Session T48: Focus Session: Advanced Optical Probes of Soft Matter - Microrheology, Microbiography

Colloidal Diffusion and Hydrodynamic Interactions near Boundaries

Holographic optical tweezers allow trapping of colloidal spheres in fluid in three dimensions. In-line digital holographic microscopy yields time-resolved information on the three dimensional distribution of material in a sample. Analysis of in-line holographic images of diffusing colloidal spheres provides their three dimensional positions with nanometer resolution. We studied diffusion of colloidal spheres in three dimensions as a function of distance from boundary by analyzing particle trajectories generated by blinking optical tweezers and digital holographic microscopy. From the trajectories we calculated the particle-particle and particle-wall hydrodynamic interactions as a function of distance from the boundary. The results will help in understanding interactions between micron-sized colloidal particles near a boundary.   

Non-contact microrheology at the air-water interface

Mechanical properties of biological interfaces, such as cell membranes, have the potential to be measured with optical tweezers. We report on an approach to measure air-water interfacial properties through microrheology of particles near, but not contacting, the surface. An inverted optical tweezer traps beads of micron size or greater in the bulk, and can then translate them perpendicular to the interface. Through the measurement of thermally driven fluctuations, the mobility of the particle is found to vary as a function of submerged depth and the boundary conditions at the interface. Near a rigid wall, the mobility is confirmed to decrease in a way consistent with Fax\`{e}n's law. Very close to the free air-water interface, the mobility changes with the opposite sign, increasing by about 30{\%} at the surface, consistent with recent calculations by Shlomovitz and Levine. In addition, the presence of a Langmuir monolayer at the interface is found to significantly change the mobility of the particle close to the interface. With an accurate theory, it should be possible to infer the shear modulus of a monolayer from the fluctuations of the particle beneath the interface. Since particles are not embedded in the monolayer, this technique avoids impacting the system of study.   

Competing effects of inertia in passive microrheology

Single-point passive microrheology is generalized to account for both bead and medium inertia, and to incorporate a nonlinear optical trap or elastic trap. We first show that inertial motion of the bead couples with the elasticity of the viscoelastic material, resulting in a resonant oscillation of the mean-square displacement (MSD) of the bead well beyond the time scales of bead inertia. However, this prediction is rather different from both the original result of GSER and what is typically observed for viscoelastic materials. We next show that medium inertia tends to attenuate the oscillations because it dissipates bead energy by radiation of transverse sound waves through the Basset force. Thus, bead inertia competes with medium inertia for the MSD's oscillation. We find that it is sufficient to damp bead oscillations via Basset forces when the bead density is $>4/7$ of the fluid density, independent of most other details in the system. We also show that the non-conservative forces that exist in an optical trap [Roichman et al., PRL, \textbf{101}, 128301 (2008)] also result in circulation in a viscoelastic medium. However, the rates are not sufficiently rapid to excite elastic modes.   

High bandwidth linear viscoelastic properties of complex fluids from the measurement of their free surface fluctuations

We present a new optical method to measure the linear viscoelastic properties of materials, ranging from complex fluids to soft solids, within a large frequency range (about 0.1--10$^{4}$ Hz). The surface fluctuation specular reflection technique is based on the measurement of the thermal fluctuations of the free surfaces of materials at which a laser beam is specularly reflected. The propagation of the thermal surface waves depends on the surface tension, density, and complex viscoelastic modulus of the material. For known surface tension and density, we show that the frequency dependent elastic and loss moduli can be deduced from the fluctuation spectrum. Using a viscoelastic solid (a cross-linked PDMS), which linear viscoelastic properties are known in a large frequency range from rheometric measurements and the time--temperature superposition principle, we show that there is a good agreement between the rheological characterization provided by rheometric and fluctuation measurements. We also present measurements conducted with complex fluids that are supramolecular polymer solutions. The agreement with other low frequency and high frequency rheological measurements is again very good, and we discuss the sensitivity of the technique to surface viscoelasticity.   

Holographic microrefractometer

In-line holographic microscopy of micrometer-scale colloidal spheres yields heterodyne scattering patterns that may be interpreted with Lorenz-Mie theory to obtain precise time-resolved information on the refractive index of the suspending medium. We demonstrate this method's efficacy with measurements on calibrated refractive index standards, and apply it to measurements of varying Sucrose concentration in a microfluidic channel. Using commercial colloidal spheres as probe particles and a standard video camera for detection yields volumetric refractive index measurements with a resolution approaching $10^{-3}$~RIU for each probe particle in each holographic snapshot. The combination of spatial resolution, temporal resolution, multi-point \emph{in situ} access and technical simplicity favor this approach for cost-effective lab-on-a-chip applications.   

Studying colloidal particles on an emulsion droplet with digital holographic microscopy

Interactions between colloidal particles at a curved liquid-liquid interface remain poorly understood. We study how the interactions between micron-sized polymethyl methacrylate (PMMA) particles bound to the surface of $\sim$5 $\mu$m decane droplets dispersed in an aqueous continuous phase influence the particle dynamics. We track the 3D position of up to 6 particles moving on a droplet by imaging particle-laden droplets with digital holographic microscopy and fitting the recorded holograms with Lorenz-Mie scattering calculations. We demonstrate particle tracking with $\sim$10 nm precision in all directions at up to millisecond frame rates, which allows the study of rapid particle motions. In addition, we use negative dielectrophoresis to keep the droplets far away from the walls of our sample holders during imaging. Our measurements probe the interparticle interactions and allow us to determine particle contact angles \textit{in situ}.   

Brownian motion goes ballistic

It is the randomness that is considered the hallmark of Brownian motion, but already in Einstein's seminal 1905 paper on Brownian motion it is implied that this randomness must break down at short time scales when the inertia of the particle kicks in. As a result, the particle's trajectories should lose its randomness and become smooth. The characteristic time scale for this transition is given by the ratio of the particle's mass to its viscous drag coefficient. For a 1 $\mu $m glass particle in water and at room temperature, this timescale is on the order of 100 ns. Early calculations, however, neglected the inertia of the liquid surrounding the particle which induces a transition from random diffusive to non-diffusive Brownian motion already at much larger timescales. In this first non-diffusive regime, particles of the same size but with different densities still move at almost the same rate as a result of hydrodynamic correlations. To observe Brownian motion that is dominated by the inertia of the particle, i.e. ballistic motion, one has to observe the particle at significantly shorter time scales on the order of nanoseconds. Due to the lack of sufficiently fast and precise detectors, such experiments were so far not possible on individual particles. I will describe how we were able to observe the transition from hydrodynamically dominated Brownian motion to ballistic Brownian motion in a liquid. I will compare our data with current theories for Brownian motion on fast timescales that take into account the inertia of both the liquid and the particle. The newly gained ability to measure the fast Brownian motion of an individual particle paves the way for detailed studies of confined Brownian motion and Brownian motion in heterogeneous media. \\[4pt] [1] Einstein, A. \"{U}ber die von der molekularkinetischen Theorie der W\"{a}rme geforderte Bewegung von in ruhenden Fl\"{u}ssigkeiten suspendierten Teilchen. Ann. Phys. 322, 549--560 (1905). \\[0pt] [2] Lukic, B., S. Jeney, C. Tischer, A. J. Kulik, L. Forro, and E.-L. Florin, 2005, Direct observation of nondiffusive motion of a Brownian particle, Physical Review Letters 95, 160601 (2005). \\[0pt] [3] Huang, R., Lukic, B., Jeney, S., and E.-L. Florin, Direct observation of ballistic Brownian motion on a single particle, arXiv:1003.1980v1 (2010). \\[0pt] [4] Huang, R., I. Chavez, K.M. Taute, B. Lukic, S. Jeney, M.G. Raizen, and E.-L. Florin, 2011, Direct observation of the full transition from ballistic to diffusive Brownian motion in a liquid, Nature Physics 7, 576--580 (2011).   

Imaging dynamics and transitions in colloidal clusters

We use digital holographic microscopy to measure the relative motions of particles in colloidal clusters containing micron-sized spherical particles interacting through short-range attractions. These clusters explore many configurations as they approach their equilibrium states. Furthermore, clusters formed with weak interactions continue to transition between equal-energy configurations. We solve the challenge of tracking closely-packed, thermally-driven colloidal spheres in three dimensions by fitting the holograms using an exact solution for the scattering from multiple spheres. The method allows us to track each sphere with 10 nm precision in all three dimensions with millisecond time resolution.   

Holography of Cells fitted to DDA scattering solutions

Understanding the dynamics of cells is important to many areas of biophysics. Digital Holography offers a way to observe these dynamics at high speed, in 3D, in relatively native conditions. I will present work studying single cell dynamics through in-line digital holography. To quantify the motion of subcellular components, we fit our holograms to models of scattering based on the Discrete Dipole Approximation. In particular, we apply the technique to determine the the fluctuations of the cell membrane. The technique allows us to interrogate the cells over a broad range of time scales, from 10$^{-3}$ s up to the time scale for cell division.   

Holographic deconvolution microscopy for high resolution particle tracking

Rayleigh-Sommerfeld back-propagation can be used to generate a volumetric reconstruction of the light field responsible for the recorded intensity in an in-line hologram. Deconvolving the three dimensional light intensity with an optimal kernel derived from the Rayleigh-Sommerfeld propagator itself emphasizes the objects responsible for the scattering pattern while suppressing undesired artifacts. Bright features in the deconvolved volume may be identified with such objects as colloidal spheres and nanorods. Tracking their thermally-driven Brownian motion through multiple holographic video images provides estimates of the tracking resolution, which approaches 1 nm in all three dimensions.   

Measuring Nanoparticle Dynamics with Real-Time, 3D Tracking

Nanoparticles in liquids are an important platform for nanofabrication and nanomanufacturing processes. Few \textit{in situ }methods are available for measuring the time-resolved dynamics of individual nanoparticles at nanoscale spatial resolution. Drawing on recent advances in real-time single-particle feedback control, we have developed an apparatus that enables us to measure the 3D motion and dynamics of individual fluorescent nanoparticles in liquid environments. Real-time feedback control methods enable us to monitor the dynamics of individual nanoparticles by locking them in focus in an optical microscope, which enhances both the temporal and spatial resolution of our instrument. We applied the technique to study diffusion dynamics of polystyrene nanoparticles adsorbed at liquid-liquid interfaces. This tool can also be applied to study nanoparticle binding, self-assembly processes, and single-molecule biophysics.   

Nano-domains of high viscosity and stiffness mapped in the cell membrane by thermal noise imaging

The cell membrane is thought to contain spatial domains, created by cholesterol-lipid clusters and by interactions with the membrane cytoskeleton. The influence of these domains on membrane protein mobility and cell signaling has clearly been demonstrate. Yet, due to their small size and transient nature, the cholesterol stabilized domains cannot be visualized directly. We show here that thermal noise imaging (TNI) which tracks the diffusion of a colloid labeled membrane protein with microsecond and nanometer precision, can visualize cholesterol stabilized domains, also know as lipid raft, in intact cells. Using TNI to confine a single membrane protein to diffuse for seconds in an area of 300nm x 300nm provides sufficient data for high resolutions maps of the local diffusion, local attraction potentials and membrane stiffness. Using a GPI-anchored GFP molecule to probe the membrane of PtK2 cells we detect domains of increased membrane stiffness, which also show increase viscosity and are the preferred location for the GPI-anchored protein. These domains are further stabilized by addition of ganglioside cross linking toxins and disappear after removal of the cholesterol.   

Fluorescence correlation spectroscopy enumerate the number of nanoparticles in optical confinement

In the presence of an optical trap, both the concentration and diffusion dynamics of the nanoparticles near the center of the laser focus are affected. This phenomenon could affect the interpretation of the result from fluorescence correlation spectroscopy (FCS) where highly focused laser is often used. A recent Monte Carlo simulation study shows, for non-interacting particles under trapping energy up to 2 KT, the zero-time autocorrelation function G(0) can be used to enumerate the mean number of particles N in the trap. It is not clear, however, how particle interactions or higher trapping will affect this prediction. To address these issues, we conducted FCS experiments to examine G(0) as a function of trapping energy and particle interaction strength. We discovered that G(0) = 1/N is true up to 6 kT as long as the particle interactions are negligible. As the particle interaction is increased, the validity of the above relation quickly breaks down. We interpret our experimental finding based on the consideration of Poisson statistics.