Probing structural relaxation in complex fluids by critical fluctuations

Complex fluids, such as polymer solutions and blends, colloids, and gels, are of growing interest in fundamental and applied soft-condensed-matter science. A common feature of all such systems is the presence of a mesoscopic structural length scale intermediate between the atomic and macroscopic scales. This mesoscopic structure of complex fluids is often fragile and sensitive to external perturbations. Complex fluids are frequently viscoelastic (showing a combination of viscous and elastic behavior), with their dynamic response depending on the time and length scales. Recently, noninvasive methods to infer the rheological response of complex fluids have gained popularity through the technique of microrheology, where the diffusion of probe spheres in a viscoelastic fluid is monitored with the aid of light scattering or microscopy. Here, we propose an alternative to traditional microrheology that does not require doping of probe particles in the fluid (which can sometimes drastically alter the molecular environment). Instead, our proposed method makes use of the phenomenon of “avoided crossing” between modes associated with the structural relaxation and critical fluctuations that are spontaneously generated in the system.     

Two-point microrheology of inhomogeneous soft materials

We demonstrate a novel method for measuring the microrheology of soft viscoelastic media, based on cross correlating the thermal motion of pairs of embedded tracer particles. The method does not depend on the exact nature of the coupling between the tracers and the medium, and yields accurate rheological data for highly inhomogeneous materials. We demonstrate the accuracy of this method with a guar solution, for which other microscopic methods fail due to the polymer's mesoscopic inhomogeneity. Measurements in an F-actin solution suggest conventional microrheology measurements may not reflect the true bulk behavior.     

Microrheology probes length scale dependent rheology

We exploit the power of microrheology to measure the viscoelasticity of entangled F-actin solutions at different length scales from 1 to 100 microm over a wide frequency range. We compare the behavior of single probe-particle motion to that of the correlated motion of two particles. By varying the average length of the filaments, we identify fluctuations that dissipate diffusively over the filament length. These provide an important relaxation mechanism of the elasticity between 0.1 and 30 rad/sec.     

Microrheology of entangled F-actin solutions

We measure the viscoelasticity of entangled F-actin over length scales between 1 and 100 microm using one- and two-particle microrheology, and directly identify two distinct microscopic contributions to the elasticity. Filament entanglements lead to a frequency-independent elastic modulus over an extended frequency range of 0.01-30 rad/sec; this is probed with one-particle microrheology. Longitudinal fluctuations of the filaments increase the elastic modulus between 0.1 and 30 rad/sec at length scales up to the filament persistence length; this is probed by two-particle microrheology.     

Driven granular fluids

Dense granular media can be prepared in a stationary state by suitable driving. Such driving can be given by a random, momentum-conserving external force acting upon, say, a fluid comprised of inelastic hard spheres. While this out-of-equilibrium stationary state violates time reversal symmetry, it can still be investigated by means similar to ordinary fluids. For high enough density, the driven granular fluid undergoes a glass transition, and for this transition an extension to the mode-coupling theory can be derived. In addition to the quiescent stationary state, a kinetic theory as well as experiments in 2D for the active microrheology can be devised, where a selected intruder is pulled through the system as a probe for either constant velocity or force.     

Fluctuation-dissipation theorem in an aging colloidal glass

We provide a direct experimental test of the fluctuation-dissipation theorem (FDT) in an aging colloidal glass. The use of combined active and passive microrheology allows us to independently measure both the correlation and response functions in this nonequilibrium situation. Contrary to previous reports, we find no deviations from the FDT over several decades in frequency (1 Hz-10 kHz) and for all aging times. In addition, we find two distinct viscoelastic contributions in the aging glass, including a nearly elastic response at low frequencies that grows during aging.     

Measuring the phase of vibration of spheres in a viscoelastic medium as an image contrast modality

Detection of calcifications in breast is an important problem in the diagnosis of breast cancer. Vibro-acoustography is a recently developed method that uses the radiation force of ultrasound to create images of the mechanical response of an object at a low frequency using the magnitude or phase of the response. Small spheres are used to explore the use of the phase of vibration as a contrast modality for use in detection and identification of calcifications in breast tissue. An experiment is presented to measure the magnitude and phase of vibration at different frequencies. The theoretical and experimental results are compared for spheres of two different sizes. Phase images are shown in which five spheres of different density can be clearly distinguished from each other. With phase measurements and images, it is demonstrated that predictable image contrast exists for spheres of different density embedded in a viscoelastic medium.     

Rheological microscopy: local mechanical properties from microrheology

We demonstrate how tracer microrheology methods can be extended to study submicron scale variations in the viscoelastic response of soft materials; in particular, a semidilute solution of lambda-DNA. The polymer concentration is depleted near the surfaces of the tracer particles, within a distance comparable to the polymer correlation length. The rheology of this microscopic layer alters the tracers' motion and can be precisely quantified using one- and two-point microrheology. Interestingly, we found this mechanically distinct layer to be twice as thick as the layer of depleted concentration, likely due to solvent drainage through the locally perturbed polymer structure.     

Comparison of NMR simulations of porous media derived from analytical and voxelized representations

We develop and compare two formulations of the random-walk method, grain-based and voxel-based, to simulate the nuclear-magnetic-resonance (NMR) response of fluids contained in various models of porous media. The grain-based approach uses a spherical grain pack as input, where the solid surface is analytically defined without an approximation. In the voxel-based approach, the input is a computer-tomography or computer-generated image of reconstructed porous media. Implementation of the two approaches is largely the same, except for the representation of porous media. For comparison, both approaches are applied to various analytical and digitized models of porous media: isolated spherical pore, simple cubic packing of spheres, and random packings of monodisperse and polydisperse spheres. We find that spin magnetization decays much faster in the digitized models than in their analytical counterparts. The difference in decay rate relates to the overestimation of surface area due to the discretization of the sample; it cannot be eliminated even if the voxel size decreases. However, once considering the effect of surface-area increase in the simulation of surface relaxation, good quantitative agreement is found between the two approaches. Different grain or pore shapes entail different rates of increase of surface area, whereupon we emphasize that the value of the “surface-area-corrected” coefficient may not be universal. Using an example of X-ray-CT image of Fontainebleau rock sample, we show that voxel size has a significant effect on the calculated surface area and, therefore, on the numerically simulated magnetization response.     

Reconstruction of a hidden topography by single AFM force–distance curves

Force–distance curves have been acquired with an Atomic Force Microscope on polymethyl methacrylate with embedded glass spheres. The glass spheres provide a stiff substrate with an irregular and complex topography hidden underneath a compliant and even polymer film. This situation is a special case of a mechanical double-layer, which we examined in detail in previous experiments. Up to now uniform and non-uniform polymer films on an even substrate were examined. The film thickness on each point of the sample surface was known and force–distance curves could be averaged in groups according to the film thickness. In this way we were able to develop a semi empirical approach which allows describing the shape of averaged force–distance curves depending on the Young’s moduli of the involved materials and on the film thickness. In this experiment we reconstruct a hidden topography, i.e., we determine the polymer thickness on each point of the sample by analyzing single force–distance curves with our semi empirical equation. The accuracy reached by this approach permits to obtain a reconstruction of the shape and position of the embedded particles limited by a maximum detection depth. Single curves are also analyzed qualitatively in order to locate areas where the adhesion at the polymer/glass interface is weak or the two phases are detached.     

Chain formation in a monolayer of dipolar hard spheres under an external field

The phase behavior of a monolayer of dipolar hard spheres under an external field, which makes all dipoles of the monolayer orientate along its direction, is investigated. Using integral equation theory in the reference hypernetted chain (RHNC) approximation we calculate the correlation functions, which are used to obtain the response matrix of grand potential with respect to density fluctuations. The smallest eigenvalue of this response matrix determines the stability of the monolayer. When the smallest ei...     

The optimum elastic wave band gaps in three dimensional phononic crystals with local resonance

Using multiple-scattering theory, we investigate the optimization of the elastic wave band gaps of three dimensional three-component phononic crystals with local resonance. The optimum gaps of two systems including Au spheres coated with Pb embedded in Si matrix and Pb spheres coated with plastic embedded in Si matrix are obtained by tuning the ratio of the inner and the outer radii of the coating layers. It also shows that the elastic wave band gaps for the two systems versus the filling fractions and the radius ratio display different features.     

Casimir forces between arbitrary compact objects

We develop an exact method for computing the Casimir energy between arbitrary compact objects, either dielectrics or perfect conductors. The energy is obtained as an interaction between multipoles, generated by quantum current fluctuations. The objects' shape and composition enter only through their scattering matrices. The result is exact when all multipoles are included, and converges rapidly. A low frequency expansion yields the energy as a series in the ratio of the objects' size to their separation. As an example, we obtain this series for two dielectric spheres and the full interaction at all separations for perfectly conducting spheres.     

Stimulus-induced response patterns of medium-embedded neurons

Neuronal ensembles in living organisms are often embedded in a media that provides additional interaction pathways and autoregulation. The underlying mechanisms include but are not limited to modulatory activity of some distantly propagated neuromediators like serotonin, variation of extracellular potassium concentration in brain tissue, and calcium waves propagation in networks of astrocytes. Interaction of these diverse processes can lead to formation of complex spatiotemporal patterns, both self-sustained or triggered by external signal. Besides network effects, many dynamical features of such systems originate from reciprocal interaction between single neuron and surrounding medium. In the present paper we study the response of such systems to the application of a single stimulus pulse. We use a minimal mathematical model representing a forced excitable unit that is embedded in a diffusive or (spatially inhomogeneous) excitable medium. We illustrate three different mechanisms for the formation of response patterns: (i) self-sustained depolarization, (ii) propagation of depolarization due to “nearest-neighbor” networks, and (iii) re-entrant waves.     

Fluorescence lifetime of a single molecule as an observable of meta-basin dynamics in fluids near the glass transition

Using single molecule spectroscopy, we show that the fluorescence lifetime trajectories of single probe molecules embedded in a glass-forming polymer melt exhibit strong fluctuations of a hopping character. Using molecular dynamics simulations targeted to explain these experimental observations, we show that the lifetime fluctuations correlate strongly with the average square displacement function of the matrix particles. The latter observable is a direct probe of the meta-basin transitions in the potential energy landscape of glass-forming liquids. We thus show here that single molecule experiments can provide detailed microscopic information on system properties that hitherto have been accessible via computer simulations only.     

Motion of a solid sphere in a viscoelastic medium in response to applied acoustic radiation force: Theoretical analysis and experimental verification

The motion of a rigid sphere in a viscoelastic medium in response to an acoustic radiation force of short duration was investigated. Theoretical and numerical studies were carried out first. To verify the developed model, experiments were performed using rigid spheres of various diameters and densities embedded into tissue-like, gel-based phantoms of varying mechanical properties. A 1.5 MHz, single-element, focused transducer was used to apply the desired radiation force. Another single-element, focused transducer operating at 25 MHz was used to track the displacements of the sphere. The results of this study demonstrate good agreement between theoretical predictions and experimental measurements. The developed theoretical model accurately describes the displacement of the solid spheres in a viscoelastic medium in response to the acoustic radiation force.     

Non-brownian microrheology of a fluid-gel interface

We use stroboscopic video microscopy to study the motion of a sheared fluid-gel interface. Mechanical noise plays a role analogous to temperature, but with a low-frequency breakdown of linear response consistent with an underlying instability. We relate the fast motion of the interface to the rheological properties of the gel, laying the foundation for a non-Brownian optical microrheology.     

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.     

Single molecule lifetime fluctuations reveal segmental dynamics in polymers

We present a single molecule fluorescence study that allows one to probe the nanoscale segmental dynamics in amorphous polymer matrices. By recording single molecular lifetime trajectories of embedded fluorophores, peculiar excursions towards longer lifetimes are observed. The asymmetric response is shown to reflect variations in the photonic mode density as a result of the local density fluctuations of the surrounding polymer. We determine the number of polymer segments involved in a local segmental rearrangement volume around the probe. A common decrease of the number of segments with temperature is found for both investigated polymers, poly(styrene) and poly(isobutylmethacrylate). Our novel approach will prove powerful for the understanding of the nanoscale rearrangements in functional polymers.     

Self-consistency and search for collective effects in semiclassical pairing theory

A simple model, in which nuclei are represented as homogeneous spheres of symmetric nuclear matter, is used to study the effects of a self-consistent pairing interaction on the isoscalar nuclear response. Effects due to the finite size of nuclei are suitably taken into account. The semiclassical equations of motion derived in a previous paper for the time-dependent Hartree-Fock-Bogoliubov problem are solved in an improved (linear) approximation in which the pairing field is allowed to oscillate and to become complex. The new solutions are in good agreement with the old ones and also with the result of well-known quantum approaches. The role of the Pauli principle in eliminating one possible set of solutions is also discussed. The density response function is explicitly evaluated and it is shown that the energy-weighted sum rule is restored to its correct value by a part of the fluctuations of the imaginary pairing field. The remaining part of these imaginary fluctuations, together with the fluctuations of the real part, could give rise to collective excitations in the density response function. A detailed analysis of the monopole and quadrupole strength functions shows that there are practically no collective effects in these channels at low excitation energy.