Roadmap on thermoelectricity.

The increasing energy demand and the ever more pressing need for clean technologies of energy conversion pose one of the most urgent and complicated issues of our age. Thermoelectricity, namely the direct conversion of waste heat into electricity, is a promising technique based on a long-standing physical phenomenon, which still has not fully developed its potential, mainly due to the low efficiency of the process. In order to improve the thermoelectric performance, a huge effort is being made by physicists, materials scientists and engineers, with the primary aims of better understanding the fundamental issues ruling the improvement of the thermoelectric figure of merit, and finally building the most efficient thermoelectric devices. In this Roadmap an overview is given about the most recent experimental and computational results obtained within the Italian research community on the optimization of composition and morphology of some thermoelectric materials, as well as on the design of thermoelectric and hybrid thermoelectric/photovoltaic devices.

Thermal conduction and rectification phenomena in nanoporous silicon membranes.

Non-equilibrium molecular dynamics simulations have been applied to study thermal transport properties, such as thermal conductivity and rectification, in nanoporous Si membranes. Cylindrical pores have been generated in crystalline Si membranes with different configurations, including step-like, ordered and random pore distributions. The effect of interface and overall porosity on thermal transport properties has been investigated as well as the impact of the porosity profile on the direction of the heat current. The lowest thermal conductivity and highest thermal rectification for equal porosity have been found for a step-like pore distribution. Increasing interface porosity resulted in an increase of thermal rectification, which has been found to be systematically higher for random pore distribution with respect to an ordered one. Furthermore, a maximum in rectification of 5.5% has been found for a specific overall porosity (Φtot = 0.02) in samples with constant interface porosity and ordered pore distribution. This has been attributed to an increased effect of asymmetric interface boundary resistance resulting from increased fluctuations of the latter with altering temperature. The average value of the interface boundary resistance has been found to decrease with increasing porosity for samples with ordered pore distribution leading to a decrease in thermal rectification.

Room temperature second sound in cumulene.

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.

The thermal boundary resistance at semiconductor interfaces: a critical appraisal of the Onsager vs. Kapitza formalisms.

We critically readdress the definition of thermal boundary resistance at an interface between two semiconductors. By means of atomistic simulations we provide evidence that the widely used Kapitza formalism predicts thermal boundary resistance values in good agreement with the more rigorous Onsager non-equilibrium thermodynamics picture. The latter is, however, better suited to provide physical insight on interface thermal rectification phenomena. We identify the factors that determine the temperature profile across the interface and the source of interface thermal rectification. To this end we perform non-equilibrium molecular dynamics computational experiments on a Si-Ge system with a graded compositional interface of varying thickness, considering thermal bias of different sign.

Electrical and Thermal Transport in Coplanar Polycrystalline Graphene-hBN Heterostructures.

We present a theoretical study of electronic and thermal transport in polycrystalline heterostructures combining graphene (G) and hexagonal boron nitride (hBN) grains of varying size and distribution. By increasing the hBN grain density from a few percent to 100%, the system evolves from a good conductor to an insulator, with the mobility dropping by orders of magnitude and the sheet resistance reaching the MΩ regime. The Seebeck coefficient is suppressed above 40% mixing, while the thermal conductivity of polycrystalline hBN is found to be on the order of 30-120 Wm-1 K-1. These results, agreeing with available experimental data, provide guidelines for tuning G-hBN properties in the context of two-dimensional materials engineering. In particular, while we proved that both electrical and thermal properties are largely affected by morphological features (e.g., by the grain size and composition), we find in all cases that nanometer-sized polycrystalline G-hBN heterostructures are not good thermoelectric materials.

Deciphering Molecular Mechanisms of Interface Buildup and Stability in Porous Si/Eumelanin Hybrids.

Porous Si/eumelanin hybrids are a novel class of organic-inorganic hybrid materials that hold considerable promise for photovoltaic applications. Current progress toward device setup is, however, hindered by photocurrent stability issues, which require a detailed understanding of the mechanisms underlying the buildup and consolidation of the eumelanin-silicon interface. Herein we report an integrated experimental and computational study aimed at probing interface stability via surface modification and eumelanin manipulation, and at modeling the organic-inorganic interface via formation of a 5,6-dihydroxyindole (DHI) tetramer and its adhesion to silicon. The results indicated that mild silicon oxidation increases photocurrent stability via enhancement of the DHI-surface interaction, and that higher oxidation states in DHI oligomers create more favorable conditions for the efficient adhesion of growing eumelanin.

Tuning the thermal conductivity of methylammonium lead halide by the molecular substructure.

By using state-of-the-art atomistic methods we provide an accurate estimate of thermal conductivity of methylammonium lead halide as a function of sample size and temperature, in agreement with experimental works. We show that the thermal conductivity of methylammonium lead halide is intrinsically low, due to the low sound velocity of the PbI lattice. Furthermore, by selectively analyzing the effect of different molecular degrees of freedom, we clarify the role of the molecular substructure by showing that the internal modes above 150 cm(-1) (in addition to rotations) are effective in reducing the thermal conductivity of hybrid perovskites. This analysis suggests strategies to tailor the thermal conductivity by modifying the internal structure of organic cations.

Heat transport through a solid-solid junction: the interface as an autonomous thermodynamic system.

We perform computational experiments using nonequilibrium molecular dynamics simulations, showing that the interface between two solid materials can be described as an autonomous thermodynamic system. We verify the local equilibrium and give support to the Gibbs description of the interface also away from the global equilibrium. In doing so, we reconcile the common formulation of the thermal boundary resistance as the ratio between the temperature discontinuity at the interface and the heat flux with a more rigorous derivation from nonequilibrium thermodynamics. We also show that thermal boundary resistance of a junction between two pure solid materials can be regarded as an interface property, depending solely on the interface temperature, as implicitly assumed in some widely used continuum models, such as the acoustic mismatch model. Thermal rectification can be understood on the basis of different interface temperatures for the two flow directions.

Thermal Rectification by Design in Telescopic Si Nanowires.

We show that thermal rectification by design is possible by joining/growing Si nanowires (SiNWs) with sections of appropriately selected diameters (i.e., telescopic nanowires). This is done, first, by showing that the heat equation can be applied at the nanoscale (NW diameters down to 5 nm). We (a) obtain thermal conductivity versus temperature, κ(T), curves from molecular dynamics (MD) simulations for SiNWs of three different diameters, then (b) we conduct MD simulations of a telescopic NW built as the junction of two segments with different diameters, and afterward (c) we verify that the MD results for thermal rectification in telescopic NWs are very well reproduced by the heat equation with κ(T) of the segments from MD. Second, we apply the heat equation to predict the amount of thermal rectification in a variety of telescopic SiNWs with segments made from SiNWs where κ(T) has been experimentally measured, obtaining r values up to 50%. This methodology can be applied to predict the thermal rectification of arbitrary heterojunctions as long as the κ(T) data of the constituents are available.

Folds and buckles at the nanoscale: experimental and theoretical investigation of the bending properties of graphene membranes.

The elastic properties of graphene crystals have been extensively investigated, revealing unique properties in the linear and nonlinear regimes, when the membranes are under either stretching or bending loading conditions. Nevertheless less knowledge has been developed so far on folded graphene membranes and ribbons. It has been recently suggested that fold-induced curvatures, without in-plane strain, can affect the local chemical reactivity, the mechanical properties, and the electron transfer in graphene membranes. This intriguing perspective envisages a materials-by-design approach through the engineering of folding and bending to develop enhanced nano-resonators or nano-electro-mechanical devices. Here we present a novel methodology to investigate the mechanical properties of folded and wrinkled graphene crystals, combining transmission electron microscopy mapping of 3D curvatures and theoretical modeling based on continuum elasticity theory and tight-binding atomistic simulations.

Lattice thermal conductivity of Si(1-x)Ge(x) nanocomposites.

We calculate the lattice thermal conductivity in model Si(1-x)Ge(x) nanocomposites by molecular dynamics in a transient thermal conduction regime. Our simulations provide evidence that thermal transport depends only marginally on stoichiometry in the range 0.2≤x≤0.8, while it is deeply affected by the granulometry. In particular, we show that Si(1-x)Ge(x) nanocomposites have lattice thermal conductivity below the corresponding bulk alloy with the same stoichiometry. The main role in affecting thermal conduction is provided by grain boundaries, which largely affect vibrational modes with a long mean-free path.

Strong Anharmonicity at the Origin of Anomalous Thermal Conductivity in Double Perovskite Cs2 NaYbCl6.

Anomalous thermal transport of Cs2 NaYbCl6 double-halide perovskite above room temperature is reported and rationalized. Calculations of phonon dispersion relations and scattering rates up to the fourth order in lattice anharmonicity have been conducted to determine their effective dependence on temperature. These findings show that specific phonon group velocities and lifetimes increase if the temperature is raised above 500 K. This, in combination with anharmonicity, provides the microscopic mechanism responsible for the increase in lattice thermal conductivity at high temperatures, contrary to the predictions of phonon transport theories based on solely cubic anharmonicity. The model accurately and quantitatively reproduces the experimental thermal conductivity data as a function of temperature.

Folded graphene membranes: mapping curvature at the nanoscale.

While the unique elastic properties of monolayer graphene have been extensively investigated, less knowledge has been developed so far on folded graphene. Nevertheless, it has been recently suggested that fold-induced curvature (without in-plane strain) could possibly affect the local chemical and electron transport properties of graphene, envisaging a material-by-design approach where tailored membranes are used in enhanced nanoresonators or nanoelectromechanical devices. In this work we propose a novel method combining apparent strain analysis from high-resolution transmission electron microscopy (HREM) images and theoretical modeling based on continuum elasticity theory and tight-binding atomistic simulations to map and measure the nanoscale curvature of graphene folds and wrinkles. If enough contrast and resolution in HREM images are obtained, this method can be successfully applied to provide a complete nanoscale geometrical and physical picture of 3D structure of various wrinkle and fold configurations.

Thermally Promoted Cation Exchange at the Solid State in the Transmission Electron Microscope: How It Actually Works.

Cation exchange offers a strong postsynthetic tool for nanoparticles that are unachievable via direct synthesis, but its velocity makes observing the onset of the reaction in the liquid state almost impossible. After successfully proving that cation exchange reactions can be triggered, performed, and followed live at the solid state by an in situ transmission electron microscopy approach, we studied the deep mechanisms ruling the onset of cation exchange reactions, i.e., the adsorption, penetration, and diffusion of cations in the host matrices of two crystal phases of CdSe. Exploiting an in situ scanning transmission electron microscopy approach with a latest generation heating holder, we were able to trigger, freeze, and image the initial stages of cation exchange with much higher detail. Also, we found a connection between the crystal structure of CdSe, the starting temperature, and the route of the cation exchange reaction. All the experimental results were further reviewed by molecular dynamics simulations of the whole cation exchange reaction divided in subsequent steps. The simulations highlighted how the cation exchange mechanism and the activation energies change with the host crystal structures. Furthermore, the simulative results strongly corroborated the activation temperatures and the cation exchange rates obtained experimentally, providing a deeper understanding of its phenomenology and mechanism at the atomic scale.

Optoelectronic properties of (ZnO)60 isomers.

We studied the optoelectronic properties of six possible structures of the (ZnO)(60) cluster using density functional theory (DFT). Vertical ionization energies and electron affinities are calculated through total energy differences, while the optical absorption spectra are obtained by using hybrid time-dependent DFT. The (ZnO)(60) cluster has been proven to be particularly stable and it is of potential interest for future applications in nanoelectronics, but its ground-state configuration has been unknown to date. Since the relative stability inferred from total energy calculations suffers from a strong dependence on the computational scheme adopted, we combined it with optical spectroscopy to identify the most abundant geometrical structure of this cluster. The calculated optical spectra are different for each isomer and they could be thus used in comparison with experimental data to explain the ground state of (ZnO)(60).

Theory and Monte Carlo simulations for the stretching of flexible and semiflexible single polymer chains under external fields.

Recent developments of microscopic mechanical experiments allow the manipulation of individual polymer molecules in two main ways: uniform stretching by external forces and non-uniform stretching by external fields. Many results can be thereby obtained for specific kinds of polymers and specific geometries. In this work, we describe the non-uniform stretching of a single, non-branched polymer molecule by an external field (e.g., fluid in uniform motion, or uniform electric field) by a universal physical framework, which leads to general conclusions on different types of polymers. We derive analytical results both for the freely-jointed chain and the worm-like chain models based on classical statistical mechanics. Moreover, we provide a Monte Carlo numerical analysis of the mechanical properties of flexible and semiflexible polymers anchored at one end. The simulations confirm the analytical achievements, and moreover allow to study the situations where the theory cannot provide explicit and useful results. In all cases, we evaluate the average conformation of the polymer and its fluctuation statistics as a function of the chain length, bending rigidity, and field strength.

Elasticity of flexible and semiflexible polymers with extensible bonds in the Gibbs and Helmholtz ensembles.

Stretching experiments on single molecules of arbitrary length opened the way for studying the statistical mechanics of small systems. In many cases in which the thermodynamic limit is not satisfied, different macroscopic boundary conditions, corresponding to different statistical mechanics ensembles, yield different force-displacement curves. We formulate analytical expressions and develop Monte Carlo simulations to quantitatively evaluate the difference between the Helmholtz and the Gibbs ensembles for a wide range of polymer models of biological relevance. We consider generalizations of the freely jointed chain and of the worm-like chain models with extensible bonds. In all cases we show that the convergence to the thermodynamic limit upon increasing contour length is described by a suitable power law and a specific scaling exponent, characteristic of each model.

Observation of second sound in a rapidly varying temperature field in Ge.

Second sound is known as the thermal transport regime where heat is carried by temperature waves. Its experimental observation was previously restricted to a small number of materials, usually in rather narrow temperature windows. We show that it is possible to overcome these limitations by driving the system with a rapidly varying temperature field. High-frequency second sound is demonstrated in bulk natural Ge between 7 K and room temperature by studying the phase lag of the thermal response under a harmonic high-frequency external thermal excitation and addressing the relaxation time and the propagation velocity of the heat waves. These results provide a route to investigate the potential of wave-like heat transport in almost any material, opening opportunities to control heat through its oscillatory nature.

Energy Relaxation and Thermal Diffusion in Infrared Pump-Probe Spectroscopy of Hydrogen-Bonded Liquids.

Infrared pump-probe spectroscopy provides detailed information about the dynamics of hydrogen-bonded liquids. Due to dissipation of the absorbed pump pulse energy, thermal equilibration dynamics also contributes to the observed signal. Disentangling this contribution from the molecular response remains a challenge. By performing non-equilibrium molecular dynamics simulations of liquid-deuterated methanol, we show that faster molecular vibrational relaxation and slower heat diffusion are decoupled and occur on different length scales. Transient structures of the hydrogen bonding network influence thermal relaxation by affecting thermal diffusivity over a length scale of several nanometers.