Librational Motion Research Articles

Low-temperature structural effects in the (TMTSF)2PF6and AsF6Bechgaard salts

We present a detailed low-temperature investigation of the statics and dynamics of the anions and methyl groups in the organic conductors (TMTSF)${}_{2}$PF${}_{6}$ and (TMTSF)${}_{2}$AsF${}_{6}$ (TMTSF: tetramethyl-tetraselenafulvalene). The 4 K neutron-scattering structure refinement of the fully deuterated (TMTSF)${}_{2}$PF${}_{6}$-D12 salt allows locating precisely the methyl groups at 4 K. This structure is compared to the one of the fully hydrogenated (TMTSF)${}_{2}$PF${}_{6}$-H12 salt previously determined at the same temperature. Surprisingly, it is found that deuteration corresponds to the application of a negative pressure of $5\ifmmode\times\else\texttimes\fi{}{10}^{2}$ MPa to the H12 salt. Accurate measurements of the Bragg intensity show anomalous thermal variations at low temperature both in the deuterated PF${}_{6}$ and AsF${}_{6}$ salts. Two different thermal behaviors have been distinguished. Small Bragg-angle measurements reflect the presence of low-frequency modes at characteristic energies ${\ensuremath{\theta}}_{E}$ $=$ 8.3 K and ${\ensuremath{\theta}}_{E}$ $=$ 6.7 K for the PF${}_{6}$-D12 and AsF${}_{6}$-D12 salts, respectively. These modes correspond to the low-temperature methyl group motion. Large Bragg-angle measurements evidence an unexpected structural change around 55 K, which probably corresponds to the linkage of the anions to the methyl groups via the formation of F\dots{}D-CD${}_{2}$ bonds observed in the 4 K structural refinement. Finally we show that the thermal expansion coefficient of (TMTSF)${}_{2}$PF${}_{6}$ is dominated by the librational motion of the PF${}_{6}$ units. We quantitatively analyze the low-temperature variation of the lattice expansion via the contribution of Einstein oscillators, which allows us to determine for the first time the characteristic frequency of the PF${}_{6}$ librations: ${\ensuremath{\theta}}_{E}$ \ensuremath{\approx} 50 K and ${\ensuremath{\theta}}_{E}$ $=$ 76 K for the PF${}_{6}$-D12 and PF${}_{6}$-H12 salts, respectively.

Phobos interior from librations determination using Doppler and star tracker measurements

Numerical simulations have been performed to assess the precision that can be obtained on Phobos libration angles by using two types of data acquired by a probe landed on the Martian moon: (1) Direct-To-Earth (DTE) Doppler data and (2) Star-Tracker (ST) data. Compared to independent estimates, combination of DTE and ST data provides the more precise estimates of Phobos libration angles at the 10−3−10−5 degree level. Short period libration amplitudes are functions of the relative moments of inertia. Thus their determination would provide constraints on mass distributions inside Phobos. We show that the longitudinal libration amplitude at the orbital period, while being clearly distinct from the resonance period, is the most interesting signal for that purpose, because it leads to the best precision on (B−A)/C (10−5 after only 10 weeks of operation). Nevertheless, we showed that inferring the individual moments of inertia A, B and C with a precision sufficient (<1%) to distinguish the rotational behavior of an homogenous from that of an heterogenous body requires the determination of one of the degree-two gravity field coefficient at the percent level.In addition, we stress that ST and DTE data combination allows de-correlating librational motion from orbital motion since ST measurements are sensitive to the moon's rotation and do not depend on its ephemeris, whereas DTE Doppler data are sensitive to both motions as well as to Phobos' surface displacement due to the tides raised by Mars. Furthermore, the ephemeris of Phobos has to be known at the centimeter level to allow measuring the tidal surface displacement with enough precision to conclude on the nature of Phobos' interior (rubble pile versus monolithic) as one step toward constraining its origin and evolution.

Orbital Maneuver for a Rotating Tethered System via Tidal Forces

Rotating tethered systems are regarded as fundamental space structures, attracting great interest among aerospace engineers, and have been discussed primarily for specific space missions including on-orbit capture and propellantless orbital transfer. The present work studies the dynamical behavior of a rapidly rotating tethered binary system under a central gravitational field and derives basic principles of orbital maneuvers. An averaging method is introduced to address the slow–fast system equation resulting from the characteristics of the coupled librational and orbital motions, and an equivalent model is derived. The general orbital motion is completely determined analytically, including the orbit geometry, the periodicity, the conservations, and the range of motion. Because the possibility of orbit control using tether reaction has been proved by previous studies, special attention is given to the transportation mode of angular momentum and mechanical energy between the orbit and the libration. The effect of tether length on the orbit is verified both in the averaged model and the original model. The results show that the orbital angular momentum and the mechanical energy can be controlled independently. Finally, the operating principles of tether reactions are derived for a special modification of the orbit.

Libration dynamics and stability of electrodynamic tethers in satellite deorbit

This paper studies libration dynamics and stability of deorbiting nano-satellites by short and bare electrodynamic tethers. A critical aspect of satellite deorbit by an electrodynamic tether is to maintain the tether aligned with the local vertical and stable while subjected to external perturbations. The dynamics of electrodynamic tether system in deorbit application is divided into the orbital motion of the center of system’s mass and the tether libration motion relative to that center. Major space environmental perturbations including the current-induced electrodynamic force, atmospheric drag, oblateness effect of the Earth, irregularity of geomagnetic field, variable plasma density, solar radiation pressure, and lunisolar gravitational attractions are considered in the dynamic analysis. Quantitative analyses are provided in order to characterize the order of the perturbative torques during the deorbit process. A single index is derived from the libration energy to stabilize the libration motion by regulating the current in the tether through simple on-off switching. Numerical results show that the libration dynamics of an electrodynamic tether has significant impacts on the deorbit process and the electrodynamic tether cannot effectively deorbit satellites without libration stability control. The proposed current regulation strategy is simple and very effective in stabilizing libration motion of an electrodynamic tether.

Quantum Behavior of Water Molecules Confined to Nanocavities in Gemstones.

When water is confined to nanocavities, its quantum mechanical behavior can be revealed by terahertz spectroscopy. We place H2O molecules in the nanopores of a beryl crystal lattice and observe a rich and highly anisotropic set of absorption lines in the terahertz spectral range. Two bands can be identified, which originate from translational and librational motions of the water molecule isolated within the cage; they correspond to the analogous broad bands in liquid water and ice. In the present case of well-defined and highly symmetric nanocavities, the observed fine structure can be explained by macroscopic tunneling of the H2O molecules within a six-fold potential caused by the interaction of the molecule with the cavity walls.

Low temperature phase properties of water confined in mesoporous silica MCM-41: Thermodynamic and neutron scattering study

The phase properties of water confined in mesoporous silica MCM-41 were investigated over a temperature range of 100-298 K as a function of pore size by specific heat capacity and inelastic neutron scattering (INS) measurements. The water content of the samples was carefully controlled to ensure the capillary filled state and no overloading of water. The values of heat capacity of the pore water are higher than those of bulk ice and liquid water over the whole temperature range measured. The contribution of water in the inner part of pores (abbreviated as the internal water) was elucidated by using the heat capacity data of monolayer water measured. The entropy of the internal water was then estimated from integration of the heat capacity of the internal water. The entropy values of the internal water increase by confinement in the pores of MCM-41 in both liquid and frozen regions, indicating an increase in the deformation of the structure and∕or a change in the dynamics in both regions. The INS spectra show the density of states for the librational motion of water frozen at 50 K, suggesting that the confined water is similar to amorphous ice rather than to crystalline ice. When the sample is warmed to melt, the band edge of the librational motion for water frozen in large pores (diameter of 3.6 nm) shifts to a lower energy side, indicating the weakening of intermolecular hydrogen bonds. For water in small pores (2.1 nm), on the contrary, the librational band shifts slightly to a higher energy side, suggesting the low density liquid to high density liquid transition (L-L transition) at 225-250 K. A plausible mechanism of the L-L transition of water in confinement is proposed in terms of incomplete growth of homogeneous nucleation of ice due to an interfacial free energy effect to inhibit crystallization of water confined in small pores.

Librational fluctuations in protein glasses

Librational motions in the region of the protein “glass” (or dynamic) transition are analysed for spin-labelled haemoglobin, serum albumin and β-lactoglobulin by EPR spectroscopy. A discontinuity in the temperature dependence of the mean-square librational amplitude, <α2>, occurs in the region of 200K as found for the mean-square atomic displacement, <r2>, at the protein dynamic transition by Mössbauer spectroscopy and neutron scattering. The discontinuity in <α2> vs. T can be described by the Vogel–Tammann–Fulcher equation, implying a finite glass transition temperature. Above the dynamic transition, <α2> vs. 1/T can be approximated by the Arrhenius law with activation energies similar to those usually found for <r2>, and relaxation processes in glass-forming media and the hydration shells of proteins. Similar results are found for librational fluctuations of membranous Na,K-ATPase spin-labelled either on superficial SH groups or on those essential to activity.

Understanding the Conduction Mechanism of the Protonic Conductor CsH2PO4 by Solid-State NMR Spectroscopy

Local dynamics and hydrogen bonding in CsH2PO4 have been investigated by 1H, 2H, and 31P solid-state NMR spectroscopy to help provide a detailed understanding of proton conduction in the paraelectric phase. Two distinct environments are observed by 1H and 2H NMR, and their chemical shifts (1H) and quadrupolar coupling constants (2H) are consistent with one strong and one slightly weaker H-bonding environment. Two different protonic motions are detected by variable-temperature 1H MAS NMR and T1 spin–lattice relaxation time measurements in the paraelectric phase, which we assign to librational and long-range translational motions. An activation energy of 0.70 ± 0.07 eV is extracted for the latter motion; that of the librational motion is much lower. 31P NMR line shapes are measured under MAS and static conditions, and spin–lattice relaxation time measurements have been performed as a function of temperature. Although the 31P line shape is sensitive to the protonic motion, the reorientation of the phosphate ...

Pressure and temperature effects on intermolecular vibrational dynamics of ionic liquids

Low frequency Raman spectra of ionic liquids have been obtained as a function of pressure up to ca. 4.0 GPa at room temperature and as a function of temperature along the supercooled liquid and glassy state at atmospheric pressure. Intermolecular vibrations are observed at ~20, ~70, and ~100 cm(-1) at room temperature in ionic liquids based on 1-alkyl-3-methylimidazolium cations. The component at ~100 cm(-1) is assigned to librational motion of the imidazolium ring because it is absent in non-aromatic ionic liquids. There is a correspondence between the position of intermolecular vibrational modes in the normal liquid state and the spectral features that the Raman spectra exhibit after partial crystallization of samples at low temperatures or high pressures. The pressure-induced frequency shift of the librational mode is larger than the other two components that exhibit similar frequency shifts. The lowest frequency vibration observed in a glassy state corresponds to the boson peak observed in light and neutron scattering spectra of glass-formers. The frequency of the boson peak is not dependent on the length scale of polar∕non-polar heterogeneity of ionic liquids, it depends instead on the strength of anion-cation interaction. As long as the boson peak is assigned to a mixing between localized modes and transverse acoustic excitations of high wavevectors, it is proposed that the other component observed in Raman spectra of ionic liquids has a partial character of longitudinal acoustic excitations.

Structure, Energetics, and Dynamics of Smectite Clay Interlayer Hydration: Molecular Dynamics and Metadynamics Investigation of Na-Hectorite

This paper presents a classical molecular dynamics (MD) and metadynamics investigation of the relationships between the structure, energetics, and dynamics of Na-hydroxyhectorite and serves to provide additional, molecular-scale insight into the interlayer hydration of this mineral. The computational results support a model for interlayer H2O structure and dynamics based on 2H NMR spectroscopy and indicate that H2O molecules undergo simultaneous fast librational motions about the H2O C2 symmetry axis and site hopping with C3 symmetry with respect to the surface normal. Hydration energy minima occur at one-, one-and-one-half-, and two-water-layer hydrates, which for the composition modeled correspond to 3, 5.5, and 10 H2O/Na+, respectively. Na+ ions are coordinated by basal O atoms (OMIN) at the lowest hydration levels and by H2O molecules (OH2O) in the two-layer hydrate, and H2O molecules have an average of three H-bonds at the greatest hydration levels. The metadynamics calculations yield activation energies for site hopping of H2O molecules of ∼6.0 kJ/mol for the one-layer structure and ∼3.3 kJ/mol for hopping between layers in the two-layer structure. Computed diffusion coefficients for water and Na+ are substantially less than in bulk liquid water, as expected in a nanoconfined environment, and are in good agreement with previous results.

Stability chart of the triangular points in the elliptic-restricted problem of three bodies

The possible observations of Trojan-like extrasolar planets stimulate the deeper understanding of the stability behaviour of the co-orbital resonant motion. By using Hill's equations and the energy-rate method an analysis of the stability map of the elliptic restricted three-body problem is performed. Regions of the $\mu-e$ parameter plane are described numerically and related to the resonant frequencies of librational motion. Stability and instability can therefore be obtained by analysing the two independent frequency modes depending on system parameters. The key role of the long period libration in determining the structure of the stability is demonstrated and also a stability mechanism is found that is responsible for extended life time of the test particle in the unstable domain of the stability map.

Dynamic limits on planar libration-orbit coupling around an oblate primary

This paper explores the dynamic properties of the planar system of an ellipsoidal satellite in an equatorial orbit about an oblate primary. In particular, we investigate the conditions for which the satellite is bound in librational motion or when the satellite will circulate with respect to the primary. We find the existence of stable equilibrium points about which the satellite can librate, and explore both the linearized and non-linear dynamics around these points. Absolute bounds are placed on the phase space of the libration-orbit coupling through the use of zero-velocity curves that exist in the system. These zero-velocity curves are used to derive a sufficient condition for when the satellite’s libration is bound to less than $$90^{\circ }$$ . When this condition is not satisfied so that circulation of the satellite is possible, the initial conditions at zero libration angle are determined which lead to circulation of the satellite. Exact analytical conditions for circulation and the maximum libration angle are derived for the case of a small satellite in orbits of any eccentricity.

Correlated Motions in Protein Crystals Measured by THz Microscopy

We introduce a new technique, Crystal Anisotropy Terahertz Microscopy (CATM) which directly measures correlated intra-molecular protein vibrations. The terahertz (THz) frequency range (5-100 cm−1) corresponds to global correlated protein motions proposed to be essential to functional conformational changes [1, 2]. CATM accesses these motions above the relaxational background of the solvent and residue side chain librational motions. We demonstrate narrowband features in the anisotropic absorbance for hen egg-white lysozyme (HEWL) single crystals as well as HEWL with triacetylglucosamine (HEWL-3NAG) inhibitor single crystals. By self-referencing to a single orientation, the absorption spectra were obtained and are free from absorption due to librational motions from biological water and artifacts due to multiple reflections within the crystal. The most prominent features for the HEWL crystals appear at 45 cm−1, 69 cm−1, and 78 cm−1 and the strength of the absorption varies with crystal orientation relative to the THz polarization. Similar anisotropic features appear in molecular mechanics calculations suggesting specific correlated mode identification is possible, giving us direct insight to the role of correlated motions in conformational changes necessary for ligand binding and catalysis. This work supported by NSF MRI∧2 grant DBI295998.View Large Image | View Hi-Res Image | Download PowerPoint Slide

Scrutinizing negative thermal expansion in MOF-5 by scattering techniques and ab initio calculations

Complementary experimental techniques and ab initio calculations were used to determine the origin and nature of negative thermal expansion (NTE) in the archetype metal-organic framework MOF-5 (Zn(4)O(1,4-benzenedicarboxylate)(3)). The organic linker was probed by inelastic neutron scattering under vacuum and at a gas pressure of 175 bar to distinguish between the pressure and temperature responses of the framework motions, and the local structure of the metal centers was studied by X-ray absorption spectroscopy. Multi-temperature powder- and single-crystal X-ray and neutron diffraction was used to characterize the polymeric nature of the sample and to quantify NTE over the large temperature range 4-400 K. Ab initio calculations complement the experimental data with detailed information on vibrational motions in the framework and their correlations. A uniform and comprehensive picture of NTE in MOF-5 has been drawn, and we provide direct evidence that the main contributor to NTE is translational transverse motion of the aromatic ring, which can be dampened by applying a gas pressure to the sample. The linker motion is highly correlated rather than local in nature. The relative energies of different framework vibrations populated in MOF-5 are suggested by analysis of neutron diffraction data. We note that the lowest-energy motion is a librational motion of the aromatic ring which does not contribute to NTE. The libration is followed by transverse motion of the linker and the carboxylate group. These motions result in unit-cell contraction with increasing temperature.

11308 テザー長制御と電流制御の組合せによる導電性テザーシステムの周期運動安定化(GS-05【制御】)

The tether satellite system treated in this paper consists of two subsatellites and a mother satellite connected together in series via massless tether. In this study, the control strategy to stabilize periodic motion in shorter time, compared to the previous studies, is that one tether is a non-electrodynamic tether using bang-bang control of tether length acceleration and the other one is an electrodynamic tether using PD control and delayed feedback control. The results of numerical simulations show that the proposed control scheme has a good performance in stabilizing the librational motion of the tether system combining non-electrodynamic and electrodynamic tethers to a periodic motion.

Embedded fragmentation of vibrational energies

Can the zero-point vibrational energies (ZPVE) of molecular clusters and crystals be evaluated as sums of ZPVE of constituent molecular fragments embedded in the cluster or crystal electrostatic environment? What is the appropriate unit of fragmentation: monomers or overlapping dimers? Can the contributions of acoustic phonons, which are fundamentally delocalized, be recuperated at satisfactory accuracy? These questions are answered by this study applying embedded monomer- and dimer-fragmentation methods to the harmonic ZPVE of hydrogen fluoride clusters, hydrogen fluoride crystal, and water clusters. Our findings are as follows: (1) ZPVE are reproduced accurately by both fragmentation schemes within a few percents of exact values or a few tenths of 1 kcal mol(-1) per molecule even for crystalline hydrogen fluoride, which has acoustic phonons. (2) Both the monomer- and dimer-based fragmentation are nearly equally accurate and useful for the absolute values of ZPVE, but the latter is more reliable than the former in reproducing the relative ZPVE of cluster isomers of the same size. (3) The embedding field is essential as it renders nonzero frequencies to the translational and rotational motions of monomers and dimers, accounting for the pseudo-translational and librational motions of the entire clusters or crystals. (4) Some of these low-frequency modes of fragments are calculated to have imaginary frequencies because the fragments are not at their equilibrium geometries, causing ZPVE to be complex. The imaginary part of ZPVE, which is nonphysical and is guaranteed to vanish in the exact limit of the many-body expansion, is nonetheless a useful estimate of errors in the real part.

Investigation on a Flexible Tether Slackness Based on In- and Out-of Plane Libration Angles

Tethered Satellite Systems (TSS) have been used in various applications such as in performing space interferometry, orbit transfer and other relevant fields. As far as the operation system of a TSS is concerned, it is crucial to ensure that the tether will not go slack as its slackness would adversely affects the overall operation outcome due to an undesirable system dynamics. Therefore, it is important to investigate the types of conditions that will cause the tether slackness. Investigations on in-plane and out-of plane libration angles can be utilized to measure at what point that the tether will go slack. Based on previous research works, usually a rigid tether comprising of a uniformed mass is considered while the connecting two satellites are regarded as point masses in order to simplify the governing dynamics equation of motion. However, in order to develop a much more accurate modeling, a flexible tether is chosen by further incorporating the reeling mechanism, attitude dynamics of rigid bodies and tether deformations. Furthermore, a tether has a tendency to go slack if the in-plane and out-of plane libration angle exceeds 65° and 60° respectively regardless of the types of tether utilized whether it being a rigid or a flexible one. Thus, the tension of the tether will serves as a constraint and plotted against the in-plane and out-of plane libration motions that would be attained via the generalized forces. The results will then be analyzed to establish in-plane and out-of plane libration boundaries. Subsequently, the in-plane and out-of plane operation contrains are established for TSS corresponding to a reference mission.

The sine-Gordon equation in the Semiclassical limit: Critical behavior near a separatrix

We study the Cauchy problem for the sine-Gordon equation in the semiclassical limit with pure-impulse initial data of sufficient strength to generate both high-frequency rotational motion near the peak of the impulse profile and also high-frequency librational motion in the tails. Subject to suitable conditions of a general nature, we analyze the fluxon condensate solution approximating the given initial data for small time near points where the initial data crosses the separatrix of the phase portrait of the simple pendulum. We show that the solution is locally constructed as a universal curvilinear grid of superluminal kinks and grazing collisions thereof, with the grid curves being determined from rational solutions of the Painlevé-II system.

Mapping the topography of Mercury with MESSENGER laser altimetry

The Mercury Laser Altimeter onboard MESSENGER involves unique design elements that deal with the challenges of being in orbit around Mercury. The Mercury Laser Altimeter (MLA) is one of seven instruments on NASA's MErcury Surface, Space ENvironment, GEochemistry, and Ranging (MESSENGER) spacecraft. MESSENGER was launched on 3 August 2004, and entered into orbit about Mercury on 18 March 2011 after a journey through the inner solar system. This involved six planetary flybys, including three of Mercury. MLA is designed to map the topography and landforms of Mercury's surface. It also measures the planet's forced libration (motion about the spin axis), which helps constrain the state of the core. The first science measurements from orbit taken with MLA were made on 29 March 2011 and continue to date. MLA had accumulated about 8.3 million laser ranging measurements to Mercury's surface, as of 31 July 2012, i.e., over six Mercury years (528 Earth days). Although MLA is the third planetary lidar built at the NASA Goddard Space Flight Center (GSFC), MLA must endure a much harsher thermal environment near Mercury than the previous instruments on Mars and Earth satellites. The design of MLA was derived in part from that of the Mars Orbiter Laser Altimeter on Mars Global Surveyor. However, MLA must range over greater distances and often in off-nadir directions from a highly eccentric orbit. In MLA we use a single-mode diode-pumped Nd:YAG (neodymium-doped yttrium aluminum garnet) laser that is highly collimated to maintain a small footprint on the planet. The receiver has both a narrow field of view and a narrow spectral bandwidth to minimize the amount of background light detected from the sunlit hemisphere of Mercury. We achieve the highest possible receiver sensitivity by employing the minimum receiver detection threshold.

Improved eIF4E Binding Peptides by Phage Display Guided Design: Plasticity of Interacting Surfaces Yield Collective Effects

Eukaryotic initiation factor (eIF)4E is over-expressed in many types of cancer such as breast, head and neck, and lung. A consequence of increased levels of eIF4E is the preferential translation of pro-tumorigenic proteins (e.g. c-Myc and vascular endothelial growth factor) and as a result is regarded as a potential therapeutic target. In this work a novel phage display peptide has been isolated against eIF4E. From the phage sequence two amino acids were delineated which improved binding when substituted into the eIF4G1 sequence. Neither of these substitutions were involved in direct interactions with eIF4E and acted either via optimization of the helical capping motif or restricting the conformational flexibility of the peptide. In contrast, substitutions of the remaining phage derived amino acids into the eIF4G1 sequence disrupted binding of the peptide to eIF4E. Interestingly when some of these disruptive substitutions were combined with key mutations from the phage peptide, they lead to improved affinities. Atomistic computer simulations revealed that the phage and the eIF4G1 derivative peptide sequences differ subtly in their interaction sites on eIF4E. This raises the issue, especially in the context of planar interaction sites such as those exhibited by eIF4E, that given the intricate plasticity of protein surfaces, the construction of structure-activity relationships should account for the possibility of significant movement in the spatial positioning of the peptide binding interface, including significant librational motions of the peptide.