1
|
Wang JJ, Gerry M, Segal D. Challenges in molecular dynamics simulations of heat exchange statistics. J Chem Phys 2024; 160:074111. [PMID: 38380748 DOI: 10.1063/5.0187357] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/13/2023] [Accepted: 01/29/2024] [Indexed: 02/22/2024] Open
Abstract
We study heat exchange in temperature-biased metal-molecule-metal molecular junctions by employing the molecular dynamics simulator LAMMPS. Generating the nonequilibrium steady state with Langevin thermostats at the boundaries of the junction, we show that the average heat current across a gold-alkanedithiol-gold nanojunction behaves physically, with the thermal conductance value matching the literature. In contrast, the full probability distribution function for heat exchange, as generated by the simulator, violates the fundamental fluctuation symmetry for entropy production. We trace this failure back to the implementation of the thermostats and the expression used to calculate the heat exchange. To rectify this issue and produce the correct statistics, we introduce single-atom thermostats as an alternative to conventional many-atom thermostats. Once averaging heat exchange over the hot and cold thermostats, this approach successfully generates the correct probability distribution function, which we use to study the behavior of both the average heat current and its noise. We further examine the thermodynamic uncertainty relation in the molecular junction and show that it holds, albeit demonstrating nontrivial trends. Our study points to the need to carefully implement nonequilibrium molecular dynamics solvers in atomistic simulation software tools for future investigations of noise phenomena in thermal transport.
Collapse
Affiliation(s)
- Jonathan J Wang
- Chemical Physics Theory Group, Department of Chemistry, University of Toronto, 80 Saint George St., Toronto, Ontario M5S 3H6, Canada
| | - Matthew Gerry
- Department of Physics, University of Toronto, 60 Saint George St., Toronto, Ontario M5S 1A7, Canada
| | - Dvira Segal
- Chemical Physics Theory Group, Department of Chemistry, University of Toronto, 80 Saint George St., Toronto, Ontario M5S 3H6, Canada
- Department of Physics, University of Toronto, 60 Saint George St., Toronto, Ontario M5S 1A7, Canada
| |
Collapse
|
2
|
Wang JJ, Gong J, McGaughey AJH, Segal D. Simulations of heat transport in single-molecule junctions: Investigations of the thermal diode effect. J Chem Phys 2022; 157:174105. [PMID: 36347668 DOI: 10.1063/5.0125714] [Citation(s) in RCA: 4] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
With the objective of understanding microscopic principles governing thermal energy flow in nanojunctions, we study phononic heat transport through metal-molecule-metal junctions using classical molecular dynamics (MD) simulations. Considering a single-molecule gold-alkanedithiol-gold junction, we first focus on aspects of method development and compare two techniques for calculating thermal conductance: (i) The Reverse Nonequilibrium MD (RNEMD) method, where heat is inputted and extracted at a constant rate from opposite metals. In this case, the thermal conductance is calculated from the nonequilibrium temperature profile that is created at the junction. (ii) The Approach-to-Equilibrium MD (AEMD) method, with the thermal conductance of the junction obtained from the equilibration dynamics of the metals. In both methods, simulations of alkane chains of a growing size display an approximate length-independence of the thermal conductance, with calculated values matching computational and experimental studies. The RNEMD and AEMD methods offer different insights, and we discuss their benefits and shortcomings. Assessing the potential application of molecular junctions as thermal diodes, alkane junctions are made spatially asymmetric by modifying their contact regions with the bulk, either by using distinct endgroups or by replacing one of the Au contacts with Ag. Anharmonicity is built into the system within the molecular force-field. We find that, while the temperature profile strongly varies (compared with the gold-alkanedithiol-gold junctions) due to these structural modifications, the thermal diode effect is inconsequential in these systems-unless one goes to very large thermal biases. This finding suggests that one should seek molecules with considerable internal anharmonic effects for developing nonlinear thermal devices.
Collapse
Affiliation(s)
- Jonathan J Wang
- Chemical Physics Theory Group, Department of Chemistry, University of Toronto, 80 Saint George St., Toronto, Ontario M5S 3H6, Canada
| | - Jie Gong
- Department of Mechanical Engineering, Carnegie Mellon University, Pittsburgh, Pennsylvania 15213, USA
| | - Alan J H McGaughey
- Department of Mechanical Engineering, Carnegie Mellon University, Pittsburgh, Pennsylvania 15213, USA
| | - Dvira Segal
- Chemical Physics Theory Group, Department of Chemistry, University of Toronto, 80 Saint George St., Toronto, Ontario M5S 3H6, Canada
| |
Collapse
|
3
|
Lai Liang F, Segal D. Long-range charge transport in homogeneous and alternating-rigidity chains. J Chem Phys 2022; 157:104106. [DOI: 10.1063/5.0101148] [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
We study the interplay of intrinsic-electronic and environmental factors in long-range charge transport across molecular chains with up to N ∼ 80 monomers. We describe the molecular electronic structure of the chain with a tight-binding Hamiltonian. Thermal effects in the form of electron decoherence and inelastic scattering are incorporated with the Landauer–Büttiker probe method. In short chains of up to ten units, we observe the crossover between coherent (tunneling, ballistic) motion and thermally-assisted conduction, with thermal effects enhancing the current beyond the quantum coherent limit. We further show that unconventional (nonmonotonic with size) transport behavior emerges when monomer-to-monomer electronic coupling is made large. In long chains, we identify a different behavior, with thermal effects suppressing the conductance below the coherent-ballistic limit. With the goal to identify a minimal model for molecular chains displaying unconventional and effective long-range transport, we simulate a modular polymer with alternating regions of high and low rigidity. Simulations show that, surprisingly, while charge correlations are significantly affected by structuring environmental conditions, reflecting charge delocalization, the electrical resistance displays an averaging effect, and it is not sensitive to this patterning. We conclude by arguing that efficient long-range charge transport requires engineering both internal electronic parameters and environmental conditions.
Collapse
Affiliation(s)
- Francisco Lai Liang
- Department of Chemistry and Centre for Quantum Information and Quantum Control, University of Toronto, 80 Saint George St., Toronto, Ontario M5S 3H6, Canada
| | - Dvira Segal
- Department of Chemistry and Centre for Quantum Information and Quantum Control, University of Toronto, 80 Saint George St., Toronto, Ontario M5S 3H6, Canada
- Department of Physics, University of Toronto, Toronto, Ontario M5S 1A7, Canada
| |
Collapse
|
4
|
Dinpajooh M, Nitzan A. Heat conduction in polymer chains: Effect of substrate on the thermal conductance. J Chem Phys 2022; 156:144901. [DOI: 10.1063/5.0087163] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/21/2023] Open
Abstract
In standard molecular junctions, a molecular structure is placed between and connected to metal leads. Understanding how mechanical tuning in such molecular junctions can change heat conductance has interesting applications in nanoscale energy transport. In this work, we use nonequilibrium molecular dynamics simulations to address the effect of stretching on the phononic contribution to the heat conduction of molecular junctions consisting of single long-chain alkanes and various metal leads, such as Ag, Au, Cu, Ni, and Pt. The thermal conductance of such junctions is found to be much smaller than the intrinsic thermal conductance of the polymer and significantly depends on the nature of metal leads as expressed by the metal–molecule coupling and metal vibrational density of states. This behavior is expected and reflects the mismatch of phonon spectra at the metal molecule interfaces. As a function of stretching, we find a behavior similar to what was observed earlier [M. Dinpajooh and A. Nitzan, J. Chem. Phys. 153, 164903 (2020)] for pure polymeric structures. At relatively short electrode distances, where the polyethylene chains are compressed, it is found that the thermal conductances of the molecular junctions remain almost constant as one stretches the polymer chains. At critical electrode distances, the thermal conductances start to increase, reaching the values of the fully extended molecular junctions. Similar behaviors are observed for junctions in which several long-chain alkanes are sandwiched between various metal leads. These findings indicate that this behavior under stretching is an intrinsic property of the polymer chain and not significantly associated with the interfacial structures.
Collapse
Affiliation(s)
| | - Abraham Nitzan
- Department of Chemistry, University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA
- School of Chemistry, Tel Aviv University, Tel Aviv 69978, Israel
| |
Collapse
|
5
|
Behera J, Bandyopadhyay M. Environment-dependent vibrational heat transport in molecular junctions: Rectification, quantum effects, vibrational mismatch. Phys Rev E 2021; 104:014148. [PMID: 34412343 DOI: 10.1103/physreve.104.014148] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/22/2021] [Accepted: 07/06/2021] [Indexed: 06/13/2023]
Abstract
Vibrational heat transport in molecular junctions is a central issue in different contemporary research areas such as chemistry, materials science, mechanical engineering, thermoelectrics, and power generation. Our model system consists of a chain of molecules which are sandwiched between two solids that are maintained at different temperatures. We employ a quantum self-consistent reservoir model, which is built on a generalized quantum Langevin equation, to investigate quantum effects and far from equilibrium conditions on thermal conduction at nanoscale. The present self-consistent reservoir model can easily mimic the phonon-phonon scattering mechanisms. Different thermal environments are modeled as (i) Ohmic, (ii) sub-Ohmic, and (iii) super-Ohmic environments, and their effects are demonstrated for the thermal rectification properties of the system with spring graded or mass graded features. The behavior of heat current across molecular junctions as a function of chain length, temperature gradient, and phonon scattering rates are studied. Further, our analysis reveals the effects of vibrational mismatch between the solids phonon spectra on heat transfer characteristics in molecular junctions for different thermal environments.
Collapse
Affiliation(s)
- Jayasmita Behera
- SBS, I.I.T. Bhubaneswar, Argul, Jatni, Khurda, Odisha 752050, India
| | | |
Collapse
|
6
|
Kaspar C, Thoss M. Efficient Steady-State Solver for the Hierarchical Equations of Motion Approach: Formulation and Application to Charge Transport through Nanosystems. J Phys Chem A 2021; 125:5190-5200. [PMID: 34102055 DOI: 10.1021/acs.jpca.1c02863] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
An iterative approach is introduced, which allows the efficient solution of the hierarchical equations of motion (HEOM) for the steady-state of open quantum systems. The approach combines the method of matrix equations with an efficient preconditioning technique to reduce the numerical effort of solving the HEOM. Illustrative applications to simulate nonequilibrium charge transport in single-molecule junctions demonstrate the performance of the method.
Collapse
Affiliation(s)
- C Kaspar
- Institute of Physics, University of Freiburg, Hermann-Herder-Straße 3, D-79104 Freiburg, Germany
| | - M Thoss
- Institute of Physics, University of Freiburg, Hermann-Herder-Straße 3, D-79104 Freiburg, Germany.,EUCOR Centre for Quantum Science and Quantum Computing, University of Freiburg, Hermann-Herder-Straße 3, D-79104 Freiburg, Germany
| |
Collapse
|
7
|
Kalantar N, Agarwalla BK, Segal D. Harmonic chains and the thermal diode effect. Phys Rev E 2021; 103:052130. [PMID: 34134267 DOI: 10.1103/physreve.103.052130] [Citation(s) in RCA: 7] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/26/2021] [Accepted: 05/05/2021] [Indexed: 06/12/2023]
Abstract
Harmonic oscillator chains connecting two harmonic reservoirs at different constant temperatures cannot act as thermal diodes, irrespective of structural asymmetry. However, here we prove that perfectly harmonic junctions can rectify heat once the reservoirs (described by white Langevin noise) are placed under temperature gradients, which are asymmetric at the two sides, an effect that we term "temperature-gradient harmonic oscillator diodes." This nonlinear diode effect results from the additional constraint-the imposed thermal gradient at the boundaries. We demonstrate the rectification behavior based on the exact analytical formulation of steady-state heat transport in harmonic systems coupled to Langevin baths, which can describe quantum and classical transport, both regimes realizing the diode effect under the involved boundary conditions. Our study shows that asymmetric harmonic systems, such as room-temperature hydrocarbon molecules with varying side groups and end groups, or a linear lattice of trapped ions may rectify heat by going beyond simple boundary conditions.
Collapse
Affiliation(s)
- Na'im Kalantar
- Department of Chemistry, University of Toronto, 80 Saint George Street, Toronto, Ontario, Canada M5S 3H6
| | - Bijay Kumar Agarwalla
- Department of Physics, Doctor Homi Bhabha Road, Indian Institute of Science Education and Research, Pune 411008, India
| | - Dvira Segal
- Department of Chemistry and Centre for Quantum Information and Quantum Control, University of Toronto, 80 Saint George Street, Toronto, Ontario, Canada M5S 3H6 and Department of Physics, University of Toronto, Toronto, Ontario, Canada M5S 1A7
| |
Collapse
|
8
|
Kalantar N, Agarwalla BK, Segal D. On the definitions and simulations of vibrational heat transport in nanojunctions. J Chem Phys 2020; 153:174101. [PMID: 33167626 DOI: 10.1063/5.0027414] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/14/2022] Open
Abstract
Thermal transport through nanosystems is central to numerous processes in chemistry, material sciences, and electrical and mechanical engineering, with classical molecular dynamics as the key simulation tool. Here, we focus on thermal junctions with a molecule bridging two solids that are maintained at different temperatures. The classical steady state heat current in this system can be simulated in different ways, either at the interfaces with the solids, which are represented by thermostats, or between atoms within the conducting molecule. We show that while the latter, intramolecular definition feasibly converges to the correct limit, the molecule-thermostat interface definition is more challenging to converge to the correct result. The problem with the interface definition is demonstrated by simulating heat transport in harmonic and anharmonic one-dimensional chains illustrating unphysical effects such as thermal rectification in harmonic junctions.
Collapse
Affiliation(s)
- Na'im Kalantar
- Chemical Physics Theory Group, Department of Chemistry, University of Toronto, 80 Saint George St., Toronto, Ontario M5S 3H6, Canada
| | - Bijay Kumar Agarwalla
- Department of Physics, Indian Institute of Science Education and Research, Dr. Homi Bhabha Road, Pune 411008, India
| | - Dvira Segal
- Chemical Physics Theory Group, Department of Chemistry and Centre for Quantum Information and Quantum Control, University of Toronto, 80 Saint George St., Toronto, Ontario M5S 3H6, Canada
| |
Collapse
|
9
|
Chen R, Sharony I, Nitzan A. Local Atomic Heat Currents and Classical Interference in Single-Molecule Heat Conduction. J Phys Chem Lett 2020; 11:4261-4268. [PMID: 32375004 DOI: 10.1021/acs.jpclett.0c00471] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/11/2023]
Abstract
We consider interference effects in vibrational heat conduction across single-molecule junctions. Previous theoretical descriptions of such effects have relied on the quantum Landauer-type expression for heat transport by harmonic molecules, and such observations are sometimes termed "quantum interference". Here we demonstrate via classical atomistic simulations of heat conduction in benzenedithiol single-molecule junctions that the room-temperature effect is essentially classical. In fact, classical simulations and quantum evaluation of room-temperature heat conduction in these systems yield similar results. Simulations of para-, meta-, and ortho-connected benzenedithiols between gold substrates yield conductions in the order para > ortho > meta, which is similar to trends found in the electronic conduction of these structures. The (essentially classical) interference origin of this ordering is indicated by the similarity of the quantum and classical behaviors of these systems.
Collapse
Affiliation(s)
- Renai Chen
- Department of Chemistry, University of Pennsylvania, Philadelphia, Pennsylvania 19104, United States
| | - Inon Sharony
- School of Chemistry, Tel Aviv University, Tel Aviv 69978, Israel
| | - Abraham Nitzan
- Department of Chemistry, University of Pennsylvania, Philadelphia, Pennsylvania 19104, United States
- School of Chemistry, Tel Aviv University, Tel Aviv 69978, Israel
| |
Collapse
|
10
|
Rivas Á. Strong Coupling Thermodynamics of Open Quantum Systems. PHYSICAL REVIEW LETTERS 2020; 124:160601. [PMID: 32383934 DOI: 10.1103/physrevlett.124.160601] [Citation(s) in RCA: 9] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/02/2019] [Accepted: 03/17/2020] [Indexed: 06/11/2023]
Abstract
A general thermodynamic framework is presented for open quantum systems in fixed contact with a thermal reservoir. The first and second law are obtained for arbitrary system-reservoir coupling strengths, and including both factorized and correlated initial conditions. The thermodynamic properties are adapted to the generally strong coupling regime, approaching the ones defined for equilibrium, and their standard weak-coupling counterparts as appropriate limits. Moreover, they can be inferred from measurements involving only system observables. Finally, a thermodynamic signature of non-Markovianity is formulated in the form of a negative entropy production rate.
Collapse
Affiliation(s)
- Ángel Rivas
- Departamento de Física Teórica, Facultad de Ciencias Físicas, Universidad Complutense, 28040 Madrid, Spain and CCS-Center for Computational Simulation, Campus de Montegancedo UPM, 28660 Boadilla del Monte, Madrid, Spain
| |
Collapse
|
11
|
Leitner DM, Pandey HD, Reid KM. Energy Transport across Interfaces in Biomolecular Systems. J Phys Chem B 2019; 123:9507-9524. [DOI: 10.1021/acs.jpcb.9b07086] [Citation(s) in RCA: 27] [Impact Index Per Article: 5.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/06/2023]
Affiliation(s)
- David M. Leitner
- Department of Chemistry, University of Nevada, Reno, Nevada 89557, United States
| | - Hari Datt Pandey
- Department of Chemistry, University of Nevada, Reno, Nevada 89557, United States
| | - Korey M. Reid
- Department of Chemistry, University of Nevada, Reno, Nevada 89557, United States
| |
Collapse
|
12
|
Asymmetrical vibrational energy propagation through double or single bonds of small organic molecules. An ab-initio molecular dynamics study. Chem Phys Lett 2019. [DOI: 10.1016/j.cplett.2019.05.056] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
|
13
|
McConnell C, Nazir A. Electron counting statistics for non-additive environments. J Chem Phys 2019. [DOI: 10.1063/1.5095838] [Citation(s) in RCA: 14] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Conor McConnell
- School of Physics and Astronomy, University of Manchester, Oxford Road, Manchester, M13 9PL, United Kingdom
| | - Ahsan Nazir
- School of Physics and Astronomy, University of Manchester, Oxford Road, Manchester, M13 9PL, United Kingdom
| |
Collapse
|