Energy Barrier For Relaxation Research Articles

Magnetic relaxation pathways in lanthanide single-molecule magnets

Single-molecule magnets are compounds that exhibit magnetic bistability caused by an energy barrier for the reversal of magnetization (relaxation). Lanthanide compounds are proving promising as single-molecule magnets: recent studies show that terbium phthalocyanine complexes possess large energy barriers, and dysprosium and terbium complexes bridged by an N2(3-) radical ligand exhibit magnetic hysteresis up to 13 K. Magnetic relaxation is typically controlled by single-ion factors rather than magnetic exchange (whether one or more 4f ions are present) and proceeds through thermal relaxation of the lowest excited states. Here we report polylanthanide alkoxide cage complexes, and their doped diamagnetic yttrium analogues, in which competing relaxation pathways are observed and relaxation through the first excited state can be quenched. This leads to energy barriers for relaxation of magnetization that exceed 800 K. We investigated the factors at the lanthanide sites that govern this behaviour.

Synthesis, Structure, and Magnetic Properties of a New Family of Tetra-nuclear {Mn2IIILn2}(Ln = Dy, Gd, Tb, Ho) Clusters With an Arch-Type Topology: Single-Molecule Magnetism Behavior in the Dysprosium and Terbium Analogues

Sequential reaction of Mn(II) and lanthanide(III) salts with a new multidentate ligand, 2,2'-(2-hydroxy-3-methoxy-5-methylbenzylazanediyl)diethanol (LH3), containing two flexible ethanolic arms, one phenolic oxygen, and a methoxy group afforded heterometallic tetranuclear complexes [Mn2Dy2(LH)4(μ-OAc)2](NO3)2·2CH3OH·3H2O (1), [Mn2Gd2(LH)4(μ-OAc)2](NO3)2·2CH3OH·3H2O (2), [Mn2Tb2(LH)4(μ-OAc)2](NO3)2·2H2O·2CH3OH·Et2O (3), and [Mn2Ho2(LH)4(μ-OAc)2]Cl2·5CH3OH (4). All of these dicationic complexes possess an arch-like structural topology containing a central Mn(III)-Ln-Ln-Mn(III) core. The two central lanthanide ions are connected via two phenolate oxygen atoms. The remaining ligand manifold assists in linking the central lanthanide ions with the peripheral Mn(III) ions. Four doubly deprotonated LH(2-) chelating ligands are involved in stabilizing the tetranuclear assembly. A magnetochemical analysis reveals that single-ion effects dominate the observed susceptibility data for all compounds, with comparably weak Ln···Ln and very weak Ln···Mn(III) couplings. The axial, approximately square-antiprismatic coordination environment of the Ln(3+) ions in 1-4 causes pronounced zero-field splitting for Tb(3+), Dy(3+), and Ho(3+). For 1 and 3, the onset of a slowing down of the magnetic relaxation was observed at temperatures below approximately 5 K (1) and 13 K (3) in frequency-dependent alternating current (AC) susceptibility measurements, yielding effective relaxation energy barriers of ΔE = 16.8 cm(-1) (1) and 33.8 cm(-1) (3).

Chiral single-molecule magnet with a 35 K energy barrier for relaxation of the magnetization

Abstract The reaction of [MnII(S-mandelato)2] complexes with 5-Methyl-salicylaldoxim (5-Me-saloxH2) leads to the chiral hexanuclear manganese(III) complex [Mn6(μ3-O)2(5-Me-salox)6(S-mandelato)2(EtOH)6]. The structure can be viewed as two neutral stacked {Mn3(μ3-O)(5-Me-salox)3(S-mandelato)(EtOH)3} triangular subunits linked together in a head-to-tail manner by two phenoxo and two oximato μ3-oxygen atoms of the deprotonated oxime groups of the ligands. The magnetic study of this chiral hexanuclear manganese(III) complex reveals a SMM behaviour with an energy barrier of the slow relaxation of the magnetisation equal to 35 K. Considering the structural features, the fitting of the temperature dependence of the magnetic susceptibility gives a good agreement with the experimental data considering two sets of interactions: J1 = +0.37 cm−1 and J2 = −0.70 cm−1 within (ferromagnetic) and between (antiferromagnetic), respectively, the {Mn3(μ3-O)(5-Me-salox)3(S-mandelato)(EtOH)3} triangular subunits.

Pentametallic lanthanide-alkoxide square-based pyramids: high energy barrier for thermal relaxation in a holmium single molecule magnet

Pentametallic Ln complexes of formula [Ln(5)O(O(i)Pr)(13)] have been made, where Ln(III) = Sm, Gd, Tb, Ho and Er; slow magnetisation relaxation to 33 K is observed for the Ho complex with an energy barrier of ca. 400 K.

Relaxation times and energy barriers of rubbing-induced birefringence in glass-forming polymers

The relaxations of rubbing-induced birefringence (RIB) in several glass-forming polymers, including polycarbonate and polystyrene (PS) derivatives with various modifications to the phenyl ring side group, are studied. Significant relaxations of RIB are observed at temperatures well below the glass transition temperature T (g) . The relaxation times span a wide range from approximately 10 s to probably geological time scale. Physical aging effects are absent in the RIB relaxations. The model proposed for the interpretation of RIB in PS describes well the RIB relaxations in all the polymers investigated here. The energy barriers are of the order of a few hundred kJ/mol and decrease with decreasing temperature, in opposition to the trend of Vogel-Fulcher form for polymer segmental relaxations above T (g) . The relaxation behaviors of different polymers are qualitatively similar but somewhat different in quantitative details, such as in the values of the saturated birefringence, the shape of the initial barrier density distribution functions, the rates of barrier decrease with decreasing temperature, and the dependence of relaxation times on temperature and parameter xi , etc. The RIB relaxations are different from any of the other relaxations below T (g) that have been reported in the literature, such as dielectric relaxations or optical probe relaxations. A microscopic model for the relaxations of RIB is much desired.

Transition rates for aS≥1spin model coupled to ad-dimensional phonon bath

We consider a $S\ensuremath{\ge}1$ spin model (or a generalized Blume\char21{}Capel model) weakly coupled to a $d$-dimensional phonon bath and investigate transition rates between different spin configurations. This study is motivated by understanding magnetization relaxation as a function of temperature in diverse magnetic systems such as arrays of magnetic nanoparticles and magnetic molecules. We assume that the magnetization of the spin system relaxes through consecutive emission or absorption of a single phonon. From a weak, linear spin-phonon coupling Hamiltonian, we derive transition rates that would be used to examine dynamic properties of the system in kinetic Monte Carlo simulations. Although the derived phonon-assisted transition rates satisfy detailed balance, in the case of two- and three-dimensional phonon baths, transitions between degenerate states are not allowed. (This is a major difference of the phonon-assisted transition rates from the Metropolis and Glauber transition rates.) Thus, if there are no alternative paths along which the spin system can relax, the relaxation time diverges. Otherwise, the system finds other paths, which leads to an increase in the relaxation time and energy barrier. However, when higher-order phonon processes are included in the transition rates, it is found that the system can reach the states which were inaccessible due to the forbidden transitions. As a result, the system recovers some of the dynamic properties obtained using the Glauber transition rate.

Characterization of the potential energy landscape of an antiplasticized polymer

The nature of the individual transitions on the potential energy landscape (PEL) associated with particle motion are directly examined for model fragile glass-forming polymer melts, and the results are compared to those of an antiplasticized polymer system. In previous work, we established that the addition of antiplasticizer reduces the fragility of glass formation so that the antiplasticized material is a stronger glass former. In the present work, we find that the antiplasticizing molecules reduce the energy barriers for relaxation compared to the pure polymer, implying that the antiplasticized system has smaller barriers to overcome in order to explore its configuration space. We examine the cooperativity of segmental motion in these bulk fluids and find that more extensive stringlike collective motion enables the system to overcome larger potential energy barriers, in qualitative agreement with both the Stillinger-Weber and Adam-Gibbs views of glass formation. Notably, the stringlike collective motion identified by our PEL analysis corresponds to incremental displacements that occur within larger-scale stringlike particle displacement processes associated with PEL metabasin transitions that mediate structural relaxation. These "substrings" nonetheless seem to exhibit changes in relative size with antiplasticization similar to those observed in "superstrings" that arise at elevated temperatures. We also study the effects of confinement on the energy barriers in each system. Film confinement makes the energy barriers substantially smaller in the pure polymer, while it has little effect on the energy barriers in the antiplasticized system. This observation is qualitatively consistent with our previous studies of stringlike motion in these fluids at higher temperatures and with recent experimental measurements by Torkelson and co-workers.

Electron Transport Dynamics in a Room-Temperature Au Nanoparticle Molten Salt

A room-temperature Au38 nanoparticle polyether melt has been prepared by exchanging poly(ethylene glycol) (PEG) thiolate ligands, HS-C6-PEG163, into the organic protecting monolayer of Au38(PhC2)24 nanoparticles. Spectral and electrochemical properties verify that the Au38 core size is preserved during the exchange. Adding LiClO4 electrolyte, free PEG plasticizer, and/or partitioned CO2 leads to an ionically conductive nanoparticle melt, on which voltammetric, chronoamperometric, and impedance measurements have been made, respectively, of the rates of electron and ion transport in the melt. Electron transport occurs by electron self-exchange reactions, or electron hopping, between diffusively relatively immobile Au38(0) and Au38(1+) nanoparticles. The rates of physical diffusion of electrolyte ions (diffusion coefficients DCION) are obtained from ionic conductivities. The measured rates of electron and of electrolyte ion transport are very similar, as are their thermal activation energy barriers, observations that are consistent with a recently introduced ion atmosphere relaxation model describing control of electron transfer in semisolid ion and electron-conductive media. The model has been previously demonstrated using a variety of metal complex polyether melts; the present results extend it to electron transfers between Au nanoparticles. In ion atmosphere relaxation control, measured rates and energy barriers for electron transfer are not intrinsic values but are instead characteristic of competition between back-electron transfer caused by a Coulombic disequilibrium resulting from an electron transfer and relaxation of counterions around donor-acceptor reaction partners so as to reachieve local electroneutrality.

Kindling Fluorescent Protein fromAnemonia sulcata: Dark-State Structure at 1.38 Å Resolution,

When the nonfluorescent chromoprotein asFP595 from Anemonia sulcata is subjected to sufficiently intense illumination near the absorbance maximum (lambda(abs)(max) = 568 nm), it undergoes a remarkable transition, termed "kindling", to a long-lived fluorescent state (lambda(em)(max) = 595 nm). In the dark recovery phase, the kindled state relaxes thermally on a time scale of seconds or can instantly be reverted upon illumination at 450 nm. The kindling phenomenon is enhanced by the Ala143 --> Gly point mutation, which slows the dark recovery time constant to 100 s at room temperature and increases the fluorescence quantum yield. To investigate the chemical nature of the chromophore and the possible role of chromophore isomerization in the kindling phenomenon, we determined the crystal structure of the "kindling fluorescent protein" asFP595-A143G (KFP) in the dark-adapted state at 1.38 A resolution and 100 K. The chromophore, derived from the Met63-Tyr64-Gly65 tripeptide, closely resembles that of the nonfluorescent chromoprotein Rtms5 in that the configuration is trans about the methylene bridge and there is substantial distortion from planarity. Unlike in Rtms5, in the native protein the polypeptide backbone is cleaved between Cys62 and Met63. The size and shape of the chromophore pocket suggest that the cis isomer of the chromophore could also be accommodated. Within the pocket, partially disordered His197 displays two conformations, which may constitute a binary switch that stabilizes different chromophore configurations. The energy barrier for thermal relaxation was found by Arrhenius plot analysis to be approximately 71 kJ/mol, somewhat higher than the value of approximately 55 kJ/mol observed for cis-trans isomerization of a model chromophore in solution.

Anelastic relaxation process of polaronic origin inLa2−xSrxCuO4: Interaction between charge stripes and pinning centers

The evolution of an anelastic relaxation process occurring around 80 K in ${\mathrm{La}}_{2\ensuremath{-}x}{\mathrm{Sr}}_{x}{\mathrm{CuO}}_{4}$ at a measuring frequency of $\ensuremath{\sim}1\mathrm{kHz}$ has been followed from $x=0.0075$ to the overdoped region $x=0.2,$ where it disappears. The dependence of the peak intensity on doping is consistent with a polaronic mechanism, identified with the disordered charge stripes overcoming pinning centers. A marked decrease of the peak amplitude and of the effective energy barrier for relaxation occurs at $x>0.045,$ the same doping range where a change of the stripe order from parallel to diagonal with respect to the Cu-O bonds has been observed by neutron diffraction. Both the energy barrier and peak amplitude also exhibit a rise near $x=1/8.$

Unusual nanogranular systems

Melt-spun Co66Nb9Cu1Si12B12 metallic glass ribbon (TC≈150K) was used to produce a series of nanocrystalline samples differing in the volume content of the crystalline phase as well as the sizes of the crystallites. An analysis of the zero-field-cooled (ZFC) and field-cooled (ZF) dependences of magnetization showed that at low temperatures the samples displayed mictomagnetic (cluster spin-glass) behavior, whereas on increasing temperature a majority of the existing crystallites, beginning from those of the smaller sizes, gradually became superparamagnetic. These characteristics also showed that the existing dipolar interactions between the crystallites decreased the energy barrier for thermal relaxation. This effect was also well visible in the dependences of the temperature derivative of the difference of ZFC and FC magnetizations which reflected a distribution of the blocking temperatures of the crystallites.

Muon Spin Rotation and Relaxation Experiments on Thin Films

The recent development at the Paul Scherrer Institute of a beam of low energy muons allows depth dependent muon spin rotation and relaxation investigations in thin samples, multilayers and near surface regions (low energy μSR, LE-μSR). After a brief overview of the LE-μSR method, some representative experiments performed with this technique will be presented. The first direct determination of the field profile just below the surface of a high-temperature superconductor in the Meissner phase illustrates the power and sensitivity of low energy muons as near-surface probe and is an example of general application to depth profiling of magnetic fields. The evolution of the flux line lattice distribution across the surface of a YBa2Cu3O7 film in the vortex phase has been investigated by implanting muons on both sides of a normal-superconducting boundary. A determination of the relaxation time and energy barrier to thermal activation in iron nanoclusters, embedded in a silver thin film matrix (500nm), demonstrates the use of slow muons to measure the properties of samples that cannot be made thick enough for the use of conventional μSR. Other experiments investigated the magnetic properties of thin Cr(001) layers at thicknesses above and below the collapse of the spin density wave.

Fragilities of liquids predicted from the random first order transition theory of glasses.

A microscopically motivated theory of glassy dynamics based on an underlying random first order transition is developed to explain the magnitude of free energy barriers for glassy relaxation. A variety of empirical correlations embodied in the concept of liquid "fragility" are shown to be quantitatively explained by such a model. The near universality of a Lindemann ratio characterizing the maximal amplitude of thermal vibrations within an amorphous minimum explains the variation of fragility with a liquid's configurational heat capacity density. Furthermore, the numerical prefactor of this correlation is well approximated by the microscopic calculation. The size of heterogeneous reconfiguring regions in a viscous liquid is inferred and the correlation of nonexponentiality of relaxation with fragility is qualitatively explained. Thus the wide variety of kinetic behavior in liquids of quite disparate chemical nature reflects quantitative rather than qualitative differences in their energy landscapes.

Low/high temperature relationships in dinitramide salts by DEA/DSC and study of oxidation of aluminum powders by DSC/TG

The dinitramide salts of ammonia (ADN), hexamethylenetetramine (HDN), potassium (KDN), and sodium (NaDN) showed a linear relationship between the DSC rate of decomposition at the peak maximum and the DEA tanδ value at the low temperature transition peak. As the cation basicity increased in the series ADN<HDN<KDN<NaDN, there was an increase in the low temperature transition peak, the energy barrier for relaxation, and the decomposition peak temperature, and a decrease in the tanδ value at the low temperature transition peak, specific heat capacity, and the rate and enthalpy of decomposition. The more basic salts were more thermally stable (i.e., higher decomposition temperature) and less energetic (i.e., lower enthalpy of decomposition). The more internal free volume (disorder) present in these salts, the higher the rates of relaxation and decomposition. Five aluminum powders of different surface areas were analyzed by DSC in platinum sample pans, and it was found that the enthalpy and rate of oxidation increased as the particle size of Al decreased while the enthalpy of the Al melt decreased. TG showed a two-step weight gain in the oxidation of Al with plateaus in the 650 and 1130°C regions and the percent weight gain increased as the particle size of Al decreased. Variable DSC and TG heating rate studies showed that the activation energies for the first step in the oxidation process increased as the particle size of Al increased.

Explanation of mechanical and electrical relaxation due to mobile ions in a superionic glass over the range 1 Hz–20 GHz by the coupling theory

The observation of mechanical relaxation due to the motion of fast cations in a superionic AgI-rich borate glass has recently been extended by several groups to ten decades in relaxation time by a combination of Brillouin scattering, ultrasonic attenuation, and low-frequency dynamic mechanical measurements. The relaxation time was found to have an almost Arrhenius temperature dependence. The relaxation function is highly nonexponential at lower temperatures or frequencies, but narrows dramatically to exponential relaxation in the gigahertz range. Electrical relaxations due to the same mobile ions have been studied over eight decades by a combination of electric modulus and dc conductivity data. In this work, the coupling theory of relaxation is shown to provide an explanation for all the available mechanical and electrical relaxation data. In particular, the mechanical loss moduli as a function of temperature at 19 GHz, 5 MHz, and 110 Hz can be accurately reproduced both in peak position and shape using values of the primitive relaxation time ${\ensuremath{\tau}}_{0}$ and coupling parameter n obtained from the electrical relaxation data and a narrow distribution of energy barriers for mechanical relaxation which is not present in electrical relaxation.

Determination of the energy barrier for structural relaxation in amorphous Si and Ge by Raman scattering

From the measured Raman linewidth of the transverse optic phonon for annealed amorphous Si and Ge we have, for the first time, determined an activation energy for the metastable state of the amorphous phase. In addition, we have evaluated the root mean square bond angle deviations from parameters for crystalline Si and Ge describing the Raman frequency shifts due to bond angle changes.

Determination of energy barrier for structural relaxation in a-Si and a-Ge by Raman scattering

We have used the expressions for the shifts due to changes in bond angle with stress previously determined for c-Si and c-Ge to calculate the mean bond angle deviation, Δθ, from the measured linewidth of the T0-phonon under various annealing temperatures. T a. The resulting strain energy corresponding to Δθ(T a) can be fitted by the relation U 0-U 1exp(−E a/k bT), where E a is the energy barrier for structural relaxation in the amorphous phase under annealing. For both a-Si and a-Ge, we have determined the energy barrier E a to be approximately 0.2 eV.

Dielectric relaxation of some rigid polar molecules in a polystyrene matrix

Dielectric absorption studies have been carried out on solutions of twelve polar solutes dispersed in an atactic polystyrene matrix over a range of temperatures in the frequency region 50 to 10 5 Hz and in one case also in the range of 10 4 to 10 7 Hz. Rigid molecules of varying size and molecular dipole moments halobenzenes, p-halotoluenes, p-halobiphenyls, p-nitrobiphenyl and p-bromoethylbenzene - have been examined. All these solute molecules have in common the fact that the molecular dipole moment lies along the main principal axis. The relaxation times and energy barrier parameters for molecular dipole relaxations are determined. The Eyring enthalpy of activation, ΔH E , is found to range from 9 for fluorobenzene to 102 kJ mol −1 for p-iodobiphenyl. Relaxation data of these molecules indicate a linear correlation between enthalpy and entropy of activation, and the former is found to depend upon the volume needed for the reorientation of molecules. Present results for halobenzenes and p-halotoluenes reveal a linear dependence of log (relaxation time) on the mean moment of inertia. The enthalpy data for these rigid molecules are useful in the study of flexible molecules when a decision has to be made as to whether the absorption is to be ascribed to molecular or intramolecular or overlap of the two relaxation processes.

Acetyl group relaxation in four aromatic ketones

Dielectric absorption studies have been made of group relaxation of acetophenone, 1,4-diacetylbenzene,4-acetylbiphenyl, and 2-acetylfluorene in a polystyrene matrix, and two rigid molecules have also been examined. For acetyl group relaxation in acetophenone, ΔHE = 29.6 ± 0.6 kJ mol−1 and ΔSE = 26 ± 3 JK−1 mol−1 (95% confidence intervals). The energy barrier for acetyl group relaxation is of the same order as that obtained from nmr data. Our results for acetophenone differ appreciably from the values reported for the gaseous phase by the far-infrared approach and from those by the dielectric absorption of aromatic ketones in benzene solution. The enthalpies of activation for acetyl group relaxation in 1,4-diacetylbenzene, 4-acetylbiphenyl, and 2-acetylfluorene are 29, 30, and 32 kJ mol−1, respectively, which values are identical within their experimental errors. These three substances have also been examined as pure solids, yielding enthalpies of activation for acetyl group relaxation of a similar magnitude.

Surface, catalytic and magnetic properties of small iron particles: III. Nitrogen induced surface reconstruction

The turnover number for ammonia synthesis was found to be smaller on very small iron particles than on larger ones, but it could be enhanced by a pretreatment which seemed to bring about a surface reconstruction induced by nitrogen. The same pretreatment decreases the uptake of carbon monoxide by the catalyst and also the anisotropy energy barrier for relaxation of the metallic iron magnetization, as determined by Mössbauer spectroscopy. These new results can be explained by the creation upon pretreatment of the catalyst, of C 7 surface atoms on the small particles, where a C i atom is one with i nearest neighbors. As the concentration of C 7 atoms is expected to be smaller on very small iron particles than on larger ones, but is enhanced by nitrogen induced surface reconstruction, it is concluded that C 7 iron atoms are more active than others in ammonia synthesis.