Internal Molecular Degrees Of Freedom Research Articles

Six-Field Theory for a Polyatomic Gas Mixture: Extended Thermodynamics and Kinetic Models

Polyatomic gases may be characterized by internal molecular degrees of freedom. As a consequence, at a macroscopic level, dynamic pressure appears, which may be related to the bulk viscosity of the gas. Inspired by the models of a single polyatomic gas with six fields, developed within rational extended thermodynamics (RET) and the kinetic theory of gases, this paper presents a six-field theory for the mixture of polyatomic gases. First, the macroscopic mixture model is developed within the framework of RET. Second, the mixture of gases with six fields is analyzed in the context of the kinetic theory of gases, and corresponding moment equations are derived. Finally, complete closure of the RET model, i.e., computation of the phenomenological coefficients, is achieved by means of a combined macroscopic/kinetic closure procedure.

Kinetic description of polyatomic gases with temperature-dependent specific heats

We present the continuous kinetic approach to modeling of thermally perfect (non-polytropic) gases with temperature dependent molecular internal degrees of freedom. Starting from the Boltzmann collision operator and a specific choice of the cross section enriched with free parameters, models are developed for transport coefficients, bulk and shear viscosities, and thermal conductivity. A procedure is proposed for simultaneously fitting parameters to match experimental data for temperature dependence of the specific heat, shear viscosity, and Prandtl number. Results for the dynamic pressure relaxation time, or equivalently, the bulk viscosity, are compared with previously existing estimates.

Thermodynamic and Kinetic Fragility of Freon 113: The Most Fragile Plastic Crystal.

We present a dynamic and thermodynamic study of the orientational glass former Freon 113 (1,1,2-trichloro-1,2,2-trifluoroethane, CCl_{2}F-CClF_{2}) in order to analyze its kinetic and thermodynamic fragilities. Freon 113 displays internal molecular degrees of freedom that promote a complex energy landscape. Experimental specific heat and its microscopic origin, the vibrational density of states from inelastic neutron scattering, together with the orientational dynamics obtained by means of dielectric spectroscopy have revealed the highest fragility value, both thermodynamic and kinetic, found for this orientational glass former. The excess in both Debye-reduced specific heat and density of states (boson peak) evidences the existence of glassy low-energy excitations. We demonstrate that early proposed correlations between the boson peak and the Debye specific heat value are elusive as revealed by the clear counterexample of the studied case.

Trapping-desorption and direct-scattering of formaldehyde at Au(111).

Nonreactive surface scattering of atoms, molecules and clusters can be almost universally described by two mechanisms: trapping-desorption and direct-scattering. A hard cube model with an attractive square well provides a zeroth order description of the branching ratio between these two mechanisms as a function of the incidence energy. However, the trapping process is likely to be enhanced by excitation of internal degrees of freedom during the collision. In this molecular beam surface scattering study, we characterize formaldehyde/Au(111) scattering using angle resolved time-of-flight techniques. The two mechanisms are found to compete in the range of the investigated normal incidence energies between 0.1 and 1.3 eV. Whereas at low incidence energies trapping-desorption dominates, direct-scattering becomes more likely at incidence energies above 0.37 eV. This incidence energy is slightly higher than the desorption energy which is found to be 0.32 ± 0.03 eV by temperature programmed desorption techniques. A simple hard cube model underestimates the observed trapping probabilities indicating the importance of trapping induced by excitation of internal molecular degrees of freedom.

An experimental toolbox for the generation of cold and ultracold polar molecules

Cold and ultracold molecules enable fascinating applications in quantum science. We present our toolbox of techniques to generate the required molecule ensembles, including buffergas cooling, centrifuge deceleration and optoelectrical Sisyphus cooling. We obtain excellent control over both the motional and internal molecular degrees of freedom, allowing us to aim at various applications.

Algorithm for reconstructing vibrational relaxation times in excitable gases by two-frequency acoustic measurements

Vibrational relaxation time is a parameter describing the macroscopic behavior of vibrational energy transition rate between molecular internal degrees of freedom (DOF) and external DOF in excitable gas, which determines the relaxation frequency of the maximum point in acoustic absorption spectrum. To measure the vibrational relaxation time, the traditional methods are used to obtain the acoustic absorption spectra by changing the ambient pressure at several operating frequencies. However, these traditional methods are not suitable for real-time measurement due to the complexity of equipment implementation and the non-ideality of test gas under high pressure. In order to solve those problems, we have developed an algorithm [2013 Meas. Sci. Technol. 24 055002] to capture the primary vibrational relaxation processes only based on the measurements of sound absorption and sound speed at two operating frequencies and a single pressure. But the algorithm only can reconstruct the absorption maximum and it cannot capture the relaxation time with high precision. To measure the frequency dependence of the complex effective specific heat of the relaxing gas, an algorithm synthesizing relaxation processes is given by Petculescu and Lueptow [2005 Phys. Rev. Lett. 94 238301]. In its derivation process, relaxational angular frequency was set to be the inverse ratio to relaxation time. However, the relaxational angular frequency was measured in the adiabatic process of transmission thermodynamic, while the relaxation time was obtained in the thermodynamic isothermal process, the derivation confused the two thermodynamic processes, making the algorithm unable to capture the relaxation frequency with high precision. In order to estimate the relaxation time with higher accuracy, in this paper we first obtain the theoretical relationship among the relaxation times under the three types of thermodynamics conditions, i. e., isothermal, adiabatic constant pressure and adiabatic constant volume. Then we correct the relaxation time derivation and propose our corrected algorithm to reconstruct the relaxation frequencies and relaxation times under the conditions of isothermal, adiabatic constant pressure and adiabatic constant volume. In experiments and simulations, the relaxation times and relaxation frequencies reconstructed by our corrected algorithm for various gas compositions including carbon dioxide, methane, chlorine, nitrogen, and oxygen around room temperature are consistent with the experimental data.

Molecular hydrogen interacts more strongly when rotationally excited at low temperatures leading to faster reactions.

The role of internal molecular degrees of freedom, such as rotation, has scarcely been explored experimentally in low-energy collisions despite their significance to cold and ultracold chemistry. Particularly important to astrochemistry is the case of the most abundant molecule in interstellar space, hydrogen, for which two spin isomers have been detected, one of which exists in its rotational ground state whereas the other is rotationally excited. Here we demonstrate that quantization of molecular rotation plays a key role in cold reaction dynamics, where rotationally excited ortho-hydrogen reacts faster due to a stronger long-range attraction. We observe rotational state-dependent non-Arrhenius universal scaling laws in chemi-ionization reactions of para-H2 and ortho-H2 by He(2(3)P2), spanning three orders of magnitude in temperature. Different scaling laws serve as a sensitive gauge that enables us to directly determine the exact nature of the long-range intermolecular interactions. Our results show that the quantum state of the molecular rotor determines whether or not anisotropic long-range interactions dominate cold collisions.

Thermal properties of halogen-ethane glassy crystals: Effects of orientational disorder and the role of internal molecular degrees of freedom.

The thermal conductivity, specific heat, and specific volume of the orientational glass former 1,1,2-trichloro-1,2,2-trifluoroethane (CCl2F-CClF2, F-113) have been measured under equilibrium pressure within the low-temperature range, showing thermodynamic anomalies at ca. 120, 72, and 20 K. The results are discussed together with those pertaining to the structurally related 1,1,2,2-tetrachloro-1,2-difluoroethane (CCl2F-CCl2F, F-112), which also shows anomalies at 130, 90, and 60 K. The rich phase behavior of these compounds can be accounted for by the interplay between several of their degrees of freedom. The arrest of the degrees of freedom corresponding to the internal molecular rotation, responsible for the existence of two energetically distinct isomers, and the overall molecular orientation, source of the characteristic orientational disorder of plastic phases, can explain the anomalies at higher and intermediate temperatures, respectively. The soft-potential model has been used as the framework to describe the thermal properties at low temperatures. We show that the low-temperature anomaly of the compounds corresponds to a secondary relaxation, which can be associated with the appearance of Umklapp processes, i.e., anharmonic phonon-phonon scattering, that dominate thermal transport in that temperature range.

A dipole-driven path for electron and positron attachments to gas-phase uracil and pyrimidine molecules: a quantum scattering analysis

Electron and positron scattering processes in the gas-phase are analysed for uracil and pyrimidine molecules using a multichannel quantum approach at energies close to threshold. The special effects on the scattering dynamics induced by the large dipole moments in both molecules on the spatial features of the continuum leptonic wavefunctions are here linked to the possible bound states of the Rydberg-like molecular anions or ‘positroned’ molecules which could be reached via further couplings with molecular internal degrees of freedom.

Single-molecule junctions with epitaxial graphene nanoelectrodes.

On the way to ultraflat single-molecule junctions with transparent electrodes, we present a fabrication scheme based on epitaxial graphene nanoelectrodes. As a suitable molecule, we identified a molecular wire with fullerene anchor groups. With these two components, stable electrical characteristics could be recorded. Electrical measurements show that single-molecule junctions with graphene and with gold electrodes display a striking agreement. This motivated a hypothesis that the differential conductance spectra are rather insensitive to the electrode material. It is further corroborated by the assignment of asymmetries and spectral features to internal molecular degrees of freedom. The demonstrated open-access graphene electrodes and the electrode-insensitive molecules provide a model system that will allow for a thorough investigation of an individual single-molecule contact with additional probes.

Mathematical model of a kinetic boundary layer

The two-dimensional (plane) problem of a hypersonic kinetic boundary layer developing on a thin body in the case of a homogeneous polyatomic gas flow with no dissociation or electron excitation is considered assuming that energy exchange between translational and internal molecular degrees of freedom is easy. (The approximation of a hypersonic kinetic boundary layer arises from the kinetic theory of gases and, within the thin-layer model, takes into account the strong nonequilibrium of the hypersonic flow with respect to translational and internal degrees of freedom of the gas particles.) A method is proposed for constructing the solution of the given kinetic problem in terms of a given solution of an equivalent well-studied classical Navier-Stokes hypersonic boundary layer problem (which is traditionally formulated on the basis of the Navier-Stokes equations).

Effects of internal molecular degrees of freedom on the thermal conductivity of some glasses and disordered crystals

The thermal conductivity $\ensuremath{\kappa}(T)$ of the fully ordered stable phase II, the metastable phase III, the orientationally disordered (plastic) phase I, as well as the nonergodic orientational glass (OG) phase, of the glass former cyclohexanol (C${}_{6}$H${}_{11}$OH) has been measured under equilibrium vapor pressure within the 2--200 K temperature range. The main emphasis is here focused on the influence of the conformational disorder upon the thermal properties of this material. Comparison of results with those regarding cyanoclyclohexane (C${}_{6}$H${}_{11}$CN), a chemically related compound, serves to quantify the role played by the terminal groups -OH and -CN on the phonon scattering processes. The picture that emerges shows that motions of such groups do play a minor role as scattering centers, both within the low-temperature orientationally ordered phases as well as in the OG states. The results are analyzed within the Debye-Peierls relaxation time model for isotropic solids comprising mechanisms for long-wave phonon scattering within the OG and orientational ordered low-temperature phases, as well as others arising from localized short-wavelength vibrational modes as pictured by the Cahill-Pohl model. By means of complementary neutron and Raman scattering we show that in the OG state the energy landscapes for both compounds are very similar.

A model of acoustic absorption in fluids based on a continuous distribution of relaxation times

This work extends the quasi-equilibrium relaxation theory of sound absorption in liquids to the case of continuous distribution of relaxation times. Such extension is needed when absorption mechanisms are not confined to the action of viscosity and heat conduction, but are mainly due to the excitation of a large number of internal molecular degrees of freedom. In this case the conventional Navier–Stokes equations are not sufficient to describe the fluid motion, and additional equations are required to model normal relaxation stresses. When relaxation frequencies form a sufficiently dense distribution, as is the case for many biological fluids, it makes sense to consider the limit of continuously distributed relaxation frequencies, in order to obtain the required equation for normal relaxation stresses.In contrast to its discrete counterparts, the proposed method avoids the use of a potentially infinite number of relaxation equations for a given set of distinct relaxation frequencies. Instead, these are replaced by a single evolution equation of Boltzmann type whose right-hand side is a linear combination of the time derivatives of density and entropy. The rheological functions appearing before these derivatives are expressed in terms of the absorption coefficient. Since the dependence of absorption coefficient on sound frequency is measurable experimentally, these rheological coefficients can be recovered from experimental data.The key feature of the present study is that a closed system of equations of motion can be formulated directly from absorption measurement data on the basis of the theory proposed for the very wide range of absorption laws that can occur in practice.As an illustration of the generality of the present method, a number of absorption laws documented in the experimental literature are considered in detail, in order to derive the coefficients of the related systems of equations of motion for these liquids. For example, the methodology based on modelling of acoustic absorption in biologically soft tissue by the employment of fractional derivatives, which has been recently developed in the literature, is shown to be a special case of the proposed theory.

Numerical simulation of hypersonic flows around space vehicles descending in the Martian atmosphere

The hypersonic flow near a space vehicle in the Martian atmosphere is studied. The flow around vehicles is considered within the model of a viscous shock layer. The effect of chemical reactions, nonequilibrium excitation of internal molecular degrees of freedom and multicomponent diffusion on the flow parameters and the heat flux to the surface of the spacecraft is investigated.

On acoustic absorption in tissue.

This work extends the relaxation theory of sound absorption to the case of continuous distribution of relaxation times. Such an extension is needed when the absorption mechanisms are not confined to viscosity and heat conduction, but are due mainly to the excitation of a large number of internal molecular degrees of freedom. In this case, the conventional Navier–Stokes equations are not sufficient, and additional equations are required to model relaxation stresses. When relaxation frequencies form a sufficiently dense distribution, as is the case for many biological fluids, it makes sense to consider the limit of continuously distributed relaxation frequencies in order to obtain the required equation for normal stresses. The proposed theory provides a means of deriving the equations of motion in physical time‐space from absorption data for a wide range of absorption laws that can occur in practice. A number of experimental absorption laws are considered in detail, and the related systems of equations of m...

ChemInform Abstract: Orientational Effects in Dissociative Adsorption/Associative Desorption Dynamics of H2(D2) on Cu and Pd

Abstract With the advent of sophisticated experimental techniques to study various dynamical processes on solid surfaces, e.g., initial molecular state preparation, energy- and state-resolved detection techniques, the study of dynamical processes occurring on solid surfaces is now at the stage where there is a more direct link between what experimental studies observe and what theory predicts. It would not be an exaggeration to say that, in surfaces we have a playground for physics, and the study of dynamical processes occurring on solid surfaces, such as the ones mentioned above, is a rich field for new discoveries and observations of novel physical phenomena, filled with many possibilities. The most natural test particle of choice for these reactions is hydrogen , which has always played a central role in the development of modern physics. Of the several dynamical factors that influence the dynamics of hydrogen-solid surface reactions (e.g., relative coordinates of reactions partners—hydrogen molecule and solid surface, molecular internal degrees of freedom, surface degrees of freedom), one important factor is molecular orientation. In this review, we will consider the dissociative adsorption and associative desorption dynamics of H 2 (D 2 ) molecules on/from Cu and Pd surfaces, which are typical examples of an activated and a non-activated system, respectively, and discuss how the orientation affects the dynamics of hydrogen on these surfaces and brings about such dynamical processes as steering and dynamical quantum filtering.

Synthetic model for Doppler broadening of neutron absorption resonances in molecular fluids

A general and systematic approach expressed in modern language, accounting for molecular motion effects on Doppler Broadening of Neutron Absorption Resonances (DBNAR) is given the form of a new model. It relies on well validated hypothesis: The separability of atomic from nuclear degrees of freedom, the use of the Van Hove scattering formalism and the fact that a conceptually identical approach produced experimentally proved predictions when applied to DBNAR in solid systems. We treat the molecular internal degrees of freedom approximately as harmonic oscillators. As a second contribution of this work, a synthetic model is presented in order to make the more complete model mentioned above suitable for neutron calculation codes. This second synthetic model reduces to the exact expressions of the complete model in the low and high neutron energy regimes and provides a plausible transition in between. Numerical results are presented for a general hypothetical case to show its strengths and limitations. Also, both models are applied to a real case of the 238U 6.674 eV resonant effective broadened absorption cross-section in UF6 (uranium hexafluoride). A direct experimental validation of our models is still necessary for which a special high resolution neutron transmission experiment ought to be devised at low temperatures and pressures on a gaseous system. It is showed how the synthetic model can be used to make thermometric predictions in an improved fashion in comparison to the effective temperature gas model at low temperatures.

Fractal growth in organic thin films: Experiments and modeling

Optical microscopy and atomic force microscopy were used to investigate the solidification process of the organic energetic material pentaerythritol tetranitrate thermally deposited on a silicon surface. The metastable films spontaneously undergo dendrite formation where the measured fractal dimensions indicate a diffusion-limited-aggregation mechanism. The branch growth rate was investigated as a function of temperature and fitted by a theoretical model that takes into account competing thermally activated processes of surface diffusion and molecular desorption. Consideration of the internal molecular degrees of freedom is shown to be essential for quantitative consistency between theory and experiment.

Effects of resonant phonon scattering from internal molecular modes on the thermal conductivity of molecular glasses

The thermal conductivity $\ensuremath{\kappa}(T)$ of the crystalline and glassy phases of the two isomers of propyl alcohol has been measured. The two isomers differ by a minor chemical detail involving the position of the hydroxyl group with respect to the carbon backbone. Such a difference in molecular structure leads, however, to disparate behaviors for the temperature dependence of $\ensuremath{\kappa}(T)$, for both glass and crystal states. The $\ensuremath{\kappa}(T)$ for the glass shows for 1-propanol an anomalously large plateau region comprising temperatures within $6--90\phantom{\rule{0.3em}{0ex}}\mathrm{K}$, while data for isomeric 2-propanol show only a small plateau up to $10\phantom{\rule{0.3em}{0ex}}\mathrm{K}$ which is comparable to data on lower alcohols. The results emphasize the role played by internal molecular degrees of freedom as sources of strong resonant phonon scattering.

Vapor Pressure and Sublimation Rate of Molecular Crystals: Role of Internal Degrees of Freedom

It is a common practice to approximate the desorption rate of atoms from crystal surfaces with an expression of the form nueff exp(-DeltaE/kBT), where DeltaE is an activation barrier to desorb and nueff is an effective vibrational frequency approximately 10(12) s(-1). For molecular solids, however, such an approximation can lead to a many orders of magnitude underestimation of vapor pressure and sublimation rates due to neglected contributions from molecular internal degrees of freedom. Here, we develop a simple working formula that yields good estimates for a general molecular (or atomic) solid and illustrate the approach by computing equilibrium vapor pressure of three different molecular solids and an atomic solid, as well as the desorption rate of a foreign (inhibitor) molecule from the surface of a molecular solid.