Interfacial microrheology: Particle tracking and related techniques

Abstract

Microrheology offers several advantages over traditional macroscopic rheology: the use of very small samples, the possibility of studying heterogeneous samples and the broad range of frequency that can be explored. In this paper the study of the microrheology of fluid interfaces is reviewed, with special emphasis on particle tracking techniques. We comment the main results and the assumptions of the different approaches for describing the hydrodynamics of a particle trapped at a surfactant or polymer monolayer.

Introduction

Many of the diverse properties of soft materials (polymer solutions, gels, filamentous proteins in cells, etc.) stem from their complex structures and dynamics with multiple characteristic length and time scales. A wide variety of technologies, from paints to foods, from oil recovery to processing of plastics, all rely heavily on understanding the flow of complex fluids [1], [2].

Rheological measurements on complex materials reveal viscoelastic responses which depend on the time scale at which the sample is probed. In order to characterize the rheological response one usually measures the shear or the Young modulus as a function of frequency by applying a small oscillatory strain; typically, commercial rheometers probe frequencies from mHz up to tens of Hz.

Although standard rheological measurements have been very useful in characterizing soft materials and complex fluids, they are not always well suited for all systems because they need sample volumes larger than a milliliter, thus precluding the study of rare or precious materials, including many biological samples that are difficult to obtain in large quantities. Moreover, conventional rheometers provide an average measurement of the bulk response, and do not allow for local measurements in inhomogeneous systems. To address these issues, a new class of rheology measurement technique has emerged, that probes the material response on micrometer length scales with microliter sample volumes. Microrheology is a term that does not describe one particular technique, but rather a number of approaches that attempt to overcome some limitations of traditional bulk rheology. Advantages over macrorheology include a significantly higher range of frequencies available without time–temperature superposition [2], the capability of measuring material inhomogeneities that are inaccessible to macrorheological methods, and rapid thermal and chemical homogenization that allow the transient rheology of evolving systems to be studied [3]. Microrheology methods typically use embedded micron-sized probes to locally deform the sample, permitting the use of very small volumes (∼ µl). Macro- and microrheology probe different aspects of the material: the former makes measurements over extremely long (macroscopic) length scales using a viscometric flow field, whereas the latter effectively measures material properties on the scale of the probe itself (since flow and deformation fields decay on this length scale). Detailed descriptions of the methods and applications of microrheology to the study of bulk systems have been given in review articles published in recent years [4], [5], [6], [7], [8], [9], [10].

Interfaces play a dominant role in the behavior of many complex fluids. Interfacial rheology has been found to be a key factor in the stability of foams and emulsions, compatibilization of polymer blends, flotation technology, fusion of vesicles, etc. [11]. Particle-laden interfaces have attracted much attention in recent years. The tendency of colloidal particles to become (almost irreversibly) trapped at interfaces and their behavior once there, has lead to their use in a wide variety of systems including drug delivery, stabilization of foams and emulsions, froth, flotation, or ice cream production. The high trapping energy of particles at interfaces provides a route to use fluid interfaces as a substrate for the self-assembly of particles into materials of specific mechanical, optical or magnetic properties [12].

The interactions of the particles at interfaces are expected to be more complex than in the bulk [13], [14], indeed, the dynamic properties of particle-laden interfaces are strongly influenced by direct interparticle forces (capillary, steric, electrostatic, van der Waals, etc.) and complicated hydrodynamic interactions mediated by the surrounding fluids. In recent books overviews of particles at liquid interfaces have been published [13], [14], [15], [16], [17]. At macroscopic scales, the rheological properties of particle-laden fluid interfaces can be viewed as those of a liquid–liquid interface with some effective surface viscoelastic properties described by effective shear and compressional viscoelastic moduli. A significant fact is that for the simplest fluid–fluid interface, different dynamic modes have to be taken into account: the capillary (out of plane) mode, and the in-plane mode, which contains dilational (or extensional) and shear contributions. For more complex interfaces, such as thicker ones, other dynamic modes (bending, splaying) have to be considered [18^•]. Moreover, the coupling of the abovementioned modes with adsorption/desorption kinetics may be very relevant for interfaces that contain soluble or partially soluble surfactants, polymers or proteins [19], [20], [21]. In recent years a number of experimental techniques have been developed for studying the dilational rheology in a broad range of frequencies (1 mHz–100 kHz), both in the linear and non-linear regimes [18•], [22], [23]. In the case of surface shear rheology, most of the information available has been obtained using macroscopic interfacial rheometers which have a sensibility limit of about 10^− 6 N s m^− 1 [18•], [24], [25], [26], but many important systems have surface shear viscosities below this limit. Particle tracking techniques have been foreseen as a powerful method to study the dynamics of interfaces with shear viscosities as low as 10^− 10 N s m^− 1. In spite that the measurement of diffusion coefficients of particles attached to interfaces is relatively straightforward with modern microrheological techniques, one has to rely on hydrodynamic models of the viscoelastic surroundings traced by the particles in order to obtain variables such as monolayer elasticity or shear viscosity. The more complex the structure of the interface the stronger are the assumptions of the model, thus resulting in more difficulties in checking their validity. In the present work we will briefly review the modern experimental techniques applied to interface dynamics. We will summarize the available theoretical models for calculating the shear microviscosity of fluid monolayers from particle tracking experiments. We will finally discuss the relatively few experimental results available of particle tracking at interfaces. We will highlight that we are far from understanding microrheology results, and we hope that this review will stimulate future works on this subject.