Shear thickening in polymer stabilized colloidal suspensions

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.     

Shear thickening in a model colloidal suspension

We study the rheology of model colloidal suspensions using molecular-dynamics simulations. We relate the onset of shear thickening to the transition from a low-viscosity regime, in which the solvent facilitates the flow of colloids, to a high-viscosity regime associated with jamming of the colloids and the formation of chains of colloids. In the low-viscosity regime, the colloidal particles are, on average, surrounded by two layers of solvent particles. On the contrary, in the high-viscosity regime, the solvent is expelled from the interstice between the jammed colloids. The thickening in suspensions is shown to obey the same criterion as in simple fluids. This demonstrates that jamming, even without the divergence of lubrication interactions, is sufficient to observe shear thickening.     

Two-dimensional colloidal aggregation: concentration effects

Extensive numerical simulations of diffusion-limited (DLCA) and reaction-limited (RLCA) colloidal aggregation in two dimensions were performed to elucidate the concentration dependence of the cluster fractal dimension and of the different average cluster sizes. Both on-lattice and off-lattice simulations were used to check the independence of our results on the simulational algorithms and on the space structure. The range in concentration studied spanned 2.5 orders of magnitude. In the DLCA case and in the flocculation regime, it was found that the fractal dimension shows a linear-type increase with the concentration phi, following the law: d(f)=d(fo)+aphi(c). For the on-lattice simulations the fractal dimension in the zero concentration limit, d(fo), was 1.451+/-0.002, while for the off-lattice simulations the same quantity took the value 1.445+/-0.003. The prefactor a and exponent c were for the on-lattice simulations equal to 0.633+/-0.021 and 1.046+/-0.032, while for the off-lattice simulations they were 1.005+/-0.059 and 0.999+/-0.045, respectively. For the exponents z and z', defining the increase of the weight-average (S(w)(t)) and number-average (S(n)(t)) cluster sizes as a function of time, we obtained in the DLCA case the laws: z=z(o)+bphi(d) and z'=z'(o)+b'phi(d'). For the on-lattice simulations, z(o), b, and d were equal to 0.593+/-0.008, 0.696+/-0.068, and 0.485+/-0.048, respectively, while for the off-lattice simulations they were 0.595+/-0.005, 0.807+/-0.093, and 0.599+/-0.051. In the case of the exponent z', the quantities z'(o), b', and d' were, for the on-lattice simulations, equal to 0.615+/-0.004, 0.814+/-0.081, and 0.620+/-0.043, respectively, while for the off-lattice algorithm they took the values 0.598+/-0.002, 0.855+/-0.035, and 0.610+/-0.018. In RLCA we have found again that the fractal dimension, in the flocculation regime, shows a similar linear-type increase with the concentration d(f)=d(fo)+aphi(c), with d(fo)=1.560+/-0.004, a=0.342+/-0.039, and c=1.000+/-0.112. In this RLCA case it was not possible to find a straight line in the log-log plots of S(w)(t) and S(n)(t) in the aggregation regime considered, and no exponents z and z' were defined. We argue however that for sufficiently long periods of time the cluster averages should tend to those for DLCA and, therefore, their exponents should coincide with z and z' of the DLCA case. Finally, we present the bell-shaped master curves for the scaling of the cluster size distribution function and their evolution when the concentration increases, for both the DLCA and RLCA cases.     

Mesoscopic structure formation in colloidal aggregation and gelation

Recent small-angle light scattering experiments have revealed that diffusively aggregating spherical particles develop structure on a mesoscopic length scale (∼ tens of particles). The mesoscopic structural length scale persists even when the aggregation proceeds to the formation of a space-spanning network (a gel). We review the technique of small-angle light scattering, survey the experimental evidence for mesoscopic structure formation, discuss attempts at understanding these experimental observations by computer simulation of irreversible and reversible diffusion-limited cluster aggregation (DLCA), and propose a coherent picture for the understanding of non-equilibrium aggregation in the context of phase transitions.     

Coupling between polymer adsorption and colloidal particle aggregation

Studies of the adsorption of high molecular weight polymers on colloidal latex and silica particles and their subsequent flocculation were carried out. Neutral polyethylene oxide samples with both a narrow and a broad molecular weight distribution were used together with low charged cationic copolymers. The influence of the particle concentration and polymer dose on the flocculation were systematically investigated under quiescent conditions.Equilibrium bridging only occurred with polyelectrolyte, even in very dilute suspensions, at high particle coverage. In contrast to this, non-equilibrium bridging occurred with both neutral polymer and polyelectrolytes but only for more concentrated suspensions and small amounts of adsorbed polymer. Polymer adsorption in dilute suspensions, which did not show particle aggregation was measured an electrophoretic technique. In more concentrated suspensions, where flocculation takes place, we found that aggregation prevents further polymer adsorption and induces both an excluded volume and a surface effect. The consequences on the shape of the isotherms differ according to the aggregation mechanism.A significant decrease of the amount, , of adsorbed polymer is observed with non-equilibrium bridging. When both mechanisms simultaneously contribute to the aggregation, the value of depends on their relative importance. In the intermediate range of copolymer dose their respective contributions are critically sensitive to the details of the mixing step and stirring, leading to non reproducible experimental results.     

Effect of aggregation on viscosity of colloidal suslension

This experimental study of viscosity of colloidal suspensions was performed using monodisperse polystyrene latex with particle diameter of 1.15 μm and a pH dependent negative zeta potential of up to 120 mV in aqueous solutions. The range of electrostatic repulsion between the particles was controlled by varying the concentration of potassium chloride. Suspensions under investigation were either in a stable, coagulated, or gelated, state depending on the salt concentration. Shear thinning behaviour was observed for all the samples studied. The dependence of viscosity on shear rate imposed was found to depend substantially on the salt concentration.     

Further insights into the universality of colloidal aggregation

Dynamic light scattering (DLS) performed at various scattering wave vectors provides detailed information about the aggregation kinetics and the cluster mass distribution (CMD) in colloidal dispersions. Detailed modeling of the aggregation kinetics with population balance equations requires a quantitative connection between the CMD and measurable quantities such as the angle dependent hydrodynamic radii obtained by DLS. For this purpose we evaluate and compare various models for the structure factor of fractal aggregates. Additionally, we introduce a simple scattering model that accounts for the contribution of internal cluster dynamics of fractal clusters to the first cumulant of the dynamic structure factor. We show that this contribution allows to quantitatively describe previously measured experimental data on the scattering wave vector dependence of the hydrodynamic radius in diffusion limited cluster-cluster aggregation (DLCA), which was shown to exhibit some kind of universality behavior (master curve). Using the same scattering model, we analyze a similar set of experimental data but in reaction limited cluster-cluster aggregation (RLCA). We find that in this case the crossover from RLCA to DLCA and gravitational settling both have a significant influence on the CMD and consequently on the scattering wave vector dependent DLS data. Only when accounting for both these effects they temporarily compensate each other and a satisfactory representation of the aggregation master curve is possible for the RLCA data at longer times. Indeed, we find that either crossover from RLCA to DLCA or gravitational settling, when present individually, causes the loss of a master curve for aggregation.     

Self-limiting aggregation leads to long-lived metastable clusters in colloidal solutions

The existence of a metastable state with limited Coulomb-blocked aggregation at the onset of instability in a colloidal solution is proposed and demonstrated both experimentally and theoretically (through Monte Carlo simulations). Such a stable state of small clusters of metallic colloids happens to be extremely important for techniques such as surface-enhanced Raman scattering (SERS), which profits explicitly from collective plasmon resonances in these clusters to boost Raman signals of specific analytes. In fact, SERS provides a unique tool to understand, monitor, and study the onset of aggregation in colloidal silver/gold and to prove the existence of the proposed state at the boundary of colloid coalescence.     

Molecular dynamics simulation of the aggregation of colloidal particles

The spontaneous time evolution of systems containing N colloidal particles (N = 12, 24, 100) in a spherical cell of volume V at a constant volume fraction φ=0.1 was studied by a molecular dynamics method in the NVT ensemble. The starting velocities of the particles are allocated according to the Maxwell distribution at T=273 K.

Pairwise interaction of the particles was specified by molecular, electrostatic and elastic forces. The changes in the potential energy of the systems were calculated during the establishment of dynamic equilibrium. Coagulation takes place at sufficiently high values of the Hamaker constant. The value of the coefficient of Brownian diffusion, which is calculated from the half-time of coagulation, is found to be close to the known value for aqueous dispersions. The inclusion of electrostatic forces prevents coagulation.

The results obtained are in agreement with those obtained using theories of aggregate formation. Some structural characteristics of aggregates and stable systems are discussed.     

Hydrodynamic and interparticle potential effects on aggregation of colloidal particles

The effects of both hydrodynamic interaction and the form of the interparticle potential on the aggregation process for dispersed spherical particles are investigated by computational simulation. The simulation methods of Brownian Dynamics (BD) and Stokesian Dynamics (SD) are applied, over a range of solid volume fraction of $0.04???0.12$. The interparticle potential is a combination of a generalized Lennard-Jones form and a Yukawa potential, the latter of which describes a screened electrostatic repulsion at longer range. The combined potential is parameterized to include a roughly constant primary minimum near contact, along with a variable repulsive barrier at slightly larger separation. The microstructure is characterized through the pair distribution function, g(r), and the static structure factor. The repulsive barrier reduces the rate of aggregation and is also seen to affect the structure, with a large repulsion associated with a more tenuous structure. This is reflected in the potential having a strong effect on the evolution of ‘bonds’ per particle. Hydrodynamic interactions were found to reduce the solid fraction required for percolation, with the influence depending upon the form of the potential; the difference in percolation threshold was significant, with ${?}_{c\text{,}\mathit{SD}}?0.06$ and ${?}_{c\text{,}\mathit{BD}}?0.08$ a typical difference for moderate repulsion barriers. These results are for 864 particles in a cubic unit cell. To address the mechanism for this influence of hydrodynamic interactions, a complementary analysis of the evolution of numerous independent three-particle aggregates was performed. The analysis shows that hydrodynamic interaction slows the evolution toward a condensed aggregate of lowest potential energy in a way which cannot be explained by a simple rescaling of the drag due to uncorrelated particle motions.     

Bimodal colloidal mixtures: from fast to slow aggregation regions

A Brownian dynamics simulation has been used to investigate the aggregation kinetics of bimodal colloidal mixtures with similar surface chemistries but different sizes, driven by the DLVO interaction potential. The time evolution of structural formation is examined by the mean number of neighbors under fast and slow aggregation regions. It was found that the electrolyte ionic strength affects the kinetic pattern of colloidal aggregation. Under the high electrolyte ionic strength conditions (fast aggregation), the selective aggregation of the least stable single component can take place in the early stage, while the other component is enriched in this least stable component in the later stage. With the ionic strength decreasing (towards the slow aggregation), the hybrid aggregation (selective aggregation and heteroaggregation) gradually dominates the aggregation kinetics. Also in the early stage, this evolves to the heteroaggregation of different components under lower ionic strength conditions. The volume fraction has no obvious influence on this kinetic pattern in the early stage.     

Light-induced aggregation of colloidal gold nanoparticles capped by thymine derivatives

The colloid stability of thymine-coated gold nanoparticles under light irradiation as a function of particle size, surface charge, and exposure time was investigated in alkaline, aqueous solutions as well as in a 0.5 vol % of DMF in H(2)O mixture. With increasing exposure to light irradiation at 280 nm, more and more particles coagulated. Light-induced aggregation of colloidal gold nanoparticles was attributed to reorientation of thymine terminal groups tethered on gold particle surfaces. A smaller particle size and negatively charged surface reduced the rate of photodimerization or even inhibited the photoreaction. UV-vis and FTIR spectroscopy confirmed the photodimerization of terminal thymine molecules under 280 nm light irradiation. The reaction kinetics of thymine photodimerization appears to be a combination of first-order reactions, each having different rates, reflecting the inhomogeneity and high curvature of the gold nanoparticle surfaces.     

Shear induced aggregation of a pectin stabilised emulsion in two dimensions

Shear induced aggregation of a Pectin stabilised emulsion trapped at the air-liquid interface was studied in a Couette system by video enhanced microscopy. From dimension analysis, Brownian motion was identified to enhance the probability of bond formation. The characteristic time scale of aggregation was found to scale as t_c ∼ η/φ rather than t_c ∼ 1/γ˙φ as expected for orthokinetic aggregation. The structure of very large clusters showed strongly rearranged strands and fractal scaling for low γ˙ and φ, analysed by density auto-correlation. At high γ˙ and φ, the cluster was dominated by larger drops and no fractal scaling could be determined for the accessible length scales. Received: 7 June 2000 Accepted: 1 August 2000     

Model of aggregation of colloidal fine particles in the presence of supersized polymer

A simple model of the process of stabilization and destabilization of fine colloidal suspensions induced by supersized linear polymers has been tested by the direct simulation method. In the model, a single polymer molecule may bind a number of colloidal particles and thus form an aggregate. It is assumed that a simultaneous attachment of a few fine particles to one macromolecule does not necessarily destabilize the suspension. The destabilization of the system (occurring if aggregate sedimentation dominates its diffusion ability) takes place only when the number of the attached particles per macromolecule exceeds the critical value which depends on the polymer coil dimension in the dispersion medium. The model permits interpretation of several experimental observations of the behavior of colloidal sols upon introduction of very high molecularweight polymers. The simulation results have been compared with the experimental data on the effect of polyacrylamide on the stability of AgI sol.     

Responsive colloidal systems: reversible aggregation and fabrication of superhydrophobic surfaces

We report on a method of fabricating stimuli-responsive core-shell nanoparticles using block copolymers covalently bound to a silica nanoparticle surface. We used the "grafting to" approach to graft amphiphilic block copolymer brushes of poly(styrene-b-2-vinylpyridine-b-ethylene oxide) and poly(styrene-b-4-vinylpyridine) onto silica nanoparticles with two different diameters: colloidal silica 200 nm in diameter and fumed silica 15 nm in diameter. We used the pH-responsive properties of the grafted brush to regulate the interactions between the particles, and between the particles and their environment. We show that this behavior can be applied for a reversible formation of particle aggregates, and can be used to tune and stabilize the secondary aggregates of particles of the appropriate size and morphology in an aqueous environment. The suspensions of the particles form a textured hydrophilic coating on various substrates upon casting and the evaporation of water. Heating above the polymer's glass transition temperature or treatment in acidic water result in back and forth switching between superhydrophobic and hydrophilic surfaces, respectively.     

Shear stresses of colloidal dispersions at the glass transition in equilibrium and in flow

We consider a model dense colloidal dispersion at the glass transition, and investigate the connection between equilibrium stress fluctuations, seen in linear shear moduli, and the shear stresses under strong flow conditions far from equilibrium, viz., flow curves for finite shear rates. To this purpose, thermosensitive core-shell particles consisting of a polystyrene core and a cross-linked poly(N-isopropylacrylamide) shell were synthesized. Data over an extended range in shear rates and frequencies are compared to theoretical results from integrations through transients and mode coupling approaches. The connection between nonlinear rheology and glass transition is clarified. While the theoretical models semiquantitatively fit the data taken in fluid states and the predominant elastic response of glass, a yet unaccounted dissipative mechanism is identified in glassy states.     

Control over colloidal aggregation in monolayers of latex particles at the oil-water interface

The controlled generation of 2D aggregate networks is studied experimentally using micrometer-sized polystyrene latex particles attached to the oil-water interface. Starting from an initially crystalline monolayer, appropriate combinations of carefully added electrolyte and surfactant enable control over both the fractal dimension and the kinetics of aggregation. Remarkably, the colloidal crystals formed upon first spreading remain stable, even for days, when substantial amounts of electrolyte are added to the aqueous phase. Pressure-area isotherms reveal a slow time evolution of the electrostatic dipole-dipole interaction. When the electrostatic interaction has been sufficiently weakened, aggregation proceeds in well-defined, reproducible manner. The aggregation process is analyzed using quantitative video microscopy. The evolution of the cluster size distribution and its moments is characterized, and static and dynamic scaling exponents are derived to identify the nature of the aggregation process. In the range of concentrations studied here, the kinetics all agree with a "fast", diffusion-limited cluster type of aggregation. However, the fractal dimension strongly depends on the composition of the aqueous subphase. Rather dense structures are found when only electrolyte is used, whereas more open structures are obtained when even small amounts of surfactant are added. It is suggested that this structural dependency is related to the effect of surfactant on the contact angle and its consequences for the anisotropic nature of the capillary interactions.     

Dispersion and aggregation of nanoparticles derived from colloidal droplets under low-pressure conditions

Formation of individually dispersed nanoparticles or compactly aggregated nanoparticles from sols via a spray-drying route at low pressure was investigated experimentally. Silica sol was used as a sample material. Effects of operating temperature, colloid size, sol concentration, pressure, pH and zeta potential of sols on the morphology of product particles were investigated. From the experimental results, it was shown that dispersed nanoparticles could be obtained at a relatively low pressure (20 Torr) and low temperature (200 degrees C). The experiment also showed that dispersed nanoparticles could be achieved by careful control of the interfacial energy (pH value) of the colloidal precursor. A possible mechanism of sol-to-dry-particle formation in the spray-drying process at low pressure is suggested, based on the experimental results and the available theories. This mechanism was able to explain the experimental results well.     

Ion-specific colloidal aggregation: population balance equations and potential of mean force

Recently reported colloidal aggregation data obtained for different monovalent salts (NaCl, NaNO(3), and NaSCN) and at high electrolyte concentrations are matched with the stochastic solutions of the master equation to obtain bond average lifetimes and bond formation probabilities. This was done for a cationic and an anionic system of similar particle size and absolute charge. Following the series Cl(-), NO(3)(-), SCN(-), the parameters obtained from the fitting procedure to the kinetic data suggest: (i) The existence of a potential of mean force (PMF) barrier and an increasing trend for it for both lattices. (ii) An increasing trend for the PMF at contact, for the cationic system, and a practically constant value for the anionic system. (iii) A decreasing trend for the depth of the secondary minimum. This complex behavior is in general supported by Monte Carlo simulations, which are implemented to obtain the PMF of a pair of colloidal particles immersed in the corresponding electrolyte solution. All these findings contrast the Derjaguin, Landau, Verwey, and Overbeek theory predictions.     

Effects of aggregation kinetics on nanoscale colloidal solution inside a rotating channel

Extended surfaces represent one of practical approaches to enhance heat transfer. Based on the laws of conductive and convective heat transfer, an increase in the area across which the object is in contact with the fluid can increase heat transfer. Due to its special structure, porous media can be seen as suitable alternatives for extended surface applications. On this basis, this research investigates the effect of connection type of sintered porous fins on heat transfer and pressure drop in the fluid flow. Connection model of four- and six-contact sintered balls of constant dimensions was evaluated by means of CFD simulation in this research. To describe the problem further, surface analysis on the reference cube is presented. The results indicate that the six-contact model has more porosity than the four-contact in reference cube by 29.45%. It was further found that the six-contact model tends to increase convective heat transfer by 33%. Results of surface analysis show that the main reasons for the difference in heat transfer between the four- and six-contact models are porosity and the angle at which balls are arranged with another.