Ideal probe single-molecule experiments reveal the intrinsic dynamic heterogeneity of a supercooled liquid

Abstract

The concept of dynamic heterogeneity and the picture of the supercooled liquid as a mosaic of environments with distinct dynamics that interchange in time have been invoked to explain the nonexponential relaxations measured in these systems. The spatial extent and temporal persistence of these regions of distinct dynamics have remained challenging to identify. Here, singlemolecule fluorescence measurements using a probe similar in size and mobility to the host o-terphenyl unambiguously reveal exponential relaxations distributed in time and space and directly demonstrate ergodicity of the system down to the glass transition temperature. In the temperature range probed, at least 200 times the structural relaxation time of the host is required to recover ensemble-averaged relaxation at every spatial region in the system.espite decades of intensive study, a full theory of the glass transition is lacking; so too is a full understanding of the causal relationships between the unusual phenomena displayed by glass-forming liquids in the supercooled regime and the glass transition. One such phenomenon is the onset of nonexponential relaxations in the supercooled regime. Consistent with such relaxations, a variety of experiments have suggested the presence of dynamic heterogeneity, where-over a given time-molecular mobility in a given region may differ by orders of magnitude from that in another region, potentially just nanometers away (1, 2). While some experiments have sought to quantify the size of these regions, others have sought to quantify their persistence in time, as supercooled liquids are assumed to be ergodic, requiring that over long times, all dynamic environments are sampled (3-5). Precise description of dynamic heterogeneity in glass formers remains challenging due to the ensemble, subensemble, and/or time averaging inherent in most experimental techniques. However, such description remains of significant interest given the poorly understood causal relationship between dynamic heterogeneity and the glass transition as well as the need for experimental observations that may distinguish between various theories of the glass transition (6, 7).Typically, putative dynamic heterogeneity has been recognized in experiments through the shape of the ensemble relaxation, which is well described by a stretched exponential (exp[−(t/τ fit ) β ]) where the deviation of β below 1 describes the degree of stretching and has been interpreted as a barometer of dynamic heterogeneity. Multiple scenarios are consistent with an ensemble stretched exponential relaxation, and two limiting cases can be straightforwardly described: The ensemble stretched exponential emerges from (i) a superposition of exponentials with different relaxation times or (ii) identical stretched exponentials with the same relaxation time. The former limit describes a system with variation of time scales distributed in space but not time, while the latter represents the opposite extreme. The former case describes a system that is not ergodic over times acce...

Probing liquid dynamics, one molecule at a time

“…Many other studies are consistent with τ ex ≈ 3τ α , where τ ex is the time a mode retains its time constant (6,7). The time until one mode has experienced all possible environments and thus restored ergodicity has to be much longer than τ ex , as found in the ideal-probe single-molecule work of Paeng et al (2). This single-molecule approach to the dynamics of glass-forming materials may also have the potential to directly observe the nontrivial length scales (Fig.…”

“…Therefore, the ideal method for studying the dynamics of materials is by an experiment that allows us to look at the sample one molecule at a time. Relative to previous single-molecule studies, the recent advance reported by Paeng et al (2) is based on using a probe molecule that reflects the liquid's behavior with high fidelity.…”

Viscosity of deeply supercooled water and its coupling to molecular diffusion

“…These observations imply that deeply supercooled liquids exhibit spatially heterogeneous dynamics (29)(30)(31). Dynamic heterogeneities have been confirmed by direct observations of several single fluorescent molecules immersed in ortho-terphenyl (32) or nanorods immersed in glycerol (33). Physically different systems also show analogous behavior.…”

Correlated matrix-fluctuation-mediated activated transport of dilute penetrants in glass-forming liquids and suspensions

“…[1][2][3][4][5] Relevant applications include gas and molecule separations, 6 water purification membranes, 7 barrier materials, self-healing systems based on microcapsules, [8][9][10] ion and solute transport in polymeric materials and biological systems, 11 and the flow of colloids in porous media. 12,13 Penetrants are here, by definition, smaller than the elementary species that constitutes the matrix, but they can still vary over a wide range of absolute and relative size and shape and the extent of attractive interactions with the matrix material.…”