Complex fluids, Colloidal sciences

Whereas the effect of adding soluble polymers to colloidal dispersions has been studied widely, relatively little work has been published on dispersions in polymeric liquids containing little or no solvent. Two situations will be considered in this work, the first being that in which the particles are coated in a dense layer of short, oligomeric chains having a molecular weight several orders of magnitude lower than that of the continuous phase. In this case, a steric repulsion between the particles on the length scale of the interfacial layer is, arguably, inevitable. The second is the counter case in which the tethered chains are macromolecular and the coverage is low relatively. Calculations made using Scheutjens-Fleer self-consistent field theory are used to show that, although the screening is very profound, it does not necessarily render the long-range repulsion negligible relative to the van der Waals force.

M. Camargo and C. N. Likos, Cluster formation in star-linear polymer mixtures: equilibrium and dynamical properties, in preparation. Chapter 3. M. Camargo and C. N. Likos, Unusual features of depletion interactions in soft polymer-based colloids mixed with homopolymers, Phys. Rev. Lett. 104, 078301 (2010).

This paper adopts a previously developed activation model of shear thickening, published by the authors, to sterically stabilized colloidal suspensions. When particles arranged along the compression axis of a sheared suspension, they may overcome the repulsive interaction and form hydroclusters associated with shear thickening. Taking advantage of the total interaction potential of polymeric brush coating and van der Waals attraction, the applicability of the activation model is shown within the validity range of a continuum theory. For the comparison with an extensive experimental investigation, where some parameters are not available, the onset of shear thickening can be predicted with realistic assumptions of the model parameters.

The electrosteric stabilization of model colloidal dispersions is quantified through high-frequency rheometry and complementary techniques. Model aqueous dispersions with a poly(butyl acrylate)polystyrene core and a layer of poly(methacrylic acid) grafted onto the surface are prepared and characterized. The influence of pH, electrolyte concentration, and amount of polymer in the stabilizing layer on dispersion stability and rheology is investigated. Dynamic light scattering, electrophoretic mobility, and rheology are used to quantify thickness, hydrodynamic permeability, and charge density of the stabilizing shell. A collapsed layer at low pH leads to aggregation after addition of salt, while a swollen layer at high pH induces stability. The colloidal interaction potential is deduced from measurements of the high-frequency elastic modulus using torsional resonators. The complex electrosteric forces are shown to be dominated by the excess osmotic pressure created by overlap of the electrosteric layer for particles in contact. The measured moduli G′ ∞ can be predicted quantitatively based on a simple model for the osmotic repulsion introduced by Vincent et al. [J. Colloid Interface Sci. 1986, 18, 261] without adjustable parameters.

We exploit the accuracy of the reference hypernetted chain equation (RHNC) to study the stability of charged colloidal suspensions. To achieve this objective with confidence, we first check the performance of the RHNC integral equation by comparison with Gibbs ensemble Monte Carlo (GEMC) simulations for a simple DLVO potential. The results show that the theory describes accurately reversible coagulation into the secondary minimum for a typical intercolloidal potential. Once we have established this point, we make use of the theory to analyze the capability of the DLVO potential to describe appropriately certain experimental observations, in particular, the crossover from irreversible to reversible coagulation. In this regard we found that the inclusion of an empirical hydrophobic potential crucially affects the stability properties of the suspension and leads to an adequate prediction of the crossover diameter.

Flow curve measurements are presented of a suspension of polymerically stabilized monodisperse spheres, with a polymer layer thickness of 0.7 times the core radius. At low shear rates a drastic change in behavior occurs at a critical ͑effective͒ volume fraction m . Below m the curves show a low shear Newtonian plateau. The concentration dependence of these plateaus together with m ϭ0.60 indicate that the particles can be modeled as Brownian hard spheres. Above this m the flow curves indicate plastic behavior, due to the direct contact between polymer layers of different spheres. At high shear rates the onset of Newtonian plateaus is observed with a gradual concentration dependence. The experimental high shear data are compared with model calculations, based on the dissipation due to lubrication forces treating the polymer layer as a Brinkman medium. The model we used was adapted to give a better description of the polymer layer. Fitting the experiments to obtain the permeability of the polymer layer, we found a value in the range of values expected from polymer theory. Our adapted lubrication model was also used to reanalyze experimental data for other polymerically stabilized suspensions. ͓S1063-651X͑99͒02703-8͔

The authors previously introduced an activation model for the onset of shear thickening in electrically stabilized colloidal suspensions. It predicts that shear thickening occurs, when particles arranged along the compression axis in a sheared suspension do overcome the electrostatic repulsion at a critical shear stress, and are captured in the primary minimum of the DLVO interaction potential. A comparison with an experimental investigation on non-aqueous silica suspensions, carried out by Maranzano and Wagner, is performed. For particle systems that fall into the applicability range of the theory, a good coincidence between the experimental data and the model predictions can be found.

A model of shear thickening in dense suspensions of Brownian soft sphere colloidal particles is established. It suggests that shear thickening in soft sphere suspensions can be interpreted as a shear induced phase transition. Based on a Landau model of the coagulation transition of stabilized colloidal particles, taking the coupling between order parameter fluctuations and the local strain-field into account, the model suggests the occurrence of clusters of coagulated particles (subcritical bubbles) by applying a continuous shear perturbation. The critical shear stress of shear thickening in soft sphere suspensions is derived while reversible shear thickening and irreversible shear thickening have the same origin. The comparison of the theory with an experimental investigation of electrically stabilized colloidal suspensions confirms the presented approach.

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Static, thermodynamic, and rheological data of polymerically stabilized colloidal dispersions are usually predicted on the basis of ad hoc hard sphere models. Here, the specific effects of the grafted polymers are explicitly taken into account through a hard core plus a soft tail potential. A systematic analysis of structural and thermodynamic quantities is performed by using the thermodynamically self-consistent integral equation scheme of Rogers and Young. Criteria to construct reference hard sphere systems, showing quantitative agreement with the true systems, are presented. It is shown that there are regions of the potential parameter space where the hard sphere modelization is not possible and where the true potential has to be used.

Flow curve measurements are presented of a suspension of polymerically stabilized monodisperse spheres, with a polymer layer thickness of 0.7 times the core radius. At low shear rates a drastic change in behavior occurs at a critical ͑effective͒ volume fraction m. Below m the curves show a low shear Newtonian plateau. The concentration dependence of these plateaus together with m ϭ0.60 indicate that the particles can be modeled as Brownian hard spheres. Above this m the flow curves indicate plastic behavior, due to the direct contact between polymer layers of different spheres. At high shear rates the onset of Newtonian plateaus is observed with a gradual concentration dependence. The experimental high shear data are compared with model calculations, based on the dissipation due to lubrication forces treating the polymer layer as a Brinkman medium. The model we used was adapted to give a better description of the polymer layer. Fitting the experiments to obtain the permeability of the polymer layer, we found a value in the range of values expected from polymer theory. Our adapted lubrication model was also used to reanalyze experimental data for other polymerically stabilized suspensions. ͓S1063-651X͑99͒02703-8͔

A binary solvent mixture close to critical demixing experiences fluctuations whose correlation length, ξ, diverges as the critical point is approached. The solvent-mediated (SM) interaction that arises between a pair of colloids immersed in such a near-critical solvent can be long-ranged and this so-called critical Casimir interaction is well-studied. How a (dense) suspension of colloids will self-assemble under these conditions is poorly understood. Using a two-dimensional lattice model for the solvent and hard disks to represent the colloids, we perform extensive Monte Carlo simulations to investigate the phase behaviour of this model colloidal suspension as a function of colloid size and wettability under conditions where the solvent reservoir is supercritical. Unlike most other approaches, where the solvent is modelled as an implicit background, our model employs an explicit solvent and treats the suspension as a ternary mixture. This enables us to capture important features, in...

Using density functional theory and Monte Carlo simulations we investigate the Asakura-Oosawa-Vrij mixture of hard sphere colloids and non-adsorbing ideal polymers under selective confinement of the colloids to a planar slab geometry. This is a model for confinement of colloid-polymer mixtures by either two parallel walls with a semi-permeable polymer coating or through the use of laser tweezers. We find that such a pore favours the colloidal gas over the colloidal liquid phase and induces capillary evaporation. A treatment based on the Kelvin equation gives a good account of the location of the capillary binodal for large slit widths. The colloid density profile is found to exhibit a minimum (maximum) at contact with the wall for large (small) slit widths.

The flow curve of sheared concentrated colloids can show a region of shear thickening. The underlying mechanisms involved in this effect has long been an issue. Recently the author and co-workers have used Stokesian dynamics approximated for high concentrations to simulate models of polymer coated particles in the thickening regime. This work continues the search for a particle level of understanding these systems in the thickening regime. Previous work found that shear thickening is associated with the formation of a network of contacts between polymer coats. Previous work by the author has examined the fabric (geometry) and texture (density distribution) of the contact network. However despite this many-body effect, it was also found that a very simple mean-field type argument at the level of a pair of particles in contact relates the particle interaction laws to the thickening part of the flow curve up to an unknown factor. In the argument this factor is determined by aspects of the destruction of particle contacts. In this paper several new results are reported. The first concerns the definition of the network and its coordination. The paper contrasts systems with different thickness of polymer coats and gives tentative evidence that the network formed sits close to what is known as the iso-static coordination. The second set of issues concerns the analysis of the lifetimes of particle contacts-in effect an examination of the unknown factor and assumptions of the pair argument. A surprising result is that some particle pairs have relatively long lifetimes. Finally, data is reported for the stress fluctuations in the thickening regime.

We examine the demixing transition in star polymer-colloid mixtures for star arm numbers f = 2, 6, 16, 32 and different star-colloid size ratios. Theoretically, we solve the thermodynamically self-consistent Rogers-Young integral equations for binary mixtures using three effective pair potentials obtained from direct molecular computer simulations. The numerical results show a spinodal instability. The demixing binodals are approximately calculated, and found to be consistent with experimental observations.

A binary solvent mixture close to critical demixing experiences fluctuations whose correlation length, ξ, diverges as the critical point is approached. The solvent-mediated (SM) interaction that arises between a pair of colloids immersed in such a near-critical solvent can be long-ranged and this so-called critical Casimir interaction is well-studied. How a (dense) suspension of colloids will self-assemble under these conditions is poorly understood. Using a two-dimensional lattice model for the solvent and hard disks to represent the colloids, we perform extensive Monte Carlo simulations to investigate the phase behaviour of this model colloidal suspension as a function of colloid size and wettability under conditions where the solvent reservoir is supercritical. Unlike most other approaches, where the solvent is modelled as an implicit background, our model employs an explicit solvent and treats the suspension as a ternary mixture. This enables us to capture important features, in...

This paper exposes an extension of an activation model previously published by the authors. When particles arranged along the compression axis of a sheared suspension, they may overcome the electrostatic repulsion and form force chains associated with shear thickening. A percolation based consideration, allows an estimation of the impact of the force chains on a flowing suspension. It suggests that, similar to mode-coupling models, the suspension becomes unstable before the critical stress evaluated from the activation model is reached. The theory is applicable only to discontinuous shear thickening, and the predictions are compared with results from two experimental studies on aqueous suspensions of inorganic oxides; in one of them hydration repulsion and in the other hydrophobic attraction can be expected. It is shown that the incorporation of non-DLVO forces greatly improve predictions of the shear thickening instability.

We exploit the accuracy of the reference hypernetted chain equation (RHNC) to study the stability of charged colloidal suspensions. To achieve this objective with confidence, we first check the performance of the RHNC integral equation by comparison with Gibbs ensemble Monte Carlo (GEMC) simulations for a simple DLVO potential. The results show that the theory describes accurately reversible coagulation into the secondary minimum for a typical intercolloidal potential. Once we have established this point, we make use of the theory to analyze the capability of the DLVO potential to describe appropriately certain experimental observations, in particular, the crossover from irreversible to reversible coagulation. In this regard we found that the inclusion of an empirical hydrophobic potential crucially affects the stability properties of the suspension and leads to an adequate prediction of the crossover diameter.

ABSTRACT: Manipulation of the micro and nanoscale objects is of great interest in a variety of engineering and scientific areas. Dielectrophoretic force (DEP) induced technique is predominantly used in the manipulation process in a liquid medium. The phenomenon behind DEP involves the creation of electric forces on particles to generate momentum in non-uniform electric fields, usually resulting from AC electric fields. In the present study, the effects of DEP for the manipulation of organic and inorganic particles at micro and nanoscale is discussed in detail.

Suspension rheology is of widespread importance to industry and research. Hard spheres represent a benchmark by which to compare other particle suspensions, and there are a variety of analytical and numerical models available to describe their rheology. However, it is experimentally challenging to produce ideal hard spheres, where surface forces are negligible between particles, and where phase volume is precisely defined. Beyond the dilute regime, the model by Maron and Pierce [1] and Quemada [2], which we refer to as the MPQ model, is commonly used analytically to describe the relative viscosity of hard sphere suspensions as a function of phase volume and a maximum packing fraction (/ m ). We show that obtaining / m from empirical fits can lead to misinterpretation of experimental data. We reveal that reasonable prediction of the viscosity is obtained using the MPQ model when / m is set to the geometric random close packing fraction / rcp , which is independently defined from the particle size distribution using the packing model of Farr and Groot [3]. This 'theoretical' approach is tested using a wide variety of experimental data on colloidal and non-colloidal hard spheres without need for any fitting parameters or empiricisms. In addition, plotting the inverse of the square-root of viscosity as a function of phase volume, which linearises the MPQ model, provides a convenient means by which to clearly see where suspensions deviate from the model due to such effects as particle aggregation, particle softness and measurement errors. We also demonstrate the necessity of this approach by accurately predicting the viscosity of microgel suspensions up to / rcp ; empirical fits across the full data set are erroneous because particle deformation and viscoelasticity lead to values of / > / rcp . This approach provides a suitable unambiguous theoretical baseline for comparison to experimental studies on suspension rheology involving polydisperse size distributions.

Results comparing experiments on a model system of mono-disperse silica-particles with the numerical simulation of a highly concentrated suspension of spherical particles subject to a constant rate of strain are presented. Giant fluctuations of the shear stress and the first and second normal force difference are studied. Stress chain formation and evolution under shear are visualized in order to make the relation between the stress fluctuations and the suspension microstructure.

Grand canonical Monte Carlo, histogram reweighting and finite-size scaling methods are used to determine the phase transitions of bulk (three-dimensional) and confined (quasi-two-dimensional) neutral colloid-polymer systems. The colloids are modeled as hard spheres and the polymer molecules as hard chains, and the only attractive forces are effective ones induced by depletion effects. In contrast to the predictions of mean field and other approximate theories, the nature of the coexistence phases is found to not depend solely on the polymer-to-colloid size ratio, q, but on the colloid diameter, the polymer radius of gyration, and the polymer monomer size. The threshold values of q for the onset of liquid-liquid phase separation differ significantly from earlier predictions, and depend strongly on the dimensionality of space. Extrapolation to the ''protein limit'' of very small colloid and very long polymer indicates that immiscibility persists at this limit in three dimensions, while it does not always do so for confined systems. r

We show how to coarse-grain polymers in a good solvent as single particles, interacting with density-independent or density-dependent interactions. These interactions can be between the centres of mass, the mid-or end-points of the polymers. We also show how to extend these methods to polymers in poor solvents and mixtures of polymers. Treating polymers as soft colloids can greatly speed up the simulation of complex many-polymer systems, including polymer-colloid mixtures.

We use thermodynamic perturbation theory to calculate the free energies and resulting phase diagrams of binary systems of spherical colloidal particles and interacting polymer coils in good solvent within an effective one-component representation of such mixtures, whereby the colloidal particles interact via a polymer-induced depletion potential. MC simulations are used to test the convergence of the high temperature expansion of the free energy. The phase diagrams calculated for several polymer to colloid size ratios differ considerably from the results of similar calculations for mixtures of colloids and ideal (non-interacting) polymers, and are in good overall agreement with the results of an explicit two-component representation of the same system, which includes more than two-body depletion forces.

We study the effective interactions and phase behavior of star polymer–colloid mixtures through theory and Monte Carlo simulations. We extend previous theoretical approaches for calculating the effective star–colloid pair potential to take into account attractive contributions, which become significant at worsening solvent conditions. In order to assess the validity of our simulation and theory, we compute the effective interactions via virtual move parallel tempering Monte Carlo simulations using a microscopic bead-spring model for the star polymer and achieve excellent agreement. Finally, we perform grand canonical Monte Carlo simulations of the coarse-grained systems to study the effect of solvent quality on the phase behavior.

We study the depletion-induced self-assembly of indented colloids. Using state-of-the-art Monte Carlo simulation techniques that treat the depletant particles explicitly, we demonstrate that colloids assemble by a lock-and-key mechanism, leading to colloidal polymerization. The morphology of the chains that are formed depends sensitively on the size of the colloidal indentation, with smaller values additionally permitting chain branching. In contrast to the case of spheres with attractive patches, Wertheim's thermodynamic perturbation theory fails to provide a fully quantitative description of the polymerization transition. We trace this failure to a neglect of packing effects and we introduce a modified theory that accounts better for the shape of the colloids, yielding improved agreement with simulation. arXiv:1304.3675v2 [cond-mat.soft]

Concentrated suspensions that reversibly shear thicken have also been reported to show a second shear-thinning regime at high shear rates and stresses beyond shear-thickening. We hypothesize that this behavior is due to the elastic particle deformation driven by the high lubrication forces acting between the particles in the hydroclusters. This limiting behavior is described here by an elastohydrodynamic model which predicts a limiting viscosity, η∝γ-1/2 Semi-quantitative agreement is found by assuming Hertzian contact between the particles and estimating the particle shear modulus. High strain rate compression-shear split Hopkinson pressure bar (CS-SHPB) experiments are performed on shear thickening silica dispersions to test for this limiting behavior.

We have studied the Saffman-Taylor instability for Laponite and mud. Our experiments showed several kinds of finger patterns which don't obey the classical theory of Saffman-Taylor instability. Our observations, on both finger patterns and rheology analyses results showed shear thinning behavior in high shear rates and shear thickening behavior in low shear rates for Laponite. This showed that the shear viscosity diverges at a point in which the shear viscosity has a bifurcation, this point has been identified. This result is in good agreement with the MRI rheology analysis results by Coussot et.al . This is one of the important reasons that make Laponite such a complex fluid. We tested Darcy's Law for Laponite, we verified that the generalized Darcy's Law, suggested by Bonn et.al is in good agreement with rheology analyses results in the shear thinning region of Laponite. Calculating the shear viscosity as a function of shear rate using generalized Darcy's Law on the fingers movements showed good agreement with rheology analyses results. We also tested Mud; the finger patterns and Darcy's Law showed Newtonian behavior for this suspension. We also tested Darcy's Law for three Newtonian Fluids, detergent, oil and clothes conditioner, All three fluids resulted in a linear relationship between the fluids velocity and the pressure gradient in different rates of shear rates and pressure gradient. This finding supports the applicability of Darcy's Law in distinguishing Newtonian and non-Newtonian behavior in Fluids.

A Landau theory is presented for the structural transition of electrically stabilized colloidal crystals under shear. The model suggests that a structural transition from an ordered layered colloidal crystal into a disordered structure occurs at a critical shear stress. The shear induced structural transition is related to a change of the rheological properties caused by the variation of the microstructure which can be verified by scattering experiments. The theory is used to establish the shape of the flow curves. A good qualitative agreement with experimental results can be achieved, while a scaling relation similar to the elastic scaling is established.

The authors previously introduced an activation model for the onset of shear thickening in electrically stabilized colloidal suspensions. It predicts that shear thickening occurs, when particles arranged along the compression axis in a sheared suspension do overcome the electrostatic repulsion at a critical shear stress, and are captured in the primary minimum of the DLVO interaction potential. A comparison with an experimental investigation on non-aqueous silica suspensions, carried out by Maranzano and Wagner, is performed. For particle systems that fall into the applicability range of the theory, a good coincidence between the experimental data and the model predictions can be found.

Grand canonical Monte Carlo and histogram reweighting techniques are used to study the fluid-phase behavior of an athermal system of colloids and nonadsorbing polymers on a fine lattice in the “protein limit,” where polymer dimensions exceed those of the colloids. The main parameters are the chains’ radius of gyration, Rg, the diameter of the colloids, σc, and the monomer diameter, σs. The phase behavior is controlled by the macroscopic size ratio, qr = 2Rg/σc, and the microscopic size ratio, d = σs/σc. The latter ratio is found to play a significant role in determining the critical monomer concentration for qr  4 and the critical colloid density for all chain lengths. However, the critical (osmotic) pressure is independent of the microscopic size ratio at all macroscopic size ratios studied. Quantitative agreement is observed between our simulation results and experimental data. We scale our results based on the polymer correlation length, which has previously been suggested to universally collapse these binodals [Bolhuis et al., Phys. Rev. Lett. 90, 068304 (2003); Fleer and Tuinier, Phys. Rev. E 76, 041802 (2007)]. While the density binodals exhibit universal characteristics along the low-colloid-density branch, such features are not present in the corresponding high-density phase. However, pressure binodals do collapse nicely under such a scaling, even far from the critical point, which allows us to produce a binodal curve whose shape is independent of either size ratio.

This paper adopts a previously developed activation model of shear thickening, published by the authors to sterically stabilized colloidal suspensions. When particles arranged along the compression axis of a sheared suspension, they may overcome the repulsive interaction and form hydroclusters associated with shear thickening. Taking advantage of the total interaction potential of polymeric brush coating and van der Waals attraction, the applicability of the activation model is shown within the validity range of a continuum theory. For the comparison with an extensive experimental investigation, where some parameters are not available, the onset of shear thickening can be predicted with realistic assumptions of the model parameters.

A theory is presented for the onset of shear thickening in colloidal suspensions of particles, stabilized by an electrostatic repulsion. Based on an activation model a critical shear stress can be derived for the onset of shear thickening in dense suspensions for a constant potential and a constant charge approach of the spheres. Unlike previous models the total interaction potential is taken into account (sum of attraction and repulsion). The critical shear stress is related to the maximum of the total interaction potential scaled by the free volume per particle. A comparison with experimental investigations shows the applicability of the theory.

We explore the Saffman-Taylor instability of a gas bubble expanding into a shear thinning liquid in a radial Hele-Shaw cell. Using Darcy's law generalized for non-Newtonian fluids, we perform simulations of the full dynamical problem. The simulations show that shear thinning significantly influences the developing interfacial patterns. Shear thinning can suppress tip splitting, and produce fingers which oscillate during growth and shed side branches. Emergent length scales show reasonable agreement with a general linear stability analysis. [S0031-9007 05226-5] PACS numbers: 47.50. + d, 47.20.Ma, 47.54. + r, 68.10. -m Complex fluids, such as liquid crystals [1], polymer solutions and melts [2], clays [3], and foams [4]