1
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Patel P, Maitra Bhattacharyya S. Effect of the presence of pinned particles on the structural parameters of a liquid and correlation between structure and dynamics at the local level. J Chem Phys 2024; 160:164501. [PMID: 38647308 DOI: 10.1063/5.0191680] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/15/2023] [Accepted: 04/04/2024] [Indexed: 04/25/2024] Open
Abstract
Pinning particles at the equilibrium configuration of the liquid is expected not to affect the structure and any property that depends on the structure while slowing down the dynamics. This leads to a breakdown of the structure dynamics correlation. Here, we calculate two structural quantities: the pair excess entropy, S2, and the mean field caging potential, the inverse of which is our structural order parameter (SOP). We show that when the pinned particles are treated the same way as the mobile particles, both S2 and SOP of the mobile particles remain the same as those of the unpinned system, and the structure dynamics correlation decreases with an increase in pinning density, "c." However, when we treat the pinned particles as a different species, even if we consider that the structure does not change, the expression of S2 and SOP changes. The microscopic expressions show that the interaction between a pinned particle and a mobile particle affects S2 and SOP more than the interaction between two mobile particles. We show that a similar effect is also present in the calculation of the excess entropy and is the primary reason for the well-known vanishing of the configurational entropy at high temperatures. We further show that, contrary to the common belief, the pinning process does change the structure. When these two effects are considered, both S2 and SOP decrease with an increase in "c," and the correlation between the structural parameters and the dynamics continues even for higher values of "c."
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Affiliation(s)
- Palak Patel
- Polymer Science and Engineering Division, CSIR-National Chemical Laboratory, Pune 411008, India
- Academy of Scientific and Innovative Research (AcSIR), Ghaziabad 201002, India
| | - Sarika Maitra Bhattacharyya
- Polymer Science and Engineering Division, CSIR-National Chemical Laboratory, Pune 411008, India
- Academy of Scientific and Innovative Research (AcSIR), Ghaziabad 201002, India
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2
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Sharma M, Nandi MK, Maitra Bhattacharyya S. A comparative study of the correlation between the structure and the dynamics for systems interacting via attractive and repulsive potentials. J Chem Phys 2023; 159:104502. [PMID: 37694749 DOI: 10.1063/5.0165417] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/28/2023] [Accepted: 08/21/2023] [Indexed: 09/12/2023] Open
Abstract
We present the study of the structure-dynamics correlation for systems interacting via attractive Lennard-Jones (LJ) and its repulsive counterpart, the Weeks-Chandler-Andersen (WCA) potentials. The structural order parameter (SOP) is related to the microscopic mean-field caging potential. At a particle level, the SOP shows a distribution. Although the two systems have similar pair structures, their average SOP differs. However, this difference alone is insufficient to explain the well known slowing down of the dynamics in the LJ system at low temperatures. The slowing down can be explained in terms of a stronger coupling between the SOP and the dynamics. To understand the origin of this system specific coupling, we study the difference in the microscopic structure between the hard and soft particles. We find that for the LJ system, the structural differences of the hard and soft particles are more significant and have a much stronger temperature dependence compared to the WCA system. Thus, the study suggests that attractive interaction creates more structurally different communities. This broader difference in the structural communities is probably responsible for stronger coupling between the structure and dynamics. Thus, the system specific structure-dynamics correlation, which also leads to a faster slowing down in the dynamics, appears to have a structural origin. A comparison of the predictive power of our SOP with the local energy and two body excess entropy in determining the dynamics shows that in the LJ system, the enthalpy plays a dominant role and in the WCA system, the entropy plays a dominant role, and our SOP can capture both these contributions.
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Affiliation(s)
- Mohit Sharma
- Polymer Science and Engineering Division, CSIR-National Chemical Laboratory, Pune 411008, India
- Academy of Scientific and Innovative Research (AcSIR), Ghaziabad 201002, India
| | - Manoj Kumar Nandi
- Université Claude Bernard Lyon 1, Institut National de la Santé et de la Recherche Médicale, Stem Cell and Brain Research Institute, Bron 69500, France
| | - Sarika Maitra Bhattacharyya
- Polymer Science and Engineering Division, CSIR-National Chemical Laboratory, Pune 411008, India
- Academy of Scientific and Innovative Research (AcSIR), Ghaziabad 201002, India
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3
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Patel P, Sharma M, Maitra Bhattacharyya S. Dynamic heterogeneity in polydisperse systems: A comparative study of the role of local structural order parameter and particle size. J Chem Phys 2023; 159:044501. [PMID: 37486056 DOI: 10.1063/5.0156794] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/03/2023] [Accepted: 07/03/2023] [Indexed: 07/25/2023] Open
Abstract
In polydisperse systems, describing the structure and any structural order parameter (SOP) is not trivial as it varies with the number of species we use to describe the system, M. Depending on the degree of polydispersity, there is an optimum value of M = M0 where we show that the mutual information of the system increases. However, surprisingly, the correlation between a recently proposed SOP and the dynamics is highest for M = 1. This effect increases with polydispersity. We find that the SOP at M = 1 is coupled with the particle size, σ, and this coupling increases with polydispersity and decreases with an increase in M. Careful analysis shows that at lower polydispersities, the SOP is a good predictor of the dynamics. However, at higher polydispersity, the dynamics is strongly dependent on σ. Since the coupling between the SOP and σ is higher for M = 1, it appears to be a better predictor of the dynamics. We also study the Vibrality, an order parameter independent of structural information. Compared to SOP, at high polydispersity, we find Vibrality to be a marginally better predictor of the dynamics. However, this high predictive power of Vibrality, which is not there at lower polydispersity, appears to be due to its stronger coupling with σ. Therefore, our study suggests that for systems with high polydispersity, the correlation of any order parameter and σ will affect the correlation between the order parameter and dynamics and need not project a generic predictive power of the order parameter.
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Affiliation(s)
- Palak Patel
- Polymer Science and Engineering Division, CSIR-National Chemical Laboratory, Pune 411008, India
- Academy of Scientific and Innovative Research (AcSIR), Ghaziabad 201002, India
| | - Mohit Sharma
- Polymer Science and Engineering Division, CSIR-National Chemical Laboratory, Pune 411008, India
- Academy of Scientific and Innovative Research (AcSIR), Ghaziabad 201002, India
| | - Sarika Maitra Bhattacharyya
- Polymer Science and Engineering Division, CSIR-National Chemical Laboratory, Pune 411008, India
- Academy of Scientific and Innovative Research (AcSIR), Ghaziabad 201002, India
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4
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Sharma M, Nandi MK, Bhattacharyya SM. Identifying structural signature of dynamical heterogeneity via the local softness parameter. Phys Rev E 2022; 105:044604. [PMID: 35590668 DOI: 10.1103/physreve.105.044604] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/13/2021] [Accepted: 03/25/2022] [Indexed: 06/15/2023]
Abstract
In this work we study the relationship between the softness of a mean-field caging potential and dynamics at the local level. We first describe the local softness, which shows a distribution, thus identifying structural heterogeneity. We show that the lifetime of the softness parameter is connected to the lifetime of the well-known cage structure in supercooled liquids. Finally, our theory predicts that the local softness and the local dynamics is causal below the onset temperature where there is a decoupling between the short and long time dynamics, thus allowing a static description of the cage. With the decrease in temperature, the correlation between structure and dynamics increases. The study shows that at lower temperatures, the structural heterogeneity increases, and since the structure becomes a better predictor of the dynamics, it leads to an increase in the dynamical heterogeneity. We also find that the softness of a hard, immobile region evolves with time and becomes soft and eventually mobile due to the rearrangements in the neighborhood, confirming the well-known facilitation effect.
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Affiliation(s)
- Mohit Sharma
- Polymer Science and Engineering Division, CSIR-National Chemical Laboratory, Pune-411008, India
| | - Manoj Kumar Nandi
- Department of Engineering, University of Campania "Luigi Vanvitelli" 81031 Aversa (Caserta), Italy
| | - Sarika Maitra Bhattacharyya
- Polymer Science and Engineering Division, CSIR-National Chemical Laboratory, Pune-411008, India
- Academy of Scientific and Innovative Research (AcSIR), Ghaziabad 201002, India
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5
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Banerjee A, Sevilla M, Rudzinski JF, Cortes-Huerto R. Finite-size scaling and thermodynamics of model supercooled liquids: long-range concentration fluctuations and the role of attractive interactions. SOFT MATTER 2022; 18:2373-2382. [PMID: 35258066 DOI: 10.1039/d2sm00089j] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/14/2023]
Abstract
We compute partial structure factors, Kirkwood-Buff integrals (KBIs) and chemical potentials of model supercooled liquids with and without attractive interactions. We aim at investigating whether relatively small differences in the tail of the radial distribution functions result in contrasting thermodynamic properties. Our results suggest that the attractive potential favours the nucleation of long-range structures. Indeed, upon decreasing temperature, Bathia-Thornton structure factors display anomalous behaviour in the k→0 limit. KBIs extrapolated to the thermodynamic limit confirm this picture, and excess coordination numbers identify the anomaly with long-range concentration fluctuations. By contrast, the purely repulsive system remains perfectly miscible for the same temperature interval and only reveals qualitatively similar concentration fluctuations in the crystalline state. Furthermore, differences in both isothermal compressibilities and chemical potentials show that thermodynamics is not entirely governed by the short-range repulsive part of the interaction potential, emphasising the nonperturbative role of attractive interactions. Finally, at higher density, where both systems display nearly identical dynamical properties and repulsive interactions become dominant, the anomaly disappears, and both systems also exhibit similar thermodynamic properties.
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Affiliation(s)
- Atreyee Banerjee
- Max Planck Institute for Polymer Research, Ackermannweg 10, 55128 Mainz, Germany.
| | - Mauricio Sevilla
- Max Planck Institute for Polymer Research, Ackermannweg 10, 55128 Mainz, Germany.
| | - Joseph F Rudzinski
- Max Planck Institute for Polymer Research, Ackermannweg 10, 55128 Mainz, Germany.
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6
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Nandi UK, Patel P, Moid M, Nandi MK, Sengupta S, Karmakar S, Maiti PK, Dasgupta C, Maitra Bhattacharyya S. Thermodynamics and its correlation with dynamics in a mean-field model and pinned systems: A comparative study using two different methods of entropy calculation. J Chem Phys 2022; 156:014503. [PMID: 34998317 DOI: 10.1063/5.0065668] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
A recent study introduced a novel mean-field model system where each particle over and above the interaction with its regular neighbors interacts with k extra pseudo-neighbors. Here, we present an extensive study of thermodynamics and its correlation with the dynamics of this system. We surprisingly find that the well-known thermodynamic integration (TI) method of calculating the entropy provides unphysical results. It predicts vanishing of the configurational entropy at temperatures close to the onset temperature of the system and negative values of the configurational entropy at lower temperatures. Interestingly, well below the temperature at which the configurational entropy vanishes, both the collective and the single-particle dynamics of the system show complete relaxation. Negative values of the configurational entropy are unphysical, and complete relaxation when the configurational entropy is zero violates the prediction of the random first-order transition theory (RFOT). However, the entropy calculated using the two-phase thermodynamics (2PT) method remains positive at all temperatures for which we can equilibrate the system, and its values are consistent with RFOT predictions. We find that with an increase in k, the difference in the entropy computed using the two methods increases. A similar effect is also observed for a system where a randomly selected fraction of the particles are pinned in their positions in the equilibrated liquid. We show that the difference in entropy calculated via the 2PT and TI methods increases with pinning density.
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Affiliation(s)
- Ujjwal Kumar Nandi
- Polymer Science and Engineering Division, CSIR-National Chemical Laboratory, Pune 411008, India
| | - Palak Patel
- Polymer Science and Engineering Division, CSIR-National Chemical Laboratory, Pune 411008, India
| | - Mohd Moid
- Centre for Condensed Matter Theory, Department of Physics, Indian Institute of Science, Bangalore 560012, India
| | - Manoj Kumar Nandi
- Department of Engineering, University of Campania "Luigi Vanvitelli", 81031 Aversa (CE), Italy
| | - Shiladitya Sengupta
- Department of Physics, Indian Institute of Technology, Roorkee 247667, India
| | - Smarajit Karmakar
- Centre for Interdisciplinary Sciences, Tata Institute of Fundamental Research, 36/P, Gopanpally Village, Serilingampally Mandal, RR District, Hyderabad 500019, India
| | - Prabal K Maiti
- Centre for Condensed Matter Theory, Department of Physics, Indian Institute of Science, Bangalore 560012, India
| | - Chandan Dasgupta
- Centre for Condensed Matter Theory, Department of Physics, Indian Institute of Science, Bangalore 560012, India
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7
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Zhang J, Zheng W, Zhang S, Xu D, Nie Y, Jiang Z, Xu N. Unifying fluctuation-dissipation temperatures of slow-evolving nonequilibrium systems from the perspective of inherent structures. SCIENCE ADVANCES 2021; 7:eabg6766. [PMID: 34321210 PMCID: PMC8318365 DOI: 10.1126/sciadv.abg6766] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 01/22/2021] [Accepted: 06/11/2021] [Indexed: 06/13/2023]
Abstract
For nonequilibrium systems, how to define temperature is one of the key and difficult issues to solve. Although effective temperatures have been proposed and studied to this end, it still remains elusive what they actually are. Here, we focus on the fluctuation-dissipation temperatures and report that such effective temperatures of slow-evolving systems represent characteristic temperatures of their equilibrium counterparts. By calculating the fluctuation-dissipation relation of inherent structures, we obtain a temperature-like quantity T IS For monocomponent crystal-formers, T IS agrees well with the crystallization temperature T c, while it matches with the onset temperature T on for glass-formers. It also agrees with effective temperatures of typical nonequilibrium systems, such as aging glasses, quasi-static shear flows, and quasi-static self-propelled flows. From the unique perspective of inherent structures, our study reveals the nature of effective temperatures and the underlying connections between nonequilibrium and equilibrium systems and confirms the equivalence between T on and T c.
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Affiliation(s)
- Jianhua Zhang
- Hefei National Laboratory for Physical Sciences at the Microscale, CAS Key Laboratory of Microscale Magnetic Resonance, Department of Physics, University of Science and Technology of China, Hefei 230026, P. R. China
| | - Wen Zheng
- Hefei National Laboratory for Physical Sciences at the Microscale, CAS Key Laboratory of Microscale Magnetic Resonance, Department of Physics, University of Science and Technology of China, Hefei 230026, P. R. China
| | - Shiyun Zhang
- Hefei National Laboratory for Physical Sciences at the Microscale, CAS Key Laboratory of Microscale Magnetic Resonance, Department of Physics, University of Science and Technology of China, Hefei 230026, P. R. China
| | - Ding Xu
- Hefei National Laboratory for Physical Sciences at the Microscale, CAS Key Laboratory of Microscale Magnetic Resonance, Department of Physics, University of Science and Technology of China, Hefei 230026, P. R. China
| | - Yunhuan Nie
- Hefei National Laboratory for Physical Sciences at the Microscale, CAS Key Laboratory of Microscale Magnetic Resonance, Department of Physics, University of Science and Technology of China, Hefei 230026, P. R. China
| | - Zhehua Jiang
- Hefei National Laboratory for Physical Sciences at the Microscale, CAS Key Laboratory of Microscale Magnetic Resonance, Department of Physics, University of Science and Technology of China, Hefei 230026, P. R. China
| | - Ning Xu
- Hefei National Laboratory for Physical Sciences at the Microscale, CAS Key Laboratory of Microscale Magnetic Resonance, Department of Physics, University of Science and Technology of China, Hefei 230026, P. R. China.
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8
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Nandi MK, Bhattacharyya SM. Microscopic Theory of Softness in Supercooled Liquids. PHYSICAL REVIEW LETTERS 2021; 126:208001. [PMID: 34110221 DOI: 10.1103/physrevlett.126.208001] [Citation(s) in RCA: 15] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/04/2020] [Accepted: 04/19/2021] [Indexed: 06/12/2023]
Abstract
We introduce a new measure of the structure of a liquid which is the softness of the mean-field potential developed by us earlier. We find that this softness is sensitive to small changes in the structure. Then, we study its correlation with the supercooled liquid dynamics. The study involves a wide range of liquids (fragile, strong, attractive, repulsive, and active) and predicts some universal behaviors such as the softness being linearly proportional to the temperature and inversely proportional to the activation barrier of the dynamics with system dependent proportionality constants. We establish a master equation between the dynamics and the softness parameter and show that, indeed, the dynamics, when scaled by the temperature and system dependent parameters, show a data collapse when plotted against softness. The dynamics of fragile liquids show a strong softness dependence, whereas that of strong liquids show a much weaker softness dependence. We also connect the present study with the earlier studies of softness involving machine learning (ML), thus, providing a theoretical framework for understanding the ML results.
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Affiliation(s)
- Manoj Kumar Nandi
- Polymer Science and Engineering Division, CSIR-National Chemical Laboratory, Pune-411008, India
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9
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Diffusion in dense supercritical methane from quasi-elastic neutron scattering measurements. Nat Commun 2021; 12:1958. [PMID: 33785748 PMCID: PMC8009954 DOI: 10.1038/s41467-021-22182-4] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/05/2020] [Accepted: 02/26/2021] [Indexed: 11/08/2022] Open
Abstract
Methane, the principal component of natural gas, is an important energy source and raw material for chemical reactions. It also plays a significant role in planetary physics, being one of the major constituents of giant planets. Here, we report measurements of the molecular self-diffusion coefficient of dense supercritical CH4 reaching the freezing pressure. We find that the high-pressure behaviour of the self-diffusion coefficient measured by quasi-elastic neutron scattering at 300 K departs from that expected for a dense fluid of hard spheres and suggests a density-dependent molecular diameter. Breakdown of the Stokes-Einstein-Sutherland relation is observed and the experimental results suggest the existence of another scaling between self-diffusion coefficient D and shear viscosity η, in such a way that Dη/ρ=constant at constant temperature, with ρ the density. These findings underpin the lack of a simple model for dense fluids including the pressure dependence of their transport properties.
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10
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Nandi UK, Kob W, Maitra Bhattacharyya S. Connecting real glasses to mean-field models. J Chem Phys 2021; 154:094506. [PMID: 33685150 DOI: 10.1063/5.0038749] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/15/2022] Open
Abstract
We propose a novel model for a glass-forming liquid, which allows us to switch in a continuous manner from a standard three-dimensional liquid to a fully connected mean-field model. This is achieved by introducing k additional particle-particle interactions, which thus augments the effective number of neighbors of each particle. Our computer simulations of this system show that the structure of the liquid does not change with the introduction of these pseudo-neighbors and by means of analytical calculations, and we determine the structural properties related to these additional neighbors. We show that the relaxation dynamics of the system slows down very quickly with the increase in k and that the onset and the mode-coupling temperatures increase. The systems with high values of k follow the mode-coupling theory power law behavior for a larger temperature range compared to the ones with lower values of k. The dynamic susceptibility indicates that the dynamic heterogeneity decreases with the increase in k, whereas the non-Gaussian parameter is independent of it. Thus, we conclude that with the increase in the number of pseudo-neighbors, the system becomes more mean-field-like. By comparing our results with previous studies on mean-field-like systems, we come to the conclusion that the details of how the mean-field limit is approached are important since they can lead to different dynamical behavior in this limit.
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Affiliation(s)
- Ujjwal Kumar Nandi
- Polymer Science and Engineering Division, CSIR-National Chemical Laboratory, Pune 411008, India
| | - Walter Kob
- Laboratoire Charles Coulomb and CNRS, University of Montpellier, Montpellier F-34095, France
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11
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Singh A, Bhattacharyya SM, Singh Y. Emergence of cooperatively reorganizing cluster and super-Arrhenius dynamics of fragile supercooled liquids. Phys Rev E 2021; 103:032611. [PMID: 33862818 DOI: 10.1103/physreve.103.032611] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/12/2020] [Accepted: 03/12/2021] [Indexed: 06/12/2023]
Abstract
In this paper, we develop a theory to calculate the structural relaxation time τ_{α} of fragile supercooled liquids. Using the information of the configurational entropy and structure, we calculate the number of dynamically free, metastable, and stable neighbors around a central particle. In supercooled liquids, the cooperatively reorganizing clusters (CRCs) in which the stable neighbors form "stable" nonchemical bonds with the central particle emerge. For an event of relaxation to take place, these bonds have to reorganize irreversibly; the energy involved in the processes is the effective activation energy of relaxation. The theory brings forth a temperature T_{a} and a temperature-dependent parameter ψ(T) which characterize slowing down of dynamics on cooling. It is shown that the value of ψ(T) is equal to 1 for T>T_{a}, indicating that the underlying microscopic mechanism of relaxation is dominated by the entropy-driven processes, while for T<T_{a}, ψ(T) decreases on cooling, indicating the emergence of the energy-driven processes. This crossover of ψ(T) from high to low temperatures explains the crossover seen in τ_{α}. The dynamics of systems that may have similar static structure but very different dynamics can be understood in terms of ψ(T). We present results for the Kob-Anderson model for three densities and show that the calculated values of τ_{α} are in excellent agreement with simulation values for all densities. We also show that when ψ(T), τ_{α}, and other quantities are plotted as a function of T/T_{a} (or T_{a}/T), the data collapse on master curves.
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Affiliation(s)
- Ankit Singh
- Department of Physics, Banaras Hindu University, Varanasi 221 005, India
| | | | - Yashwant Singh
- Department of Physics, Banaras Hindu University, Varanasi 221 005, India
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12
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Xu WS, Douglas JF, Sun ZY. Polymer Glass Formation: Role of Activation Free Energy, Configurational Entropy, and Collective Motion. Macromolecules 2021. [DOI: 10.1021/acs.macromol.0c02740] [Citation(s) in RCA: 20] [Impact Index Per Article: 6.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/21/2022]
Affiliation(s)
- Wen-Sheng Xu
- State Key Laboratory of Polymer Physics and Chemistry, Changchun Institute of Applied Chemistry, Chinese Academy of Sciences, Changchun 130022, P. R. China
| | - Jack F. Douglas
- Materials Science and Engineering Division, National Institute of Standards and Technology, Gaithersburg, Maryland 20899, United States
| | - Zhao-Yan Sun
- State Key Laboratory of Polymer Physics and Chemistry, Changchun Institute of Applied Chemistry, Chinese Academy of Sciences, Changchun 130022, P. R. China
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13
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González-López K, Shivam M, Zheng Y, Ciamarra MP, Lerner E. Mechanical disorder of sticky-sphere glasses. II. Thermomechanical inannealability. Phys Rev E 2021; 103:022606. [PMID: 33735957 DOI: 10.1103/physreve.103.022606] [Citation(s) in RCA: 9] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/21/2020] [Accepted: 01/13/2021] [Indexed: 11/07/2022]
Abstract
Many structural glasses feature static and dynamic mechanical properties that can depend strongly on glass formation history. The degree of universality of this history dependence and what it is possibly affected by are largely unexplored. Here we show that the variability of elastic properties of simple computer glasses under thermal annealing depends strongly on the strength of attractive interactions between the glasses' constituent particles-referred to here as glass "stickiness." We find that in stickier glasses the stiffening of the shear modulus with thermal annealing is strongly suppressed, while the thermal-annealing-induced softening of the bulk modulus is enhanced. Our key finding is that the characteristic frequency and density per frequency of soft quasilocalized modes becomes effectively invariant to annealing in very sticky glasses; the latter are therefore deemed "thermomechanically inannealable." The implications of our findings and future research directions are discussed.
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Affiliation(s)
- Karina González-López
- Institute for Theoretical Physics, University of Amsterdam, Science Park 904, Amsterdam, the Netherlands
| | - Mahajan Shivam
- School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore 637371, Singapore
| | - Yuanjian Zheng
- School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore 637371, Singapore
| | - Massimo Pica Ciamarra
- School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore 637371, Singapore.,CNR-SPIN, Dipartimento di Scienze Fisiche, Universitá di Napoli Federico II, I-80126 Naples, Italy
| | - Edan Lerner
- Institute for Theoretical Physics, University of Amsterdam, Science Park 904, Amsterdam, the Netherlands
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14
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Patel P, Nandi MK, Nandi UK, Maitra Bhattacharyya S. Effective structure of a system with continuous polydispersity. J Chem Phys 2021; 154:034503. [PMID: 33499618 DOI: 10.1063/5.0038812] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Abstract
In a system of N particles, with continuous size polydispersity, there exists an N(N - 1) number of partial structure factors, making it analytically less tractable. A common practice is to treat the system as an effective one component system, which is known to exhibit an artificial softening of the structure. The aim of this study is to describe the system in terms of M pseudospecies such that we can avoid this artificial softening but, at the same time, have a value of M ≪ N. We use potential energy and pair excess entropy to estimate an optimum number of species, M0. We then define the maximum width of polydispersity, Δσ0, that can be treated as a monodisperse system. We show that M0 depends on the degree and type of polydispersity and also on the nature of the interaction potential, whereas Δσ0 weakly depends on the type of polydispersity but shows a stronger dependence on the type of interaction potential. Systems with a softer interaction potential have a higher tolerance with respect to polydispersity. Interestingly, M0 is independent of system size, making this study more relevant for bigger systems. Our study reveals that even 1% polydispersity cannot be treated as an effective monodisperse system. Thus, while studying the role of polydispersity by using the structure of an effective one component system, care must be taken in decoupling the role of polydispersity from that of the artificial softening of the structure.
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Affiliation(s)
- Palak Patel
- Polymer Science and Engineering Division, CSIR-National Chemical Laboratory, Pune 411008, India
| | - Manoj Kumar Nandi
- Polymer Science and Engineering Division, CSIR-National Chemical Laboratory, Pune 411008, India
| | - Ujjwal Kumar Nandi
- Polymer Science and Engineering Division, CSIR-National Chemical Laboratory, Pune 411008, India
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15
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González-López K, Lerner E. An energy-landscape-based crossover temperature in glass-forming liquids. J Chem Phys 2020; 153:241101. [PMID: 33380095 DOI: 10.1063/5.0034719] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/04/2023] Open
Abstract
The systematic identification of temperature scales in supercooled liquids that are key to understanding those liquids' underlying glass properties, and their formation-history dependence, is a challenging task. Here, we study the statistics of particles' squared displacements δr2 between equilibrium liquid configurations at temperature T and their underlying inherent states, using computer simulations of 11 different computer glass formers. We show that the relative fluctuations of δr2 are nonmonotonic in T, exhibiting a maximum whose location defines the crossover temperature TX. Therefore, TX marks the point of maximal heterogeneity during the process of tumbling down the energy landscape, starting from an equilibrium liquid state at temperature T down to its underlying inherent state. We extract TX for the 11 employed computer glasses, ranging from tetrahedral glasses to packs of soft elastic spheres, and demonstrate its usefulness in putting the elastic properties of different glasses on the same footing. Interestingly, we further show that TX marks the crossover between two distinct regimes of the mean ⟨δr2⟩: a high temperature regime in which ⟨δr2⟩ scales approximately as T0.5 and a deeply supercooled regime in which ⟨δr2⟩ scales approximately as T1.3. Further research directions are discussed.
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Affiliation(s)
- Karina González-López
- Institute for Theoretical Physics, University of Amsterdam, Science Park 904, Amsterdam, The Netherlands
| | - Edan Lerner
- Institute for Theoretical Physics, University of Amsterdam, Science Park 904, Amsterdam, The Netherlands
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Prestipino S, Giaquinta PV. Entropy Multiparticle Correlation Expansion for a Crystal. ENTROPY (BASEL, SWITZERLAND) 2020; 22:E1024. [PMID: 33286793 PMCID: PMC7597117 DOI: 10.3390/e22091024] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 08/21/2020] [Revised: 09/09/2020] [Accepted: 09/11/2020] [Indexed: 11/27/2022]
Abstract
As first shown by H. S. Green in 1952, the entropy of a classical fluid of identical particles can be written as a sum of many-particle contributions, each of them being a distinctive functional of all spatial distribution functions up to a given order. By revisiting the combinatorial derivation of the entropy formula, we argue that a similar correlation expansion holds for the entropy of a crystalline system. We discuss how one- and two-body entropies scale with the size of the crystal, and provide fresh numerical data to check the expectation, grounded in theoretical arguments, that both entropies are extensive quantities.
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Affiliation(s)
- Santi Prestipino
- Dipartimento di Scienze Matematiche ed Informatiche, Scienze Fisiche e Scienze della Terra, Università degli Studi di Messina, Viale F. Stagno d’Alcontres 31, 98166 Messina, Italy;
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Bell IH, Dyre JC, Ingebrigtsen TS. Excess-entropy scaling in supercooled binary mixtures. Nat Commun 2020; 11:4300. [PMID: 32855393 PMCID: PMC7453028 DOI: 10.1038/s41467-020-17948-1] [Citation(s) in RCA: 24] [Impact Index Per Article: 6.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/16/2020] [Accepted: 07/22/2020] [Indexed: 11/09/2022] Open
Abstract
Transport coefficients, such as viscosity or diffusion coefficient, show significant dependence on density or temperature near the glass transition. Although several theories have been proposed for explaining this dynamical slowdown, the origin remains to date elusive. We apply here an excess-entropy scaling strategy using molecular dynamics computer simulations and find a quasiuniversal, almost composition-independent, relation for binary mixtures, extending eight orders of magnitude in viscosity or diffusion coefficient. Metallic alloys are also well captured by this relation. The excess-entropy scaling predicts a quasiuniversal breakdown of the Stokes-Einstein relation between viscosity and diffusion coefficient in the supercooled regime. Additionally, we find evidence that quasiuniversality extends beyond binary mixtures, and that the origin is difficult to explain using existing arguments for single-component quasiuniversality.
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Affiliation(s)
- Ian H Bell
- Applied Chemicals and Materials Division, National Institute of Standards and Technology, Boulder, CO, 80305, USA
| | - Jeppe C Dyre
- Glass and Time, IMFUFA, Department of Science and Environment, Roskilde University, Postbox 260, Roskilde, DK-4000, Denmark
| | - Trond S Ingebrigtsen
- Glass and Time, IMFUFA, Department of Science and Environment, Roskilde University, Postbox 260, Roskilde, DK-4000, Denmark.
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18
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Landes FP, Biroli G, Dauchot O, Liu AJ, Reichman DR. Attractive versus truncated repulsive supercooled liquids: The dynamics is encoded in the pair correlation function. Phys Rev E 2020; 101:010602. [PMID: 32069631 DOI: 10.1103/physreve.101.010602] [Citation(s) in RCA: 28] [Impact Index Per Article: 7.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/24/2019] [Indexed: 11/07/2022]
Abstract
We compare glassy dynamics in two liquids that differ in the form of their interaction potentials. Both systems have the same repulsive interactions but one has also an attractive part in the potential. These two systems exhibit very different dynamics despite having nearly identical pair correlation functions. We demonstrate that a properly weighted integral of the pair correlation function, which amplifies the subtle differences between the two systems, correctly captures their dynamical differences. The weights are obtained from a standard machine learning algorithm.
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Affiliation(s)
- François P Landes
- Université Paris-Saclay, CNRS, Inria, Laboratoire de recherche en informatique, TAU team, 91405 Orsay, France.,Laboratoire de Physique de l'École normale supérieure, ENS, Université PSL, CNRS, Sorbonne Université, Université Paris-Diderot, Sorbonne Paris Cité, 75005 Paris, France.,Department of Physics and Astronomy, University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA.,Department of Chemistry, Columbia University, 3000 Broadway, New York, New York 10027, USA
| | - Giulio Biroli
- Laboratoire de Physique de l'École normale supérieure, ENS, Université PSL, CNRS, Sorbonne Université, Université Paris-Diderot, Sorbonne Paris Cité, 75005 Paris, France
| | - Olivier Dauchot
- UMR Gulliver 7083 CNRS, ESPCI ParisTech, PSL Research University, 10 rue Vauquelin, 75005 Paris, France
| | - Andrea J Liu
- Department of Physics and Astronomy, University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA
| | - David R Reichman
- Department of Chemistry, Columbia University, 3000 Broadway, New York, New York 10027, USA
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Chattoraj J, Ciamarra MP. Role of Attractive Forces in the Relaxation Dynamics of Supercooled Liquids. PHYSICAL REVIEW LETTERS 2020; 124:028001. [PMID: 32004055 DOI: 10.1103/physrevlett.124.028001] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/27/2019] [Indexed: 06/10/2023]
Abstract
The attractive tail of the intermolecular interaction affects very weakly the structural properties of liquids, while it affects dramatically their dynamical ones. Via the numerical simulations of model systems not prone to crystallization, both in three and in two spatial dimensions, here we demonstrate that the nonperturbative dynamical effects of the attractive forces are tantamount to a rescaling of the activation energy by the glass transition temperature T_{g}: systems only differing in their attractive interaction have the same structural and dynamical properties if compared at the same value of T/T_{g}.
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Affiliation(s)
- Joyjit Chattoraj
- School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore 637371, Singapore
| | - Massimo Pica Ciamarra
- School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore 637371, Singapore
- CNR-SPIN, Dipartimento di Scienze Fisiche, Università di Napoli Federico II, I-80126 Napoli, Italy
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Parmar ADS, Sengupta S, Sastry S. Power law relationship between diffusion coefficients in multi-component glass forming liquids. THE EUROPEAN PHYSICAL JOURNAL. E, SOFT MATTER 2018; 41:90. [PMID: 30078172 DOI: 10.1140/epje/i2018-11702-0] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/23/2018] [Accepted: 07/13/2018] [Indexed: 06/08/2023]
Abstract
The slow down of dynamics in glass forming liquids as the glass transition is approached has been characterised through the Adam-Gibbs relation, which relates relaxation time scales to the configurational entropy. The Adam-Gibbs relation cannot apply simultaneously to all relaxation times scales unless they are coupled, and exhibit closely related temperature dependences. The breakdown of the Stokes-Einstein relation presents an interesting situation to the contrary, and in analysing it, it has recently been shown that the Adam-Gibbs relation applies to diffusion coefficients rather than to viscosity or structural relaxation times related to the decay of density fluctuations. However, for multi-component liquids --the typical cases considered in computer simulations, metallic glass formers, etc.-- such a statement raises the question of which diffusion coefficient is described by the Adam-Gibbs relation. All diffusion coefficients can be consistently described by the Adam-Gibbs relation if they bear a power law relationship with each other. Remarkably, we find that for a wide range of glass formers, and for a wide range of temperatures spanning the normal and the slow relaxation regimes, such a relationship holds. We briefly discuss possible rationalisations of the observed behaviour.
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Affiliation(s)
- Anshul D S Parmar
- Theoretical Sciences Unit, Jawaharlal Nehru Centre for Advanced Scientific Research, Jakkur Campus, 560064, Bengaluru, India
- Tata Institute of Fundamental Research, 500107, Hyderabad, Ranga Reddy District, India
| | - Shiladitya Sengupta
- Department of Fundamental Engineering, Institute of Industrial Science, The University of Tokyo, Komaba 4-6-1, 153-8505, Meguro-ku, Tokyo, Japan
| | - Srikanth Sastry
- Theoretical Sciences Unit, Jawaharlal Nehru Centre for Advanced Scientific Research, Jakkur Campus, 560064, Bengaluru, India.
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Santos A, Saija F, Giaquinta PV. Residual Multiparticle Entropy for a Fractal Fluid of Hard Spheres. ENTROPY 2018; 20:e20070544. [PMID: 33265633 PMCID: PMC7513066 DOI: 10.3390/e20070544] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 07/01/2018] [Revised: 07/18/2018] [Accepted: 07/20/2018] [Indexed: 01/14/2023]
Abstract
The residual multiparticle entropy (RMPE) of a fluid is defined as the difference, Δs, between the excess entropy per particle (relative to an ideal gas with the same temperature and density), sex, and the pair-correlation contribution, s2. Thus, the RMPE represents the net contribution to sex due to spatial correlations involving three, four, or more particles. A heuristic "ordering" criterion identifies the vanishing of the RMPE as an underlying signature of an impending structural or thermodynamic transition of the system from a less ordered to a more spatially organized condition (freezing is a typical example). Regardless of this, the knowledge of the RMPE is important to assess the impact of non-pair multiparticle correlations on the entropy of the fluid. Recently, an accurate and simple proposal for the thermodynamic and structural properties of a hard-sphere fluid in fractional dimension 1<d<3 has been proposed (Santos, A.; López de Haro, M. Phys. Rev. E 2016, 93, 062126). The aim of this work is to use this approach to evaluate the RMPE as a function of both d and the packing fraction ϕ. It is observed that, for any given dimensionality d, the RMPE takes negative values for small densities, reaches a negative minimum Δsmin at a packing fraction ϕmin, and then rapidly increases, becoming positive beyond a certain packing fraction ϕ0. Interestingly, while both ϕmin and ϕ0 monotonically decrease as dimensionality increases, the value of Δsmin exhibits a nonmonotonic behavior, reaching an absolute minimum at a fractional dimensionality d≃2.38. A plot of the scaled RMPE Δs/|Δsmin| shows a quasiuniversal behavior in the region -0.14≲ϕ-ϕ0≲0.02.
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Affiliation(s)
- Andrés Santos
- Departamento de Física and Instituto de Computación Científica Avanzada (ICCAEx), Universidad de Extremadura, E-06006 Badajoz, Spain
- Correspondence: ; Tel.: +34-924-289-651
| | - Franz Saija
- CNR-IPCF, Viale F. Stagno d’Alcontres, 37-98158 Messina, Italy
| | - Paolo V. Giaquinta
- Dipartimento di Scienze Matematiche e Informatiche, Scienze Fisiche e Scienze della Terra, Università degli Studi di Messina, Contrada Papardo, 98166 Messina, Italy
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Nandi MK, Maitra Bhattacharyya S. Analysis of the anomalous mean-field like properties of Gaussian core model in terms of entropy. J Chem Phys 2018; 148:034504. [PMID: 29352781 DOI: 10.1063/1.5013644] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/11/2022] Open
Abstract
Studies of the Gaussian core model (GCM) have shown that it behaves like a mean-field model and the properties are quite different from standard glass former. In this work, we investigate the entropies, namely, the excess entropy (Sex) and the configurational entropy (Sc) and their different components to address these anomalies. Our study corroborates most of the earlier observations and also sheds new light on the high and low temperature dynamics. We find that unlike in standard glass former where high temperature dynamics is dominated by two-body correlation and low temperature by many-body correlations, in the GCM both high and low temperature dynamics are dominated by many-body correlations. We also find that the many-body entropy which is usually positive at low temperatures and is associated with activated dynamics is negative in the GCM suggesting suppression of activation. Interestingly despite the suppression of activation, the Adam-Gibbs (AG) relation that describes activated dynamics holds in the GCM, thus suggesting a non-activated contribution in AG relation. We also find an overlap between the AG relation and mode coupling power law regime leading to a power law behavior of Sc. From our analysis of this power law behavior, we predict that in the GCM the high temperature dynamics will disappear at dynamical transition temperature and below that there will be a transition to the activated regime. Our study further reveals that the activated regime in the GCM is quite narrow.
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Affiliation(s)
- Manoj Kumar Nandi
- Polymer Science and Engineering Division, CSIR-National Chemical Laboratory, Pune 411008, India
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