Probing shear-induced rearrangements in Fourier space. II. Differential dynamic microscopy

Convolutional neural networks applied to differential dynamic microscopy reduces noise when quantifying heterogeneous dynamics

Differential dynamic microscopy (DDM) typically relies on movies containing hundreds or thousands of frames to accurately quantify motion in soft matter systems. Using movies much shorter in duration produces noisier and less accurate results. This limits the applicability of DDM to situations where the dynamics are stationary over extended times. Here, we investigate a method to denoise the DDM process, particularly suited to when a limited number of imaging frames are available or when dynamics are quickly evolving in time. We use a convolutional neural network encoder-decoder (CNN-ED) model to reduce the noise in the intermediate scattering function that is computed via DDM. We demonstrate this approach of combining machine learning and DDM on samples containing diffusing micron-sized colloidal particles. We quantify how the particles' diffusivities change over time as the fluid they are suspended in gels. We also quantify how the diffusivity of particles varies with position in a sample containing a viscosity gradient. These test cases demonstrate how studies of non-equilibrium dynamics and high-throughput screens could benefit from a method to denoise the outputs of DDM.

Modeling and correction of image drift in dynamic shadowgraphy experiments

The study of phoretic transport phenomena under non-stationary conditions presents several challenges, mostly related to the stability of the experimental apparatus. This is particularly true when investigating with optical means the subtle temperature and concentration fluctuations that arise during diffusion processes, superimposed to the macroscopic state of the system. Under these conditions, the tenuous signal from fluctuations is easily altered by the presence of artifacts. Here, we address an experimental issue frequently reported in the investigation by means of dynamic shadowgraphy of the non-equilibrium fluctuations arising in liquid mixtures under non-stationary conditions, such as those arising after the imposition or removal of a thermal stress, where experiments show systematically the presence of a spurious contribution in the reconstructed structure function of the fluctuations, which depends quadratically from the time delay. We clarify the mechanisms responsible for this artifact, showing that it is caused by the imperfect alignment of the sample cell with respect to gravity, which couples the temporal evolution of the concentration profile within the sample with the optical signal collected by the shadowgraph diagnostics. We propose a data analysis protocol that enables disentangling the spurious contributions and the genuine dynamics of the fluctuations, which can be thus reliably reconstructed.

Probing Microscale Structuring-Induced Phase Separation with Fluorescence Recovery Diffusion Dynamics in Poly(ethylene glycol) Solutions

Apart from biocompatibility, poly(ethylene glycol) (PEG)-based biomedical constructs require mechanical tunability and optimization of microscale transport for regulation of the release kinetics of biomolecules. This study illustrates the role of inhomogeneities due to aggregates and structuring in the PEG matrix in the microscale diffusion of a fluorescent probe. Comparative analysis of fluorescence recovery after photobleaching (FRAP) profiles with the help of diffusion half-time is used to assess the diffusion coefficient (D). The observations support a nontrivial dependence of diffusion dynamics on polymer concentration (volume fraction, φ) and that of fillers carboxymethyl cellulose (CMC) and nanoclay bentonite (B). D values follow the Rouse scaling D ∼ φ-0.54 in PEG solutions. The diffusion time of the fluorescent probe in the PEG+bentonite matrix reveals the onset of depletion interaction-induced phase separation with an increase in bentonite concentration in the PEG matrix beyond 0.1 wt %. Beyond this concentration, structure factors obtained from prebleach FRAP images show a rapid increase at low Q. The two-phase system (PEG-rich and bentonite-rich) was characterized by the hierarchical structural topology of bentonite aggregates, and aggregate sizes were obtained at different length scales with phase contrast imaging, small-angle neutron scattering, and small-angle X-ray scattering. The microscale transport detection presented captures sensitively the commencement of phase separation in the PEG + bentonite matrix, as opposed to the PEG or PEG + CMC matrix, which are observed to be one-phase systems. This method of diffusion half-time and prebleach image analysis can be used for the fast, high-throughput experimental investigation of microscale mechanical response and its correlation with structuring in the polymer matrix.

Unraveling gelation kinetics, arrested dynamics and relaxation phenomena in filamentous colloids by photon correlation imaging

The fundamental understanding of the gelation kinetics, stress relaxation and temporal evolution in colloidal filamentous gels is central to many aspects of soft and biological matter, yet a complete description of the inherent complex dynamics of these systems is still missing. By means of photon correlation imaging (PCI), we studied the gelation of amyloid fibril solutions, chosen as a model filamentous colloid with immediate significance to biology and nanotechnology, upon passage of ions through a semi-permeable membrane. We observed a linear-in-time evolution of the gelation front and rich rearrangement dynamics of the gels, the magnitude and the spatial propagation of which depend on how effectively electrostatic interactions are screened by different ionic strengths. Our analysis confirms the pivotal role of salt concentration in tuning the properties of amyloid gels, and suggests potential routes for explaining the physical mechanisms behind the linear advance of the salt ions.

Probing the dynamics of turbid colloidal suspensions using differential dynamic microscopy

Few techniques can reliably measure the dynamics of colloidal suspensions or other soft materials over a wide range of turbidities. Here we systematically investigate the capability of Differential Dynamic Microscopy (DDM) to characterise particle dynamics in turbid colloidal suspensions based on brightfield optical microscopy. We measure the Intermediate Scattering Function (ISF) of polystyrene microspheres suspended in water over a range of concentrations, turbidities, and up to 4 orders of magnitude in time-scales. These DDM results are compared to data obtained from both Dynamic Light Scattering (DLS) and Two-colour Dynamic Light Scattering (TCDLS). The latter allows for suppression of multiple scattering for moderately turbid suspensions. We find that DDM can obtain reliable diffusion coefficients at up to 10 and 1000 times higher particle concentrations than TCDLS and standard DLS, respectively. Additionally, we investigate the roles of the four length-scales relevant when imaging a suspension: the sample thickness L, the imaging depth z, the imaging depth of field DoF, and the photon mean free path . More detailed experiments and analysis reveal the appearance of a short-time process as turbidity is increased, which we associate with multiple scattering events within the imaging depth of the field. The long-time process corresponds to the particle dynamics from which particle-size can be estimated in the case of non-interacting particles. Finally, we provide a simple theoretical framework, ms-DDM, for turbid samples, which accounts for multiple scattering.

Characterising shear-induced dynamics in flowing complex fluids using differential dynamic microscopy

Microscopic dynamics reveal the origin of the bulk rheological response in complex fluids. In model systems particle motion can be tracked, but for industrially relevant samples this is often impossible. Here we adapt differential dynamic microscopy (DDM) to study flowing highly-concentrated samples without particle resolution. By combining an investigation of oscillatory flow, using a novel "echo-DDM" analysis, and steady shear, through flow-DDM, we characterise the yielding of a silicone oil emulsion on both the microscopic and bulk level. Through measuring the rate of shear-induced droplet rearrangements and the flow velocity, the transition from a solid-like to liquid-like state is shown to occur in two steps: with droplet mobilisation marking the limit of linear visco-elasticity, followed by the development of shear localisation and macroscopic yielding. Using this suite of techniques, such insight could be developed for a wide variety of challenging complex fluids.

Deformation profiles and microscopic dynamics of complex fluids during oscillatory shear experiments

Oscillatory shear tests are widely used in rheology to characterize the linear and non-linear mechanical response of complex fluids, including the yielding transition. There is an increasing urge to acquire detailed knowledge of the deformation field that is effectively present across the sample during these tests; at the same time, there is mounting evidence that the macroscopic rheological response depends on the elusive microscopic behavior of the material constituents. Here we employ a strain-controlled shear-cell with transparent walls to visualize and quantify the dynamics of tracers embedded in various cyclically sheared complex fluids, ranging from almost-ideal elastic to yield stress fluids. For each sample, we use image correlation processing to measure the macroscopic deformation field, and echo-differential dynamic microscopy to probe the microscopic irreversible sample dynamics in reciprocal space; finally, we devise a simple scheme to spatially map the rearrangements in the sheared sample, once again without tracking the tracers. For the yield stress sample, we obtain a wave-vector dependent characterization of shear-induced diffusion across the yielding transition, which is accompanied by a three-order-of-magnitude speed-up of the dynamics and by a transition from localized, intermittent rearrangements to a more spatially homogeneous and temporally uniform activity. Our tracking free approach is intrinsically multi-scale, can successfully discriminate between different types of dynamics, and can be automated to minimize user intervention. Applications are many, as it can be translated to other imaging modes, including fluorescence, and can be used with sub-resolution tracers and even without tracers, for samples that provide intrinsic optical contrast.

Dynamic Speckle Holography

We introduce dynamic speckle holography, a new technique that combines imaging and scattering to measure three-dimensional maps of displacements as small as ten nanometers over several centimeters, greatly extending the capabilities of traditional imaging systems. We attain this sensitivity by imaging speckle patterns of light collected at three scattering angles and measuring the decay in the temporal correlation due to local motion. We use dynamic speckle holography to measure the strain field of a colloidal gel undergoing fracture and establish the surprising role of internal tension in driving the fracture.

Particle sizing for flowing colloidal suspensions using flow-differential dynamic microscopy

Particle size is a key variable in understanding the behaviour of the particulate products that underpin much of our modern lives. Typically obtained from suspensions at rest, measuring the particle size under flowing conditions would enable advances for in-line testing during manufacture and high-throughput testing during development. However, samples are often turbid, multiply scattering light and preventing the direct use of common sizing techniques. Differential dynamic microscopy (DDM) is a powerful technique for analysing video microscopy of such samples, measuring diffusion and hence particle size without the need to resolve individual particles while free of substantial user input. However, when applying DDM to a flowing sample, diffusive dynamics are rapidly dominated by flow effects, preventing particle sizing. Here, we develop "flow-DDM", a novel analysis scheme that combines optimised imaging conditions, a drift-velocity correction and modelling of the impact of flow. Flow-DDM allows a decoupling of flow from diffusive motion that facilitates successful particle size measurements at flow speeds an order of magnitude higher than for DDM. We demonstrate the generality of the technique by applying flow-DDM to two separate microscopy methods and flow geometries.

Rheology of colloidal and metallic glass formers

Colloidal hard-sphere suspensions are convenient experimental models to understand soft matter, and also by analogy the structural-relaxation behavior of atomic or small-molecular fluids. We discuss this analogy for the flow and deformation behavior close to the glass transition. Based on a mapping of temperature to effective hard-sphere packing, the stress–strain curves of typical bulk metallic glass formers can be quantitatively compared with those of hard-sphere suspensions. Experiments on colloids give access to the microscopic structure under deformation on a single-particle level, providing insight into the yielding mechanisms that are likely also relevant for metallic glasses. We discuss the influence of higher-order angular signals in connection with non-affine particle rearrangements close to yielding. The results are qualitatively explained on the basis of the mode-coupling theory. We further illustrate the analogy of pre-strain dependence of the linear-elastic moduli using data on PS-PNiPAM suspensions.

Microscopic precursors of failure in soft matter

The mechanical properties of soft matter are of great importance in countless applications, in addition of being an active field of academic research. Given the relative ease with which soft materials can be deformed, their non-linear behavior is of particular relevance. Large loads eventually result in material failure. In this Perspective article, we discuss recent work aiming at detecting precursors of failure by scrutinizing the microscopic structure and dynamics of soft systems under various conditions of loading. In particular, we show that the microscopic dynamics is a powerful indicator of the ultimate fate of soft materials, capable of unveiling precursors of failure up to thousands of seconds before any macroscopic sign of weakening.

Probing shear-induced rearrangements in Fourier space. I. Dynamic light scattering

Understanding the microscopic origin of the rheological behavior of soft matter is a long-lasting endeavour. While early efforts concentrated mainly on the relationship between rheology and structure, current research focuses on the role of microscopic dynamics. We present in two companion papers a thorough discussion of how Fourier space-based methods may be coupled to rheology to shed light on the relationship between the microscopic dynamics and the mechanical response of soft systems. In this first companion paper, we report a theoretical, numerical and experimental investigation of dynamic light scattering coupled to rheology. While in ideal solids and simple viscous fluids the displacement field under a shear deformation is purely affine, additional non-affine displacements arise in many situations of great interest, for example in elastically heterogeneous materials or due to plastic rearrangements. We show how affine and non-affine displacements can be separately resolved by dynamic light scattering, and discuss in detail the effect of several non-idealities in typical experiments.