Structural and Dynamical Properties of Soft Matter Systems

: From Cholesterics to Nanoconfined Fluids

Abstract

This thesis investigates a range of complex soft matter systems through the unifying
framework of topology, geometry, and energetics, with particular emphasis on cholesteric
liquid crystals. Using a combination of continuum field theories, topological classification,
and advanced computational techniques, we systematically characterise a rich spectrum
of metastable and morphologically intricate structures. These include twisted configurations
under confinement, biaxial disclinations, Skyrmions, and Hopf solitons, alongside the emergent
behaviour of nanoconfined supercooled liquids.
Central to the study is the employment of both director field and Landau–de Gennes Qtensor descriptions, enabling a tensorial treatment of orientational order and the inclusion
of biaxiality, defect structure, and spatial inhomogeneity. Elastic contributions from both the
one-constant and anisotropic Frank–Oseen formulations are incorporated, alongside the full
bulk thermodynamic potential, allowing for the exploration of equilibrium and metastable states
across diverse boundary conditions and confinement geometries.
We present a detailed analysis of the energy landscape of cholesterics in (1+2) dimensions
via numerical gradient descent, the Doubly Nudged Elastic Band (DNEB) method, and the HighIndex Optimisation-Based Shrinking Dimer (Hi-OSD) algorithm. This enables the identification
of minimum energy transition pathways and saddle points connecting topologically distinct
configurations. Furthermore, via the energy minimisation of Hopf solitons, we demonstrate the
stability of novel dipolar defect structures that persist under a range of conditions, suggesting an
intrinsic topological protection arising from confinement and anchoring.
Moreover, we report a striking asymmetry in energetic cost between the relief and generation
of twist: transitions from highly twisted states (w = 5) to less twisted ones (w = 1) are energetically
favourable, whereas the reverse process incurs a significant energy penalty when the intrinsic
twist parameter q0 favours the opposite handedness. This directional bias highlights the role of
chirality and elastic frustration in the energetic landscape of confined cholesterics.
Finally, the thesis transitions to the study of supercooled liquids confined to nanoscale geometries, analysed within the framework of isomorph theory. We provide evidence that the
Roskilde-simple class of liquids maintains structural isomorph invariance even under nanoscale
confinement. Employing the Lennard-Jones and Kob-Andersen binary Lennard-Jones (KABLJ)
systems, we show that higher-order structural metrics, including Topological Cluster Classification (TCC), are conserved along isomorphs, even within slit-pore geometries. These findings
suggest a robust invariance of many-body structure under conditions that are far from bulk
equilibrium.
Overall, this work contributes a unified theoretical and computational framework to the
study of complex soft matter systems, revealing deep connections between geometry, topology,
and energetics. The insights gained hold implications for the design of multistable liquid crystal
devices, the understanding of defect dynamics in chiral media, and the structural characterisation of supercooled fluids in confinement.

Date of Award	9 Dec 2025
Original language	English
Awarding Institution	University of Bristol
Supervisor	Nigel B Wilding (Supervisor) & Francesco Turci (Supervisor)