X-ray photon correlation spectroscopy (XPCS) enables the study of sample dynamics between micrometer and atomic length scales. As a coherent scattering technique, it benefits from the increased brilliance of the next-generation synchrotron radiation and Free-Electron Laser (FEL) sources. In this article, we will introduce the XPCS concepts and review the latest developments of XPCS with special attention on the extension of accessible time scales to sub-μs and the application of XPCS at FELs. Furthermore, we will discuss future opportunities of XPCS and the related technique X-ray speckle visibility spectroscopy (XSVS) at new X-ray sources. Due to its particular signal-to-noise ratio, the time scales accessible by XPCS scale with the square of the coherent flux, allowing to dramatically extend its applications. This will soon enable studies over more than 18 orders of magnitude in time by XPCS and XSVS.

From Femtoseconds to Hours—Measuring Dynamics over 18 Orders of Magnitude with Coherent X-rays

In this perspective article we highlight research opportunities and challenges in probing structural dynamics of molecular systems using X-ray Photon Correlation Spectroscopy (XPCS). The development of new X-ray sources, such as 4th generation storage rings and X-ray free-electron lasers (XFELs), provides promising new insights into molecular motion. Employing XPCS at these sources allows to capture a very broad range of timescales and lengthscales, spanning from femtoseconds to minutes and atomic scales to the mesoscale. Here, we discuss the scientific questions that can be addressed with these novel tools for two prominent examples: the dynamics of proteins in biomolecular condensates and the dynamics of supercooled water. Finally, we provide practical tips for designing and estimating feasibility of XPCS experiments as well as on detecting and mitigating radiation damage.

/pdf/towards-molecular-movies-with-x-ray-photon-correlation-31ww8tm3o0.pdf

Towards molecular movies with X-ray photon correlation spectroscopy

Brownian motion of Cowpea mosaic virus (CPMV) in water was measured using small-angle X-ray photon correlation spectroscopy (SA-XPCS) at 19.2 µs time resolution. It was found that the decorrelation time τ(Q) = 1/DQ2 up to Q = 0.091 nm-1. The hydrodynamic radius RH determined from XPCS using Stokes-Einstein diffusion D = kT/(6πηRH) is 43% larger than the geometric radius R0 determined from SAXS in the 0.007 M K3PO4 buffer solution, whereas it is 80% larger for CPMV in 0.5 M NaCl and 104% larger in 0.5 M (NH4)2SO4, a possible effect of aggregation as well as slight variation of the structures of the capsid resulting from the salt-protein interactions. 

/pdf/direct-measurement-of-stokes-einstein-diffusion-of-cowpea-1jbqfxn4.pdf

Direct measurement of Stokes–Einstein diffusion of Cowpea mosaic virus with 19 µs-resolved XPCS

The dynamics and structure of mixed phases in a complex fluid can significantly impact its material properties, such as viscoelasticity. Small-angle X-ray Photon Correlation Spectroscopy (SA-XPCS) can probe the spontaneous spatial fluctuations of the mixed phases under various in situ environments over wide spatiotemporal ranges (10-6-103 s /10-10-10-6 m). Tailored material design, however, requires searching through a massive number of sample compositions and experimental parameters, which is beyond the bandwidth of the current coherent X-ray beamline. Using 3.7-μs-resolved XPCS synchronized with the clock frequency at the Advanced Photon Source, we demonstrated the consistency between the Brownian dynamics of ~100 nm diameter colloidal silica nanoparticles measured from an enclosed pendant drop and a sealed capillary. The electronic pipette can also be mounted on a robotic arm to access different stock solutions and create complex fluids with highly-repeatable and precisely controlled composition profiles. This closed-loop, AI-executable protocol is applicable to light scattering techniques regardless of the light wavelength and optical coherence, and is a first step towards high-throughput, autonomous material discovery. 

Robotic pendant drop: containerless liquid for μs-resolved, AI-executable XPCS

The ability of pulsed nature of synchrotron radiation opens up the possibility of studying microsecond dynamics in complex materials via speckle-based techniques. Here, we present the study of measuring the dynamics of a colloidal system by combining single and multiple X-ray pulses of a storage ring. In addition, we apply speckle correlation techniques at various pulse patterns to collect correlation functions from nanoseconds to milliseconds. The obtained sample dynamics from all correlation techniques at different pulse patterns are in very good agreement with the expected dynamics of Brownian motions of silica nanoparticles in water. Our study will pave the way for future pulsed X-ray investigations at various synchrotron X-ray sources using individual X-ray pulse patterns.

Single and multi-pulse based X-ray photon correlation spectroscopy.

This paper reports on coherent scattering experiments in the low-count regime with less than one photon per pixel per acquisition on average, conducted with two detectors based on the Eiger single-photon-counting chip. The obtained photon-count distributions show systematic deviations from the expected Poisson-gamma distribution, which result in a strong overestimation of the measured speckle contrast. It is shown that these deviations originate from an artificial increase of double-photon events, which is proportional to the detected intensity and inversely proportional to the exposure time. The observed miscounting effect may have important implications for new coherent scattering experiments emerging with the advent of high-brilliance X-ray sources. Different correction schemes are discussed in order to obtain the correct photon distributions from the data. A successful correction is demonstrated with the measurement of Brownian motion from colloidal particles using X-ray speckle visibility spectroscopy.

Implications of disturbed photon-counting statistics of Eiger detectors for X-ray speckle visibility experiments.

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Implications of disturbed photon-counting statistics of Eiger detectors for X-ray speckle visibility experiments.