Room-temperature ballistic energy transport in molecules with repeating units

Probing the Hydrophobic Region of a Lipid Bilayer at Specific Depths Using Vibrational Spectroscopy

A novel spectroscopic approach for studying the flexibility and mobility in the hydrophobic interior of lipid bilayers at specific depths is proposed. A set of test compounds featuring an azido moiety and a cyano or carboxylic acid moiety, connected by an alkyl chain of different lengths, was synthesized. FTIR data and molecular dynamics calculations indicated that the test compounds in a bilayer are oriented so that the cyano or carboxylic acid moiety is located in the lipid head-group region, while the azido group stays inside the bilayer at the depth determined by its alkyl chain length. We found that the asymmetric stretching mode of the azido group (νN3) can serve as a reporter of the membrane interior dynamics. FTIR and two-dimensional infrared (2DIR) studies were performed at different temperatures, ranging from 22 to 45 °C, covering the Lβ-Lα phase transition temperature of dipalmitoylphosphatidylcholine (∼41 °C). The width of the νN3 peak was found to be very sensitive to the phase transition and to the temperature in general. We introduced an order parameter, SN3, which characterizes restrictions to motion inside the bilayer. 2DIR spectra of νN3 showed different extents of inhomogeneity at different depths in the bilayer, with the smallest inhomogeneity in the middle of the leaflet. The spectral diffusion dynamics of the N3 peak was found to be dependent on the depth of the N3 group location in the bilayer. The obtained results enhance our understanding of the bilayer dynamics and can be extended to investigate membranes with more complex compositions.

Competition of Several Energy-Transport Initiation Mechanisms Defines the Ballistic Transport Speed

The ballistic regime of vibrational energy transport in oligomeric molecular chains occurs with a constant, often high, transport speed and high efficiency. Such a transport regime can be initiated by exciting a chain end group with a mid-infrared (IR) photon. To better understand the wavepacket formation process, two chemically identical end groups, azido groups with normal, ¹⁴N₃-, and isotopically substituted, ¹⁵N₃-, nitrogen atoms, were tested for wavepacket initiation in compounds with alkyl chains of n = 5, 10, and 15 methylene units terminated with a carboxylic acid (-a) group, denoted as ¹⁴N₃Cn-a and ¹⁵N₃Cn-a. The transport was initiated by exciting the azido moiety stretching mode, the ν_N≡N tag, at 2100 cm^–1 (¹⁴N₃Cn-a) or 2031 cm^–1 (¹⁵N₃Cn-a). Opposite to the expectation, the ballistic transport speed was found to decrease upon ¹⁴N₃ → ¹⁵N₃ isotope editing. Three mechanisms of the transport initiation of a vibrational wavepacket are described and analyzed. The first mechanism involves the direct formation of a wavepacket via excitation with IR photons of several strong Fermi resonances of the tag mode with the ν_N=N + ν_N–C combination state while each of the combination state components is mixed with delocalized chain states. The second mechanism relies on the vibrational relaxation of an end-group-localized tag into a mostly localized end-group state that is strongly coupled to multiple delocalized states of a chain band. Harmonic mixing of ν_N=N of the azido group with CH₂ wagging states of the chain permits a wavepacket formation within a portion of the wagging band, suggesting a fast transport speed. The third mechanism involves the vibrational relaxation of an end-group-localized mode into chain states. Two such pathways were found for the ν_N≡N initiation: The ν_N=N mode relaxes efficiently into the twisting band states and low-frequency acoustic modes, and the ν_N–C mode relaxes into the rocking band states and low-frequency acoustic modes. The contributions of the three initiation mechanisms in the ballistic energy transport initiated by ν_N≡N tag are quantitatively evaluated and related to the experiment. We conclude that the third mechanism dominates the transport in alkane chains of 5–15 methylene units initiated with the ν_N≡N tag and the wavepacket generated predominantly at the CH₂ twisting band. The isotope effect of the transport speed is attributed to a larger contribution of the faster wavepackets for ¹⁴N₃Cn-a or to the different breadth of the wavepacket within the twisting band. The study offers a systematic description of different transport initiation mechanisms and discusses the requirements and features of each mechanism. Such analysis will be useful for designing novel materials for energy management.

Unidirectional coherent energy transport via conjugated oligo(p-phenylene) chains

We discovered a way to funnel high-frequency vibrational quanta rapidly and unidirectionally over large distances using oligo(p-phenylene) chains. After mid-IR photon photoexcitation of a -COOH end group, the excess energy is injected efficiently into the chain, forming vibrational wavepackets that propagate freely along the chain. The transport delivers high-energy vibrational quanta with a range of transport speeds reaching 8.6 km/s, which exceeds the speed of sound in common metals (∼5 km/s) and polymers (∼2 km/s). Efficiencies of energy injection into the chain and transport along the chain are found to be very high and dependent on the extent of conjugation across the structure. By tuning the degree of conjugation via electronic doping of the chain, the transport speed and efficiency can be controlled. The study opens avenues for developing materials with controllable energy transport properties for heat management, schemes with efficient energy delivery to hard-to-reach regions, including transport against thermal gradients, and ways for initiating chemical reactions remotely.

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.

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.

Energy, Work, Entropy, and Heat Balance in Marcus Molecular Junctions

We present a consistent theory of energy balance and conversion in a single-molecule junction with strong interactions between electrons on the molecular linker (dot) and phonons in the nuclear environment where the Marcus-type electron hopping processes predominate in the electron transport. It is shown that the environmental reorganization and relaxation that accompany electron hopping energy exchange between the electrodes and the nuclear (molecular and solvent) environment may bring a moderate local cooling of the latter in biased systems. The effect of a periodically driven dot level on the heat transport and power generated in the system is analyzed, and energy conservation is demonstrated both within and beyond the quasistatic regime. Finally, a simple model of atomic scale engine based on a Marcus single-molecule junction with a driven electron level is suggested and discussed.

Topology, landscapes, and biomolecular energy transport

While ubiquitous, energy redistribution remains a poorly understood facet of the nonequilibrium thermodynamics of biomolecules. At the molecular level, finite-size effects, pronounced nonlinearities, and ballistic processes produce behavior that diverges from the macroscale. Here, we show that transient thermal transport reflects macromolecular energy landscape architecture through the topological characteristics of molecular contacts and the nonlinear processes that mediate dynamics. While the former determines transport pathways via pairwise interactions, the latter reflects frustration within the landscape for local conformational rearrangements. Unlike transport through small-molecule systems, such as alkanes, nonlinearity dominates over coherent processes at even quite short time- and length-scales. Our exhaustive all-atom simulations and novel local-in-time and space analysis, applicable to both theory and experiment, permit dissection of energy migration in biomolecules. The approach demonstrates that vibrational energy transport can probe otherwise inaccessible aspects of macromolecular dynamics and interactions that underly biological function.

Understanding vibrational energy transfer in macromolecules has been challenging to both theory and experiment. Here the authors use non-equilibrium molecular dynamics to reveal the relationship between heat transport in a model peptide, emergent nonlinearity, and the underlying free energy landscape.

Vibrational Cooling in Oligomeric Viologens of Different Sizes and Topologies

Vibrational cooling was investigated in a set of homologous dimers and trimers with methyl viologen repeat units (MV²⁺). The rapid, <500 fs decay of the D₁ excited state of monoreduced viologen (MV^+•) via a conical intersection allows the preparation of a vibrationally hot D₀ ground state with a large excess energy of 1.7 eV, which is equivalent to the initial effective temperature of ∼800 K. Pump-probe spectroscopy was used to monitor the disappearance of the characteristic D₀ → D₁ hot absorption band, which appears at longer wavelengths than the steady-state spectrum of "cold" MV^+• in equilibrium with the solvent. It is assumed that the vibrational excitation of the ground is initially confined to the same monoreduced viologen repeat unit, which was optically excited to the localized electronic D₁ state, although some degree of redistribution may occur already in the excited state. The observed cooling rates depend on the size and topology of the oligomer, with the linear trimer exhibiting significantly faster thermalization than the branched one. The experimental results were corroborated by molecular dynamics simulations carried out in the harmonic approximation. The dynamics of the thermal equilibration in these systems appears to be consistent with primarily ballistic initial propagation of the vibrational excess energy over distances as large as ∼4 nm and suggests the presence of interference between the equivalent pathways in the branched trimer.

Intermolecular energy flows between surface molecules on metal nanoparticles

Three model systems are designed to investigate energy transport between molecules on metal nanoparticle surfaces. Energy is rapidly transferred from one carbon monoxide (CO) molecule to another CO molecule or an organic molecule on adjacent surface sites of 2 nm Pt particles within a few picoseconds. On the contrary, energy flow from a surface organic molecule to an adjacent CO molecule is significantly slower and, in fact, within experimental sensitivity and uncertainty the transfer is not observed. The energy transport on particle surfaces (about 2 km s-1) is almost ten times faster than inside a molecule (200 m s-1). The seemingly perplexing observations can be well explained by the combination of electron/vibration and vibration/vibration coupling mechanisms, which mediate molecular energy dynamics on metal nanoparticle surfaces: the strong electron/vibration coupling rapidly converts CO vibrational energy into heat that can be immediately sensed by nearby molecules; but the vibration/vibration coupling dissipates the vibrational excitation in the organic molecule as low-frequency intramolecular vibrations that may or may not couple to surface electronic motions.

Ballistic and diffusive vibrational energy transport in molecules

Energy transport in molecules is essential for many areas of science and technology. Strong covalent bonds of a molecular backbone can facilitate the involvement of the molecule's high-frequency modes in energy transport, which, under certain conditions, makes the transport fast and efficient. We discuss such conditions and describe various transport regimes in molecules, including ballistic, diffusive, directed diffusion, and intermediate regime cases, in light of recently developed experimental and theoretical approaches.

Electron transfer across a thermal gradient

Charge transfer is a fundamental process that underlies a multitude of phenomena in chemistry and biology. Recent advances in observing and manipulating charge and heat transport at the nanoscale, and recently developed techniques for monitoring temperature at high temporal and spatial resolution, imply the need for considering electron transfer across thermal gradients. Here, a theory is developed for the rate of electron transfer and the associated heat transport between donor-acceptor pairs located at sites of different temperatures. To this end, through application of a generalized multidimensional transition state theory, the traditional Arrhenius picture of activation energy as a single point on a free energy surface is replaced with a bithermal property that is derived from statistical weighting over all configurations where the reactant and product states are equienergetic. The flow of energy associated with the electron transfer process is also examined, leading to relations between the rate of heat exchange among the donor and acceptor sites as functions of the temperature difference and the electronic driving bias. In particular, we find that an open electron transfer channel contributes to enhanced heat transport between sites even when they are in electronic equilibrium. The presented results provide a unified theory for charge transport and the associated heat conduction between sites at different temperatures.

Vibrational Heat Transport in Molecular Junctions

We review studies of vibrational energy transfer in a molecular junction geometry, consisting of a molecule bridging two heat reservoirs, solids or large chemical compounds. This setup is of interest for applications in molecular electronics, thermoelectrics, and nanophononics, and for addressing basic questions in the theory of classical and quantum transport. Calculations show that system size, disorder, structure, dimensionality, internal anharmonicities, contact interaction, and quantum coherent effects are factors that combine to determine the predominant mechanism (ballistic/diffusive), effectiveness (poor/good), and functionality (linear/nonlinear) of thermal conduction at the nanoscale. We review recent experiments and relevant calculations of quantum heat transfer in molecular junctions. We recount the Landauer approach, appropriate for the study of elastic (harmonic) phononic transport, and outline techniques that incorporate molecular anharmonicities. Theoretical methods are described along with examples illustrating the challenge of reaching control over vibrational heat conduction in molecules.

Ballistic Energy Transport in Oligomers

The development of nanocomposite materials with desired heat management properties, including nanowires, layered semiconductor structures, and self-assembled monolayer (SAM) junctions, attracts broad interest. Such materials often involve polymeric/oligomeric components and can feature high or low thermal conductivity, depending on their design. For example, in SAM junctions made of alkane chains sandwiched between metal layers, the thermal conductivity can be very low, whereas the fibers of ordered polyethylene chains feature high thermal conductivity, exceeding that of many pure metals. The thermal conductivity of nanostructured materials is determined by the energy transport between and within each component of the material, which all need to be understood for optimizing the properties. For example, in the SAM junctions, the energy transport across the metal-chain interface as well as the transport through the chains both determine the overall heat conductivity, however, to separate these contributions is difficult. Recently developed relaxation-assisted two-dimensional infrared (RA 2DIR) spectroscopy is capable of studying energy transport in individual molecules in the time domain. The transport in a molecule is initiated by exciting an IR-active group (a tag); the method records the influence of the excess energy on another mode in the molecule (a reporter). The energy transport time can be measured for different reporters, and the transport speed through the molecule is evaluated. Various molecules were interrogated by RA 2DIR: in molecules without repeating units (disordered), the transport mechanism was expected and found to be diffusive. The transport via an oligomer backbone can potentially be ballistic, as the chain offers delocalized vibrational states. Indeed, the transport regime via three tested types of oligomers, alkanes, polyethyleneglycols, and perfluoroalkanes was found to be ballistic, whereas the transport within the end groups was diffusive. Interestingly, the transport speeds via these chains were different. Moreover, the transport speed was found to be dependent on the vibrational mode initiating the transport. For the difference in the transport speeds to be explained, the chain bands involved in the wavepacket formation were analyzed, and specific optical bands of the chain were identified as the energy transporters. For example, the transport initiated in alkanes by the stretching mode of the azido end group (2100 cm(-1)) occurs predominantly via the CH2 twisting and wagging chain bands, but the transport initiated by the C=O stretching modes of the carboxylic acid or succinimide ester end groups occurs via C-C stretching and CH2 rocking bands of the alkane chain. Direct formation of the wavepacket within the CH2 twisting and wagging chain bands occurs when the transport is initiated by the N═N stretching mode (1270 cm-1) of the azido end-group. The transport via optical chain bands in oligomers involves rather large vibrational quanta (700-1400 cm(-1)), resulting in efficient energy delivery to substantial distances. Achieved quantitative description of various energy transport steps in oligomers, including the specific contributions of different chain bands, can result in a better understanding of the transport steps in nanocomposite materials, including SAM junctions, and lead towards designing systems for molecular electronics with a controllable energy transport speed.