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Lee JH, Jung Y. Dynamical Phase Transition in Kinetically Constrained Models with Energy-Activity Double-Bias Trajectory Ensemble. J Phys Chem Lett 2024; 15:1553-1563. [PMID: 38300602 DOI: 10.1021/acs.jpclett.3c03160] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/02/2024]
Abstract
We investigate the dynamical phase transitions in two representative kinetically constrained models, the 1D Fredrickson-Andersen and East models, by utilizing a recently developed s,g double-bias ensemble approach. In this ensemble, the fields s and g are applied to bias the dynamical activity and trajectory energy, respectively, in the trajectory ensemble. We first confirm that the dynamical phase transitions are indeed first-order in both the models. The phase diagrams in (s, g, T) space obtained via extensive numerical simulations show good qualitative agreement with the mean-field results. We also demonstrate that the temperature-dependent dynamical phase transition is possible in the systems when both fields are applied simultaneously. The trajectory energy and dynamical activity exhibit strong correlations for both systems. From extensive finite-size scaling analyses using the system size and observation time, we obtain scaling functions for the susceptibility and field and find scaling exponents that are model-dependent.
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Affiliation(s)
- Jay-Hak Lee
- Department of Chemistry, Seoul National University, Seoul 08826, Korea
| | - YounJoon Jung
- Department of Chemistry, Seoul National University, Seoul 08826, Korea
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2
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Nakane T, Sasaki T. Thickness Dependence of Segmental Dynamics in Free-Standing Thin Films Predicted by a Dynamically Correlated Network Model. J Phys Chem B 2023. [PMID: 37201178 DOI: 10.1021/acs.jpcb.3c00841] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 05/20/2023]
Abstract
The anomalous dynamics and glass transition behaviors of supercooled liquids under nanoconfinement, such as ultrathin polymer films, have attracted much attention in recent decades. However, a complete elucidation of this mechanism has not yet been achieved. For the dynamics of bulk materials without confinement, we previously proposed a dynamically correlated network (DCN) model, which was found to agree well with the experimental data. The model assumes that segments with thermal fluctuations are dynamically correlated to their neighbors to form string-like clusters, which eventually grow into networks as temperature decreases. In this study, we applied the DCN model to nanoconfined free-standing films by using a simple cubic lattice sandwiched between two free surface layers consisting of virtual "uncorrelated" segments. The average size of DCNs at lower temperatures decreased with decreasing thickness because of confinement. This trend was associated with a decrease in the percolation temperature at which the size of DCN diverges. It was also revealed that the fractal dimension of the generated DCNs exhibits a peak with respect to temperature. The segmental relaxation time for free-standing polystyrene films was evaluated, and the predicted thickness dependence of the glass transition temperature qualitatively agreed with the experimental data. The results suggest that the concept of DCN is compatible with the dynamics of free-standing thin films.
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Affiliation(s)
- Tatsuki Nakane
- Department of Materials Science and Engineering, University of Fukui, Fukui 9108507, Japan
| | - Takashi Sasaki
- Department of Materials Science and Engineering, University of Fukui, Fukui 9108507, Japan
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Ortlieb L, Ingebrigtsen TS, Hallett JE, Turci F, Royall CP. Probing excitations and cooperatively rearranging regions in deeply supercooled liquids. Nat Commun 2023; 14:2621. [PMID: 37147284 PMCID: PMC10163050 DOI: 10.1038/s41467-023-37793-2] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/06/2022] [Accepted: 03/28/2023] [Indexed: 05/07/2023] Open
Abstract
Upon approaching the glass transition, the relaxation of supercooled liquids is controlled by activated processes, which become dominant at temperatures below the so-called dynamical crossover predicted by Mode Coupling theory (MCT). Two of the main frameworks rationalising this behaviour are dynamic facilitation theory (DF) and the thermodynamic scenario which give equally good descriptions of the available data. Only particle-resolved data from liquids supercooled below the MCT crossover can reveal the microscopic mechanism of relaxation. By employing state-of-the-art GPU simulations and nano-particle resolved colloidal experiments, we identify the elementary units of relaxation in deeply supercooled liquids. Focusing on the excitations of DF and cooperatively rearranging regions (CRRs) implied by the thermodynamic scenario, we find that several predictions of both hold well below the MCT crossover: for the elementary excitations, their density follows a Boltzmann law, and their timescales converge at low temperatures. For CRRs, the decrease in bulk configurational entropy is accompanied by the increase of their fractal dimension. While the timescale of excitations remains microscopic, that of CRRs tracks a timescale associated with dynamic heterogeneity, [Formula: see text]. This timescale separation of excitations and CRRs opens the possibility of accumulation of excitations giving rise to cooperative behaviour leading to CRRs.
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Affiliation(s)
- Levke Ortlieb
- H.H. Wills Physics Laboratory, Tyndall Avenue, Bristol, BS8 1TL, UK.
- Centre for Nanoscience and Quantum Information, Tyndall Avenue, Bristol, BS8 1FD, UK.
| | - Trond S Ingebrigtsen
- DNRF Centre for Glass and Time, IMFUFA, Department of Science, Systems and Models, Roskilde University, Postbox 260, DK-4000, Roskilde, Denmark.
| | - James E Hallett
- Department of Chemistry, School of Chemistry, Food and Pharmacy, University of Reading, Whiteknights, PO Box 224, Reading RG6 6AD, UK.
| | - Francesco Turci
- H.H. Wills Physics Laboratory, Tyndall Avenue, Bristol, BS8 1TL, UK.
| | - C Patrick Royall
- H.H. Wills Physics Laboratory, Tyndall Avenue, Bristol, BS8 1TL, UK.
- School of Chemistry, University of Bristol, Cantock's Close, Bristol, BS8 1TS, UK.
- Gulliver UMR CNRS 7083, ESPCI Paris, Université PSL, 75005, Paris, France.
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Diezemann G. Nonlinear response theory for Markov processes. IV. The asymmetric double-well potential model revisited. Phys Rev E 2022; 106:064122. [PMID: 36671146 DOI: 10.1103/physreve.106.064122] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/16/2022] [Accepted: 12/02/2022] [Indexed: 06/17/2023]
Abstract
The dielectric response of noninteracting dipoles is discussed in the framework of the classical model of stochastic reorientations in an asymmetric double-well potential (ADWP). In the nonlinear regime, this model exhibits some pecularities in the static response. We find that the saturation behavior of the symmetric double-well potential model does not follow the Langevin function and only in the linear regime are the standard results recovered. If a finite asymmetry is assumed, then the nonlinear susceptibilities are found to change the sign at a number of characteristic temperatures that depend on the magnitude of the asymmetry, as has been observed earlier for the third-order and fifth-order responses. If the kinetics of the barrier crossing in the ADWP model is described as a two-state model, then we can give analytical expressions for the values of the characteristic temperatures. The results for the response obtained from a (numerical) solution of the Fokker-Planck equation for the Brownian motion in a model ADWP behaves very similarly to the two-state model for high barriers. For small barriers no clear-cut timescale separation between the barrier crossing process and the intrawell relaxation exists and the model exhibits a number of timescales. In this case, the frequency-dependent linear susceptibility at low temperatures is dominated by the fast intrawell transitions and at higher temperatures by the barrier crossing kinetics. We find that for nonlinear susceptibilities the latter process appears to be more important and the intrawell transitions play only a role at the lowest temperatures.
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Affiliation(s)
- Gregor Diezemann
- Department Chemie, Johannes Gutenberg Universität Mainz, 55128 Mainz, Germany
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Carbone MR, Baity-Jesi M. Competition between energy- and entropy-driven activation in glasses. Phys Rev E 2022; 106:024603. [PMID: 36109895 DOI: 10.1103/physreve.106.024603] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/23/2022] [Accepted: 07/21/2022] [Indexed: 06/15/2023]
Abstract
In simplified models of glasses we clarify the existence of two different kinds of coexisting activated dynamics, with one of the two dominating over the other. One is the energy barrier hopping that is typically used to understand activation, and the other, which we call entropic activation, is driven by the scarcity of convenient directions in phase space. When entropic activation dominates, the height of the energy barriers is no longer the primary factor governing the system's slowdown. In our analysis, dominance of one mechanism over the other depends on temperature and the shape of the density of states. We also find that at low temperatures a phase transition between the two kinds of activation can occur. Our observations are used to provide a scenario that can harmonize the facilitation and thermodynamic pictures of the slowdown of glasses into a single description.
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Affiliation(s)
- Matthew R Carbone
- Computational Science Initiative, Brookhaven National Laboratory, Upton, New York 11973, USA
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Ganapathi D, Sood AK, Ganapathy R. Structural origin of excitations in a colloidal glass-former. J Chem Phys 2022; 156:214502. [DOI: 10.1063/5.0088500] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Despite decades of intense research, whether the transformation of supercooled liquids into glass is a kinetic phenomenon or a thermodynamic phase transition remains unknown. Here, we analyzed optical microscopy experiments on 2D binary colloidal glass-forming liquids and investigated the structural links of a prominent kinetic theory of glass transition. We examined a possible structural origin for localized excitations, which are building blocks of the dynamical facilitation theory—a purely kinetic approach for the glass transition. To accomplish this, we utilize machine learning methods to identify a structural order parameter termed “softness” that has been found to be correlated with reorganization events in supercooled liquids. Both excitations and softness qualitatively capture the dynamical slowdown on approaching the glass transition and motivated us to explore spatial and temporal correlations between them. Our results show that excitations predominantly occur in regions with high softness and the appearance of these high softness regions precedes excitations, thus suggesting a causal connection between them. Thus, unifying dynamical and thermodynamical theories into a single structure-based framework may provide a route to understand the glass transition.
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Affiliation(s)
- Divya Ganapathi
- Department of Physics, Indian Institute of Science, Bangalore 560012, India
| | - A. K. Sood
- Department of Physics, Indian Institute of Science, Bangalore 560012, India
- International Centre for Materials Science, Jawaharlal Nehru Centre for Advanced Scientific Research, Jakkur, Bangalore 560064, India
| | - Rajesh Ganapathy
- International Centre for Materials Science, Jawaharlal Nehru Centre for Advanced Scientific Research, Jakkur, Bangalore 560064, India
- School of Advanced Materials (SAMat), Jawaharlal Nehru Centre for Advanced Scientific Research, Jakkur, Bangalore 560064, India
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Sasaki T, Tsuzuki Y, Nakane T. A Dynamically Correlated Network Model for the Collective Dynamics in Glass-Forming Molecular Liquids and Polymers. Polymers (Basel) 2021; 13:3424. [PMID: 34641239 PMCID: PMC8512962 DOI: 10.3390/polym13193424] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/18/2021] [Revised: 10/02/2021] [Accepted: 10/03/2021] [Indexed: 11/23/2022] Open
Abstract
The non-Arrhenius behavior of segmental dynamics in glass-forming liquids is one of the most profound mysteries in soft matter physics. In this article, we propose a dynamically correlated network (DCN) model to understand the growing behavior of dynamically correlated regions during cooling, which leads to the viscous slowdown of supercooled liquids. The fundamental concept of the model is that the cooperative region of collective motions has a network structure that consists of string-like parts, and networks of various sizes interpenetrate each other. Each segment undergoes dynamical coupling with its neighboring segments via a finite binding energy. Monte Carlo simulations showed that the fractal dimension of the DCNs generated at different temperatures increased and their size distribution became broader with decreasing temperature. The segmental relaxation time was evaluated based on a power law with four different exponents for the activation energy of rearrangement with respect to the DCN size. The results of the present DCN model are consistent with the experimental results for various materials of molecular and polymeric liquids.
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Affiliation(s)
- Takashi Sasaki
- Department of Materials Science and Engineering, University of Fukui, Fukui 9108507, Japan; (Y.T.); (T.N.)
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Royall CP, Faers MA, Fussell SL, Hallett JE. Real space analysis of colloidal gels: triumphs, challenges and future directions. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2021; 33:453002. [PMID: 34034239 DOI: 10.1088/1361-648x/ac04cb] [Citation(s) in RCA: 6] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/07/2021] [Accepted: 05/25/2021] [Indexed: 06/12/2023]
Abstract
Colloidal gels constitute an important class of materials found in many contexts and with a wide range of applications. Yet as matter far from equilibrium, gels exhibit a variety of time-dependent behaviours, which can be perplexing, such as an increase in strength prior to catastrophic failure. Remarkably, such complex phenomena are faithfully captured by an extremely simple model-'sticky spheres'. Here we review progress in our understanding of colloidal gels made through the use of real space analysis and particle resolved studies. We consider the challenges of obtaining a suitable experimental system where the refractive index and density of the colloidal particles is matched to that of the solvent. We review work to obtain a particle-level mechanism for rigidity in gels and the evolution of our understanding of time-dependent behaviour, from early-time aggregation to ageing, before considering the response of colloidal gels to deformation and then move on to more complex systems of anisotropic particles and mixtures. Finally we note some more exotic materials with similar properties.
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Affiliation(s)
- C Patrick Royall
- Gulliver UMR CNRS 7083, ESPCI Paris, Université PSL, 75005 Paris, France
- HH Wills Physics Laboratory, Tyndall Avenue, Bristol, BS8 1TL, United Kingdom
- School of Chemistry, University of Bristol, Cantock Close, Bristol, BS8 1TS, United Kingdom
- Centre for Nanoscience and Quantum Information, Tyndall Avenue, Bristol, BS8 1FD, United Kingdom
| | - Malcolm A Faers
- Bayer AG, Crop Science Division, Formulation Technology, Alfred Nobel Str. 50, 40789 Monheim, Germany
| | - Sian L Fussell
- School of Chemistry, University of Bristol, Cantock Close, Bristol, BS8 1TS, United Kingdom
- Bristol Centre for Functional Nanomaterials, University of Bristol, Tyndall Avenue, Bristol, BS8 1TL, United Kingdom
| | - James E Hallett
- Physical and Theoretical Chemistry Laboratory, South Parks Road, University of Oxford, OX1 3QZ, United Kingdom
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Speck T. Modeling non-linear dielectric susceptibilities of supercooled molecular liquids. J Chem Phys 2021; 155:014506. [PMID: 34241396 DOI: 10.1063/5.0056657] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Advances in high-precision dielectric spectroscopy have enabled access to non-linear susceptibilities of polar molecular liquids. The observed non-monotonic behavior has been claimed to provide strong support for theories of dynamic arrest based on the thermodynamic amorphous order. Here, we approach this question from the perspective of dynamic facilitation, an alternative view focusing on emergent kinetic constraints underlying the dynamic arrest of a liquid approaching its glass transition. We derive explicit expressions for the frequency-dependent higher-order dielectric susceptibilities exhibiting a non-monotonic shape, the height of which increases as temperature is lowered. We demonstrate excellent agreement with the experimental data for glycerol, challenging the idea that non-linear response functions reveal correlated relaxation in supercooled liquids.
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Affiliation(s)
- Thomas Speck
- Institut für Physik, Johannes Gutenberg-Universität Mainz, Staudingerweg 7-9, 55128 Mainz, Germany
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