Vibrational Density Of States Research Articles

Disorder classification of the vibrational spectra of modern glasses

Using the coherent-potential approximation in heterogeneous-elasticity theory with a log-normal distribution of elastic constants for the description of the Raman spectrum and the temperature dependence of the specific heat, we are able to reconstruct the vibrational density of states and characteristic descriptors of the elastic heterogeneity of a wide range of glassy materials. These descriptors are the nonaffine contribution to the shear modulus, the mean-square fluctuation of the local elasticity, and its correlation length. They enable a physical classification scheme for disorder in modern, industrially relevant glass materials. We apply our procedure to a broad range of real-world glass compositions, including metallic, oxide, chalcogenide, hybrid, and polymer glasses. Universal relationships between the descriptors on the one side, and the height and frequency position of the boson peak, the Poisson ratio and the liquid fragility index on the other side are established.

Comment on "Universal Origin of Boson Peak Vibrational Anomalies in Ordered Crystals and in Amorphous Materials".

In a recent article M. Baggioli and A. Zaccone (Phys. Rev. Lett. {\bf 112}, 145501 (2019)) claimed that an anharmonic damping, leading to a sound attenuation proportional to $\omega^2$ (Akhiezer-type damping) would imply a boson peak, i.e.\ a maximum in the vibrational density of states, divided by the frequency squared (reduced density of states). This would apply both to glasses and crystals.Here we show that this is not the case. In a mathematically correct treatment of the model the reduced density of states monotonously decreases, i.e.\ there is no boson peak. We further show that the formula for the would-be boson peak, presented by the authors, corresponds to a very short one-dimensional damped oscillator system. The peaks they show correspond to resonances, which vanish in the thermodynamic limit.

Two Faces of the Two-Phase Thermodynamic Model.

The quantum harmonic model and the two-phase thermodynamic method (2PT) are widely used to obtain quantum-corrected properties such as isobaric heat capacities or molar entropies. 2PT heat capacities were calculated inconsistently in the literature. For water, the classical heat capacity was also considered, but for organic liquids, it was omitted. We reanalyzed the performance of different quantum corrections on the heat capacities of common organic solvents against experimental data. We have pointed out serious flaws in previous 2PT studies. The vibrational density of states was calculated incorrectly causing a 39% relative error in diffusion coefficients and 45% error in the 2PT heat capacities. The wrong conversion of isobaric and isochoric heat capacities also caused about 40% error but in the other direction. We have introduced the concept of anharmonic correction (AC), which is simply the deviation of the classical heat capacity from that of the harmonic oscillator model. This anharmonic contribution is around +30 to 40 J/(mol K) for water depending on the water model and −8 to −10 J/(mol K) for hydrocarbons and halocarbons. AC is unrealistically large, +40 J/(K mol) for alcohols and amines, indicating some deficiency of the OPLS force field. The accuracy of the computations was also assessed with the determination of the self-diffusion coefficients.

Specific Heat Capacity of Confined Water in Extremely Narrow Graphene Nanochannels

Specific heat capacity of extremely confined water determines its performance in the heat transfer as the sizes of devices decrease to nanoscales. Here, we report the basic data of the specific heat capacity of water confined in narrow graphene nanochannels below 5 nm in height using molecular dynamics simulations. The results show that the specific heat capacity of confined water is size-dependent, and the commensurability effect of the specific heat capacity presents as the confinement decreases to 1.7 nm. The deviation of specific heat capacity of confined water with that of bulk water is attributed to the variation of configuration features, including density distribution and hydrogen bonds, and vibration features, including velocity auto-correlation function and vibrational density of states. This work unveils the confinement effects and their physical mechanisms of the specific heat capacity of nanoconfined water, and the data provided here have wide prospects for energy applications at nanoscales.

Influence of Surface Defects on the Thermal Conductivity of Hexagonal Boron Nitride/Poly(dimethylsiloxane) Nanocomposites: A Molecular Dynamics Simulation.

In this simulation, the reverse nonequilibrium molecular dynamics simulation is employed to explore how the surface defects in hexagonal boron nitride (h-BN) influence the thermal conductivity of poly(dimethylsiloxane) (PDMS)-based composites. First, the interfacial thermal conductivity and the intrinsic thermal conductivity of h-BN are obtained by tuning the defect density, the inhomogeneity of the defect distribution, and the number of h-BN layers. The defects enhance the interfacial thermal conductivity, especially for h-BNs with high inhomogeneity of the defect distribution and multilayer. However, the intrinsic thermal conductivity of h-BN is declined significantly by the defects. They can be explained well by the vibrational density of states of PDMS and h-BNs and their overlap. Then, by combining the effective medium approximation model with the simulation, the overall thermal conductivity of composites is obtained. It exhibits a gradual decrease with increasing defect density or reducing the inhomogeneity of the defect distribution. Meanwhile, the enhancement extent of the overall thermal conductivity by improving the concentration and size of h-BNs depends on the defect density and the defect distribution. Finally, the comparison between the simulation and experiment is discussed. In summary, our work provides some valuable insights into how the defect density, the defect distribution, and the number of layers influence the thermal conductivity of the PDMS-based composite.

Thermodynamic properties of propane and methane hydrates doped with sodium hydroxide

Pure and sodium hydroxide doped with single-component hydrates of methane and propane are studied using molecular and lattice dynamics methods. Vibration density of states and the dependence of Helmholtz free energy on temperature and cell volume are calculated. Dynamic stability of empty and filled by gas sI and sII structures doped with 1 or 2 NaOH molecule is shown in the wide range of temperature values. Comparison of free energy values allows calculating the thermal expansion coefficient and demonstrating the possibility of self-preservation effect in NaOH-doped methane and propane hydrates with ~1.8 and ~1.4 mol% of sodium hydroxide, respectively.

Effects of hydrophobic solute on water normal modes

In this work, we examine the effects of methane, on the normal modes of water. We find methane has a weaker influence on water normal modes. We estimate the vibrational density of states and the infrared spectral density. We decompose these modes based on different vibrational characters. We observe a general decrease in intensity throughout the water stretch region in the methane-water system compared to the bulk water data. This lower intensity reflects the reduction of the number of average water molecules in the methane-water system. The stretch-bend decomposition reflects a pronounced coupling between the methane asymmetric stretch mode and the water symmetric stretch mode. We examine the methane-water data in terms of the symmetry of the central water molecule’s vibrations and find that asymmetric modes do not contribute. We also find that the vibrational modes having non-zero contributions from methane molecule are extremely localized in nature.

Theoretical investigation of metal oxides for SO2 capture through first‐principles calculations

AbstractAtmospheric pollution is an accelerating environmental issue. Thus, methods to mitigate this problem are highly important. In this study, metal oxide‐based materials for capturing SO2 were theoretically identified using first‐principles calculations. In specific, the thermodynamic properties of MnO, Na2O, K2O, and Ag2O for capturing SO2 were assessed by computing their vibrational density of states. The rank of the maximum temperature for capturing SO2 as sulfites in decreasing order was K2O > Na2O > MnO > Ag2O at a wide range of SO2 pressure. For Na2O and K2O that showed a higher range of SO2 capture temperatures than MnO and Ag2O as sulfites, the maximum temperature of these two compounds for capturing SO2 as sulfates was further explored. The maximum temperature of the metal oxides for capturing SO2 changed upon pressurization of metal oxides. The maximum temperature of each metal oxide increased with increasing positive pressure (i.e., compression) and decreased with increasing negative pressure (i.e., expansion).

Investigation of the vibrational density of states of sodium carboxymethyl starch glass via terahertz time-domain spectroscopy

We investigated the vibrational density of states of sodium carboxymethyl starch (CM-starch) by terahertz (THz) time-domain spectroscopy. The CM-starch showed a broad peak at ∼3 THz. The structure of the peak was similar to those corresponding to glucose-based polymer glasses possessing hydrogen bonds. The boson peak (BP) appeared at 1.16 THz at the lowest temperature and disappeared because of the existence of excess wing at higher temperatures. However, based on our novel BP frequency determination method using the inflection point of the extinction coefficient, the BP frequency showed almost no dependence on temperature. Further, the chain length dependence of the BP frequency of the glucose-based glasses showed that the BP frequency of the polymer glass was slightly lower than that of the monomer glass. The power law behaviour of the absorption coefficient suggested the existence of fractons, and the fractal dimension was estimated to be 2.33.

Liquid state properties of SEI components in dimethoxyethane

The solid-electrolyte interphase (SEI) layer is a critical constituent of battery technology, which incorporates the use of lithium metals. Since the formation of the SEI is difficult to avoid, the engineering and harnessing of the SEI are absolutely critical to advancing energy storage. One problem is that much fundamental information about SEI properties is lacking due to the difficulty in probing a chemically complex interfacial system. One such property that is currently unknown is the dissolution of the SEI. This process can have significant effects on the stability of the SEI, which is critical to battery performance but is difficult to probe experimentally. Here, we report the use of ab initio computational chemistry simulations to probe the solution state properties of SEI components LiF, Li2O, LiOH, and Li2CO3 in order to study their dissolution and other solution-based characteristics. Ab initio molecular dynamics was used to study the solvation structures of the SEI with a combination of radial distribution functions, discrete solvation structure maps, and vibrational density of states, which allows for the determination of free energies. From the change in free energy of dissolution, we determined that LiOH is the most likely component to dissolve in the electrolyte followed by LiF, Li2CO3, and Li2O although none were favored thermodynamically. This indicates that dissolution is not probable, but Li2O would make the most stable SEI with regard to dissolution in the electrolyte.

Heat capacity anomalies of the molecular crystal 1-fluoro-adamantane at low temperatures

Disorder–disorder phase transitions are rare in nature. Here, we present a comprehensive low-temperature experimental and theoretical study of the heat capacity and vibrational density of states of 1-fluoro-adamantane (C10H15F), an intriguing molecular crystal that presents a continuous disorder–disorder phase transition at T = 180 K and a low-temperature tetragonal phase that exhibits fractional fluorine occupancy. It is shown that fluorine occupancy disorder in the low-T phase of 1-fluoro-adamantane gives rise to the appearance of low-temperature glassy features in the corresponding specific heat (i.e., “boson peak” -BP-) and vibrational density of states. We identify the inflation of low-energy optical modes as the main responsible for the appearance of such glassy heat-capacity features and propose a straightforward correlation between the first localized optical mode and maximum BP temperature for disordered molecular crystals (either occupational or orientational). Thus, the present study provides new physical insights into the possible origins of the BP appearing in disordered materials and expands the set of molecular crystals in which “glassy-like” heat-capacity features have been observed.

Disorder-induced vibrational anomalies from crystalline to amorphous solids

The origin of boson peak -- an excess of density of states over Debye's model in glassy solids -- is still under intense debate, among which some theories and experiments suggest that boson peak is related to van-Hove singularity. Here we show that boson peak and van-Hove singularity are well separated identities, by measuring the vibrational density of states of a two-dimensional granular system, where packings are tuned gradually from a crystalline, to polycrystals, and to an amorphous material. We observe a coexistence of well separated boson peak and van-Hove singularities in polycrystals, in which the van-Hove singularities gradually shift to higher frequency values while broadening their shapes and eventually disappear completely when the structural disorder $\eta$ becomes sufficiently high. By analyzing firstly the strongly disordered system ($\eta=1$) and the disordered granular crystals ($\eta=0$), and then systems of intermediate disorder with $\eta$ in between, we find that boson peak is associated with spatially uncorrelated random flucutations of shear modulus $\delta G/\langle G \rangle$ whereas the smearing of van-Hove singularities is associated with spatially correlated fluctuations of shear modulus $\delta G/\langle G \rangle$.

Localization, Disorder, and Entropy in a Coarse-Grained Model of the Amorphous Solid.

We study the role of disorder in producing the metastable states in which the extent of mass localization is intermediate between that of a liquid and a crystal with long-range order. We estimate the corresponding entropy with the coarse-grained description of a many-particle system used in the classical density functional model. We demonstrate that intermediate localization of the particles results in a change of the entropy from what is obtained from a microscopic approach using for sharply localized vibrational modes following a Debye distribution. An additional contribution is included in the density of vibrational states to account for this excess entropy. A corresponding peak in / vs. frequency matches the characteristic boson peak seen in amorphous solids. In the present work, we also compare the shear modulus for the inhomogeneous solid having localized density profiles with the corresponding elastic response for the uniform liquid in the limit of high frequencies.

Testing mean-field theory for jamming of non-spherical particles: contact number, gap distribution, and vibrational density of states.

We perform numerical simulations of the jamming transition of non-spherical particles in two dimensions. In particular, we systematically investigate how the physical quantities at the jamming transition point behave when the shapes of the particle deviate slightly from the perfect disks. For efficient numerical simulation, we first derive an analytical expression of the gap function, using the perturbation theory around the reference disks. Starting from disks, we observe the effects of the deformation of the shapes of particles by the n-th-order term of the Fourier series [Formula: see text]. We show that the several physical quantities, such as the number of contacts, gap distribution, and characteristic frequencies of the vibrational density of states, show the power-law behaviors with respect to the linear deviation from the reference disks. The power-law behaviors do not depend on n and are fully consistent with the mean-field theory of the jamming of non-spherical particles. This result suggests that the mean-field theory holds very generally for nearly spherical particles.

Low temperature heat capacity of nanosize amorphous solids

Contrary to previous studies based on bulk materials, we analyze the behavior of the vibrational density of states (VDOS) and specific heat of an amorphous solid of nano-scales (∼3 nm) at low temperature. With Hamiltonian formulation based on the intermolecular dispersion forces, our analysis indicates a universal semi-circle form of the average VDOS in the bulk of the spectrum along with a super-exponentially increasing behavior in its edge. The latter in turn leads to a specific heat with a superlinear temperature (T) dependence below T < 1 K even at nano-scales, and, surprisingly agreeing with the experiments although the latter are carried out at macroscopic scales. The omnipresence of dispersion forces at microscopic scales indicates the application of our results to other disordered materials too.

Chemically Accurate Vibrational Free Energies of Adsorption from Density Functional Theory Molecular Dynamics: Alkanes in Zeolites.

We present a methodology to compute, at reduced computational cost, Gibbs free energies, enthalpies, and entropies of adsorption from molecular dynamics. We calculate vibrational partition functions from vibrational energies, which we obtain from the vibrational density of states by projection on the normal modes. The use of a set of well-chosen reference structures along the trajectories accounts for the anharmonicities of the modes. For the adsorption of methane, ethane, and propane in the H-CHA zeolite, we limit our treatment to a set of vibrational modes localized at the adsorption site (zeolitic OH group) and the alkane molecule interacting with it. Only two short trajectories (1–20 ps) are required to reach convergence (<1 kJ/mol) for the thermodynamic functions. The mean absolute deviations from the experimentally measured values are 2.6, 2.8, and 4.7 kJ/mol for the Gibbs free energy, the enthalpy, and the entropy term (−TΔS), respectively. In particular, the entropy terms show a major improvement compared to the harmonic approximation and almost reach the accuracy of the previous use of anharmonic frequencies obtained with curvilinear distortions of individual modes. The thermodynamic functions so obtained follow the trend of the experimental values for methane, ethane, and propane, and the Gibbs free energy of adsorption at experimental conditions is correctly predicted to change from positive for methane (5.9 kJ/mol) to negative for ethane (−4.8 kJ/mol) and propane (−7.1 kJ/mol).

Thermal conductivity of molten alkali halides: The phenomenology and molecular dynamic simulations

Semi-phenomenological consideration of the thermal conductivity based on experimental and molecular dynamics (MD) data for molten alkali halides (AHs) near their melting points was carried out on the basis of scaling concepts associated with the vibrational mechanism of heat transfer. As a result, a general formula for the thermal conductivity is proposed for all molten alkali halides which takes into account the difference in vibrational motion of cation and anion. Characteristic frequencies of the cation and anion vibrations were evaluated through vibrational densities of states. These frequencies allow the values of the thermal conductivity among all AHs melts near their melting points to be estimated to a degree of accuracy close to 10%. Additionally, independent of the assumed heat transfer mechanism, direct simulation of the heat flux was performed within the non-equilibrium molecular dynamics approach. The estimated thermal conductivity of alkali halides’ (AHs) melts (M = Li, Na, K; X = F, Cl, Br, I) are in good agreement with most experimental and MD studies via the Kubo-Green linear response formalism.

Glucosamine to gold nanoparticles binding studied using Raman spectroscopy

The binding of glucosamine to gold in water solutions of glucosamine hydrochloride mixed with clean colloidal gold nanoparticles obtained by laser ablation in liquid was studied using surface-enhanced Raman scattering (SERS), dynamic light scattering (DLS) and UV–VIS spectroscopy. The purpose of this study was to establish whether the binding of charged aminogroup to gold nanoparticles (AuNPs) is taking place, and if it does, how can it be identified by means of SERS.The average size of dried gold nanoparticles was (20 ± 4) nm determined by averaging the sizes observed in transmission electron microscopy micrographs, which is smaller than the average size of gold nanoparticles in water solution as determined by DLS: (52 ± 2) nm. Upon adding the glucosamine solutions to gold colloid, average hydrodynamic diameter of ions was slightly larger for 0.1 mM glucosamine solution (55 ± 2 nm), while it increased to (105 ± 22) nm in the case of 1 mM solution, and was (398 ± 54) nm when 10 mM glucosamine solution was added.Most prominent Raman bands observed both for 0.1 mM and 1 mM glucosamine solutions were located at 1165 cm−1, 1532 and 1586 cm−1 and assigned to C-N coupled with C-C stretching, and C-NH3+ deformation angles bending. In SERS spectrum of 1 mM GlcN+ solution, two strong bands at 999 and 1075 cm−1 were found and attributed to C-Oring stretching coupled with C-NH3+ bending (999 cm−1) and to dominantly C-O stretching vibration. The differences in SERS spectra are attributed to different number of glucosamine molecules that attach to gold nanoparticles and their orientation with respect to the metal particle surface, partly due to presence of beta anomers protonated at anomeric oxygen position. The assignment of glucosamine bands was further corroborated by comparison with vibrational spectra of alpha and beta glucose and of polycrystalline powder of glucosamine hydrochloride. For all three substances comprehensive calculation of vibrational density of states was conducted using density functional theory. Benchmark bands for polycrystalline glucose anomers distinction are 846 and 915 cm−1 for alpha glucose, and 902 cm−1 for beta glucose. However, the bands observed in SERS spectra of 0.1 mM glucosamine solution at 831, 899, and 946 cm−1 or in 1 mM solution at 934 cm−1 cannot be easily identified as belonging either to alpha or beta glucosamine anomer, due to complexity of atomic motions involved. The identification of vibrational bands associated with –CNH3+ group will aid SERS studies on amino acids, especially in cases when several atomic groups could possibly bind to AuNPs.

Vibrational properties of graphene quantum dots: Effects of confinement, geometrical structure, and edge orientation

We perform ab initio density functional theory calculations to study the lattice vibrations of graphene quantum dots (GQDs) with triangular, quadrate, and hexagonal shapes in lateral confinement of 1 to 3 nm and terminated in both zigzag and armchair orientations. We see the vibrational properties of GQD transform from molecular type into bulk-like type with increasing dot size and the features of the vibrational density of state also highly depend on the symmetry of the GQD. We find that the out-of-plane vibrated standing waves induced by lateral confinement instead of the in-plane vibrations dominate the lattice vibrations of small GQDs. By projecting the vibrational eigenvectors of GQDs on those of single-layer graphene, we see the mixture of the out-of-plane and in-plane vibrational characters in GQDs as the result of the strong lateral confinement. We identify coherent acoustic phonon modes in GQDs and find that the size dependence of coherent acoustic phonon frequency increases with increasing the isotropy of nanostructures. Moreover, different confinement effects on lattice vibrations along zigzag and armchair edge orientations are identified from ab initio calculations. We describe the Raman intensity of GQDs and observe a blue shift of the G-mode position in GQDs comparing to that of the single-layer graphene. Combining the bond length distribution at the edge of GQDs with the positive Gr\"uneisen parameters, we link such blue shift to the surface effect of GQDs.

Long-wavelength fluctuations and dimensionality crossover in confined liquids

The phase behavior of liquids confined in a slit geometry does not reveal a crossover from a three- to a two-dimensional behavior as the gap size decreases. Indeed, the prototypical two-dimensional hexatic phase only occurs in liquids confined to a monolayer. Here, we demonstrate that the dimensionality crossover is apparent in the lateral size dependence of the relaxation dynamics of confined liquids, developing a Debye model for the density of vibrational states of confined systems and performing extensive numerical simulations. In confined systems, Mermin-Wagner fluctuations enhance the amplitude of vibrational motion---or the Debye-Waller factor---by a quantity scaling as the inverse gap width and proportional to the logarithm of the aspect ratio, as a clear signature of a two-dimensional behavior. As the temperature or lateral system size increases, the crossover to a size-independent relaxation dynamics occurs when structural relaxation takes place before the vibrational modes with the longest wavelength develop.