Statistical physics of bulk and confined ionic liquids

Room temperature ionic liquids are molten salts at ambient temperature. This thesis is concerned with the structure of room temperature ionic liquids both in the bulk and in confinement. A particular theme is the rich statistical physics of such systems, which is primarily due to strong Coulomb correlations.
We begin by examining the structure of ionic liquids in the bulk. One of the most important questions in understanding the structure of ionic liquids is whether ions are truly "free" and mobile (a concentrated ionic solution), or are rather bundled up as ion pairs (a dilute solution of free ions dissolved in a sea of ion pairs). We propose a mathematical model for the thermodynamics and kinetics of ion pairing in ionic liquids. Our model reveals that roughly 2/3 of ions are free, whilst those ion pairs that do exist are short- lived. We conclude that ionic liquids ought to be considered to be concentrated, rather than dilute, electrolytes.
We then examine the structure of ionic liquids confined between charged surfaces. Motivated by surface force balance experiments, we use a 1D Coulomb gas model to study ionic liquids confined between charged mica surfaces. We show that the disjoining pressure– surface separation curve depends on the fugacity (the bulk cohesive energy) of the ionic liquid, and the electrostatic interaction energy of ions at closest approach. The model shows good qualitative agreement with experimental data, with all parameters independently estimated without fitting.
We then turn our attention to a single layer of ionic liquid ions confined between metal surfaces, and develop a mean field model for equilibrium charge storage in a nanoporous supercapacitor. The development of nanoporous supercapacitors is hindered by the perceived tradeoff between capacitance, power delivery and reversible charging - a trilemma. Our model identifies the affinity of ions to the pore wall as a key parameter that controls charging behaviour. From this, we elucidate a region of "ionophilicity" in which the capacitance-power-hysteresis trilemma can be avoided.
The non-equilibrium physics of ion transport in ionic liquids is then considered. We derive a novel system of continuum electrokinetic equations for ionic liquids that is based ￼on coarse graining a simple exclusion process defined on a lattice. The resulting dynamical equations are written as a gradient flow with a degenerate mobility function. This form of the mobility function gives rise to novel charging behaviours that are qualitatively different to those known in electrolytic solutions.
Finally, we consider active non-equilibrium fluids, in which energy is continuously consumed from the surrounding environment. Those systems are inherently far from thermo- dynamic equilibrium. By developing a top-down description for non-equilibrium systems with the fluctuation spectrum as the central quantity, we show that the form of the disjoin- ing force may reveal crucial elements of the microscopic physics. Our framework explains the long-ranged force observed in recent molecular dynamics simulation of active Brownian particles.

Advisor: Goriely, A
Vella, D