Triggering Gaussian-to-Exponential Transition of Displacement Distribution in Polymer Nanocomposites via Adsorption-Induced Trapping

Abstract

In many disordered systems, the diffusion of classical particles is described by a displacement distribution P(x, t) that displays exponential tails instead of Gaussian statistics expected for Brownian motion. However, the experimental demonstration of control of this behavior by increasing the disorder strength has remained challenging. In this work, we explore the Gaussian-to-exponential transition by using diffusion of poly­(ethylene glycol) (PEG) in attractive nanoparticle–polymer mixtures and controlling the volume fraction of the nanoparticles. In this work, we find “knobs”, namely nanoparticle concentration and interaction, which enable the change in the shape of P(x,t) in a well-defined way. The Gaussian-to-exponential transition is consistent with a modified large deviation approach for a continuous time random walk and also with Monte Carlo simulations involving a microscopic model of polymer trapping via reversible adsorption to the nanoparticle surface. Our work bears significance in unraveling the fundamental physics behind the exponential decay of the displacement distribution at the tails, which is commonly observed in soft materials and nanomaterials.

Nanorod Diffusion near the Solid–Liquid Interface with Varied Wall Nonuniformity

“…In our work, the adsorption and desorption behaviors of NRs, primarily controlled by their interaction with patterned surfaces, triggers CTRW motion through the capture of particles by surface adsorption. This phenomenon, similar to those reported in , is also responsible for the transition of the PDFs from Gaussian to exponential decay. During the entirety of the adsorption–desorption process, the trajectories of the NRs contain both capture-induced CTRW motion and Brownian motion upon entering the bulk solution, with the tail of the PDFs still following an exponential distribution despite only a portion of the NRs conforming to CTRW statistics (Figure ).…”

“…30,50 A CTRW process involves intermittent switching between randomly fixed capture cycles and jumping steps. 51,52 The duration of adsorption dictates the stochastic fluctuation in the number of displacement steps at a given time t, resulting in an exponential decay of PDFs. 53 In our work, the adsorption and desorption behaviors of NRs, primarily controlled by their interaction with patterned surfaces, triggers CTRW motion through the capture of particles by surface adsorption.…”

Laplace’s first law of errors applied to diffusive motion

“…An opposing comment was quickly raised by Berthier et al [87]. The phenomenon, particularly the non-trivial exponent 1/3, was observed in several other experiments [17,24,25,58]. More specifically, in Ref.…”

“…More specifically, in Ref. [58], experimental data were successfully fitted using the CTRW model. At the same time, one can fit the data with a scaling function λ(t).…”

“…The connection between Laplace diffusion and CTRW in polymer nanocomposites was further explored by Hu et al [58]. They demonstrated the ability to manipulate the emergence of exponential tails in contrast to Gaussian diffusion by modifying the strength of the disorder.…”