Single Activation Barrier Research Articles

Rotational Dynamics of an Amphidynamic Zirconium Metal-Organic Framework Determined by Dielectric Spectroscopy.

A zirconium metal-organic framework with a difluorophenylene rotator bearing a permanent electric dipole of ∼3.2 D was synthesized, and its rotational motion was analyzed by temperature- and frequency-dependent broadband dielectric spectroscopy. While solid-state NMR confirms fast rotation qualitatively, the dissipation factors measured between 113 and 153 K suggested an activation energy Ea = 2.6 kcal/mol, but deviations from a single Debye relaxation suggested a dynamic process that cannot be accounted for by a well-defined potential with a single activation barrier. The dynamic heterogeneity of the dipolar rotor was confirmed by analysis in terms of a Cole-Cole relaxation, which suggested a mean barrier of ∼1.9 kcal/mol, with a heterogeneity that decreases as temperature increases. Based on the single-crystal structure, we propose that the kinetic heterogeneity results from a temperature-dependent potential where rotation motion is mediated by the escape of the rotator from an energy well created by a double Ph-H···F-Ph hydrogen bond.

Kinetic Barriers and Microscopic Mechanisms of Noble Gas Adsorption by Nanoporous γ‐Mg(BH4)2 Obtained by Means of Sub‐Second X‐Ray Diffraction

AbstractGas adsorption by porous frameworks sometimes results in structure “breathing”, “pores opening/closing”, “negative gas adsorption”, and other phenomena. Time‐dependent diffraction can address both kinetics of the guest uptake and structural response of the host framework. Using sub‐second in situ powder X‐ray diffraction, three intracrystalline diffusion scenarios have been evaluated from the isothermal kinetics of Ar, Kr, and Xe adsorption by nanoporous γ‐Mg(BH4)2. These scenarios are dictated by two possible simultaneous transport mechanisms: diffusion through the intra‐ (i) and interchannel apertures (ii) of γ‐Mg(BH4)2 crystal structure. The contribution of (i) and (ii) changes depending on the kinetic diameter of the noble gas molecule and temperature regime. The lowest single activation barrier for the smallest Ar suggests equal diffusion of the atoms trough both pathways. Contrary, for the medium sized Kr we resolve the contributions of two parallel transport mechanisms, which tentatively can be attributed to the smaller barrier of the migration paths via the channel like pores and the higher barrier for the diffusion via narrow aperture between these channels. The largest Xe atoms diffuse only along 1D channels and show the highest single activation barrier.

Kinetic Barriers and Microscopic Mechanisms of Noble Gas Adsorption by Nanoporous γ-Mg(BH4 )2 Obtained by Means of Sub-Second X-Ray Diffraction.

Gas adsorption by porous frameworks sometimes results in structure "breathing", "pores opening/closing", "negative gas adsorption", and other phenomena. Time-dependent diffraction can address both kinetics of the guest uptake and structural response of the host framework. Using sub-second in situ powder X-ray diffraction, three intracrystalline diffusion scenarios have been evaluated from the isothermal kinetics of Ar, Kr, and Xe adsorption by nanoporous γ-Mg(BH4 )2 . These scenarios are dictated by two possible simultaneous transport mechanisms: diffusion through the intra- (i) and interchannel apertures (ii) of γ-Mg(BH4 )2 crystal structure. The contribution of (i) and (ii) changes depending on the kinetic diameter of the noble gas molecule and temperature regime. The lowest single activation barrier for the smallest Ar suggests equal diffusion of the atoms trough both pathways. Contrary, for the medium sized Kr we resolve the contributions of two parallel transport mechanisms, which tentatively can be attributed to the smaller barrier of the migration paths via the channel like pores and the higher barrier for the diffusion via narrow aperture between these channels. The largest Xe atoms diffuse only along 1D channels and show the highest single activation barrier.

Magnetic field tuning of low-energy spin dynamics in the single-atomic magnet Li2(Li1−xFex)N

We present a systematic ${}^{57}\mathrm{Fe}$ M\"ossbauer study on highly diluted Fe centers in ${\mathrm{Li}}_{2}({\mathrm{Li}}_{1\ensuremath{-}x}{\mathrm{Fe}}_{x})\mathrm{N}$ single crystals as a function of temperature and magnetic field applied transverse and longitudinal with respect to the single-ion anisotropy axis. Below 30 K, the Fe centers exhibit a giant magnetic hyperfine field of ${\overline{B}}_{A}=70.25(2)\phantom{\rule{4pt}{0ex}}\mathrm{T}$ parallel to the axis of strongest electric field gradient ${\overline{V}}_{zz}=\ensuremath{-}154.0(1)\phantom{\rule{4pt}{0ex}}\mathrm{V}/{\AA{}}^{2}$. Fluctuations of the magnetic hyperfine field are observed between 50 and 300 K and described by the Blume two-level relaxation model. From the temperature dependence of the fluctuation rate, an Orbach spin-lattice relaxation process is deduced. An Arrhenius analysis yields a single thermal activation barrier of ${\overline{E}}_{A}=570(6)\phantom{\rule{4pt}{0ex}}\mathrm{K}$ and an attempt frequency ${\overline{\ensuremath{\nu}}}_{0}=309(10)\phantom{\rule{4pt}{0ex}}\mathrm{GHz}$. M\"ossbauer spectroscopy studies with applied transverse magnetic fields up to 5 T reveal a large increase of the fluctuation rate by more than one order of magnitude. In longitudinal magnetic fields, a splitting of the fluctuation rate into two branches is observed consistent with a Zeeman induced modification of the energy levels. The experimental observations are qualitatively reproduced by a single-ion effective spin Hamiltonian analysis assuming a ${\mathrm{Fe}}^{1+}\phantom{\rule{4pt}{0ex}}{d}^{7}$ charge state with the unquenched orbital moment and a $J=7/2$ ground state. It is demonstrated that a weak axial single-ion anisotropy $D$ of the order of a few Kelvin can cause a two orders of magnitude larger energy barrier for longitudinal spin fluctuations.

A study on the progress of mutarotation above and below the Tg and the relationship between constant rates and structural relaxation times.

Comprehensive FTIR studies on the progress of mutarotation in d-fructose mixed with maltitol have been carried out over a wide range of temperatures, both above and below the glass transition temperature Tg. In addition to the analysis of single bands, we have developed a completely new approach considering the full spectral range to follow the overall progress of the reaction. We have found that at the calorimetric Tg, there is a clear change in the temperature dependence of constant rates. The activation barrier for mutarotation changes from around 59 kJ mol-1 (the supercooled state) to around 249 kJ mol-1 (the glassy state). This dramatic variation in the activation barrier is consistent with the change in the mechanism of this specific chemical conversion, as theoretically considered by Wlodarczyk et al. [Phys. Chem. Chem. Phys., 2014, 16, 4694-4698]. Alternatively, it can also be connected to the change in the viscosity of the sample. Additionally, we investigated the relationship between constant rates (k) of mutarotation, structural relaxation times (τα), and dc conductivity (σdc) above and below the glass transition temperature. It was found that there was a linear correlation between all these quantities; they scale with various exponents changing at Tg. Our results also indicate that a single activation barrier might not be sufficient to describe the mutarotation process.

Diffusion of molecular hydrogen in carbon aerogel

The diffusion of hydrogen molecules adsorbed in a highly porous carbon aerogel has been studied with quasi-elastic neutron scattering. Hydrogen diffusion in this carbon substrate followed an activated jump process with a single activation barrier. The temperature dependence of the diffusion rate agrees well with previous results from activated carbons and other highly porous carbons. The carbon aerogel sample showed a strongly enhanced conversion between the ortho- and para-hydrogen spin states. The ortho-para conversion process, however, was inhibited for a fraction of the hydrogen molecules. This inhibition process is attributed to a rotational confinement of the hydrogen molecules at the nanometre scale.

Label-free measurement of amyloid elongation by suspended microchannel resonators.

Protein aggregation is a widely studied phenomenon that is associated with many human diseases and with the degradation of biotechnological products. Here, we establish a new label-free method for characterizing the aggregation kinetics of proteins into amyloid fibrils by suspended microchannel resonators (SMR). SMR devices are unique in their ability to provide mass-based measurements under reaction-limited conditions in a 10 pL volume. To demonstrate the method, insulin seed fibrils of defined length, characterized by atomic force microscopy (AFM) and transmission electron microscopy (TEM), were covalently immobilized inside microchannels embedded within a micromechanical resonator, and the elongation of these fibrils under a continuous flow of monomer solution (rate ∼1 nL/s) was measured by monitoring the resonance frequency shift. The kinetics for concentrations below ∼0.6mg/mL fits well with an irreversible bimolecular binding model with the rate constant kon = (1.2 ± 0.1) × 10(3) M(-1) s(-1). Rate saturation occurred at higher concentrations. The nonlinear on-rate for monomer concentrations from 0 to 6 mg/mL and for temperatures from 20 to 42 °C fit well globally with an energy landscape model characterized by a single activation barrier. Finally, elongation rates were studied under different solution conditions and in the presence of a small molecule inhibitor of amyloid growth. Due to the low volume requirements, high precision, and speed of SMR measurements, the method may become a valuable new tool in the screening for inhibitors and the study of fundamental biophysical mechanisms of protein aggregation processes.

Lithium diffusion in the spinel phaseLi4Ti5O12and in the rocksalt phaseLi7Ti5O12of lithium titanate from first principles

Lithium titanate (LTO) is a promising candidate as an anode material in future generations of lithium ion batteries due to its high intrinsic safety and stability. In this work, we investigate the diffusion barriers for lithium ions in two different crystal structures of LTO using the density functional theory. Our calculations show that the activation barriers vary between 0.30--0.48 eV for the spinel phase ${\mathrm{Li}}_{4}{\mathrm{Ti}}_{5}{\mathrm{O}}_{12}$ and between 0.20--0.51 eV in the lithiated rocksalt phase ${\mathrm{Li}}_{7}{\mathrm{Ti}}_{5}{\mathrm{O}}_{12}$. The origins of the rather broad ranges of activation energies are related to different chemical environments of the diffusion channels due to mixed occupancies of some sites in LTO. Our results reveal that the determination of lithium diffusion constants in LTO can not be carried out by using a single activation barrier. Instead, the local environment of the diffusion paths must be considered to correctly capture the variety of activation barriers. Moreover, we find the sites which have mixed occupation in LTO to trap lithium vacancies in the spinel phase. This effect is not observed in the rocksalt phase. This behavior explains the low lithium diffusivity found in experiments for lithium concentrations in the vicinity of the spinel phase.

A systematic DFT study of hydrogen diffusion on transition metal surfaces

Density functional theory calculations of the diffusion of hydrogen atoms on 23 transition metal surfaces in their closed-packed structure have been carried out. The d-metals chosen are all the metals in the 4th, 5th and 6th periods, from Sc to Au, except Mn, Tc, and Hf. Potential energy surfaces of H atom on these metals are constructed and the diffusion barrier from one minima to another is compared with nudged elastic band calculations. Most of the minimum energy paths have a single activation barrier, except on two surfaces where a dip in the bridge position (W and Pt) is observed. Trends in the adsorption and activation energies are observed where the former is explained with the d-band model. All the activation energies for diffusion are relatively low, or from 0.04eV for Pt to 0.28eV on Y and Zr. Finally, we estimate the temperature where tunneling effects should start to take place.

Dielectric relaxation and ion transport in silver–boro-tellurite glasses

Glass systems of composition xAg2SO4–20Ag2O–(80−x) [0.50 B2O3–0.50 TeO2], where x = 5, 10, 15, 20, 25 and 30 mol% have been prepared by melt-quenching technique. Frequency- and temperature-dependent conductivity measurements have been carried out in the frequency range 10 Hz to 10 MHz and at a temperature range of 303–353 K, respectively. DC conductivities exhibit Arrhenius behavior over the entire temperature range with a single activation barrier. Addition of Ag2SO4 expands the glass network and, consequently, conductivity increases. This suggests that the structure and network expansion are the key parameters for enhancing conductivity. Impedance spectra of these glasses show a single semicircle, indicating one type of conduction. AC conductivity behavior of the glasses was analyzed using both single power law and Kolhrauh–William–Watts (KWW) stretched exponential relaxation function. The power law exponent (s) is temperature-dependent, while the stretched exponent (β) is insensitive to temperature. Scaling behavior has also been carried out using reduced plots of conductivity with frequency, which suggests the ion transport mechanism remains unaffected by temperature and composition.

How to mark off paths on the protein energy landscape

Protein folding has run the gamut from complexity, to simplicity, and in a way, back to complexity. In the beginning, there were the slow and complex folding mechanisms of multidomain proteins involving multiple parallel or sequential intermediates en route to the native state (1). Then followed small proteins that can fold by a rapid two-state mechanism (2). Finally, when the single leftover activation barrier was reduced as much as possible through protein engineering, energy landscape roughness was revealed in folding kinetics (3). Landscape roughness temporarily traps very fast folders as they navigate many pathways toward the native state (4). The article by Noe et al. (5) in this issue of PNAS shows how molecular dynamics simulations can be used very efficiently to create a roadmap of the pathways on which a protein explores the energy landscape.

Single-molecule force spectroscopy: Practical limitations beyond Bell’s model

Single-molecule force spectroscopy experiments, and a number of other physical systems, are governed by thermally activated transitions out of a metastable state under the action of a steadily increasing external force. The main observable in such experiments is the distribution of the forces, at which the escape events occur. The challenge in interpreting the experimental data is to relate them to the microscopic system properties. We work out a maximum likelihood approach and show that it is the optimal method to tackle this problem. When fitting actual experimental data it is unavoidable to assume some functional form for the force-dependent escape rate. Focusing on escape processes over a single activation barrier, we consider a quite general and common such functional form and demonstrate by means of data from a realistic computer experiment that the maximum number of fit parameters that can be determined reliably is three. They are related to the force-free escape rate and the position and height of the activation barrier. Furthermore, the results for the first two of these fit parameters show little dependence on the assumption about the manner in which the barrier decreases with the applied force, while the last one, the barrier height in the absence of force, depends strongly on this assumption.

Ion conductivity and dielectric relaxation behavior in FIC silver based phospho-molybdate glasses

Electrical conductivity and dielectric relaxation studies of silver ion-conducting glasses have been prepared using xAg(2)SO(4)-15Ag(2)O-(90-X)(90P(2)O(5)-10MoO(3)) glass system over a temperature range of 298-353 K and frequencies of 10 Hz to 10 MHz. DC conductivities exhibit Arrhenius behavior over the entire temperature range with a single activation barrier. The ac conductivity behavior of these glasses has been analyzed using single power law; conductivity increases linearly in logarithmic scale with Ag2SO4 concentration. The power law exponent (s) decreases, while stretched exponent (beta) is insensitive to increase of temperature. Scaling behavior has also been carried out using the reduced plots of conductivity and frequency, which suggest that ion transport mechanism remains unaffected at all temperatures and compositions.

Glass-rubber constitutive model for amorphous polymers near the glass transition

The constitutive behaviour of amorphous polymers near the glass transition contains many features general to this class of materials. A new, physically based, three-dimensional constitutive model has been developed for simulating this wide range of features in models of polymer products and processes. In particular, the model displays glassy response at low temperatures and short time-scales, and rubber-like response at high temperatures and long time-scales, and is therefore an example of a glass-rubber constitutive model. Its basis is the assumed additivity of free energies of bond distortion and conformation perturbation. For the elastic bond distortion stress-strain law and flow model, and the conformational entropy function, the model employs linear elasticity, Eyring viscous flow and the Edwards-Vilgis entropy function, respectively. Glass structure and temperature dependence are introduced through the Vogel-Tammann-Fulcher and Arrhenius equations for viscosity, respectively. With parameters obtained for poly(ethylene terephthalate) in a companion paper, the model was solved numerically to simulate a variety of uniaxial strain sequences, and found to replicate well the characteristic patterns of behaviour of amorphous polymers in the temperature region of interest, over a wide range of experimental situations from small to large strains. The only major deficiency, resulting from the simplifying assumption of a single activation barrier height, is its being too localized in the time domain. At high temperatures and long times, applicability of the model is limited by the onset of conformational relaxation.

The dependence on temperature of rate constants for solvolysis of alkyl halides and related compounds in water

Various explanations are considered for the observation that plots of In[k(obs)] against T–1 for solvolysis of alkyl halides in water are generally curved. It is suggested that the two stage reaction scheme proposed by Albery and Robinson accounts for the patterns of behaviour in derived parameters previously reported which were calculated assuming that the mechanism involves a single activation barrier.

Semi-classical theory for non-separable systems:. Construction of “good” action-angle variables for reaction rate constants

A semiclassical expression for bimolecular rate constants for reactions which have a single activation barrier is obtained in terms of the “good” action variables of the (classical) Hamiltonian that are associated with the saddle point region of the potential energy surface. The formulae apply to non-separable, as well as separable saddle points.