Equilibration pathways beyond density fluctuations: the slow Arrhenius process (SAP)

by Prof. Simone Simon Napolitano (Laboratory of Polymer and Soft Matter Dynamics, Experimental Soft Matter and Thermal Physics (EST), Université libre de Bruxelles (ULB), Brussels 1050, Belgium)

Thursday 8 May 2025, 11:00 → 12:00 UTC

The properties of an ensemble of objects at thermodynamic equilibrium do not change with time. Experience tells us, however, that such observation is rarely encountered in nature. The transformation of buds into flowers and then fruits, the rearrangements of plates on the surface of planets, and even the whole human body over its lifetime are just a few, among the many, examples of systems far from thermodynamic equilibrium.

At the molecular level, equilibration kinetics –the time evolution of a system’s properties toward a less energetic state– are intimately coupled to molecular motion. In line with the Onsager’s regression hypothesis (1), the macroscopic relaxation of a nonequilibrium system (dissipation) obeys the same laws of molecular dynamics in equilibrium conditions (spontaneous microscopic fluctuations).

In the case of liquids, equilibration is usually driven by the so-called a-modes, which are responsible for density fluctuations and require time scales quickly diverging upon cooling (2). Growing experimental evidence indicates, however, the presence of a different, alternative pathway of weaker temperature dependence. Such equilibration processes exhibit a temperature-invariant activation barrier, on the order of 100 kJ mol⁻¹.

We identified the underlying molecular process responsible for this class of equilibration mechanisms showing a temperature-invariant activation barrier (» 100 kJ mol⁻¹), with the slow Arrhenius process (SAP), a microscopic mechanism detected by dielectric spectroscopy and techniques (3). The SAP is described in terms of the collective small displacements (CSD) model (4), a mechanistic picture wherein local amorphous packing is reshaped by molecular movements that are small in comparison to those in the 𝛼-modes. Using a statistical mechanics-based equation of state to obtain nonbonded segmental interaction energies, CSD predicts the SAP’s activation energies a priori, based solely on thermodynamic analysis of material properties.

Finally, based on the experimental findings collected so far on polymers and small molecules, we present a new framework for the equilibration of materials. In support of its potential, we demonstrate that our model is capable to provide quantitative predictions on properties of technological interest as the adsorption rate of polymers on silicon wafers and the crystal growth rate of small organic molecules in the glassy state

 

 

1.            Onsager Phys. Rev. 37, 405–426 (1931)

2.            Donth The glass transition: relaxation dynamics in liquids and disordered materials Springer Science (2001).

3.            Song et al. Science Advances 8, eabm7154 (2022); Caporaletti and Napolitano Phys. Chem. Chem. Phys. 26, 745 (2024); Thoms and Napolitano J. Chem. Phys. 159, 161103 (2023); Thoms et al J Phys Chem Letters 15, 4838 (2024)

4.            White Napolitano Lipson, Phys. Rev. Lett. 134, 098203 (2025)

5.            Thoms et al Phys. Rev. Lett. 132, 248101 (2024), Caporaletti et al (in preparation)