Effective Activation Barrier Research Articles

Predicting self-diffusion in metal oxides from first principles: The case of oxygen in tetragonal ZrO2

Theoretical prediction of self-diffusion in a metal oxide in a wide range of thermodynamic conditions has been a long-standing challenge. Here, we establish that combining the formation free energies and migration barriers of all charged oxygen defects as calculated by density functional theory, within the random-walk diffusion theory framework, is a viable approach to predicting oxygen self-diffusion in metal oxides. We demonstrate this approach on tetragonal ZrO${}_{2}$ by calculating oxygen self-diffusivity as a function of temperature and oxygen partial pressure or, alternatively, temperature and off-stoichiometry. Arrhenius analysis on the isobaric (or constant off-stoichiometry) self-diffusivities yields a spectrum of effective activation barriers and prefactors. This provides reconciliation for the wide scatter in the experimentally determined activation barriers and prefactors for many oxides.

CrN–Ag nanocomposite coatings: Control of lubricant transport by diffusion barriers

1-μm-thick self-lubricating CrN–Ag composite coatings containing 16at.% Ag were deposited on Si substrates by reactive co-sputtering at Ts=400°C, and were covered with CrN cap layers with a columnar microstructure and a thickness d=0–1000nm. Vacuum annealing at Ta=500 and 600°C for 1h causes Ag transport to the sample surface and the formation of Ag surface grains. Quantitative scanning electron microscopy and energy dispersive spectroscopy analyses show that increasing d from 0 to 10 to 100nm for Ta=500°C leads to a decrease in the areal density of Ag surface grains from 0.86 to 0.45 to 0.04μm−2, while their lateral size remains constant at 360±60nm. However, increasing Ta to 600°C causes a doubling of the Ag grain size, and a 4–30 times larger overall Ag transport. These results are explained by kinetic barriers for Ag diffusion through the porous cap layer with a porosity that decreases with increasing d, resulting in an effective activation barrier for Ag transport that increases from 0.78eV in the absence of a cap layer to 0.89eV for d=10nm and 1.07eV for d=30nm. Auger electron spectroscopy depth profile analyses of annealed layers reveal no detectable Ag within the CrN cap layer and a uniform depletion of the Ag reservoir throughout the composite coating thickness, indicating unhindered Ag transport within the composite. The overall results show that a CrN diffusion barrier cap layer is an effective approach to control Ag lubricant transport to the surface of CrN–Ag composite coatings.

Vortex creep and critical current densities in superconducting (Ba,K)Fe2As2single crystals

The surprisingly rapid relaxation of the sustainable current density in the critical state of single crystalline Ba$_{1-x}$K$_{x}$Fe$_{2}$As$_{2}$ is investigated for magnetic fields oriented parallel to the c-axis and to the $ab$--plane respectively. Due to the inadequacy of standard analysis procedures developed for flux creep in the high temperature superconducting cuprates, we develop a simple, straightforward data treatment technique that reveals the creep mechanism and the creep exponent $\mu$. At low magnetic fields, below the second magnetization peak, $\mu$ varies only slightly as function of temperature and magnetic flux density $B$. From the data, we determine the temperature- and field dependence of the effective activation barrier for creep. At low temperatures, the measured current density approaches the zero--temperature critical current density (in the absence of creep) to within a factor 2, thus lending credence to earlier conclusions drawn with respect to the pinning mechanism. The comparable values of the experimental screening current density and the zero-temperature critical current density reveals the limited usefulness of the widely used "interpolation formula".

Preparations, Crystal Structures, and Magnetic Properties of N,N-Dipyridylaminoxyl as a New Magnetic Coupler and Its One-Dimensional Cobalt(II) Chains

N,N-Dipyridilaminoxyl, NOpy(2), having a stable aminoxyl, was prepared as a new magnetic coupler for heterospin systems. Solutions of NOpy(2) were mixed with those of bis{1,1,1,5,5,5, hexafluoro-4-(phenylimino)-2-pentanonate}cobalt derivatives, Co(hfpip-X)(2), at a 1:1 ratio to afford the polymeric cobalt(II) complexes, [Co(hfpip-X)(2)(NOpy(2))](n); X = H (1), F (2), F(3) (3), F(5) (4), Cl (5), Cl(3) (6), Br (7), and I (8) as single crystals. In all complexes, the local structures of the cobalt-complex units were compressed octahedra and the pyridine ligands in NOpy(2) units coordinated to the cobalt ions in trans configuration to form linear chains for 1-4 and in cis configuration to form helical chains for 5-8. In the chains, the aminoxyl in NOpy(2) ferromagnetically interacted with the cobalt ions to produce the ferromagnetic chains with J(intra)/k(B) = 9-14 K. In the magnetic susceptibility experiments of aligned sample of 6, the magnetic easy axis was determined to be the a* axis, which was the direction perpendicular to the b axis of the chain axis. The resulting chains, all except 4, interacted antiferromagnetically among each other, and especially in 1, 5, 7, and 8, the magnetic behaviors characteristic to canted two-dimensional (2D) antiferromagnets with T(c) = 5.6, 4.0, 4.0, and 6.2 K, respectively, were observed. All complexes showed slow magnetic relaxations affected by the interchain antiferromagnetic interaction. The effective activation barriers, Δ(eff)/k(B), for the reorientation of the magnetism for all complexes except 4 were estimated to be 25-39 K in the presence of a direct current (dc) field.

Magnetic properties of 1 : 4 complexes of CoCl2 and pyridines carrying carbenes (S0 = 4/2, 6/2, and 8/2) in diluted frozen solution; influence of carbene multiplicity on heterospin single-molecule magnets

The microcrystalline sample of a parent complex, [CoCl(2)(py)(4)], showed a single-molecule magnet (SMM) behavior with an effective activation barrier, U(eff)/k(B), of 16 K for reversal of the magnetism in the presence of a dc field of 3 kOe. Pyridine ligands having 2-4 diazo moieties, DYpy; Y = 2, 3l, 3b, and 4, were prepared and confirmed to be quintet, septet, septet, and nonet in the ground state, respectively, after irradiation. The 1 : 4 complexes, CoCl(2)(DYpy)(4); Y = 2, 3l, 3b, and 4 in frozen solutions after irradiation showed the magnetic behaviors of SMMs with total spin multiplicity, S(total) = 17/2, 25/2, 25/2, and 33/2, respectively. Hysteresis loops depending on the temperature were observed and the values of coercive force, H(c), at 1.9 K were 12, 8.4, 11, and 8.1 kOe for CoCl(2)(CYpy)(4); Y = 2, 3l, 3b, and 4, respectively. In dynamic magnetic susceptibility experiments, ac magnetic susceptibility data obeyed the Arrhenius law to give U(eff)/k(B) values of 94, 92, 93, and 87 K for CoCl(2)(CYpy)(4); Y = 2, 3l, 3b, and 4, respectively, while the relaxation times for CoCl(2)(CYpy)(4); Y = 2 and 3l, obtained by dc magnetization decay in the range of 3.5-1.9 K slightly deviated downward from Arrhenius plots on cooling. The dynamic magnetic behaviors for CoCl(2)(CYpy)(4) including [CoCl(2)(py)(4)] and CoCl(2)(C1py)(4) suggested that the generated carbenes interacted with the cobalt ion to increase the relaxation time, τ(q), due to the spin quantum tunneling magnetization, which became larger with increasing S(total) of the complex.

Dewetting dynamics of silicon-on-insulator thin films

Using low-energy electron microscopy (LEEM), we have measured, in real time, the dewetting of single-crystal Si(001) thin films on amorphous silicon dioxide substrates, which transforms the two-dimensional (2D) thin film into three-dimensional (3D) compact Si nanocrystals. The dewetting scenario has been reported by Bussmann et al. [New J. Phys. 13, 043017 (2011)]. Analytic 2D and 3D models based on simple approximate geometries of the dewetting front have been developed to analyze LEEM measurements. They enable us to estimate the driving force for dewetting ${E}_{s}\ensuremath{\sim}14$ eV/nm${}^{2}$. Starting from a Si-film thickness dependent effective dewetting activation barrier, a single Si(001) surface self-diffusion energy of ${E}_{a}=2.0\ifmmode\pm\else\textpm\fi{}0.2$ eV is derived. First nanoisland-formation dynamics measurements are discussed. Finally, grazing incidence small-angle x-ray scattering (GISAXS) is used to characterize the structure and the morphology of the Si nanocrystals created by the dewetting process.

Does a Concerted Non‐Insertive Mechanism Prevail over a σ‐Insertive Mechanism in Catalytic Cyclohydroamination by Magnesium Tris(oxazolinyl)phenylborate Compounds? A Computational Study

The present study comprehensively explores alternative mechanistic pathways for intramolecular hydroamination of 2,2-dimethyl-4-penten-1-amine (1) by [{To(M)}MgMe] (To(M)=tris(4,4-dimethyl-2-oxazolinyl)phenylborate) (2) with the aid of density functional theory (DFT) calculations. A single-step amidoalkene → cycloamine conversion through a concerted proton transfer associated with N-C ring closure has been explored as one possible mechanism; its key features have been described. This non-insertive pathway evolves via a six-centre TS structure featuring activation of the olefin unit towards nucleophilic amido attack outside the immediate vicinity of the metal centre by amino proton delivery and describes a viable mechanistic variant for alkaline-earth metal-mediated aminoalkene hydroamination. However, herein is presented sound evidence for the operation of the Mg-N amido σ-bond insertive mechanism, its turnover-limiting activation barrier is found to be 5.0 kcal mol(-1) lower than for the non-insertive mechanism, for the cyclohydroamination of 2,2-disubstituted 4-aminoalkenes by a [{To(M)}Mg-NHR] catalyst. The operative mechanism involves rapid equilibria of the {To(M)}Mg-amidoalkene resting state 3 with its amine adduct, easily accessible and thermodynamically disfavoured, hence reversible, 1,2-olefin insertion into the Mg-N amido σ-bond with ring closure at 3, linked to turnover-limiting Mg-C azacycle tether aminolysis by an adduct substrate molecule, followed by facile cycloamine liberation to regenerate the active catalyst species 3. The following aspects are in support of this scenario: 1) the derived rate law is consistent with the experimentally obtained empirical rate law; 2) the reasonable agreement between the computationally estimated and the observed value of the primary KIE; 3) the assessed effective activation barrier for turnover-limiting aminolysis matches empirically determined Eyring parameters remarkably well; and 4) the observed resistance of isolated 3 to undergo amidoalkene cycloamine/cycloamido transformation until further quantities of substrate is added is consistently explained. The herein unveiled insights into the structure-reactivity relationships will undoubtedly govern the rational design of alkaline-earth metal-based catalysts and likely facilitate further advances in the area.

Magnetic Properties after Irradiation of 1:4 Complexes Consisting of CoX2, X = NCS–, Cl–, and NCO–, and Phenylpyridyldiazomethane in Dilute Frozen Solutions: Axial Ligand Effect in Heterospin Single-Molecule Magnets

The solutions of 1:4 complexes of Co(X)(2)(D1py)(4), X = Cl(-), and NCO(-) and D1py = phenylpyridyldiazomethane, were photolyzed under cryogenic conditions, and their magnetic properties were investigated by direct current (DC) and alternating current (AC) magneto/susceptometries. After irradiation, the resulting cobalt-carbene complexes, Co(X)(2)(C1py)(4), exhibited the behaviors of heterospin single-molecule magnets (SMMs) strongly depending on the axial ligands. In Co(X)(2)(C1py)(4): X = Cl(-) and NCO(-), the effective activation barriers, U(eff), for the reorientation of the magnetic moment and the resonant quantum tunneling time, τ(Q), characteristic to SMM properties were estimated to be 91 and 130 K, and 4 × 10(3) and 2 × 10(5) s, respectively. The τ(Q) of Co(NCS)(2)(C1py)(4) with U(eff) = 89 K was found to be 6 × 10(2) s. In Co(X)(2)(C1py)(4): X = Cl(-) and NCO(-), temperature-dependent hysteresis loops were also observed below the blocking temperature (T(B) = 3.2 and 4.8 K, respectively) and the coercive forces, H(c), of 7.0 and 20 kOe at 1.9 K, respectively, were obtained. In a series of 1:4 complexes of Co(X)(2)(C1py)(4), X = NCS(-), Cl(-), and NCO(-), the axial ligands strongly affected the heterospin SMM properties, and the NCO(-) ion having the large magnitude of the ligand-field splitting in a spectrochemical series, gave the largest U(eff) and H(c) and the longest τ(Q).

Mechanistic Insights into the Decomposition of Fructose to Hydroxy Methyl Furfural in Neutral and Acidic Environments Using High-Level Quantum Chemical Methods

Efficient catalytic chemical transformation of fructose to hydroxy methyl furfural (HMF) is one of the key steps for attaining industrial level conversion of biomass to useful chemicals. We report an investigation of the reaction mechanisms for the decomposition of fructose to HMF in both neutral and acidic environments at the Gaussian-4 level of theory including calculation of enthalpies, free energies, and effective solvation interactions. In neutral water solvent, the transformation of fructose to HMF involves a four step reaction sequence with four transition states. The effective activation energy relative to fructose in neutral water at 298 K is very large, about 74 kcal/mol, so that transformation in neutral media around this temperature is unlikely. In contrast, the computed potential energy surface is much more favorable for the transformation in acidic media at 498 K, as the effective activation barrier is about 39 kcal/mol. The transformation in acidic media is a much more complex mechanism involving dehydration and hydrogen transfer steps, which are more favorable when protonated intermediates are involved.

Computing the viscosity of supercooled liquids: Markov Network model.

The microscopic origin of glass transition, when liquid viscosity changes continuously by more than ten orders of magnitude, is challenging to explain from first principles. Here we describe the detailed derivation and implementation of a Markovian Network model to calculate the shear viscosity of deeply supercooled liquids based on numerical sampling of an atomistic energy landscape, which sheds some light on this transition. Shear stress relaxation is calculated from a master-equation description in which the system follows a transition-state pathway trajectory of hopping among local energy minima separated by activation barriers, which is in turn sampled by a metadynamics-based algorithm. Quantitative connection is established between the temperature variation of the calculated viscosity and the underlying potential energy and inherent stress landscape, showing a different landscape topography or “terrain” is needed for low-temperature viscosity (of order 107 Pa·s) from that associated with high-temperature viscosity (10−5 Pa·s). Within this range our results clearly indicate the crossover from an essentially Arrhenius scaling behavior at high temperatures to a low-temperature behavior that is clearly super-Arrhenius (fragile) for a Kob-Andersen model of binary liquid. Experimentally the manifestation of this crossover in atomic dynamics continues to raise questions concerning its fundamental origin. In this context this work explicitly demonstrates that a temperature-dependent “terrain” characterizing different parts of the same potential energy surface is sufficient to explain the signature behavior of vitrification, at the same time the notion of a temperature-dependent effective activation barrier is quantified.

Collective Hydrogen Bond Reorganization in Water Studied with Temperature-Dependent Ultrafast Infrared Spectroscopy

We use temperature-dependent ultrafast infrared spectroscopy of dilute HOD in H(2)O to study the picosecond reorganization of the hydrogen bond network of liquid water. Temperature-dependent two-dimensional infrared (2D IR), pump-probe, and linear absorption measurements are self-consistently analyzed with a response function formalism that includes the effects of spectral diffusion, population lifetime, reorientational motion, and nonequilibrium heating of the local environment upon vibrational relaxation. Over the range 278-345 K, we find the time scales of spectral diffusion and reorientational relaxation decrease from approximately 2.4 to 0.7 ps and 4.6 to 1.2 ps, respectively, which corresponds to barrier heights of 3.4 and 3.7 kcal/mol, respectively. We compare the temperature dependence of the time scales to a number of measures of structural relaxation and find similar effective activation barrier heights and slightly non-Arrhenius behavior, which suggests that the reaction coordinate for the hydrogen bond rearrangement in water is collective. Frequency and orientational correlation functions computed from molecular dynamics (MD) simulations over the same temperature range support our interpretations. Finally, we find the lifetime of the OD stretch is nearly the same from 278 K to room temperature and then increases as the temperature is increased to 345 K.

Kinetic modelling of molecular hydrogen transport in microporous carbon materials

The proposal of kinetic molecular sieving of hydrogen isotopes is explored by employing statistical rate theory methods to describe the kinetics of molecular hydrogen transport in model microporous carbon structures. A Lennard-Jones atom-atom interaction potential is utilized for the description of the interactions between H(2)/D(2) and the carbon framework, while the requisite partition functions describing the thermal flux of molecules through the transition state are calculated quantum mechanically in view of the low temperatures involved in the proposed kinetic molecular sieving application. Predicted kinetic isotope effects for initial passage from the gas phase into the first pore mouth are consistent with expectations from previous modeling studies, namely, that at sufficiently low temperatures and for sufficiently narrow pore mouths D(2) transport is dramatically favored over H(2). However, in contrast to expectations from previous modeling, the absence of any potential barrier along the minimum energy pathway from the gas phase into the first pore mouth yields a negative temperature dependence in the predicted absolute rate coefficients-implying a negative activation energy. In pursuit of the effective activation barrier, we find that the minimum potential in the cavity is significantly higher than in the pore mouth for nanotube-shaped models, throwing into question the common assumption that passage through the pore mouths should be the rate-determining step. Our results suggest a new mechanism that, depending on the size and shape of the cavity, the thermal activation barrier may lie in the cavity rather than at the pore mouth. As a consequence, design strategies for achieving quantum-mediated kinetic molecular sieving of H(2)/D(2) in a microporous membrane will need, at the very least, to take careful account of cavity shape and size in addition to pore-mouth size in order to ensure that the selective step, namely passage through the pore mouth, is also the rate determining step.

Non-isothermal crystallization kinetics of polypropylene/silicon nitride nanocomposites

The non-isothermal crystallization kinetics of polypropylene/silicon nitride (PP/Si 3N 4) nanocomposites was investigated. The Avrami method, Ozawa method and a method proposed by Mo were applied to the analysis of the non-isothermal crystallization of the PP nanocomposites. Nucleation activity of the Si 3N 4 nanoparticles on the PP matrix was also explored. The nucleation activity was strongest when the Si 3N 4 content was 2 wt%. The effective activation barrier (Δ E) for non-isothermal crystallization was also estimated as a function of the relative degree of crystallinity using the isoconversional analysis of calorimetric data. The value of Δ E was found to vary with the relative degree of crystallinity, as well as with the presence of Si 3N 4 filler.

Unfaulting mechanism of trapped self-interstitial atom clusters in bcc Fe: A kinetic study based on the potential energy landscape

We report on the complete unfaulting mechanism of a trapped self-interstitial atom cluster in the form of a nonparallel configuration (NPC), investigated using the autonomous basin climbing (ABC) method. A detailed set of transition state atomic trajectories in the unfaulting process from the trapped to the mobile glide $⟨111⟩$ configuration and the corresponding potential energy landscape were identified. The breaking of the initial ring structure of the three trimers on (111) planes followed by the rotation of the $⟨111⟩$ crowdion in the NPC are the main rate limiting processes of the unfaulting mechanism. The effective activation barrier in the transition from the NPC to the glide $⟨111⟩$ configuration was calculated by combining the ABC and kinetic Monte Carlo methods and was further benchmarked against molecular dynamics (MD) simulations. The effective activation barrier was found as 0.82 eV; smaller than its previously reported value of 1.68 eV. The ABC method was confirmed to be more efficient than MD, especially for the defect structure evolution processes associated with high barriers and at low temperatures.

Radiation effects in single-walled carbon nanotube papers

The effects of ionizing radiation on the temperature-dependent conductivity of single-walled carbon nanotube (SWCNT) papers have been investigated in situ in a high vacuum environment. Irradiation of the SWCNT papers with 4.2MeV alpha particles results in a steady decrease in the SWCNT paper conductivity, resulting in a 25% reduction in room temperature conductivity after a fluence of 3×1012 alpha particles/cm2. The radiation-induced temperature-dependent conductivity modification indicates that radiation damage causes an increase in the effective activation barrier for tunneling-like conductivity and a concomitant increase in wavefunction localization of charge carriers within individual SWCNTs. The spatial defect generation within the SWCNT paper was modeled and confirms that a uniform displacement damage dose was imparted to the paper. This allows the damage coefficient (i.e., differential change in conductivity with fluence) for alpha particles, carbon ions, and protons to be compared with the corresponding nonionizing energy loss (NIEL) of the incident particle. The resulting nonlinear relationship with NIEL between these parameters is distinct from the more typical linear response observed in many bulk semiconductors and superconductors and indicates that localized radiation damage in the SWCNT papers has a greater impact than distributed damage. Although SWCNT papers behave largely as a bulk material with properties that are a convolution of the underlying SWCNT distribution, the radiation response appears to be largely dominated by degradation in the preferred one-dimensional conduction within these two-dimensionally confined nanostructures.

23.1: Invited Paper: Luminescence Quenching by Charge Carriers in Organic Light‐Emitting Diodes

AbstractWe report photoluminescence quenching studies on model DCJTB‐doped Alq3 electroluminescent devices. The spectroscopy versus doping density suggests that solvatochromic effects are minor but that energy transfer plays a large role. Quenching of DCJTB fluorescence is due to Förster energy transfer to DCJTB cations, and measurements of the bleaching recovery dynamics show that charge extraction from ionized DCJTB sites is slow and consistent with biexponential kinetics. Temperature‐dependent studies find effective activation barriers for detrapping that are too small to be consistent with simple HOMO offsets between host and dopant.

Arrest of Fluid Demixing by Nanoparticles: A Computer Simulation Study

We use lattice Boltzmann simulations to investigate the formation of arrested structures upon demixing of a binary solvent containing neutrally wetting colloidal particles. Previous simulations for symmetric fluid quenches pointed to the formation of "bijels": bicontinuous interfacially jammed emulsion gels. These should be created when a glassy monolayer of particles forms at the fluid-fluid interface, arresting further demixing and rigidifying the structure. Experimental work has broadly confirmed this scenario, but it shows that bijels can also be formed in volumetrically asymmetric quenches. Here, we present new simulation results for such quenches, compare these to the symmetric case, and find a crossover to an arrested droplet phase at strong asymmetry. We then make extensive new analyses of the postarrest dynamics in our simulated bijel and droplet structures, on time scales comparable to the Brownian time for colloid motion. Our results suggest that, on these intermediate time scales, the effective activation barrier to ejection of particles from the fluid-fluid interface is smaller by at least 2 orders of magnitude than the corresponding barrier for an isolated particle on a flat interface.

Defect Chemistry of LiFePO4

Based on experimental results, in particular, obtained on single crystals, the nature of the decisive point defects and charge carriers in is discussed, and the dependencies of their concentrations on the control parameters Li activity, doping content, and temperature are worked out. In the native regime characterized by Li deficiency δ, lithium vacancies being decisive for ion conduction are compensated by holes as decisive electronic carriers. Very close to the concentration of order (where δ is strictly zero) frozen-in native defects or non-intentional impurities dominate. We typically found lithium vacancies compensated by iron atoms on Li sites . Intentionally introduced donors such as or , have the same donor effect. The Brouwer diagrams displaying the logarithm of the defect concentration vs log lithium activity or vs log donor/acceptor content are derived. As to the temperature dependence of conductivities, trapping of holes by lithium vacancies is crucial and dominates the effective activation barrier at frozen lithium content. In particular, for the Al-doped samples, ionic association also proves important. Defect reaction and migration enthalpies are derived for electronic and ionic transport. Trapping of holes by lithium vacancies and association of lithium vacancies with impurities also turn out to be key for understanding the temperature dependence of the chemical diffusion coefficient of lithium.

Crystal Design of Monometallic Single-Molecule Magnets Consisting of Cobalt-Aminoxyl Heterospins

Five N-aryl-N-pyridylaminoxyls, which have no substituent (PhNOpy), one substituent (MeOPhNOpy and tert-BuPhNOpy) at the 4-position, and three substituents (TPPNOpy and TBPNOpy) at the 2, 4, and 6-positions of the phenyl ring, were prepared as new ligands for cobalt-aminoxyl heterospin systems. The 1:4 complexes, [Co(NCS)2(PhNOpy)4] (1), [Co(NCS)2(MeOPhNOpy)4] (2), [Co(NCS)2(tertBuPhNOpy)4] (3), [Co(NCS)2(TPPNOpy)4] (4), [Co(NCS)2(TBPNOpy)4] (5a), and [Co(NCO)2(TBPNOpy)4] (5b), were obtained as single crystals. The molecular geometry revealed by X-ray crystallography for all complexes except 4 is a compressed octahedron. In the crystal structure of 1, 2, and 3, the organic spin centers have various short contacts within 4 A with the neighboring molecules to form 3D and 2D spin networks. On the other hand, complexes 5a and 5b have no significant short intermolecular contacts, indicating that they are magnetically isolated. 1 and 2 behaved as a 3D antiferromagnet with a Neel temperature, T(N), of 22 K and as a weak 3D antiferromagnet with a T(N) of 2.9 K and a spin-flop field at 1.9 K, Hsp(1.9), of 0.7 kOe, respectively. 3 was a canted 2D antiferromagnet (a weak ferromagnet) with T(N) = 4.8 K and showed a hysteresis loop with a coercive force, Hc, of 1.3 kOe at 1.9 K. On the other hand, the trisubstituted complexes 4, 5a, and 5b functioned as single-molecule magnets (SMMs). 5b had an effective activation barrier, U(eff), value of 28 K in a microcrystalline state and 48 K in a frozen solution.

Relationships between the single particle barrier hopping theory and thermodynamic, disordered media, elastic, and jamming models of glassy systems

The predictions of the ultralocal limit of the activated hopping theory of highly viscous simple fluids and colloidal suspensions [K. S. Schweizer and G. Yatsenko, J. Chem. Phys. 127, 164505 (2007), preceding paper] for the relaxation time and effective activation barrier are compared with those of diverse alternative theoretical approaches and computer simulation. A nonlinear connection between the barrier height and excess pressure as empirically suggested by simulations of polydisperse repulsive force fluids is identified. In the dense normal and weakly dynamical precursor regime, where entropic barriers of hard spheres are nonexistent or of order the thermal energy, agreement with an excess entropy ansatz is found. In the random close packing or jamming limit, the barrier hopping theory predicts an essential singularity stronger than the free volume model, which is in agreement with the simplest entropic droplet nucleation and replica field theoretic approaches. Upon further technical simplification of the theory, close connections with renormalization group and nonperturbative memory function based studies of activated transport of a Brownian particle in a disordered medium can been identified. Several analytic arguments suggest a qualitative consistency between the barrier hopping theory and solid-state elastic models based on the high frequency shear modulus and a molecular-sized apparent activation volume. Implications of the analysis for the often high degeneracy of conflicting explanations of glassy dynamics are discussed.