1
|
Kalz E, Vuijk HD, Sommer JU, Metzler R, Sharma A. Oscillatory Force Autocorrelations in Equilibrium Odd-Diffusive Systems. PHYSICAL REVIEW LETTERS 2024; 132:057102. [PMID: 38364150 DOI: 10.1103/physrevlett.132.057102] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/02/2023] [Revised: 07/19/2023] [Accepted: 11/28/2023] [Indexed: 02/18/2024]
Abstract
The force autocorrelation function (FACF), a concept of fundamental interest in statistical mechanics, encodes the effect of interactions on the dynamics of a tagged particle. In equilibrium, the FACF is believed to decay monotonically in time, which is a signature of slowing down of the dynamics of the tagged particle due to interactions. Here, we analytically show that in odd-diffusive systems, which are characterized by a diffusion tensor with antisymmetric elements, the FACF can become negative and even exhibit temporal oscillations. We also demonstrate that, despite the isotropy, the knowledge of FACF alone is not sufficient to describe the dynamics: the full autocorrelation tensor is required and contains an antisymmetric part. These unusual properties translate into enhanced dynamics of the tagged particle quantified via the self-diffusion coefficient that, remarkably, increases due to particle interactions.
Collapse
Affiliation(s)
- Erik Kalz
- University of Potsdam, Institute of Physics and Astronomy, D-14476 Potsdam, Germany
| | - Hidde Derk Vuijk
- University of Augsburg, Institute of Physics, D-86159 Augsburg, Germany
| | - Jens-Uwe Sommer
- Leibniz-Institute for Polymer Research, Institute Theory of Polymers, D-01069 Dresden, Germany
- Technical University of Dresden, Institute for Theoretical Physics, D-01069 Dresden, Germany
- Technical University of Dresden, Cluster of Excellence Physics of Life, D-01069 Dresden, Germany
| | - Ralf Metzler
- University of Potsdam, Institute of Physics and Astronomy, D-14476 Potsdam, Germany
- Asia Pacific Centre for Theoretical Physics, KR-37673 Pohang, Republic of Korea
| | - Abhinav Sharma
- University of Augsburg, Institute of Physics, D-86159 Augsburg, Germany
- Leibniz-Institute for Polymer Research, Institute Theory of Polymers, D-01069 Dresden, Germany
| |
Collapse
|
2
|
Rusch R, Franosch T, Jung G. Noise-cancellation algorithm for simulations of Brownian particles. Phys Rev E 2024; 109:015303. [PMID: 38366417 DOI: 10.1103/physreve.109.015303] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/14/2023] [Accepted: 12/12/2023] [Indexed: 02/18/2024]
Abstract
We investigate the usage of a recently introduced noise-cancellation algorithm for Brownian simulations to enhance the precision of measuring transport properties such as the mean-square displacement or the velocity-autocorrelation function. The algorithm is based on explicitly storing the pseudorandom numbers used to create the randomized displacements in computer simulations and subtracting them from the simulated trajectories. The resulting correlation function of the reduced motion is connected to the target correlation function up to a cross-correlation term. Using analytical theory and computer simulations, we demonstrate that the cross-correlation term can be neglected in all three systems studied in this paper. We further expand the algorithm to Monte Carlo simulations and analyze the performance of the algorithm and rationalize that it works particularly well for unbounded, weakly interacting systems in which the precision of the mean-square displacement can be improved by orders of magnitude.
Collapse
Affiliation(s)
- Regina Rusch
- Institut für Theoretische Physik, Technikerstraße 21-A, Universität Innsbruck, A-6020 Innsbruck, Austria
| | - Thomas Franosch
- Institut für Theoretische Physik, Technikerstraße 21-A, Universität Innsbruck, A-6020 Innsbruck, Austria
| | - Gerhard Jung
- Laboratoire Charles Coulomb (L2C), Université de Montpellier, Centre National de la Recherche Scientifique, 34095 Montpellier, France
| |
Collapse
|
3
|
Hoang Ngoc Minh T, Stoltz G, Rotenberg B. Frequency and field-dependent response of confined electrolytes from Brownian dynamics simulations. J Chem Phys 2023; 158:104103. [PMID: 36922117 DOI: 10.1063/5.0139258] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/17/2023] Open
Abstract
Using Brownian dynamics simulations, we investigate the effects of confinement, adsorption on surfaces, and ion-ion interactions on the response of confined electrolyte solutions to oscillating electric fields in the direction perpendicular to the confining walls. Nonequilibrium simulations allows to characterize the transitions between linear and nonlinear regimes when varying the magnitude and frequency of the applied field, but the linear response, characterized by the frequency-dependent conductivity, is more efficiently predicted from the equilibrium current fluctuations. To that end, we (rederive and) use the Green-Kubo relation appropriate for overdamped dynamics, which differs from the standard one for Newtonian or underdamped Langevin dynamics. This expression highlights the contributions of the underlying Brownian fluctuations and of the interactions of the particles between them and with external potentials. Although already known in the literature, this relation has rarely been used to date, beyond the static limit to determine the effective diffusion coefficient or the DC conductivity. The frequency-dependent conductivity always decays from a bulk-like behavior at high frequency to a vanishing conductivity at low frequency due to the confinement of the charge carriers by the walls. We discuss the characteristic features of the crossover between the two regimes, most importantly how the crossover frequency depends on the confining distance and the salt concentration, and the fact that adsorption on the walls may lead to significant changes both at high and low frequencies. Conversely, our results illustrate the possibility to obtain information on diffusion between walls, charge relaxation, and adsorption by analyzing the frequency-dependent conductivity.
Collapse
Affiliation(s)
- Thê Hoang Ngoc Minh
- CNRS, Physicochimie des Électrolytes et Nanosystèmes Interfaciaux, Sorbonne Université, F-75005 Paris, France
| | | | - Benjamin Rotenberg
- CNRS, Physicochimie des Électrolytes et Nanosystèmes Interfaciaux, Sorbonne Université, F-75005 Paris, France
| |
Collapse
|
4
|
Feng M, Hou Z. Mode-coupling theory for the dynamics of dense underdamped active Brownian particle system. J Chem Phys 2023; 158:024102. [PMID: 36641396 DOI: 10.1063/5.0131080] [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
We present a theory to study the inertial effect on glassy dynamics of the underdamped active Brownian particle (UABP) system. Using the assumption of the nonequilibrium steady-state, we obtain an effective Fokker-Planck equation for the probability distribution function (PDF) as a function of positions and momentums. With this equation, we achieve the evolution equation of the intermediate scattering function through the Zwanzig-Mori projection operator method and the mode-coupling theory (MCT). Theoretical analysis shows that the inertia of the particle affects the memory function and corresponding glass transition by influencing the structure factor and a velocity correlation function. The theory provides theoretical support and guidance for subsequent simulation work.
Collapse
Affiliation(s)
- Mengkai Feng
- Hefei National Research Center for Physical Sciences at the Microscale and Department of Chemical Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
| | - Zhonghuai Hou
- Hefei National Research Center for Physical Sciences at the Microscale and Department of Chemical Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
| |
Collapse
|
5
|
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.
Collapse
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
| |
Collapse
|
6
|
Wittmann R, Löwen H, Brader JM. Order-preserving dynamics in one dimension – single-file diffusion and caging from the perspective of dynamical density functional theory. Mol Phys 2021. [DOI: 10.1080/00268976.2020.1867250] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/22/2022]
Affiliation(s)
- René Wittmann
- Institut für Theoretische Physik II: Weiche Materie, Heinrich-Heine-Universität Düsseldorf, Düsseldorf, Germany
| | - Hartmut Löwen
- Institut für Theoretische Physik II: Weiche Materie, Heinrich-Heine-Universität Düsseldorf, Düsseldorf, Germany
| | - Joseph M. Brader
- Department of Physics, University of Fribourg, Fribourg, Switzerland
| |
Collapse
|
7
|
Jung G, Schrack L, Franosch T. Tagged-particle dynamics in confined colloidal liquids. Phys Rev E 2020; 102:032611. [PMID: 33075887 DOI: 10.1103/physreve.102.032611] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/17/2020] [Accepted: 09/01/2020] [Indexed: 11/07/2022]
Abstract
We present numerical results for the tagged-particle dynamics by solving the mode-coupling theory in confined geometry for colloidal liquids (cMCT). We show that neither the microscopic dynamics nor the type of intermediate scattering function qualitatively changes the asymptotic dynamics in vicinity of the glass transition. In particular, we find similar characteristics of confinement in the low-frequency susceptibility spectrum which we interpret as footprints of parallel relaxation. We derive predictions for the localization length and the scaling of the diffusion coefficient in the supercooled regime and discover a pronounced nonmonotonic dependence on the confinement length. For dilute liquids in the hydrodynamic limit we calculate an analytical expression for the intermediate scattering functions, which is in perfect agreement with event-driven Brownian dynamics simulations. From this, we derive an expression for persistent anticorrelations in the velocity autocorrelation function (VACF) for confined motion. Using numerical results of the cMCT equations for the VACF we also identify a crossover between different scalings corresponding to a transition from unconfined to confined behavior.
Collapse
Affiliation(s)
- Gerhard Jung
- Institut für Theoretische Physik, Universität Innsbruck, A-6020 Innsbruck, Austria
| | - Lukas Schrack
- Institut für Theoretische Physik, Universität Innsbruck, A-6020 Innsbruck, Austria
| | - Thomas Franosch
- Institut für Theoretische Physik, Universität Innsbruck, A-6020 Innsbruck, Austria
| |
Collapse
|
8
|
Zhu K, Su H. Generalization of Langevin Dynamics from Spatio-Temporal Dressed Dynamics Perspective. J Phys Chem A 2020; 124:3269-3275. [PMID: 32162515 DOI: 10.1021/acs.jpca.0c00343] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
Understanding multiscale dynamics characteristics has been the holy grail in a broad range of scientific disciplines from physics, chemistry, to biology, and beyond. The seminal Langevin equation successfully unravels remarkable details of Brownian motion dynamics involving stochastic collisions from the fluidic medium. However, extraordinary phenomena beyond the scope of Langevin dynamics were observed to exhibit a series of multiscale dynamic features in recent years. Here, an explicit spatio-temporal coupled kernel is developed to provide the microscopic account for delicate dynamic coupling between particle and medium in the dressed dynamics perspective. This methodology is applied to investigate an aqueous solvation shell model with an explicit spatial boundary to illustrate the significance of spatial and temporal coupling, leading to a general temporal profile of dressed dynamics over 12 orders of magnitude in time In particular, the time-resolved viscosity is formulated to address the remarkable enhancement of viscosity measured by the liquid cell electron microscopy. The understanding of dressed dynamics processes will be greatly enriched by further studies on the detailed dynamics that manifests the microscopic inhomogeneity of medium.
Collapse
Affiliation(s)
- Kaicheng Zhu
- Department of Chemistry, The Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong
| | - Haibin Su
- Department of Chemistry, The Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong
| |
Collapse
|
9
|
Löwen H. Inertial effects of self-propelled particles: From active Brownian to active Langevin motion. J Chem Phys 2020; 152:040901. [DOI: 10.1063/1.5134455] [Citation(s) in RCA: 82] [Impact Index Per Article: 20.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/06/2023] Open
Affiliation(s)
- Hartmut Löwen
- Institut für Theoretische Physik II: Weiche Materie, Heinrich-Heine-Universität Düsseldorf, D-40225 Düsseldorf, Germany
| |
Collapse
|