Colloidal dynamics over a tilted periodic potential: Nonequilibrium steady-state distributions

Ma, Xiaoguang; Lai, Pik‐Yin; Ackerson, Bruce J.; Tong, Penger

doi:10.1103/physreve.91.042306

Cited by 15 publications

(18 citation statements)

References 55 publications

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“…The measured v(F,E b ) and D(F,E b ) agree well with the exact results of the 1D drift velocity [28] and diffusion coefficient [6,29]. Furthermore, for a tilted periodic potential, we measured the NESS probability density function (NESS-PDF) P ss (x,y), which deviates from the equilibrium distribution P B (x,y) to a different extent, depending on the driving or distance from equilibrium [30].…”

Section: Introductionsupporting

confidence: 80%

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Colloidal dynamics over a tilted periodic potential: Forward and reverse transition probabilities and entropy production in a nonequilibrium steady state

Lai

et al. 2017

Phys. Rev. E

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We report a systematic study of the forward and reverse transition probability density functions (TPDFs) and entropy production in a nonequilibrium steady state (NESS). The NESS is realized in a two-layer colloidal system, in which the bottom-layer colloidal crystal provides a two-dimensional periodic potential U_{0}(x,y) for the top-layer diffusing particles. By tilting the sample at an angle with respect to gravity, a tangential component of the gravitational force F is applied to the diffusing particles, which breaks the detailed balance (DB) condition and generates a steady particle flux along the [1,0] crystalline orientation. While both the measured forward and reverse TPDFs reveal interesting space-time dependence, their ratio is found to be independent of time and obeys a DB-like relation. The experimental results are in good agreement with the theoretical predictions. This study thus provides a better understanding on how entropy is generated and heat is dissipated to the reservoir during a NESS transition process. It also demonstrates the applications of the two-layer colloidal system in the study of NESS transition dynamics.

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Section: Introductionsupporting

confidence: 80%

“…In this case, the DB condition is expected to be broken; i.e., P ss (x 1 ) (x 1 ,x 2 ,τ ) = P ss (x 2 ) (x 2 ,x 1 ,τ ). It was shown in a previous study [30] that the steady-state distribution P ss (x) in the periodic potential U 0 (x) has a non-Boltzmann form,…”

Section: Theorymentioning

confidence: 99%

Colloidal dynamics over a tilted periodic potential: Forward and reverse transition probabilities and entropy production in a nonequilibrium steady state

Lai

et al. 2017

Phys. Rev. E

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“…We describe the origin of this energy landscape later in the paper, but for now we say that it is V(x) = 0.5ΔE sin(2πx/ b), where ΔE is the activation energy barrier and b is the bead size (the corrugation length). With this assumption, the diffusivity becomes 34,35 …”

mentioning

confidence: 99%

Jamming of Knots along a Tensioned Chain

2016

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ABSTRACT:We examine the motion of a knot along a tensioned chain whose backbone is corrugated due to excluded volume effects. At low applied tensions, the knot traverses the chain diffusively, while at higher tensions the knot makes slow, discrete hops that can be described as a Poisson process. In this "jammed" regime, the knot's long-time diffusivity decreases exponentially with increasing tension. We quantify how these measurements are altered by chain rigidity and the corrugation of the polymer backbone. We also characterize the energy barrier of the reptation moves that gives rise to the knot's motion. For the simple knot types examined thus far (3 1 , 4 1 , 5 1 , 5 2 ), the dominant contribution to the energy landscape appears in the first step of reptationi.e., polymer entering the knotted core. We hope this study gives insight into what physics contributes to the internal friction of highly jammed knots. E ver since the discovery of knots in DNA, 1−3 there has been immense interest in understanding how these structures affect the mechanical and dynamical properties of these molecules. 4 A knot is defined as a self-entanglement that cannot be undone when the polymer chain is closed. 5 The topology of a knot is well-defined as long as it is far from the ends of a polymer chain, and the topology can be determined by closing the chain and then computing Alexander polynomials.6 Experimentally, knots have been tied onto DNA 7 and actin 8 filaments via optical traps, and chemical synthesis techniques have been developed to create knotted loops up to five crossings. 9 Recently, researchers have also determined facile methods to create knotted DNA via an electric field, 10,11 and this work has led to microfluidic experiments examining how the coil−stretch transition is affected by the presence of knots. 12In some sense, knots are unavoidable for very long polymeric chains, as it has been proven that the knotting probability approaches unity as the chain size gets very large.13,14 Indeed, knots have been found in capsid DNA, 1 proteins, 15−17 and other biological systems.4 Bao et al. discovered that knots can self-reptate along a polymer contour due to thermal fluctuations.7 This discovery has led several computational studies to quantify the knot's motion along a chain, whether it be convection due to a directed force 18−20 or diffusion under uniform tension. 21−23 In most of these studies, the tension on the polymer is comparable to or smaller than the Brownian forcesi.e., f ∼ O(kT/l p ) or smaller, where kT is the thermal energy and l p is the persistence length of the chain. However, it is known that at large tensions knots can dynamically arrest this has been observed for knots jamming during translocation through a nanopore. 24−27 Huang and Makarov briefly study jamming in their simulations, 23 positing that the knot's arrest is caused by the "bumpiness of the energy landscape of the knot created by intrachain interactions". We explore this topic in this Letter. We note that this area of research is of ...

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“…The particles' effective diffusivity peaks at a critical value of the tilt, where it attains a value that can exceed the diffusivity in a uniform potential, D 0 , by orders of magnitude. GAD has been observed in such varied systems as trapped particles circling corrugated optical vortices [3], colloidal spheres moving across an undulating surface tilted in a gravitational field [4], and the rotating F 1 -ATPase protein motor [5]. It is theoretically predicted that Brownian particles conveyed across entropic barriers can exhibit GAD [6][7][8]; however, this has not been shown experimentally.…”

mentioning

confidence: 95%