Topographic control of order-disorder phase transitions in a quasi-2D granular system

Downs, James Gordon (2023) Topographic control of order-disorder phase transitions in a quasi-2D granular system. PhD thesis, University of Nottingham.

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The focus of current research in two-dimensional phase transitions has shifted

towards non-equilibrium systems such as active matter and fluid dynamics.

However, unlike in equilibrium systems, we lack a complete framework to

describe their behaviour. Although previous work has shown that some basic

concepts from statistical mechanics can be applied to non-equilibrium systems,

the extent to which they can be applied remains unclear.

One intriguing problem in equilibrium systems is the two-dimensional hard-disc

liquid-to-crystal phase transition. The nature of this phase transition differs

from that in three-dimensions and was, until recently, a matter of much debate.

Extending this debate, two-dimensional granular systems have also been studied

to investigate the applicability of hard-disc model descriptions to non-equilibrium

systems. Granular systems are convenient for manipulation and offer easy

observations at the particle level and therefore represent an ideal test case for

these investigations.

In this thesis, I present an investigation of the order-disorder phase transition in

a 2D driven granular system. Previous research has shown that these systems

undergo a continuous two-step phase transition. We explore a mechanism for

changing the nature of this transition from continuous to first-order by introducing

a triangular lattice of dimples milled into the surface. The change in phase

transition behaviour, for the system we focus on for much of this thesis, enables

further study of other behaviours from equilibrium physics, such as hysteresis,

surface tension and wetting.

The phase behaviour of our system was studied on these dimpled surfaces for

three different spacings. One of these spacings produced first-order like behaviour

and was focussed on for much of the thesis.

We also investigated how changing the geometry and the inelasticity at the

boundary affects the wetting of different phases. This allowed us to spatially

control the coexisting liquid and solid phases. Our findings showed behaviour

similar to wetting in equilibrium systems. Furthermore, I present a quantitative

study confirming the first-order nature of the phase transition in this system.

While doing this, I demonstrate evidence of coexistence, hysteresis and surface

tension which are all ideas that are commonly associated with first-order phase

transitions in equilibrium systems.

Inspired by the hydrophobic effect observed in equilibrium systems, a similar

effect called the orderphobic effect was recently proposed. This is where disorder inducing

intruders placed in an ordered solid experience a force of attraction. The

authors suggest that this effect should be general to any system that experiences a

first-order order-disorder phase transition. Since our results showed the necessary

pre-prerequisites for observing such an effect, we investigated whether such a

force could be observed. Although our attempts to reproduce this effect in our

non-equilibrium system were inconclusive, we believe the results are promising

for future investigation.

Finally, I present a more detailed investigation into how changing the spacing of

the dimpled lattice changes the nature of the transitions for a broader range of

spacings. Our results indicate that different phases form depending on the lattice

spacing. We also discuss how the equilibrium ideas of stability can be applied to

the system using spacings that display a combination of different phases.

Item Type: Thesis (University of Nottingham only) (PhD)
Supervisors: Smith, Michael
Swift, Michael
Keywords: Two-dimensional phase transitions; Non-equilibrium systems; Two-dimensional granular systems; Phase transition behaviour; Dimpled lattice
Subjects: Q Science > QC Physics > QC170 Atomic physics. Constitution and properties of matter
Faculties/Schools: UK Campuses > Faculty of Science > School of Physics and Astronomy
Item ID: 74251
Depositing User: Downs, James
Date Deposited: 12 Dec 2023 04:40
Last Modified: 12 Dec 2023 04:40

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