Differential Variance Analysis: a direct method to quantify and visualize dynamic heterogeneities

Raffaele Pastore,Marco Caggioni,Giuseppe Pesce

doi:10.1038/srep43496

Abstract

Many amorphous materials show spatially heterogenous dynamics, as different regions of the same system relax at different rates. Such a signature, known as Dynamic Heterogeneity, has been crucial to understand the nature of the jamming transition in simple model systems and is currently considered very promising to characterize more complex fluids of industrial and biological relevance. Unfortunately, measurements of dynamic heterogeneities typically require sophisticated experimental set-ups and are performed by few specialized groups. It is now possible to quantitatively characterize the relaxation process and the emergence of dynamic heterogeneities using a straightforward method, here validated on video microscopy data of hard-sphere colloidal glasses. We call this method Differential Variance Analysis (DVA), since it focuses on the variance of the differential frames, obtained subtracting images at different time-lags. Moreover, direct visualization of dynamic heterogeneities naturally appears in the differential frames, when the time-lag is set to the one corresponding to the maximum dynamic susceptibility. This approach opens the way to effectively characterize and tailor a wide variety of soft materials, from complex formulated products to biological tissues.

Highlights

Many amorphous materials show spatially heterogenous dynamics, as different regions of the same system relax at different rates
We validate the result of Differential Variance Analysis (DVA) by performing established single particle tracking analysis and demonstrating that the dynamic order parameter obtained from DVA closely matches the commonly measured Intermediate Self Scattering Function (ISSF) at a wave-length of the order of the particle size
We introduced DVA as a novel and simple experimental method to characterize the dynamics of hard-sphere colloidal glasses of micron-sized particles

Summary

Introduction

Many amorphous materials show spatially heterogenous dynamics, as different regions of the same system relax at different rates. The size and the lifetime of these dynamical clusters increase on approaching the transition, playing a role similar to density fluctuations close to an ordinary critical point[4,5,6] This motivated the glass community to develop a robust framework for characterizing DHs. In glass forming liquids, the structural relaxation process as a function of time, Δt, can be monitored through a dynamic order parameter probing the local motion on the length scale of the particle size. Differential Dynamic Microscopic (DDM), that provides information similar to DLS from video microscopy data, is an easy and promising technique[30,31], but currently limited to monitor the structural relaxation[32,33] and not DHs. It appears clearly that an easy way to characterize complex fluids with dynamic heterogeneity is highly desirable, considering that soft glassy materials are common in technological applications and biological systems. The key of this visualization is to consider differential frames close to the time-lag Δt*, which is determined by the dynamics and can be measured from DVA as the time corresponding to the maximum of χ4

Methods

Results

Discussion

Conclusion