Cross-correlation analysis of X-ray photon correlation spectroscopy to extract rotational diffusion coefficients

Significance

X-ray photon correlation spectroscopy (XPCS) is a powerful technique that can probe a broad range of space and time scales and will become increasingly powerful due to coming advancements in coherence. Assessing translational and rotational diffusion is a key quantity in analyzing material structures and dynamics, with applications across molecular biology, drug discovery, and materials science. While methods for estimating translational diffusion coefficients from XPCS data are well-developed, there are no algorithms for measuring the rotational diffusion. Here, we present a mathematical formulation and algorithm based on angular-temporal cross-correlations for extracting this rotational information, providing tools for data analysis of XPCS. Although we focus on XPCS, the proposed method can be applied to other experimental techniques due to its generality.

Abstract

Coefficients for translational and rotational diffusion characterize the Brownian motion of particles. Emerging X-ray photon correlation spectroscopy (XPCS) experiments probe a broad range of length scales and time scales and are well-suited for investigation of Brownian motion. While methods for estimating the translational diffusion coefficients from XPCS are well-developed, there are no algorithms for measuring the rotational diffusion coefficients based on XPCS, even though the required raw data are accessible from such experiments. In this paper, we propose angular-temporal cross-correlation analysis of XPCS data and show that this information can be used to design a numerical algorithm (Multi-Tiered Estimation for Correlation Spectroscopy [MTECS]) for predicting the rotational diffusion coefficient utilizing the cross-correlation: This approach is applicable to other wavelengths beyond this regime. We verify the accuracy of this algorithmic approach across a range of simulated data.