Elastic Incoherent Structure Factor Research Articles

X-ray diffraction and quasielastic neutron scattering studies of the structure and dynamic properties of water confined in ordered microporous carbon pores

The structure and dynamic properties of capillary-condensed water confined in ordered microporous carbon (OMC) of pores diameter 18.7 Å are investigated over a temperature range of 200–300 K by adsorption/desorption isotherms, X-ray diffraction (XRD), and quasielastic neutron scattering (QENS). The nitrogen adsorption/desorption isotherm of OMC pores at 77 K exhibits an I-type pattern. The water adsorption/desorption isotherm of OMC pores at 298 K is of type V. The XRD data on water confined in OMC reveal that the tetrahedral network structure of water is perturbed from the bulk water structure, but not to such an extent as found for water confined in MCM-41 and Ph-PMO previously reported. With decreasing the temperature, the ∼2.8 Å peak shifts to shorter distances, while the second-neighbor H2O– H2O interaction distances gradually increase from 3.95 Å and 4.49 Å to 4.43 Å and 4.84 Å, indicating a tendency to form a more tetrahedral-like hydrogen-bonded water structure at subzero temperatures. Below 230 K, the hexagonal ice Ih was partially formed in OMC pores. The QENS spectra were analyzed using a jump-diffusion model to translate water molecules. The translational diffusion of water molecules in OMC pores is comparable to that of bulk water at 300 K and higher than that in MCM-41, and the mobility slows as the temperature decreases. The elastic incoherent structure factor (EISF) analysis found evidence for immobile and mobile fractions of confined water. The mobile fraction exhibited jump diffusion, with a jump length consistent with a sphere of confinement radius of 4–8 Å. The results obtained in the present work are compared with those reported for MCM-41 with a hydrophilic interface and Ph-PMO with an amphiphilic interface, and the influence of interface effect on local structure and dynamic properties of confined water is discussed.

Microscopic molecular mobility of high-performance polymers of intrinsic microporosity revealed by neutron scattering - bend fluctuations and signature of methyl group rotation.

Polymers of intrinsic microporosity exhibit a combination of high gas permeability and reasonable permselectivity, which makes them attractive candidates for gas separation membrane materials. The diffusional selective gas transport properties are connected to the molecular mobility of these polymers in the condensed state. Incoherent quasielastic neutron scattering was carried out on two polymers of intrinsic microporosity, PIM-EA-TB(CH3) and its demethylated counterpart PIM-EA-TB(H2), which have high Brunauer-Emmett-Teller surface area values of 1030 m2 g-1 and 836 m2 g-1, respectively. As these two polymers only differ in the presence of two methyl groups at the ethanoanthracene unit, the effect of methyl group rotation can be investigated solely. To cover a broad dynamic range, neutron time-of-flight was combined with neutron backscattering. The demethylated PIM-EA-TB(H2) exhibits a relaxation process with a weak intensity at short times. As the backbone is rigid and stiff this process was assigned to bend-and-flex fluctuations. This process was also observed for the PIM-EA-TB(CH3). A further relaxation process is found for PIM-EA-TB(CH3), which is the methyl group rotation. It was analyzed by a jump-diffusion in a three-fold potential considering also the fact that only a fraction of the present hydrogens in PIM-EA-TB(CH3) participate in the methyl group rotation. This analysis can quantitatively describe the q dependence of the elastic incoherent structure factor. Furthermore, a relaxation time for the methyl group rotation can be extracted. A high activation energy of 35 kJ mol-1 was deduced. This high activation energy evidences a strong hindrance of the methyl group rotation in the bridged PIM-EA-TB(CH3) structure.

Effect of starch retrogradation on molecular dynamics of cooked rice by quasi-elastic neutron scattering

Starch retrogradation can be evaluated using X-ray diffraction (XRD) techniques, which can estimate the crystallinity of starch. It is well known that the crystallinity is reflected in the mechanical properties of foods and materials. Crystallinity should be also related to the structural dynamics of starch, but there are no reports on the relationship between these properties. In this study, we used quasi-elastic neutron scattering (QENS) to investigate changes in the molecular dynamics of cooked rice starch during retrogradation. The width of the measured QENS narrowed with retrogradation. The elastic incoherent structure factor (EISF) increased, which indicated that the molecular dynamics are spatially suppressed upon retrogradation. However, the width of the quasi-elastic scattering component was independent of retrogradation in the measured Q-range. Analysis of EISF with a bimodal continuous diffusion model, where low and high mobilities are assumed to correspond to crystalline and amorphous phases, respectively, showed that the fraction of the low-mobility component increases with retrogradation. The suppression of the molecular dynamics during retrogradation was correlated with the crystallinity evaluated by XRD. The molecular dynamics of the crystalline region that appeared after gelatinization and retrogradation were different from that of raw rice starch. These results suggest that molecular dynamics reflect the state of retrogradation and can be used to monitor retrogradation of starch in foods.

The effect of Si/Al ratio on local and nanoscale water diffusion in H-ZSM-5: A quasielastic neutron scattering and molecular dynamics simulation study

The dynamics of water confined in H-ZSM-5 (protonated form of the Zeolite Socony Mobil – 5) has been studied using quasielastic neutron scattering (QENS) and classical molecular dynamics simulations (MD). QENS measurements probed water confined in ZSM-5 samples with Si/Al ratios of 15, 40 and 140 at 2.8 wt% loadings. In the lower silica samples, fitting of the elastic incoherent structure factor (EISF) showed that water diffusion was confined to a sphere (with radii ranging from 3.4 to 4.3 Å), suggesting the mobile water was located within the MFI (framework type of H-ZSM-5) channel intersections, giving localised diffusion coefficients in the range of ∼0.9–1.8 × 10−9 m2s−1. In the high silica zeolite, the diffusion was observed to be far less confined and more long range in nature, with diffusion coefficients significantly higher than in the lower silica systems (∼1.8–4.8 × 10−9 m2s−1). MD simulations further investigated the effect of the Si/Al ratio on water diffusivity at 2.8 wt% loading (9 molecules/unit cell (UC)) in H-ZSM-5 with Si/Al ratio = 15, 47, 95 and fully siliceous. The Si/Al ratio had a significant effect on the MD calculated nanoscale diffusivity of water, reducing the self-diffusion coefficient by a factor of 2 from a fully siliceous system to that with Si/Al = 15, due to the strong coordination and increased residence time of water molecules at the Brønsted acid sites which range from ∼5 ps to ∼2 ps in the Si/Al = 15 and Si/Al = 95 systems respectively. QENS observables, both the EISF and quasielastic line broadenings, were reproduced from the MD trajectories upon sampling the experimental timescale giving both qualitative and quantitative agreement with the QENS experiments. Fitting of the MD calculated EISF showed that the experimentally observed diffusion confined to a sphere of radii ranging from 3.5 to 6.8 Å was also present in our simulations, with diffusion coefficients calculated to within a factor of 0.5 of experiment.

Rotation of complex ions with ninefold hydrogen coordination studied by quasielastic neutron scattering and first-principles molecular dynamics calculations

Quasielastic neutron scattering (QENS) and neutron powder diffraction of the complex transition metal hydrides ${\mathrm{Li}}_{5}{\mathrm{MoH}}_{11}$ and ${\mathrm{Li}}_{6}{\mathrm{NbH}}_{11}$ were measured in a temperature range of 10--300 K to study their structures and dynamics, especially the dynamics of the hydrogen atoms. These hydrides contain unusual ninefold H-coordinated complex ions (${\mathrm{MoH}}_{9}^{3\ensuremath{-}}$ or ${\mathrm{NbH}}_{9}^{4\ensuremath{-}}$) and hydride ions $({\mathrm{H}}^{\ensuremath{-}})$. A QENS signal appeared >150 K due to the relaxation of H atoms. The intermediate scattering functions derived from the QENS spectra are well fitted by a stretched exponential function called the Kohlrausch-Williams-Watts functions with a small stretching exponent \ensuremath{\beta} \ensuremath{\approx} 0.3--0.4, suggesting a wide relaxation time distribution. The $Q$ dependence of the elastic incoherent structure factor is reproduced by the rotational diffusion of $M{\mathrm{H}}_{9}$ ($M=\mathrm{Mo}$ or Nb) anions. The results are well supported by a van Hove analysis for the motion of H atoms obtained using first-principles molecular dynamics calculations. We conclude that the wide relaxation time distribution of the $M{\mathrm{H}}_{9}$ rotation is due to the positional disorder of the surrounding Li ions and a unique rotation with $M{\mathrm{H}}_{9}$ anion deformation (pseudorotation).

Confinement Effects in Dynamics of Ionic Liquids with Polymer-Grafted Nanoparticles.

Ionic liquid mixed with poly(methyl methacrylate)-grafted Fe3 O4 nanoparticle aggregates at low particle concentrations was found to exhibit different dynamics and ionic conductivity than that of pure ionic liquid in our previous studies. In this work, we report on the quasi-elastic neutron scattering results of ionic liquid containing polymer-grafted Fe3 O4 nanoparticles at higher particle concentrations. The diffusivity of imidazolium (HMIM+ ) cations of 1-hexyl-3-methylimidazolium bis(trifluoromethylsulfonyl)imide (HMIM-TFSI) in the presence of poly(methyl methacrylate)-grafted Fe3 O4 nanoparticles is discussed through the confinement. Analysis of the elastic incoherent structure factor revealed that the confinement radius decreased with the addition of grafted particles in HMIM-TFSI/solvent mixture. We propose the confinement that is induced by the high concentration of grafted particles shrinks the HMIM-TFSI restricted volume. We further conjecture that this enhanced diffusivity occurs as a result of the local ordering of cations within aggregates of poly(methyl methacrylate)-grafted Fe3 O4 nanoparticles.

Microscopic dynamics of highly permeable super glassy polynorbornenes revealed by quasielastic neutron scattering

The molecular dynamics of addition-type poly(tricyclononenes) with Si-substituted bulky side groups has been investigated by a combination of neutron time-of-flight and neutron backscattering spectroscopy on a time scale from 0.1 ps to ca. 3 ns. The investigated poly(tricyclononenes) PTCNSi1 and PTCNSi2g both bear a high microporosity which makes them promising candidates for active separation layers for gas separation membranes. At least for larger gas molecules it is assumed that the pathways for diffusion require an enlargement of pre-existing micropores in terms of an activated zone. A low temperature relaxation process was found for both polymers by the performed neutron scattering experiments. This process was assigned to the methyl group rotation. It was analysed in terms of a jump diffusion in a three-fold potential. The analysis of the dependence of the elastic incoherent structure factor on the scattering vector yields the number of methyl groups which might be immobilized. For PTCNSi1 (3 methyl groups in the monomeric unit) it was found that all methyl groups take part in the methyl group rotation whereas for PTCNSi2g (6 methyl groups in monomeric unit) a considerable number of methyl groups are blocked in their rotation. This immobilization of methyl groups is due to the sterically demanding arrangement of the methyl groups in PTCNSi2g. This conclusion is further supported by the result that the activation energy for the methyl group rotation is three times higher for PTCNSi2g than that of PTCNSi1.

Methanol dynamics in H-ZSM-5 with Si/Al ratio of 25: a quasi-elastic neutron scattering (QENS) study

Methanol dynamics in zeolite H-ZSM-5 (Si/Al of 25) with a methanol loading of ~ 30 molecules per unit cell has been studied at 298, 323, 348 and 373 K by incoherent quasi-elastic neutron scattering (QENS). The elastic incoherent structure factor (EISF) reveals that the majority of methanol is immobile, in the range between 70 and 80%, depending on the measurement temperature. At 298 K, ≈ 20% methanol is mobile on the instrumental timescale, exhibiting isotropic rotational dynamics with a rotational diffusion coefficient (DR) of 4.75 × 1010 s−1. Upon increasing the measurement temperature from 298 to 323 K, the nature of the methanol dynamics changes from rotational to translational diffusion dynamics. Similar translational diffusion rates are measured at 348 and 373 K, though with a larger mobile fraction as temperature increases. The translational diffusion is characterised as jump diffusion confined to a sphere with a radius close to that of a ZSM-5 channel. The diffusion coefficients may be calculated using either the Volino–Dianoux (VD) model of diffusion confined to a sphere, or the Chudley–Elliot (CE) jump diffusion model. The VD model gives rise to a self-diffusion co-efficient (Ds) of methanol in the range of 7.8–8.4 × 10–10 m2 s−1. The CE model gives a Ds of around 1.2 (± 0.1) × 10–9 m2 s−1 with a jump distance of 2.8 (either + 0.15 or − 0.1) Å and a residence time (τ) of ~ 10.8 (either + 0.1 or − 0.2) ps. A correlation between the present and earlier studies that report methanol dynamics in H-ZSM-5 with Si/Al of 36 is made, suggesting that with increasing Si/Al ratio, the mobile fraction of methanol increases while DR decreases.

A modern approach to QENS data analysis in Mantid

Data analysis of Quasi-elastic Neutron Scattering (QENS) experiments often requires multiple steps involving fitting the elastic and quasi-elastic parts of spectra with several empirical functions and analytical models. Parameters of those models can be interdependent and also dependent on the momentum transfer vector Q. Here we present a modern data analysis interface dedicated for QENS data analysis implemented within the open source software Mantid. The interface has been implemented using the state-of-the-art design pattern Model-View-Presenter (MVP). The MVP, an architectural software design pattern, facilitates automated unit tests as well as decoupling of the business logic, presentation logic and the graphical interface. Several models are implemented for analysing both elastic and quasi-elastic parts of the dynamical scattering function S(Q, ω) and intermediate scattering function I(Q, t). To understand the nature of dynamics in a QENS experiments, several models are also implemented for elastic incoherent structure factor (EISF) and jump diffusions. The interface has been validated by analysing a sample of liquid water at room temperature. The nature of hydrogen bond dynamics of the hydrogen bonded organic ferroelectric 2, 4, 5 − Br3 imidazole, for the first time has been analysed using this newly implemented software. It is found that protons exhibit localised random motion in this material.

On the interpretation of the temperature dependence of the mean square displacement (MSD) of protein, obtained from the incoherent neutron scattering

A variety of models and hypothesis have been proposed to interpret the temperature dependence of the mean square displacement (MSD) of protein, that is obtained from the incoherent neutron scattering measurement, but a consensus seems yet to be achieved. The most controversial point is concerned with the physics behind the abrupt change of gradient of MSD plotted against temperature. The phenomenon is attributed to different physics by different authors, such as glass transition, alpha to beta transition, harmonic to anharmonic transition, coupling of protein and hydrated-water dynamics, and so forth. In the present paper, we propose a theory to analyse the elastic incoherent neutron scattering (EINS) data of aqueous solutions of protein, based on the generalized Langevin theory combined with the 3D-RISM/RISM equation [B. Kim and F. Hirata, J. Chem. Phys., 138, 054108 (2012)]. The theory gives closed equations for the elastic incoherent structure factor (EISF) and MSD as a function of temperature. Based on the theory, the abrupt change of the gradient of MSD in the temperature dependence is interpreted as an onset of “solvent-induced elasticity,” or “free energy elasticity,” with increasing temperature.

57Fe nuclear resonant inelastic scattering of Fe1.1Te

This study reports results of 57Fe Mossbauer spectroscopy and nuclear resonant inelastic scattering (NRIS) in Fe1.1Te. The Fe-specific partial phonon densities of states (PDOSs) were extracted from the observed spectra. No detectable change at the tetragonal-monoclinic phase transition around 65 K was observed. Therefore the variations in lattice constants and/or distortion in FeTe4 tetrahedron through the structural transition was minute. From the observed Fe-PDOS, the Lamb-Mossbauer factor was 0.90(3) at 10 K and the Debye temperature was evaluated as 300(10) K. In 57Fe Mossbauer spectroscopy, the clear magnetic spittings of spectra were measured below Neel temperature. The obtained values of isomer shifts showed characteristics of Fe2+ species and clear difference with the phase transition was observed in temperature dependence of quadrupole splitting (QS). The change of QS must be caused by substantial change of the charge density distribution around the Fe site. This suggests that the band structure or the nature of the Fe-Te bonds becomes highly anisotropic. These results might provide additional information about the respective mechanisms for FeTe1−xSex superconductivity.

Reorientational dynamics of organic cations in perovskite-like coordination polymers.

Here we report the dynamics of organic cations as guest molecules in a perovskite host-framework. The molecular motion of CH3NH3+ (MAFe), (CH3)2NH2+ (DMAFe) and (CH3)3NH+ (TrMAFe) in the cage formed by KFe(CN)63- units was studied using a combination of experimental methods: (i) thermal analysis, (ii) dielectric and electric studies, (iii) optical observations, (iv) EPR and 1H NMR spectroscopy and (v) quasielastic neutron scattering (QENS). In the case of MAFe and TrMAFe, the thermal analysis reveals one solid-to-solid phase transition (PT) and two PTs for the DMAFe crystal. A markedly temperature-dependent dielectric constant indicates the tunable and switchable properties of the complexes. Also, their semiconducting properties are confirmed by a dc conductivity measurement. The broadband dielectric relaxation is analyzed for the TrMAFe sample in the frequency range of 100 Hz-1 GHz. QENS shows that we deal rather with the localized motion of the cation than a diffusive one. Three models, which concern the simultaneous rotation of the CH3 and/or NH3 group, π-flips and free rotations of the organic cation, are used to fit the elastic incoherent structure factor. The 1H NMR spin-lattice relaxation time for all compounds under study, as well as the second moments, has been measured in a wide temperature range. In all studied samples, the temperature dependence of the second moment of the proton NMR line indicated the gradual evolution of the molecular movements from the rigid state up to a highly disordered one.

Quadrupole splitting and Eu partial lattice dynamics in europium orthophosphate EuPO 4

Hyperfine interactions in europium orthophosphate EuPO4 were investigated using 151Eu Mossbauer spectroscopy from 6 to 300 K. The value of the quadrupole splitting and the asymmetry parameter were refined and further substantiated by nuclear forward scattering data obtained at room temperature. The temperature dependence of the relative absorption was modeled with an Eu specific Debye temperature of 221(1) K. Eu partial lattice dynamics were probed by means of nuclear inelastic scattering and the mean force constant, the Lamb-Mossbauer factor, the internal energy, the vibrational entropy, the average phonon group velocity were calculated using the extracted density of phonon states. In general, Eu specific vibrations are characterized by rather small phonon energies and contribute strongly to the total entropy of the system. Although there is no classical Debye like behavior at low vibrational energies, the average phonon group velocity can be reasonably approximated using a linear fit.

Hydrogen dynamics in β-Mg(BH4)2 on the picosecond timescale.

A quasielastic neutron scattering study on β-Mg(BH4)2 has been performed to investigate the hydrogen dynamics on the picosecond time-scale. Both vibrational and rotational motions of the [BH4](-) tetrahedra contribute to the signal at low energy transfers. A comprehensive analysis of the elastic and quasielastic incoherent structure factors allowed the separation of different parts. Below 200 K, vibrations and rotations (around the C2 or C3 symmetry axis of the [BH4](-) tetrahedra) are well separated. Above that temperature, a transition is observed in the vibrational part, and the spectral weight is shifted towards the quasielastic region. The dynamic transition is not accompanied by any structural phase change but we suggest that it is correlated with the anomalous thermal expansion that has been reported for β-Mg(BH4)2 [Filinchuk, et al., Chem. Mater., 2009, 21, 925].

Motional displacements in proteins: The origin of wave-vector-dependent values.

The average mean-square displacement, 〈r(2)〉, of H atoms in a protein is frequently determined using incoherent neutron-scattering experiments. 〈r(2)〉 is obtained from the observed elastic incoherent dynamic structure factor, S(i)(Q,ω=0), assuming the form S(i)(Q,ω=0) =exp(-Q(2)〈r(2)〉/3). This is often referred to as the Gaussian approximation (GA) to S(i)(Q,ω=0). 〈r(2)〉 obtained in this way depends on the value of the wave vector, Q considered. Equivalently, the observed S(i)(Q,ω=0) deviates from the GA. We investigate the origin of the Q dependence of 〈r(2)〉 by evaluating the scattering functions in different approximations using molecular dynamics (MD) simulation of the protein lysozyme. We find that keeping only the Gaussian term in a cumulant expansion of S(Q,ω) is an accurate approximation and is not the origin of the Q dependence of 〈r(2)〉. This is demonstrated by showing that the term beyond the Gaussian is negligible and that the GA is valid for an individual atom in the protein. Rather, the Q dependence (deviation from the GA) arises from the dynamical heterogeneity of the H in the protein. Specifically it arises from representing, in the analysis of data, this diverse dynamics by a single average scattering center that has a single, average 〈r(2)〉. The observed Q dependence of 〈r(2)〉 can be used to provide information on the dynamical heterogeneity in proteins.

High-pressure dynamics of hydrated protein in bioprotective trehalose environment.

We present a pressure-dependence study of the dynamics of lysozyme protein powder immersed in deuterated α,α-trehalose environment via quasielastic neutron scattering (QENS). The goal is to assess the baroprotective benefits of trehalose on biomolecules by comparing the findings with those of a trehalose-free reference study. While the mean-square displacement of the trehalose-free protein (hydrated to dD2O≃40 w%) as a whole, is reduced by increasing pressure, the actual observable relaxation dynamics in the picoseconds to nanoseconds time range remains largely unaffected by pressure--up to the maximum investigated pressure of 2.78(2) Kbar. Our observation is independent of whether or not the protein is mixed with the deuterated sugar. This suggests that the hydrated protein's conformational states at atmospheric pressure remain unaltered by hydrostatic pressures, below 2.78 Kbar. We also found the QENS response to be totally recoverable after ambient pressure conditions are restored. Small-angle neutron diffraction measurements confirm that the protein-protein correlation remains undisturbed. We observe, however, a clear narrowing of the QENS response as the temperature is decreased from 290 to 230 K in both cases, which we parametrize using the Kohlrausch-Williams-Watts stretched exponential model. Only the fraction of protons that are immobile on the accessible time window of the instrument, referred to as the elastic incoherent structure factor, is observably sensitive to pressure, increasing only marginally but systematically with increasing pressure.

On the lack of capillary Mössbauer spectroscopic effect for SnII-containing aqueous solutions trapped in corning Vycor ‘thirsty’ glass

Liquids trapped in the pores of certain silicate glasses (such as Corning Vycor ‘thirsty’ glass) were found to display frozen solutions like behavior at temperatures much higher than their actual freezing point. For example, recoilless γ-resonance absorption was observed for Mossbauer active solutes such as 119Sn and 57Fe salts at room temperature (i.e., without the need of quenching). Thus capillary Mossbauer spectroscopy (CMS) proved to be a new and useful experimental tool with great potential in solution chemistry. As part of a research project concerned with the hydrolysis of SnII salts, we attempted to perform 119Sn CMS measurements for solutions containing stannous ion in a range of aqueous environments. Somewhat surprisingly, we found that under ambient conditions, SnII aqueous liquid solutions, both the acidic and the basic systems, are essentially CMS-silent. This can be attributed to the strong temperature dependence of Lamb–Mossbauer factor of SnII species, which may result in the complete disappearance of Mossbauer pattern well below room temperature. These observations can also explain why previous publications concerned with the use of CMS dealt exclusively with SnIV and not with SnII containing liquids.

Hydrogen dynamics in Laves-phase hydride YFe2H2.6: Inelastic and quasielastic neutron scattering studies

The vibrational spectrum of hydrogen and the parameters of H jump motion in the C15-type compound YFe2H2.6 have been studied by means of inelastic and quasielastic neutron scattering. It is found that hydrogen atoms occupying tetrahedral interstitial g (Y2Fe2) sites participate in the fast localized jump motion. The behavior of the elastic incoherent structure factor as a function of momentum transfer (measured up to Qmax≈4Å−1) is consistent with the two-site motion of H atoms within pairs of closely spaced g sites. In the studied T range of 140–390K, the temperature dependence of the jump rate of this localized motion is found to be non-Arrhenius; however, it can be described by two Arrhenius-like terms with the activation energies of 42 and 10meV in the ranges 295–390K and 140–240K, respectively. Our results also indicate that hydrogen dynamics in YFe2H2.6 is affected by considerable local lattice distortions resulting from hydrogenation of YFe2.

Motional heterogeneity in human acetylcholinesterase revealed by a non-Gaussian model for elastic incoherent neutron scattering

We study the dynamical transition of human acetylcholinesterase by analyzing elastic neutron scattering data with a simulation gauged analytical model that goes beyond the standard Gaussian approximation for the elastic incoherent structure factor [G. R. Kneller and K. Hinsen, J. Chem. Phys. 131, 045104 (2009)]. The model exploits the whole available momentum transfer range in the experimental data and yields not only a neutron-weighted average of the atomic mean square position fluctuations, but also an estimation for their distribution. Applied to the neutron scattering data from human acetylcholinesterase, it reveals a strong increase of the motional heterogeneity at the two transition temperatures T = 150 K and T = 220 K, respectively, which can be located with less ambiguity than with the Gaussian model. We find that the first transition is essentially characterized by a change in the form of the elastic scattering profile and the second by a homogeneous increase of all motional amplitudes. These results are in agreement with previous combined experimental and simulation studies of protein dynamics, which attribute the first transition to an onset of methyl rotations and the second to more unspecific diffusion processes involving large amplitude motions.

Observation on Elastic Incoherent Structure Factor for Rotational Aromatic Groups of Thermotropic Copolyester

Observation on Elastic Incoherent Structure Factor for Rotational Aromatic Groups of Thermotropic Copolyester