Relaxation Time Τα Research Articles

Dynamics and spatial correlation of voids in dense two dimensional colloids.

Two dimensional (2D) colloids show interesting phase and dynamic behaviors. In 2D, there is another intermediate phase, called hexatic, between isotropic liquid and solid phases. 2D colloids also show strongly correlated dynamic behaviors in hexatic and solid phases. We perform molecular dynamics simulations for 2D colloids and illustrate how the local structure and dynamics of colloids near phase transitions are reflected in the spatial correlations and dynamics of voids. Colloids are modeled as hard discs and a void is defined as a tangent circle (a pore) to three nearest hard discs. The variation in pore diameters represents the degree of disorder in voids and decreases sharply with the area fraction (ϕ) of colloids after a hexagonal structural motif of colloids becomes significant and the freezing transition begins at ϕ ≈ 0.7. The growth of ordered domains of colloids near the phase transition is captured in the spatial correlation functions of pores. We also investigate the topological hopping probability and the topological lifetime of colloids in different topological states, and find that the stability of different topological states should be related to the size variation of local pores: colloids in six-fold states are surrounded by the most ordered and smallest pores with the longest topological lifetime. The topological lifetime of six-fold states increases by about 50 times as ϕ increases from liquid to hexatic to solid phases. We also compare four characteristic times in order to understand the slow and unique dynamics of two dimensional colloids: a caging time (τ(c)), a topological lifetime (τ(top)), a pore lifetime (τ(p)), and a translational relaxation time (τ(α)).

Fast Crystal Growth from Organic Glasses: Comparison of o-Terphenyl with its Structural Analogs

Crystal growth kinetics and liquid dynamics of 1,2-diphenylcyclopentene (DPCP) and 1,2-diphenylcyclohexene (DPCH) were characterized by optical microscopy and dielectric spectroscopy. These two molecules are structurally homologous and dynamically similar to the well-studied glassformer ortho-terphenyl (OTP). In the supercooled liquid states of DPCP and DPCH, the kinetic component of crystal growth ukin has a power law relationship with the primary structural relaxation time τα, ukin [proportionality] τα(–ξ) (ξ ≈ 0.7), similar to OTP and other fragile liquids. Near the glass transition temperature (Tg), both DPCP and DPCH develop much faster crystal growth via the so-called GC (glass to crystal) mode, again similar to the behavior of OTP. We find that the α-relaxation process apparently controls the onset of GC growth, with GC growth possible only at sufficiently low fluidity. These results support the view that GC crystal growth can only occur in systems where the liquid and crystal exhibit similar local packing arrangements.

A connection between the structural α-relaxation and the β-relaxation found in bulk metallic glass-formers

New metallic glasses containing La or Ce have been introduced having dynamic properties bordering on two extremes of conventional metallic glasses. This provides opportunity to test if the trends or correlations established before in molecular and polymeric glass-formers also exist in the broader family of metallic glasses. Due to the drastically different chemical and physical structures of metallic glass-formers than soft matter, there is no guarantee that any correlation found in the latter will hold in the former. If the trends and correlations are found, the result brings metallic glasses closer to the much wider classes of glass-formers in the similarity of properties. In non-metallic glass-formers, a general and fundamental connection has been established between the non-exponentiality parameter of the structural α-relaxation and the separation between its relaxation time τα and the β-relaxation time τβ. In this paper, we explore the experimental data of metallic glass-formers and show the correlation applies. An explanation of this correlation is given by the Coupling Model. The establishment of the correlation may facilitate the understanding of the roles played by the β-relaxation in macroscopic properties of metallic glasses including the relations to shear transformation zone, ductile-brittle transition in deformation, crystallization, and diffusion.

Thermodynamic hydration shell behavior of glycine

Glycine aqueous solutions have been studied as a function of temperature and concentration by means of UV Brillouin and Raman spectroscopes. Brillouin spectra provided information on the average relaxation time τα related to the mechanisms of hydrogen bonds (HBs) formation and breaking. The concentration-temperature behavior of τ has been compared to the vibrational dephasing lifetime of atoms involved in HBs, as derived by a lineshape analysis of Raman spectra. We point out how it is possible to trace the thermodynamic behavior of a selected HB from Raman data. In particular, our results confirm the predominant role played in the hydration process by the water molecules surrounding the hydrophobic groups and, furthermore, evidence how at low temperature the HB strength between these molecules is greater than those found in bulk water and between glycine and water molecules.

Crossover from fragile liquids to strong liquids near the glass transition created by isotropic two-body short-range interactions

The extensive molecular-dynamics simulations on binary mixtures A80B20 with a Stillinger–Weber potential are performed to obtain two types of glass-forming liquids near the glass transition, fragile and strong liquids. The simulations are done for different mass ratios Q(=mB/mA) under the same potential with mA being fixed, where mα denotes a mass of α particle. The simulation results for the self-diffusion coefficient D are then analyzed by two types of master curves recently proposed as D=d0x−1(1−x)2+ηexp[62x3+η(1−x)2+η] with η=4/3 for fragile liquids and 5/3 for strong liquids, where x is a reduced inverse temperature and d0 a positive constant. Then, it is shown that for Q<Qc the simulation results for the diffusion coefficient obey the fragile master curve with η=4/3, while for Q>Qc they obey the strong master curve with η=5/3, where Qc≃20. The structural relaxation time τα and the β-relaxation time τβ are also shown to obey the power laws recently proposed as τα∼D−(1+μ) and τβ∼D−(1−μ) in a supercooled region, respectively, while τα∼τβ∼D−2/3 in a liquid region, where μ=2/(3(η+2)). Here μ≃1/5 for fragile liquids and 2/11 for strong liquids. These situations are exactly the same as those in usual glass-forming liquids. Thus, it is emphasized that two types of glass-forming liquids can be simply created by simple short-range potentials.

Temperature-Volume Entropic Model for Viscosities and Structural Relaxation Times of Glass Formers.

In this Letter, an entropic model recently formulated by Mauro et al. for the temperature dependence of viscosity in glass-forming materials is generalized to describe the temperature-volume dependences of viscosities and structural relaxation times near the glass transition. It is found that the generalization shows limitations of its temperature precursor. The extended model describes well the structural dielectric relaxation times τα(T,V) of supercooled van der Waals liquids. The obtained results are discussed in the context of the thermodynamic scaling law for molecular dynamics of viscous systems.

Anomalous Transformation of Vapor-Deposited Highly Stable Glasses of Toluene into Mixed Glassy States by Annealing Above Tg.

Vapor-deposited glasses have recently emerged as a remarkable new class of materials that can form much denser and stable glasses than those obtained by cooling the liquid. These new amorphous materials reach lower regions of the energy landscape and may impact important technologies that use vapor-deposition. Here, we report on the formation of a glass with two distinct glassy states obtained through the partial annealing of highly stable vapor-deposited glassy films of toluene. The resulting glass exhibits two clear heat capacity overshoots with different onset and fictive temperatures. The transformation times of the ultrastable glass are around 10(5) times slower than the structural relaxation time (τα) of supercooled liquid toluene. We show that the nature of the transformed glass depends on the annealing temperature above Tg. This finding suggests the formation of distinct supercooled liquids at temperatures slightly above Tg during the transformation of the highly stable glass. Our results are compatible with the existence of polyamorphism in toluene.

Positron annihilation and relaxation dynamics from dielectric spectroscopy and nuclear magnetic resonance: Cis–trans-1,4-poly(butadiene)

We report a joint analysis of positron annihilation lifetime spectroscopy (PALS), dielectric spectroscopy (BDS), and nuclear magnetic resonance (NMR) on cis-trans-1,4-poly(butadiene) (c-t-1,4-PBD). Phenomenological analysis of the orthopositronium lifetime τ(3)-T dependence by linear fitting reveals four characteristic PALS temperatures: T(b1)(G)=0.63T(g)(PALS), T(g)(PALS), T(b1)(L)=1.22T(g)(PALS), and T(b2)(L)=1.52T(g)(PALS). Slight bend effects in the glassy and supercooled liquid states are related to the fast or slow secondary β process, from neutron scattering, respectively, the latter being connected with the trans-isomers. In addition, the first bend effect in the supercooled liquid coincides with a deviation of the slow effective secondary β(eff) relaxation related to the cis-isomers from low-T Arrhenius behavior to non-Arrhenius one and correlates with the onset of the primary α process from BDS. The second plateau effect in the liquid state occurs when τ(3) becomes commensurable with the structural relaxation time τ(α)(T(b2)). It is also approximately related to its crossover from non-Arrhenius to Arrhenius regime in the combined BDS and NMR data. Finally, the combined BDS and NMR structural relaxation data, when analyzed in terms of the two-order parameter (TOP) model, suggest the influence of solidlike domains on both the annihilation behavior and the local and segmental chain mobility in the supercooled liquid. All these findings indicate the influence of the dynamic heterogeneity in both the primary and secondary relaxations due to the cis-trans isomerism in c-t-1,4-PBD and their impact into the PALS response.

Self-diffusion of the amorphous pharmaceutical indomethacin near Tg

Secondary ion mass spectrometry has been utilized to measure self-diffusion coefficients D in supercooled indomethacin from 310 K to 350 K (Tg = 315 K). Over this temperature range, D varies from 10−17 cm2s−1 to 10−11 cm2s−1. The temperature dependence of D is significantly weaker than the temperature dependence of the viscosity or the structural relaxation time τα, and scales as τα−0.76. At Tg, D is enhanced by more than a factor of 100 in comparison to the viscosity and the expectations of the Stokes–Einstein equation. For deeply supercooled indomethacin, the temperature dependence of D matches the temperature dependence of crystal growth rates for all three polymorphs.

Spatial and temporal heterogeneity in supercooled glycerol: Evidence from wide field single molecule imaging

We quantify spatial and temporal heterogeneity in supercooled glycerol at T=T(g)+14 K employing a widefield detection scheme and using rubrene as the probe molecule. We describe how microscopy configuration affects measured intensity, linear dichroism, and the resulting autocorrelation function. Rotational relaxation times tau(c) of 241 probe molecules are measured, and we find spatial heterogeneity over almost three orders of magnitude present at this temperature. An approach for detecting temporally heterogeneous molecules and quantifying exchange times is introduced. Of molecules that can be assessed, approximately 15% display evidence of temporal heterogeneity-changes of tau(c) during the measurement-that are detected with the analysis technique employed. Exchanges between dynamically disparate environments occur rarely but in the proportion expected given the rarity of very slowly rotating molecules present. Heterogeneous molecules are characterized by persistence and exchange times. Median exchange and persistence times of the molecules identified as heterogeneous relative to glycerol's structural relaxation time tau(alpha) are found to be tau(ex)/tau(alpha)=202 and tau(pers)/tau(alpha)=405, respectively. These results are discussed in the context of values of exchange times that have been determined in other experiments.

Non-Gaussian effects in the cage dynamics of polymers

The correlation between the fast cage dynamics and structural relaxation is investigated in a model polymer system. It is shown that the cage vibration amplitude, as expressed by the Debye–Waller factor, and the relaxation time τα collapse on a single universal curve with a simple analytic form when the temperature, the density, the chain length and the monomer–monomer interaction potential are changed. For the physical states with the same τα the coincidence of the mean-square displacement, the intermediate scattering function and the non-Gaussian parameter is observed in a wide time window spanning from the ballistic regime to the onset of the Rouse dynamics driven by the chain connectivity. The role of the non-Gaussian effects is discussed.

Intrinsic and non-local Gilbert damping in polycrystalline nickel studied by Ti : sapphire laser fs spectroscopy

The use of femtosecond laser pulses generated by a Ti : sapphire laser system allows us to gain an insight into the magnetization dynamics on time scales from sub-picosecond up to 1 ns directly in the time domain. This experimental technique is used to excite a polycrystalline nickel (Ni) film optically and probe the dynamics afterwards. Different spin-wave modes (the Kittel mode, perpendicular standing spin-wave modes and dipolar spin-wave modes (Damon–Eshbach modes)) are identified as the Ni thickness is increased. The Kittel mode allows determination of the Gilbert damping parameter α extracted from the magnetization relaxation time τα. The non-local damping by spin currents emitted into a non-magnetic metallic layer of vanadium (V), palladium (Pd) and the rare earth dysprosium (Dy) are studied for wedge-shaped Ni films of 1–30 nm. The damping parameter increases from α = 0.045 intrinsic for nickel to α > 0.10 for the heavy materials, such as Pd and Dy, for the thinnest Ni films below 10 nm thickness. Also, for the thinnest reference Ni film thickness, an increased magnetic damping below 4 nm is observed. The origin of this increase is discussed within the framework of line broadening by locally different precessional frequencies within the laser spot region.

Heterogeneous Dynamics and Pressure Dependence of the Dynamics in van der Waals Liquids

We consider the dependence of the dynamics in nonpolar liquids as a function of pressure close to the glass transition. We show how dynamical heterogeneities lead naturally to a dependence of the dominant relaxation time τα on two independent parameters, i.e., on both pressure P and temperature T or on both density ρeq and temperature, without assuming the presence of energy barriers. The predictions of our model regarding the dependence of τα as a function of pressure are discussed and compared to experimental data. Our model can account quantitatively for this dependence in the case of nonpolar molecular liquids such as 1,1′-di(4-methoxy-5-methylphenyl)cyclohexane (BMMPC) and 1,1′-bis(p-methoxyphenyl)cyclohexane (BMPC) up to pressures a few hundred atmospheres and can account approximately for the slope [d log(τα)]/dP at zero pressure in the case of flexible polymers such as poly(methyltolylsiloxane) (PMTS) and poly(methylphenylsiloxane) (PMPS). We propose that nonpolar molecular liquids could be more s...

Universal scaling between structural relaxation and vibrational dynamics in glass-forming liquids and polymers

If liquids, polymers, bio-materials, metals and molten salts can avoid crystallization during cooling or compression, they freeze into a microscopically disordered solid-like state, a glass1,2. On approaching the glass transition, particles become trapped in transient cages—in which they rattle on picosecond timescales—formed by their nearest neighbours; the particles spend increasing amounts of time in their cages as the average escape time, or structural relaxation time τα, increases from a few picoseconds to thousands of seconds through the transition. Owing to the huge difference between relaxation and vibrational timescales, theoretical3,4,5,6,7,8,9 studies addressing the underlying rattling process have challenged our understanding of the structural relaxation. Numerical10,11,12,13 and experimental studies on liquids14 and glasses8,15,16,17,18,19 support the theories, but not without controversies20 (for a review see ref. 21). Here we show computer simulations that, when compared with experiments, reveal the universal correlation of the structural relaxation time (as well as the viscosity η) and the rattling amplitude from glassy to low-viscosity states. According to the emerging picture the glass softens when the rattling amplitude exceeds a critical value, in agreement with the Lindemann criterion for the melting of crystalline solids22 and the free-volume model23.

Relation between the Widom line and the breakdown of the Stokes–Einstein relation in supercooled water

Supercooled water exhibits a breakdown of the Stokes–Einstein relation between the diffusion constant D and the alpha relaxation time τ α . For water simulated with two different potentials, TIP5P and ST2, we find that the temperature of the decoupling of diffusion and alpha relaxation correlates with the temperature of the maximum in specific heat that corresponds to crossing the Widom line T W ( P ). Specifically, we find that our results for D τ α / T collapse onto a single “master curve” if temperature is replaced by T − T W ( P ). We further find that the size of the mobile molecule clusters (dynamical heterogeneities) increases sharply near T W ( P ). Moreover, our calculations of mobile particle cluster size &lt; n ( t *)&gt; w for different pressures, where t * is the time for which the mobile particle cluster size is largest, also collapse onto a single master curve if T is replaced by T − T W ( P ). The crossover to a more locally structured low density liquid (LDL) as T → T W ( P ) appears to be well correlated both with the breakdown of the Stokes–Einstein relation and with the growth of dynamic heterogeneities. Our results are consistent with the possibility that the breakdown of the SE relation in supercooled water at low pressures is associated with the hypothesized liquid–liquid phase transition.

Study of the dynamic structure factor of hydrogen fluoride by inelastic X-ray scattering

The dynamic structure factor S(Q, ω) of liquid hydrogen fluoride is investigated by inelastic X-ray scattering at T = 239 K in a momentum transfer region between 2 and 31 nm−1. The extracted apparent sound velocity c(Q) shows a transition due to the structural or α relaxation with a relaxation time τα(Q) on the subpicosecond (less than 10−12 s) time scale. Nevertheless, from a comparison with existing molecular dynamics simulations, it arises that a second faster relaxation is present. This allows us to discuss our experimental results in terms of a two-relaxation-process scenario.

High-frequency transverse dynamics in glasses

The improvement in performance of the inelastic x-ray scattering technique hasled to accurate determination of the dynamic structure factors of glassy and liquidglycerol, in the region of exchanged momentum Q = 2– 23 nm−1and in the temperature range 80–570 K. Thanks to the improved statisticalaccuracy, it has been possible to identify, in the spectra at the lowertemperatures, besides the propagating longitudinal mode, a secondnon-Q-dispersingpeak at ℏΩT ≈ 8.5 meV.We interpret this peak as a signature of the transverse dynamics that,in topologically disordered systems, acquires a longitudinal symmetrycomponent. This assignment is substantiated by the observation thatthis peak still survives, across the glass transition, in the liquid state,and vanishes when the structural relaxation time τα approachesΩT−1:a behaviour consistent with the condition τα ΩT ≫ 1required for the existence of a non-relaxational transverse-like dynamics in theliquid state.

Dynamics and rheology of a supercooled polymer melt in shear flow

Using molecular dynamics simulations, we study dynamics of a model polymer melt composed of short chains with bead number N=10 in supercooled states. In quiescent conditions, the stress relaxation function G(t) is calculated, which exhibits a stretched exponential relaxation on the time scale of the α relaxation time τα and ultimately follows the Rouse dynamics characterized by the time τR∼N2τα. After application of shear γ̇, transient stress growth σxy(t)/γ̇ first obeys the linear growth ∫0tdt′G(t′) for strain less than 0.1 but saturates into a non-Newtonian viscosity for larger strain. In steady states, shear thinning and elongation of chains into ellipsoidal shapes take place for shear γ̇ larger than τR−1. In such strong shear, we find that the chains undergo random tumbling motion taking stretched and compact shapes alternatively. We examine the validity of the stress–optical relation between the anisotropic parts of the stress tensor and the dielectric tensor, which are violated in transient states due to the presence of a large glassy component of the stress. We furthermore introduce time-correlation functions in shear to calculate the shear-dependent relaxation times, τα(T,γ̇) and τR(T,γ̇), which decrease nonlinearly as functions of γ̇ in the shear-thinning regime.

Temperature, density, and pressure dependence of relaxation times in supercooled liquids

We have examined experimental and simulation data on the relaxation times (τα) and the viscosities in liquids and supercooled liquids as functions of temperature (T), density (ρ), and pressure (p). We achieve a data collapse by placing the data on master curves that depend only on a single density- and species-dependent (but T independent) effective interaction energy, E∞(ρ).

Free-volume microstructure ofglycerol and its supercooled liquid-state dynamics

A positron annihilation lifetime spectroscopic (PALS) study wascarried out on a typical representative of simplehydrogen-bonded glass formers - glycerol - over a widetemperature region from 100 K up to room temperature. Severalcrossover temperatures, Tbi, were identified in the temperature dependences of the ortho-positronium (o-Ps) lifetime andthe relative o-Ps intensity. The onset temperature of free-volume change, 137 K, was compared with the value of 135±3 K obtained from extrapolating thermodynamic data and withthe temperatures from relaxation data. In order to determinethe influence of the free-volume evolution on the relaxation dynamics above the glass transition temperature Tg, thefree-volume fraction from the PALS data was related to thebehaviour of the dielectric loss of glycerol. A newrelationship between the temperature parameters of the onset offree-volume change and of the high-frequency wing of the dielectric loss is presented. Taking the PALS free-volume dataas input for a free-volume model (Doolittle ansatz), it wasfound that the relaxation times τα can bereproduced above the bend temperature Tb2 = 241 K; thelatter lies in the vicinity of crossover temperatures reportedfrom mode coupling theory analyses of dynamic data. In the lower-temperature region Tb2>T>Tb1≅Tg, a contribution from thermally activated mobility has to beincluded to reproduce the dielectric relaxation time data.