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Saito T. Langevin analogy between particle trajectories and polymer configurations. Phys Rev E 2023; 107:034502. [PMID: 37072961 DOI: 10.1103/physreve.107.034502] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/08/2022] [Accepted: 03/02/2023] [Indexed: 04/20/2023]
Abstract
A diffusive trajectory drawn by the generalized Langevin equation (GLE) for a colloidal particle evokes a random fractal of a static polymer configuration. This article proposes a static GLE-like description that enables the generation of a single configuration of a polymer chain with the noise formulated to satisfy the static fluctuation-response relation (FRR) along a one-dimensional chain structure but not along a temporal coordinate. A remarkable point is qualitative differences and similarities in the FRR formulation between the static and the dynamic GLEs. Guided by the static FRR, we further make analogous arguments in light of stochastic energetics and the steady-state fluctuation theorem.
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Affiliation(s)
- Takuya Saito
- Department of Physical Sciences, Aoyama Gakuin University, Chuo-ku, Sagamihara 252-5258, Japan
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2
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Caspers J, Ditz N, Krishna Kumar K, Ginot F, Bechinger C, Fuchs M, Krüger M. How are mobility and friction related in viscoelastic fluids? J Chem Phys 2023; 158:024901. [PMID: 36641417 DOI: 10.1063/5.0129639] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/24/2022] Open
Abstract
The motion of a colloidal probe in a viscoelastic fluid is described by friction or mobility, depending on whether the probe is moving with a velocity or feeling a force. While the Einstein relation describes an inverse relationship valid for Newtonian solvents, both concepts are generalized to time-dependent memory kernels in viscoelastic fluids. We theoretically and experimentally investigate their relation by considering two observables: the recoil after releasing a probe that was moved through the fluid and the equilibrium mean squared displacement (MSD). Applying concepts of linear response theory, we generalize Einstein's relation and, thereby, relate recoil and MSD, which both provide access to the mobility kernel. With increasing concentration, however, MSD and recoil show distinct behaviors, rooted in different behaviors of the two kernels. Using two theoretical models, a linear two-bath particle model, and hard spheres treated by mode coupling theory, we find a Volterra relation between the two kernels, explaining differing timescales in friction and mobility kernels under variation of concentration.
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Affiliation(s)
- Juliana Caspers
- Institute for Theoretical Physics, Georg-August Universität Göttingen, 37077 Göttingen, Germany
| | - Nikolas Ditz
- Fachbereich Physik, Universität Konstanz, 78457 Konstanz, Germany
| | | | - Félix Ginot
- Fachbereich Physik, Universität Konstanz, 78457 Konstanz, Germany
| | | | - Matthias Fuchs
- Fachbereich Physik, Universität Konstanz, 78457 Konstanz, Germany
| | - Matthias Krüger
- Institute for Theoretical Physics, Georg-August Universität Göttingen, 37077 Göttingen, Germany
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3
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Relaxation, temporal diffusion, and polarity of aromatic hydrocarbons in ionic liquid. APPLIED NANOSCIENCE 2022. [DOI: 10.1007/s13204-022-02696-z] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/16/2022]
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4
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Saito T. Preaveraging description of polymer nonequilibrium stretching. Phys Rev E 2022; 105:014502. [PMID: 35193303 DOI: 10.1103/physreve.105.014502] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/01/2021] [Accepted: 11/26/2021] [Indexed: 11/07/2022]
Abstract
This article focuses on a preaveraging description of polymer nonequilibrium stretching, where a single polymer undergoes a transient process from equilibrium to nonequilibrium steady state by pulling one chain end. The preaveraging method combined with mode analysis reduces the original Langevin equation to a simplified form for both a stretched steady state and an equilibrium state, even in the presence of self-avoiding repulsive interactions spanning a long range. However, the transient stretching process exhibits evolution of a hierarchal regime structure, which means a qualitative temporal change in probabilistic distributions assumed in preaveraging. We investigate the preaveraging method for evolution of the regime structure with consideration of the nonequilibrium work relations and deviations from the fluctuation-dissipation relation.
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Affiliation(s)
- Takuya Saito
- Department of Physical Sciences, Aoyama Gakuin University, Chuo-ku, Sagamihara 252-5258, Japan
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Saito T. Projection of strong coupling interaction with thermal bath in a polymer. Phys Rev E 2022; 105:014501. [PMID: 35193307 DOI: 10.1103/physreve.105.014501] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/01/2021] [Accepted: 12/06/2021] [Indexed: 11/07/2022]
Abstract
We investigate modifications of a stochastic polymer picture through a shift in the boundary between the system and an external environment. A conventional bead-and-spring model serving as the coarse-graining model is given by the Langevin equation for all the monomers subject to white noise. However, stochastic motion for only a tagged monomer is observed to occur in the presence of colored noise. The qualitative change in the observations arises from the boundary shift decided by the observer. The Langevin dynamics analyses interpret the colored noise as the emergence of the polymeric elastic force, resulting in additional heat in the tagged monomer observation. Being distinguished from coarse-graining based on scale separation, the projection of comparable internal degrees of freedom is also discussed in light of the fluctuation theorem and the stochastic polymer thermodynamics.
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Affiliation(s)
- Takuya Saito
- Department of Physical Sciences, Aoyama Gakuin University, Chuo-ku, Sagamihara 252-5258, Japan
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Atamas N, Yablochkova K, Lazarenko M. Microscopic dynamics and the dynamic heterogeneity of motion of polar molecules in ionic liquids. J Mol Liq 2021. [DOI: 10.1016/j.molliq.2021.115900] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
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Atamas NA, Lazarenko MM, Yablochkova KS, Taranyik G. Strongly diluted dimethyl-imidazolium chloride–alcohol solutions: solvents are structurally different but dynamic heterogeneities are similar. RSC Adv 2021; 11:37307-37316. [PMID: 35496433 PMCID: PMC9043748 DOI: 10.1039/d1ra05633f] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/23/2021] [Accepted: 11/05/2021] [Indexed: 11/21/2022] Open
Abstract
Based on the analysis of dynamic properties of ionic liquid solutions, the descriptions of diffusion mechanisms are built for dimethylimidazolium chloride (dmim+/Cl−)–alcohol solute systems and the influence of the monohydric alcohols' molecular structure on their diffusion mechanisms in dmim+/Cl−–alcohol at T = 400 K by molecular dynamics simulations are studied. From the analysis of radial distribution functions, MSDs, velocity autocorrelation function, and autocorrelation functions of dispersion we found that the motion of all components in IL dmim+/Cl−–alcohol (ethanol, propanol) systems at T = 400 K occurs in the sub-diffuse regime and that the dynamics of the dmim+/Cl−–alcohol (ethanol, propanol) systems is heterogeneous. The increase of the alkyl chain length of the alcohol molecule does not affect the motion of the ionic liquid components; instead, it increases the characteristic times describing the model representation of alcohol molecule diffusion at short and medium times, without affecting diffusion mechanisms. The increase of the alkyl chain length of the alcohol molecule does not affect the motion of the ionic liquid components.![]()
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Affiliation(s)
- N. A. Atamas
- Taras Shevchenko National University of Kyiv, 64, Volodymyrska Street, Kyiv, UA 01601, Ukraine
| | - M. M. Lazarenko
- Taras Shevchenko National University of Kyiv, 64, Volodymyrska Street, Kyiv, UA 01601, Ukraine
| | - K. S. Yablochkova
- Taras Shevchenko National University of Kyiv, 64, Volodymyrska Street, Kyiv, UA 01601, Ukraine
| | - G. Taranyik
- International European University, 42V, Akademika Hlushkova Ave, Kyiv, Ukraine
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Mitterwallner BG, Lavacchi L, Netz RR. Negative friction memory induces persistent motion. THE EUROPEAN PHYSICAL JOURNAL. E, SOFT MATTER 2020; 43:67. [PMID: 33099707 DOI: 10.1140/epje/i2020-11992-5] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/25/2020] [Accepted: 09/30/2020] [Indexed: 06/11/2023]
Abstract
We investigate the mean-square displacement (MSD) for random motion governed by the generalized Langevin equation for memory functions that contain two different time scales: In the first model, the memory kernel consists of a delta peak and a single-exponential and in the second model of the sum of two exponentials. In particular, we investigate the scenario where the long-time exponential kernel contribution is negative. The competition between positive and negative friction memory contributions produces an enhanced transient persistent regime in the MSD, which is relevant for biological motility and active matter systems.
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Affiliation(s)
| | - Laura Lavacchi
- Fachbereich Physik, Freie Universität Berlin, 14195, Berlin, Germany
| | - Roland R Netz
- Fachbereich Physik, Freie Universität Berlin, 14195, Berlin, Germany
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Inferring Active Noise Characteristics from the Paired Observations of Anomalous Diffusion. Polymers (Basel) 2018; 11:polym11010002. [PMID: 30959986 PMCID: PMC6401841 DOI: 10.3390/polym11010002] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/22/2018] [Revised: 12/17/2018] [Accepted: 12/17/2018] [Indexed: 11/24/2022] Open
Abstract
Anomalous diffusion has been most often argued in terms of a position fluctuation of a tracer. We here propose the other fluctuating observable, i.e., momentum transfer defined as the time integral of applied force to hold a tracer’s position. Being a conjugated variable, the momentum transfer is thought of as generating the anomalous diffusion paired with the position’s one. By putting together the paired anomalous diffusions, we aim to extract useful information in complex systems, which can be applied to experiments like tagged monomer observations in chromatin. The polymer being in the equilibrium, the mean square displacement (or variance) of position displacement or momentum transfer exhibits the sub- or superdiffusion, respectively, in which the sum of the anomalous diffusion indices is conserved quite generally, but the nonequilibrium media that generate the active noise may manifest the derivations from the equilibrium relation. We discuss the deviations that reflect the characteristics of the active noise.
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Grimm J, Dolgushev M. Dynamics of networks in a viscoelastic and active environment. SOFT MATTER 2018; 14:1171-1180. [PMID: 29349466 DOI: 10.1039/c7sm02050c] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/07/2023]
Abstract
We investigate the dynamics of fractals and other networks in a viscoelastic and active environment. The viscoelastic dynamics is modeled based on the generalized Langevin equation, where the activity is introduced to it by means of the exponentially correlated noise. The intramolecular interactions are taken into account by the bead-spring picture. The microscopic connectivity (studied in the form of Vicsek fractals, of dual Sierpiński gaskets, of NTD trees, and of a family of deterministic small-world networks) reveals itself in the multiscale monomeric dynamics, which shows vastly different behaviors in the active and passive baths. In particular, the dynamics under active forces leads to a swelling that is characterized through power laws which are not present in the passive case. In all cases, the dynamics reflects the broad scaling behavior of the density of states and not necessarily the maximal relaxation time of the structures in a passive bath, as it is exemplified on the NTD trees.
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Affiliation(s)
- Jonas Grimm
- Institute of Physics, University of Freiburg, Hermann-Herder-Str. 3, D-79104 Freiburg, Germany.
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Saito T. Deviation from fluctuation-dissipation relation for driven superdiffusion: Polymer stretching as an example. Phys Rev E 2018; 96:032502. [PMID: 29347049 DOI: 10.1103/physreve.96.032502] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/26/2017] [Indexed: 11/07/2022]
Abstract
We discuss a deviation of the fluctuation-dissipation relation (FDR) in a driven superdiffusive system as exemplified by polymer stretching. The superdiffusion is found by monitoring momentum transfer to a tracer, which is a conjugate observable with the position. Molecular-dynamics simulation demonstrates that the FDR deviates during the nonequilibrium transient process. We then propose nonequilibrium mode analysis for superdiffusion, which is a counterpart to that for driven subdiffusion. The mode analysis yields results that are in qualitative agreement with the simulation results, suggesting that the fluctuations of the stiffness in the system from initial equilibrium to stretching account for the FDR deviation.
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Affiliation(s)
- Takuya Saito
- Earthquake Research Institute, University of Tokyo, Tokyo 113-0032, Japan
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