Image-based Measurements of Diffusion Coefficients from Diffraction-Limited Nanoparticles

Image-based techniques can be used to estimate the diffusion coefficient of particles in a fluid. Techniques such as dynamic light scattering, fluorescence recovery after photobleaching, and fluorescence correlation microscopy have limited resolution and are highly sensitive to experimental conditions. Particle image velocimetry (PIV) methods provide better accuracy and repeatability. A modified PIV approach called image-based probability estimation of displacement (iPED) was developed and tested on particle sizes ranging from 200nm to 1000nm. iPED allows for higher accuracy and robustness in the estimation of diffusion coefficients of nanoparticle solutions compared to established PIV methods without assumptions on particle behavior and shape. However, the effectiveness, parametrization, and limitations of iPED have yet to be established for a wide range of diffraction-limited nanoparticles. In this work, we present an adaptation and application study of iPED for 20nm to 100nm particles. This study improves upon the image pre-processing and cross-correlation processing stages of iPED. The effectiveness of the method is determined by performing a convergence analysis of iPED and comparing the best estimate of the diffusion coefficient with the theoretical value obtained from the Stokes-Einstein equation. Results demonstrate that images in this range of nanoparticles exhibit an extremely low signal-to-noise ratio, leading to a low primary peak ratio in the ensemble cross-correlation plane. This requires additional efforts in image pre-processing and the use of filtering techniques such as phase correlation in order to improve the quality of the signal, thus, reducing the error in the diffusion coefficient measurements.