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Volume 113
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Robust particle size distribution recovery in ultra-dilute dynamic light scattering via bi-exponential refitting–guided generalized regression neural network
Mingyang Zhang, Min Xia, Wenping Guo, Li Xia, Wei Li *
School of Optical and Electronic Information, Huazhong University of Science and Technology, Wuhan, 430074, China
10.1016/j.partic.2026.03.008
Volume 113, June 2026, Pages 1-11
Received 24 January 2026, Revised 3 March 2026, Accepted 5 March 2026, Available online 23 March 2026, Version of Record 31 March 2026.
E-mail: weili@hust.edu.cn
Highlights

• Improves PSD recovery accuracy for ultra-dilute DLS where conventional inversion fails.

• Bi-exponential refitting stabilizes distorted ACFs and mitigates long-lag corruption.

• Refitting suppresses long-lag artifacts while retaining diffusion information in the slow term.

• GA-optimized GRNN yields stable PSD peaks down to single-digit ⟨N⟩ (max 6.39% error).

• Avoids cumulant overestimation and spurious large-particle peaks at low ⟨N⟩.


Abstract

Dynamic light scattering (DLS) is widely used for particle sizing; however, at ultra-low concentrations, limited acquisition time distorts the intensity autocorrelation function (ACF), and the reduced signal-to-noise ratio further compromises the reliability of particle size distribution (PSD) recovery. To address these challenges, we develop a low-concentration DLS analysis framework based on Bi-exponential Refitting–Guided Generalized Regression Neural Network (BRG-GRNN), where BRG denotes Bi-exponential Refitting–Guided. The measured g(2)(τ) is parameterized by a bi-exponential superposition of a Brownian-motion term and a number-fluctuation term, yielding a forward model that explicitly accounts for number fluctuations. This model is used to generate training data for GRNN, while a genetic algorithm (GA) is employed to automatically select the GRNN smoothing parameter σGRNN. Experimental results obtained from four samples (456, 710, 805, and 1000 nm) at three low-concentration levels demonstrate that the proposed method effectively mitigates the adverse impact of low concentration on PSD recovery. Compared with the conventional cumulant method, it achieves superior inversion performance. Moreover, the recovered PSDs are in close agreement with those obtained under conventional concentration conditions, with no noticeable discrepancies. Under low-concentration conditions, the maximum relative PSD recovery error is 6.39%, and it remains below 4% in most cases.

Graphical abstract
Keywords
Dynamic light scattering; Particle size distribution; Inversion model; Ultra-low concentration; Particle number fluctuation; Neural network
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