Rheological properties of suspensions of interacting rodlike FD‐virus particles

Flows of Linear Polymer Solutions and Other Suspensions of Rod-like Particles: Anisotropic Micropolar-Fluid Theory Approach

We formulate equations governing flows of suspensions of rod-like particles. Such suspensions include linear polymer solutions, FD-virus, and worm-like micelles. To take into account the particles that form and their rotation, we treat the suspension as a Cosserat continuum and apply the theory of micropolar fluids. Anisotropy of suspensions is determined through the inclusion of the microinertia tensor in the rheological constitutive equations. We check that the model is consistent with the basic principles of thermodynamics. In addition to anisotropy, the theory also captures gradient banding instability, coexistence of isotropic and nematic phases, sustained temporal oscillations of macroscopic viscosity, shear thinning and hysteresis. For the flow between two planes, we also establish that the total flow rate depends not only on the pressure gradient, but on the history of its variation as well.

The Thermoviscosifying Behavior of Water-Soluble Polymer Based on Graft Polymerization of Pluronic F127 with Acrylamide and 2-Acrylamido-2-methylpropane Sulfonic Acid Sodium Salt

A new concept of thermoviscosifying polymers is proposed to address the problems about decreasing viscosity of polymer solution under high temperatures. However, existing thermoviscosifying polymers have complicated synthesis processes and high costs, and both of them restrict the wide practical applications of thermoviscosifying polymers. Although polyethers have the characteristics of thermal gelatinization, they just display thermoviscosifying behaviors only under extremely high concentrations (>15 wt %). Therefore, the graft copolymerization of the commercialized Pluronic F127 (PEO₁₀₀-PPO₆₅-PEO₁₀₀) with acrylamide and 2-acrylamide-methylpropionic acid sodium salt was studied here. A series of graft modified polyether polymers were prepared and it was expected to get thermoviscosifying polymers with high molecular weights and low association temperatures. Several factors on thermoviscosifying behaviors were investigated, such as polymerization condition, polymer concentration, hydrophilic monomer, molecular structure and molecular weight. It was also proven that the apparent viscosity of polymer solution is influenced by polymer concentration, molecular weight of polymer, and content of anion groups.

Effects of particle stiffness on the extensional rheology of model rod-like nanoparticle suspensions

The linear and nonlinear rheological behavior of two rod-like particle suspensions as a function of concentration is studied using small amplitude oscillatory shear, steady shear and capillary breakup extensional rheometry. The rod-like suspensions are composed of fd virus and its mutant fdY21M, which are perfectly monodisperse, with a length on the order of 900 nm. The particles are semiflexible yet differ in their persistence length. The effect of stiffness on the rheological behavior in both, shear and extensional flow, is investigated experimentally. The linear viscoelastic shear data is compared in detail with theoretical predictions for worm-like chains. The extensional properties are compared to Batchelor's theory, generalized for the shear thinning nature of the suspensions. Theoretical predictions agree well with the measured complex moduli at low concentrations as well as the nonlinear shear and elongational viscosities at high flow rates. The results in this work provide guidelines for enhancing the elongational viscosity based on purely frictional effects in the absence of strong normal forces which are characteristic for high molecular weight polymers.

The Connection between Biaxial Orientation and Shear Thinning for Quasi-Ideal Rods

The complete orientational ordering tensor of quasi-ideal colloidal rods is obtained as a function of shear rate by performing rheo-SANS (rheology with small angle neutron scattering) measurements on isotropic fd-virus suspensions in the two relevant scattering planes, the flow-gradient (1-2) and the flow-vorticity (1-3) plane. Microscopic ordering can be identified as the origin of the observed shear thinning. A qualitative description of the rheological response by Smoluchowski, as well as Doi⁻Edwards⁻Kuzuu theory is possible, as we obtain a master curve for different concentrations, scaling the shear rate with the apparent collective rotational diffusion coefficient. However, the observation suggests that the interdependence of ordering and shear thinning at small shear rates is stronger than predicted. The extracted zero-shear viscosity matches the concentration dependence of the self-diffusion of rods in semi-dilute solutions, while the director tilts close towards the flow direction already at very low shear rates. In contrast, we observe a smaller dependence on the shear rate in the overall ordering at high shear rates, as well as an ever-increasing biaxiality.

Transient viscoelasticity study of tobacco mosaic virus/Ba(2+) superlattice

Recently, we reported a new method to synthesize the rod-like tobacco mosaic virus (TMV) superlattice. To explore its potentials in nanolattice templating and tissue scaffolding, this work focused the viscoelasticity of the superlattice with a novel transient method via atomic force microscopy (AFM). For measuring viscoelasticity, in contrast to previous methods that assessed the oscillating response, the method proposed in this work enabled us to determine the transient response (creep or relaxation) of micro/nanobiomaterials. The mathematical model and numerical process were elaborated to extract the viscoelastic properties from the indentation data. The adhesion between the AFM tip and the sample was included in the indentation model. Through the functional equation method, the elastic solution for the indentation model was extended to the viscoelastic solution so that the time dependent force vs. displacement relation could be attained. To simplify the solving of the differential equation, a standard solid model was modified to obtain the elastic and viscoelastic components of the sample. The viscoelastic responses with different mechanical stimuli and the dynamic properties were also investigated.

Translational and rotational dynamics of colloidal particles in suspension: effect of shear

We report a generalization of a nonequilibrium thermodynamic theory for the mesoscopic dynamics of radially symmetric interacting particles to anisotropic pairwise interactions and attain the one- and two-particle Fokker-Planck kinetics equations at a low-density limit that provides the translational-rotational coupling of their motion due to hydrodynamic interactions, from which we derived the balance equations of linear, angular momentum, and energy dissipation due to particle interactions and energy interchange with heat bath. In this low-density approximation, an already-known virial expression for the long-time translational collective diffusion coefficient of an orientational isotropic suspension in terms of the fluid equilibrium microstructure is recovered. An external shear flow induces, in the diffusive regime, vorticity effects into the rotational diffusion property of the colloidal particles. They manifest in the appearance of the particle's rotational viscosity due to vortex flow. The Smoluchowski equation that governs the dynamical relaxation of colloid microstructure due to particle's Brownian motion under stationary flow is provided.

Depletion induced clustering in mixtures of colloidal spheres and fd-virus

We determined the phase boundary of an ideal rod-sphere mixture consisting of fd-virus, which is an established model system for mono-disperse colloidal rods, and density matched mono-disperse polystyrene beads employing diffuse wave spectroscopy. The low volume fraction of fd needed to induce a phase separation at relatively low ionic strength exemplifies the fact that slender rods are very effective depletion agents. Confocal microscopy showed that stable clusters are formed during phase separation. Relaxation after shear deformation of these clusters showed that the phase separation is gas-liquid-like and that the interfacial tension involved is very low as in colloid-polymer mixtures.

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.

Interaction potential and near wall dynamics of spherical colloids in suspensions of rod-like fd-virus

Averaged diffusivities of spherical colloids in solutions of rod-like particles, i.e. fd-virus, were measured with EWDLS and TIRM. While the experimentally observed near wall dynamics of the spheres in the absence of fd are well described by standard hydrodynamic theories, there are significant deviations at finite fd concentrations. Both experimental methods yield data which are significantly smaller than the theoretical predictions.

Diffusion of spheres in isotropic and nematic networks of rods: electrostatic interactions and hydrodynamic screening

Translational diffusion of a small charged tracer sphere in isotropic and nematic suspensions of long and thin charged rods is investigated as a function of ionic strength and rod concentration. A theory for the diffusive properties of a small sphere is developed, where both (screened) hydrodynamic interactions and charge interactions between the tracer sphere and the rod network are analyzed. Hydrodynamic interactions are formulated in terms of the hydrodynamic screening length. As yet, there are no independent theoretical predictions for the hydrodynamic screening length for rod networks. Experimental tracer-diffusion data are presented for various ionic strengths as a function of the rod concentration, both in the isotropic and nematic states. Orientational order parameters are measured for the same ionic strengths as a function of the rod concentration. The hydrodynamic screening length is determined from these experimental data and scaling relations obtained from the above mentioned theory. For the isotropic networks, a master curve is found for the hydrodynamic screening length as a function of the rod concentration. For the nematic networks the screening length turns out to be a very sensitive function of the orientational order parameter.

Diffusion of spheres in isotropic and nematic suspensions of rods

Diffusion of a small tracer sphere (apoferritin) in isotropic and nematic networks [of fd virus] is discussed. For a tracer sphere that is smaller than the mesh size of the network, screened hydrodynamic interactions between the sphere and the network determine its diffusion coefficient. A theory is developed for such interactions as well as their relation to the long-time self-diffusion coefficient. Fluorescence correlation spectroscopy measurements on mixtures of apoferritin and fd virus are presented. The long-time self-diffusion coefficient of apoferritin is measured as a function of the fd-virus concentration, both in the isotropic and nematic state, in directions parallel and perpendicular to the nematic director. The hydrodynamic screening length of the fd-virus network as a function of fd concentration is obtained by combining these experimental data with the theory. Surprisingly, the screening length increases with increasing concentration in nematic networks. This is due to the increase in the degree of alignment, which apparently leads to a strong increase of the screening length. Hydrodynamic screening is thus strongly diminished by alignment. A self-consistent calculation of the screening length does not work at higher concentrations, probably due to the strong variation of the typical incident flow fields over the contour of a rod.

Flow behavior of colloidal rodlike viruses in the nematic phase

The behavior of a colloidal suspension of rodlike fd viruses in the nematic phase, subjected to steady state and transient shear flows, is studied. The monodisperse nature of these rods combined with relatively small textural contribution to the overall stress make this a suitable model system to investigate the effects of flow on the nonequilibrium phase diagram. Transient rheological experiments are used to determine the critical shear rates at which director tumbling, wagging, and flow-aligning occurs. The present model system enables us to study the effect of rod concentration on these transitions. The results are in quantitatively agreement with the Doi-Edwards-Hess model. Moreover, we observe that there is a strong connection between the dynamic transitions and structure formation, which is not incorporated in theory.

Diffusion of spheres in crowded suspensions of rods

Translational tracer diffusion of spherical macromolecules in crowded suspensions of rodlike colloids is investigated. Experiments are done using several kinds of spherical tracers in fd-virus suspensions. A wide range of size ratios L/2a of the length L of the rods and the diameter 2a of the tracer sphere is covered by combining several experimental methods: fluorescence correlation spectroscopy for small tracer spheres, dynamic light scattering for intermediate sized spheres, and video microscopy for large spheres. Fluorescence correlation spectroscopy is shown to measure long-time diffusion only for relatively small tracer spheres. Scaling of diffusion coefficients with a/xi, predicted for static networks, is not found for our dynamical network of rods (with xi the mesh size of the network). Self-diffusion of tracer spheres in the dynamical network of freely suspended rods is thus fundamentally different as compared to cross-linked networks. A theory is developed for the rod-concentration dependence of the translational diffusion coefficient at low rod concentrations for freely suspended rods. The proposed theory is based on a variational solution of the appropriate Smoluchowski equation without hydrodynamic interactions. The theory can, in principle, be further developed to describe diffusion through dynamical networks at higher rod concentrations with the inclusion of hydrodynamic interactions. Quantitative agreement with the experiments is found for large tracer spheres, and qualitative agreement for smaller spheres. This is probably due to the increasing importance of hydrodynamic interactions as compared to direct interactions as the size of the tracer sphere decreases.

Microrheology of solutions of semiflexible biopolymer filaments using laser tweezers interferometry

Semiflexible polymers are of great biological importance in determining the mechanical properties of cells. Techniques collectively known as microrheology have recently been developed to measure the viscoelastic properties of solutions of submicroliter volumes. We employ one such technique, which uses a focused laser beam to trap a micron-sized silica bead and interferometric photodiode detection to measure passively the position fluctuations of the trapped bead with nanometer resolution and high bandwidth. The frequency-dependent complex shear modulus G*(f) can be extracted from the position fluctuations via the fluctuation-dissipation theorem and the generalized Stokes-Einstein relation. Using particle tracking microrheology, we report measurements of shear moduli of solutions of fd viruses, which are filamentous, semiflexible, and monodisperse bacteriophages, each 0.9 microm long, 7 nm in diameter, and having a persistence length of 2.2 microm. Recent theoretical treatments of semiflexible polymer dynamics provide quantitative predictions of the rheological properties of such a model system. The fd samples measured span the dilute, semidilute, and concentrated regimes. In the dilute regime G*(f) is dominated by (rigid rod) rotational relaxation, whereas the high-frequency regime reflects single-semiflexible filament dynamics consistent with the theoretical prediction. Due to the short length of fd viruses used in this study, the intermediate regime does not exhibit a well-developed plateau. A dynamic scaling analysis gives rise to a concentration scaling of c(1.36) (r=0.99) in the transition regime and a frequency scaling of f(0.63) (r=0.98) at high frequencies.

Effective interactions between electric double layers

This review summarizes and assesses recent theoretical and experimental advances, with special emphasis on the effective interaction between charge-stabilized colloids, in the bulk or in confined geometries, and on the ambiguities of defining an effective charge of the colloidal particles. Some consideration is given to the often neglected discrete solvent effects.