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Jin S, Fan X, Stamper C, Mole RA, Yu Y, Hong L, Yu D, Baggioli M. On the temperature dependence of the density of states of liquids at low energies. Sci Rep 2024; 14:18805. [PMID: 39138323 PMCID: PMC11322638 DOI: 10.1038/s41598-024-69504-2] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/24/2024] [Accepted: 08/06/2024] [Indexed: 08/15/2024] Open
Abstract
We report neutron-scattering measurements of the density of states (DOS) of water and liquid Fomblin in a wide range of temperatures. In the liquid phase, we confirm the presence of a universal low-energy linear scaling of the experimental DOS as a function of the frequency, g ( ω ) = a ( T ) ω , which persists at all temperatures. The low-frequency scaling of the DOS exhibits a sharp jump at the melting point of water, below which the standard Debye's law, g ( ω ) ∝ ω 2 , is recovered. On the contrary, in Fomblin, we observe a continuous transition between the two exponents reflecting its glassy dynamics, which is confirmed by structure measurements. More importantly, in both systems, we find that the slope a(T) grows with temperature following an exponential Arrhenius-like form, a ( T ) ∝ exp ( - ⟨ E ⟩ / T ) . We confirm this experimental trend using molecular dynamics simulations and show that the prediction of instantaneous normal mode (INM) theory for a(T) is in qualitative agreement with the experimental data.
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Affiliation(s)
- Sha Jin
- School of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai, 200240, China
- Wilczek Quantum Center, Shanghai Jiao Tong University, Shanghai, 200240, China
- Shanghai Research Center for Quantum Sciences, Shanghai, 201315, China
| | - Xue Fan
- Shanghai National Center for Applied Mathematics, Shanghai Jiao Tong University, Shanghai, 200240, China
- Materials Genome Institute, Shanghai University, Shanghai, 200444, China
- School of Materials Science and Engineering, Georgia Institute of Technology, Atlanta, GA, 30332, USA
| | - Caleb Stamper
- Institute for Superconducting and Electronic Materials, University of Wollongong, Wollongong, NSW, 2500, Australia
- The Australian Nuclear Science and Technology Organisation, Lucas Heights, NSW, 2232, Australia
| | - Richard A Mole
- The Australian Nuclear Science and Technology Organisation, Lucas Heights, NSW, 2232, Australia
| | - Yuanxi Yu
- School of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai, 200240, China
| | - Liang Hong
- School of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai, 200240, China
- Shanghai National Center for Applied Mathematics, Shanghai Jiao Tong University, Shanghai, 200240, China
- Institute of Natural Sciences, Shanghai Jiao Tong University, Shanghai, 200240, China
| | - Dehong Yu
- The Australian Nuclear Science and Technology Organisation, Lucas Heights, NSW, 2232, Australia.
| | - Matteo Baggioli
- School of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai, 200240, China.
- Wilczek Quantum Center, Shanghai Jiao Tong University, Shanghai, 200240, China.
- Shanghai Research Center for Quantum Sciences, Shanghai, 201315, China.
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2
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Xu H, Baggioli M, Keyes T. A fresh look at the vibrational and thermodynamic properties of liquids within the soft potential model. J Chem Phys 2023; 159:154501. [PMID: 37846955 DOI: 10.1063/5.0158089] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/15/2023] [Accepted: 10/02/2023] [Indexed: 10/18/2023] Open
Abstract
Contrary to the case of solids and gases, where Debye theory and kinetic theory offer a good description for most of the physical properties, a complete theoretical understanding of the vibrational and thermodynamic properties of liquids is still missing. Liquids exhibit a vibrational density of states (VDOS) which does not obey Debye law, and a heat capacity which decreases monotonically with temperature, rather than growing as in solids. Despite many attempts, a simple, complete and widely accepted theoretical framework able to formally derive the aforementioned properties has not been found yet. Here, we revisit one of the theoretical proposals, and in particular we re-analyze the properties of liquids within the soft-potential model, originally formulated for glasses. We confirm that, at least at a qualitative level, many characteristic properties of liquids can be rationalized within this model. We discuss the validity of several phenomenological expressions proposed in the literature for the density of unstable modes, and in particular for its temperature and frequency dependence. We discuss the role of negative curvature regions and unstable modes as fundamental ingredients to have a linear in frequency VDOS. Finally, we compute the heat capacity within the soft potential model for liquids and we show that it decreases with temperature, in agreement with experimental and simulation data.
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Affiliation(s)
- Haichen Xu
- University of Michigan-Shanghai Jiao Tong University Joint Institute, Shanghai Jiao Tong University, Shanghai 200240, China
- Wilczek Quantum Center, School of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai 200240, China
- Shanghai Research Center for Quantum Sciences, Shanghai 201315, China
| | - Matteo Baggioli
- Wilczek Quantum Center, School of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai 200240, China
- Shanghai Research Center for Quantum Sciences, Shanghai 201315, China
| | - Tom Keyes
- Chemistry Department, Boston University, Boston, Massachusetts 02215, USA
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3
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Teramoto T, Ohoyama H. Evidence of Direct Dissolution of CO 2 into the Ionic Liquid [C 4min] [NTf 2] during Their Initial Interaction. J Phys Chem B 2020; 124:8331-8339. [PMID: 32856912 DOI: 10.1021/acs.jpcb.0c05172] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
Ionic liquids (ILs) are known for their high ability to capture CO2. However, the mechanism of CO2 solubility into ILs during their initial interaction remains controversial. In this study, we analyzed the initial dissolution of CO2 into an IL 1-butyl-3-methylimidazolium bis-(trifluoromethylsulfonyl)imide ([C4min] [NTf2]) by measuring its solubility using a combination of a molecular beam and a flowing liquid jet sheet beam (FJSB) and the King and Wells method (KW method). The temperature dependence of the initial dissolution probability indicates that the solubility of CO2 in the IL [C4min] [NTf2] increases with increasing temperature. This result is not consistent with what has been reported in an equilibrium state. The initial dissolution probability was well-fitted by the Vogel-Fulcher-Tammann (VFT) equation, which describes the dynamical cage structure in IL systems. We also find that the initial dissolution probability was correlated to the cage lifetime and correlation length. The simple model of CO2 dissolution into an IL with the cage model was implemented to explain the experimental results in this study. Our results indicate that the initial dissolution of CO2 into the IL corresponds to a direct solution and not an uptake process.
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Affiliation(s)
- Takahiro Teramoto
- Institute for Radiation Sciences, Osaka University, 1-1 Machikaneyama, Toyonaka, Osaka 560-0043, Japan
| | - Hiroshi Ohoyama
- Department of Chemistry, Graduate School of Science, Osaka University, 1-1 Machikaneyama, Toyonaka, Osaka 560-0043, Japan
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Sha M, Ma X, Li N, Luo F, Zhu G, Fayer MD. Dynamical properties of a room temperature ionic liquid: Using molecular dynamics simulations to implement a dynamic ion cage model. J Chem Phys 2019; 151:154502. [PMID: 31640381 DOI: 10.1063/1.5126231] [Citation(s) in RCA: 10] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/16/2022] Open
Abstract
The transport behavior of ionic liquids (ILs) is pivotal for a variety of applications, especially when ILs are used as electrolytes. Many aspects of the transport dynamics of ILs remain to be understood. Here, a common ionic liquid, 1-butyl-3-methylimidazolium bis(trifluoromethylsulfonyl)imide (BmimNTf2), was studied with molecular dynamics simulations. The results show that BmimNTf2 displays typical structural relaxation, subdiffusive behavior, and a breakdown of the Stokes-Einstein diffusion relation as in glass-forming liquids. In addition, the simulations show that the translational dynamics, reorientation dynamics, and structural relaxation dynamics are well described by the Vogel-Fulcher-Tammann equation like fragile glass forming liquids. Building on previous work that employed ion cage models, it was found that the diffusion dynamics of the cations and anions were well described by a hopping process random walk where the step time is the ion cage lifetime obtained from the cage correlation function. Detailed analysis of the ion cage structures indicated that the electrostatic potential energy of the ion cage dominates the diffusion dynamics of the caged ion. The ion orientational relaxation dynamics showed that ion reorientation is a necessary step for ion cage restructuring. The dynamic ion cage model description of ion diffusion presented here may have implications for designing ILs to control their transport behavior.
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Affiliation(s)
- Maolin Sha
- Department of Physics and Materials Engineering, Hefei Normal University, Hefei 230061, China
| | - Xiaohang Ma
- Department of Physics and Materials Engineering, Hefei Normal University, Hefei 230061, China
| | - Na Li
- Department of Chemistry and Chemical Engineering, Hefei Normal University, Hefei 230061, China
| | - Fabao Luo
- Department of Chemistry and Chemical Engineering, Hefei Normal University, Hefei 230061, China
| | - Guanglai Zhu
- Institute of Atomic and Molecular Physics, Anhui Normal University, Wuhu 241000, China
| | - Michael D Fayer
- Department of Chemistry, Stanford University, Stanford, California 94305, USA
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5
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Higler R, Krausser J, van der Gucht J, Zaccone A, Sprakel J. Linking slow dynamics and microscopic connectivity in dense suspensions of charged colloids. SOFT MATTER 2018; 14:780-788. [PMID: 29302676 DOI: 10.1039/c7sm01781b] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/07/2023]
Abstract
The quest to unravel the nature of the glass transition, where the viscosity of a liquid increases by many orders of magnitude, while its static structure remains largely unaffected, remains unresolved. While various structural and dynamical precursors to vitrification have been identified, a predictive and quantitative description of how subtle changes at the microscopic scale give rise to the steep growth in macroscopic viscosity is missing. It was recently proposed that the presence of long-lived bonded structures within the liquid may provide the long-sought connection between local structure and global dynamics. Here we directly observe and quantify the connectivity dynamics in liquids of charged colloids en route to vitrification using three-dimensional confocal microscopy. We determine the dynamic structure from the real-space van Hove correlation function and from the particle trajectories, providing upper and lower bounds on connectivity dynamics. Based on these data, we extend Dyre's model for the glass transition to account for particle-level structural dynamics; this results in a microscopic expression for the slowing down of relaxations in the liquid that is in quantitative agreement with our experiments. These results indicate how vitrification may be understood as a dynamical connectivity transition with features that are strongly reminiscent of rigidity percolation scenarios.
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Affiliation(s)
- Ruben Higler
- Physical Chemistry and Soft Matter, Wageningen University & Research, Stippeneng 4, Wageningen, The Netherlands.
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6
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Niblett SP, Biedermann M, Wales DJ, de Souza VK. Pathways for diffusion in the potential energy landscape of the network glass former SiO 2. J Chem Phys 2017; 147:152726. [PMID: 29055343 DOI: 10.1063/1.5005924] [Citation(s) in RCA: 17] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/23/2022] Open
Abstract
We study the dynamical behaviour of a computer model for viscous silica, the archetypal strong glass former, and compare its diffusion mechanism with earlier studies of a fragile binary Lennard-Jones liquid. Three different methods of analysis are employed. First, the temperature and time scale dependence of the diffusion constant is analysed. Negative correlation of particle displacements influences transport properties in silica as well as in fragile liquids. We suggest that the difference between Arrhenius and super-Arrhenius diffusive behaviour results from competition between the correlation time scale and the caging time scale. Second, we analyse the dynamics using a geometrical definition of cage-breaking transitions that was proposed previously for fragile glass formers. We find that this definition accurately captures the bond rearrangement mechanisms that control transport in open network liquids, and reproduces the diffusion constants accurately at low temperatures. As the same method is applicable to both strong and fragile glass formers, we can compare correlation time scales in these two types of systems. We compare the time spent in chains of correlated cage breaks with the characteristic caging time and find that correlations in the fragile binary Lennard-Jones system persist for an order of magnitude longer than those in the strong silica system. We investigate the origin of the correlation behaviour by sampling the potential energy landscape for silica and comparing it with the binary Lennard-Jones model. We find no qualitative difference between the landscapes, but several metrics suggest that the landscape of the fragile liquid is rougher and more frustrated. Metabasins in silica are smaller than those in binary Lennard-Jones and contain fewer high-barrier processes. This difference probably leads to the observed separation of correlation and caging time scales.
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Affiliation(s)
- S P Niblett
- University Chemical Laboratories, Lensfield Road, Cambridge CB2 1EW, United Kingdom
| | - M Biedermann
- Institute of Physical Chemistry, University of Muenster, Corrensstraße 28/30, 48149 Muenster, Germany
| | - D J Wales
- University Chemical Laboratories, Lensfield Road, Cambridge CB2 1EW, United Kingdom
| | - V K de Souza
- University Chemical Laboratories, Lensfield Road, Cambridge CB2 1EW, United Kingdom
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7
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Shi R, Wang Y. Ion-Cage Interpretation for the Structural and Dynamic Changes of Ionic Liquids under an External Electric Field. J Phys Chem B 2013; 117:5102-12. [DOI: 10.1021/jp311017r] [Citation(s) in RCA: 46] [Impact Index Per Article: 4.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/05/2023]
Affiliation(s)
- Rui Shi
- State Key Laboratory of Theoretical
Physics, Institute
of Theoretical Physics, Chinese Academy of Sciences, 55 East Zhongguancun Road, P.O. Box 2735, Beijing 100190, China
| | - Yanting Wang
- State Key Laboratory of Theoretical
Physics, Institute
of Theoretical Physics, Chinese Academy of Sciences, 55 East Zhongguancun Road, P.O. Box 2735, Beijing 100190, China
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8
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de Souza VK, Wales DJ. Connectivity in the potential energy landscape for binary Lennard-Jones systems. J Chem Phys 2009; 130:194508. [DOI: 10.1063/1.3131690] [Citation(s) in RCA: 46] [Impact Index Per Article: 3.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
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10
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de Souza VK, Wales DJ. Energy landscapes for diffusion: Analysis of cage-breaking processes. J Chem Phys 2008; 129:164507. [DOI: 10.1063/1.2992128] [Citation(s) in RCA: 76] [Impact Index Per Article: 4.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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11
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Klähn M, Seduraman A, Wu P. A Model for Self-Diffusion of Guanidinium-Based Ionic Liquids: A Molecular Simulation Study. J Phys Chem B 2008; 112:13849-61. [DOI: 10.1021/jp8048845] [Citation(s) in RCA: 27] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/21/2022]
Affiliation(s)
- Marco Klähn
- Institute of High Performance Computing, 1 Fusionopolis Way #16-16, Connexis, Singapore 138632
| | - Abirami Seduraman
- Institute of High Performance Computing, 1 Fusionopolis Way #16-16, Connexis, Singapore 138632
| | - Ping Wu
- Institute of High Performance Computing, 1 Fusionopolis Way #16-16, Connexis, Singapore 138632
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12
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Abstract
We applied the quantum path integral Monte Carlo method for the study of (para-H)N (N = 5-33) clusters at T = 2 K, exploring static and dynamic order, which originates from the effects of zero-point energy, kinetic energy, and thermal fluctuations in quantum clusters. Information on dynamic structure was inferred from the asymptotic tails of the cage correlation function calculated from the centroid Monte Carlo trajectory. The centroid cage correlation function decays to zero for large clusters (N = 15-33), manifesting the interchange of molecules between different solvation shells, with statistically diminishing back interchange. Further evidence for the floppiness of para-hydrogen clusters emerges from the Monte Carlo evolution of the centroid of a tagged molecule, which exhibits significant changes in the list of its first and second solvation shells due to the interchange of molecules between these shells.
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Affiliation(s)
- Eran Rabani
- School of Chemistry, The Sackler Faculty of Exact Sciences, Tel Aviv University, Tel Aviv 69978, Israel.
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13
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Magro A, Frezzato D, Polimeno A, Moro GJ, Chelli R, Righini R. Dynamics of liquid benzene: A cage analysis. J Chem Phys 2005; 123:124511. [PMID: 16392501 DOI: 10.1063/1.2018629] [Citation(s) in RCA: 12] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Dynamics of single molecules in liquids, inspected in the picosecond time scale by means of spectroscopic measurements or molecular-dynamics (MD) simulations, reveals a complex behavior which can be addressed as due to local confinement (cage). This work is devoted to the analysis of cage structures in liquid benzene, obtained from MD simulations. According to a paradigm proposed for previous analysis of atomic and molecular liquids [see, for example, A. Polimeno, G. J. Moro, and J. H. Freed, J. Chem. Phys. 102, 8094 (1995)], the istantaneous cage structure is specified by the frame of axes which identifies the molecular configuration at the closest minimum on the potential-energy landscape. In addition, the modeling of the interaction potential between probe molecule and molecular environment, based on symmetry considerations, and its parametrization from the MD trajectories, allows the estimation of the structural parameters which quantify the strength of molecular confinement. Roto-translational dynamics of probe and related cage with respect to a laboratory frame, dynamics of the probe within the cage (vibrations, librations, re-orientational motions), and the restructuring processes of the cage itself are analyzed in terms of selected time self-correlation functions. A time-scale separation between the processes is established. Moreover, by exploiting the evidence of fast vibrational motions of the probe with respect to the cage center, an orientational effective potential is derived to describe the caging in the time scale longer than approximately 0.2 ps.
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Affiliation(s)
- Andrea Magro
- Dipartimento di Scienze Chimiche, Università degli Studi di Padova, Via Marzolo 1, I-35131 Padova, Italy
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14
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Vollmayr-Lee K. Single particle jumps in a binary Lennard-Jones system below the glass transition. J Chem Phys 2004; 121:4781-94. [PMID: 15332912 DOI: 10.1063/1.1778155] [Citation(s) in RCA: 63] [Impact Index Per Article: 3.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We study a binary Lennard-Jones system below the glass transition with molecular dynamics simulations. To investigate the dynamics we focus on events (jumps) where a particle escapes the cage formed by its neighbors. Using single particle trajectories we define a jump by comparing for each particle its fluctuations with its changes in average position. We find two kinds of jumps: "reversible jumps," where a particle jumps back and forth between two or more average positions, and "irreversible jumps," where a particle does not return to any of its former average positions, i.e., successfully escapes its cage. For all investigated temperatures both kinds of particles jump and both irreversible and reversible jumps occur. With increasing temperature, relaxation is enhanced by an increasing number of jumps and growing jump lengths in position and potential energy. However, the waiting time between two successive jumps is independent of temperature. This temperature independence might be due to aging, which is present in our system. We therefore also present a comparison of simulation data with three different histories. The ratio of irreversible to reversible jumps is also increasing with increasing temperature, which we interpret as a consequence of the increased likelihood of changes in the cages, i.e., a blocking of the "entrance" back into the previous cage. In accordance with this interpretation, the fluctuations both in position and energy are increasing with increasing temperature. A comparison of the fluctuations of jumping particles and nonjumping particles indicates that jumping particles are more mobile even when not jumping. The jumps in energy normalized by their fluctuations are decreasing with increasing temperature, which is consistent with relaxation being increasingly driven by thermal fluctuations. In accordance with subdiffusive behavior are the distributions of waiting times and jump lengths in position.
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Affiliation(s)
- K Vollmayr-Lee
- Department of Physics, Bucknell University, Lewisburg, Pennsylvania 17837, USA.
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15
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Witkoskie JB, Yang S, Cao J. Brownian motion in dynamically disordered media. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2002; 66:051111. [PMID: 12513471 DOI: 10.1103/physreve.66.051111] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/22/2002] [Revised: 08/12/2002] [Indexed: 05/24/2023]
Abstract
The motion of Brownian test particles in a model random potential with time dependent correlations is investigated using four methods: renormalized perturbation, perturbation using Martin, Siggia, and Rose functional formalism (MSR), the Edwards variational method on the MSR functional, and renormalization group with the MSR function. The disorder averaged one-particle propagators determined by the renormalized perturbation expansion and MSR perturbation expansion are identical to the second and possibly higher order, and the two-particle propagators determined by these perturbation methods are identical at the first and possibly higher order. The one-particle propagator determined by the Edwards method is identical to the perturbation expansions at the first order, but the second-order analogue of the Edwards method has a more complex expression, which reduces to the second-order perturbation expression with additional higher-order terms. The diffusion constant and two-particle correlations are calculated from these propagators and are used to determine the effects of the random potential on the Brownian particles. Generally, the diffusion rate decreases with the disorder strength and increases with the temporal decay rate. The two competing mechanisms result in an enhancement of the diffusion constant for weak potentials with fast temporal fluctuations. The system exhibits two-particle correlations that are inherently non-Gaussian and indicate clustering behavior. The diffusion constant is also determined from a simple one-loop renormalization group calculation. In the static limit, the diffusion constant calculated by the renormalization group recovers the results of Deem and Chandler [M.W. Deem and D. Chandler, J. Stat. Phys. 76, 911 (1994)].
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Affiliation(s)
- James B Witkoskie
- Department of Chemistry, Massachusetts Institute of Technology, Cambridge 02139, USA
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16
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Berezhkovskii AM, Sutmann G. Time and length scales for diffusion in liquids. PHYSICAL REVIEW E 2002; 65:060201. [PMID: 12188692 DOI: 10.1103/physreve.65.060201] [Citation(s) in RCA: 16] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/24/2001] [Revised: 03/28/2002] [Indexed: 11/07/2022]
Abstract
The first six even moments of the displacement of a molecule in water and an atom in liquid argon are found by molecular dynamics simulations and compared with the moments predicted by diffusion theory. We find a noticeable difference between the moments higher than the second. The ratio between predicted and calculated moments approaches unity as 1/t for times larger than 10 ps. Continuous time random walk is used to explain this slow approach of the moments to their diffusion limit.
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Affiliation(s)
- A M Berezhkovskii
- Center for Information Technology, National Institutes of Health, Bethesda, Maryland 20892, USA.
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17
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Vardeman CF, Gezelter JD. Comparing Models for Diffusion in Supercooled Liquids: The Eutectic Composition of the Ag−Cu Alloy. J Phys Chem A 2001. [DOI: 10.1021/jp0035784] [Citation(s) in RCA: 12] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Charles F. Vardeman
- Department of Chemistry and Biochemistry, University of Notre Dame, Notre Dame, Indiana 46556
| | - J. Daniel Gezelter
- Department of Chemistry and Biochemistry, University of Notre Dame, Notre Dame, Indiana 46556
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18
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Zurcher U, Keyes T. Comment on "Direct observation of stretched-exponential relaxation in low-temperature lennard-jones systems using the cage correlation function". PHYSICAL REVIEW LETTERS 2000; 85:466. [PMID: 10991310 DOI: 10.1103/physrevlett.85.466] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/24/1999] [Revised: 01/27/2000] [Indexed: 05/23/2023]
Affiliation(s)
- U Zurcher
- Chemistry DepartmentBoston UniversityBoston, Massachusetts 02215, USA
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19
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Rabani E, Gezelter JD, Berne BJ. Rabani, gezelter, and berne reply:. PHYSICAL REVIEW LETTERS 2000; 85:467. [PMID: 10991311 DOI: 10.1103/physrevlett.85.467] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/06/2000] [Indexed: 05/23/2023]
Affiliation(s)
- E Rabani
- School of ChemistryTel Aviv University, Tel Aviv 69978, Israel
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20
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Reichman DR, Voth GA. Self-consistent harmonic theory of solvation in glassy systems: Classical solvation. J Chem Phys 2000. [DOI: 10.1063/1.480910] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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21
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Li WX, Keyes T. Instantaneous normal mode theory of diffusion and the potential energy landscape: Application to supercooled liquid CS2. J Chem Phys 1999. [DOI: 10.1063/1.479810] [Citation(s) in RCA: 29] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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