When the Heterogeneous Appears Homogeneous: Discrepant Measures of Heterogeneity in Single-Molecule Observables

Abstract

Supercooled liquids demonstrate stretched exponential relaxations consistent with the presence of spatially heterogeneous dynamics. Many experimental results are consistent with this picture, but differences in experimental approach may lead to different conclusions about the degree of heterogeneity in a given system. Here, we investigate whether observables accessible with single molecule (SM) approaches are consistent with each other and with ensemble measurements. In particular, the distribution of rotational relaxation times, τ c , obtained from SM measurements is compared with the stretching exponent determined from a quasi-ensemble treatment of the same data. It is shown that the time-limited trajectories typical of SM experiments can lead to a stretching exponent that suggests homogeneous dynamics even in the presence of heterogeneous dynamics. After correction for the time-limited trajectories, additional discrepancy remains between stretching exponents measured via SM experiments and ensemble techniques. The remaining difference is attributed to the limited dynamic range of the SM experiments.Keywords supercooled liquids; single molecule; simulations; glass transition; rotational relaxation Supercooled liquids and glasses have provoked substantial interest, in large measure due to the interesting dynamics these systems display. Based on experiments, simulations, and theoretical work, a picture of the supercooled liquid as a mosaic of local and interchanging dynamic environments has emerged 1 . Such heterogeneous dynamics are not limited to molecular supercooled liquids but indeed are found in a variety of crowded systems [2][3][4] . One * Corresponding Author: kaufman@chem.columbia.edu. In such experiments, the deviation of β from 1 is typically associated with the degree of heterogeneity in the system 1 . The stretched exponential relaxations in supercooled liquids are most commonly attributed to spatial and/or temporal averaging over a distribution of single exponential relaxations. NIH Public AccessThe existence of heterogeneous dynamics in supercooled liquids encourages the application of sub-ensemble approaches to their study. In particular, in recent years single molecule (SM) fluorescence microscopy following the rotational relaxation of fluorescent probes in supercooled liquids has been used to establish the presence of dynamic heterogeneity in these systems as well as to investigate the length scales over which regions of particular dynamics exist and the timescales over which they persist [5][6][7][8][9][10][11] . While SM approaches yield information concealed in ensemble experiments, when sufficient data on sufficient single molecules are collected, these experiments are also expected to return results obtained in bulk experiments. However, for a variety of reasons, this is not always found to be the case [12][13][14] . Discrepancies may emerge due to the fact that SM fluorescence microscopy generally yields much shorter trajectories relative to the timescales of interest as a result...

Temperature-Dependent Two-State Dynamics of Individual Cooperatively Rearranging Regions on a Glass Surface

“…As discussed by Kaufman and coworkers, temporal heterogeneity of individual clusters may be greater on time scales outside our dynamic range of a few hours [13] spanned by our data. Near the bulk glass transition T g , kinetically facilitated models do not predict such a neat partitioning into CRR-to-CRR vs.…”

“…We imaged individual CRRs at metallic glass surfaces while ramping their temperature, obtaining real-time movies of their temperature-dependent dynamics. We studied a Fe 78 B 13 Si 8 alloy (asreceived 25.4 μm thick MetGlas® SA1 samples from MetGlas Inc., Conway SC, USA) with a glass transition temperature of T g = 780 K. Samples were degassed for 8 hours at 373 K and cleaned using 2 keV argon ion sputtering with a dose of ~1 to 10×10 16 ions/cm 2 . The surface composition analyzed by X-ray photoelectron spectroscopy was very similar to the bulk.…”

Non-Gaussian rotational diffusion in heterogeneous media

“…Recent experiments and simulations showed that when the rotational correlation function U (t) was averaged over many molecules in different regions, U (t) was stretched exponential, i.e., U (t) ∼ exp[−(t/τ ) β ] with 0 < β < 1 [2,9,14,15]. The stretched-exponential form of U (t) is considered a clear indication of dynamic heterogeneity [2,9,[16][17][18][19][20][21].…”

Biphasic rate exchange in supercooled o -terphenyl from an ensemble analysis of single-molecule data

“…Second, photobleaching of the probe molecule limits the dynamic range in time: low light intensities extend the time window, but also require larger time bins to collect sufficient signal. Last and most disturbing, sampling noise-noise due to measuring a finite number of relaxations-is large and has seemed to be unavoidable [25][26][27][28].…”