1
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Kumar S, Sarkar S, Bagchi B. Glassy dynamics in a liquid of anisotropic molecules: Bifurcation of relaxation spectrum. J Chem Phys 2024; 160:224501. [PMID: 38856065 DOI: 10.1063/5.0210699] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/26/2024] [Accepted: 05/24/2024] [Indexed: 06/11/2024] Open
Abstract
In experimental and theoretical studies of glass transition phenomena, one often finds a sharp crossover in dynamical properties at a temperature Tcr. A bifurcation of a relaxation spectrum is also observed at a temperature TB≈Tcr; both lie significantly above the glass transition temperature. In order to better understand these phenomena, we introduce a new model of glass-forming liquids, a binary mixture of prolate and oblate ellipsoids. This model system exhibits sharp thermodynamic and dynamic anomalies, such as the specific heat jump during heating and a sharp variation in the thermal expansion coefficient around a temperature identified as the glass transition temperature, Tg. The same temperature is obtained from the fit of the calculated relaxation times to the Vogel-Fulcher-Tammann (VFT) form. As the temperature is lowered, the calculated single peak rotational relaxation spectrum splits into two peaks at TB above the estimated Tg. Similar bifurcation is also observed in the distribution of short-to-intermediate time translational diffusion. Interrogation of the two peaks reveals a lower extent of dynamic heterogeneity in the population of the faster mode. We observe an unexpected appearance of a sharp peak in the product of rotational relaxation time τ2 and diffusion constant D at a temperature Tcr, close to TB, but above the glass transition temperature. Additionally, we coarse-grain the system into cubic boxes, each containing, on average, ∼62 particles, to study the average dynamical properties. Clear evidence of large-scale sudden changes in the diffusion coefficient and rotational correlation time signals first-order transitions between low and high-mobility domains.
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Affiliation(s)
- Shubham Kumar
- Solid State and Structural Chemistry Unit, Indian Institute of Science, Bangalore 560012, India
| | - Sarmistha Sarkar
- Solid State and Structural Chemistry Unit, Indian Institute of Science, Bangalore 560012, India
| | - Biman Bagchi
- Solid State and Structural Chemistry Unit, Indian Institute of Science, Bangalore 560012, India
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2
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Herrera Segura C, Montoya E, Tapias D. Subaging in underparametrized Deep Neural Networks. MACHINE LEARNING: SCIENCE AND TECHNOLOGY 2022. [DOI: 10.1088/2632-2153/ac8f1b] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022] Open
Abstract
Abstract
In this work, we consider a simple classification problem to show that the dynamics of finite--width Deep Neural Networks in the underparametrized regime gives rise to effects similar to those associated with glassy systems, namely a slow evolution of the loss function and aging. Remarkably, the aging is sublinear in the waiting time (subaging) and the power--law exponent characterizing it is robust to different architectures under the constraint of a constant total number of parameters. Our results are maintained in the more complex scenario of the MNIST database. We find that for this database there is a unique exponent ruling the subaging behavior in the whole phase.
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3
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Dicks L, Wales DJ. Elucidating the solution structure of the K-means cost function using energy landscape theory. J Chem Phys 2022; 156:054109. [DOI: 10.1063/5.0078793] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Affiliation(s)
- L. Dicks
- University Chemical Laboratories, Lensfield Road, Cambridge CB2 1EW, United Kingdom
| | - D. J. Wales
- University Chemical Laboratories, Lensfield Road, Cambridge CB2 1EW, United Kingdom
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4
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Röder K, Wales DJ. The Energy Landscape Perspective: Encoding Structure and Function for Biomolecules. Front Mol Biosci 2022; 9:820792. [PMID: 35155579 PMCID: PMC8829389 DOI: 10.3389/fmolb.2022.820792] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/23/2021] [Accepted: 01/07/2022] [Indexed: 12/02/2022] Open
Abstract
The energy landscape perspective is outlined with particular reference to biomolecules that perform multiple functions. We associate these multifunctional molecules with multifunnel energy landscapes, illustrated by some selected examples, where understanding the organisation of the landscape has provided new insight into function. Conformational selection and induced fit may provide alternative routes to realisation of multifunctionality, exploiting the possibility of environmental control and distinct binding modes.
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Affiliation(s)
| | - David J. Wales
- Yusuf Hamied Department of Chemistry, University of Cambridge, Cambridge, United Kingdom
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5
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Banerjee A, Wales DJ. Energy landscapes for a modified repulsive Weeks-Chandler-Andersen potential. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2021; 34:034004. [PMID: 34644698 DOI: 10.1088/1361-648x/ac2f6d] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/05/2021] [Accepted: 10/13/2021] [Indexed: 06/13/2023]
Abstract
The short-range nature of the repulsive Weeks-Chandler-Anderson (WCA) potential can create free particles/rattlers in a condensed system. The presence of rattlers complicates the analysis of the energy landscape due to extra zero-frequency normal modes. By employing a long-range Gaussian tail modification, we remove the rattlers without changing the structure and the dynamics of the system, and successfully describe the potential energy landscape in terms of minima and transition states. This coarse-grained description of the landscape and the dynamical properties of the modified potential exhibit characteristic signatures of glass-forming liquids. However, we show that despite having qualitatively similar behaviour, the modified WCA potential is less frustrated compared to its attractive counterpart.
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Affiliation(s)
- Atreyee Banerjee
- Yusuf Hamied Department of Chemistry, University of Cambridge, Lensfield Road, Cambridge CB2 1EW, United Kingdom
- Max Planck Institute for Polymer Research, Ackermannweg 10, 55128 Mainz, Germany
| | - David J Wales
- Yusuf Hamied Department of Chemistry, University of Cambridge, Lensfield Road, Cambridge CB2 1EW, United Kingdom
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6
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Vogiatzis GG, van Breemen LCA, Hütter M. Structural Transitions in Glassy Atactic Polystyrene Using Transition-State Theory. J Phys Chem B 2021; 125:7273-7289. [PMID: 34161106 PMCID: PMC8279558 DOI: 10.1021/acs.jpcb.1c02618] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/04/2022]
Abstract
![]()
Transition pathways
on the energy landscape of atactic polystyrene
(aPS) glassy specimens are probed below its glass-transition temperature.
Each of these transitions is considered an elementary structural relaxation
event, whose corresponding rate constant is calculated by applying
multidimensional transition-state theory. Initially, a wide spectrum
of first-order saddle points surrounding local minima on the energy
landscape is discovered by a stabilized hybrid eigenmode-following
method. Then, (minimal-energy) “reaction paths” to the
adjacent minima are constructed by a quadratic descent method. The
heights of the free energy, the potential energy, and the entropy
barriers are estimated for every connected triplet of transition state
and minima. The resulting distribution of free energy barriers is
asymmetric and extremely broad, extending to very high barrier heights
(over 50 kBT); the corresponding
distribution of rate constants extends over 30 orders of magnitude,
with well-defined peaks at the time scales corresponding to the subglass
relaxations of polystyrene. Analysis of the curvature along the reaction
paths reveals a multitude of different rearrangement mechanisms; some
of them bearing multiple distinct phases. Finally, connections to
theoretical models of the glass phenomenology allows for the prediction,
based on first-principles, of the “ideal” glass-transition
temperature entering the Vogel–Fulcher–Tammann (VFT)
equation describing the super-Arrhenius temperature dependence of
glassy dynamics. Our predictions of the time scales of the subglass
relaxations and the VFT temperature are in favorable agreement with
available experimental literature data for systems of similar molecular
weight under the same conditions.
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Affiliation(s)
- Georgios G Vogiatzis
- Polymer Technology, Department of Mechanical Engineering, Eindhoven University of Technology, PO Box 513, 5600 MB Eindhoven, The Netherlands.,Dutch Polymer Institute, PO Box 902, 5600 AX Eindhoven, The Netherlands
| | - Lambèrt C A van Breemen
- Polymer Technology, Department of Mechanical Engineering, Eindhoven University of Technology, PO Box 513, 5600 MB Eindhoven, The Netherlands
| | - Markus Hütter
- Polymer Technology, Department of Mechanical Engineering, Eindhoven University of Technology, PO Box 513, 5600 MB Eindhoven, The Netherlands
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7
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Röder K. Is the H4 histone tail intrinsically disordered or intrinsically multifunctional? Phys Chem Chem Phys 2021; 23:5134-5142. [PMID: 33624669 DOI: 10.1039/d0cp05405d] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/28/2022]
Abstract
The structural versatility of histone tails is one of the key elements in the organisation of chromatin, which allows for the compact storage of genomic information. However, this structural diversity also complicates experimental and computational studies. Here, the potential and free energy landscape for the isolated and bound H4 histone tail are explored. The landscapes exhibit a set of distinct structural ensembles separated by high energy barriers, with little difference between isolated and bound tails. This consistency is a desirable feature that facilitates the formation of transient interactions, which are required for the liquid-like chromatin organisation. The existence of multiple, distinct structures on a multifunnel energy landscape is likely to be associated with multifunctionality, i.e. a set of evolved, distinct functions. Contrasting it with previously reported results for other disordered peptides, this type of landscape may be associated with a conformational selection based binding mechanism. Given the similarity to other systems exhibiting similar multifunnel energy landscapes, the disorder in histone tails might be better described in context of multifunctionality.
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Affiliation(s)
- Konstantin Röder
- Yusuf Hamied Department of Chemistry, University of Cambridge, Lensfield Road, Cambridge, CB2 1EW, UK.
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8
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Structural Disorder and Collective Behavior of Two-Dimensional Magnetic Nanostructures. NANOMATERIALS 2021; 11:nano11061392. [PMID: 34070306 PMCID: PMC8225155 DOI: 10.3390/nano11061392] [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: 03/27/2021] [Revised: 05/18/2021] [Accepted: 05/19/2021] [Indexed: 12/13/2022]
Abstract
Structural disorder has been shown to be responsible for profound changes of the interaction-energy landscapes and collective dynamics of two-dimensional (2D) magnetic nanostructures. Weakly-disordered 2D ensembles have a few particularly stable magnetic configurations with large basins of attraction from which the higher-energy metastable configurations are separated by only small downward barriers. In contrast, strongly-disordered ensembles have rough energy landscapes with a large number of low-energy local minima separated by relatively large energy barriers. Consequently, the former show good-structure-seeker behavior with an unhindered relaxation dynamics that is funnelled towards the global minimum, whereas the latter show a time evolution involving multiple time scales and trapping which is reminiscent of glasses. Although these general trends have been clearly established, a detailed assessment of the extent of these effects in specific nanostructure realizations remains elusive. The present study quantifies the disorder-induced changes in the interaction-energy landscape of two-dimensional dipole-coupled magnetic nanoparticles as a function of the magnetic configuration of the ensembles. Representative examples of weakly-disordered square-lattice arrangements, showing good structure-seeker behavior, and of strongly-disordered arrangements, showing spin-glass-like behavior, are considered. The topology of the kinetic networks of metastable magnetic configurations is analyzed. The consequences of disorder on the morphology of the interaction-energy landscapes are revealed by contrasting the corresponding disconnectivity graphs. The correlations between the characteristics of the energy landscapes and the Markovian dynamics of the various magnetic nanostructures are quantified by calculating the field-free relaxation time evolution after either magnetic saturation or thermal quenching and by comparing them with the corresponding averages over a large number of structural arrangements. Common trends and system-specific features are identified and discussed.
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9
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Banerjee A, Wales DJ. Fragility and correlated dynamics in supercooled liquids. J Chem Phys 2020; 153:124501. [PMID: 33003758 DOI: 10.1063/5.0015091] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/30/2022] Open
Abstract
A connection between the super-Arrhenius behavior of dynamical properties and the correlated dynamics for supercooled liquids is examined for a well known glass forming binary Lennard-Jones mixture and its repulsive counterpart, the Weeks-Chandler-Andersen potential, over a range of densities. When considering short time nonergodic trajectory segments of a longer ergodic trajectory, we observe that, independent of the potentials and densities, the apparent diffusivity follows Arrhenius behavior until low temperatures. Comparing the two potentials, where the ergodic diffusivities are known to be rather different, we find that the short-time nonergodic part is similar throughout the temperature range. By including a correlation factor in the nonergodic diffusivity, a rescaled value is calculated, which provides a reasonable estimate of the true ergodic diffusivity. The true diffusion coefficient and the correction factor collapse to a master plot for all densities at any given time interval. Hence, our results confirm a strong connection between fragility and dynamical correlation.
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Affiliation(s)
- Atreyee Banerjee
- Department of Chemistry, University of Cambridge, Lensfield Road, Cambridge CB2 1EW, United Kingdom
| | - David J Wales
- Department of Chemistry, University of Cambridge, Lensfield Road, Cambridge CB2 1EW, United Kingdom
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10
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Verpoort PC, Lee AA, Wales DJ. Archetypal landscapes for deep neural networks. Proc Natl Acad Sci U S A 2020; 117:21857-21864. [PMID: 32843349 PMCID: PMC7486703 DOI: 10.1073/pnas.1919995117] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022] Open
Abstract
The predictive capabilities of deep neural networks (DNNs) continue to evolve to increasingly impressive levels. However, it is still unclear how training procedures for DNNs succeed in finding parameters that produce good results for such high-dimensional and nonconvex loss functions. In particular, we wish to understand why simple optimization schemes, such as stochastic gradient descent, do not end up trapped in local minima with high loss values that would not yield useful predictions. We explain the optimizability of DNNs by characterizing the local minima and transition states of the loss-function landscape (LFL) along with their connectivity. We show that the LFL of a DNN in the shallow network or data-abundant limit is funneled, and thus easy to optimize. Crucially, in the opposite low-data/deep limit, although the number of minima increases, the landscape is characterized by many minima with similar loss values separated by low barriers. This organization is different from the hierarchical landscapes of structural glass formers and explains why minimization procedures commonly employed by the machine-learning community can navigate the LFL successfully and reach low-lying solutions.
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Affiliation(s)
- Philipp C Verpoort
- Department of Physics, University of Cambridge, Cambridge CB3 0HE, United Kingdom;
| | - Alpha A Lee
- Department of Physics, University of Cambridge, Cambridge CB3 0HE, United Kingdom
| | - David J Wales
- Department of Chemistry, University of Cambridge, Cambridge CB2 1EW, United Kingdom
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11
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Iyer SS, Srivastava A. Degeneracy in molecular scale organization of biological membranes. SOFT MATTER 2020; 16:6752-6764. [PMID: 32628232 DOI: 10.1039/d0sm00619j] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/11/2023]
Abstract
The scale-rich spatiotemporal organization in biological membranes has its origin in the differential inter- and intra-molecular interactions among their constituents. In this work, we explore the molecular-origin behind that variety and possible degeneracy in lateral organization in membranes. For our study, we post-process microsecond long all-atom molecular dynamics trajectories for three systems that exhibit fluid phase coexistence: (i) PSM/POPC/Chol (0.47/0.32/0.21), (ii) PSM/DOPC/Chol (0.43/0.38/0.19) and (iii) DPPC/DOPC/Chol (0.37/0.36/0.27). To distinguish the liquid ordered and disordered regions at molecular scales, we calculate the degree of non-affineness of individual lipids in their neighbourhood and track their topological rearrangements. Disconnectivity graph analysis with respect to membrane organization shows that the DPPC/DOPC/Chol and PSM/DOPC/Chol systems exhibit funnel-like energy landscapes as opposed to a highly frustrated energy landscape for the more biomimetic PSM/POPC/Chol system. We use these measurements to develop a continuous lattice Hamiltonian and evolve that using Monte Carlo simulated annealing to explore the possibility of structural degeneracy in membrane organization. Our data show that model membranes with lipid constituents that are biomimetic (PSM/POPC/Chol) have the ability to access a large range of membrane sub-structure space (higher degeneracy) as compared to the other two systems, which form only one kind of substructure even with changing composition. Since the spatiotemporal organization in biological membranes dictates the "molecular encounters" and in turn larger scale biological processes such as molecular transport, trafficking and cellular signalling, we posit that this structural degeneracy could enable access to a larger repository to functionally important molecular organization in systems with physiologically relevant compositions.
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Affiliation(s)
- Sahithya S Iyer
- Molecular Biophysics Unit, Indian Institute of Science, Bangalore, India.
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12
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Gray TH, Yong EH. Effective diffusion in one-dimensional rough potential-energy landscapes. Phys Rev E 2020; 102:022138. [PMID: 32942433 DOI: 10.1103/physreve.102.022138] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/17/2019] [Accepted: 08/11/2020] [Indexed: 06/11/2023]
Abstract
Diffusion in spatially rough, confining, one-dimensional continuous energy landscapes is treated using Zwanzig's proposal, which is based on the Smoluchowski equation. We show that Zwanzig's conjecture agrees with Brownian dynamics simulations only in the regime of small roughness. Our correction of Zwanzig's framework corroborates well with numerical results. A numerical simulation scheme based on our coarse-grained Langevin dynamics offers significant reductions in computational time. The mean first-passage time problem in the case of random roughness is treated. Finally, we address the validity of the separation of length scales assumption for the case of polynomial backgrounds and cosine-based roughness. Our results are applicable to hierarchical energy landscapes such as that of a protein's folding and transport processes in disordered media, where there is clear separation of length scale between smooth underlying potential and its rough perturbation.
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Affiliation(s)
- Thomas H Gray
- Department of Chemical Engineering and Biotechnology, West Cambridge Site, Philippa Fawcett Drive, University of Cambridge, CB3 0AS, Cambridge, United Kingdom
- T.C.M. Group, Cavendish Laboratory, JJ Thomson Avenue, Cambridge, CB3 0HE, United Kingdom
| | - Ee Hou Yong
- Division of Physics and Applied Physics, School of Physical and Mathematical Sciences, Nanyang Technological University, 21 Nanyang Link, Singapore 637371
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13
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Yungbluth JC, Medvedev GA, Savoie BM, Caruthers JM. Temperature and pressure dependence of the alpha relaxation in ortho-terphenyl. J Chem Phys 2020; 152:094504. [PMID: 33480716 DOI: 10.1063/1.5144283] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/11/2022] Open
Abstract
Molecular dynamics (MD) simulations of ortho-terphenyl using an all-atom model with the optimized potentials for liquid simulations (OPLS) force field were performed both in the high temperature Arrhenian region and at lower temperatures that include the onset of the super-Arrhenian region. From the MD simulations, the internal energy of both the equilibrium liquid and crystal was determined from 300 K to 600 K and at pressures from 0.1 MPa to 1 GPa. The translational and rotational diffusivities were also determined at these temperatures and pressures for the equilibrium liquid. It is shown that within a small offset, the excess internal energy Ūx from the MD simulations is consistent with the experimentally determined excess internal energy reported earlier [Caruthers and Medvedev, Phys. Rev. Mater. 2, 055604, (2018)]. The MD mobility data {including extremely long-time 1 atm simulations from the study by Eastwood et al. [J. Phys. Chem. B 117, 12898, (2013)]} were combined with experimental data to form a unified dataset, where it was shown that in both the high temperature Arrhenian region and the lower temperature super-Arrhenian region, the mobility is a linear function of 1/Ūx(T,p), albeit with different proportionality constants. The transition between the Arrhenian and super-Arrhenian regions is relatively sharp at a critical internal energy Ūx α. The 1/Ūx(T,p) model is able to describe the mobility data over nearly 16 orders-of-magnitude. Other excess thermodynamic properties such as excess enthalpy and excess entropy (i.e., the Adam-Gibbs model) are unable to unify the pressure dependence of the mobility.
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Affiliation(s)
- Jack C Yungbluth
- Davidson School of Chemical Engineering, Purdue University, West Lafayette, Indiana 47907, USA
| | - Grigori A Medvedev
- Davidson School of Chemical Engineering, Purdue University, West Lafayette, Indiana 47907, USA
| | - Brett M Savoie
- Davidson School of Chemical Engineering, Purdue University, West Lafayette, Indiana 47907, USA
| | - James M Caruthers
- Davidson School of Chemical Engineering, Purdue University, West Lafayette, Indiana 47907, USA
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14
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Vogiatzis GG, van Breemen LCA, Hütter M. Network Topology of the States Probed by a Glassy Polymer during Physical Aging. MACROMOL THEOR SIMUL 2019. [DOI: 10.1002/mats.201900036] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/21/2023]
Affiliation(s)
- Georgios Grigorios Vogiatzis
- Polymer TechnologyDepartment of Mechanical EngineeringEindhoven University of Technology PO Box 513 5600 MB Eindhoven The Netherlands
- Dutch Polymer Institute PO Box 902 5600 AX Eindhoven The Netherlands
| | - Lambèrt Cécile Angelo van Breemen
- Polymer TechnologyDepartment of Mechanical EngineeringEindhoven University of Technology PO Box 513 5600 MB Eindhoven The Netherlands
| | - Markus Hütter
- Polymer TechnologyDepartment of Mechanical EngineeringEindhoven University of Technology PO Box 513 5600 MB Eindhoven The Netherlands
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15
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Röder K, Joseph JA, Husic BE, Wales DJ. Energy Landscapes for Proteins: From Single Funnels to Multifunctional Systems. ADVANCED THEORY AND SIMULATIONS 2019. [DOI: 10.1002/adts.201800175] [Citation(s) in RCA: 42] [Impact Index Per Article: 8.4] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 01/19/2023]
Affiliation(s)
- Konstantin Röder
- Department of ChemistryUniversity of CambridgeLensfield Road CB2 1EW Cambridge UK
| | - Jerelle A. Joseph
- Department of ChemistryUniversity of CambridgeLensfield Road CB2 1EW Cambridge UK
| | - Brooke E. Husic
- Department of ChemistryUniversity of CambridgeLensfield Road CB2 1EW Cambridge UK
| | - David J. Wales
- Department of ChemistryUniversity of CambridgeLensfield Road CB2 1EW Cambridge UK
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16
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Niblett SP, de Souza VK, Jack RL, Wales DJ. Effects of random pinning on the potential energy landscape of a supercooled liquid. J Chem Phys 2018; 149:114503. [DOI: 10.1063/1.5042140] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- S. P. Niblett
- University Chemical Laboratories, Lensfield Road, Cambridge CB2 1EW, United Kingdom
| | - V. K. de Souza
- University Chemical Laboratories, Lensfield Road, Cambridge CB2 1EW, United Kingdom
| | - R. L. Jack
- University Chemical Laboratories, Lensfield Road, Cambridge CB2 1EW, United Kingdom
- Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, United Kingdom
| | - D. J. Wales
- University Chemical Laboratories, Lensfield Road, Cambridge CB2 1EW, United Kingdom
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17
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Kuon N, Flenner E, Szamel G. Comparison of single particle dynamics at the center and on the surface of equilibrium glassy films. J Chem Phys 2018; 149:074501. [PMID: 30134663 DOI: 10.1063/1.5039505] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/14/2022] Open
Abstract
Glasses prepared by vapor depositing molecules onto a properly prepared substrate can have enhanced kinetic stability when compared with glasses prepared by cooling from the liquid state. The enhanced stability is due to the high mobility of particles at the surface, which allows them to find lower energy configurations than for liquid cooled glasses. Here we use molecular dynamics simulations to examine the temperature dependence of the single particle dynamics in the bulk of the film and at the surface of the film. First, we examine the temperature dependence of the self-intermediate scattering functions for particles in the bulk and at the surface. We then examine the temperature dependence of the probability of the logarithm of single particle displacements for bulk and surface particles. Both bulk and surface particle displacements indicate populations of slow and fast particles, i.e., heterogeneous dynamics. We find that the temperature dependence of the surface dynamics mirrors the bulk despite being several orders of magnitude faster.
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Affiliation(s)
- Nicholas Kuon
- Department of Physics, Colorado State University, Fort Collins, Colorado 80523-1875, USA
| | - Elijah Flenner
- Department of Chemistry, Colorado State University, Fort Collins, Colorado 80523-1872, USA
| | - Grzegorz Szamel
- Department of Chemistry, Colorado State University, Fort Collins, Colorado 80523-1872, USA
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18
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Abstract
Recent advances in the potential energy landscapes approach are highlighted, including both theoretical and computational contributions. Treating the high dimensionality of molecular and condensed matter systems of contemporary interest is important for understanding how emergent properties are encoded in the landscape and for calculating these properties while faithfully representing barriers between different morphologies. The pathways characterized in full dimensionality, which are used to construct kinetic transition networks, may prove useful in guiding such calculations. The energy landscape perspective has also produced new procedures for structure prediction and analysis of thermodynamic properties. Basin-hopping global optimization, with alternative acceptance criteria and generalizations to multiple metric spaces, has been used to treat systems ranging from biomolecules to nanoalloy clusters and condensed matter. This review also illustrates how all this methodology, developed in the context of chemical physics, can be transferred to landscapes defined by cost functions associated with machine learning.
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Affiliation(s)
- David J Wales
- Department of Chemistry, University of Cambridge, Cambridge CB2 1EW, United Kingdom;
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19
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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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Pastore R, Pesce G, Sasso A, Pica Ciamarra M. Cage Size and Jump Precursors in Glass-Forming Liquids: Experiment and Simulations. J Phys Chem Lett 2017; 8:1562-1568. [PMID: 28301929 DOI: 10.1021/acs.jpclett.7b00187] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/06/2023]
Abstract
Glassy dynamics is intermittent, as particles suddenly jump out of the cage formed by their neighbors, and heterogeneous, as these jumps are not uniformly distributed across the system. Relating these features of the dynamics to the diverse local environments explored by the particles is essential to rationalize the relaxation process. Here we investigate this issue characterizing the local environment of a particle with the amplitude of its short time vibrational motion, as determined by segmenting in cages and jumps the particle trajectories. Both simulations of supercooled liquids and experiments on colloidal suspensions show that particles in large cages are likely to jump after a small time-lag, and that, on average, the cage enlarges shortly before the particle jumps. At large time-lags, the cage has essentially a constant size, which is smaller for longer-lasting cages. Finally, we clarify how this coupling between cage size and duration controls the average behavior and opens the way to a better understanding of the relaxation process in glass-forming liquids.
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Affiliation(s)
- Raffaele Pastore
- CNR-SPIN, sezione di Napoli, Dipartimento di Fisica, Campus universitario di Monte S. Angelo, Via Cintia, 80126 Napoli, Italy
| | - Giuseppe Pesce
- Dipartimento di Fisica, Universitá di Napoli Federico II, Campus universitario di Monte S. Angelo, Via Cintia, 80126 Napoli, Italy
| | - Antonio Sasso
- Dipartimento di Fisica, Universitá di Napoli Federico II, Campus universitario di Monte S. Angelo, Via Cintia, 80126 Napoli, Italy
| | - Massimo Pica Ciamarra
- CNR-SPIN, sezione di Napoli, Dipartimento di Fisica, Campus universitario di Monte S. Angelo, Via Cintia, 80126 Napoli, Italy
- Division of Physics and Applied Physics, School of Physical and Mathematical Sciences, Nanyang Technological University , Singapore , 639798
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Morgan JWR, Mehta D, Wales DJ. Properties of kinetic transition networks for atomic clusters and glassy solids. Phys Chem Chem Phys 2017; 19:25498-25508. [DOI: 10.1039/c7cp03346j] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/13/2022]
Abstract
Small-world and scale-free properties are analysed for kinetic transition networks of clusters and glassy systems.
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Affiliation(s)
- John W. R. Morgan
- Department of Chemical Engineering
- University of Michigan
- Ann Arbor
- USA
| | - Dhagash Mehta
- Department of Applied and Computational Mathematics and Statistics
- University of Notre Dame
- Notre Dame
- USA
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