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Taloni A, Flomenbom O, Castañeda-Priego R, Marchesoni F. Single file dynamics in soft materials. SOFT MATTER 2017; 13:1096-1106. [PMID: 28119987 DOI: 10.1039/c6sm02570f] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/06/2023]
Abstract
The term single file (SF) dynamics refers to the motion of an assembly of particles through a channel with cross-sections comparable to the particles' diameter. Single file diffusion (SFD) is then the diffusion of a tagged particle in a single file, i.e., under the condition that particle passing is not allowed. SFD accounts for a large variety of processes in nature, including diffusion of colloids in synthetic and natural channels, biological motors along molecular chains, electrons in proteins and liquid helium, ions through membranes, just to mention a few examples. Albeit introduced in 1965s, over the last decade the classical notion of SF dynamics has been generalised to account for a more realistic modelling of the particle properties, file geometry, particle-particle and channel-particle interactions, which paves the way to remarkable applications of the SF model, for instance, in the technology of bio-integrated nanodevices. We provide here a comprehensive review of the recent advances in the theory of SF dynamics with the purpose of spurring further experimental work.
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Affiliation(s)
- Alessandro Taloni
- Center for Complexity & Biosystems, Physics Department, University of Milan "La Statale", Via Giovanni Celoria 16, 20133 Milano, Italy and CNR-ISC - Center for Complex Systems, Via dei Taurini 19, 00185, Roma, Italy.
| | | | - Ramón Castañeda-Priego
- Division of Science and Engineering, University of Guanajuato, Loma del Bosque 103, Lomas del Campestre, 37150, Leon, Gto., Mexico
| | - Fabio Marchesoni
- Dipartimento di Fisica, Universitá di Camerino, I-62032 Camerino, Italy.
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Coste C, Delfau JB, Saint Jean M. Longitudinal and Transverse Single File Diffusion in Quasi-1D Systems. ACTA ACUST UNITED AC 2014. [DOI: 10.1142/s1793048014400025] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022]
Abstract
We review our recent results on Single File Diffusion (SFD) of a chain of particles that cannot cross each other, in a thermal bath, with long ranged interactions, and arbitrary damping. We exhibit new behaviors specifically associated to small systems and to small damping. The fluctuation dynamics is explained by the decomposition of the particles' motion in the normal modes of the chain. For longitudinal fluctuations, we emphasize the relevance of the soft mode linked to the translational invariance of the system to the long time SFD behavior. We show that close to the zigzag threshold, the transverse fluctuations also exhibit the SFD behavior, characterized by a mean square displacement that increases as the square root of time. This cannot be explained by the single file ordering, and the SFD behavior results from the strong correlation of the transverse displacements of neighbouring particles near the bifurcation. Extending our analytical modelization, we demonstrate the existence of this subdiffusive regime near the zigzag transition, in the thermodynamic limit. The zigzag transition is a supercritical pitchfork bifurcation, and we show that the transverse SFD behavior is closely linked to the vanishing of the frequency of the zigzag transverse mode at the bifurcation threshold. [Formula: see text] Special Issue Comments: This article presents mathematical results on the dynamics in files with longitudinal movements. This article is connected to the Special Issue articles about advanced statistical properties in single file dynamics,28 expanding files,63 and files with force and advanced formulations.29
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Affiliation(s)
- Christophe Coste
- Laboratoire "Matière et Systèmes Complexes" (MSC), UMR 7057 CNRS, Université Paris 7 Diderot, 75205 Paris Cedex 13, France
| | - Jean-Baptiste Delfau
- Laboratoire "Matière et Systèmes Complexes" (MSC), UMR 7057 CNRS, Université Paris 7 Diderot, 75205 Paris Cedex 13, France
| | - Michel Saint Jean
- Laboratoire "Matière et Systèmes Complexes" (MSC), UMR 7057 CNRS, Université Paris 7 Diderot, 75205 Paris Cedex 13, France
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Takeshi O, Goto S, Matsumoto T, Nakahara A, Otsuki M. Analytical calculation of four-point correlations for a simple model of cages involving numerous particles. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2013; 88:062108. [PMID: 24483387 DOI: 10.1103/physreve.88.062108] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/29/2013] [Indexed: 06/03/2023]
Abstract
Dynamics of a one-dimensional system of Brownian particles with short-range repulsive interaction (diameter σ) is studied with a liquid-theoretical approach. The mean square displacement, the two-particle displacement correlation, and the overlap-density-based generalized susceptibility are calculated analytically by way of the Lagrangian correlation of the interparticulate space, instead of the Eulerian correlation of density that is commonly used in the standard mode-coupling theory. In regard to the mean square displacement, the linear analysis reproduces the established result on the asymptotic subdiffusive behavior of the system. A finite-time correction is given by incorporating the effect of entropic nonlinearity with a Lagrangian version of mode-coupling theory. The notorious difficulty in derivation of the mode-coupling theory concerning violation of the fluctuation-dissipation theorem is found to disappear by virtue of the Lagrangian description. The Lagrangian description also facilitates analytical calculation of four-point correlations in the space-time, such as the two-particle displacement correlation. The two-particle displacement correlation, which is asymptotically self-similar in the space-time, illustrates how the cage effect confines each particle within a short radius on one hand and creates collective motion of numerous particles on the other hand. As the time elapses, the correlation length grows unlimitedly, and the generalized susceptibility based on the overlap density converges to a finite value which is an increasing function of the density. The distribution function behind these dynamical four-point correlations and its extension to three-dimensional cases, respecting the tensorial character of the two-particle displacement correlation, are also discussed.
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Affiliation(s)
- Ooshida Takeshi
- Department of Mechanical and Aerospace Engineering, Tottori University, Tottori 680-8552, Japan
| | - Susumu Goto
- Graduate School of Engineering Science, Osaka University, Toyonaka, Osaka 560-8531, Japan
| | - Takeshi Matsumoto
- Division of Physics and Astronomy, Graduate School of Science, Kyoto University, Kyoto 606-8502, Japan
| | - Akio Nakahara
- Laboratory of Physics, College of Science and Technology, Nihon University, Funabashi, Chiba 274-8501, Japan
| | - Michio Otsuki
- Department of Physics and Mathematics, Aoyama Gakuin University, Sagamihara, Kanagawa 229-8558, Japan
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Delfau JB, Coste C, Saint Jean M. Noisy zigzag transition, fluctuations, and thermal bifurcation threshold. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2013; 87:062135. [PMID: 23848655 DOI: 10.1103/physreve.87.062135] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/03/2013] [Indexed: 06/02/2023]
Abstract
We study the zigzag transition in a system of particles with screened electrostatic interaction, submitted to a thermal noise. At finite temperature, this configurational phase transition is an example of noisy supercritical pitchfork bifurcation. The measurements of transverse fluctuations allow a complete description of the bifurcation region, which takes place between the deterministic threshold and a thermal threshold beyond which thermal fluctuations do not allow the system to flip between the symmetric zigzag configurations. We show that a divergence of the saturation time for the transverse fluctuations allows a precise and unambiguous definition of this thermal threshold. Its evolution with the temperature is shown to be in good agreement with theoretical predictions from noisy bifurcation theory.
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Affiliation(s)
- Jean-Baptiste Delfau
- Laboratoire Matière et Systèmes Complexes (MSC), UMR 7057 CNRS, Université Paris 7 Diderot, 75205 Paris Cedex 13, France
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Ryabov A. Single-file diffusion in an interval: First passage properties. J Chem Phys 2013; 138:154104. [DOI: 10.1063/1.4801326] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Euán-Díaz EC, Misko VR, Peeters FM, Herrera-Velarde S, Castañeda-Priego R. Single-file diffusion in periodic energy landscapes: the role of hydrodynamic interactions. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2012; 86:031123. [PMID: 23030882 DOI: 10.1103/physreve.86.031123] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/04/2012] [Indexed: 06/01/2023]
Abstract
We report on the dynamical properties of interacting colloids confined to one dimension and subjected to external periodic energy landscapes. We particularly focus on the influence of hydrodynamic interactions on the mean-square displacement. Using Brownian dynamics simulations, we study colloidal systems with two types of repulsive interparticle interactions, namely, Yukawa and superparamagnetic potentials. We find that in the homogeneous case, hydrodynamic interactions lead to an enhancement of the particle mobility and the mean-square displacement at long times scales as t(α), with α=1/2+ε and ε being a small correction. This correction, however, becomes much more important in the presence of an external field, which breaks the homogeneity of the particle distribution along the line and, therefore, promotes a richer dynamical scenario due to the hydrodynamical coupling among particles. We provide here the complete dynamical scenario in terms of the external potential parameters: amplitude and commensurability.
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Affiliation(s)
- E C Euán-Díaz
- Division of Sciences and Engineering, University of Guanajuato, Loma del Bosque 103, Lomas del Campestre, 37150 León, Guanajuato, Mexico
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