Two-step Relaxation Process Research Articles

Emergent facilitation and glassy dynamics in supercooled liquids

In supercooled liquids, dynamical facilitation refers to a phenomenon where microscopic motion begets further motion nearby, resulting in spatially heterogeneous dynamics. This is central to the glassy relaxation dynamics of such liquids, which show super-Arrhenius growth of relaxation timescales with decreasing temperature. Despite the importance of dynamical facilitation, there is no theoretical understanding of how facilitation emerges and impacts relaxation dynamics. Here, we present a theory that explains the microscopic origins of dynamical facilitation. We show that dynamics proceeds by localized bond-exchange events, also known as excitations, resulting in the accumulation of elastic stresses with which new excitations can interact. At low temperatures, these elastic interactions dominate and facilitate the creation of new excitations near prior excitations. Using the theory of linear elasticity and Markov processes, we simulate a model, which reproduces multiple aspects of glassy dynamics observed in experiments and molecular simulations, including the stretched exponential decay of relaxation functions, the super-Arrhenius behavior of relaxation timescales as well as their two-dimensional finite-size effects. The model also predicts the subdiffusive behavior of the mean squared displacement (MSD) on short, intermediate timescales. Furthermore, we derive the phonon contributions to diffusion and relaxation, which when combined with the excitation contributions produce the two-step relaxation processes, and the ballistic-subdiffusive-diffusive crossover MSD behaviors commonly found in supercooled liquids.

Dynamic heterogeneity and mechanical relaxation of Ti20Zr20Cu20Ni20Be20 high-entropy metallic glass probed by quasi-elastic neutron scattering and stress relaxation

Heterogeneity is an intrinsic property of metallic glasses (MGs) and is closely related to their physical properties. Relaxation dynamics provides a powerful approach to understanding the heterogeneity of MGs. State-of-the-art quasi-elastic neutron scattering (QENS) and stress relaxation are used to study the atomic relaxation dynamics, dynamic heterogeneity, diffusion coefficients and mechanical relaxation of Ti20Zr20Cu20Ni20Be20 high-entropy metallic glass (HE-MG). The dynamic susceptibility derived from the QENS self-intermediate scattering function was used to evaluate the presence of dynamic heterogeneity, which increases gradually with decreasing temperature. The average self-diffusion coefficient of Ni and Ti atoms in the Ti20Zr20Cu20Ni20Be20 HE-MG melt is much higher than that in the Ti13.8Zr41.2Cu12.5Ni10Be22.5 Vit1 MG melt. The Ti20Zr20Cu20Ni20Be20 HE-MG melt has higher atomic mobility with respect to the Vit1 MG melt. In addition, the activation energy for crystallization of the Ti20Zr20Cu20Ni20Be20 HE-MG is considerably larger than that of the Vit1 MG. In the stress relaxation test, both Ti20Zr20Cu20Ni20Be20 HE-MG and Vit1 MG exhibit a relaxation decoupling phenomenon, indicating a two-step relaxation process. The slow and fast relaxation processes of the two alloy ribbons have a stretched exponential decay. At the measured temperatures, the relaxation times for both of the relaxation processes for the Ti20Zr20Cu20Ni20Be20 HE-MG are larger than those for the Vit1 MG, meaning that the Ti20Zr20Cu20Ni20Be20 ribbon has a slower stress decay. This in-depth investigation will improve our understanding of the intrinsic heterogeneity and mechanical relaxation mechanism in HE-MG.

Ab initio calculations and empirical potential assessments of the energy and structure of symmetric tilt grain boundaries in tungsten

Molecular statics/dynamics (MS/MD) based on empirical interatomic potentials (IAPs) is an effective means for conducting grain boundary (GB) related studies. The accuracy of these MS/MD simulations, however, can be greatly affected by the IAP used. Unfortunately, the large discrepancies between the ab-initio values make it difficult to evaluate, improve and further develop IAPs. Motivated by this issue, in the present work we perform a systematic investigation of 〈100〉 and 〈110〉 symmetric tilt GBs in tungsten (W) via atomistic simulations, including the stable structure, GB energy, work of separation, excess volume, and vacancy formation energy. We here use a two-step relaxation process, initially obtaining the candidate structures from MS and then performing DFT validation of these structures to determine the ground state structure, where six empirical IAPs and four exchange–correlation (xc) functionals are used. And the step-like feature is revealed that can be used to reduce the cost of time-consuming optimization processes. Taking the results yielded by PBEsol xc-functional as a benchmark, it is shown that for the same xc-functional, the relative errors of GB energy and work of separation are almost identical, independent of the GB character. The performance of six typical empirical IAPs considered for W is also evaluated by comparing it with the DFT data. The quantities chosen for the comparison include the structure and energetic properties of GBs, as mentioned before. We demonstrate that these empirical IAPs tend to better describe only part of the properties of GBs; for example, some IAPs can predict the energetic properties well, while others can better describe the structure. This suggests that a fully reliable description of GBs remains an elusive objective, requiring further efforts in the development and optimization of the IAP.

Recyclable dual-curing thiol-isocyanate-epoxy vitrimers with sequential relaxation profiles

Two series of poly(thiourethane)s-poly(thiol-epoxy) hybrids were prepared from dual-curing, stoichiometric thiol:isocyanate:epoxy mixtures. 1-methylimidazole (MI) was used as initiator for the thiol-isocyanate and thiol-epoxy curing reactions. A salt of tetraphenylborate derived from highly basic amine 1,5,7 triazabicyclo [4,4,0]dec-5-ene (TBD) was used as catalyst for the activation of bond exchange reactions. The curing kinetics and the glass transition temperature (Tg) of the samples were studied by differential scanning calorimetry (DSC). Thermal stability was characterized by thermogravimetric analysis (TGA). Stress relaxation dynamics related to the bond exchange reactions were studied by dynamic mechanical analysis (DMA). Recyclability of the fully cured samples according to the DMA results was carried out by hot-pressing at elevated temperatures. The results show that the curing process takes place in a controlled and sequential way: the thiol-isocyanate reaction takes place first, at moderate temperatures, followed by the thiol-epoxy reaction, which is completed at higher temperatures. The analysis of stress relaxation evidences a complex two-step relaxation behavior depending on the contribution of isocyanate and epoxy groups to the mixture. Isocyanate-rich materials show a simple relaxation process corresponding to the trans-thiocarbamoylation exchange reactions. Epoxy-rich materials show, in contrast, a two-step relaxation processes evidencing that trans-thiocarbamoylation alone may not be sufficient to relax the stress completely, due to an apparently permanent network structure. However, complete stress relaxation is possible for epoxy-rich materials through additional bond exchange reactions such as transesterification or dynamic thiol-Michael, but at a slower rate. Depending on the composition and the temperature, full recycling of the material can be achieved at moderate temperatures in a timescale of minutes to hours.

Regulating Magnetic Relaxations of Cyano-Bridged {DyIII MoV } Systems by Tuning the N-Sites in β-Diketone Ligands.

Cyano-bridged 4d-4f molecular nanomagnets have re-called increasing research interests in molecular magnetism since they offer more possibilities in achieving novel nanomagnets with versatile structures and magnetic interactions. In this work, four β-diketone ligands bearing different substitution N-sites were designed and synthesized, namely 1-(2-pyridyl)-3-(3-pyridyl)-1,3-propanedione (HL1 ), 1,3-Bis (3-pyridyl)-1,3-propanedione (HL2 ), 1-(4-pyridyl)-3-(3-pyridyl)-1,3-propanedione (HL3 ), and 1,3-Bis (4-pyridyl)-1,3-propanedione (HL4 ), to tune the magnetic relaxation behaviors of cyano-bridged {DyIII MoV } systems. By reacting with DyCl3 ⋅ 6H2 O and K4 Mo(CN)8 ⋅ 2H2 O, four cyano-bridged complexes, namely {[Dy[MoV (CN)8 ](HL1 )2 (H2 O)3 ]} ⋅ 6H2 O (1), {[Dy[MoV (CN)8 ](HL2 )(H2 O)3 (CH3 OH)]}2 ⋅ 2CH3 OH ⋅ 3H2 O (2), {[Dy[MoV (CN)8 ](HL3 )(H2 O)2 (CH3 OH)] ⋅ H2 O}n (3), and {[Dy[MoV (CN)8 ](HL4 )2 (H2 O)3 ]} ⋅ 2H2 O⋅CH3 OH (4) were obtained. Structural analyses revealed that 1 and 4 are binuclear complexes, 2 has a tetragonal structure, and 3 exhibits a stair-like polymer chain structure. The DyIII ions in all complexes have eight-coordinated configurations with the coordination spheres DyO7 N1 for 1 and 4, DyO6 N2 for 2, and DyO5 N3 for 3. Magnetic measurements indicate that 1 is a zero-field single-molecule magnet (SMM) and complexes 2-4 are field-induced SMMs, with complex 4 featuring a two-step relaxation process. The magnetic characterizations and ab initio calculations revealed that changing the N-sites in the β-diketone ligands can effectively alter the structures and magnetic properties of cyano-bridged 4d-4f nanomagnets by adjusting the coordination environments of the DyIII centers.

Distinct magnetic relaxation behaviors in nitronyl nitroxide-based cocrystalline supramolecular system with DyIII-O-H⋯O-N hydrogen bond

The self-assembly of Dy(hfac)3·2H2O, Co(hfac)2·2H2O or Mn(hfac)2·2H2O (hfac = hexafiuoroacetylacetonate) with NITPh-triazole radical (NITPh-triazole = 2-[2-(1H-1,2,4-triazol-1-yl)phenyl]-4,4,5,5-tetramethyl-imidazoline-1-oxyl-3-oxide) produces two 2p-3d-4f compounds of formula {[Dy(hfac)3(H2O)2][Co2(hfac)4(NITPh-triazole)2]2.CH2Cl2}n (1) and {[Dy(hfac)3(H2O)2][Mn2(hfac)4(NITPh-triazole)2]2}n (2) featuring extraordinary intermolecular hydrogen bonds between coordinated H2O molecules and uncoordinated NO groups linking into a supramolecular one-dimensional chain. Notably, the LnIII-O-H⋯O-N hydrogen bond bridge has been rarely observed in nitronyl nitroxide-metal system. Magnetic performance and heat capacity of both 2p-3d-4f compounds are detected. Interestingly, 1 and 2 both show apparent double peaks of χ′′ signals with two-step magnetic relaxation processes. Furthermore, the effective barrier of 1 is obviously higher than 2. As far as we know, employing unusual intermolecular LnIII-O-H⋯O-N hydrogen bond, it is the first to obtain supramolecular 2p-3d-4f one-dimensional heterospin materials with apparent slow magnetic relaxation and heat capacity behaviors.

Impact and structure of water in aqueous octanol mixtures: Hz-GHz dielectric relaxation measurements and computer simulations

Temperature (283 ≤ T/K ≤ 323) dependent dielectric relaxation (DR) measurements of aqueous binary mixtures of octanol at three different water mole fractions (XH2O = 0.05, 0.10, 0.20) were performed employing two different frequency windows: 0.00002 ≤ν/MHz≤ 10 and 0.2 ≤ν/GHz≤ 50. In addition, DR measurements were carried out for pure octanol and water saturated octanol at 298 K. All these measurements showed, irrespective of solution temperature, a small decrease of the static dielectric constant (εs) upon addition of water in octanol. Two-step relaxation process with time constants ∼ 3–0.3 ns and ∼ 120–40 ps characterized the measured DR spectra with no signature of bulk water-like DR time constant (∼10 ps). Differential scanning calorimetric (DSC) measurements of octanol + water mixtures reflect only water concentration dependent depression of octanol freezing temperature. Our computer simulations of aqueous octanol mixtures with SPC/E water suggests a dramatic decrease of the average number of water-water H-bonds 〈NHBw-w〉 per water molecule and a spectacular increase of water populations possessing OOO angles distributed over 0°≤θ≤ 60°. Consequently, a negative value for the average tetrahedral order parameter (〈Q〉) and an εs as low as ∼ 2 for water have been predicted. A severe damage to the global tetrahedrality of water in these mixtures has been predicted and the angle distributions corresponding to negative and positive Q values explicitly shown. These simulation results therefore explain the microscopic origin for small effects of water at low mole fractions on εs of octanol + water binary mixtures.

Prethermalization, thermalization, and Fermi's golden rule in quantum many-body systems

We study the prethermalization and thermalization dynamics of local observables in weakly perturbed nonintegrable systems, with Hamiltonians of the form $\hat{H}_0+g\hat{V}$, where $\hat{H}_0$ is nonintegrable and $g\hat{V}$ is a perturbation. We explore the dynamics of far from equilibrium initial states in the thermodynamic limit using a numerical linked cluster expansion (NLCE), and in finite systems with periodic boundaries using exact diagonalization. We argue that generic observables exhibit a two-step relaxation process, with a fast prethermal dynamics followed by a slow thermalizing one, only if the perturbation breaks a conserved quantity of $\hat{H}_0$ and if the value of the conserved quantity in the initial state is $\mathcal{O}(1)$ different from the one after thermalization. We show that the slow thermalizing dynamics is characterized by a rate $\propto g^2$, which can be accurately determined using a Fermi golden rule (FGR) equation. We also show that during such a slow dynamics, observables can be described using projected diagonal and Gibbs ensembles, and we contrast their accuracy.

Regulating Spin Dynamics of Nitronyl Nitroxide Biradical Lanthanide Complexes through Introducing Different Transition Metals.

Four biradical-Ln complexes with different transition metal ions, namely [LnM(hfac)5 (NITPh-PyPzbis)] (MII =MnII and LnIII =Gd 1, Dy 2; MII =NiII and LnIII =Tb 3, Dy 4), were prepared by the reaction of Ln(hfac)3 ⋅ 2H2 O, Mn(hfac)2 ⋅ 2H2 O or Ni(hfac)2 ⋅ 2H2 O with NITPh-PyPzbis biradical (hfac=hexafluoroacetylacetonate, NITPh-PyPzbis=5-(3-(2-pyridinyl)-1H-pyrazol-1-yl)-1,3-bis(1'-oxyl-3'-oxido- 4',4',5',5'-tetramethyl-4,5-hydro-1H-imidazol-2-yl)benzene). In complexes 1-4, the NITPh-PyPzbis biradical chelates one LnIII ion by means of its aminoxyl moieties and the transition metal ion is introduced through the two N donors from the pyridyl pyrazolyl moiety. Magnetic investigations indicate that complex 4 displays visible maxima in frequency/temperature-dependent χ'' signals with two-step relaxation processes, but complex 2 exhibits no slow magnetization relaxation. The comparison of structure parameters of both Dy complexes indicates that the symmetries of coordination spheres of two Dy ions are D2d for 2 and C2v for 4, which thus probably results in different magnetic relaxation behaviors. This work provides new insight for improving properties of Ln-biradical based SMMs.

Evolution from a single relaxation process to two-step relaxation processes of Dy2 single-molecule magnets via the modulations of the terminal solvent ligands.

To explore the influences of magnetic interactions on the relaxation dynamics of single-molecule magnets (SMMs) and to understand the relationship between single-ion relaxation and the relaxation of a molecular entity, it is very important to design dinuclear lanthanide-based SMMs with two-step relaxation processes. Here, three Dy2 complexes of compositions [Dy2(L)2(NO3)2(MeOH)2] (1), [Dy2(L)2(NO3)2(EtOH)2] (2), and [Dy2(L)2(NO3)2(DMF)2]·0.5EtOH (3) (H2L = 2-(((2-hydroxy-3-methoxybenzyl)imino)methyl)-4-methoxyphenol) were successfully synthesized via elaborately introducing different terminal solvent ligands. X-ray single-crystal diffraction analyses revealed that complexes 1-3 are isostructural. The two DyIII ions of 1 and 2 both adopt D2d symmetry, while the two DyIII centres of 3 display D2d and D4d symmetries, respectively. The magnetic property studies of 1-3 indicated that all three complexes exhibit single-molecule magnet (SMM) behaviours with energy barriers of 104 K for 1, 98.94 K for 2, and 76.28 K and 45.54 K for 3 under zero dc field. The target of assembling Dy2 SMMs with two-step relaxation processes was achieved by gradually increasing the sizes of the terminal solvent ligands. Complex 3 exhibits two-step relaxation processes. Complete active space self-consistent field (CASSCF) calculations were performed on 1-3 to rationalize the observed differences in the magnetic behaviour. It is found that both the angles θ between the magnetic axis and the vector connecting two DyIII ions and the symmetries of DyIII ions are vital factors that affect the energy barriers of 1-3. The high local symmetries of the central metals in 1 and 2 make the complexes act as SMMs with higher energy barriers, while the smaller θ angle and different symmetries of the two DyIII ions render complex 3 as a SMM with a two-step relaxation process. This work demonstrates a new methodology for preparing SMMs with two-step relaxation processes by fine-tuning the terminal solvent ligands.

A phenoxo-O bridged Dy2 compound showing two-step magnetic relaxation processes behavior

A new dinuclear Dy(III)-based compound, [Dy(bfac)2L]2(1) ([bfac = benzoyltrifluoroacetone, and HL = 2-[(4-chlorophenyl)imino]methyl]-8-hydroxyquinoline), was synthesized, structurally and magnetically characterized. The X-ray structural analysis exhibits compound 1 is a binuclear dysprosium complex, in which Dy1 and Dy1a atoms are bridged by two phenoxo-O atoms of two 8-hydroxyquinoline Schiff base ligands. Magnetic properties research indicated that two magnetic relaxation processes were clearly observed in 1 under Hdc = 0 fild. It is a rare and interesting magnetic phenomenon in the reported dinuclear Ln(III)-based compounds.

Designing asymmetric Dy2 single-molecule magnets with two-step relaxation processes by the modification of the coordination environments of Dy(iii) ions.

The reaction of Dy(NO3)3·6H2O and an asymmetric Schiff-base linker 5-chloro-2-(((2-hydroxy-3-methoxybenzyl)imino)methyl) phenol (H2L) afforded a dinuclear compound [Dy2L2(HL)(NO3)(EtOH)]·0.5C2H5OH (1). Complex 1 features two inequivalent Dy(iii) sites, where three ligand sets (one HL- moiety and two L2- groups) are shared by two Dy(iii) ions. The strategic introduction of CH3COOH in the reaction system used for synthesizing 1 induces the replacement of the HL- ligand by the CH3COO- ion, consequently resulting in the generation of [Et3NH][Dy2L2(NO3)(CH3COO)2] (2). In complex 2, two Dy(iii) centers adopt NO7 (D2d geometry) and NO6 (C2v) coordination sphere, respectively. DC magnetic susceptibility studies for the two complexes indicate ferromagnetic interactions. Complexes 1 and 2 exhibit single-molecule magnet behavior with two-step slow relaxation processes due to the possession of inequivalent metal sites. The energy barriers of 69.19 and 45.73 K for 1, and 92.77 and 72.95 K for 2 are determined. Theoretical calculations reveal that the two-step relaxation processes in both 1 and 2 mainly originate from the single-ion magnetism of two distinct Dy(iii) ions with inequivalent coordination environments.

Two-step relaxation and the breakdown of the Stokes-Einstein relation in glass-forming liquids.

It is well known that glass-forming liquids exhibit a number of anomalous dynamical phenomena, most notably a two-step relaxation in the self-intermediate scattering function and the breakdown of the Stokes-Einstein (SE) relation, as they are cooled toward the glass transition temperature. While these phenomena are generally ascribed to dynamic heterogeneity, specifically to the presence of slow- and fast-moving particles, a quantitative elucidation of the two-step relaxation and the violation of the SE relation in terms of these concepts has not been successful. In this work, we propose a classification of particles according to the rank order of their displacements (from an arbitrarily defined origin of time), and we divide the particles into long-distance (LD), medium-distance, and short-distance (SD) traveling particle groups. Using molecular-dynamics simulation data of the Kob-Andersen model, we show quantitatively that the LD group is responsible for the fast relaxation in the two-step relaxation process in the intermediate scattering function, while the SD group gives rise to the slow (α) relaxation. Furthermore, our analysis reveals that τ_{α} is controlled by the SD group, while the ensemble-averaged diffusion coefficient D is controlled by both the LD and SD groups. The combination of these two features provides a natural explanation for the breakdown in the SE relation at low temperature. In addition, we find that the α-relaxation time, τ_{α}, of the overall system is related to the relaxation time of the LD particles, τ_{LD}, as τ_{α}=τ_{0}exp(Ωτ_{LD}/k_{B}T).

Relaxation of Strain in Si Layers Formed on (110)-Oriented SiGe/Si Heterostructures

Relaxation phenomena of the strain in a Si film in the course of the growth on a Si0.64Ge0.36/Si(110) heterostructure was investigated by using the micro Raman mapping measurements. A two-step strain relaxation process in the growth of a (110)-oriented Si film was found. It was confirmed that the lattice strain is maintained until the film thickness exceeds 70 nm.

Transient response of an electrolyte to a thermal quench.

We study the transient response of an electrolytic cell subject to a small, suddenly applied temperature increase at one of its two bounding electrode surfaces. An inhomogeneous temperature profile then develops, causing, via the Soret effect, ionic rearrangements towards a state of polarized ionic charge density q and local salt density c. For the case of equal cationic and anionic diffusivities, we derive analytical approximations to q,c, and the thermovoltage V_{T} for early (t≪τ_{T}) and late (t≫τ_{T}) times as compared to the relaxation time τ_{T} of the temperature. We challenge the conventional wisdom that the typically large Lewis number, the ratio a/D of thermal to ionic diffusivities, of most liquids implies a quickly reached steady-state temperature profile onto which ions relax slowly. Though true for the evolution of c, it turns out that q (and V_{T}) can respond much faster. Particularly when the cell is much bigger than the Debye length, a significant portion of the transient response of the cell falls in the t≪τ_{T} regime, for which our approximated q (corroborated by numerics) exhibits a density wave that has not been discussed before in this context. For electrolytes with unequal ionic diffusivities, V_{T} exhibits a two-step relaxation process, in agreement with experimental data of Bonetti etal. [J. Chem. Phys. 142, 244708 (2015)JCPSA60021-960610.1063/1.4923199].

Enhancing Magnetic Behaviors of Dysprosium Single-Molecule Magnets from Crystal Field Perturbation by Deprotonating Schiff-Base Ligand

For studying how crystal field perturbation influence magnetic relaxation behaviors of Ln-SMMs, four complexes of [Ln(H2L)(NO3)(H2O)(EtOH)](NO3)2·H2O (Ln = Dy (1), Tb (2)) and [Ln(L)(NO3)(MeOH)2] (Ln = Dy (3), Tb (4)) were synthesized by utilizing planar pentadentated Schiff-base ligand H2L [2,6-diylbis(ethan-1-yl-1-ylidene)di(isonicotinohydrazide)] under different alkaline conditions. They all have similar mononuclear structures with LnIII ion in nine-coordinated muffin geometry. Crystal field was slightly perturbed by deprotonating H2L ligand and using different solvent molecules in DyIII complex 3, which result in field-induced two-step relaxation processes with almost 3-fold increase in Ueff of 57.52 K (SR) and 28.49 K (FR) than 20.63 K for complex 1 showing one-step relaxation process. This work gives another example of improving SMM behavior simply by subtle crystal field perturbation.

Slow dynamics in glass-forming materials at [formula omitted]- and [formula omitted]-relaxation stages based on time-convolutionless mode-coupling theory

The slow dynamics of glass-forming materials in α and β stages are analyzed based on the time-convolutionless mode-coupling theory recently proposed by the present author. Similarly to the analyses used in the mode-coupling theory, the two-step relaxation processes, so called critical decay with a time exponent a and von Schweidler decay with a time exponent b, are first discussed in β stage. In α stage, the Kohlrausch–Williams–Watts type function, often called stretched exponential with a time exponent β, is also investigated in the manner similar to that in β stage. The exponents a, b, and β are then shown to satisfy the relations Γ[1−a]2Γ[1−2a]=Γ[1+b]2Γ[1+2b]=Γ[2β−1]Γ[2β+1]Γ[β+1]Γ[−β−1]=λ,12a+12b=γ,where λ is an exponent parameter, γ a power-law exponent of the α-relaxation time, and Γ[x] an usual Γ-function. Thus, the numerical values of those exponents calculated under a given value of γ are compared with the simulation results for three types of glass-forming liquids with three different values of γ and are shown to describe them well within error.

Rheological modifiers based on supramolecular block copolymers: From weak associations to interconnected micelles

The rheological spectra of poly(n-butyl acrylate) in the presence of a series of P(nBA-b-HEMA) rheology modifiers show a two-step relaxation process originating from the PnBA matrix and the self-assemblies. The HEMA segments are further grafted with strong, hydrogen bonding UPy groups, which both magnifies and slows down the relaxation of the assemblies. The extents of associations are enlightened by studying thermal transitions in DSC, morphological developments by SAXS, and description of rheological properties using a tube-based model. It is revealed that a weak association tendency, due to long hydrophobic blocks, leads to the formation of double-linear or star assemblies, while increasing the association strength results in the formation of micelles. In an optimum block length and UPy content, loosely entangled diblock additives can form an interconnected micellar network with significantly long relaxation time.

Dramatic impact of auxiliary ligands on the two-step magnetic relaxation process in Dy4(iii) single-molecule magnets.

To better understand the factors determining the multi-step relaxation processes in polynuclear lanthanide single molecule magnets (SMMs), two Dy(iii)4 SMMs showing two-step relaxation processes were elaborately designed and investigated for their structure-dependent magnetic properties. Through targetedly fine-tuning the auxiliary ligand (from the anion of 1-phenylbutane-1,3-dione to 2-acetylcyclopentanone) on specific Dy(iii) sites while retaining the same type of coordination atoms, one of the two relaxation processes shifted to higher temperature with an increase of energy barrier, which permits the unambiguous assignment of the relaxation processes to specific metal sites. Therefore, the present {Dy4} systems provide a good example to probe the factors determining the relaxation dynamics, and point to a simple way to optimize the magnetic performance of polynuclear dysprosium SMMs.

Asynchronous dissipative filter design of nonhomogeneous Markovian jump fuzzy systems via relaxation of triple-parameterized matrix inequalities

This paper investigates the problem of designing a dissipativity-based asynchronous filter for a class of nonhomogeneous discrete-time Markovian jump fuzzy systems with uncertainties. Different from previous works, the proposed approach opens a possibility to tackle more realistic problems of handling both asynchronism and nonhomogeneity phenomena of plant and filter modes. To be more concrete, this paper proposes a novel relaxation method capable of handling triple-parameterized matrix inequalities in such a way that central constraints on multiple time-varying parameters can be sufficiently exploited. Especially, an attempt to utilize the conditional relation between two nonhomogeneous Markov chains is first made to reduce the conservatism of two-step relaxation process that has to employ mutually uncorrelated slack variables for plant and filter modes.