Water exists in high- and low-density amorphous ice forms (HDA and LDA), which could correspond to the glassy states of high- (HDL) and low-density liquid (LDL) in the metastable part of the phase diagram. However, the nature of both the glass transition and the high-to-low-density transition are debated and new experimental evidence is needed. Here we combine wide-angle X-ray scattering (WAXS) with X-ray photon-correlation spectroscopy (XPCS) in the small-angle X-ray scattering (SAXS) geometry to probe both the structural and dynamical properties during the high-to-low-density transition in amorphous ice at 1 bar. By analyzing the structure factor and the radial distribution function, the coexistence of two structurally distinct domains is observed at = 125 K. XPCS probes the dynamics in momentum space, which in the SAXS geometry reflects structural relaxation on the nanometer length scale. The dynamics of HDA are characterized by a slow component with a large time constant, arising from viscoelastic relaxation and stress release from nanometer-sized heterogeneities. Above 110 K a faster, strongly temperature-dependent component appears, with momentum transfer dependence pointing toward nanoscale diffusion. This dynamical component slows down after transition into the low-density form at 130 K, but remains diffusive. The diffusive character of both the high- and low-density forms is discussed among different interpretations and the results are most consistent with the hypothesis of a liquid-liquid transition in the ultraviscous regime.

We demonstrate that inverse statistical mechanical optimization can be used to discover simple (e.g., short-range, isotropic, and convex-repulsive) pairwise interparticle potentials with three-dimensional diamond or simple cubic lattice ground states over a wide range of densities.The properties of condensed phases are often linked to their structure. For example, heterogeneous materials with threedimensional (3D) dielectric diamond morphologies can exhibit a photonic band gap 1 , making them useful architectures for applications that range from lasers and sensors to solar cells. Although alternative methods for fabricating such materials have been recently introduced, considerable interest remains in understanding how to create systems that spontaneously self-assemble into structures with desirable properties. Moreover, since various aspects of the effective interactions between nanometer-to micron-scale particles can be tuned experimentally via modification of solution or particle properties 2,3 , the following fundamental materials design question becomes especially relevant. Which types of interparticle potentials provide a thermodynamic driving force for the particles to self-assemble into a given target lattice?Results from statistical mechanical theories, computer simulations, and experiments have produced valuable insights into how to design interparticle interactions for self-assembly into periodic structures. For example, it is widely appreciated that spherical particles with steeply repulsive interactions spontaneously assemble into highly-coordinated 3D structures 4,5 , such as the face-centered cubic (FCC) lattice, at sufficiently high particle concentrations. Interactions that favor a targeted low-coordinated lattice ground state over other competing structures can also be designed by introducing specific types of complexity into the interparticle potential (e.g., multiple wells 6,7 , non-spherical particle shapes 8-10 , or orientationdependent "patches" on a particle surface 11-18 ), but those phases are generally stable over narrow ranges of thermodynamic conditions 17,18 . On the other hand, whether interactions with considerably simpler functional forms can also produce targeted low-coordinated 3D ground states-stable over a

A revised version of this manuscript has been accepted in the AIChE Journal [website link] and can be cited as

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Grazing incidence small angle X-ray scattering (GISAXS) measurements reveal that superlattices of 1.7 nm diameter, gold (Au) nanocrystals capped with octadecanethiol become significantly more ordered when heated to moderate temperatures (50-60 °C). This enhancement in order is reversible and the superlattice returns to its initially disordered structure when cooled back to room temperature. Disorder-order transition temperatures were estimated from the GISAXS data using the Hansen-Verlet criterion. Differential scanning calorimetry (DSC) measurements of the superlattices exhibited exotherms (associated with disordering during cooling) and endotherms (associated with ordering during heating) near the transition temperatures. The superlattice transition temperatures also correspond approximately to the melting and solidification points of octadecanethiol. Therefore, it appears that a change in capping ligand packing that occurs upon ligand melting underlies the structural transition of the superlattices. We liken the heat-induced ordering of the superlattices to an inverse melting transition.

Dynamics and kinetics in soft matter physics, biology, and nanoscience frequently occur on fast (sub)microsecond but not ultrafast timescales which are difficult to probe experimentally. The European X-ray Free-Electron Laser (European XFEL), a megahertz hard X-ray Free-Electron Laser source, enables such experiments via taking series of diffraction patterns at repetition rates of up to 4.5 MHz. Here, we demonstrate X-ray photon correlation spectroscopy (XPCS) with submicrosecond time resolution of soft matter samples at the European XFEL. We show that the XFEL driven by a superconducting accelerator provides unprecedented beam stability within a pulse train. We performed microsecond sequential XPCS experiments probing equilibrium and nonequilibrium diffusion dynamics in water. We find nonlinear heating on microsecond timescales with dynamics beyond hot Brownian motion and superheated water states persisting up to 100 μs at high fluences. At short times up to 20 μs we observe that the dynamics do not obey the Stokes–Einstein predictions.

Molecular dynamics simulations and a stochastic method based on the Fokker-Planck equation are used to explore the consequences of inhomogeneous density profiles on the thermodynamic and dynamic properties of the hard-sphere fluid and supercooled liquid water. Effects of the inhomogeneity length scale are systematically considered via the imposition of sinusoidal density profiles of various wavelengths. For long-wavelength density profiles, bulk-like relationships between local structure, thermodynamics, and diffusivity are observed as expected. However, for both systems, a crossover in behavior occurs as a function of wavelength, with qualitatively different correlations between the local static and dynamic quantities emerging as density variations approach the scale of a particle diameter. Irrespective of the density variation wavelength, average diffusivities of hard-sphere fluids in the inhomogeneous and homogeneous directions are coupled and approximately correlate with the volume available for insertion of another particle. Unfortunately, a quantitatively reliable static predictor of position-dependent dynamics has yet to be identified for even the simplest of inhomogeneous fluids.

We use inverse methods of statistical mechanics and computer simulations to investigate whether an isotropic interaction designed to stabilize a given two-dimensional lattice will also favor an analogous three-dimensional structure, and vice versa. Specifically, we determine the 3D-ordered lattices favored by isotropic potentials optimized to exhibit stable 2D honeycomb (or square) periodic structures, as well as the 2D-ordered structures favored by isotropic interactions designed to stabilize 3D diamond (or simple cubic) lattices. We find a remarkable "transferability" of isotropic potentials designed to stabilize analogous morphologies in 2D and 3D, irrespective of the exact interaction form, and we discuss the basis of this cross-dimensional behavior. Our results suggest that the discovery of interactions that drive assembly into certain 3D periodic structures of interest can be assisted by less computationally intensive optimizations targeting the analogous 2D lattices. Material properties are intimately linked to structural characteristics featured at various length scales. Thus, discovering new ways to create materials with prescribed morphologies is a key challenge in their design for specific applications. In addition to the development of top-down material fabrication strategies, there has been considerable progress in bottom-up approaches in which the primary components (molecules, nanoparticles, colloids, etc.) A critical part of any self-assembly design problem is understanding how tunable aspects of the interactions affect the thermodynamic stability of competing assembled states with different morphologies. For nanoscale to microscale particles, this understanding has been guided in part via exploratory experiments and simulations to characterize the structures that spontaneously form from systems with various particle chemistries [7,8], shapes [9][10][11][12][13][14][15], and surface properties [16][17][18][19], as well as different dispersing solvents [20] and mixtures of assembling particles [21,22]. Highly coordinated lattices with, e.g., face-centered cubic or hexagonal symmetries in three dimensions [7] and triangular symmetry in two dimensions [23] are commonly observed in the experimental assembly of monodisperse particles with short-range, isotropic interactions. A broader array of thermodynamically stable 3D structures-including low-coordinated diamond and simple cubic (Sc) lattices of interest for technological applications [24,25]