechanical response of the droplet to local stress. The WGM-spectroscopy and simulations are complemented by experimental measurements to demonstrate the determination of local anisotropic stress and Young's modulus. Finally, the versatility and advantages of WGM spectroscopy are demonstrated through several additional biosensing applications, including ultra-precise microdroplet generation and barcoding, deep-tissue and intracellular localization of microbeads (unaffected by scattering), and simultaneous tracking and sensing. Local refractive indices were measured with high precision, demonstrating the ability to monitor intracellular changes during cellular processes. The work presented in this thesis will allow for a better understanding of the topology and structure of blue phases and advance WGM-based applications in biomedicine and the study of soft materials.

• Jezik: Angleški jezik
• Ključne besede: numerical simulations, blue phase III, chiral liquid crystal, skyrmions, whispering gallery modes, liquid inclusions, elastocapillarity, soft biological matter, mechanical metamaterial
• Vrsta gradiva: Doktorsko delo/naloga
• Tipologija: 2.08 - Doktorska disertacija
• Organizacija: FMF - Fakulteta za matematiko in fiziko
• Leto izida: 2025
• PID: 20.500.12556/RUL-175317
• COBISS.SI-ID: 254889475
• Datum objave v RUL: 24.10.2025

Sekundarni jezik

• Jezik: Slovenski jezik
• Naslov: Prilagodljivi mehanski metamateriali v mehki in biološki snovi

Izvleček

V tej disertaciji so predstavljene numerične raziskave mehanike kompleksnih mehkih in bioloških materialov in sicer vzdolž dveh raziskovalnih smeri. Prva raziskovalna smer se osredotoča na topološke strukture v modrih fazah tekočih kristalov (BP), ki so stabilizirane z izrazito kiralno anizotropno elastičnostjo, druga smer pa na uporabo kapljičnih optičnih mikroresonatorjev kot biosenzorjev za lokalno zaznavanje mehanskih lastnosti v mehkih elastičnih in bioloških materialih. Prvi del disertacije je posvečen preučevanju in vizualizaciji mezoskopskih gradnikov modre faze, to so pol-skirmioni ter valjasti skirmionski filamenti. Z uporabo Landau–de Gennesove teorije in površinskega sidranja raziščemo vpliv ograjene geometrije, kjer se omejimo na eksperimentalno relevantno ploščato celico, s posebnim poudarkom na manj raziskani modri fazi BPIII. Z naprednimi vizualizacijskimi tehnikami se 3D-struktura BPIII pokaže kot amorfna tekočina skirmionov z delnim nabojem, stabilizirana s povezano mrežo topoloških defektov. Pri omejitvi na plasti tanjše od približno polovice kiralnega koraka se ta struktura preoblikuje v amorfno kvazi-2D mrežo polskirmionov, med njimi pa se tvorijo navpične disklinacijske črte. Numerično smo izračunali celoten fazni diagram kiralnih struktur. Raziskani sta bili tudi kubični fazi BPI in BPII, še posebej vpliv enodimenzionalnih periodičnih vzorcev površinskega sidranja, ki vsiljujejo določeno usmerjenost in stabilizirajo monokristalno ureditev. V drugem delu disertacije so predstavljene numerične simulacije in teorija, ki omogočajo razvoj nove metodologije za lokalno merjenje mehanskih lastnosti mehkih in bioloških materialov z obetavnimi biomedicinskimi aplikacijami. V ta namen razvijemo whispering gallery mode (WGM) spektroskopijo, ki preko merjenja spektralnih premikov WGM resonanc v mikrokapljicah omogoča visoko natančno merjenje lomnega količnika, velikosti in oblike kapljice. Dodatno z metodo končnih elementov numerično simuliramo deformacijo tekoče kapljice v mehkem elastičnem materialu, kjer elastokapilarni učinki narekujejo podrobnosti mehanskega odziva kapljice. Simulacija, skupaj z WGM spektroskopijo in dodatnimi eksperimentalnimi meritvami, omogoča merjenje lokalne anizotropne napetosti in Youngovega modula. Na koncu pokažemo uporabo in prednosti WGM spektroskopije še v drugih biosenzorskih aplikacijah, vključno z generiranjem mikrokapljic z natančno določeno velikostjo, kar omogoča kodiranje informacij, ter lokalizacijo mikroresonatorjev v močno sipajočem biološkem tkivu in znotraj celic, ki hkrati omogoča merjenje lokalnih parametrov. Meritve lokalnega lomnega količnika z visoko natančnostjo demonstrirajo zmožnost spremljanja znotrajceličnih sprememb med celičnimi procesi. Rezultati te disertacije prispevajo k boljšemu razumevanju strukture in topologije modrih faz ter odpirajo nove možnosti za uporabo WGM-tehnologij v biomedicini in raziskavah mehkih materialov.

• Ključne besede: numerične simulacije, modra faza III, kiralni tekoči kristali, skirmioni, whispering gallery modes, tekoče inkluzije, elastokapilarnost, mehka biološka snov, mehanski metamaterial