Manifestations of static and dynamic heterogeneity in single molecule translational measurements in glassy systems

Abstract

Rotational-translational decoupling in systems near T g, in which translational diffusion is apparently enhanced relative to rotation, has been observed in ensemble and single molecule experiments and has been linked to dynamic heterogeneity. Here, simulations of single molecules experiencing homogeneous diffusion and static and dynamic heterogeneous diffusion are performed to clarify the contributions of heterogeneity to such enhanced translational diffusion. Results show that time-limited trajectories broaden the distribution of diffusion coefficients in the presence of homogeneous diffusion but not when physically reasonable degrees of static heterogeneity are present. When dynamic heterogeneity is introduced, measured diffusion coefficients uniformly increase relative to input diffusion coefficients, and the widths of output distributions decrease, providing support for the idea that dynamic heterogeneity can drive apparent translational enhancement. Among simulations with dynamic heterogeneity, when frequency of dynamic exchange is correlated with initial diffusion coefficient, measured diffusion coefficient behavior as a function of observation time matches that seen experimentally, the only set of simulations explored in which this occurs. Taken together with experimental results, this suggests enhanced translational diffusion in glassy systems occurs through dynamic exchange consistent with wide underlying distributions of diffusion coefficients and exchange coupled to local spatiotemporal dynamics.

Two-Dimensional Fluctuation Correlation Spectroscopy (2D-FlucCS): A Method to Determine the Origin of Relaxation Rate Dispersion

“…Static heterogeneity is defined as the simultaneous existence of different relaxation rates experienced by different molecules, which leads to rate dispersion. Dynamic heterogeneity is defined as a sequential transformation of rates to different values on a given molecule, which also leads to rate dispersion. , In conventional one-dimensional experiments, without prior information about the system, it requires numerous control measurements to be able to characterize the system as having homogeneous or heterogeneous rate dispersion. Multidimensional correlation analysis methods do not require prior information about the system and define the system based on the information content of the observable time series.…”

“…Relaxation in simple systems is characterized by exponential decay or single-rate kinetics, which results in a narrow distribution of rates on a rate spectrum . Deviation from exponentiality, or multirate kinetics, i.e., nonexponential relaxation, are widely observed when measuring relaxation in complex systems such as polymers, unconventional liquids, nanostructures, and biological systems. − This leads to broad distribution on a rate spectrum . For instance, the rotational rates of a small molecule in a polymer near its glass transition are distributed over a wide range of values. , The solvation rate around a small organic probe molecule in ionic liquids is dispersed over multiple decades. , Multiexponential behavior is reported in translational diffusion and solvation in deep eutectic solvents .…”

“…18 For instance, the rotational rates of a small molecule in a polymer near its glass transition are distributed over a wide range of values. 2,15 The solvation rate around a small organic probe molecule in ionic liquids is dispersed over multiple decades. 3,4 Multiexponential behavior is reported in translational diffusion and solvation in deep eutectic solvents.…”

“…Deviation from exponentiality, or multirate kinetics, i.e., nonexponential relaxation, are widely observed when measuring relaxation in complex systems such as polymers, unconventional liquids, nanostructures, and biological systems. − This leads to broad distribution on a rate spectrum . For instance, the rotational rates of a small molecule in a polymer near its glass transition are distributed over a wide range of values. , The solvation rate around a small organic probe molecule in ionic liquids is dispersed over multiple decades. , Multiexponential behavior is reported in translational diffusion and solvation in deep eutectic solvents . Dynamics of protein molecules are spread over several decades in time. , Broad distribution of diffusion time is observed in the cytoplasm of living cells. , Conformational changes in proteins are often associated with observed nonexponential relaxation kinetics. , …”