Broad bandwidth optical and mechanical rheometry of wormlike micelle solutions

Magnesium alginate as a low-viscosity (intramolecularly cross-linked) system for the sustained and neuroprotective release of magnesium

The administration of Mg ions is advantageous in pathological scenarios such as pre-enclampsia and forms of neuroinflammation (e.g. stroke or injury); yet, few systems exist for their sustained delivery. Here, we present the (static light scattering and diffusing-wave spectroscopy) characterization of magnesium alginate (MgAlg) as a potentially injectable vehicle ifor the delivery of Mg. Differently from other divalent cations, Mg does not readily induce gelation: it acts within MgAlg coils, making them more rigid and less prone to entangle. As a result, below a threshold concentration (notionally below 0.5 % wt.) MgAlg are inherently less viscous than those of sodium alginate (NaAlg), which is a major advantage for injectables; at higher concentrations, however, (stable, Mg-based) aggregation starts occurring. Importantly, Mg can then be released e.g. in artificial cerebrospinal fluid, via a slow (hours) process of ion exchange. Finally, we here show that MgAlg protects rat neural stem cells from the consequence of an oxidative insult (100 μM H2O2), an effect that we can only ascribe to the sustained liberation of Mg ions, since it was not shown by NaAlg, MgSO4 or the NaAlg/MgSO4 combination. Our results therefore indicate that MgAlg is a promising vehicle for Mg delivery under pathological (inflammatory) conditions.

Competition among physical, chemical, and hybrid gelation mechanisms in biopolymers

Depending on how they form their linkages, biopolymer gelatin gels are commonly classified as physical, chemical, or hybrid; in gelatin hybrid gels, the physical and chemical crosslinking mechanisms occur simultaneously. The viscoelastic behavior of gels following different gelation processes was determined around the gel point. Their gel fractal dimensions were obtained using the BST-scaling model from large amplitude oscillatory shear results. The fractal dimension of hybrid gels is between 1.46 and 1.60, depending on the dominant crosslinking process. The main features of the Lissajous-Bowditch curves were determined for maturated gels that follow different gelation processes, and it is possible to observe the dominant gelation mechanism. The gelation kinetics process is followed by measuring the mean squared displacement (MSD) of microspheres embedded in gelatin solutions using diffusion wave spectroscopy, which in turn allows evaluating G'(ω) and G''(ω), the persistence length, and the mesh size as a function of time throughout the gelation process. The MSD, as a function of elapsed time from the start of the gelation process, follows a behavior that depends on the gelation processes. As time elapses after gelation starts, the persistence length of the unstructured, non-bonded flexible polymer sections decreases due to the formation of bonds. In the hybrid case, it is not a mixture of both processes; they are not independent when occurring simultaneously. The time evolution of the gel network's mesh size roughly follows an exponential decay.

Multiscale investigation of viscoelastic properties of aqueous solutions of sodium alginate and evaluation of their biocompatibility

In order to get better knowledge of mechanical properties from microscopic to macroscopic scale of biopolymers, viscoelastic bulk properties of aqueous solutions of sodium alginate were studied at different scales by combining macroscopic shear rheology (Hz), diffusing-wave spectroscopy microrheology (kHz-MHz) and Brillouin spectroscopy (GHz). Structural properties were also directly probed by small-angle X-ray scattering (SAXS). The results demonstrate a change from polyelectrolyte behavior to neutral polymer behavior by increasing polymer concentration with the determination of characteristic sizes (persistence length, correlation length). The viscoelastic properties probed at the phonon wavelength much higher than the ones obtained at low frequency reflect the variation of microscopic viscosity. First experiments obtained by metabolic activity assays with mouse embryonic fibroblasts showed biocompatibility of sodium alginate aqueous solutions in the studied range of concentrations (2.5-10 g L-1) and consequently their potential biomedical applications.

Dynamics and Rheology of Supramolecular Assemblies at Elevated Pressures

A methodology to investigate the linear viscoelastic properties of complex fluids at elevated pressures (up to 120 MPa) is presented. It is based on a dynamic light scattering (DLS) setup coupled with a stainless steel chamber, where the test sample is pressurized by means of an inert gas. The viscoelastic spectra are extracted through passive microrheology. We discuss an application to hydrogen-bonding motif 2,4-bis(2-ethylhexylureido)toluene (EHUT), which self-assembles into supramolecular structures (tubes and filaments) in apolar solvents dodecane and cyclohexane. High levels of pressure (roughly above 20 MPa) are found to slow down the terminal relaxation process; however, the increases in the entanglement plateau modulus and the associated persistence length are not significant. The concentration dependence of the plateau modulus, relaxation times (fast and slow), and correlation length is practically the same for all pressures and exhibits distinct power-law behavior in different regimes. Within the tube phase in dodecane, the relative viscosity increment is weakly enhanced with increasing pressure and reaches a plateau at about 60 MPa. In fact, depending on concentration, the application of pressure in the tube regime may lead to a transition from a viscous (unentangled) to a viscoelastic (partially entangled to well-entangled) solution. For well-entangled, long tubes, the extent of the plateau regime (ratio of high- to low-moduli crossover frequencies) increases with pressure. The collective information from these observations is summarized in a temperature-pressure state diagram. These findings provide ingredients for the formulation of a solid theoretical framework to better understand and exploit the role of pressure in the structure and dynamics of supramolecular polymers.

Activation energy, spatial confinement, and mean first passage and escape times of a tracer in a wormlike micellar fluid: an effective potential approach

Wormlike micelles are long semiflexible cylindrical polymer structures formed by amphiphiles. In solution, these linear micelles percolate in multiconected entangled networks, where cross-links can break and recombine dynamically. Technological applications of wormlike micellar fluids include tunable encapsulation/delivery of molecules or colloids in biomedicine, oil industry, and/or cleaning processes. In this work, we propose that the experimental activation energy, the spatial confinement, and the mean first passage and escape times of a spherical tracer immersed in wormlike micellar network, in which caging effects are observed, can be estimated from economic Brownian dynamics simulations of a single particle interacting with an effective one-dimensional cosine-like potential of amplitudeU₀and periodicityL. The proposed one-fitting parameter method has been used to characterize the long-time dynamics of wormlike micellar solutions formed by the self-assembly of a mixture of zwitterionic and anionic surfactants at several temperatures and different concentrations of surfactant and brine. The amplitudeU₀has displayed a good agreement regarding the corresponding experimental activation energy at different temperatures. The periodicityLhas shown to be an upper bound of the mesh sizeξand of the same order of magnitude regarding the entanglement lengthl_e, obtained from rheology and microrheology experiments. The escape time of the tracer in the effective potentialτ_escapeand the timet*, at which a change of curvature in the mean square displacement occurs, are upper and lower limits, respectively, of the experimental relaxation time. Our method is simple and fast, and we foresee that it should be applicable to model the long-time behaviour of tracers in other polymer systems, in which caging effects are present.

Microrheological Approach for Probing the Entanglement Properties of Polyelectrolyte Solutions

The entanglement dynamics and viscoelasticity of polyelectrolyte solutions remain active research topics. Previous studies have reported conflicting experimental results when compared to Dobrynin's scaling predictions derived from the Doi-Edwards (DE) tube model for entangled polymers. Herein, by combining classical bulk shear rheometry with diffusing wave spectroscopy (DWS) microrheometry, we investigate how the key viscoelastic parameters (the specific viscosity η_sp, the plateau modulus G_e, and the ratio of the reptation time to the Rouse time of an entanglement strand τ_rep/τ_e) depend on the polymer concentration for semidilute entangled (SE) solutions containing poly(sodium styrenesulfonate) with high molecular weight. Our experimental measurements yield G_e ∝ c^1.51±0.04, in good agreement with the scaling of G_e ∝ c^1.5 predicted by Dobrynin's model for salt-free polyelectrolyte SE solutions, suggesting that the electrostatic interaction influences the viscoelastic properties of polyelectrolyte SE solutions. On the other hand, the deviation in the scaling exponent for η_sp ∝ c^2.56±0.04 and τ_rep/τ_e ∝ c^1.82±0.28 is observed between our DWS experiments and Dobrynin's model prediction (∝ c^1.5), likely due to the fact that Dobrynin's scaling model does not account for mechanisms such as the contour length fluctuation, the constraint release, and the retardation of solvent dynamics, which are known to occur for SE solutions of neutral polymers. Our results demonstrate that DWS serves as a powerful rheological tool to study the entanglement dynamics of polyelectrolyte solutions. The scaling relationships obtained in this study provide new insights to the long-standing debate on the entanglement dynamics of polyelectrolyte solutions.

Microrheology to Understand the Viscosity Behavior of a Sophorolipid Biosurfactant

The microstructure of the aqueous solutions of purified acidic Sophorolipid (SL) has previously been studied using highly sophisticated methods such as SANS and Cryo-TEM. We were interested in whether (a) the main findings also apply to commercially available SL (which is a mixture of acidic and lactonic SL) and (b) more readily available methods such as DLS can be used to gain insight into the molecular aggregation of SL. Our work was motivated by the increasing interest in biosurfactants for applications in personal and household care. Moreover, the origin behind the more or less lack of rheological response to changes in pH is of practical relevance, as it is somewhat unusual for a carboxylate-group containing surfactant. By using DLS microrheology, we could elucidate the aggregation structure and dynamics of the surfactant on a microscopic scale. Surprisingly, the different degrees of protonation only impacted the microscopic properties such as exchange kinetics and the plateau values of the storage moduli.

Measuring mesoscopic scales in complex fluids embedded with giant cylindrical micelles with diffusing wave spectroscopy micro-rheology

This review paper presents a procedure for measuring the mesoscopic scales in micellar solutions embedded with giant cylindrical micelles using the mean square displacement determined with a quasi-elastic multiple light scattering method (diffusing wave spectroscopy) and theory. The mesoscopic scales of interest are the micelles' total contour length, persistence and entanglement lengths, and the mesh size of the entangled micellar network. All of them depend on the physicochemical parameters of the solutions and determine the rheological behavior. We present an assessment of the whole procedure, the scattering experiments performance, the recovery of optical parameters, which includes dealing with the light absorption and its treatment, and how to develop the micro-rheology for obtaining the mesoscopic scales in these complex fluids.

Stabilization of Supramolecular Polymer Phase at High Pressures

We utilize dynamic light scattering (DLS) and passive microrheology to examine the phase behavior of a supramolecular polymer at very high pressures. The monomer, 2,4-bis(2-ethylhexylureido)toluene (EHUT), self-assembles into supramolecular polymeric structures in the nonpolar solvent cyclohexane by means of hydrogen bonding. By varying the concentration and temperature at atmospheric pressure, the formation of the viscoelastic network (at lower temperatures) and predominantly viscous phases, based on self-assembled tube and filament structures, respectively, has been established. The associated changes in the rheological properties have been attributed to a structural thickness transition. Here, we investigate the effects of pressure variation from atmospheric up to 1 kbar at a given concentration. We construct a temperature-pressure diagram that reveals the predominance of the viscoelastic network phase at high pressures. The transition from the viscoelastic network organization of the tubes to a weaker viscous-dominated structure of the filaments is rationalized by using the Clapeyron equation, which yields an associated volume change of about 8 ų per EHUT molecule. This change is further explained by means of Molecular Dynamics simulations of the two phases, which show a decrease in the molecular volume at the filament-tube transition, originating from increased intermolecular contacts in the tube with respect to the filament. These findings offer insights into the role of pressure in stabilizing self-assemblies.

The wormlike micelles formed using an ionic liquid surfactant and polar organic solvents at low temperature without additives and their lubricant properties

Wormlike micelles (or reverse wormlike micelles) are flexible cylindrical chains that are normally formed in water (or a nonpolar organic solvent) at 25.0 °C or above; the formation of wormlike micelles at lower temperatures is rare. Here, we have reported wormlike micelles formed at low temperature using an ionic liquid surfactant (1-octadecyl-3-nonyl imidazolium bromide) in polar organic solvents (including 1,3-propanediol, 1,2-propylene glycol, N,N-dimethylformamide, and glycerol/1,2-propylene glycol mixture) in the absence of any additives. The viscoelasticity and morphology of the wormlike micelles were studied using rheology, small-angle X-ray scattering, and cryo-transmission electron microscopy. The viscoelastic properties of the wormlike micelles in polar solvents are affected by the solvent type (or the weight ratio of glycerol to 1,2-propylene glycol), surfactant concentration, and temperature. Moreover, the G' and G'' crossover twice in the dynamic curves, which is different from the case in water. The first crossover (at low frequency) corresponds to the relaxation time for the alkyl chains to disentangle from the transient network, and the second crossover (at high frequency) is related to the segmental motion of the chains. Furthermore, the tribological performance of these wormlike micelles is investigated at low temperature. It is found that the protective film (formed by the physical adhesion of the wormlike micelles on the surface of friction disk pair) and the tribochemical reaction together lead to good antifriction and antiwear performance, which indicates the application prospects of these wormlike micelles in low-temperature lubrication.

Dirhamnolipid ester - formation of reverse wormlike micelles in a binary (primerless) system

We report new dirhamnolipid ester forming reverse wormlike micelles in nonpolar solvents without the addition of any primer. Therefore, these compounds represent a rare case of a binary system showing this gel-like behavior. In this study, the influence of the concentration of the rhamnolipid ester and the ester alkyl chain length on the rheological properties of the reverse wormlike micelles in toluene was investigated in detail. Highly viscoelastic solutions were obtained even at a relatively low concentration of less than 1 wt %. The phase transition temperatures indicate that the formation of reverse wormlike micelles is favored for dirhamnolipid esters with shorter alkyl chain lengths. Oscillatory shear measurements for the viscoelastic samples reveal that the storage modulus (G') and the loss modulus (G'') cross each other and fit the Maxwell model very well in the low-ω region. As is typical for wormlike micelle systems, the normalized Cole-Cole plot of G''/G'' max against G'/G'' max was obtained as a semicircle centered at G'/G'' max = 1. The formation of network structures was also verified by polarized light microscopy. The sample was birefringent at ambient temperature and anisotropic at an elevated temperature. Differential scanning calorimetry analysis yielded a transition enthalpy of about ΔH SG/GS = ±7.2 kJ/mol. This value corresponds to a strong dispersion energy and explains the formation of the highly viscous gels by the entanglement of wormlike micelles through the interaction of the alkyl chains.

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.

Chain flexibility and dynamics of alginate solutions in different solvents

Mechanical rheometry, specifically rotational rheometry, squeeze flow, and capillary rheometry, and two microrheology methods, namely multiple-particle tracking (MPT) and diffusing wave spectroscopy (DWS) have been used to get new insight into structural and dynamical properties of alginate dissolved in solvents widely used for bioprinting, namely deionized water, phosphate-buffered saline (PBS), and Dulbecco Modified Eagle Medium (DMEM) cell media. Results demonstrate that alginate rheological properties depend on the solvent quality at concentrations higher than 1 wt.%. In this high concentration regime, in aqueous salt-free and PBS solutions, experimental scaling exponents for the concentration dependence of the specific viscosity ηsp and the plateau modulus G0 agree well with theoretical predictions for neutral polymers in good solvent whereas for the terminal relaxation time TR, the exponent is slightly higher than theoretically predicted, presumably due to the formation of aggregates. For alginate dissolved in DMEM, all exponents for ηsp, G0, and TR agree with predictions for polymers in theta solvents, which might be related to the formation of polyelectrolyte complex as a result of interactions between alginate and amino acids. Chain persistence length lp values, as determined directly from high frequency rheometry for the first time, are independent of alginate concentration and temperature. Lower absolute lp values were found for DMEM solutions compared with the other solvents. Moreover, scaling exponents for ηsp, G0, and TR do not change with temperature, within 20 and 60 °C. These findings suggest no change in the conformation of alginate chains with temperature.

Evidence of Sticky Contacts between Wormlike Micelles in Viscoelastic Surfactant Solutions

Many cationic surfactants form highly viscoelastic solutions at concentrations of only a few percent. These solutions contain wormlike micelles (WLM) which can be several micrometers long. The structural relaxation time, τ_s in these solutions can be as long as many seconds, and the zero-shear viscosity can be in the range of 10⁶ Pas. Electric birefringence measurements on such solutions showed four different relaxation times with increasing concentration. The two shortest ones, τ₁ and τ₂ in the μs region were due to the alignment of small rodlike or ringlike micelles. The third one, τ₃, was observed in the viscoelastic region in the ms region and finally, a fourth one, τ₄, which was the same as the structural relaxation time, τ_s. In this article, it is shown that the τ₃ process is due to the formation and opening of contacts between the WLM. The reason for the contacts is the attraction between the WLM which is due to the hydrophobic surfaces of the micelles. The contacts crosslink the WLM and thus form a three-dimensional network. This network is the reason for the high viscosity and viscoelastic properties of the samples. If the attraction between the WLM is reduced by adding glycerol to the solution, the viscosity of the solution breaks down. The same happens if the surface of the WLM is made hydrophilic by the addition of small amphiphilic molecules. The WLM are not destroyed by these procedures.

Diffusing wave microrheology of highly scattering concentrated monodisperse emulsions

Motivated by improvements in diffusing wave spectroscopy (DWS) for nonergodic, highly optically scattering soft matter and by cursory treatment of collective scattering effects in prior DWS microrheology experiments, we investigate the low-frequency plateau elastic shear moduli [Formula: see text] of concentrated, monodisperse, disordered oil-in-water emulsions as droplets jam. In such experiments, the droplets play dual roles both as optical probes and as the jammed objects that impart shear elasticity. Here, we demonstrate that collective scattering significantly affects DWS mean-square displacements (MSDs) in dense colloidal emulsions. By measuring and analyzing the scattering mean free path as a function of droplet volume fraction φ, we obtain a φ-dependent average structure factor. We use this to correct DWS MSDs by up to a factor of 4 and then calculate [Formula: see text] predicted by the generalized Stokes-Einstein relation. We show that DWS-microrheological [Formula: see text] agrees well with mechanically measured [Formula: see text] over about three orders of magnitude when droplets are jammed but only weakly deformed. Moreover, both of these measurements are consistent with predictions of an entropic-electrostatic-interfacial (EEI) model, based on quasi-equilibrium free-energy minimization of disordered, screened-charge-stabilized, deformable droplets, which accurately describes prior mechanical measurements of [Formula: see text] made on similar disordered monodisperse emulsions over a wide range of droplet radii and φ. This very good quantitative agreement between DWS microrheology, mechanical rheometry, and the EEI model provides a comprehensive and self-consistent view of weakly jammed emulsions. Extensions of this approach may improve DWS microrheology on other systems of dense, jammed colloids that are highly scattering.

Structure, rheology, and microrheology of wormlike micelles made of PB-PEO diblock copolymers

A diblock copolymer made of poly(1,4-butadiene)-block-polyethylene oxide, with a degree of polymerization of the polybutadiene and polyethylene oxide blocks of 37 and 57, respectively, self-assembles in water as worm-like micelles determined by small angle neutron scattering with an average diameter of ∼12.7 nm, a core radius of ∼2.7 nm, a shell radius of ∼3 nm, and an estimated persistence length of >225 nm. Worm-like micelles of almost the same diblock copolymer, but with a smaller polyethylene oxide block (degree of polymerization 45) were also measured. The worm-like micelles were also observed with negative staining using low energy electron microscopy. The boundary between dilute and semidilute regimes was estimated to be ∼0.8 wt%. The viscoelastic spectra at low and intermediate frequencies do not follow the Maxwell model. These micelles do not present the same rheological behavior of worm-like micelle solutions of conventional surfactants. The slow dynamics of the self-assembly explains this uncommon behavior for the system. Any micellar rearrangement is impeded due to the extremely high hydrophobicity of the polybutadiene block; stress mainly relaxes by the reptation mechanism. Using diffusive wave spectroscopy, we measured the mean square displacement of particles in the micellar solution. From the mean square displacement, we obtained G'(ω) and G''(ω) at high frequencies. |G*| exhibits a power law behavior showing the stress relaxation changes as frequency increases, first dominated by the Rouse-Zimm modes and then by the bending modes of the Kuhn segments. This allowed us to estimate the worm-like micelle persistence lengths that depend on the copolymer concentration.

Dynamic Light Scattering Microrheology Reveals Multiscale Viscoelasticity of Polymer Gels and Precious Biological Materials

The development of experimental techniques capable of probing the viscoelasticity of soft materials over a broad range of time scales is essential to uncovering the physics that governs their behavior. In this work, we develop a microrheology technique that requires only 12 μL of sample and is capable of resolving dynamic behavior ranging in time scales from 10^-6 to 10 s. Our approach, based on dynamic light scattering in the single-scattering limit, enables the study of polymer gels and other soft materials over a vastly larger hierarchy of time scales than macrorheology measurements. Our technique captures the viscoelastic modulus of polymer hydrogels with a broad range of stiffnesses from 10 to 10⁴ Pa. We harness these capabilities to capture hierarchical molecular relaxations in DNA and to study the rheology of precious biological materials that are impractical for macrorheology measurements, including decellularized extracellular matrices and intestinal mucus. The use of a commercially available benchtop setup that is already available to a variety of soft matter researchers renders microrheology measurements accessible to a broader range of users than existing techniques, with the potential to reveal the physics that underlies complex polymer hydrogels and biological materials.

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.

Quantifying the dispersion quality of partially aggregated colloidal dispersions by high frequency rheology

An important parameter for the performance of nanomaterials is the degree by which the nanoparticles are dispersed in a matrix. Optical microscopy or scattering methods are useful to characterise the state of dispersion, but are not generally applicable to all materials. Electron microscopy methods are laborious in preparation and typically offer only quantitative information on a very local scale. In the present work we investigate how high frequency rheological measurements can be used for partially dispersed suspensions at intermediate to higher particle loadings, even for high viscous matrices. Although the contribution of the particles is particularly visible in the low frequency linear viscoelastic behaviour, a more direct relationship between rheological properties and degree of dispersion can be derived from the loss modulus in the high frequency limit. To this end, a home-built piezo shear rheometer is constructed to extend the frequency range typically accessible by commercial rotational rheometers. Measurements on spherical silica particles, with a varying degree of dispersion in low molecular weight PDMS, are used to demonstrate how high frequency rheometry can be used to quantify dispersion quality. The linear viscoelastic properties are compared to analytical scaling theories to demonstrate that a hydrodynamically dominated regime is reached. The dependence of the relative high frequency loss modulus on volume fraction is then compared to predictions of a hydrodynamic viscosity model for the derivation of a dispersion quality index. It is used to follow the evolution of the dispersion quality as a function of mixing time and consumed power.

Molecular, Local, and Network-Level Basis for the Enhanced Stiffness of Hydrogel Networks Formed from Coassembled Racemic Peptides: Predictions from Pauling and Corey

Hydrogels prepared from self-assembling peptides are promising materials for medical applications, and using both l- and d-peptide isomers in a gel's formulation provides an intuitive way to control the proteolytic degradation of an implanted material. In the course of developing gels for delivery applications, we discovered that a racemic mixture of the mirror-image β-hairpin peptides, named MAX1 and DMAX1, provides a fibrillar hydrogel that is four times more rigid than gels formed by either peptide alone-a puzzling observation. Herein, we use transmission electron microscopy, small angle neutron scattering, solid state NMR, diffusing wave, infrared, and fluorescence spectroscopies, and modeling to determine the molecular basis for the increased mechanical rigidity of the racemic gel. We find that enantiomeric peptides coassemble in an alternating fashion along the fibril long axis, forming an extended heterochiral pleat-like β-sheet, a structure predicted by Pauling and Corey in 1953. Hydrogen bonding between enantiomers within the sheet dictates the placement of hydrophobic valine side chains in the fibrils' dry interior in a manner that allows the formation of nested hydrophobic interactions between enantiomers, interactions not accessible within enantiomerically pure fibrils. Importantly, this unique molecular arrangement of valine side chains maximizes inter-residue contacts within the core of the fibrils resulting in their local stiffening, which in turn, gives rise to the significant increase in bulk mechanical rigidity observed for the racemic hydrogel.

Local collective motion analysis for multi-probe dynamic imaging and microrheology

Dynamical artifacts, such as mechanical drift, advection, and hydrodynamic flow, can adversely affect multi-probe dynamic imaging and passive particle-tracking microrheology experiments. Alternatively, active driving by molecular motors can cause interesting non-Brownian motion of probes in local regions. Existing drift-correction techniques, which require large ensembles of probes or fast temporal sampling, are inadequate for handling complex spatio-temporal drifts and non-Brownian motion of localized domains containing relatively few probes. Here, we report an analytical method based on local collective motion (LCM) analysis of as few as two probes for detecting the presence of non-Brownian motion and for accurately eliminating it to reveal the underlying Brownian motion. By calculating an ensemble-average, time-dependent, LCM mean square displacement (MSD) of two or more localized probes and comparing this MSD to constituent single-probe MSDs, we can identify temporal regimes during which either thermal or athermal motion dominates. Single-probe motion, when referenced relative to the moving frame attached to the multi-probe LCM trajectory, provides a true Brownian MSD after scaling by an appropriate correction factor that depends on the number of probes used in LCM analysis. We show that LCM analysis can be used to correct many different dynamical artifacts, including spatially varying drifts, gradient flows, cell motion, time-dependent drift, and temporally varying oscillatory advection, thereby offering a significant improvement over existing approaches.

Revealing New Structural Insights from Surfactant Micelles through DLS, Microrheology and Raman Spectroscopy

The correlation between molecular changes and microstructural evolution of rheological properties has been demonstrated for the first time in a mixed anionic/zwitterionic surfactant-based wormlike micellar system. Utilizing a novel combination of DLS-microrheology and Raman Spectroscopy, the effect of electrostatic screening on these properties of anionic (SLES) and zwitterionic (CapB) surfactant mixtures was studied by modulating the NaCl concentration. As Raman Spectroscopy delivers information about the molecular structure and DLS-microrheology characterizes viscoelastic properties, the combination of data delivered allows for a deeper understanding of the molecular changes underlying the viscoelastic ones. The high frequency viscoelastic response obtained through DLS-microrheology has shown the persistence of the Maxwell fluid response for low viscosity solutions at high NaCl concentrations. The intensity of the Raman band at 170 cm⁻¹ exhibits very strong correlation with the viscosity variation. As this Raman band is assigned to hydrogen bonding, its variation with NaCl concentration additionally indicates differences in water structuring due to potential microstructural differences at low and high NaCl concentrations. The microstructural differences at low and high NaCl concentrations are further corroborated by persistence of a slow mode at the higher NaCl concentrations as seen through DLS measurements. The study illustrates the utility of the combined DLS, DLS-optical microrheology and Raman Spectroscopy in providing new molecular structural insights into the self-assembly process in complex fluids.

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.

Viscoelasticity and interface bending properties of lecithin reverse wormlike micelles studied by diffusive wave spectroscopy in hydrophobic environment

Upon the addition of minute quantities of water into a phosphatidylcholine (PC) solution in certain organic solvents, PC micelles elongate into giant reverse wormlike micelles that entangle and form highly viscous microemulsions, called lecithin organogels. We investigated the microrheological properties of concentrated PC-cyclohexane reverse wormlike micellar systems by diffusive wave spectroscopy (DWS) in apolar medium, combined with bulk shear rheology. We applied DWS to our oil-continuous system by using hydrophobic poly(hydroxystearic acid)-grafted PMMA particles as monodisperse tracer particles. Relevant parameters such as the micellar scission energy and persistence length were extracted from the microrheology data and interpreted according to the sphere-to-rod-to-sphere structural transition. On the basis of these quantities, we calculated the bending and saddle-splay moduli of the PC-covered water-cyclohexane interface. This approach represents a new method for the quantitative estimation of these fundamental parameters, which are thought to underpin the self-assembly of surfactants.

Microrheology of colloidal systems

Microrheology was proposed almost twenty years ago as a technique to obtain rheological properties in soft matter from the microscopic motion of colloidal tracers used as probes, either freely diffusing in the host medium, or subjected to external forces. The former case is known as passive microrheology, and is based on generalizations of the Stokes-Einstein relation between the friction experienced by the probe and the host-fluid viscosity. The latter is termed active microrheology, and extends the measurement of the friction coefficient to the nonlinear-response regime of strongly driven probes. In this review article, we discuss theoretical models available in the literature for both passive and active microrheology, focusing on the case of single-probe motion in model colloidal host media. A brief overview of the theory of passive microrheology is given, starting from the work of Mason and Weitz. Further developments include refined models of the host suspension beyond that of a Newtonian-fluid continuum, and the investigation of probe-size effects. Active microrheology is described starting from microscopic equations of motion for the whole system including both the host-fluid particles and the tracer; the many-body Smoluchowski equation for the case of colloidal suspensions. At low fluid densities, this can be simplified to a two-particle equation that allows the calculation of the friction coefficient with the input of the density distribution around the tracer, as shown by Brady and coworkers. The results need to be upscaled to agree with simulations at moderate density, in both the case of pulling the tracer with a constant force or dragging it at a constant velocity. The full many-particle equation has been tackled by Fuchs and coworkers, using a mode-coupling approximation and the scheme of integration through transients, valid at high densities. A localization transition is predicted for a probe embedded in a glass-forming host suspension. The nonlinear probe-friction coefficient is calculated from the tracer's position correlation function. Computer simulations show qualitative agreement with the theory, but also some unexpected features, such as superdiffusive motion of the probe related to the breaking of nearest-neighbor cages. We conclude with some perspectives and future directions of theoretical models of microrheology.

Attractive interactions among intermediate filaments determine network mechanics in vitro

Mechanical and structural properties of K8/K18 and vimentin intermediate filament (IF) networks have been investigated using bulk mechanical rheometry and optical microrheology including diffusing wave spectroscopy and multiple particle tracking. A high elastic modulus G₀ at low protein concentration c, a weak concentration dependency of G₀ (G₀∼c^0.5±0.1) and pronounced strain stiffening are found for these systems even without external crossbridgers. Strong attractive interactions among filaments are required to maintain these characteristic mechanical features, which have also been reported for various other IF networks. Filament assembly, the persistence length of the filaments and the network mesh size remain essentially unaffected when a nonionic surfactant is added, but strain stiffening is completely suppressed, G₀ drops by orders of magnitude and exhibits a scaling G₀∼c^1.9±0.2 in agreement with microrheological measurements and as expected for entangled networks of semi-flexible polymers. Tailless K8Δ/K18ΔT and various other tailless filament networks do not exhibit strain stiffening, but still show high G₀ values. Therefore, two binding sites are proposed to exist in IF networks. A weaker one mediated by hydrophobic amino acid clusters in the central rod prevents stretched filaments between adjacent cross-links from thermal equilibration and thus provides the high G₀ values. Another strong one facilitating strain stiffening is located in the tail domain with its high fraction of hydrophobic amino acid sequences. Strain stiffening is less pronounced for vimentin than for K8/K18 due to electrostatic repulsion forces partly compensating the strong attraction at filament contact points.

Random walks of colloidal probes in viscoelastic materials

To overcome limitations of using a single fixed time step in random walk simulations, such as those that rely on the classic Wiener approach, we have developed an algorithm for exploring random walks based on random temporal steps that are uniformly distributed in logarithmic time. This improvement enables us to generate random-walk trajectories of probe particles that span a highly extended dynamic range in time, thereby facilitating the exploration of probe motion in soft viscoelastic materials. By combining this faster approach with a Maxwell-Voigt model (MVM) of linear viscoelasticity, based on a slowly diffusing harmonically bound Brownian particle, we rapidly create trajectories of spherical probes in soft viscoelastic materials over more than 12 orders of magnitude in time. Appropriate windowing of these trajectories over different time intervals demonstrates that random walk for the MVM is neither self-similar nor self-affine, even if the viscoelastic material is isotropic. We extend this approach to spatially anisotropic viscoelastic materials, using binning to calculate the anisotropic mean square displacements and creep compliances along different orthogonal directions. The elimination of a fixed time step in simulations of random processes, including random walks, opens up interesting possibilities for modeling dynamics and response over a highly extended temporal dynamic range.

Rotational microrheology of Maxwell fluids using micron-sized wires

We demonstrate a simple method for rotational microrheology in complex fluids using micrometric wires. The three-dimensional rotational Brownian motion of the wires suspended in Maxwell fluids is measured from their projection on the focal plane of a microscope. We analyze the mean-squared angular displacement of the wires of length between 1 and 40 μm. The viscoelastic properties of the suspending fluids are examined from this analysis and found to be in good agreement with macrorheology data. Viscosities of simple and complex fluids between 10(-2) and 30 Pa s could be measured. As for the elastic modulus, values up to ∼5 Pa could be determined. This simple technique, allowing for a broad range of probed length scales, opens new perspectives in microrheology of heterogeneous materials such as gels, glasses and cells.

Laser-speckle-visibility acoustic spectroscopy in soft turbid media

We image the evolution in space and time of an acoustic wave propagating along the surface of turbid soft matter by shining coherent light on the sample. The wave locally modulates the speckle interference pattern of the backscattered light, which is recorded using a camera. We show both experimentally and theoretically how the temporal and spatial correlations in this pattern can be analyzed to obtain the acoustic wavelength and attenuation length. The technique is validated using shear waves propagating in aqueous foam. It may be applied to other kinds of acoustic waves in different forms of turbid soft matter such as biological tissues, pastes, or concentrated emulsions.

Magnetic wire-based sensors for the microrheology of complex fluids

We propose a simple microrheology technique to evaluate the viscoelastic properties of complex fluids. The method is based on the use of magnetic wires of a few microns in length submitted to a rotational magnetic field. In this work, the method is implemented on a surfactant wormlike micellar solution that behaves as an ideal Maxwell fluid. With increasing frequency, the wires undergo a transition between a steady and a hindered rotation regime. The study shows that the average rotational velocity and the amplitudes of the oscillations obey scaling laws with well-defined exponents. From a comparison between model predictions and experiments, the rheological parameters of the fluid are determined.

Rheology and DWS microrheology of concentrated suspensions of the semiflexible filamentous fd virus

Microrheology measurements were performed on suspensions of bacteriophage fd with diffusive wave spectroscopy in the concentrated regime, at different values of ionic strength. Viscosity vs. shear rate was also measured, and the effect of bacteriophage concentration and salt addition on shear thinning was determined, as well as on the peaks in the viscosity vs. shear curves corresponding to a transition from tumbling to wagging flow. The influence of concentration and salt addition on the mean square displacement of microspheres embedded in the suspensions was determined, as well as on their viscoelastic moduli up to high angular frequencies. Our results were compared with another microrheology technique previously reported where the power spectral density of thermal fluctuations of embedded micron-sized particles was evaluated. Although both results in general agree, the diffusive wave spectroscopy results are much less noisy and can reach larger frequencies. A comparison was made between measured and calculated shear modulus. Calculations were made employing the theory for highly entangled isotropic solutions of semiflexible polymers using a tube model, where various ways of calculating the needed parameters were used. Although some features are captured by the model, it is far from the experimental results mainly at high frequencies.

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.

Particle tracking microrheology of lyotropic liquid crystals

We present comprehensive results on the microrheological study of lyotropic liquid crystalline phases of various space groups constituted by water-monoglyceride (Dimodan) mixtures. In order to explore the viscoelastic properties of these systems, we use particle tracking of probe colloidal particles suitably dispersed in the liquid crystals and monitored by diffusing wave spectroscopy. The identification of the various liquid crystalline phases was separately carried out by small-angle X-ray scattering. The restricted motion of the particles was monitored and identified by the decay time of intensity autocorrelation function and the corresponding time-dependent mean square displacement (MSD), which revealed space group-dependent behavior. The characteristic time extracted by the intersection of the slopes of the MSD at short and long time scales, provided a characteristic time which could be directly compared with the relaxation time obtained by microrheology. Further direct comparison of microrheology and bulk rheology measurements was gained via the Laplace transform of the generalized time-dependent MSD, yielding the microrheology storage and loss moduli, G'(ω) and G''(ω), in the frequency domain ω. The general picture emerging from the microrheology data is that all liquid crystals exhibit viscoelastic properties in line with results from bulk rheology and the transition regime (elastic to viscous) differs according to the specific liquid crystal considered. In the case of the lamellar phase, a plastic fluid is measured by bulk rheology, while microrheology indicates viscoelastic behavior. Although we generally find good qualitative agreement between the two techniques, all liquid crystalline systems are found to relax faster when studied with microrheology. The most plausible explanation for this difference is due to the different length scales probed by the two techniques: that is, microscopical relaxation on these structured fluids, is likely to occur at shorter time scales which are more suitably probed by microrheology, whereas bulk, macroscopic relaxations occurring at longer time scales can only be probed by bulk rheology.

Self-aggregation of mixtures of oppositely charged polyelectrolytes and surfactants studied by rheology, dynamic light scattering and small-angle neutron scattering

In this study, the phase behavior, structure and properties of systems composed of the cationic, cellulose-based polycation JR 400 and the anionic surfactants sodium dodecylbenzenesulfonate (SDBS) or sodium dodecylethoxysulfate (SDES), mainly in the semidilute regime, were examined. This system shows the interesting feature of a very large viscosity increase by nearly 4 orders of magnitude as compared to the pure polymer solution already at very low concentrations of 1 wt%. By using rheology, dynamic light scattering (DLS), and small-angle neutron scattering (SANS), we are able to deduce systematic correlations between the molecular composition of the systems (characterized by the charge ratio Z=[+(polymer)]/[−(surfactant)]), their structural organization and the resulting macroscopic flow behavior. Mixtures in the semidilute regime with an excess of polycation charge form highly viscous network structures containing rodlike aggregates composed of surfactant and polyelectrolyte that are interconnected by the long JR 400 chains. Viscosity and storage modulus follow scaling laws as a function of surfactant concentration (η~c(s)(4); G(0)~c(s)(1.5)) and the very pronounced viscosity increase mainly arises from the strongly enhanced structural relaxation time of the systems. In contrast, mixtures with excess surfactant charges form solutions with viscosities even below those of the pure polymer solution. The combination of SANS, DLS, and rheology shows that the structural, dynamical, and rheological properties of these oppositely charged polyelectrolyte/surfactant systems can be controlled in a systematic fashion by appropriately choosing the systems composition.

Noise in laser speckle correlation and imaging techniques

We study the noise of the intensity variance and of the intensity correlation and structure functions measured in light scattering from a random medium in the case when these quantities are obtained by averaging over a finite number N of pixels of a digital camera. We show that the noise scales as 1/N in all cases and that it is sensitive to correlations of signals corresponding to adjacent pixels as well as to the effective time averaging (due to the finite integration time) and spatial averaging (due to the finite pixel size). Our results provide a guide to estimation of noise levels in such applications as multi-speckle dynamic light scattering, time-resolved correlation spectroscopy, speckle visibility spectroscopy, laser speckle imaging etc.

Structural hierarchy governs fibrin gel mechanics

Fibrin gels are responsible for the mechanical strength of blood clots, which are among the most resilient protein materials in nature. Here we investigate the physical origin of this mechanical behavior by performing rheology measurements on reconstituted fibrin gels. We find that increasing levels of shear strain induce a succession of distinct elastic responses that reflect stretching processes on different length scales. We present a theoretical model that explains these observations in terms of the unique hierarchical architecture of the fibers. The fibers are bundles of semiflexible protofibrils that are loosely connected by flexible linker chains. This architecture makes the fibers 100-fold more flexible to bending than anticipated based on their large diameter. Moreover, in contrast with other biopolymers, fibrin fibers intrinsically stiffen when stretched. The resulting hierarchy of elastic regimes explains the incredible resilience of fibrin clots against large deformations.

Effect of counterion binding efficiency on structure and dynamics of wormlike micelles

We have studied the effect of counterion binding efficiency on the linear viscoelastic properties of wormlike micelles formed from hexadecyltrimethylammonium bromide (CTAB) in the presence of different nonpenetrating inorganic salts: potassium bromide (KBr), sodium nitrate (NaNO(3)), and sodium chlorate (NaClO(3)). We have varied the salt/surfactant ratio R at fixed surfactant concentration of 350 mM. Results are compared to data for the system cetylpyridinium chloride (CPyCl) and the penetrating counterion sodium salicylate (NaSal) (Oelschlaeger, C.; Schopferer, M.; Scheffold, F.; Willenbacher, N. Langmuir 2009, 25, 716-723). Mechanical high-frequency rheology and diffusing wave spectroscopy (DWS) based tracer microrheology are used to determine the shear moduli G' and G'' in the frequency range from 0.1 Hz up to 1 MHz (Willenbacher, N.; Oelschlaeger, C.; Schopferer, M.; Fischer, P.; Cardinaux, F.; Scheffold, F. Phys. Rev. Lett. 2007, 99, 068302, 1-4). This enables us to determine the plateau modulus G(0), which is related to the cross-link density or mesh size of the entanglement network, the bending stiffness kappa (also expressed as persistence length l(p) = kappa/k(B)T) corresponding to the semiflexible nature of the micelles, and the scission energy E(sciss), which is related to their contour length. The viscosity maximum shifts to higher R values, and the variation of viscosity with R is less pronounced as the binding strength decreases. The plateau modulus increases with R at low ionic strength and is constant around the viscosity maximum; the increase in G(0) at high R, which is presumably due to branching, is weak compared to the system with penetrating counterion. The scission energy E(sciss) approximately = 20 k(B)T is independent of counterion binding efficiency irrespective of R and is slightly higher compared to the system CPyCl/NaSal, indicating that branching may be significant already at the viscosity maximum in this latter case. The micellar flexibility increases with increasing binding efficiency of counterions according to the Hofmeister series. The persistence length values for systems CTAB/KBr, CTAB/NaNO(3), and CTAB/NaClO(3) are 40, 34, and 29 nm, respectively, independent of R, and are significantly higher than in the case of CPyCl/NaSal.