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Zhou Y, Lopez GE, Giovambattista N. The Harmonic and Gaussian Approximations in the Potential Energy Landscape Formalism for Quantum Liquids. J Chem Theory Comput 2024; 20:1847-1861. [PMID: 38323779 PMCID: PMC11166017 DOI: 10.1021/acs.jctc.3c01085] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/08/2024]
Abstract
The potential energy landscape (PEL) formalism has been used in the past to describe the behavior of classical low-temperature liquids and glasses. Here, we extend the PEL formalism to describe the behavior of liquids and glasses that obey quantum mechanics. In particular, we focus on the (i) harmonic and (ii) Gaussian approximations of the PEL, which have been commonly used to describe classical systems, and show how these approximations can be applied to quantum liquids/glasses. Contrary to the case of classical liquids/glasses, the PEL of quantum liquids is temperature-dependent, and hence, the main expressions resulting from approximations (i) and (ii) depend on the nature (classical vs quantum) of the system. The resulting theoretical expressions from the PEL formalism are compared with results from path-integral Monte Carlo (PIMC) simulations of a monatomic model liquid. In the PIMC simulations, every atom of the quantum liquid is represented by a ring-polymer. Our PIMC simulations show that at the local minima of the PEL (inherent structures, or IS), sampled over a wide range of temperatures and volumes, the ring-polymers are collapsed. This considerably facilitates the description of quantum liquids using the PEL formalism. Specifically, the normal modes of the ring-polymer system/quantum liquid at an IS can be calculated analytically if the normal modes of the classical liquid counterpart are known (as obtained, e.g., from classical MC or molecular dynamics simulations of the corresponding atomic liquid).
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Affiliation(s)
- Yang Zhou
- Department of Physics, Brooklyn College of the City University of New York, Brooklyn, New York 11210, United States
- Ph.D. Program in Physics, The Graduate Center of the City University of New York, New York, New York 10016, United States
| | - Gustavo E Lopez
- Department of Chemistry, Lehman College of the City University of New York, Bronx, New York 10468, United States
- Ph.D. Program in Chemistry, The Graduate Center of the City University of New York, New York, New York 10016, United States
| | - Nicolas Giovambattista
- Department of Physics, Brooklyn College of the City University of New York, Brooklyn, New York 11210, United States
- Ph.D. Program in Physics, The Graduate Center of the City University of New York, New York, New York 10016, United States
- Ph.D. Program in Chemistry, The Graduate Center of the City University of New York, New York, New York 10016, United States
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Dattani UA, Karmakar S, Chaudhuri P. Athermal quasistatic cavitation in amorphous solids: Effect of random pinning. J Chem Phys 2023; 159:204501. [PMID: 38010327 DOI: 10.1063/5.0171905] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/11/2023] [Accepted: 10/19/2023] [Indexed: 11/29/2023] Open
Abstract
Amorphous solids are known to fail catastrophically via fracture, and cavitation at nano-metric scales is known to play a significant role in such a failure process. Micro-alloying via inclusions is often used as a means to increase the fracture toughness of amorphous solids. Modeling such inclusions as randomly pinned particles that only move affinely and do not participate in plastic relaxations, we study how the pinning influences the process of cavitation-driven fracture in an amorphous solid. Using extensive numerical simulations and probing in the athermal quasistatic limit, we show that just by pinning a very small fraction of particles, the tensile strength is increased, and also the cavitation is delayed. Furthermore, the cavitation that is expected to be spatially heterogeneous becomes spatially homogeneous by forming a large number of small cavities instead of a dominant cavity. The observed behavior is rationalized in terms of screening of plastic activity via the pinning centers, characterized by a screening length extracted from the plastic-eigenmodes.
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Affiliation(s)
- Umang A Dattani
- The Institute of Mathematical Sciences, C.I.T. Campus, Taramani, Chennai 600113, India
- Homi Bhabha National Institute, Anushakti Nagar, Mumbai 400094, India
| | - Smarajit Karmakar
- Tata Institute of Fundamental Research, 36/P, Gopanpally Village, Serilingampally Mandal, Ranga Reddy District, Hyderabad 500046, Telangana, India
| | - Pinaki Chaudhuri
- The Institute of Mathematical Sciences, C.I.T. Campus, Taramani, Chennai 600113, India
- Homi Bhabha National Institute, Anushakti Nagar, Mumbai 400094, India
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Shimada M, Oyama N. Gas-liquid phase separation at zero temperature: mechanical interpretation and implications for gelation. SOFT MATTER 2022; 18:8406-8417. [PMID: 36285640 DOI: 10.1039/d2sm00628f] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/16/2023]
Abstract
The relationship between glasses and gels has been intensely debated for decades; however, the transition between these two phases remains elusive. To investigate a gel formation process in the zero-temperature limit and its relation to the glass phase, we conducted numerical experiments on athermal quasistatic decompression. During decompression, the system experiences a cavitation event similar to phase separation and this is a gelation process at zero temperature. A normal mode analysis revealed that the phase separation is signaled by the vanishing of the lowest eigenenergy, similar to plastic events of glasses under shear. One primary difference from the shear-induced plasticity is that the vanishing mode experiences a qualitative change in its spatial energy distribution at the phase separation point. These findings enable us to define the glass-gel phase boundary based on mechanics.
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Affiliation(s)
- Masanari Shimada
- Graduate School of Arts and Sciences, The University of Tokyo, Tokyo 153-8902, Japan
- Department of Physics, Toronto Metropolitan University, M5B 2K3, Toronto, Canada.
| | - Norihiro Oyama
- Graduate School of Arts and Sciences, The University of Tokyo, Tokyo 153-8902, Japan
- Mathematics for Advanced Materials-OIL, AIST, Sendai 980-8577, Japan
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Dattani UA, Karmakar S, Chaudhuri P. Universal mechanical instabilities in the energy landscape of amorphous solids: Evidence from athermal quasistatic expansion. Phys Rev E 2022; 106:055004. [PMID: 36559417 DOI: 10.1103/physreve.106.055004] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/24/2021] [Accepted: 11/02/2022] [Indexed: 11/30/2022]
Abstract
Using numerical simulations, we study the failure of an amorphous solid under athermal quasistatic expansion starting from a homogeneous high-density state. During the expansion process, plastic instabilities occur, manifested via sudden jumps in pressure and energy, with the largest event happening via cavitation leading to the material's yielding. We demonstrate that all these plastic events are characterized by saddle-node bifurcation, during which the smallest nonzero eigenvalue of the Hessian matrix vanishes via a square-root singularity. We find that after yielding and prior to complete fracture, the statistics of pressure or energy jumps corresponding to the plastic events show subextensive system-size scaling, similar to the case of simple shear but with different exponents. Thus, overall, our paper reveals universal features in the fundamental characteristics during mechanical failure in amorphous solids under any quasistatic deformation protocol.
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Affiliation(s)
- Umang A Dattani
- The Institute of Mathematical Sciences, CIT Campus, Taramani, Chennai 600113, India.,Homi Bhabha National Institute, Anushaktinagar, Mumbai 400094, India
| | - Smarajit Karmakar
- Tata Institute of Fundamental Research, 36/P, Gopanpally Village, Serilingampally Mandal,Ranga Reddy District, Hyderabad, 500107 Telangana, India
| | - Pinaki Chaudhuri
- The Institute of Mathematical Sciences, CIT Campus, Taramani, Chennai 600113, India.,Homi Bhabha National Institute, Anushaktinagar, Mumbai 400094, India
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Zhou Y, Lopez GE, Giovambattista N. Anomalous properties in the potential energy landscape of a monatomic liquid across the liquid-gas and liquid-liquid phase transitions. J Chem Phys 2022; 157:124502. [PMID: 36182441 PMCID: PMC9525132 DOI: 10.1063/5.0106923] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/30/2022] [Accepted: 08/26/2022] [Indexed: 11/14/2022] Open
Abstract
As a liquid approaches the gas state, the properties of the potential energy landscape (PEL) sampled by the system become anomalous. Specifically, (i) the mechanically stable local minima of the PEL [inherent structures (IS)] can exhibit cavitation above the so-called Sastry volume, vS, before the liquid enters the gas phase. In addition, (ii) the pressure of the liquid at the sampled IS [i.e., the PEL equation of state, PIS(v)] develops a spinodal-like minimum at vS. We perform molecular dynamics simulations of a monatomic water-like liquid and verify that points (i) and (ii) hold at high temperatures. However, at low temperatures, cavitation in the liquid and the corresponding IS occurs simultaneously and a Sastry volume cannot be defined. Remarkably, at intermediate/high temperatures, the IS of the liquid can exhibit crystallization, i.e., the liquid regularly visits the regions of the PEL that belong to the crystal state. The model liquid considered also exhibits a liquid-liquid phase transition (LLPT) between a low-density and a high-density liquid (LDL and HDL). By studying the behavior of PIS(v) during the LLPT, we identify a Sastry volume for both LDL and HDL. The HDL Sastry volume marks the onset above which IS are heterogeneous (composed of LDL and HDL particles), analogous to points (i) and (ii) above. However, the relationship between the LDL Sastry volume and the onset of heterogeneous IS is less evident. We conclude by presenting a thermodynamic argument that can explain the behavior of the PEL equation of state PIS(v) across both the liquid-gas phase transition and LLPT.
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Gish CM, Nan K, Hoy RS. Does the Sastry transition control cavitation in simple liquids? J Chem Phys 2020; 153:184504. [DOI: 10.1063/5.0023236] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Caitlin M. Gish
- Department of Physics, University of South Florida, Tampa, Florida 33620, USA
| | - Kai Nan
- Department of Physics, University of South Florida, Tampa, Florida 33620, USA
| | - Robert S. Hoy
- Department of Physics, University of South Florida, Tampa, Florida 33620, USA
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