Measurement of Electrophoretic Mobility Fluctuations of Single Particles Trapped by Optical Tweezers

Abstract

In this study, we focus on electrophoresis, a phenomenon that describes the movement of particles in a liquid when an external electric field is present. This movement is caused by the Coulomb force on the surface charge of the particles. Most particles develop a surface charge in water. This charge will attract or repel ions in the liquid, creating a charge shielding area known as the Electric Double Layer. Electrophoresis is inherently a surface phenomenon, closely related to the Electric Double Layer. When an external field is applied, it induces force on both the ions and the particle. This interaction results in electrophoretic drift. The speed of this drift depends on the zeta potential at the slip plane. In this project, we use optical tweezers to investigate fluctuations in the electrophoretic movement of individual colloidal particles. Optical tweezers can hold particles from tens of nanometers to tens of microns within a tightly focused laser beam. We use a 1064 nm continuous wave laser to capture and study individual particles. The measurement is carried out by a quadrant photodiode (QPD). Since these particles undergo Brownian motion, we use this behavior for system calibration, correlating the movement of the particle with the displacement of the laser beam. A lock-in amplifier processes the signals from the QPD. By measuring the in-phase and out-of-phase noise of the QPD signal, we can separate the Brownian motion and fluctuations in electrophoretic drift. We propose that the in-phase component is composed of a mix of two signals: one from fluctuations in electrophoretic drift and the other from Brownian motion. This observation forms the cornerstone of our methodology. We performed simulations based on the Langevin equation to model fluctuating mobility. These simulations confirmed that the fluctuating term only affects the in-phase component of the lock-in amplifier signal. Therefore, our method can accurately distinguish fluctuations in electrophoretic mobility. A significant observation is the presence of large, slow, and non-Gaussian fluctuations. Given these fluctuations and the known relationship between charge and electrophoretic mobility, we hypothesize that the difference between zeta potential and diffuse layer potential can be explained by the Jensen inequality. Using Power Spectral Density (PSD) analysis, we estimate the autocorrelation function of the mobility fluctuations. The resulting autocorrelation function shows much larger time constants than initially expected. The possible link between these fluctuations and surface charge dynamics is an intriguing path for further research. If demonstrated, it would deepen our understanding of colloidal dynamics. This knowledge is crucial in sectors like pharmaceuticals, food processing, and materials science.