Length-Scale Dependence of the Stokes-Einstein and Adam-Gibbs Relations in Model Glass Formers

Abstract

The Adam-Gibbs (AG) relation connects the dynamics of a glass-forming liquid to its the thermodynamics via. the configurational entropy, and is of fundamental importance in descriptions of glassy behaviour. The breakdown of the Stokes-Einstein (SEB) relation between the diffusion coefficient and the viscosity (or structural relaxation times) in glass formers raises the question as to which dynamical quantity the AG relation describes. By performing molecular dynamics simulations, we show that the AG relation is valid over the widest temperature range for the diffusion coefficient and not for the viscosity or relaxation times. Studying relaxation times defined at a given wavelength, we find that SEB and the deviation from the AG relation occur below a temperature at which the correlation length of dynamical heterogeneity equals the wavelength probed.It is now clear from extensive research over the last two decades that, as a liquid is gradually (super)cooled, its dynamics becomes spatially heterogeneous ("dynamical heterogeneity") [1][2][3] and the collective nature of the underlying relaxation processes can be quantified by various growing correlation length scales [4, 5]. Dynamics can be described by different measures -the translational diffusion coefficient (D), the shear viscosity (η) or the α-relaxation time (τ α ). At high temperatures, where particle motions are diffusive, all these time scales are mutually coupled. D and η are related via the Stokes-Einstein (SE) relation [6, 7] : D = mk B cπ T Rη , (m, R are respectively mass and radius of a diffusing particle, T is the temperature of the liquid and the constant c depends on stick or slip boundary condition). At high temperatures, owing to exponential decay of self-intermediate scattering function F s (k, t) = exp(−Dk 2 t) at all probe wave vectors k, D also gets coupled to the relaxation time τ (k) measured from F s (k, t) : Dk 2 τ (k) = constant. Further, τ α is often used as a proxy for η (or η/T ) in the SE relation to save computational cost. At low temperatures in dense, viscous liquids, D becomes much bigger than the value estimated from τ α (η) using the SE relation. This phenomenon is known as the breakdown of the SE relation (SEB) [2,[8][9][10][11][12][13] [1, 2, 7, 8] interprets the SEB as a consequence of the dynamical heterogeneity (DH) developing in the liquid upon cooling. DH simply means that there are populations of slow and fast particles which form transient clusters, making the dynamics spatially heterogeneous. The existence of DH leads to the expectation of a distribution of diffusion coefficients and relaxation times [12,14] corresponding to populations of different mobility. The observed D is dominated by the fast population, while the observed τ (or η) is governed mainly by the slow population, leading to the decoupling and the SEB. The observed decoupling (SEB) is an average effect in such a picture, which however, does not clarify the role played by a heterogeneity length scale.The breakdown of the SE relation poses a puzzle...

Excess-entropy scaling in supercooled binary mixtures

“…using thermodynamic integration, where F ex is the excess Helmholtz free energy, and U ex ≡ U is the potential energy. Application of thermodynamic integration to supercooled liquids is standard 6,34,38 . First, a path at a high temperature T ref above the critical point was chosen, integrating the equation…”

“…The Stokes-Einstein (SE) relation connects the diffusion coefficient D of a large particle immersed in a solvent with viscosity η, predicting that D ∝ η −1 T. The SE relation breaks down in the supercooled regime and explanations have been presented from various theoretical perspectives 33,38,[63][64][65][66][67][68][69][70] . Flenner et al 68 obtained a good collapse of the diffusion coefficient plotted against the structural relaxation time (which may be used as a proxy for the viscosity) for supercooled binary mixtures by scaling the diffusion coefficient and the relaxation time.…”

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

“…* yylu@ciac.ac.cn † ljan@ciac.ac.cn ‡ zgw@caltech.edu Another anomalous behavior in the glass-forming liquids is the breakdown of the Stokes-Einstein (SE) relation, which relates the self-diffusion coefficient D to the viscosity or equivalently to the relaxation time τ α [9][10][11][12]. While for normal liquids the product Dτ α is temperature-independent, numerous studies [13][14][15][16][17][18][19] in recent decades have shown that this relation is violated in glass-forming liquids at low temperatures.…”

Non-Gaussianity of the van Hove function and dynamic-heterogeneity length scale

“…In Ref. [27], it is shown that if one calculates the wave-vector dependent α-relaxation time, τ α (q) in the supercooled temperature regime, then one finds that Stokes-Einstein relation does not break down above a characteristic wave vector, q * which depends on the studied temperature, T . The inverse of this characteristic wave vector defines a length scale, ξ * (T ) = 2π/q * (T ).…”