High-frequency microrheology of wormlike micelles

Making Hidden Cell Particle Interactions Visible by Thermal Noise Frequency Decomposition

Thermal noise drives cellular structures, bacteria, and viruses on different temporal and spatial scales. Their weak interactions with their environment can change on subsecond scales. However, particle interactions can be hidden or invisible-even when measured with thermal noise sensitivity, leading to misconceptions about their binding behavior. Here, it is demonstrated how invisible particle interactions at the cell periphery become visible by MHz interferometric thermal noise tracking and frequency decomposition at a spectral update rate of only 0.5 s. The particle fluctuations are analyzed in radial and lateral directions by a viscoelastic modulus G(ω,tex ) over the experiment time tex , revealing a surprisingly similar, frequency dependent response for different cell types. This response behavior can be explained by a mathematical model for molecular scale elasticity and damping. The method to reveal hidden interactions is tested at two examples: the stiffening of macrophage filopodia tips within 2 s with particle contact invisible by the fluctuation width. Second, the extent and stiffness of the soft cell glycocalyx is measured, which can be sensed by a particle only on microsecond-timescales, but which remains invisible on time-average. This concept study shows how to uncover hidden cellular interactions, if particle motions are measured at high-speed.

Speckle rheological spectroscopy reveals wideband viscoelastic spectra of biological tissues

Mechanical transformation of tissue is not merely a symptom but a decisive driver in pathological processes. Comprising intricate network of cells, fibrillar proteins, and interstitial fluid, tissues exhibit distinct solid-(elastic) and liquid-like (viscous) behaviours that span a wide band of frequencies. Yet, characterization of wideband viscoelastic behaviour in whole tissue has not been investigated, leaving a vast knowledge gap in the higher frequency range that is linked to fundamental intracellular processes and microstructural dynamics. Here, we present wideband Speckle rHEologicAl spectRoScopy (SHEARS) to address this need. We demonstrate, for the first time, analysis of frequency-dependent elastic and viscous moduli up to the sub-MHz regime in biomimetic scaffolds and tissue specimens of blood clots, breast tumours, and bone. By capturing previously inaccessible viscoelastic behaviour across the wide frequency spectrum, our approach provides distinct and comprehensive mechanical signatures of tissues that may provide new mechanobiological insights and inform novel disease prognostication.

Physicochemical characterization of green sodium oleate-based formulations. Part 3. Molecular and collective dynamics in rodlike and wormlike micelles by proton nuclear magnetic resonance relaxation

HYPOTHESIS

Sodium oleate (NaOL) self-aggregates in water forming rodlike micelles with different length depending on NaOL concentration; when KCl is added wormlike micelles form, which entangle giving rise to a viscoelastic dispersion. It is expected that aggregates with different size and shape exhibit different internal and overall molecular motions and collective dynamics.

EXPERIMENTS

Two low viscosity NaOL/water and two viscoelastic NaOL/KCl/water formulations with different NaOL concentration (0.23 and 0.43 M) were investigated by ¹H fast field cycling NMR relaxometry over broad temperature and Larmor frequency ranges, after a first screening by ¹H and ¹³C NMR spectroscopy at high frequency.

FINDINGS

The analysis of the collected data indicated that fast conformational isomerization and rotation of NaOL about its long molecular axis and lateral diffusion of NaOL around the axis of the cylindrical aggregates are slightly affected by the aggregate shape and length. On the other hand, fluctuations of the local order director are quite different in the fluid and viscoelastic systems, reflecting the shape and size of the aggregates. Quantitative information was obtained on activation energy for fast internal and overall motions, correlation times and activation energy for lateral diffusion, and coherence length for collective order fluctuations.

Experiment and model for a Stokes layer in a strongly coupled dusty plasma

A Stokes layer, which is a flow pattern that arises in a viscous fluid adjacent to an oscillatory boundary, was observed in an experiment using a two-dimensional strongly coupled dusty plasma. Liquid conditions were maintained using laser heating, while a separate laser manipulation applied an oscillatory shear that was localized and sinusoidal. The evolution of the resulting flow was analyzed using space-time diagrams. These figures provide an intuitive visualization of a Stokes layer, including features such as the depth of penetration and wavelength. Another feature, the characteristic speed for the penetration of the oscillatory flow, also appears prominently in space-time diagrams. To model the experiment, the Maxwell-fluid model of a Stokes layer was generalized to describe a two-phase liquid. In our experiment, the phases were gas and dust, where the dust cloud was viscoelastic due to strong Coulomb coupling. The model is found to agree with the experiment, in the appearance of the space-time diagrams, and in the values of the characteristic speed, depth of penetration, and wavelength.

Multiscale Microrheology Using Fluctuating Filaments as Stealth Probes

The mechanical properties of soft materials can be probed on small length scales by microrheology. A common approach tracks fluctuations of micrometer-sized beads embedded in the medium to be characterized. This approach yields results that depend on probe size when the medium has structure on comparable length scales. Here, we introduce filament-based microrheology using high-aspect-ratio semiflexible filaments as probes. Such quasi-1D probes are much less invasive than beads due to their small cross sections. Moreover, by imaging transverse bending modes, we simultaneously determine the micromechanical response of the medium on multiple length scales corresponding to the mode wavelengths. We use semiflexible single-walled carbon nanotubes as probes that can be accurately and rapidly imaged based on their stable near-IR fluorescence. We find that the viscoelastic properties of sucrose, polyethylene oxide, and hyaluronic acid solutions measured in this way are in good agreement with those measured by conventional micro- and macrorheology.

Two step micro-rheological behavior in a viscoelastic fluid

We perform micro-rheological experiments with a colloidal bead driven through a viscoelastic worm-like micellar fluid and observe two distinctive shear thinning regimes, each of them displaying a Newtonian-like plateau. The shear thinning behavior at larger velocities is in qualitative agreement with macroscopic rheological experiments. The second process, observed at Weissenberg numbers as small as a few percent, appears to have no analog in macro-rheological findings. A simple model introduced earlier captured the observed behavior and implied that the two shear thinning processes correspond to two different length scales in the fluid. This model also reproduces oscillations, which have been observed in this system previously. While the system under macro-shear seems to be near equilibrium for shear rates in the regime of the intermediate Newtonian-like plateau, the one under micro-shear is thus still far from it. The analysis suggests the existence of a length scale of a few micrometres, the nature of which remains elusive.

Physicochemical characterization of green sodium oleate-based formulations. Part 1. Structure and rheology

HYPOTHESIS

The structure, rheology and other physicochemical properties of dilute aqueous dispersions of sodium oleate (NaOL) are well known. This paper is the first report in which a moderately concentrated (13% w/w) dispersion of NaOL in water is investigated. In fact, at this concentration the phase and rheology behavior of the surfactant remarkably deviates from those of its dilute solutions in water and a significant effect is imparted by the addition of potassium chloride.

EXPERIMENTAL

The structural, thermal and rheological properties of a 13% w/w dispersion of NaOL in water were investigated by cryo-TEM, rheology, and DSC experiments with and without the addition of potassium chloride. The system is comprised of elongated wormlike micelles that turn into a gel-like more disordered viscous material upon addition of small amounts of KCl (4% w/w).

FINDINGS

This paper illustrates the multifaceted behavior of sodium oleate dispersions at intermediate concentrations that depends on the presence of other cosolutes (such as KCl). The results show that viscoelastic aqueous dispersions of NaOL are excellent candidates for the preparation of stimuli-responsive green materials to be used in a number of different applications. We also discuss the genesis of wormlike micelles (WLMs) in terms of the general theory of self-assembly.

The Unusual Rheology of Wormlike Micelles in Glycerol: Comparable Timescales for Chain Reptation and Segmental Relaxation

Wormlike micelles (WLMs) are polymer-like chains formed by surfactant self-assembly in water. Recently, we have shown that WLMs can also be self-assembled in polar organic liquids like glycerol using a cationic surfactant and an aromatic salt. In this work, we focus on the dynamic rheology of the WLMs in glycerol and demonstrate that their rheology is very different from that of WLMs in water. Aqueous WLMs that are entangled into transient networks exhibit the rheology of a perfect Maxwell fluid having a single relaxation time t_R-thereby, their elastic modulus G' and viscous modulus G″ intersect at a crossover frequency ω_c = 1/t_R. WLMs in glycerol also form entangled networks, but they are not Maxwell fluids; instead, they exhibit a double-crossover of G' and G″ (at ω_c1 and ω_c2) within the ω-window accessible by rheometry (10^-2 to 10² rad/s). The first crossover at ω_c1 (∼1 rad/s) corresponds to the terminal relaxation time (i.e., the timescale for chains to disentangle from the transient network and relax by reptation). At the other extreme, at frequencies above ω_c2 (which is ∼10 rad/s), the rheology is dominated by the segmental motion of the chains. This "breathing regime" has rarely been accessed via experiments for aqueous WLMs because it falls around 10⁵ rad/s. We believe that glycerol, a solvent that is much more viscous than water, exerts a crucial influence in pushing ω_c2 to 1000-fold lower frequencies. On the basis of the rheology, we also hypothesize that WLMs in glycerol are shorter and weakly entangled compared to WLMs in water. Moreover, we suggest that WLMs in glycerol are "unbreakable" chains-i.e., the chains remain mostly intact instead of breaking and re-forming frequently-and this polymer-like behavior explains why the samples are quite unlike Maxwell fluids.

A symmetrical method to obtain shear moduli from microrheology

Passive microrheology typically deduces shear elastic loss and storage moduli from displacement time series or mean-squared displacements (MSD) of thermally fluctuating probe particles in equilibrium materials. Common data analysis methods use either Kramers-Kronig (KK) transformation or functional fitting to calculate frequency-dependent loss and storage moduli. We propose a new analysis method for passive microrheology that avoids the limitations of both of these approaches. In this method, we determine both real and imaginary components of the complex, frequency-dependent response function χ(ω) = χ'(ω) + iχ''(ω) as direct integral transforms of the MSD of thermal particle motion. This procedure significantly improves the high-frequency fidelity of χ(ω) relative to the use of KK transformation, which has been shown to lead to artifacts in χ'(ω). We test our method on both model and experimental data. Experiments were performed on solutions of worm-like micelles and dilute collagen solutions. While the present method agrees well with established KK-based methods at low frequencies, we demonstrate significant improvement at high frequencies using our symmetric analysis method, up to almost the fundamental Nyquist limit.

Oscillating modes of driven colloids in overdamped systems

Microscopic colloidal particles suspended in liquids are a prominent example of an overdamped system where viscous forces dominate over inertial effects. Frequently, colloids are used as sensitive probes, e.g., in biophysical applications from which molecular forces are inferred. The interpretation of such experiments rests on the assumption that, even when the particles are driven, the liquid remains in equilibrium. Here we experimentally demonstrate that this is not valid for particles in viscoelastic fluids. Even at small driving forces, we observe particle oscillations with several tens of seconds. They are attributed to non-equilibrium fluctuations of the fluid being excited by the particle’s motion. The oscillatory dynamics is in quantitative agreement with an overdamped Langevin equation with negative friction-memory term being equivalent to a stochastically driven underdamped oscillator. Such oscillatory modes are expected to widen the use of colloids as model systems but must also be considered in colloidal probe experiments.

The motion of microparticles suspended in liquids is assumed to be dominated by viscous forces. Here, Berner et al. challenge this consensus by observing underdamped particle oscillations in a viscoelastic fluid and attributing it to the non-equilibrium fluctuations of liquid excited by particles.

Viscoelastic behaviour and relaxation modes of one polyamic acid organogel studied by rheometers and dynamic light scattering

A novel polyamic acid (PAA from BAPMPO-BPDA) organogel was synthesized and characterized via dynamic light scattering (DLS), a classical rheometer, and diffusion wave spectroscopy (DWS). In situ monitoring was performed using a classical rheometer to observe the formation of the PAA organogel. The rheological curves confirm the formation of the PAA gel network and the origin of hydrogen bonding from the -NH- group (donor) and P[double bond, length as m-dash]O group (acceptor). The autocorrelation functions of PAA under different conditions (pure gel, gel with NaNO₃, gel with formamide) are measured via DLS, and different characteristic times are obtained via the CONTIN method. Three different relaxation modes of the PAA gel, i.e., fast, intermediate and slow modes, are observed. The fast and intermediate modes show a diffusive behaviour (τ ∼ q^-2), whereas the slow mode did not. When enough formamide is added into the PAA gel, the fast mode disappears; addition of enough salt (NaNO₃) leads to disappearance of the slow mode. The relationship between characteristic time and diffusion vector demonstrates that the different decorrelation modes consisted of two homodyne and two heterodyne components. Two single-exponential functions and two stretched exponential functions were used, and the different decorrelation modes of the PAA gel are expressed with a non-linear function, which fits the autocorrelation function very well. And the different decorrelation modes are also discussed. DWS results in the high-frequency region not only demonstrate the formation of a PAA gel network but also indicate that the semiflexible chains of PAA are due to electrostatic interaction. The DWS results at different time scales are analyzed by applying the de Gennes' reptation model.

Passive microrheology in the effective time domain: analyzing time dependent colloidal dispersions

We studied the aging dynamics of an aqueous suspension of LAPONITE®, a model time dependent soft glassy material, using a passive microrheology technique. This system is known to undergo physical aging during which its microstructure evolves progressively to explore lower free energy states. Optical microscopy is used to monitor the motion of micron-sized tracer probes embedded in a sample kept between two glass plates. The mean square displacements (MSD) obtained from the motion of the tracer particles show a systematic change from a purely diffusive behavior at short aging times to a subdiffusive behavior as the material ages. Interestingly, the MSDs at all the aging times as well as different LAPONITE® concentrations superpose remarkably to show a time-aging time master curve when the system is transformed from the real time domain to the effective time domain, which is obtained by rescaling the material clock to account for the age dependent relaxation time. The transformation of the master curve from the effective time domain to the real time domain leads to the prediction of the MSD in real time over a span of 5 decades when the measured data at individual aging times are only over 2 decades. Since the MSD obtained from microrheology is proportional to the creep compliance of a material, by using the Boltzmann superposition principle along with the convolution relation in the effective time domain, we predict the stress relaxation behavior of the system in real time. This work shows that the effective time approach applied to microrheology facilitates the prediction of long time creep and relaxation dynamics of a time dependent soft material by carrying out short time experiments at different aging times.

Measuring Local Viscosities near Plasma Membranes of Living Cells with Photonic Force Microscopy

The molecular processes of particle binding and endocytosis are influenced by the locally changing mobility of the particle nearby the plasma membrane of a living cell. However, it is unclear how the particle's hydrodynamic drag and momentum vary locally and how they are mechanically transferred to the cell. We have measured the thermal fluctuations of a 1 μm-sized polystyrene sphere, which was placed in defined distances to plasma membranes of various cell types by using an optical trap and fast three-dimensional (3D) interferometric particle tracking. From the particle position fluctuations on a 30 μs timescale, we determined the distance-dependent change of the viscous drag in directions perpendicular and parallel to the cell membrane. Measurements on macrophages, adenocarcinoma cells, and epithelial cells revealed a significantly longer hydrodynamic coupling length of the particle to the membrane than those measured at giant unilamellar vesicles (GUVs) or a plane glass interface. In contrast to GUVs, there is also a strong increase in friction and in mean first passage time normal to the cell membrane. This hydrodynamic coupling transfers a different amount of momentum to the interior of living cells and might serve as an ultra-soft stimulus triggering further reactions.

Accounting for inertia effects to access the high-frequency microrheology of viscoelastic fluids

We study the Brownian motion of microbeads immersed in water and in a viscoelastic wormlike micelles solution by optical trapping interferometry and diffusing wave spectroscopy. Through the mean-square displacement obtained from both techniques, we deduce the mechanical properties of the fluids at high frequencies by explicitly accounting for inertia effects of the particle and the surrounding fluid at short time scales. For wormlike micelle solutions, we recover the 3/4 scaling exponent for the loss modulus over two decades in frequency as predicted by the theory for semiflexible polymers.

Microstructure and rheology of a flow-induced structured phase in wormlike micellar solutions

Surfactant molecules can self-assemble into various morphologies under proper combinations of ionic strength, temperature, and flow conditions. At equilibrium, wormlike micelles can transition from entangled to branched and multiconnected structures with increasing salt concentration. Under certain flow conditions, micellar structural transitions follow different trajectories. In this work, we consider the flow of two semidilute wormlike micellar solutions through microposts, focusing on their microstructural and rheological evolutions. Both solutions contain cetyltrimethylammonium bromide and sodium salicylate. One is weakly viscoelastic and shear thickening, whereas the other is strongly viscoelastic and shear thinning. When subjected to strain rates of ∼10(3) s(-1) and strains of ∼10(3), we observe the formation of a stable flow-induced structured phase (FISP), with entangled, branched, and multiconnected micellar bundles, as evidenced by electron microscopy. The high stretching and flow alignment in the microposts enhance the flexibility and lower the bending modulus of the wormlike micelles. As flexible micelles flow through the microposts, it becomes energetically favorable to minimize the number of end caps while concurrently promoting the formation of cross-links. The presence of spatial confinement and extensional flow also enhances entropic fluctuations, lowering the energy barrier between states, thus increasing transition frequencies between states and enabling FISP formation. Whereas the rheological properties (zero-shear viscosity, plateau modulus, and stress relaxation time) of the shear-thickening precursor are smaller than those of the FISP, those of the shear-thinning precursor are several times larger than those of the FISP. This rheological property variation stems from differences in the structural evolution from the precursor to the FISP.

Optical tweezers with fluorescence detection for temperature-dependent microrheological measurements

We introduce a setup of optical tweezers, capable of carrying out temperature-dependent rheological measurements of soft materials. In our setup, the particle displacement is detected by imaging a bright spot due to fluorescence emitted from a dye-labeled particle against a dark background onto a quadrant photodiode. This setup has a relatively wide space around the sample that allows us to further accessorize the optical tweezers by a temperature control unit. The applicability of the setup was examined on the basis of the rheological measurements using a typical viscoelastic system, namely a worm-like micelle solution. The temperature and frequency dependences of the local viscoelastic functions of the worm-like micelle solution obtained by this setup were in good accordance with those obtained by a conventional oscillatory rheometer, confirming the capability of the optical tweezers as a tool for the local rheological measurements of soft materials. Since the optical tweezers measurements only require a tiny amount of sample (~40 μL), the rheological measurements using our setup should be useful for soft materials of which the available amount is limited.

Properties of intermediate filament networks assembled from keratin 8 and 18 in the presence of Mg²+

The mechanical properties of epithelial cells are modulated by structural changes in keratin intermediate filament networks. To investigate the relationship between network architecture and viscoelasticity, we assembled keratin filaments from recombinant keratin proteins 8 (K8) and 18 (K18) in the presence of divalent ions (Mg(2+)). We probed the viscoelastic modulus of the network by tracking the movement of microspheres embedded in the network during assembly, and studied the network architecture using scanning electron microscopy. Addition of Mg(2+) at physiological concentrations (<1 mM) resulted in networks whose structure was similar to that of keratin networks in epithelial cells. Moreover, the elastic moduli of networks assembled in vitro were found to be within the same magnitude as those measured in keratin networks of detergent-extracted epithelial cells. These findings suggest that Mg(2+)-induced filament cross-linking represents a valid model for studying the cytoskeletal mechanics of keratin networks.

High-resolution microrheology in the pericellular matrix of prostate cancer cells

Many cells express a membrane-coupled external mechanical layer, the pericellular matrix (PCM), which often contains long-chain polymers. Its role and properties are not entirely known, but its functions are believed to include physical protection, mechanosensing, chemical signalling or lubrication. The viscoelastic response of the PCM, with polysaccharides as the main structural components, is therefore crucial for the understanding of its function. We have here applied microrheology, based on optically trapped micrometre-sized colloids, to the PCM of cultured PC3 prostate cancer cells. This technology allowed us to measure the extremely soft response of the PCM, with approximately 1 µm height resolution. Exogenously added aggrecan, a hyaluronan-binding proteoglycan, caused a remarkable increase in thickness of the viscoelastic layer and also triggered filopodia-like protrusions. The viscoelastic response of the PCM, however, did not change significantly.

Treating inertia in passive microbead rheology

The dynamic modulus G(*) of a viscoelastic medium is often measured by following the trajectory of a small bead subject to Brownian motion in a method called "passive microbead rheology." This equivalence between the positional autocorrelation function of the tracer bead and G(*) is assumed via the generalized Stokes-Einstein relation (GSER). However, inertia of both bead and medium are neglected in the GSER so that the analysis based on the GSER is not valid at high frequency where inertia is important. In this paper we show how to treat both contributions to inertia properly in one-bead passive microrheological analysis. A Maxwell fluid is studied as the simplest example of a viscoelastic fluid to resolve some apparent paradoxes of eliminating inertia. In the original GSER, the mean-square displacement (MSD) of the tracer bead does not satisfy the correct initial condition. If bead inertia is considered, the proper initial condition is realized, thereby indicating an importance of including inertia, but the MSD oscillates at a time regime smaller than the relaxation time of the fluid. This behavior is rather different from the original result of the GSER and what is observed. What is more, the discrepancy from the GSER result becomes worse with decreasing bead mass, and there is an anomalous gap between the MSD derived by naïvely taking the zero-mass limit in the equation of motion and the MSD for finite bead mass as indicated by McKinley et al. [J. Rheol. 53, 1487 (2009)]. In this paper we show what is necessary to take the zero-mass limit of the bead safely and correctly without causing either the inertial oscillation or the anomalous gap, while obtaining the proper initial condition. The presence of a very small purely viscous element can be used to eliminate bead inertia safely once included in the GSER. We also show that if the medium contains relaxation times outside the window where the single-mode Maxwell behavior is observed, the oscillation can be attenuated inside the window. This attenuation is realized even in the absence of a purely viscous element. Finally, fluid inertia also affects the bead autocorrelation through the Basset force and the fluid dragged around with the bead. We show that the Basset force plays the same role as the purely viscous element in high-frequency regime, and the oscillation of MSD is suppressed if fluid density and bead density are comparable.

Viscoelastic response of a model endothelial glycocalyx

Many cells cover themselves with a multifunctional polymer coat, the pericellular matrix (PCM), to mediate mechanical interactions with the environment. A particular PCM, the endothelial glycocalyx (EG), is formed by vascular endothelial cells at their luminal side, forming a mechanical interface between the flowing blood and the endothelial cell layer. The glycosaminoglycan (GAG) hyaluronan (HA) is involved in the main functions of the EG, mechanotransduction of fluid shear stress and molecular sieving. HA, due to its length, is the only GAG in the EG or any other PCM able to form an entangled network. The mechanical functions of the EG are, however, impaired when any one of its components is removed. We here used microrheology to measure the effect of the EG constituents heparan sulfate, chondroitin sulfate, whole blood plasma and albumin on the high-bandwidth mechanical properties of a HA solution. Furthermore, we probed the effect of the hyaldherin aggrecan, a constituent of the PCM of chondrocytes, and very similar to versican (present in the PCM of various cells, and possibly in the EG). We show that components directly interacting with HA (chondroitin sulfate and aggrecan) can increase the viscoelastic shear modulus of the polymer composite.

Microrheology with fluorescence correlation spectroscopy

We show that fluorescence correlation spectroscopy (FCS) using a commercial spectrometer can be applied to passive microrheological (MR) experiments. The method probes the local rheological properties of materials on length scales of the focus dimension of the confocal microscope. For a feasibility study, we performed measurements on a high molecular weight poly(ethylene oxide)-water solution to allow direct comparison of the results to previous studies using diffusing wave spectroscopy, quasielastic light scattering, and particle tracking methods. We were able to detect mean-square center-of-mass displacements ranging from somewhat better than [SYMBOL: SEE TEXT]2(t) approximately 100 nm2 up to above Deltar2(t) approximately 10(6) nm2. Thus, we were able to derive the bulk rheological shear moduli covering more than five decades in frequency (from omega<or=10(-1) rad/s to omega approximately 10(4) rad/s). The MR results are compared to results obtained from conventional rheological experiments on the same samples using a rotational rheometer as well as a piezo-driven squeeze flow apparatus. Good agreement between MR results probing the local rheological properties and those obtained by the conventional methods measuring the macroscopic mechanical response is found in the whole frequency range. Spatial resolution in combination with the possibility of using small tracer beads open the opportunity to probe the local, length scale-dependent rheological properties in heterogeneous samples. Small tracer concentrations and small sample sizes make FCS spectroscopy a powerful tool in particular for biological and medical applications.

High-bandwidth viscoelastic properties of aging colloidal glasses and gels

We report measurements of the frequency-dependent shear moduli of aging colloidal systems that evolve from a purely low-viscosity liquid to a predominantly elastic glass or gel. Using microrheology, we measure the local complex shear modulus G;{*}(omega) over a very wide range of frequencies (from 1Hzto100kHz ). The combined use of one- and two-particle microrheology allows us to differentiate between colloidal glasses and gels-the glass is homogenous, whereas the colloidal gel shows a considerable degree of heterogeneity on length scales larger than 0.5microm . Despite this characteristic difference, both systems exhibit similar rheological behaviors which evolve in time with aging, showing a crossover from a single-power-law frequency dependence of the viscoelastic modulus to a sum of two power laws. The crossover occurs at a time t_{0} , which defines a mechanical transition point. We found that the data acquired during the aging of different samples can be collapsed onto a single master curve by scaling the aging time with t_{0} . This raises questions about the prior interpretation of two power laws in terms of a superposition of an elastic network embedded in a viscoelastic background.

Zeta potentials and Debye screening lengths of aqueous, viscoelastic surfactant solutions (cetyltrimethylammonium bromide/sodium salicylate system)

In a series of experiments, we studied the dynamic properties of aqueous surfactant solutions of cetyltrimethylammonium bromide (CTAB) at conditions after adding different amounts of sodium salicylate (NaSal). The aggregates, present in these solutions, are elongated, wormlike micelles, which tend to form entanglement networks. The viscoelastic, gel-like samples were analyzed by means of static, dynamic, and electrophoretic light scattering techniques. We separately investigated the effects of surfactant concentration and added salt on intermicellar interactions. The electrostatic interactions between the anisometric micelles were analyzed by considering the effective dimensions of the aggregates. We calculated the Debye-Huckel lengths from experimental data of the osmotic second virial coefficient and from the diffusion second virial coefficient. It turned out that the results were in good agreement with theoretically estimated values. We also measured the zeta potential and intensity of scattered light in a large range of different salt concentrations keeping the CTAB concentration constant. We observed an isoelectric point and charge reversal of the threadlike micelles at an excess salicylate concentration of about 100 mM. The observed decrease of the zeta potential points to striking processes of counterion condensation. In these solutions, the salicylate ion acts as a cosurfactant, due to its discrepancy between polar and hydrophobic groups. We also detected a simple linear correlation between the zeta potentials and the Debye screening lengths of the surfactant solutions.

Short-time inertial response of viscoelastic fluids measured with Brownian motion and with active probes

We have directly observed short-time stress propagation in viscoelastic fluids using two optically trapped particles and a fast interferometric particle-tracking technique. We have done this both by recording correlations in the thermal motion of the particles and by measuring the response of one particle to the actively oscillated second particle. Both methods detect the vortexlike flow patterns associated with stress propagation in fluids. This inertial vortex flow propagates diffusively for simple liquids, while for viscoelastic solutions the pattern spreads superdiffusively, depending on the shear modulus of the medium.

Dynamic structure factor of a stiff polymer in a glassy solution

We provide a comprehensive overview of the current theoretical understanding of the dynamic structure factor of stiff polymers in semidilute solution based on the wormlike chain (WLC) model. We extend previous work by computing exact numerical coefficients and an expression for the dynamic mean square displacement (MSD) of a free polymer and compare various common approximations for the hydrodynamic interactions, which need to be treated accurately if one wants to extract quantitative estimates for model parameters from experimental data. A recent controversy about the initial slope of the dynamic structure factor is thereby resolved. To account for the interactions of the polymer with a surrounding (sticky) polymer solution, we analyze an extension of the WLC model, the glassy wormlike chain (GWLC), which predicts near power law and logarithmic long-time tails in the dynamic structure factor.

Broad bandwidth optical and mechanical rheometry of wormlike micelle solutions

We characterize the linear viscoelastic shear properties of an aqueous wormlike micellar solution using diffusing wave spectroscopy (DWS) based tracer microrheology as well as various mechanical techniques such as rotational rheometry, oscillatory squeeze flow, and torsional resonance oscillation covering the frequency range from 10(-1) to 10(6) rad/s. Since DWS as well as mechanical oscillatory squeeze flow and torsional resonance oscillation cover a sufficiently high frequency range, the persistence length of wormlike micelles could be determined directly from rheological measurements for the first time.

Colloid dynamics in semiflexible polymer solutions

We investigate the dynamics of monodisperse colloidal polystyrene particles suspended in solutions of the semiflexible polymer filamentous actin, over a range of filament lengths that either exceed or are substantially less than the particle radius. The filament length is controlled by the capping protein gelsolin, and particle surface chemistries that minimize the adsorption of filaments are used. The particle dynamics are measured on short time scales using diffusing wave spectroscopy. A sharp transition in the initial particle diffusivity marks the expected shift from a dilute to a tightly entangled polymer network as the filament average length increases. In both the dilute and entangled regimes, the measured particle dynamics are compared with the theories of rodlike and semiflexible polymer solution rheology using the generalized Stokes-Einstein relationship. In the dilute limit, the particle dynamics are in good agreement with theory. However, in the tightly entangled regime, the particle response is consistent with polymer depleted near the surfaces of the particles. The magnitude of the depletion layer thickness depends strongly on particle size and weakly on filament length. This behavior is in agreement with nonlocal entropic repulsions and the loss of conformational entropy associated with rodlike molecules near impenetrable particles. These results illustrate the use of microrheology as a method to investigate local structure and dynamics in colloid-polymer solutions.

Correlated fluctuations of microparticles in viscoelastic solutions: quantitative measurement of material properties by microrheology in the presence of optical traps

The Brownian motions of microscopic particles in viscous or viscoelastic fluids can be used to measure rheological properties. This is the basis of recently developed one- and two-particle microrheology techniques. For increased temporal and spatial resolution, some microrheology techniques employ optical traps, which introduce additional forces on the particles. We have systematically studied the effect that confinement of particles by optical traps has on their auto- and cross-correlated fluctuations. We show that trapping causes anticorrelations in the motion of two particles at low frequencies. We demonstrate how these anticorrelations depend on trap strength and the shear modulus of viscoelastic media. We present a method to account for the effects of optical traps, which permits the quantitative measurement of viscoelastic properties in one- and two-particle microrheology over an extended frequency range in a variety of viscous and viscoelastic media.

Quasi-anomalous diffusion processes in entangled solutions of wormlike surfactant micelles

In this article, we present a detailed analysis of the dynamic properties of entangled solutions of semi-flexible, threadlike surfactant micelles. These aggregates were formed by self-association processes in aqueous solutions of cationic surfactants such as cetylpyridinium chloride (CPyCl) or cetyltrimethylammonium bromide (CTAB) after the addition of different amounts of sodium salicylate (NaSal). We performed dynamic light scattering (DLS) experiments in combination with rheological measurements in order to investigate the dynamic properties of these viscoelastic surfactant solutions. In all samples, we observed three distinct relaxation regimes: initial monoexponential decay, followed by a power-law behavior at intermediate observation times. A second monoexponential region was detected at very long times, and this terminal regime described the viscoelastic features of the samples. The fast decay mode was induced by local cooperative motions in the gellike network. The intermediate and slowest decay modes point to the existence of quasi-anomalous diffusion processes. These phenomena are characterized by linear-diffusion properties at long times, and they obeyed anomalous logarithmic slow-dynamics behavior at intermediate time zones. The anomalous diffusion properties at intermediate time scales can be induced by the bending motions of the rod-shaped micelles between two entanglement points. This regime, which was more extended at lower temperatures, was described by the power-law form of the correlation function. The power-law exponent depended on the chemical structure of the surfactants and the temperature. The power-law regime shifted toward earlier times as the gellike network evolved. The slowest mode of the correlation function coincided very well with the shear stress relaxation times of the three-dimensional, transient networks. We observed that the temperature dependence of the slowest mode followed Arrhenius laws. This result provides experimental evidence for thermally activated topological relaxation processes of random fluid phases. We obtained activation energies of approximately 30 kcal/mol, and these data coincided well with previously reported literature values, which were determined in similar surfactant solutions. Characteristic "screening lengths", over which viscous effects became important, could also be determined from the activation energy. The elastic modulus G0, calculated from the slowest mode of the correlation function, was in pretty good agreement with rheological data. The light-scattering spectra were consistent with the theoretical model of dynamical coupling of the concentration fluctuations to viscoelasticity. Since only minute sample volumes are required for advanced DLS experiments, this method to extract viscoelasticity is well suited for advanced studies of gellike biomaterials.

Short-time inertial response of viscoelastic fluids: observation of vortex propagation

We probe the response of viscous and viscoelastic fluids on micrometer and microsecond length and time scales using two optically trapped beads. In this way we resolve the flow field, which exhibits clear effects of fluid inertia. Specifically, we resolve the short-time vortex flow and the corresponding evolution of this vortex, which propagates diffusively for simple liquids. For viscoelastic fluids, this propagation is shown to be faster than diffusive and the displacement correlations reflect the frequency-dependent shear modulus of the medium.