Structural Relaxation Time Research Articles

Power law relationship between diffusion coefficients in multi-component glass forming liquids.

The slow down of dynamics in glass forming liquids as the glass transition is approached has been characterised through the Adam-Gibbs relation, which relates relaxation time scales to the configurational entropy. The Adam-Gibbs relation cannot apply simultaneously to all relaxation times scales unless they are coupled, and exhibit closely related temperature dependences. The breakdown of the Stokes-Einstein relation presents an interesting situation to the contrary, and in analysing it, it has recently been shown that the Adam-Gibbs relation applies to diffusion coefficients rather than to viscosity or structural relaxation times related to the decay of density fluctuations. However, for multi-component liquids --the typical cases considered in computer simulations, metallic glass formers, etc.-- such a statement raises the question of which diffusion coefficient is described by the Adam-Gibbs relation. All diffusion coefficients can be consistently described by the Adam-Gibbs relation if they bear a power law relationship with each other. Remarkably, we find that for a wide range of glass formers, and for a wide range of temperatures spanning the normal and the slow relaxation regimes, such a relationship holds. We briefly discuss possible rationalisations of the observed behaviour.

Scaling analysis of the viscoelastic response of linear polymers.

Viscoelastic response in terms of the complex shear modulus G*(ω) of the linear polymers poly(ethylene-alt-propylene), poly(isoprene), and poly(butadiene) is studied for molar masses (M) from 3k up to 1000k and over a wide temperature range starting from the glass transition temperature Tg (174 K-373 K). Master curves G'(ωτα) and G″(ωτα) are constructed for the polymer-specific relaxation. Segmental relaxation occurring close to Tg is independently addressed by single spectra. Altogether, viscoelastic response is effectively studied over 14 decades in frequency. The structural relaxation time τα used for scaling is taken from dielectric spectra. We suggest a derivative method for identifying the different power-law regimes and their exponents along G″(ωτα) ∝ ωε″. The exponent ε″ = ε″(ωτα) ≡ d ln G″(ωτα)/d ln(ωτα) reveals more details compared to conventional analyses and displays high similarity among the polymers. Within a simple scaling model, the original tube-reptation model is extended to include contour length fluctuations (CLFs). The model reproduces all signatures of the quantitative theory by Likhtman and McLeish. The characteristic times and power-law exponents are rediscovered in ε″(ωτα). The high-frequency flank of the terminal relaxation closely follows the prediction for CLF (ε″ = -0.25), i.e., G″(ω) ∝ ω-0.21±0.02. At lower frequencies, a second regime with lower exponent ε″ is observed signaling the crossover to coherent reptation. Application of the full Likhtman-McLeish calculation provides a quantitative interpolation of ε″(ωτα) at frequencies below those of the Rouse regime. The derivative method also allows identifying the entanglement time τe. However, as the exponent in the Rouse regime (ωτe > 1) varies along εeRouse = 0.66 ± 0.04 (off the Rouse prediction εRouse = 0.5) and that at ωτe < 1 is similar, only a weak manifestation of the crossover at τe is found at highest M. Yet, calculating τe/τα= (M/Mo)2, we find good agreement among the polymers when discussing ε″(ωτe). The terminal relaxation time τt is directly read off from ε″(ωτα). Plotting τt/τe as a function of Z = M/Me, we find universal behavior as predicted by the TR model. The M dependence crosses over from an exponent significantly larger than 3.0 at intermediate M to an exponent approaching 3.0 at highest M in agreement with previous reports. The frequency of the minimum in G″(ωτα) scales as τmin ∝ M1.0±0.1. An M-independent frequency marks the crossover to glassy relaxation at the highest frequencies. Independent of the amplitude of G″(ω), which may be related to sample-to-sample differences, the derivative method is a versatile tool to provide a detailed phenomenological analysis of the viscoelastic response of complex liquids.

Molecular mobility in driven monomeric and polymeric glasses.

We show that in monomeric supercooled liquids and glasses that are plastically flowing at a constant shear stress σ while being deformed with strain rate ε[over ̇], the microscopic structural relaxation time τ_{str} is given by the universal relation σ/G_{∞}ε[over ̇] with G_{∞} a modulus. This equality holds for all rheological regimes from temperatures above the glass transition all the way to the athermal limit, and arises from the competing effects of elastic loading and viscous dissipation. In macromolecular (polymeric) glasses, however, the stress decouples from this relaxation time and τ_{str} is in fact further reduced even though σ rises during glassy strain hardening. We develop expressions to capture both effects and thus provide a framework for analyzing mobility measurements in glassy materials.

Fractional Stokes–Einstein relation in TIP5P water at high temperatures**Project supported by the National Natural Science Foundation of China (Grant No. 2153200) and the China Postdoctoral Science Foundation (Grant No. 2016M602712).

Fractional Stokes–Einstein relation described by D ∼ (τ/T)ξ is observed in supercooled water, where D is the diffusion constant, τ the structural relaxation time, T the temperature, and the exponent ξ ≠ −1. In this work, the Stokes–Einstein relation in TIP5P water is examined at high temperatures within 400 K–800 K. Our results indicate that the fractional Stokes–Einstein relation is explicitly existent in TIP5P water at high temperatures, demonstrated by the two usually adopted variants of the Stokes–Einstein relation, D ∼ τ−1 and D ∼ T/τ, as well as by D ∼ T/η, where η is the shear viscosity. Both D ∼ τ−1 and D ∼ T/τ are crossed at temperature Tx = 510 K. The D ∼ τ−1 is in a fractional form as D ∼ τξ with ξ = −2.09 for T ≤ Tx and otherwise ξ = −1.25. The D ∼ T/τ is valid with ξ = −1.01 for T ≤ Tx but in a fractional form for T > Tx. The Stokes–Einstein relation D ∼ T/η is satisfied below Tx = 620 K but in a fractional form above Tx. We propose that the breakdown of D ∼ T/η may result from the system entering into the super critical region, the fractional forms of D ∼ τ−1 and D ∼ T/τ are due to the disruption of the hydration shell and the local tetrahedral structure as well as the increase of the shear viscosity.

Glass transition of soft colloids.

We explore the glassy dynamics of soft colloids using microgels and charged particles interacting by steric and screened Coulomb interactions, respectively. In the supercooled regime, the structural relaxation time τ_{α} of both systems grows steeply with volume fraction, reminiscent of the behavior of colloidal hard spheres. Computer simulations confirm that the growth of τ_{α} on approaching the glass transition is independent of particle softness. By contrast, softness becomes relevant at very large packing fractions when the system falls out of equilibrium. In this nonequilibrium regime, τ_{α} depends surprisingly weakly on packing fraction, and time correlation functions exhibit a compressed exponential decay consistent with stress-driven relaxation. The transition to this novel regime coincides with the onset of an anomalous decrease in local order with increasing density typical of ultrasoft systems. We propose that these peculiar dynamics results from the combination of the nonequilibrium aging dynamics expected in the glassy state and the tendency of colloids interacting through soft potentials to refluidize at high packing fractions.

Effect of deformation history on the stress relaxation behaviour of Colombian Caribbean coastal cheese from goat milk

Textural attributes are a manifestation of the rheological properties and physical structure of foods, cheeses among these. In order to describe these physical properties, the objective of this work was to analyse the effect of deformation history on the stress relaxation behaviour of Colombian Caribbean coastal cheese made from goat milk with 3.75% (F1), 4.00% (F2) and 4.25% (F3) fat content, through prediction made by a four-term Prony series based on Chen's model. For this, stress relaxation data and stress relaxation spectra were analysed. Moreover, textural attributes by texture profile analysis were measured. Physicochemical results were similar to those published by other authors, and all samples meet national and international standards. Results from this work showed that Chen's model could be successfully used to describe the effect of deformation history on the stress relaxation behaviour of Colombian Caribbean coastal cheese made from goat milk. F1 had the highest elastic response, with the most significant residual modules ( P0) and relaxation times (τ1, τ2 and τ3). On the other hand, residual modules and relaxation times (τ1, τ2 and τ3) for cheeses F2 and F3 did not present statistically significant differences (p > 0.05). Besides, by interpretation of the stress relaxation spectra, F1 presented the firmest structure (greatest distribution function and relaxation time) which was characterised by the highest elastic behaviour. Finally, according to texture profile analysis test, F1 had the highest hardness, cohesiveness and chewiness, whereas F2 and F3 did not present statistically significant differences (p > 0.05) between them.

Breakdown of the Simple Arrhenius Law in the Normal Liquid State.

It is common practice to discuss the temperature effect on molecular dynamics of glass formers above the melting temperature in terms of the Arrhenius law. Using dielectric spectroscopy measurements of dc conductivity and structural relaxation time on the example of the typical glass former propylene carbonate, we provide experimental evidence that this practice is not justified. Our conclusions are supported by employing thermodynamic density scaling and the occurrence of inflection points in isothermal dynamic data measured at elevated pressure. Additionally, we propose a more suitable approach to describe the dynamics both above and below the inflection point based on a modified MYEGA model.

Revealing the Link between Structural Relaxation and Dynamic Heterogeneity in Glass-Forming Liquids.

Despite the use of glasses for thousands of years, the nature of the glass transition is still mysterious. On approaching the glass transition, the growth of dynamic heterogeneity has long been thought to play a key role in explaining the abrupt slowdown of structural relaxation. However, it still remains elusive whether there is an underlying link between structural relaxation and dynamic heterogeneity. Here, we unravel the link by introducing a characteristic time scale hiding behind an identical dynamic heterogeneity for various model glass-forming liquids. We find that the time scale corresponds to the kinetic fragility of liquids. Moreover, it leads to scaling collapse of both the structural relaxation time and dynamic heterogeneity for all liquids studied, together with a characteristic temperature associated with the same dynamic heterogeneity. Our findings imply that studying the glass transition from the viewpoint of dynamic heterogeneity is more informative than expected.

Water, the special liquid

Some prominent special properties of liquid water are summarized and related to the characteristics of the water molecule. It is shown that the substance appears to be anomalous only when compared to hard-sphere models with molecular interactions restricted to excluded-volume effects. Besides the electric charge distribution and the balanced number of hydrogen bond donating and accepting sites, the strength of the hydrogen bonds and also of the covalent bonds are identified significant factors in making water so special. As another major feature the small size of the water molecule is emphasized. It is often neglected but is relevant in every respect. It contributes, for example, to the large permittivity of water which plays an important role in the solvent behavior of water. The paper also demonstrates that the smallness of the water molecule is a key property in the molecular mobility of the liquid. The single-dipole (molecular) reorientation time is deduced from the experimentally available relaxation time of the macroscopic dielectric polarization and is discussed in terms of the so-called wait-and-switch model of dielectric relaxation. By comparison of the waiting periods of the model with structure relaxation times from ultraviolet and X-ray Brillouin spectra, close coupling between the reorientational motions and translational motions, i.e. the hydrogen network fluctuations in water, is disclosed. This finding confirms the idea of the wait-and-switch model. In addition, the waiting period is seen to nicely follow Eyring behavior, indicating an activated switch (or jump) mechanism.

Effects of the bond polarity on the structural and dynamical properties of silica-like liquids.

Silica is a network-forming liquid that shares many properties with water due to its tetrahedral structure. It undergoes a transition from a fragile to a strong liquid as the temperature is decreased, which is accompanied by a structural change to lower density and higher tetrahedral order. In order to disentangle the effects of Coulomb and van der Waals interactions on the structure and dynamics of liquid silica, we modify the bond polarity by changing the partial charges assigned to each atom. Using molecular dynamics simulations, we show that density, tetrahedral order, and structural relaxation times decrease when reducing bond polarity. Moreover, we find that the density maximum and the fragile-to-strong transition move to lower temperatures until they eventually vanish when the partial charges are decreased below approximately 75% of their regular value. Irrespective of whether strong or fragile behavior exists, structural relaxation is governed by hopping motion at sufficiently low temperatures. As long as there is a strong regime, the energy barrier associated with strong dynamics decreases with decreasing partial charges, but the dependence on the bond polarity differs from that of the activation energy in the Arrhenius regime at high temperatures. We show that the fragile-to-strong transition is associated with structural changes occurring between the first and second coordination shells that lead to a decrease in density and an increase in tetrahedral order. In particular, independent of the value of the partial charges, the distribution of the local structures is the same at this dynamic crossover, but we find no evidence that the effect occurs upon crossing the Widom line. In the fragile regime at intermediate temperatures, the relaxation times are well described by a previously proposed model which decomposes the apparent activation energy into a constant single-particle contribution and a temperature-dependent collective contribution. However, our results for silica-like melts do not obey several common relations of the model parameters reported for molecular glass formers.

Growing length scale accompanying vitrification: A perspective based on nonsingular density fluctuations.

A model for describing growing length scale accompanying the vitrification is introduced, in which we assume that in a subsystem whose density is above a certain threshold value, ρ_{c}, due to steric constraints, particle rearrangements are highly suppressed for a sufficiently long time period (∼structural relaxation time). We regard such a subsystem as a glassy cluster. With this assumption and without introducing any complicated thermodynamic arguments, we predict that with compression (increasing average density ρ) at a fixed temperature T in supercooled states, the characteristic length of the clusters, ξ, diverges as ξ∼(ρ_{c}-ρ)^{-2/d}, where d is the spatial dimensionality. This ξ measures the average persistence length of the steric constraints in blocking the rearrangement motions and is determined by the subsystem density. Additionally, with decreasing T at a fixed ρ, the length scale diverges in the same manner as ξ∼(T-T_{c})^{-2/d}, for which ρ is identical to ρ_{c} at T=T_{c}. The exponent describing the diverging length scale is the same as the one predicted by some theoretical models and indeed has been observed in some simulations and experiments. However, the basic mechanism for this divergence is different; that is, we do not invoke thermodynamic anomalies associated with the thermodynamic phase transition as the origin of the growing length scale. We further present arguements for the cooperative properties of the structural relaxation based on the clusters.

Structural relaxation and highly viscous flow.

The highly viscous flow is due to thermally activated Eshelby transitions which transform a region of the undercooled liquid to a different structure with a different elastic misfit to the viscoelastic surroundings. A self-consistent determination of the viscosity in this picture explains why the average structural relaxation time is a factor of eight longer than the Maxwell time. The physical reason for the short Maxwell time is the very large contribution of strongly strained inherent states to the fluidity (the inverse viscosity). At the Maxwell time, the viscous no-return processes coexist with the back-and-forth jumping retardation processes.

Energy Renormalization for Coarse-Graining the Dynamics of a Model Glass-Forming Liquid.

Coarse-grained modeling achieves the enhanced computational efficiency required to model glass-forming materials by integrating out "unessential" molecular degrees of freedom, but no effective temperature transferable coarse-graining method currently exists to capture dynamics. We address this fundamental problem through an energy-renormalization scheme, in conjunction with the localization model of relaxation relating the Debye-Waller factor ⟨u2⟩ to the structural relaxation time τ. Taking ortho-terphenyl as a model small-molecule glass-forming liquid, we show that preserving ⟨u2⟩ (at picosecond time scale) under coarse-graining by renormalizing the cohesive interaction strength allows for quantitative prediction of both short- and long-time dynamics covering the entire temperature range of glass formation. Our findings provide physical insights into the dynamics of cooled liquids and make progress for building temperature-transferable coarse-grained models that predict key properties of glass-forming materials.

Molecular layers in thin supported films exhibit the same scaling as the bulk between slow relaxation and vibrational dynamics.

We perform molecular-dynamics simulations of a supported molecular thin film. By varying thickness and temperature, we observe anisotropic mobility as well as strong gradients of both the vibrational motion and the structural relaxation through film layers with monomer-size thickness. We show that the gradients of the fast and the slow dynamics across the layers (except the adherent layer to the substrate) comply, without any adjustment, with the same scaling between the structural relaxation time and the Debye-Waller factor originally observed in the bulk [Larini et al., Nat. Phys., 2008, 4, 42]. The scaling is not observed if the average dynamics of the film is inspected. Our results suggest that the solidification process of each layer may be tracked by knowing solely the vibrational properties of the layer and the bulk.

Effects of Silica Surfaces on the Structure and Dynamics of Room-Temperature Ionic Liquids: A Molecular Dynamics Simulation Study

Room-temperature ionic liquids (ILs) at solid surfaces have been recognized for their significant interfacial properties in electrochemical and electronic devices. To ascertain the interface effects, we investigate the dynamical and structural properties of two ILs in nanoscale confinement at various temperatures. Specifically, we perform all-atom molecular dynamics simulations for ILs composed of 1-butyl-3-methylimidazolium cations and hexafluorophosphate ([Bmim][PF6]) or tetrafluoroborate ([Bmim][BF4]) anions sandwiched between amorphous silica slabs. Analyses of the structure indicate a bilayered arrangement in the interfacial region and preferred cation orientation at the surface with the methyl groups pointing toward the wall and the butyl tails projected inward. Mean square displacements and incoherent scattering functions reveal slowed and heterogeneous dynamics of all ionic species in the slit pore. In particular, spatially resolved analyses show that the structural relaxation times increase by ab...

Structural predictor for nonlinear sheared dynamics in simple glass-forming liquids

Glass-forming liquids subjected to sufficiently strong shear universally exhibit striking nonlinear behavior; for example, a power-law decrease of the viscosity with increasing shear rate. This phenomenon has attracted considerable attention over the years from both fundamental and applicational viewpoints. However, the out-of-equilibrium and nonlinear nature of sheared fluids have made theoretical understanding of this phenomenon very challenging and thus slower to progress. We find here that the structural relaxation time as a function of the two-body excess entropy, calculated for the extensional axis of the shear flow, collapses onto the corresponding equilibrium curve for a wide range of pair potentials ranging from harsh repulsive to soft and finite. This two-body excess entropy collapse provides a powerful approach to predicting the dynamics of nonequilibrium liquids from their equilibrium counterparts. Furthermore, the two-body excess entropy scaling suggests that sheared dynamics is controlled purely by the liquid structure captured in the form of the two-body excess entropy along the extensional direction, shedding light on the perplexing mechanism behind shear thinning.

Amorphous wall materials properties and degradation of carotenoids in spray dried formulations

The present study investigated structural relaxations of spray dried emulsions with trehalose-maltodextrin (M100), trehalose-maltodextrin (M250), and trehalose-WPI mixtures as wall materials at different aw and wall materials properties on carotenoids degradation. The exponential decrease in structural relaxation times (τ) above the Tg was described using strength of the solids (S). S generally decreased with increasing aw and was affected by the wall materials with carbohydrate-carbohydrate mixtures exhibiting higher S and lower carotenoids degradation rates. Non-Arrhenian temperature dependence of carotenoids degradation was attributed to increased S due to collapse above the Tg. Carotenoids degradation was not only described by S but also by layer-by-layer (LBL) interfacial structure. Single layer and LBL systems with the same wall materials had corresponding S but carotenoids degradation was slower in LBL systems. The use of S allows stability and quality control of food materials during processing and storage, and to estimate degradation of encapsulated bioactives.

String-like collective motion and diffusion in the interfacial region of ice.

We investigate collective molecular motion and the self-diffusion coefficient Ds of water molecules in the mobile interfacial layer of the secondary prismatic plane (112¯0) of hexagonal ice by molecular dynamics simulation based on the TIP4P/2005 water potential and a metrology of collective motion drawn from the field of glass-forming liquids. The width ξ of the mobile interfacial layer varies from a monolayer to a few nm as the temperature is increased towards the melting temperature Tm, in accordance with recent simulations and many experimental studies, although different experimental methods have differed in their precise estimates of the thickness of this layer. We also find that the dynamics within this mobile interfacial ice layer is "dynamically heterogeneous" in a fashion that has many features in common with glass-forming liquids and the interfacial dynamics of crystalline Ni over the same reduced temperature range, 2/3 < T/Tm < 1. In addition to exhibiting non-Gaussian diffusive transport, decoupling between mass diffusion and the structural relaxation time, and stretched exponential relaxation, we find string-like collective molecular exchange motion in the interfacial zone within the ice interfacial layer and colored noise fluctuations in the mean square molecular atomic displacement 〈u2〉 after a "caging time" of 1 ps, i.e., the Debye-Waller factor. However, while the heterogeneous dynamics of ice is clearly similar in many ways to molecular and colloidal glass-forming materials, we find distinct trends between the diffusion coefficient activation energy Ea for diffusion Ds and the interfacial width ξ from the scale of collective string-like motion L than those found in glass-forming liquids.

Selective Acceleration of Crystal Growth of Indomethacin Polymorphs by Low-Concentration Poly(ethylene oxide).

Physical stability of pharmaceutical amorphous solid dispersions is one of the critical attributes to the successful development of the formulation. Herein, we studied the impact of low-concentration poly(ethylene oxide) (PEO) on the crystallization rates of three polymorphs of indomethacin (IMC, γ-, α-, and δ-form). We observed that the addition of 3% w/w PEO significantly increased the crystal growth rates of γ-form and α-form of IMC, but had a negligible effect on the δ-form. The reduction of the activation energy for the crystal growth of IMC polymorphs after adding the PEO follows the order γ-form > α-form > δ-form, which is consistent with the trend toward the accelerating effects of PEO on the crystal growth rates of three polymorphs. With the addition of low-concentration PEO, there is an increase of molecular mobility of IMC as evidenced by the decreased structural relaxation times and viscosities. This study suggests that the substantially different effects of PEO on the crystal growth rates of IMC polymorphs are attributable to the different adsorption of PEO on the crystal surface of those polymorphs, which in turn exerts a selective accelerating effect on IMC molecules to organize into the different crystalline phases. These findings are relevant for understanding the crystallization behavior of amorphous solid dispersions containing polymorphic drugs.

Nanostructures and Dynamics of Isochorically Confined Amorphous Drug Mediated by Cooling Rate, Interfacial, and Intermolecular Interactions.

The production and stabilization of amorphous drugs by the nanoconfinement effect has recently become a research hotspot in pharmaceutical sciences. Herein, two guest/host systems, indomethacin (IMC) and griseofulvin (GSF) confined in anodic aluminum oxide (AAO) templates with different pore diameters (25-250 nm) are investigated by differential scanning calorimetry (DSC) and broadband dielectric spectroscopy (BDS). The crystallization of the confined drugs is suppressed, and their glass transition temperatures show an evident pore-size dependency. Moreover, a combination of dielectric and calorimetric results demonstrates that the significant change in the temperature dependence of the structural relaxation time during the cooling process is attributed to the vitrification of the interfacial molecules and the local density heterogeneity under isochoric confinement. Interestingly, compared with the case of IMC/AAO, which can be described by a typical two-layer model, GSF/AAO presents an rare scenario of three glass transition temperatures under fast cooling (40-10 K/min), indicating that there exists a thermodynamic nonequilibrium interlayer between the bulk-like core and interfacial layer. In contrast, the slow cooling process (0.5 K/min) would lead confined GSF into the stable core-shell nanostructure. Using surface modification, the interfacial effect is confirmed to be an important reason for the different phenomena between these two guest/host systems, and intermolecular hydrogen bonding is also suggested to be emphasized considering the long-range effect of interfacial interactions. Our results not only provide insight into the glass transition behavior of geometrically confined supercooled liquids, but also offer a means of adjusting and stabilizing the nanostructure of amorphous drugs under two-dimensional confinement.