Anomalous Nanoparticle Surface Diffusion in Liquid Cell TEM is Revealed by Deep Learning-Assisted Analysis

Abstract

The motion of nanoparticles near surfaces is of fundamental importance in physics, biology, and chemistry. Liquid cell transmission electron microscopy (LCTEM) is a promising technique for studying motion of nanoparticles with high spatial resolution. Yet, the lack of understanding of how the electron beam of the microscope affects the particle motion has held back advancement in using LCTEM for in situ single nanoparticle and macromolecule tracking at interfaces. Here, we experimentally studied the motion of a model system of gold nanoparticles dispersed in water and moving adjacent to the silicon nitride membrane of a commercial liquid cell in a broad range of electron beam dose rates. We find that the nanoparticles exhibit anomalous diffusive behavior modulated by the electron beam dose rate. We characterized the anomalous diffusion of nanoparticles in LCTEM using a convolutional deep neural network model and canonical statistical tests. The results demonstrate that the nanoparticle motion is governed by fractional Brownian motion at low dose rates, resembling diffusion in a viscoelastic medium, and continuous time random walk at high dose rates, resembling diffusion on an energy landscape with pinning sites. Both behaviors can be explained by the presence of silanol molecular species on the surface of the silicon nitride membrane and the ionic species in solution formed by radiolysis of water in presence of the electron beam.

Anomalous diffusion, nonergodicity, and ageing for exponentially and logarithmically time-dependent diffusivity: striking differences for massive versus massless particles

“…Recently, a number of diffusion models of continuous-time random walk type [62][63][64][65][66][67][68][69][70][71][72][73], viscoelastic diffusion [10,[74][75][76], fractional BM [5,[77][78][79][80], some combinations of continuoustime random walk and fractional BM [81][82][83], diffusion based on the fractional Langevin equation [10,84], heterogeneous diffusion processes with the space-dependent diffusivity [85][86][87][88][89][90][91][92][93][94]…”

“…A number of single-trajectory-based algorithms of assessment-and-ranking and parameter-estimation of realizable models of diffusion for a data set of tracer positions (as recorded in single-particle-tracking experiments [153][154][155][156]) were developed [51,142,[157][158][159][160][161][162]. This list includes the recent Bayesian-statistics-based methods [51,142,163,165], machine-learning approaches [83,159,[166][167][168][169][170][171], concepts of recurrent neural networks [162], inference-based methods [158,161] and the spectral-density single-trajectory analysis [160]. We mention here the models with 'switching' between different types of (anomalous) diffusion (intermittent processes) [60,124,147,161,162,164,[172][173][174][175].…”