1
|
Melis C, Fugallo G, Colombo L. Room temperature second sound in cumulene. Phys Chem Chem Phys 2021; 23:15275-15281. [PMID: 34240726 DOI: 10.1039/d1cp00501d] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
Second sound is known as the thermal transport regime occurring in a wave-like fashion, usually identified in a limited number of materials only at cryogenic temperatures. Here we show that second sound in a μm-long carbon chain (cumulene) might occur even at room temperature. To this aim, we calibrate a many-body force field on the first principles calculated phonon dispersion relations of cumulene and, through molecular dynamics, we mimic laser-induced transient thermal grating experiments. We provide evidence that by tuning temperature as well as the space modulation of its initial profile we can reversibly drive the system from a wave-like to a diffusive-like thermal transport. By following three different theoretical methodologies (molecular dynamics, the Maxwell-Cattaneo-Vernotte equation, and heat transport microscopic theory) we estimate for cumulene a second sound velocity in the range of 2.4-3.2 km s-1.
Collapse
Affiliation(s)
- Claudio Melis
- Department of Physics, University of Cagliari, Cittadella Universitaria, I-09042 Monserrato (CA), Italy.
| | - Giorgia Fugallo
- LTeN, UMR 6607 CNRS PolytechNantes, Université de Nantes, 44306 Nantes, France
| | - Luciano Colombo
- Department of Physics, University of Cagliari, Cittadella Universitaria, I-09042 Monserrato (CA), Italy.
| |
Collapse
|
2
|
Lepri S, Livi R, Politi A. Too Close to Integrable: Crossover from Normal to Anomalous Heat Diffusion. PHYSICAL REVIEW LETTERS 2020; 125:040604. [PMID: 32794827 DOI: 10.1103/physrevlett.125.040604] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/08/2020] [Accepted: 07/08/2020] [Indexed: 06/11/2023]
Abstract
Energy transport in one-dimensional chains of particles with three conservation laws is generically anomalous and belongs to the Kardar-Parisi-Zhang dynamical universality class. Surprisingly, some examples where an apparent normal heat diffusion is found over a large range of length scales were reported. We propose a novel physical explanation of these intriguing observations. We develop a scaling analysis that explains how this may happen in the vicinity of an integrable limit, such as, but not only, the famous Toda model. In this limit, heat transport is mostly supplied by quasiparticles with a very large mean free path ℓ. Upon increasing the system size L, three different regimes can be observed: a ballistic one, an intermediate diffusive range, and, eventually, the crossover to the anomalous (hydrodynamic) regime. Our theoretical considerations are supported by numerical simulations of a gas of diatomic hard-point particles for almost equal masses and of a weakly perturbed Toda chain. Finally, we discuss the case of the perturbed harmonic chain, which exhibits a yet different scenario.
Collapse
Affiliation(s)
- Stefano Lepri
- Consiglio Nazionale delle Ricerche, Istituto dei Sistemi Complessi, Via Madonna del Piano 10, I-50019 Sesto Fiorentino, Italy
- Istituto Nazionale di Fisica Nucleare, Sezione di Firenze, via G. Sansone 1, I-50019 Sesto Fiorentino, Italy
| | - Roberto Livi
- Consiglio Nazionale delle Ricerche, Istituto dei Sistemi Complessi, Via Madonna del Piano 10, I-50019 Sesto Fiorentino, Italy
- Istituto Nazionale di Fisica Nucleare, Sezione di Firenze, via G. Sansone 1, I-50019 Sesto Fiorentino, Italy
- Dipartimento di Fisica e Astronomia and CSDC, Università di Firenze, via G. Sansone 1, I-50019 Sesto Fiorentino, Italy
| | - Antonio Politi
- Institute for Complex Systems and Mathematical Biology & SUPA University of Aberdeen, Aberdeen AB24 3UE, United Kingdom
| |
Collapse
|
3
|
G R A, Barik D. Temperature-dependent divergence of thermal conductivity in momentum-conserving one-dimensional lattices with asymmetric potential. Phys Rev E 2019; 99:022103. [PMID: 30934250 DOI: 10.1103/physreve.99.022103] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/17/2018] [Indexed: 06/09/2023]
Abstract
In this study we used a nonequilibrium simulation method to investigate the temperature dependent divergence of thermal conductivity in a one-dimensional momentum conserving system with an asymmetric double well nearest-neighbor interaction potential. We show that across all temperatures thermal conductivity exhibits power-law divergence with the chain length and the value of the divergence exponent (α) depends on the temperature of the system. At low and high temperatures α reaches close to ∼0.5 and ∼0.33, respectively. Whereas in the intermediate temperature the divergence of thermal conductivity with the chain length saturates with α∼0.07. Subsequent analysis showed that the estimated value of α in the intermediate temperature may not have reached its thermodynamic limit. Further calculations of local α revealed that its approach towards the thermodynamic limit is crucially dependent on the temperature of the system. At low and high temperatures local α reaches its thermodynamic limits in shorter chain lengths. On the contrary, in the case of intermediate temperature its progress towards the asymptotic limit is nonmonotonic.
Collapse
Affiliation(s)
- Archana G R
- School of Chemistry, University of Hyderabad, Gachibowli 500046, Hyderabad, India
| | - Debashis Barik
- School of Chemistry, University of Hyderabad, Gachibowli 500046, Hyderabad, India
| |
Collapse
|
4
|
Lee-Dadswell GR, Barrett N, Power M. Cluster sizes in a classical Lennard-Jones chain. Phys Rev E 2018; 96:032144. [PMID: 29346925 DOI: 10.1103/physreve.96.032144] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/30/2017] [Indexed: 11/07/2022]
Abstract
The definitions of breaks and clusters in a one-dimensional chain in equilibrium are discussed. Analytical expressions are obtained for the expected cluster length, 〈K〉, as a function of temperature and pressure in a one-dimensional Lennard-Jones chain. These expressions are compared with results from molecular dynamics simulations. It is found that 〈K〉 increases exponentially with β=1/k_{B}T and with pressure, P in agreement with previous results in the literature. A method is illustrated for using 〈K〉(β,P) to generate a "phase diagram" for the Lennard-Jones chain. Some implications for the study of heat transport in Lennard-Jones chains are discussed.
Collapse
Affiliation(s)
- G R Lee-Dadswell
- Math, Physics and Geology Department, Cape Breton University, Sydney, Nova Scotia, Canada
| | - Nicholas Barrett
- Math, Physics and Geology Department, Cape Breton University, Sydney, Nova Scotia, Canada
| | - Michael Power
- Math, Physics and Geology Department, Cape Breton University, Sydney, Nova Scotia, Canada
| |
Collapse
|
5
|
Xiong D. Heat perturbation spreading in the Fermi-Pasta-Ulam-β system with next-nearest-neighbor coupling: Competition between phonon dispersion and nonlinearity. Phys Rev E 2017; 95:062140. [PMID: 28709315 DOI: 10.1103/physreve.95.062140] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/25/2017] [Indexed: 06/07/2023]
Abstract
We employ the heat perturbation correlation function to study thermal transport in the one-dimensional Fermi-Pasta-Ulam-β lattice with both nearest-neighbor and next-nearest-neighbor couplings. We find that such a system bears a peculiar phonon dispersion relation, and thus there exists a competition between phonon dispersion and nonlinearity that can strongly affect the heat correlation function's shape and scaling property. Specifically, for small and large anharmoncities, the scaling laws are ballistic and superdiffusive types, respectively, which are in good agreement with the recent theoretical predictions; whereas in the intermediate range of the nonlinearity, we observe an unusual multiscaling property characterized by a nonmonotonic delocalization process of the central peak of the heat correlation function. To understand these multiscaling laws, we also examine the momentum perturbation correlation function and find a transition process with the same turning point of the anharmonicity as that shown in the heat correlation function. This suggests coupling between the momentum transport and the heat transport, in agreement with the theoretical arguments of mode cascade theory.
Collapse
Affiliation(s)
- Daxing Xiong
- Department of Physics, Fuzhou University, Fuzhou, 350108 Fujian, China
| |
Collapse
|
6
|
Gendelman OV, Savin AV. Heat conduction in a chain of colliding particles with a stiff repulsive potential. Phys Rev E 2016; 94:052137. [PMID: 27967160 DOI: 10.1103/physreve.94.052137] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/02/2016] [Indexed: 11/07/2022]
Abstract
One-dimensional billiards, i.e., a chain of colliding particles with equal masses, is a well-known example of a completely integrable system. Billiards with different particle masses is generically not integrable, but it still exhibits divergence of a heat conduction coefficient (HCC) in the thermodynamic limit. Traditional billiards models imply instantaneous (zero-time) collisions between the particles. We relax this condition of instantaneous impact and consider heat transport in a chain of stiff colliding particles with the power-law potential of the nearest-neighbor interaction. The instantaneous collisions correspond to the limit of infinite power in the interaction potential; for finite powers, the interactions take nonzero time. This modification of the model leads to a profound physical consequence-the probability of multiple (in particular triple) -particle collisions becomes nonzero. Contrary to the integrable billiards of equal particles, the modified model exhibits saturation of the heat conduction coefficient for a large system size. Moreover, the identification of scattering events with triple-particle collisions leads to a simple definition of the characteristic mean free path and a kinetic description of heat transport. This approach allows us to predict both the temperature and density dependencies for the HCC limit values. The latter dependence is quite counterintuitive-the HCC is inversely proportional to the particle density in the chain. Both predictions are confirmed by direct numerical simulations.
Collapse
Affiliation(s)
- Oleg V Gendelman
- Faculty of Mechanical Engineering, Technion-Israel Institute of Technology, Haifa 32000, Israel
| | - Alexander V Savin
- Semenov Institute of Chemical Physics, Russian Academy of Sciences, Moscow 119991, Russia
| |
Collapse
|
7
|
Hurtado PI, Garrido PL. A violation of universality in anomalous Fourier's law. Sci Rep 2016; 6:38823. [PMID: 27958318 PMCID: PMC5153844 DOI: 10.1038/srep38823] [Citation(s) in RCA: 14] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/21/2016] [Accepted: 11/15/2016] [Indexed: 12/04/2022] Open
Abstract
Since the discovery of long-time tails, it has been clear that Fourier's law in low dimensions is typically anomalous, with a size-dependent heat conductivity, though the nature of the anomaly remains puzzling. The conventional wisdom, supported by renormalization-group arguments and mode-coupling approximations within fluctuating hydrodynamics, is that the anomaly is universal in 1d momentum-conserving systems and belongs in the Lévy/Kardar-Parisi-Zhang universality class. Here we challenge this picture by using a novel scaling method to show unambiguously that universality breaks down in the paradigmatic 1d diatomic hard-point fluid. Hydrodynamic profiles for a broad set of gradients, densities and sizes all collapse onto an universal master curve, showing that (anomalous) Fourier's law holds even deep into the nonlinear regime. This allows to solve the macroscopic transport problem for this model, a solution which compares flawlessly with data and, interestingly, implies the existence of a bound on the heat current in terms of pressure. These results question the renormalization-group and mode-coupling universality predictions for anomalous Fourier's law in 1d, offering a new perspective on transport in low dimensions.
Collapse
Affiliation(s)
- Pablo I. Hurtado
- Institute Carlos I for Theoretical and Computational Physics and Departamento de Electromagnetismo y Física de la Materia, Universidad de Granada, 18071 Granada, Spain
| | - Pedro L. Garrido
- Institute Carlos I for Theoretical and Computational Physics and Departamento de Electromagnetismo y Física de la Materia, Universidad de Granada, 18071 Granada, Spain
| |
Collapse
|