Influence of thermalization on thermal conduction through molecular junctions: Computational study of PEG oligomers

Phonon transport along long polymer chains with varying configurations: Effects of phonon scattering

Following recent molecular dynamic simulations [M. Dinpajooh and A. Nitzan, J. Chem. Phys. 153, 164903 (2020)], we theoretically analyze how the phonon heat transport along a single polymer chain may be affected by varying the chain configuration. We suggest that phonon scattering controls the phonon heat conduction in strongly compressed (and tangled) chain when multiple random bends act as scattering centers for vibrational phonon modes, which results in the diffusive character of heat transport. As the chain is straightening up, the number of scatterers decreases, and the heat transport acquires nearly ballistic character. To analyze these effects, we introduce a model of a long atomic chain made out of identical atoms where some atoms are put in contact with scatterers and treat the phonon heat transfer through such a system as a multichannel scattering problem. We simulate the changes in the chain configurations by varying the number of the scatterers and mimic a gradual straightening of the chain by a gradual reducing of the number of scatterers attached to the chain atoms. It is demonstrated, in agreement with recently published simulation results, that the phonon thermal conductance shows a threshold-like transition from the limit where nearly all atoms are attached to the scatterers to the opposite limit where the scatterers vanish, which corresponds to a transition from the diffusive to the ballistic phonon transport.

Simulation toolkits at the molecular scale for trans-scale thermal signaling

Thermogenesis is a physiological activity of releasing heat that originates from intracellular biochemical reactions. Recent experimental studies discovered that externally applied heat changes intracellular signaling locally, resulting in global changes in cell morphology and signaling. Therefore, we hypothesize an inevitable contribution of thermogenesis in modulating biological system functions throughout the spatial scales from molecules to individual organisms. One key issue examining the hypothesis, namely, the "trans-scale thermal signaling," resides at the molecular scale on the amount of heat released via individual reactions and by which mechanism the heat is employed for cellular function operations. This review introduces atomistic simulation tool kits for studying the mechanisms of thermal signaling processes at the molecular scale that even state-of-the-art experimental methodologies of today are hardly accessible. We consider biological processes and biomolecules as potential heat sources in cells, such as ATP/GTP hydrolysis and multiple biopolymer complex formation and disassembly. Microscopic heat release could be related to mesoscopic processes via thermal conductivity and thermal conductance. Additionally, theoretical simulations to estimate these thermal properties in biological membranes and proteins are introduced. Finally, we envisage the future direction of this research field.

Tracking Energy Transfer across a Platinum Center

Rigid, conjugated alkyne bridges serve as important components in various transition-metal complexes used for energy conversion, charge separation, sensing, and molecular electronics. Alkyne stretching modes have potential for modulating charge separation in donor–bridge–acceptor compounds. Understanding the rules of energy relaxation and energy transfer across the metal center in such compounds can help optimize their electron transfer switching properties. We used relaxation-assisted two-dimensional infrared spectroscopy to track energy transfer across metal centers in platinum complexes featuring a triazole-terminated alkyne ligand of two or six carbons, a perfluorophenyl ligand, and two tri(p-tolyl)phosphine ligands. Comprehensive analyses of waiting-time dynamics for numerous cross and diagonal peaks were performed, focusing on coherent oscillation, energy transfer, and cooling parameters. These observables augmented with density functional theory computations of vibrational frequencies and anharmonic force constants enabled identification of different functional groups of the compounds. Computations of vibrational relaxation pathways and mode couplings were performed, and two regimes of intramolecular energy redistribution are described. One involves energy transfer between ligands via high-frequency modes; the transfer is efficient only if the modes involved are delocalized over both ligands. The energy transport pathways between the ligands are identified. Another regime involves redistribution via low-frequency delocalized modes, which does not lead to interligand energy transport.

Role of the phonon confinement effect and boundary scattering in reducing the thermal conductivity of argon nanowire

The thermal conductivity of model argon nanowires over a wide range of temperatures from 20 K to 70 K has been calculated using the formula obtained by solving the Boltzmann equation and independently by molecular dynamic (MD) simulations. The theoretical predictions for thermal conductivity take into account the effect of phonon confinement and boundary scattering. Two known theoretical approaches were used. The first approach is based on the solution of the Boltzmann equation with given boundary conditions and uses bulk acoustic phonon dispersion and neglects the phonon confinement effect. The second approach includes also the modification of acoustic phonon dispersion due to spatial confinement. In simulations, the square and circular shapes of wire with the transverse size of nanowires from 4.3 nm to 42.9 nm have been considered. It was found that MD simulation results match the theoretical predictions reasonably well. The obtained results showed that the phonon confinement effect influences the thermal conductivity of nanowires, but the dominant factor decreasing the thermal conductivity with the thickness of nanowires is boundary scattering. Moreover, the values of the interface specular parameter indicate that the specular phonon-boundary scattering prevails over diffuse phonon-boundary scattering.

Heat conduction in polymer chains with controlled end-to-end distance

The low thermal conductance of polymers is one of the major drawbacks for many polymer-based products. However, a single polymer chain when stretched can have high thermal conductivities. We use non-equilibrium molecular dynamics simulations to study the steady-state thermal conductance along finite macromolecules under mechanical control of the end-to-end distance. We find that the nature of heat transport along such chains strongly depends on mechanical tuning, leading to significantly different heat conductions and temperature profiles along the chain in the compressed-chain and stretched-chain limits. This transition between modes of behaviors appears to be a threshold phenomenon: at relatively small end-to-end distances, the thermal conductance remains almost constant as one stretches the polymer chain. At given critical end-to-end distances, thermal conductances start to increase, reaching the fully extended chain values. Correlated with this behavior are two observations: first, the temperature bias falls mostly at contacts in the fully stretched chain, while part of it falls along the molecule in the compressed limit. Second, the heat conduction does not change significantly with the chain length in the stretched-chain limit but decreases dramatically when this length increases in the compressed molecule. This suggests that heat transfer along stretched chains is mostly ballistic, while in the compressed chain, heat is transferred by diffusive mechanisms. Significantly, these trends persist also for a large range of molecular structures and force fields, and the changing behavior correlates well with mode localization properties. Similar studies conducted with disordered chains and bundles of several chains show remnants of the same behavior.

Energy Transfer across Nonpolar and Polar Contacts in Proteins: Role of Contact Fluctuations

Molecular dynamics simulations of the villin headpiece subdomain HP36 have been carried out to examine relations between rates of vibrational energy transfer across non-covalently bonded contacts and equilibrium structural fluctuations, with focus on van der Waals contacts. Rates of energy transfer across van der Waals contacts vary inversely with the variance of the contact length, with the same constant of proportionality for all nonpolar contacts of HP36. A similar relation is observed for hydrogen bonds, but the proportionality depends on contact pairs, with hydrogen bonds stabilizing the α-helices all exhibiting the same constant of proportionality, one that is distinct from those computed for other polar contacts. Rates of energy transfer across van der Waals contacts are found to be up to 2 orders of magnitude smaller than rates of energy transfer across polar contacts.

Stochastic simulation of nonequilibrium heat conduction in extended molecular junctions

Understanding phononic heat transport processes in molecular junctions is a central issue in the developing field of nanoscale heat conduction. Here, we present a Langevin dynamics simulation framework to investigate heat transport processes in molecular junctions at and beyond the linear response regime and apply it to saturated and unsaturated linear hydrocarbon chains connecting two gold substrates. Thermal boundary conditions represented by Markovian noise and damping are filtered through several (up to four) gold layers to provide a realistic and controllable bath spectral density. Classical simulations using the full universal force field are compared with quantum calculations that use only the harmonic part of this field. The close agreement found at about room temperature between these very different calculations suggests that heat transport at such temperatures is dominated by lower frequency vibrations whose dynamics is described well by classical mechanics. The results obtained for alkanedithiol molecules connecting gold substrates agree with previous quantum calculations based on the Landauer formula and match recent experimental measurements [e.g., thermal conductance around 20 pW/K for alkanedithiols in single-molecule junctions (SMJs)]. Heat conductance simulations on polyynes of different lengths illuminate the effects of molecular conjugation on thermal transport. The difference between alkanes and polyynes is not large but correlates with the larger rigidity and stronger mode localization that characterize the polyyne structure. This computational approach has been recently used [R. Chen, I. Sharony, and A. Nitzan, J. Phys. Chem. Lett. 11, 4261-4268 (2020)] to unveil local atomic heat currents and phononic interference effect in aromatic-ring based SMJs.

Crucial effect of transverse vibrations on the transport through polymer chains

The low temperature transport of electron, or vibrational or electronic exciton toward polymer chains, turns out to be dramatically sensitive to its interaction with transverse acoustic vibrations. We show that this interaction leads to a substantial polaron effect and decoherence, which are generally stronger than those associated with longitudinal vibrations. For site-dependent interactions, transverse phonons form subohmic bath leading to the quantum phase transition accompanied by full suppression of the transport at zero temperature and fast decoherence characterized by temperature dependent rate k₂ ∝ T^3/4 at low temperature, while k₂ ∝ T² for site-independent interactions. The latter dependence was used to interpret recent measurements of temperature dependent vibrational energy transport in polyethylene glycol oligomers.

Perturbation theory of thermal rectification

In this paper, a perturbation theory of thermal rectification is developed for a thermal system where an effective thermal conductivity throughout the system can be identified and changes smoothly and slightly. This theory provides an analytical formula of the thermal rectification ratio with rigorous mathematical derivations and physical assumptions. The physical meanings and limitations of the present theory are discussed in detail. Furthermore, a physical relationship among the thermal rectification, system length, temperature difference, and thermal conductivity is built. It reveals the linear relationship between the thermal rectification ratio and temperature difference. Also, the size dependence of the thermal rectification relies on the specific form of the thermal conductivity. In addition, several previous experimental and numerical observations are well explained by this theory.

Low-Temperature Vibrational Energy Transport via PEG Chains

We used relaxation-assisted two-dimensional infrared spectroscopy to study the temperature dependence (10-295 K) of end-to-end energy transport across end-decorated PEG oligomers of various chain lengths. The excess energy was introduced by exciting the azido end-group stretching mode at 2100 cm^-1 (tag); the transport was recorded by observing the asymmetric C═O stretching mode of the succinimide ester end group at 1740 cm^-1. The overall transport involves diffusive steps at the end groups and a ballistic step through the PEG chain. We found that at lower temperatures the through-chain energy transport became faster, while the end-group diffusive transport time and the tag lifetime increase. The modeling of the transport using a quantum Liouville equation linked the observations to the reduction of decoherence rate and an increase of the mean-free-path for the vibrational wavepacket. The energy transport at the end groups slowed down at low temperatures due to the decreased number and efficiency of the anharmonic energy redistribution pathways.

Tuning Molecular Vibrational Energy Flow within an Aromatic Scaffold via Anharmonic Coupling

From guiding chemical reactivity in synthesis or protein folding to the design of energy diodes, intramolecular vibrational energy redistribution harnesses the power to influence the underlying fundamental principles of chemistry. To evaluate the ability to steer these processes, the mechanism and time scales of intramolecular vibrational energy redistribution through aromatic molecular scaffolds have been assessed by utilizing two-dimensional infrared (2D IR) spectroscopy. 2D IR cross peaks reveal energy relaxation through an aromatic scaffold from the azido- to the cyano-vibrational reporters in para-azidobenzonitrile (PAB) and para-(azidomethyl)benzonitrile (PAMB) prior to energy relaxation into the solvent. The rates of energy transfer are modulated by Fermi resonances, which are apparent by the coupling cross peaks identified within the 2D IR spectrum. Theoretical vibrational mode analysis allowed the determination of the origins of the energy flow, the transfer pathway, and a direct comparison of the associated transfer rates, which were in good agreement with the experimental results. Large variations in energy-transfer rates, approximately 1.9 ps for PAB and 23 ps for PAMB, illustrate the importance of strong anharmonic coupling, i.e., Fermi resonance, on the transfer pathways. In particular, vibrational energy rectification is altered by Fermi resonances of the cyano- and azido-modes allowing control of the propensity for energy flow.

Chaotic Dynamics in a Quantum Fermi-Pasta-Ulam Problem

We investigate the emergence of chaotic dynamics in a quantum Fermi—Pasta—Ulam problem for anharmonic vibrations in atomic chains applying semi-quantitative analysis of resonant interactions complemented by exact diagonalization numerical studies. The crossover energy separating chaotic high energy phase and localized (integrable) low energy phase is estimated. It decreases inversely proportionally to the number of atoms until approaching the quantum regime where this dependence saturates. The chaotic behavior appears at lower energies in systems with free or fixed ends boundary conditions compared to periodic systems. The applications of the theory to realistic molecules are discussed.

Molecules and the Eigenstate Thermalization Hypothesis

We review a theory that predicts the onset of thermalization in a quantum mechanical coupled non-linear oscillator system, which models the vibrational degrees of freedom of a molecule. A system of N non-linear oscillators perturbed by cubic anharmonic interactions exhibits a many-body localization (MBL) transition in the vibrational state space (VSS) of the molecule. This transition can occur at rather high energy in a sizable molecule because the density of states coupled by cubic anharmonic terms scales as N³, in marked contrast to the total density of states, which scales as exp(aN), where a is a constant. The emergence of a MBL transition in the VSS is seen by analysis of a random matrix ensemble that captures the locality of coupling in the VSS, referred to as local random matrix theory (LRMT). Upon introducing higher order anharmonicity, the location of the MBL transition of even a sizable molecule, such as an organic molecule with tens of atoms, still lies at an energy that may exceed the energy to surmount a barrier to reaction, such as a barrier to conformational change. Illustrative calculations are provided, and some recent work on the influence of thermalization on thermal conduction in molecular junctions is also discussed.