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Nanoporous gold (np-Au) has found its use in applications ranging from catalysis to biosensing, where pore morphology plays a critical role in performance. While the morphology evolution of bulk np-Au has been widely studied, knowledge about its thin-film form is limited. This work hypothesizes that the mechanical compliance of the thin film substrate can play a critical role in the morphology evolution. Via experimental and finite-element-analysis approaches, we investigate the morphological variation in np-Au thin films deposited on compliant silicone (PDMS) substrates of a range of thicknesses anchored on rigid glass supports and compare those to the morphology of np-Au deposited on glass. More macroscopic (10 s to 100 s of microns) cracks and discrete islands form in the np-Au films on PDMS compared to on glass. Conversely, uniformly distributed microscopic (100 s of nanometers) cracks form in greater numbers in the np-Au films on glass than those on PDMS, with the cracks located within the discrete islands. The np-Au films on glass also show larger ligament and pore sizes, possibly due to higher residual stresses compared to the np-Au/PDMS films. The effective elastic modulus of the substrate layers decreases with increasing PDMS thickness, resulting in secondary np-Au morphology effects, including a reduction in macroscopic crack-to-crack distance, an increase in microscopic crack coverage, and a widening of the microscopic cracks. However, changes in the ligament/pore widths with PDMS thickness are negligible, allowing for independent optimization for cracking. We expect these results to inform the integration of functional np-Au films on compliant substrates into emerging applications, including flexible electronics.

 

The morphological evolution of nanoporous gold is generally believed to be governed by surface diffusion. This work specifically explores the dependence of mass transport by surface diffusion on the curvature of a gold surface. The surface diffusivity is estimated by molecular dynamics simulations for a variety of surfaces of constant mean curvature, eliminating any chemical potential gradients and allowing the possible dependence of the surface diffusivity on mean curvature to be isolated. The apparent surface diffusivity is found to have an activation energy of ~0.74 eV with a weak dependence on curvature, but is consistent with the values reported in the literature. The apparent concentration of mobile surface atoms is found to be highly variable, having an Arrhenius dependence on temperature with an activation energy that also has a weak curvature dependence. These activation energies depend on curvature in such a way that the rate of mass transport by surface diffusion is nearly independent of curvature, but with a higher activation energy of ~1.01 eV. The curvature dependencies of the apparent surface diffusivity and concentration of mobile surface atoms is believed to be related to the expected lifetime of a mobile surface atom, and has the practical consequence that a simulation study that does not account for this finite lifetime could underestimate the activation energy for mass transport via surface diffusion by ~0.27 eV. 

As phenomena that necessarily emerge from the collective behavior of interacting particles, phase transitions continue to be difficult to predict using statistical thermodynamics. A recent proposal called the topological hypothesis suggests that the existence of a phase transition could perhaps be inferred from changes to the topology of the accessible part of the configuration space. This paper instead suggests that such a topological change is often associated with a dramatic change in the configuration space geometry, and that the geometric change is the actual driver of the phase transition. More precisely, a geometric change that brings about a discontinuity in the mixing time required for an initial probability distribution on the configuration space to reach steady-state is conjectured to be related to the onset of a phase transition in the thermodynamic limit. This conjecture is tested by evaluating the diffusion diameter and epsilon-mixing time of the configuration spaces of hard disk and hard sphere systems of increasing size. Explicit geometries are constructed for the configuration spaces of these systems, and numerical evidence suggests that a discontinuity in the epsilon-mixing time coincides with the solid-fluid phase transition in the thermodynamic limit. 

Hard disks systems are often considered as prototypes for simple fluids. In a statistical mechanics context, the hard disk configuration space is generally quotiented by the action of various symmetry groups. The changes in the topological and geometric properties of the configuration spaces effected by such quotient maps are studied for small numbers of disks on a square and hexagonal torus. A metric is defined on the configuration space and the various quotient spaces that respects the desired symmetries. This is used to construct explicit triangulations of the configuration spaces as$$\alpha$$$\alpha$-complexes. Critical points of the hard disk potential on a configuration space are associated with changes in the topology of the accessible part of the configuration space as a function of disk radius, are conjectured to be related to the configurational entropy of glassy systems, and could reveal the origins of phase transitions in other systems. The number of critical points and their topological and geometric properties are found to depend on the symmetries by which the configuration space is quotiented.