Non-Gaussian normal diffusion in low dimensional systems

Yin, Qingqing; Li, Yunyun; Marchesoni, F.; Nayak, Subhadip; Ghosh, Parthasarathi

doi:10.1007/s11467-020-1022-0

Cited by 9 publications

(3 citation statements)

References 64 publications

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“…[13][14][15] In liquids, however, a general theoretical description of the nanoparticle transport is still lacking, 16,17 despite the fact that considerable progress has been achieved over the past decades. [18][19][20] A particle moving in a fluid experiences a drag force, which governs the particle transport. 21 According to the Einstein relationship, the diffusion coefficient of a particle in a fluid is proportional to the drag force coefficient.…”

Section: Introductionmentioning

confidence: 99%

Drag on nanoparticles in a liquid: from slip to stick boundary conditions

Liu,

Wang,

Xia

et al. 2024

Nanoscale

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Section: Introductionmentioning

confidence: 99%

Drag on nanoparticles in a liquid: from slip to stick boundary conditions

Liu,

Wang,

Xia

et al. 2024

Nanoscale

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“…Microscopic models have also been proposed, where they have rigorously, mathematically studied interesting physical scenarios such as the study of diffusion of ellipsoidal particles, active particles, diffusion of colloidal particles in fluctuating corrugated channels, and Brownian motion in arrays of planar convective rolls [ 23 ]; non-Gaussian diffusion in static disordered media via a quenched trap model, where the diffusivity is spatially correlated [ 24 ]; and the Hitchhiker model [ 25 ].…”

Section: Introductionmentioning

confidence: 99%

A Novel Physical Mechanism to Model Brownian Yet Non-Gaussian Diffusion: Theory and Application

2022

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In the last years, a few experiments in the fields of biological and soft matter physics in colloidal suspensions have reported ”normal diffusion“ with a Laplacian probability distribution in the particle’s displacements (i.e., Brownian yet non-Gaussian diffusion). To model this behavior, different stochastic and microscopic models have been proposed, with the former introducing new random elements that incorporate our lack of information about the media and the latter describing a limited number of interesting physical scenarios. This incentivizes the search of a more thorough understanding of how the media interacts with itself and with the particle being diffused in Brownian yet non-Gaussian diffusion. For this reason, a comprehensive mathematical model to explain Brownian yet non-Gaussian diffusion that includes weak molecular interactions is proposed in this paper. Based on the theory of interfaces by De Gennes and Langevin dynamics, it is shown that long-range interactions in a weakly interacting fluid at shorter time scales leads to a Laplacian probability distribution in the radial particle’s displacements. Further, it is shown that a phase separation can explain a high diffusivity and causes this Laplacian distribution to evolve towards a Gaussian via a transition probability in the interval of time as it was observed in experiments. To verify these model predictions, the experimental data of the Brownian motion of colloidal beads on phospholipid bilayer by Wang et al. are used and compared with the results of the theory. This comparison suggests that the proposed model is able to explain qualitatively and quantitatively the Brownian yet non-Gaussian diffusion.

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“…Einstein’s theory of Brownian diffusion predicts that the displacement of a group of particles follows a Gaussian distribution, with the variance increasing linearly with time t. However, in materials close to the glass and jamming transitions, exponential decay of P ( x , t ) was observed. − Interestingly, the exponential decay of P ( x , t ) was found in a wide variety of scenarios: desorption-mediated diffusion on solid–liquid interfaces, − Brownian motion in polymer solutions, , cellular environments, − active systems, heterogeneously crowded and confined media, − and even the fluctuations of price–time series in the stock market . Well-designed theories and simulations have been put forward to rationalize the appearance of the exponential tail, such as the “diffusing diffusivity” model, − superstatistical approaches, − the quenched trap model, − and the hitchhiker-type model. − More recently, the large deviation theory was applied to a continuous-time random walk (CTRW) model to describe the exponential decay of P ( x , t ). A CTRW process comprises intermittent switching between random immobile trapping periods and jumping steps. − The trapping duration dictates the random fluctuations in the number of displacement steps at a given t , which leads to an exponential decay of P ( x , t ). ,, …”

mentioning

confidence: 99%

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

Hu,

Chen,

Wang

et al. 2023

ACS Nano

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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.

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Non-Gaussian normal diffusion in low dimensional systems

Cited by 9 publications

References 64 publications

Drag on nanoparticles in a liquid: from slip to stick boundary conditions

Drag on nanoparticles in a liquid: from slip to stick boundary conditions

A Novel Physical Mechanism to Model Brownian Yet Non-Gaussian Diffusion: Theory and Application

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

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