Dynamics Of Glass-forming Materials Research Articles

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.

Structural signature of slow dynamics and dynamic heterogeneity in two-dimensionalcolloidal liquids: glassy structural order

Glassy states are formed if crystallization is avoided upon cooling or increasing density.However, the physical factors controlling the ease of vitrification and the nature of glasstransition remain elusive. Among various glass-forming systems, colloidal liquids are one ofthe most ideal glass-forming systems because of the simplicity and controllability of theinteractions. We use numerical simulations of two-dimensional polydisperse andbinary hard discs to tackle both of these longstanding questions. For polydispersesystems, we systematically control the polydispersity, which can be regarded asthe strength of frustration effects on crystallization. We reveal that crystal-likehexatic order grows in size and lifetime with an increase in the colloid volumefraction or with a decrease in polydispersity (or frustration). We stress that hexaticordering in hard disc systems is a direct consequence of dense packing and amanifestation of low configurational entropy. Our study suggests an intriguingscenario that the strength of frustration controls both the ease of vitrificationand the nature of the glass transition. Vitrification may be a process of hiddencrystal-like ordering under frustration for this system. This may provide not only aphysical basis for glass formation, but also an answer to another longstandingquestion on the structure of amorphous materials: ‘order in disorder’ may be anintrinsic feature of a glassy state of many materials. For binary mixtures, onthe other hand, the relevant structural feature linked to slow dynamics is nothexatic order, but an amorphous structure of low structural entropy. These resultssuggest that slow dynamics is associated with bond orientational order linked tothe crystal for a weakly frustrated system, whereas to amorphous structures oflow configurational entropy for a strongly frustrated system. This suggests anintrinsic link between structure and dynamics in glass-forming materials: slowdynamics is linked to structuring (‘glassy ordering’) towards low configurationalentropy. We discuss the nature of ‘glassy order’ responsible for slow dynamics.

Relaxation Phenomena in Vitrifying Polymers and Molecular Liquids

Recent experimental results on the dynamics of glass-forming materials, particularly polymers, are surveyed. The focus is on aspects of the behavior that are connected to or correlated with structural relaxation. These results include the invariance to thermodynamic conditions (temperature, pressure, volume) of a number of properties—breadth of the relaxation dispersion, number of dynamically correlating molecules, Johari−Goldstein secondary relaxation time, onset of the dynamic crossover, and the product of temperature and specific volume with the latter raised to a material constant—provided the structural relaxation time is maintained constant. Additional salient experimental findings include the correlation of various high-frequency processes, usually measured in the glassy state, with properties of the equilibrium material above Tg. These correlations indicate that the glass transition, although conventionally defined by the relaxation time becoming larger than experimental time scales (>100 s), has ...

Temperature Accelerated Dynamics in Glass-Forming Materials

In this work we propose a methodology for improving dynamical sampling in molecular simulations via temperature acceleration. The proposed approach combines the novel methods of Voter for temperature-accelerated dynamics with the multiple histogram reweighting method of Ferrenberg and Swendsen, its dynamical extension by Nieto-Draghi et al., and with hazard plot analysis, allowing optimal sampling with small computational cost over time scales inaccessible to classical molecular dynamics simulations by utilizing the "inherent structure" idea. The time evolution of the system is viewed as a succession of transitions between "basins" in its potential energy landscape, each basin containing a local minimum of the energy (inherent structure). Applying the proposed algorithm to a glass-forming material consisting of a mixture of spherical atoms interacting via Lennard-Jones potentials, we show that it is possible to perform an exhaustive search and evaluate rate constants for basin-to-basin transitions that cover several orders of magnitude on the time scale, far beyond the abilities of any competitive dynamical study, revealing an extreme ruggedness of the potential energy landscape in the vicinity of the glass transition temperature. By analyzing the network of inherent structures, we find that there are characteristic distances and rate constants related to the dynamical entrapment of the system in a neighborhood of basins (a metabasin), whereas evidence to support a random energy model is provided. The multidimensional configurational space displays a self-similar character depicted by a fractal dimension around 2.7 (+/-0.5) for the set of sampled inherent structures. Only transitions with small Euclidean measure can be considered as localized.

Universal relation between viscous flow and fast dynamics in glass-forming materials

The connection between viscous flow and vibrational properties in glass-forming materials is scrutinized examining the fragility of a wide set of liquids and the nonergodicity factor of the corresponding glasses. Building on the same line of reasoning which allows us to extend the connection between viscosity and thermodynamics in complex systems, we show here how the two quantities are strongly correlated once the effect of those secondary relaxation processes due to internal degrees of freedom is correctly accounted for. This result provides a missing thermodynamic rationale for the recently debated universality of the correlation between fast and slow degrees of freedom.

Erratum: Percolation Model for Slow Dynamics in Glass-Forming Materials [Phys. Rev. Lett.102, 015702 (2009)

Erratum: Percolation Model for Slow Dynamics in Glass-Forming Materials [Phys. Rev. Lett.102, 015702 (2009)

Percolation Model for Slow Dynamics in Glass-Forming Materials

We identify a link between the glass transition and percolation of regions of mobility in configuration space. We find that many hallmarks of glassy dynamics, for example, stretched-exponential response functions and a diverging structural relaxation time, are consequences of the critical properties of mean-field percolation. Specific predictions of the percolation model include the range of possible stretching exponents 1/3< or =beta< or =1 and the functional dependence of the structural relaxation time tau_{alpha} and exponent beta on temperature, density, and wave number.

Some remarks on the low-energy excitations in glasses: interpretation of Boson peak data

The frequency-reduced representation, g(ω)/ω2, of the vibrational density of states g(ω), known as the Boson peak is frequently used to extract information on structural and dynamical properties of glasses and supercooled liquids. The g(ω)/ω2 representation is preferred over the true excess of the vibrational modes, defined as the difference between the total g(ω) and the Debye contribution, for practical reasons. Analysis of a large body of the available experimental data from inelastic neutron and Raman scattering reveals that reduction procedures distort to a great extent the otherwise symmetric excess density of states. The frequency and the intensity of the Boson peak are very sensitive to minor modifications of the distribution of the excess. The quantitative use of the g(ω)/ω2 function leads to some peculiar results that contradict our general perception about structure and dynamics of glass-forming materials. We stress that the physics of the low-energy excitations are hidden in the excess density of states, which should attract more attention both from the experimental as well as the theoretical point of view.

From heterogeneous probe rotation to the hydrodynamic limit

The recognition of heterogeneous dynamics in single component supercooled liquids has greatly advanced our understanding of the dynamics in glass-forming materials. However, details such as persistence times and length scales associated with dynamically distinct domains remain to be resolved. The rotational correlation function of probe molecules in viscous liquids is used as a tool for exploring the rate exchange or the time a domain memorizes its initial relaxation rate. With high precision dielectric experiments, the dynamics of probe molecules is observed to slow down with increasing size of the guest relative to the host molecules. For the case of di-n-butylether in 3-methylpentane, the situation of purely exponential probe dynamics within dispersive host relaxation is achieved as a result of time averaging. The results suggest that rate exchange occurs on a time scale which is equal to the longest structural relaxation time of the system.

Dielectric Fluctuations and the Origins of Noncontact Friction

Dielectric fluctuations underlie a wide variety of physical phenomena, from ion mobility in electrolyte solutions and decoherence in quantum systems to dynamics in glass-forming materials and conformational changes in proteins. Here we show that dielectric fluctuations also lead to noncontact friction. Using high sensitivity, custom fabricated, single crystal silicon cantilevers we measure energy losses over poly(methyl methacrylate), poly(vinyl acetate), and polystyrene thin films. A new theoretical analysis, relating noncontact friction to the dielectric response of the film, is consistent with our experimental observations. This work constitutes the first direct, mechanical detection of noncontact friction due to dielectric fluctuations.

Limitations of the stretched exponential function for describing dynamics in disordered solid materials

Around the glass transition temperature, relaxation dynamics in glass-forming materials follows a strong nonexponential behavior. It is widely accepted that an empirically based stretched exponential function, known as the Kohlrausch–Williams–Watts (KWW) function, ϕ(t)=e−(t∕τ)β, describes universally a broad variety of experimental data. Using intuitive pictures and ellipsometric measurements, we show that (1) in order to describe the dynamics in disordered materials such as in polymers using a KWW function, the response has to be considered over a specific region of time, (2) a single KWW function is not sufficient for correctly describing more than one relaxation processes, and (3) in certain cases, stretching exponents depending on temperature do not cover the ranges previously suggested (from 0 to 1, e.g., as a sigmoid function). As an example, we show that the temperature dependence of the stretching exponent β(T) depends highly on how the curve fits with the KWW function are performed.

Translational Diffusion on Heterogeneous Lattices: A Model for Dynamics in Glass Forming Materials

Simulations of translational motion on lattices with spatially heterogeneous dynamics have been performed. Translation occurs by nearest neighbor jumps on a three-dimensional simple cubic lattice. The overall lattice is subdivided into cubic blocks. The rate for jumps within a given block is controlled by the local relaxation time (or rotation time) for that block. Blocks exchange their local relaxation times on a specified time scale. If the local distribution of relaxation times is given by a Kohlrausch−Williams−Watts distribution, the simulation results can reproduce experimental observations of enhanced translational diffusion in supercooled liquids. This adds further weight to arguments that dynamics in deeply supercooled liquids are spatially heterogeneous and that this heterogeneity is responsible for the non-exponential relaxation functions which are often observed. For systems with only two local relaxation times, the simulation results are in good agreement with effective medium theory.

Possible Causes of the Change of Dynamics in Glass-Forming Materials Subjected to Reduced Dimension

ABSTRACTThere is currently many ongoing investigations of the change in the glass transition temperature when a material is reduced in dimension from the normal bulk state. The reduction in dimension can be accomplished by casting the material as thin films with or without a substrate or putting it in nanometer size pores. In this work, we explore possible causes of the change in dynamics of the bulk material when the glass-former is subjected to such modifications. The existence of a growing cooperative length scale L(T) with decreasing temperature in bulk fragile glass-forming liquids reaching the size of approximately 1.5–2.0 nm at the glass transition temperature is the basis of our consideration. When the reduced dimension is comparable to L(Tg), cooperative dynamics within a lengthscale equal to L(Tg) can no longer be maintained in all three dimensions throughout the sample. The imposed reduction of the cooperative length scale speeds up the dynamics and causes a reduction of the glass transition temperature. For polymeric glass-formers particularly at higher molecular weights, reduction of one dimension in thin films engenders orientation of the polymer chains when their radius of gyration becomes comparable to the film thickness. The latter is known to cause also a reduction of the glass transition temeperature.