Slow dynamics of nanocomposite polymer aerogels as revealed by X-ray photocorrelation spectroscopy (XPCS)

Two-Dimensional Fluctuation Correlation Spectroscopy (2D-FlucCS): A Method to Determine the Origin of Relaxation Rate Dispersion

Relaxation rate dispersion, i.e., nonexponential or multicomponent kinetics, is observed in complex systems when measuring relaxation kinetics. Often, the origin of rate dispersion is associated with the heterogeneity in the system. However, both homogeneous (where all molecules experience the same rate but inherently nonexponential) and heterogeneous (where all molecules experience different rates) systems can exhibit rate dispersion. A multidimensional correlation analysis method has been demonstrated to detect and quantify rate dispersion observed in molecular rotation, diffusion, solvation, and reaction kinetics. One-dimensional (1D) autocorrelation function detects rate dispersion and measures its extent. Two-dimensional (2D) autocorrelation function measures the origin of rate dispersion and distinguishes homogeneous from heterogeneous. In a heterogeneous system, implicitly there exist subensembles of molecules experiencing different rates. A three-dimensional (3D) autocorrelation function measures subensemble exchange if present and reveals if the system possesses static or dynamic heterogeneity. This perspective discusses the principles, applications, and potential and also presents a future outlook of two-dimensional fluctuation correlation spectroscopy (2D-FlucCS). The method is applicable to any experiment or simulation where a time series of fluctuation in an observable (emission, scattering, current, etc.) around a mean value can be obtained in steady state (equilibrium or nonequilibrium), provided the system is ergodic.

The effect of dynamically heterogeneous interphases on the particle dynamics of polymer nanocomposites

The entanglements of dynamically asymmetric polymer layers influence relaxations of nanoparticles in polymer nanocomposites. In this work, the dynamics of polymer-adsorbed and polymer-grafted nanoparticles in a poly(methyl acrylate) matrix polymer was investigated using X-ray photon correlation spectroscopy (XPCS) to understand the role of chain rigidity and chemical heterogeneities in particle dynamics. Locations of dynamic heterogeneities close to nanoparticles and away from particle surfaces were examined with the comparison of adsorbed and grafted nanoparticles. Our results show that the chemical heterogeneities around dispersed nanoparticles transitioned the particle dynamics from Brownian diffusion into hyperdiffusion, and moreover, the high rigidity of chains in the chemically heterogeneous interfacial layers slowed down the particle dynamics. The hyperdiffusion measured both in grafted particles and adsorbed particles was attributed to the dense interfacial mixing of dynamically heterogeneous chains.

Effects of temperature and ionic strength on the microscopic structure and dynamics of egg white gels

We investigate the thermal gelation of egg white proteins at different temperatures with varying salt concentrations using x-ray photon correlation spectroscopy in the geometry of ultra-small angle x-ray scattering. Temperature-dependent structural investigation suggests a faster network formation with increasing temperature, and the gel adopts a more compact network, which is inconsistent with the conventional understanding of thermal aggregation. The resulting gel network shows a fractal dimension δ, ranging from 1.5 to 2.2. The values of δ display a non-monotonic behavior with increasing amount of salt. The corresponding dynamics in the q range of 0.002-0.1 nm^-1 is observable after major change of the gel structure. The extracted relaxation time exhibits a two-step power law growth in dynamics as a function of waiting time. In the first regime, the dynamics is associated with structural growth, whereas the second regime is associated with the aging of the gel, which is directly linked with its compactness, as quantified by the fractal dimension. The gel dynamics is characterized by a compressed exponential relaxation with a ballistic-type of motion. The addition of salt gradually makes the early stage dynamics faster. Both gelation kinetics and microscopic dynamics show that the activation energy barrier in the system systematically decreases with increasing salt concentration.

Reverse-engineering method for XPCS studies of non-equilibrium dynamics

X-ray photon correlation spectroscopy (XPCS) is a powerful tool in the investigation of dynamics covering a broad time and length scale. It has been widely used to probe dynamics for systems in both equilibrium and non-equilibrium states; in particular, for systems undergoing a phase transition where the structural growth kinetics and the microscopic dynamics are strongly intertwined. The resulting time-dependent dynamic behavior can be described using the two-time correlation function (TTC), which, however, often contains more interesting features than the component along the diagonal, and cannot be easily interpreted via the classical simulation methods. Here, a reverse engineering (RE) approach is proposed based on particle-based heuristic simulations. This approach is applied to an XPCS measurement on a protein solution undergoing a liquid-liquid phase separation. It is demonstrated that the rich features of experimental TTCs can be well connected with the key control parameters including size distribution, concentration, viscosity and mobility of domains. The dynamic information obtained from this RE analysis goes beyond the existing theory. The RE approach established in this work is applicable for other processes such as film growth, coarsening or evolving systems.

In-Operando Study of Shape Retention and Microstructure Development in a Hydrolyzing Sol-Gel Ink during 3D-Printing

3D printing of amorphous and crystalline ceramics is of paramount importance for the fabrication of a wide range of devices with applications across different technology fields. Printed ceramics are remarkably enabled by the sol-gel synthesis method in conjunction with continuous filament direct ink writing. During printing, multiple processes contribute to the evolution of inks including shape retention, chemical conversion, solidification, and microstructure formation. Traditionally, depending on the ink composition and printing environment, several mechanisms have been associated with the shape retention and solidification of 3D printed structures: gelation, rapid solvent evaporation, energy-driven phase transformation, and chemical-driven phase transformation. Understanding the fundamental differences between these mechanisms becomes key since they strongly influence the spatiotemporal evolution of the materials, as the out-of-equilibrium processes inherent to the extrusion, relaxation, and solidification of printed materials have significant effects on the materials properties. In this work, we investigate the shape retention mechanism and the hydrolysis-induced material conversion and microstructure formation during the 3D printing of a water reactive sol-gel ink that transforms into titanium dioxide-based ceramic. This study aims at identifying characteristic mechanisms associated with the material transformation, establishing connections between the microstructure development and the timescales associated with solidification under operando 3D-printing conditions. The investigation of this material's out-of-equilibrium pathways under processing conditions is enabled by time-resolved coherent X-ray scattering, providing simultaneous access to temporospatially resolved microstructural and dynamics information. Furthermore, we explore X-ray speckle tracking as a tool to resolve deformations of the microstructure in a printed filament associated with the deposition of consecutive filaments. Through this work, we aim at providing a fundamental understanding of the relationships behind these transformative processes in 3D printing and their timescales as the basis for achieving unprecedented control over printed materials microstructure.

Velocity measurement by coherent x-ray heterodyning

We present a small-angle coherent x-ray scattering technique used for measuring flow velocities in slow moving materials. The technique is an extension of X-ray Photon Correlation Spectroscopy (XPCS): It involves mixing the scattering from moving tracer particles with a static reference that heterodynes the signal. This acts to elongate temporal effects caused by flow in homodyne measurements, allowing for a more robust measurement of flow properties. Using coherent x-ray heterodyning, velocities ranging from 0.1 to 10 μm/s were measured for a viscous fluid pushed through a rectangular channel. We describe experimental protocols and theory for making these Poiseuille flow profile measurements and also develop the relevant theory for using heterodyne XPCS to measure velocities in uniform and Couette flows.

X-ray photon correlation spectroscopy

In recent years, X-ray photon correlation spectroscopy (XPCS) has emerged as one of the key probes of slow nanoscale fluctuations, applicable to a wide range of condensed matter and materials systems. This article briefly reviews the basic principles of XPCS as well as some of its recent applications, and discusses some novel approaches to XPCS analysis. It concludes with a discussion of the future impact of diffraction-limited storage rings on new types of XPCS experiments, pushing the temporal resolution to nanosecond and possibly even picosecond time scales.