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Baggioli M, Landry M, Zaccone A. Deformations, relaxation, and broken symmetries in liquids, solids, and glasses: A unified topological field theory. Phys Rev E 2022; 105:024602. [PMID: 35291146 DOI: 10.1103/physreve.105.024602] [Citation(s) in RCA: 9] [Impact Index Per Article: 4.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/21/2021] [Accepted: 01/12/2022] [Indexed: 06/14/2023]
Abstract
We combine hydrodynamic and field theoretic methods to develop a general theory of phonons as Goldstone bosons in crystals, glasses, and liquids based on nonaffine displacements and the consequent Goldstone phase relaxation. We relate the conservation, or lack thereof, of specific higher-form currents with properties of the underlying deformation field-nonaffinity-which dictates how molecules move under an applied stress or deformation. In particular, the single-valuedness of the deformation field is associated with conservation of higher-form charges that count the number of topological defects. Our formalism predicts, from first principles, the presence of propagating shear waves above a critical wave vector in liquids, thus giving a formal derivation of the phenomenon in terms of fundamental symmetries. The same picture provides also a theoretical explanation of the corresponding "positive sound dispersion" phenomenon for longitudinal sound. Importantly, accordingly to our theory, the main collective relaxation timescale of a liquid or a glass (known as the α relaxation for the latter) is given by the phase relaxation time, which is not necessarily related to the Maxwell time. Finally, we build a nonequilibrium effective action using the in-in formalism defined on the Schwinger-Keldysh contour, that further supports the emerging picture. In summary, our work suggests that the fundamental difference between solids, fluids, and glasses has to be identified with the associated generalized higher-form global symmetries and their topological structure, and that the Burgers vector for the displacement fields serves as a suitable topological order parameter distinguishing the solid (ordered) phase and the amorphous ones (fluids, glasses).
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Affiliation(s)
- Matteo Baggioli
- Wilczek Quantum Center, School of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai 200240, China
- Shanghai Research Center for Quantum Sciences, Shanghai 201315, China
| | - Michael Landry
- Department of Physics, Center for Theoretical Physics, Columbia University, 538 West 120th Street, New York, New York 10027, USA
| | - Alessio Zaccone
- Department of Physics "A. Pontremoli," University of Milan, via Celoria 16, 20133 Milan, Italy
- Cavendish Laboratory, University of Cambridge, J. J. Thomson Avenue, CB30HE Cambridge, United Kingdom
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Song J, Hsu DD, Shull KR, Phelan FR, Douglas JF, Xia W, Keten S. Energy Renormalization Method for the Coarse-Graining of Polymer Viscoelasticity. Macromolecules 2018; 51:10.1021/acs.macromol.7b02560. [PMID: 30996476 PMCID: PMC6463302 DOI: 10.1021/acs.macromol.7b02560] [Citation(s) in RCA: 28] [Impact Index Per Article: 4.7] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
Developing temperature transferable coarse-grained (CG) models is essential for the computational prediction of polymeric glass-forming (GF) material behavior, but their dynamics are often greatly altered from those of all-atom (AA) models mainly because of the reduced fluid configurational entropy under coarse-graining. To address this issue, we have recently introduced an energy renormalization (ER) strategy that corrects the activation free energy of the CG polymer model by renormalizing the cohesive interaction strength ε as a function of temperature T, i.e., ε(T), thus semiempirically preserving the T-dependent dynamics of the AA model. Here we apply our ER method to consider-in addition to T-dependency-the frequency f-dependent polymer viscoelasticity. Through smallamplitude oscillatory shear molecular dynamics simulations, we show that changing the imposed oscillation f on the CG systems requires changes in ε values (i.e., ε(T, f)) to reproduce the AA viscoelasticity. By accounting for the dynamic fragility of polymers as a material parameter, we are able to predict ε(T, f) under coarse-graining in order to capture the AA viscoelasticity, and consequently the activation energy, across a wide range of T and f in the GF regime. Specifically, we showcase our achievements on two representative polymers of distinct fragilities, polybutadiene (PB) and polystyrene (PS), and show that our CG models are able to sample viscoelasticity up to the megahertz regime, which approaches state-of-the-art experimental resolutions, and capture results sampled via AA simulations and prior experiments.
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Affiliation(s)
- Jake Song
- Department of Materials Science & Engineering, Northwestern University, 2145 Sheridan Road, Evanston, Illinois 60208-3109, United States
| | - David D. Hsu
- Department of Physics and Engineering, Wheaton College, 501 College Avenue, Wheaton, Illinois 60187, United States
| | - Kenneth R. Shull
- Department of Materials Science & Engineering, Northwestern University, 2145 Sheridan Road, Evanston, Illinois 60208-3109, United States
| | - Frederick R. Phelan
- Materials Science & Engineering Division, National Institute of Standards and Technology, Gaithersburg, Maryland 20899, United States
| | - Jack F. Douglas
- Materials Science & Engineering Division, National Institute of Standards and Technology, Gaithersburg, Maryland 20899, United States
| | - Wenjie Xia
- Department of Civil & Environmental Engineering, Northwestern University, 2145 Sheridan Road, Evanston, Illinois 60208-3109, United States
- Center for Hierarchical Materials Design, Northwestern University, 2145 Sheridan Road, Evanston, Illinois 60208-3109, United States
- Materials Science & Engineering Division, National Institute of Standards and Technology, Gaithersburg, Maryland 20899, United States
| | - Sinan Keten
- Department of Civil & Environmental Engineering, Northwestern University, 2145 Sheridan Road, Evanston, Illinois 60208-3109, United States
- Department of Mechanical Engineering, Northwestern University, 2145 Sheridan Road, Evanston, Illinois 60208-3109, United States
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Ahart M, Aihaiti D, Hemley RJ, Kojima S. Pressure Dependence of the Boson Peak of Glassy Glycerol. J Phys Chem B 2017; 121:6667-6672. [PMID: 28561592 DOI: 10.1021/acs.jpcb.7b01993] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Abstract
The pressure dependence of the boson peak (BP) of glycerol, including its behavior across the liquid-glass transition, has been studied using Raman scattering. A significant increase of the BP frequency was observed with pressure up to 11 GPa at room temperature. The pressure dependence of BP frequency νBP is proportional to (1+P/P0)1/3, where P and P0 are the pressure and a constant, respectively, consistent with a soft potential model. The characteristic length of medium range order is close in size to a cyclic trimer of glycerol molecules, as predicted by the medium range order of a BP excitation using molecular dynamics simulations, and the pressure dependence of a characteristic medium range order is nearly constant. The pressure induced structural changes in glycerol can be understood in terms of the shrinkage of voids with cyclic trimers persisting to at least 11 GPa. Pressure dependence of the intermolecular O-H stretching mode indicates that the intermolecular hydrogen bond distances gradually decrease up to the glass transition pressure of ∼5 GPa and become nearly constant in the glassy state, indicating the disappearance of free volume in the dense glass.
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Affiliation(s)
- Muhtar Ahart
- Geophysical Laboratory, Carnegie Institution of Washington , Washington D.C. 20015, United States
| | - Dilare Aihaiti
- College of Science, George Mason University , Fairfax, Virginia 22030, United States
| | - Russell J Hemley
- Department of Civil and Environmental Engineering, The George Washington University , Washington D.C. 20052, United States
| | - Seiji Kojima
- Division of Materials Science, Faculty of Pure and Applied Sciences, University of Tsukuba , Tsukuba, Ibaraki 305-8573, Japan
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