Two-particle microrheology of quasi-2D viscous systems

Interfacial rheology of lanthanide binding peptide surfactants at the air-water interface

Peptide surfactants (PEPS) are studied to capture and retain rare earth elements (REEs) at air-water interfaces to enable REE separations. Peptide sequences, designed to selectively bind REEs, depend crucially on the position of ligands within their binding loop domain. These ligands form a coordination sphere that wraps and retains the cation. We study variants of lanthanide binding tags (LBTs) designed to complex strongly with Tb3+. The peptide LBT5- (with net charge -5) is known to bind Tb3+ and adsorb with more REE cations than peptide molecules, suggesting that undesired non-specific coulombic interactions occur. Rheological characterization of interfaces of LBT5- and Tb3+ solutions reveal the formation of an interfacial gel. To probe whether this gelation reflects chelation among intact adsorbed LBT5-:Tb3+ complexes or destruction of the binding loop, we study a variant, LBT3-, designed to form net neutral LBT3-:Tb3+ complexes. Solutions of LBT3- and Tb3+ form purely viscous layers in the presence of excess Tb3+, indicating that each peptide binds a single REE in an intact coordination sphere. We introduce the variant RR-LBT3- with net charge -3 and anionic ligands outside of the coordination sphere. We find that such exposed ligands promote interfacial gelation. Thus, a nuanced requirement for interfacial selectivity of PEPS is proposed: that anionic ligands outside of the coordination sphere must be avoided to prevent the non-selective recruitment of REE cations. This view is supported by simulation, including interfacial molecular dynamics simulations, and interfacial metadynamics simulations of the free energy landscape of the binding loop conformational space.

Non-Stick Length of Polymer-Polymer Interfaces under Small-Amplitude Oscillatory Shear Measurement

Interfaces in soft materials often exhibit deviation from non-slip/stick response and play a determining role in the rheological response of the overall system. We discuss detection techniques for the excess interface rheology using small-amplitude oscillatory shear (SAOS) measurements. A stacked bilayer of different polymers is sheared parallel to the interface and the dynamic shear response is measured. Deviation of the bilayer shear modulus from the superposition of the shear moduli of the component layers is analysed. Furthermore, we introduce a frequency-dependent non-stick length based on the bilayer SAOS response to characterize the excess interface rheology. We observe an approximate stick response in the interface in bilayers composed of the chemically same monomer as well as an apparent slip in the interface between immiscible polymers. The results suggest that the proposed non-stick length in SAOS is capable of detecting the apparent interfacial slip. The non-stick length in SAOS is readily applicable to other complex interfaces of different soft materials and offers a convenient tool to characterize the excess interface rheology.

Evidence for Enhanced Tracer Diffusion in Densely Packed Interfacial Assemblies of Hairy Nanoparticles

Nearly monodisperse nanoparticle (NP) spheres attached to a nonvolatile ionic liquid surface were tracked by in situ scanning electron microscopy to obtain the tracer diffusion coefficient Dtr as a function of the areal fraction ϕ. The in situ technique resolved both tracer (gold) and background (silica) particles for ∼1-2 min, highlighting their mechanisms of diffusion, which were strongly dependent on ϕ. Structure and dynamics at low and moderate ϕ paralleled those reported for larger colloidal spheres, showing an increase in order and a decrease in Dtr by over 4 orders of magnitude. However, ligand interactions were more important near jamming, leading to different caging and jamming dynamics for smaller NPs. The normalized Dtr at ultrahigh ϕ depended on particle diameter and ligand molecular weight. Increasing the PEG molecular weight by a factor of 4 increased Dtr by 2 orders of magnitude at ultrahigh ϕ, indicating stronger ligand lubrication for smaller particles.

Dynamic correlations in lipid bilayer membranes over finite time intervals

Recent single-molecule measurements [Schoch et al., Proc. Natl. Acad. Sci. U. S. A. 118, e2113202118 (2021)] have observed dynamic lipid-lipid correlations in membranes with submicrometer spatial resolution and submillisecond temporal resolution. While short from an instrumentation standpoint, these length and time scales remain long compared to microscopic molecular motions. Theoretical expressions are derived to infer experimentally measurable correlations from the two-body diffusion matrix appropriate for membrane-bound bodies coupled by hydrodynamic interactions. The temporal (and associated spatial) averaging resulting from finite acquisition times has the effect of washing out correlations as compared to naive predictions (i.e., the bare elements of the diffusion matrix), which would be expected to hold for instantaneous measurements. The theoretical predictions are shown to be in excellent agreement with Brownian dynamics simulations of experimental measurements. Numerical results suggest that the experimental measurement of membrane protein diffusion, in complement to lipid diffusion measurements, might help to resolve the experimental ambiguities encountered for certain black lipid membranes.

The confined Generalized Stokes-Einstein relation and its consequence on intracellular two-point microrheology

Two-point microrheology (TPM) is used to infer material properties of complex fluids from the correlated motion of hydrodynamically interacting probes embedded in the medium. The mechanistic connection between probe motion and material properties is propagation of disturbance flows, encoded in current TPM theory for unconfined materials. However, confined media e.g. biological cells and particle-laden droplets, require theory that encodes confinement into the flow propagator (Green's function). To test this idea, we use Confined Stokesian Dynamics simulations to explicitly represent many-body hydrodynamic couplings between colloids and with the enclosing cavity at arbitrary concentration and cavity size. We find that previous TPM theory breaks down in confinement, and we identify and replace the underlying key elements. We put forth a Confined Generalized Stokes-Einstein Relation and report the viscoelastic spectrum. We find that confinement alters particle dynamics and increases viscosity, owing to hydrodynamic and entropic coupling with the cavity. The new theory produces a master curve for all cavity sizes and concentrations and reveals that for colloids larger than 0.005 times the enclosure size, the new model is required.

Correlated diffusion in lipid bilayers

Dynamic processes on membrane surfaces are essential for biological function. Traditionally, quantitative measurements of lipid/protein motion have been interpreted in the framework of membrane hydrodynamics. However, some recent single-molecule tracking studies have proven difficult to interpret via hydrodynamic arguments. Does this suggest a failure of hydrodynamic theory or simply highlight the dangers in attempting to extend hydrodynamic arguments down to molecular scales? Intermolecular correlations are superior to single-molecule observations for studying hydrodynamics due to the longer length scales involved. The current work reports dynamic pair correlations of lipids in model membranes. Submicron distance-dependent correlations are well resolved, and complementary numerical calculations indicate that hydrodynamic theory can predict membrane dynamics over distances of tens of nanometers and longer.

Lipid membranes are complex quasi–two-dimensional fluids, whose importance in biology and unique physical/materials properties have made them a major target for biophysical research. Recent single-molecule tracking experiments in membranes have caused some controversy, calling the venerable Saffman–Delbrück model into question and suggesting that, perhaps, current understanding of membrane hydrodynamics is imperfect. However, single-molecule tracking is not well suited to resolving the details of hydrodynamic flows; observations involving correlations between multiple molecules are superior for this purpose. Here dual-color molecular tracking with submillisecond time resolution and submicron spatial resolution is employed to reveal correlations in the Brownian motion of pairs of fluorescently labeled lipids in membranes. These correlations extend hundreds of nanometers in freely floating bilayers (black lipid membranes) but are severely suppressed in supported lipid bilayers. The measurements are consistent with hydrodynamic predictions based on an extended Saffman–Delbrück theory that explicitly accounts for the two-leaflet bilayer structure of lipid membranes.

Interfacial Flow around Brownian Colloids

Understanding the flow created by particle motion at interfaces is a critical step toward understanding hydrodynamic interactions and colloidal self organization. We have developed correlated displacement velocimetry to measure flow fields around interfacially trapped Brownian particles. These flow fields can be decomposed into interfacial hydrodynamic multipoles, including force monopole and dipole flows. These structures provide key insights essential to understanding the interface's mechanical response. Importantly, the flow structure shows that the interface is incompressible for scant surfactant near the ideal gaseous state and contains information about interfacial properties and hydrodynamic coupling with the bulk fluid. The same dataset can be used to predict the response of the interface to applied, complex forces, enabling virtual experiments that produce higher order interfacial multipoles.

Tunable Collective Dynamics of Active Inclusions in Viscous Membranes

We study hydrodynamic interactions and clustering mechanisms of active membrane inclusions within lipid bilayers. Pairs of inclusions display unique oscillatory dynamics that disappear when the 3D fluid adjacent to the membrane is confined. We reduce the governing equations to a coupled dynamical system whose phase behavior reveals the striking role of bulk confinement in enhancing cluster formation within the membrane. Using numerical simulations, we then extend this finding to demonstrate the role of confinement in controlling large-scale aggregation of membrane inclusions.

Surfactant dynamics: hidden variables controlling fluid flows

Surfactants - molecules and particles that preferentially adsorb to fluid interfaces - play a ubiquitous role in the fluids of industry, of nature, and of life. Since most surfactants cannot be seen directly, their behavior must be inferred from their impact on observed flows, like the buoyant rise of a bubble, or the thickness of a coating film. In so doing, however, a difficulty arises: physically distinct surfactant processes can affect measurable flows in qualitatively identical ways, raising the specter of confusion or even misinterpretation. This Perspective describes, in one coherent piece, both the equilibrium properties and dynamic processes of surfactants, to better enable the fluid mechanics community to understand, interpret, and design surfactant/fluid systems. Specifically, §2 treats the equilibrium thermodynamics of surfactants at interfaces, including surface pressure, isotherms of soluble and insoluble surfactants, and surface dilatational moduli (Gibbs and Marangoni). §3 describes surfactant dynamics in fluid systems, including surfactant transport and interfacial stress boundary conditions, the competition between surface diffusion, advection, and adsorption/desorption, Marangoni stresses and flows, and surface excess rheology. §4 discusses paradigmatic problems from fluid mechanics that are impacted by surfactants, including translating drops and bubbles, surfactant adsorption to clean and oscillating interfaces; capillary wave damping, thin film dynamics, foam drainage, and the dynamics of particles and probes at surfactant-laden interfaces. Finally, §5 discusses the additional richness and complexity that frequently arise in 'real' surfactants, including phase transitions, phase coexistence, and polycrystalline phases within surfactant monolayers, and their impact on non-Newtonian surface rheology.

Motion of objects embedded in lipid bilayer membranes: Advection and effective viscosity

An interfacial regularized Stokeslet scheme is presented to predict the motion of solid bodies (e.g., proteins or gel-phase domains) embedded within flowing lipid bilayer membranes. The approach provides a numerical route to calculate velocities and angular velocities in complex flow fields that are not amenable to simple Faxén-like approximations. Additionally, when applied to shearing motions, the calculations yield predictions for the effective surface viscosity of dilute rigid-body-laden membranes. In the case of cylindrical proteins, effective viscosity calculations are compared to two prior analytical predictions from the literature. Effective viscosity predictions for a dilute suspension of rod-shaped objects in the membrane are also presented.

Patchy colloidal particles at the fluid-fluid interface

Colloidal particles have significantly different characteristics when they are at interfaces from when they are in the bulk. In this study, we applied Monte Carlo simulations to investigate the stability and dynamics of smooth patchy particles and rough patchy particles near or at the fluid-fluid interface. By adjusting the surface area ratio of the two faces of a smooth Janus particle, we show how its stability, in terms of free energy, in either side of the interface can be tuned relative to the smooth homogeneous particle. We demonstrate how roughness can affect the stability and the orientation of a colloidal particle. Moreover, position-dependent diffusion constants in directions parallel and perpendicular to the interface are calculated for the colloidal particles as a function of distance from the interface. We report drastic slowdowns in the perpendicular diffusivity (and less severe slowdowns for the parallel diffusivity) for all the colloidal particles when they approach the fluid-fluid interface. While such a slowdown is well-known for the fluid-solid interface in the literature in terms of frictional force in hydrodynamics, why this happens for the fluid-fluid interface has not been adequately discussed. We provide evidence for the decrease in terms of discrepancy in the fluid density that leads to depletion forces.

Spatial Cross-Correlated Diffusion of Colloids under Shear Flow

The spatial cross-correlated diffusion of colloidal particles is often used as an essential tool to study the dynamic properties of a fluid because it directly describes the hydrodynamic interaction between two particles in a fluid. However, the experimental measurement of cross-correlated diffusion can be substantially modified by even a weak shear flow. In this work, the effect of a shear flow on spatial cross-correlated diffusion is demonstrated using experimental measurements that show a clear dependence on pair angles. An analytical solution is proposed to explain the experimental observations. A numerical simulation is performed to systemically demonstrate the influence of shear flow on spatial cross-correlated diffusion. The results of the experiment, theoretical analysis, and numerical simulation agree well with each other. Therefore, this research provides a sensitive experimental method to determine the weak shear flow in any quasi-two-dimensional fluid systems.

Many-particle mobility and diffusion tensors for objects in viscous sheets

We derive a mobility tensor for many cylindrical objects embedded in a viscous sheet. This tensor guarantees a positive dissipation rate for any configuration of particles and forces, analogous to the Rotne-Prager-Yamakawa tensor for spherical particles in a three-dimensional viscous fluid. We test our result for a ring of radially driven particles, demonstrating the positive-definite property at all particle densities. The derived tensor can be utilized in Brownian dynamics simulations with hydrodynamic interactions for such systems as proteins in biomembranes and inclusions in free-standing liquid films.

Microrheology, advances in methods and insights

Microrheology is an emerging technique that probes mechanical response of soft material at micro-scale. Generally, microrheology technique can be divided into active and passive versions. During last two decades, extensive efforts have been paid to improve both the experiment techniques and data analysis methods, especially about how to link consequential particle positions into trajectories. We review the recent advances in microrheology, including improvements in labeling, imaging, data acquiring, data processing and data interpretation. Some of the recent insights in soft matter and living systems gained by using this technique are given. Before these, we also give a very brief description of the basic principles of both active and passive microrheology techniques, and some details about optical particle tracking and DWS.

Broken detailed balance and non-equilibrium dynamics in living systems: a review

Living systems operate far from thermodynamic equilibrium. Enzymatic activity can induce broken detailed balance at the molecular scale. This molecular scale breaking of detailed balance is crucial to achieve biological functions such as high-fidelity transcription and translation, sensing, adaptation, biochemical patterning, and force generation. While biological systems such as motor enzymes violate detailed balance at the molecular scale, it remains unclear how non-equilibrium dynamics manifests at the mesoscale in systems that are driven through the collective activity of many motors. Indeed, in several cellular systems the presence of non-equilibrium dynamics is not always evident at large scales. For example, in the cytoskeleton or in chromosomes one can observe stationary stochastic processes that appear at first glance thermally driven. This raises the question how non-equilibrium fluctuations can be discerned from thermal noise. We discuss approaches that have recently been developed to address this question, including methods based on measuring the extent to which the system violates the fluctuation-dissipation theorem. We also review applications of this approach to reconstituted cytoskeletal networks, the cytoplasm of living cells, and cell membranes. Furthermore, we discuss a more recent approach to detect actively driven dynamics, which is based on inferring broken detailed balance. This constitutes a non-invasive method that uses time-lapse microscopy data, and can be applied to a broad range of systems in cells and tissue. We discuss the ideas underlying this method and its application to several examples including flagella, primary cilia, and cytoskeletal networks. Finally, we briefly discuss recent developments in stochastic thermodynamics and non-equilibrium statistical mechanics, which offer new perspectives to understand the physics of living systems.

Irreversible particle motion in surfactant-laden interfaces due to pressure-dependent surface viscosity

The surface shear viscosity of an insoluble surfactant monolayer often depends strongly on its surface pressure. Here, we show that a particle moving within a bounded monolayer breaks the kinematic reversibility of low-Reynolds-number flows. The Lorentz reciprocal theorem allows such irreversibilities to be computed without solving the full nonlinear equations, giving the leading-order contribution of surface pressure-dependent surface viscosity. In particular, we show that a disc translating or rotating near an interfacial boundary experiences a force in the direction perpendicular to that boundary. In unbounded monolayers, coupled modes of motion can also lead to non-intuitive trajectories, which we illustrate using an interfacial analogue of the Magnus effect. This perturbative approach can be extended to more complex geometries, and to two-dimensional suspensions more generally.

Active microrheology of smectic membranes

Thin fluid membranes embedded in a bulk fluid of different viscosity are of fundamental interest as experimental realizations of quasi-two-dimensional fluids and as models of biological membranes. We have probed the hydrodynamics of thin fluid membranes by active microrheology using small tracer particles to observe the highly anisotropic flow fields generated around a rigid oscillating post inserted into a freely suspended smectic liquid crystal film that is surrounded by air. In general, at distances more than a few Saffman lengths from the meniscus around the post, the measured velocities are larger than the flow computed by modeling a moving disklike inclusion of finite extent by superposing Levine-MacKintosh response functions for pointlike inclusions in a viscous membrane. The observed discrepancy is attributed to additional coupling of the film with the air below the film that is displaced directly by the shaft of the moving post.

Hydrodynamic interactions in freely suspended liquid crystal films

Hydrodynamic interactions play an important role in biological processes in cellular membranes, a large separation of length scales often allowing such membranes to be treated as continuous, two-dimensional (2D) fluids. We study experimentally and theoretically the hydrodynamic interaction of pairs of inclusions in two-dimensional, fluid smectic liquid crystal films suspended in air. Such smectic membranes are ideal systems for performing controlled experiments as they are mechanically stable, of highly uniform structure, and have well-defined, variable thickness, enabling experimental investigation of the crossover from 2D to 3D hydrodynamics. Our theoretical model generalizes the Levine-MacKintosh theory of point-force response functions and uses a boundary-element approach to calculate the mobility matrix for inclusions of finite extent. We describe in detail the theoretical and computational approach previously outlined in Z. Qi et al., Phys. Rev. Lett. 113, 128304 (2014)PRLTAO0031-900710.1103/PhysRevLett.113.128304 and extend the method to study the mutual mobilities of inclusions with asymmetric shapes. The model predicts well the observed mutual mobilities of pairs of circular inclusions in films and the self-mobility of a circular inclusion in the vicinity of a linear boundary.

Strong influence of periodic boundary conditions on lateral diffusion in lipid bilayer membranes

The Saffman-Delbrück hydrodynamic model for lipid-bilayer membranes is modified to account for the periodic boundary conditions commonly imposed in molecular simulations. Predicted lateral diffusion coefficients for membrane-embedded solid bodies are sensitive to box shape and converge slowly to the limit of infinite box size, raising serious doubts for the prospects of using detailed simulations to accurately predict membrane-protein diffusivities and related transport properties. Estimates for the relative error associated with periodic boundary artifacts are 50% and higher for fully atomistic models in currently feasible simulation boxes. MARTINI simulations of LacY membrane protein diffusion and LacY dimer diffusion in DPPC membranes and lipid diffusion in pure DPPC bilayers support the underlying hydrodynamic model.

Interfacial rheometry of polymer at a water-oil interface by intra-pair magnetophoresis

We describe an interfacial rheometry technique based on pairs of micrometer-sized magnetic particles at a fluid-fluid interface. The particles are repeatedly attracted and repelled by well-controlled magnetic dipole-dipole forces, so-called interfacial rheometry by intra-pair magnetophoresis (IPM). From the forces (∼pN), displacements (∼μm) and velocities (∼μm s(-1)) of the particles we are able to quantify the interfacial drag coefficient of particles within a few seconds and over very long timescales. The use of local dipole-dipole forces makes the system insensitive to fluid flow and suited for simultaneously recording many particles in parallel over a long period of time. We apply IPM to study the time-dependent adsorption of an oil-soluble amino-modified silicone polymer at a water-oil interface using carboxylated magnetic particles. At low polymer concentration the carboxylated particles remain on the water side of the water-oil interface, while at high polymer concentrations the particles transit into the oil phase. Both conditions show a drag coefficient that does not depend on time. However, at intermediate polymer concentrations data show an increase of the interfacial drag coefficient as a function of time, with an increase over more than three orders of magnitude (10(-7) to 10(-4) N s m(-1)), pointing to a strong polymer-polymer interaction at the interface. The time-dependence of the interfacial drag appears to be highly sensitive to the polymer concentration and to the ionic strength of the aqueous phase. We foresee that IPM will be a very convenient technique to study fluid-fluid interfaces for a broad range of materials systems.

Advances in the microrheology of complex fluids

New developments in the microrheology of complex fluids are considered. Firstly the requirements for a simple modern particle tracking microrheology experiment are introduced, the error analysis methods associated with it and the mathematical techniques required to calculate the linear viscoelasticity. Progress in microrheology instrumentation is then described with respect to detectors, light sources, colloidal probes, magnetic tweezers, optical tweezers, diffusing wave spectroscopy, optical coherence tomography, fluorescence correlation spectroscopy, elastic- and quasi-elastic scattering techniques, 3D tracking, single molecule methods, modern microscopy methods and microfluidics. New theoretical techniques are also reviewed such as Bayesian analysis, oversampling, inversion techniques, alternative statistical tools for tracks (angular correlations, first passage probabilities, the kurtosis, motor protein step segmentation etc), issues in micro/macro rheological agreement and two particle methodologies. Applications where microrheology has begun to make some impact are also considered including semi-flexible polymers, gels, microorganism biofilms, intracellular methods, high frequency viscoelasticity, comb polymers, active motile fluids, blood clots, colloids, granular materials, polymers, liquid crystals and foods. Two large emergent areas of microrheology, non-linear microrheology and surface microrheology are also discussed.

Fluctuating hydrodynamics of multicomponent membranes with embedded proteins

A simulation method for the dynamics of inhomogeneous lipid bilayer membranes is presented. The membrane is treated using stochastic Saffman-Delbrück hydrodynamics, coupled to a phase-field description of lipid composition and discrete membrane proteins. Multiple applications are considered to validate and parameterize the model. The dynamics of membrane composition fluctuations above the critical point and phase separation dynamics below the critical point are studied in some detail, including the effects of adding proteins to the mixture.

Two-Point Microrheology of Phase-Separated Domains in Lipid Bilayers

Though the importance of membrane fluidity for cellular function has been well established for decades, methods for measuring lipid bilayer viscosity remain challenging to devise and implement. Recently, approaches based on characterizing the Brownian dynamics of individual tracers such as colloidal particles or lipid domains have provided insights into bilayer viscosity. For fluids in general, however, methods based on single-particle trajectories provide a limited view of hydrodynamic response. The technique of two-point microrheology, in which correlations between the Brownian dynamics of pairs of tracers report on the properties of the intervening medium, characterizes viscosity at length-scales that are larger than that of individual tracers and has less sensitivity to tracer-induced distortions, but has never been applied to lipid membranes. We present, to our knowledge, the first two-point microrheological study of lipid bilayers, examining the correlated motion of domains in phase-separated lipid vesicles and comparing one- and two-point results. We measure two-point correlation functions in excellent agreement with the forms predicted by two-dimensional hydrodynamic models, analysis of which reveals a viscosity intermediate between those of the two lipid phases, indicative of global fluid properties rather than the viscosity of the local neighborhood of the tracer.

Calculating hydrodynamic interactions for membrane-embedded objects

A recently introduced numerical scheme for calculating self-diffusion coefficients of solid objects embedded in lipid bilayer membranes is extended to enable calculation of hydrodynamic interactions between multiple objects. The method is used to validate recent analytical predictions by Oppenheimer and Diamant [Biophys. J. 96, 3041 2009] related to the coupled diffusion of membrane embedded proteins and is shown to converge to known near-field lubrication results as objects closely approach one another; however, the present methodology also applies outside of the limiting regimes where analytical results are available. Multiple different examples involving pairs of disk-like objects with various constraints imposed on their relative motions demonstrate the importance of hydrodynamic interactions in the dynamics of proteins and lipid domains on membrane surfaces. It is demonstrated that the relative change in self-diffusion of a membrane embedded object upon perturbation by a similar proximal solid object displays a maximum for object sizes comparable to the Saffman-Delbrück length of the membrane.

Monitoring phases and phase transitions in phosphatidylethanolamine monolayers using active interfacial microrheology

Active interfacial microrheology is a sensitive tool to detect phase transitions and headgroup order in phospholipid monolayers. The re-orientation of a magnetic nickel nanorod is used to explore changes in the surface rheology of 1,2-dilauroyl-sn-glycero-3-phosphoethanolamine (DLPE) and 1,2-dimyristoyl-sn-glycero-3-phosphoethanolamine (DMPE), which differ by two CH2 groups in their alkyl chains. Phosphatidylethanolamines such as DLPE and DMPE are a major component of cell membranes in bacteria and in the nervous system. At room temperature, DLPE has a liquid expanded (LE) phase for surface pressure, Π < ∼38 mN m(-1); DMPE has an LE phase for Π < ∼7 mN m(-1). In their respective LE phases, DLPE and DMPE show no measurable change in surface viscosity with Π, consistent with a surface viscosity <10(-9) N s m(-1), the resolution of our technique. However, there is a measurable, discontinuous change in the surface viscosity at the LE to liquid condensed (LC) transition for both DLPE and DMPE. This discontinuous change is correlated with a significant increase in the surface compressibility modulus (or isothermal two-dimensional bulk modulus). In the LC phase of DMPE there is an exponential increase in surface viscosity with Π consistent with a two-dimensional free area model. The second-order LC to solid (S) transition in DMPE is marked by an abrupt onset of surface elasticity; there is no measurable elasticity in the LC phase. A measurable surface elasticity in the S phase suggests a change in the molecular ordering or interactions of the DMPE headgroups that is not reflected in isotherms or in grazing incidence X-ray diffraction. This onset of measurable elasticity is also seen in DLPE, even though no indication of a LC-S transition is visible in the isotherms.

Colloidal dynamics over a tilted periodic potential: Nonequilibrium steady-state distributions

We report a systematic study of the effects of the external force F on the nonequilibrium steady-state (NESS) dynamics of the diffusing particles over a tilted periodic potential, in which detailed balance is broken due to the presence of a steady particle flux. A tilted two-layer colloidal system is constructed for this study. The periodic potential is provided by the bottom-layer colloidal spheres forming a fixed crystalline pattern on a glass substrate. The corrugated surface of the bottom colloidal crystal provides a gravitational potential field for the top-layer diffusing particles. By tilting the sample at an angle θ with respect to the vertical (gravity) direction, a tangential component of the gravitational force F is applied to the diffusing particles. The measured NESS probability density function P(ss)(x,y) of the particles is found to deviate from the equilibrium distribution P(x,y) to a different extent, depending on the driving or distance from equilibrium. The experimental results are compared with the exact solution of the one-dimensional (1D) Smoluchowski equation and the numerical results of the 2D Smoluchowski equation. From the obtained exact solution of the 1D Smoluchowski equation, we develop an analytical method to accurately extract the 1D potential U(0)(x) from the measured P(ss)(x). This work demonstrates that the tilted periodic potential provides a useful platform for the study of forced barrier-crossing dynamics beyond the Arrhenius-Kramers equation.

Temporally Anticorrelated Motion of Nanoparticles at a Liquid Interface

Quantum dots at the hexane-glycerol interface exhibited unexpected behavior including highly dynamic adsorption/desorption, where the lateral nanoparticle motion was anomalously fast immediately after adsorption and prior to desorption. At the interface, particles exhibited pseudo-Brownian lateral motion, in which the instantaneous diffusion coefficient was temporally anticorrelated, in agreement with our simulations involving fractional Brownian motion in the surface-normal direction. These phenomena suggest that, in contrast to the conventional picture for colloidal particles, nanoparticles explore a landscape of metastable interfacial positions, with different exposures to the two adjacent phases.

Brownian motion of optically anisotropic spherical particles in polymeric suspensions

We studied the rotational and translational diffusion of optically anisotropic liquid crystal particles embedded in semidiluted polymer solutions of Poly-Ethylene-Oxide (PEO) at different concentrations and different molecular weights. The polymer radius of gyration was chosen to be similar to the size of the probe particles and the polymer concentrations used are just above the crossover concentration. Thus, the system consists of solid probe particles moving in a sea of overlapping particles of similar size. We found that the behavior of both particle dynamics, rotational and translational, is similar in the range of concentrations considered here. In both cases, two linear diffusive regimes are observed, separated by a subdiffusive time interval. The spatial scale at which this intermediate regime appears shows a dependence on both the polymer concentration and molecular weight, and has a value similar to the thickness of the polymer-depleted layer usually found in this kind of systems. Additionally, we observe that the colloidal dynamic scales with the overlapping degree of the polymer particles.

Micro and macrorheology at fluid-fluid interfaces

Interfacial transport phenomena play an important role in the dynamics of liquid interfaces found in emulsions, foams, and membranes. Both macroscopic and microscopic measurements of interfacial transport and rheology can be made, the former typically relying on the use of at least millimeter-scale probes, and the latter exploiting the motion of micrometer-scale probes. Recent publications have shown multiple orders of magnitude differences between experimentally observed diffusivities in passive microrheology, and the diffusivities expected based on macroscopic measurements of the surface rheology. In the present work, interfacial rheological measurements were made with both microrheological and macrorheological methods and the results are compared for different monolayers at an air-water interface. We have identified multiple aspects of particle-tracking microrheology that can contribute to orders-of-magnitude disagreement with macrorheological methods. In particular, unintentional tracking of particles not residing at the interface, the presence of large-scale interfacial heterogeneities, and underestimating static noise can all decrease estimates of surface viscosity from particle-tracking microrheology by orders of magnitude. After taking care to address these artifacts, we show that viscosities obtained from both methods agree well for poly(tert-butyl methacrylate) (PtBMA), and for dipalmitoylphosphatidylcholine (DPPC), but disagree by orders of magnitude for hexadecanol. In poly(tert-butyl acrylate) (PtBA), large-scale heterogeneities prevented us from obtaining representative surface viscosities. By making surface viscosity measurements in an interfacial stress rheometer (ISR) with needles of different aspect ratio, we show that compressibility or Marangoni stress related effects may be contributing to the orders of magnitude disagreement in micro and macrorheological measurements observed in the hexadecanol system.

Linear and nonlinear microrheology of lysozyme layers forming at the air-water interface

We report experiments studying the mechanical evolution of layers of the protein lysozyme adsorbing at the air-water interface using passive and active microrheology techniques to investigate the linear and nonlinear rheological response, respectively. Following formation of a new interface, the linear shear rheology, which we interrogate through the Brownian motion of spherical colloids at the interface, becomes viscoelastic with a complex modulus that has approximately power-law frequency dependence. The power-law exponent characterizing this frequency dependence decreases steadily with increasing layer age. Meanwhile, the nonlinear microrheology, probed via the rotational motion of magnetic nanowires at the interface, reveals a layer response characteristic of a shear-thinning power-law fluid with a flow index that decreases with age. We discuss two possible frameworks for understanding this mechanical evolution: gelation and the formation of a soft glass phase.

Mutual diffusion of inclusions in freely suspended smectic liquid crystal films

We study experimentally and theoretically the hydrodynamic interaction of pairs of circular inclusions in two-dimensional, fluid smectic membranes suspended in air. By analyzing their Brownian motion, we find that the radial mutual mobilities of identical inclusions are independent of their size but that the angular coupling becomes strongly size dependent when their radius exceeds a characteristic hydrodynamic length. These observations are described well for arbitrary inclusion separations by a model that generalizes the Levine-MacKintosh theory of point-force response functions and uses a boundary-element approach to calculate the mobility matrix for inclusions of finite extent.

Simultaneous interfacial rheology and microstructure measurement of densely aggregated particle laden interfaces using a modified double wall ring interfacial rheometer

The study of particle laden interfaces has increased significantly due to the increasing industrial use of particle stabilized foams and Pickering emulsions, whose bulk rheology and stability are highly dependent on particle laden interface's interfacial rheology, which is a function of interfacial microstructure. To understand the physical mechanisms that dictate interfacial rheology of particle laden interfaces requires correlating rheology to microstructure. To achieve this goal, a double wall ring interfacial rheometer has been modified to allow real time, simultaneous interfacial visualization and shear rheology measurements. The development of this tool is outlined, and its ability to provide novel and unique measurements is demonstrated on a sample system. This tool has been used to examine the role of microstructure on the steady shear rheology of densely packed, aggregated particle laden interfaces at three surface concentrations. Through examination of the rheology and analysis of interfacial microstructure response to shear, a transition from shear thinning due to aggregated cluster breakup to yielding at a slip plane within the interface has been identified. Interestingly, it is found that aggregated interfaces transition to yielding well before they reached a jammed state. Furthermore, these systems undergo significant shear induced order when densely packed. These results indicate that the mechanics of these interfaces are not simply jammed or unjammed and that the interfacial rheology relationship with microstructure can give us significant insight into understanding how to engineer particle laden interfaces in the future. By examining both rheology and microstructure, the mechanisms that dictate observed rheology are now understood and can be used to predict and control the rheology of the interface.

Particle laden fluid interfaces: dynamics and interfacial rheology

We review the dynamics of particle laden interfaces, both particle monolayers and particle+surfactant monolayers. We also discuss the use of the Brownian motion of microparticles trapped at fluid interfaces for measuring the shear rheology of surfactant and polymer monolayers. We describe the basic concepts of interfacial rheology and the different experimental methods for measuring both dilational and shear surface complex moduli over a broad range of frequencies, with emphasis in the micro-rheology methods. In the case of particles trapped at interfaces the calculation of the diffusion coefficient from the Brownian trajectories of the particles is calculated as a function of particle surface concentration. We describe in detail the calculation in the case of subdiffusive particle dynamics. A comprehensive review of dilational and shear rheology of particle monolayers and particle+surfactant monolayers is presented. Finally the advantages and current open problems of the use of the Brownian motion of microparticles for calculating the shear complex modulus of monolayers are described in detail.

Surface shear inviscidity of soluble surfactants

Foam and emulsion stability has long been believed to correlate with the surface shear viscosity of the surfactant used to stabilize them. Many subtleties arise in interpreting surface shear viscosity measurements, however, and correlations do not necessarily indicate causation. Using a sensitive technique designed to excite purely surface shear deformations, we make the most sensitive and precise measurements to date of the surface shear viscosity of a variety of soluble surfactants, focusing on SDS in particular. Our measurements reveal the surface shear viscosity of SDS to be below the sensitivity limit of our technique, giving an upper bound of order 0.01 μN·s/m. This conflicts directly with almost all previous studies, which reported values up to 10(3)-10(4) times higher. Multiple control and complementary measurements confirm this result, including direct visualization of monolayer deformation, for SDS and a wide variety of soluble polymeric, ionic, and nonionic surfactants of high- and low-foaming character. No soluble, small-molecule surfactant was found to have a measurable surface shear viscosity, which seriously undermines most support for any correlation between foam stability and surface shear rheology of soluble surfactants.

Correlated diffusion of colloidal particles near a liquid-liquid interface

Optical microscopy and multi-particle tracking are used to investigate the cross-correlated diffusion of quasi two-dimensional colloidal particles near an oil-water interface. The behaviors of the correlated diffusion along longitudinal and transverse direction are asymmetric. It is shown that the characteristic length for longitudinal and transverse correlated diffusion are particle diameter and the distance from particle center to the interface, respectively, for large particle separation . The longitudinal and transverse correlated diffusion coefficient and are independent of the colloidal area fraction when , which indicates that the hydrodynamic interactions(HIs) among the particles are dominated by HIs through the surrounding fluid for small . For high area fraction , the power law exponent for the spatial decay of begins to decrease, which suggests the HIs are more contributed from the 2D particle monolayer self for large .

Universal scaling of correlated diffusion in colloidal monolayers

Using the techniques of optical microscopy and particle tracking, we measure the correlated diffusion in a monolayer of uniform silica spheres dispersed at a water-air interface. It is found that the correlated motion of the interfacial particles can be well described by two universal response functions, the normalized longitudinal and transverse diffusion coefficients D(∥)(r/r0) and D(⊥)(r/r0), where r is the interparticle distance and r0=a(λS/a)(3/2) is a new scaling length, which depends on both the Saffman length λS and particle radius a. The obtained response functions characterize the crossover behavior of the colloidal monolayers from the subphase-dominated three-dimensional hydrodynamics at low surface coverage to the monolayer-dominated 2D hydrodynamics at high concentrations. The surface viscosity ηs(2) of the colloidal monolayer obtained by two-particle rheology compares well with the one-particle measurements.

Measurement of monolayer viscosity using noncontact microrheology

Microrheological studies of phospholipid monolayers, bilayers, and other Langmuir monolayer systems are traditionally performed by observing the thermal fluctuations of tracers attached to the membrane or interface. Measurements of this type obtain surface moduli that are orders of magnitude different from those obtained using macroscopic or active techniques. These large discrepancies can result from uncertainties in the tracer's coupling to the monolayer or the local disruption of the monolayer by the tracer. To avoid such problems, we perform a microrheological experiment with the tracer particle placed at a known depth beneath the monolayer; this avoids the issues mentioned at the cost of generating a weaker, purely hydrodynamic coupling between the tracer and the monolayer. We calculate the appropriate response functions for this submerged particle microrheology and demonstrate the technique on three model monolayer systems.

Interface-induced disassembly of a self-assembled two-component nanoparticle system

We present a study of static and dynamic interfacial properties of self-assembled polyelectrolyte complex nanoparticles (size 110-120 nm) containing entrapped surfactant molecules at a fluid/fluid interface. Surface tension vs time measurements of an aqueous solution of these polyelectrolyte complex nanoparticles (PCNs) show a concentration-dependent biphasic adsorption to the air/water interface while interfacial microrheology data show a concentration-dependent initial increase in the surface viscosity (up to 10(-7) N·m/s), followed by a sharp decrease (10(-9) N·m/s). Direct visualization of the air/water interface shows disappearance of particles from the interface over time. On the basis of these observations, we propose that the PCNs at fluid/fluid interfaces exist in two states: initial accumulation of PCNs at the air/water interface as nanoparticles, followed by interface induced disassembly of the accumulated PCNs into their components. The lack of change in particle size, charge, and viscosity of the bulk aqueous solution of PCNs with time indicates that this disintegration of the self-assembled PCNs is an interfacial phenomenon. Changes in energy encountered by the PCNs at the interface lead to instability of the self-assembled system and dissociation into its components. Such systems can be used for applications requiring directed delivery and triggered release of entrapped surfactants or macromolecules at fluid/fluid interfaces.

Test of the universal scaling law of diffusion in colloidal monolayers

Using the techniques of optical microscopy and particle tracking, we measure the pair correlation function and Brownian diffusion in monolayers of strongly interacting colloidal particles suspended at or near three different interfaces and test the universal scaling law of the normalized diffusion coefficient, D[over ˜]≃e(αΔS), as a function of the excess entropy ΔS for a wide range of particle concentrations. It is found that the universal scaling law with α=1 holds well for highly charged polystyrene spheres suspended at an air-water interface, where the strong electrostatic interactions play a dominant role. For monolayer suspensions of hard-sphere-like particles, where hydrodynamic interactions become important, deviations from the universal scaling law are observed. The experiment indicates that the hydrodynamic corrections could be incorporated into the universal scaling law of diffusion with an exponent α<1.

Interfacial dynamics and rheology of polymer-grafted nanoparticles at air-water and xylene-water interfaces

Particle-stabilized emulsions and foams offer a number of advantages over traditional surfactant-stabilized systems, most notably a greater stability against coalescence and coarsening. Nanoparticles are often less effective than micrometer-scale colloidal particles as stabilizers, but nanoparticles grafted with polymers can be particularly effective emulsifiers, stabilizing emulsions for long times at very low concentrations. In this work, we characterize the long-time and dynamic interfacial tension reduction by polymer-grafted nanoparticles adsorbing from suspension and the corresponding dilatational moduli for both xylene-water and air-water interfaces. The dilatational moduli at both types of interfaces are measured by a forced sinusoidal oscillation of the interface. Surface tension measurements at the air-water interface are interpreted with the aid of independent ellipsometry measurements of surface excess concentrations. The results suggest that the ability of polymer-grafted nanoparticles to produce significant surface and interfacial tension reductions and dilatational moduli at very low surface coverage is a key factor underlying their ability to stabilize Pickering emulsions at extremely low concentrations.

Dynamic scaling in phase separation kinetics for quasi-two-dimensional membranes

We consider the dynamics of phase separation in lipid bilayer membranes, modeled as flat two-dimensional liquid sheets within a bulk fluid, both in the creeping flow approximation. We present scaling arguments that suggest asymptotic coarsening in these systems is characterized by a length scale R(t) ~ t(1/2) for critical (bicontinuous) phase separation and R(t) ~t(1/3) for off-critical concentrations (droplet morphology). In this limit, the bulk fluid is the primary source of dissipation. We also address these questions with continuum stochastic hydrodynamic simulations. We see evidence of scaling violation in critical phase separation, where isolated circular domains coarsen slower than elongated ones. However, we also find a region of apparent scaling where R(t) ~ t(1/2) is observed. This appears to be due to the competition of thermal and hydrodynamic effects. We argue that the diversity of scaling exponents measured in experiment and prior simulations can in part be attributed to certain measurements lying outside the asymptotic long-length-scale regime, and provide a framework to help understand these results. We also discuss a few simple generalizations to confined membranes and membranes in which inertia is relevant.

Interface shear microrheometer with an optically driven oscillating probe particle

We report the first experimental demonstration of an active interfacial shear microrheometer (ISMR) that uses a particle trapped by oscillating optical tweezers (OT) to probe the shear modulus G(s)(*)(ω) of a gas/liquid interface. The most significant advantages of the oscillating OT in a rheology study are: (1) very high sensitivity compared to other active microrheology methods and (2) the ability to measure both the real and imaginary components of the complex shear modulus without relying on the use of Kramers-Kronig relation, which can be problematic at low frequencies for most of the passive methods. We demonstrate the utilities of our ISMR in two case studies: (1) a 1,2-dipalmitoyl-sn-glycero-3-phosphocholine monolayer and (2) a composite of poly(styrene sulfonate) and dioctadecyldimethylammonium at the air/water interface in regimes where no other active instruments can explore.