Direct measurements of growing amorphous order and non-monotonic dynamic correlations in a colloidal glass-former

Abstract

The transformation of flowing liquids into rigid glasses is thought to involve increasingly cooperative relaxation dynamics as the temperature approaches that of the glass transition. However, the precise nature of this motion is unclear, and a complete understanding of vitrification thus remains elusive. Of the numerous theoretical perspectives 1-4 devised to explain the process, random first-order theory (RFOT; refs 2,5) is a well-developed thermodynamic approach, which predicts a change in the shape of relaxing regions as the temperature is lowered. However, the existence of an underlying 'ideal' glass transition predicted by RFOT remains debatable, largely because the key microscopic predictions concerning the growth of amorphous order and the nature of dynamic correlations lack experimental verification. Here, using holographic optical tweezers, we freeze a wall of particles in a two-dimensional colloidal glass-forming liquid and provide direct evidence for growing amorphous order in the form of a static point-to-set length. We uncover the non-monotonic dependence of dynamic correlations on area fraction and show that this non-monotonicity follows directly from the change in morphology and internal structure of cooperatively rearranging regions 6,7 . Our findings support RFOT and thereby constitute a crucial step in distinguishing between competing theories of glass formation.In a seminal paper dated nearly fifty years ago, Adam and Gibbs 8 associated the rapid growth of a supercooled liquid's relaxation time with a decrease in its configurational entropy S c . Within RFOT, S c is related to the number of metastable minima in the free energy landscape of the liquid that can be explored by the system at a given temperature. This theory further claims that the supercooled liquid freezes into a mosaic whose domains correspond to configurations in these metastable minima 1 . The typical domain size is expected to diverge at the 'ideal' glass transition temperature, where S c vanishes. The existence of a growing static 'mosaic' length scale that serves as a clear indicator of the glass transition is therefore intrinsic to RFOT (ref. 2), although a systematic procedure for measuring it from point-to-set correlations was established much later 9 . Since the findings of ref. 9, a variety of growing static length scales have been identified and computed in numerical simulations [10][11][12][13] . Of these, the point-to-set correlation length ξ PTS (ref. 10) is of central importance, as it follows directly from the mosaic picture. ξ PTS is measured by freezing a subset of particles in the liquid's equilibrium configuration, and examining their influence on the configuration of the remaining free particles. As such, when evaluated for appropriate pinning geometries, ξ PTS can provide an estimate of the typical domain size of the mosaic 10 . In addition, it has been shown analytically that a divergence in the relaxation time is indeed associated with a diverging ξ PTS (ref. 14). ξ PTS was first extracted in simulation...

A topologically driven glass in ring polymers

“…This protocol is inspired by recent theoretical and experimental studies on the nature of glass transitions and idealizes the case in which a fraction c of polymers in the system might be arbitrarily frozen, perhaps by mixing two polymeric species with different T g or by using optical tweezers (24,25), although the primary interest in this work is in its role as a conceptual tool.…”

“…This method introduces a field of "quenched" disorder by freezing in space and time a subset of the system (21)(22)(23)(24)(25)(26)(27).…”

Topological Interactions in Ring Polymers

“…This is why in this Section I will attack this problem from an unconventional perspective. I will in fact make use of techniques adopted by studies on glass-forming systems and in particular I will take inspiration from a number of recent papers that advanced the idea, and investigated the behaviour, of glassforming systems under an external pinning field [Bouchaud and Biroli, 2004, Biroli et al, 2008, Cammarota and Biroli, 2012, Karmakar and Parisi, 2013, Cammarota, 2013, Gokhale et al, 2014, Nagamanasa et al, 2015, Ozawa et al, 2015.…”

“…This means that the systems are more prone to reach the ideal glass-transition state (at which the systems displays zero configurational entropy) at temperatures higher than the natural T g Biroli, 2012,Karmakar andParisi, 2013], thereby facilitating their experimental and numerical investigation. Several protocols have been used to probe the response of systems to this artificial perturbation, and in particular, different geometries have been adopted where the frozen fraction of constituents, spins or particles, are distributed either on a plane [Nagamanasa et al, 2015], randomly Biroli, 2012, Gokhale et al, 2014] or to form cavities [Mézard andParisi, 2001, Cammarota, 2009].…”

Free energy cost of forming an interface between a crystal and its frozen version

“…Recently, an experimental investigation of such a system was carried out using colloidal particles [20]. Such computational and experimental studies extract a growing length scale based on a slowing down of the dynamics near the wall and relate it to the slowing down of glassy dynamics in the bulk.…”