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

Abstract

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 glass 1,2 . 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 τ α , increases from a few picoseconds to thousands of seconds through the transition. Owing to the huge difference between relaxation and vibrational timescales, theoretical 3-9 studies addressing the underlying rattling process have challenged our understanding of the structural relaxation. Numerical 10-13 and experimental studies on liquids 14 In the solid state atoms oscillate with mean square amplitude u 2 around their equilibrium positions (henceforth to be referred to as the Debye-Waller (DW) factor). With increasing temperature, solids meet different fates depending on the structural degree of order. In the crystalline state the ordered structure melts at T m , whereas in the amorphous state the disordered structure softens at the glass transition temperature T g , above which flow occurs with viscosity η. The empirical law T g 2/3T m (refs 1,2,7) suggests that the two phenomena have a common basis. In fact, this viewpoint motivated extensions to glasses 24 of the Lindemann melting criterion for crystalline solids 22 and pictures the glass transition as a freezing in an aperiodic crystal structure (ACS) 5 .According to the ACS model, the viscous flow is due to activated jumps over energy barriers E ∝ k B T a 2 / u 2 , where a is the displacement to overcome the barrier, k B is the Boltzmann constant and T the temperature. The usual rate theory leads to the Hall-Wolynes (HW) equation 5,21 τ α , η ∝ exp(a 2 /2 u 2 ). u 2 is the DW factor of the liquid, that is, it is the amplitude of the rattling motion within the cage of the surrounding atoms. This vibrational regime is assumed to occur on short timescales largely separated by those of the brownian diffusion. The ACS model is expected to fail when τ α becomes comparable to the typical rattling times corresponding to picosecond timescales, a condition that is met at high temperatures (for example, in selenium it occurs at T m + 104 K (ref. 14)).

Correlations between Vibrational Entropy and Dynamics in Liquids

“…In this "elastic" view of the glass transition the vibrational entropy most directly reflects the liquid dynamics, in consistence with the present analysis. Empirical evidences for such a stiffening range from vibrational spectra [18,24,25], mean square displacements [2,3] and elastic moduli [12,31] measurements. In all cases strong correlations with the dynamics are found.…”

Cage rattling does not correlate with the local geometry in molecular liquids

“…In the present model t ⋆ ≃ 1 in MD units, irrespective of the physical state [52], and ST-MSD is defined as u 2 = r 2 (t = t * ) .…”

“…u 2 is the short-time MSD (ST-MSD) evaluated at the time t * when MSD changes the concavity in the log-log plot. Bottom: location of the sets of states in the master curve log τ α vs u 2 −1 (orange line) [52]. Note that ISF and MSD of states of the same set coincide from…”

“…Recently, extensive molecular-dynamics (MD) simulations evidencing the universal correlation between the structural relaxation time τ α and u 2 were reported in polymeric systems [52][53][54], binary atomic mixtures [55], colloidal gels [56] and antiplasticized polymers [41] and compared with the experimental data concerning several glassformers in a wide fragility range (20 ≤ m ≤ 191) [52,55,57,59]. One major finding was that states with equal ST-MSD u 2 have equal relaxation times τ α too.…”

Supercooled liquids with enhanced orientational order

“…Depending on their energy landscape and on the thermodynamic and kinetic path they follow, they acquire a periodic structure with full translational order (crystals) or maintain a morphology lacking in long-range order (glasses) [2][3][4][5] . The structural relaxation time increases upon cooling, and the glassy state is achieved when t exceeds the experimental observation time; upon quenching, this condition occurs at the glass transition temperature, T g .…”