Department of Mathematics, University of California, Berkeley, CA 94720;
Center for Advanced Mathematics for Energy Research Applications, Lawrence Berkeley National Laboratory, Berkeley, CA 94720.
Proc Natl Acad Sci U S A. 2021 Aug 24;118(34). doi: 10.1073/pnas.2105826118.
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.
扩散系数可用于描述粒子的布朗运动。新兴的 X 射线光子相关光谱学（XPCS）实验可探测广泛的长度和时间尺度，非常适合研究布朗运动。虽然已经有了从 XPCS 估算平移扩散系数的方法，但还没有基于 XPCS 测量旋转扩散系数的算法，尽管此类实验可以获得所需的原始数据。在本文中，我们提出了 XPCS 数据的角度-时间互相关分析，并表明可以利用互相关信息来设计一种数值算法（相关光谱学的多层估计法[MTECS]）来预测旋转扩散系数：该方法适用于该实验范围之外的其他波长。我们在一系列模拟数据中验证了该算法的准确性。
