Accounting for effective interactions among charged microgels.

We introduce a theoretical approach to describe structural correlations among charged permeable spheres at finite particle concentrations. This theory explicitly accounts for correlations among microions and between microions and macroions and allows for the proposal of an effective interaction among macroions that successfully captures structural correlations observed in poly-N-isopropyl acrylamide microgel systems. In our description the bare charge is fixed and independent of the microgel size, the microgel concentration, and the ionic strength, which contrasts with results obtained using linear response approximations, where the bare charge needs to be adapted to properly account for microgel correlations obtained at different conditions.

On the scattered light by dilute aqueous dispersions of nanogel particles.

This work deals with the scattered light by nanoparticles formed by a temperature sensitive polymer networks, namely nanogel particles. The scattered light is measured as a function of the scattering angle at temperatures below and above the volume phase transition temperature (VPTT) of nanogel particles. Our experimental results indicate that nanogel particles have a core-shell structure, formed by a uniform highly cross-linked core surrounded by a fuzzy shell where the polymer density decays to zero gradually for swollen configurations and sharply for shrunken states. The theoretical fitting of the experimental curves shows that the scattered light at low angle obeys a decreasing power law with the scattering vector, q(-α). The value of exponent α provides information about the radial dependence of the polymer density at the external shell of the particles for swollen nanogels, and about the degree of roughness of the surface for the case of shrunken nanogels. On the one hand, at low temperatures (below the VPPT), the nanogel particle is in the swollen state and the light scattering data show that its shell structure follows a fractal behaviour, with a polymer density that decays as r(α-3), where r is the distance to the particle centre. On the other hand, above the VPPT the results indicate that nanogel collapses into a core of uniform polymer density and a rough shell, with a fractal surface dimension of 2.5.

Effective electrostatic interactions arising in core-shell charged microgel suspensions with added salt.

The mixture formed by charged (ionic) microgels in the presence of 1:1 added salt, with explicit consideration of a core-shell structure of the microgel particles, is studied. By solving numerically the three-component Ornstein-Zernike integral equations, the counter- and coion penetration inside the microgel network and the resulting effective microgel-microgel electrostatic interaction are calculated. This is done in the limit of very low microgel concentration, so that the resulting pair-wise effective potential is not affected by many-body particle-particle interactions. The ion-ion, microgel-ion, and microgel-microgel correlations are all treated within the Hypernetted-Chain approximation. The results obtained clearly show that the addition of salt to the microgel suspension has a deep impact on the screening of the bare charge of the particles, confirming an already well-known result: the strong reduction of the effective charge of the microgel occurring even for diluted electrolyte concentrations. We show that this effect becomes more important as we increase the shell size of the particle and derive a semi-empirical model for the effective charge as a function of the electrolyte concentration and the shell extension. The resulting microgel-microgel effective pair potential is analysed as a function of the shell extension and salt concentration. In all cases the interaction is a soft potential when particles overlap. For non-overlapping distances, our theoretical results indicate that microgel particles can be regarded as hard spherical colloids bearing an effective charge given by the net charge inside the particle and the microgel-microgel interaction shows a Yukawa-like behaviour as a function of the interparticle distance. It is also observed that increasing the bare-charge of the microgel induces a strong microgel-counterion coupling in the limit of very low electrolyte concentrations, which cannot be justified using linearized theories. This leads to an even more important adsorption of counterions inside the microgel network and to a reduction of the microgel-microgel effective repulsion.

Effective interaction in asymmetric charged binary mixtures: the non-monotonic behaviour with the colloidal charge.

In this work we study the effective force between charged spherical colloids induced by the presence of smaller charged spheres using Monte Carlo simulations. The analysis is performed for two size ratios, q = R(s)/R(b), two screened direct repulsions, κ, and two small particle packing fractions, Ø(s). We specially focus on the effect of the charge of the big colloids (Z(b)), and observe that the repulsion between big particles shows a non-monotonic behaviour: for sufficiently small charge, we find an anomalous regime where the total repulsion weakens by increasing the big colloid charge. For larger charges, the system recovers the usual behaviour and the big-big interaction becomes more repulsive increasing Z(b). This effect is linked to the existence of strong attractive depletion interactions caused by the small-big electrostatic repulsion. We have also calculated the effective force using the Ornstein-Zernike equation with the HNC closure. In general, this theory agrees with the simulation results, and is able to capture this non-monotonic behaviour.

Role of the electrostatic depletion attraction on the structure of charged liposome-polymer mixtures.

The effect of adding charged nonadsorbing polymers to electrostatically structured suspensions of charged liposomes has been experimentally studied by means of light scattering techniques. The static structure factor of the mixtures is analyzed using two polymers of different sizes. As the polymer concentration increases, the main peak of the structure factor decreases and shows an important shift to larger values of the scattering vector. Such displacement is the consequence of the electrostatic-enhanced depletion attraction induced by the polymers that counteracts the electrostatic repulsion. For the shorter polymer, the system remains stable for all studied polymer concentrations. However, for the long polymer chains, the effective attraction induced at the highest polymer density studied is strong enough to destabilize the mixture. In this case, the aggregation of the liposomes leads to clusters of nearly linear morphology. The PRISM theory is employed to calculate the effective pair potential between liposomes. The theoretical predictions are able to support the experimental observations, and provide an explanation of the interplay between the electrostatic repulsive interaction and the depletion attraction. In particular, they show that the depletion attraction is especially long ranged, and is dominated by electrostatic effects rather than entropic.

Charged colloid-polymer mixtures: a study on electrostatic depletion attraction.

In this work, light scattering methods have been used to study the effect of adding charged polymer chains on the structural and dynamic properties of a charged colloidal system. The experimental measurements of the static structure factor S(cc)(q) show that as the polymer concentration increases, the main peak moves to higher q-values, which is interpreted in terms of the electrostatically enhanced depletion attraction induced by the polymer. Moreover, we found that the shift of the peak depends on the interplay between two relevant length scales, the polymer radius of gyration, R(g), and the Debye length, κ(-1). To reach these conclusions, the polymer reference interaction site model has been employed to explain the experimental results and to study how the effective depletion attraction depends on the polymer concentration, R(g) and κ(-1). Additionally, the measurements of the dynamic structure factor f(q, τ) indicate that the colloidal diffusion increases with the polymer concentration. Both static and dynamic analysis point out that the repulsion between colloids becomes weaker as the charged polymer is added.

Primary and secondary bonds in field induced aggregation of electric double layered magnetic particles.

Magnetic filaments able to survive on removal of the magnetic field have led to new applications in biotechnology and microfluidics. In this work, the stability of linear field induced aggregates composed of electric double layered magnetic particles has been studied in the framework of the DLVO theory. A suitable system of differential equations is proposed in order to determine how the percentage of bonds formed in a primary or a secondary energy minimum depends on the exposure time to the magnetic field. The theoretical predictions were compared with experimental data obtained by means of dynamic light scattering. The aggregation experiments were performed at different electrolyte concentrations and exposure times to the magnetic field. Fitting the experimental results according to the proposed theory allowed us to determine the rate at which bonds formed in a secondary energy minimum turn into stable bonds.

Dynamic arrest in charged colloidal systems exhibiting large-scale structural heterogeneities.

Suspensions of charged liposomes are found to exhibit typical features of strongly repulsive fluid systems at short length scales, while exhibiting structural heterogeneities at larger length scales that are characteristic of attractive systems. We model the static structure factor of these systems using effective pair interaction potentials composed of a long-range attraction and a shorter range repulsion. Our modeling of the static structure yields conditions for dynamically arrested states at larger volume fractions, which we find to agree with the experimentally observed dynamics.

Kinetic study of coupled field-induced aggregation and sedimentation processes arising in magnetic fluids.

In this work, the kinetics of coupled aggregation and sedimentation processes arising in magnetic fluids has been studied. Aggregation was induced applying a constant uniaxial magnetic field. The time evolution of the cluster-size distribution and the weight-average chain length was monitored using optical microscopy and digital image analysis. The experimental results are compared with the corresponding solutions of Smoluchowski's equation. For this purpose, a recently proposed aggregation kernel was employed. When sedimentation effects are taken into account, the fits improve especially at long aggregation times.

Controlling the magnetic filaments length by tuning the particle interactions.

Initially stable samples of monodisperse superparamagnetic particles were aggregated in the presence of an external magnetic field and different amounts of electrolyte. The aggregation process was monitored using dynamic light scattering (DLS). When the magnetic field was turned off, a significant change of the effective diffusion coefficient was observed at all electrolyte concentrations. This jump was interpreted in terms of filament break-up and additional rotational diffusive modes. Therefore, the length of the magnetic filaments (MF) was determined from the measured average diffusion coefficients applying an adequate theoretical approach. The results prove that the MFs disassemble completely at low electrolyte concentrations. At intermediate amounts of electrolyte added, a partial cluster break-up is observed. Only at high salt concentrations, the chains withstand the absence of the magnetic field. The results show that average filament size can be predicted and controlled by tuning the relative strength of the magnetic and electric interactions.

Formation of magnetic filaments: a kinetic study.

In order to form magnetic filaments or chains, aqueous suspensions of superparamagnetic colloidal particles were aggregated under the action of an external magnetic field in the presence of different amounts of an indifferent 1:1 electrolyte (KBr). This allowed the influence of the anisotropic magnetic and isotropic electrostatic interactions on the aggregation behavior of these electric double-layered magnetic particles to be studied. Dynamic light scattering was used for monitoring the average diffusion coefficient of the magnetic filaments formed. Hydrodynamic equations were employed for obtaining the average chain lengths from the experimental mean diffusion coefficients. The results show that, for the same exposure time to the magnetic field, the average filament size is monotonously related to the amount of electrolyte added. The chain growth behavior was found to follow a power law with a similar exponent for all electrolyte concentrations used in this work. The time evolution of the average filament size can be rescaled such that all the curves collapse on a single master curve. Since the electrolyte added does not have any effect on the scaling behavior, the mechanism of aggregation seems to be completely controlled by the dipolar interaction. However, electrolyte addition not only controls the range of the total interaction between the particles, but also enhances the growth rate of the aggregation process. Taking into account the anisotropic character of these aggregation processes we propose a kernel that depends explicitly on the range of the dipolar interaction. The corresponding solutions of the Smoluchowski equation combined with theoretical models for the diffusion and light scattering by rigid rods reproduce the measured time evolution of the average perpendicular aggregate diffusion coefficient quite satisfactorily.

Aggregation kinetics of latex microspheres in alcohol-water media.

We report zeta potential and aggregation kinetics data on colloidal latex particles immersed in water-alcohol media. Zeta potential values show absolute maxima for volume fractions of alcohol of 0.10 and 0.05 for ethanol and 1-propanol, respectively. For methanol, no maximum of the absolute value of the zeta potential was found. Aggregation kinetics was studied by means of a single-cluster optical sizing equipment and for alcohol volume fractions ranging from 0 to 0.1. The aggregation processes are induced by adding different potassium bromide concentrations to the samples. We expected to find a slowdown of the overall aggregation kinetics for ethanol and 1-propanol, and no significant effect for methanol, as compared with pure water data. That is, we expected the zeta potential to govern the overall aggregation rate. However, we obtained a general enhancement of the aggregation kinetics for methanol and 1-propanol and a general slowdown of the aggregation rate for ethanol. In addition, aggregation data under ethanol show a slower kinetics for large electrolyte concentration than that obtained for intermediate electrolyte concentration. We think that these anomalous behaviors are linked to layering, changes in hydrophobicity of particle surfaces due to alcohol adsorption, complex ion-water-alcohol-surface structuring, and competition between alcohol-surface adsorption and alcohol-alcohol clustering.

Forming chainlike filaments of magnetic colloids: the role of the relative strength of isotropic and anisotropic particle interactions.

The influence of the interplay between anisotropic magnetic and isotropic electrostatic interactions on the aggregation behavior of aqueous suspensions of electric double layered magnetic particles was studied. Therefore, the particles were aggregated under the action of an external magnetic field and in the presence of different amounts of an indifferent 1:1 electrolyte. After removing the field, linear aggregates remained in the sample. Static light scattering and electron micrographs confirmed the chainlike cluster morphology. Dynamic light scattering was used for monitoring the average diffusion coefficient of these magnetic filaments. A theoretical model that allows the experimental mean diffusion coefficient to be related to the average chain length was successfully employed. The results show that, at fixed exposure time and field strength, the average filament size is proportional to the amount of electrolyte added. The light scattering data and transmission electron microscopy micrographs prove that permanent chains coexist with a relatively large fraction of individual particles when no or little electrolyte was added to the samples. A plausible explanation for this "selective aggregation" phenomenon could be given in terms of surface charge heterogeneities. The chain growth was found to follow a power law with a similar exponent for all the electrolyte concentrations studied. Scaling theories were employed for estimating the ratio of particles taking part in the aggregation process.

Renormalization in charged colloids: non-monotonic behaviour with the surface charge.

The static structure factor S(q) is measured for a set of deionized latex dispersions with different numbers of ionizable surface groups per particle and similar diameters. For a given volume fraction, the height of the main peak of S(q), which is a direct measure of the spatial ordering of latex particles, does not increase monotonically with the number of ionizable groups. This behaviour cannot be described using the classical renormalization scheme based on the cell model. We analyse our experimental data using a renormalization model based on the jellium approximation, which predicts the weakening of the spatial order for moderate and large particle charges.

Irreversible versus reversible aggregation: mean field theory and experiments.

Colloidal aggregation processes arising at different electrolyte concentrations were studied by means of experiments and confronted with theoretical predictions of different kinetic aggregation models. For this purpose, aqueous dispersions of relatively large polystyrene microspheres were chosen as experimental systems. Aggregation was induced by adding KBr electrolyte to the initially stable particle dispersions. During the aggregation processes, the cluster-size distribution was monitored by means of single cluster light scattering. Analyzing the time evolution of the monomer concentration, we found that the processes arising even at moderate electrolyte concentrations cannot be described by pure time-independent irreversible aggregation models. Hence, alternative models such as time-dependent irreversible aggregation and several reversible aggregation models were also tested. The model that considers a time-dependent sticking probability was found to fit the data quite satisfactorily. Nevertheless, the fitted was so slow that it seems not very likely to find such a behavior in real systems. The aggregation-fragmentation models reported in the literature were unable to reproduce the experimental observations. Hence, a more realistic reversible aggregation model was developed. This model accounts also for reenforced or double bonds between the constituent particles. The corresponding fit improved significantly and reached the same quality as the time-dependent model. Moreover, the obtained fitting parameters were in qualitative agreement with the DLVO predictions and so, reversible aggregation seems to be a more reasonable explanation for the experimental data than time-dependent irreversible aggregation. However, no definite statement on the possible secondary bond fragmentation mechanism may be made since both the applied shear stress in the measuring cell and thermal fluctuations can cause weaker bonds to break.

Cluster discrimination in electrostatic heteroaggregation processes.

Electrostatic heteroaggregation processes arising in 1:1 mixtures of oppositely charged microspheres at low and very low electrolyte concentrations were investigated by means of single-cluster light scattering. Cluster discrimination, i.e., the fact that clusters differing by only one constituent particle behave quite differently, was found for monomers and dimers. This effect was recently predicted by Brownian dynamic simulations but, to the best of our knowledge, not yet confirmed by experiments. The experimental data were confronted with the simulations and a good qualitative and quantitative agreement was obtained. The origin of the cluster discrimination phenomenon could be related to the range of the attractive electrostatic interactions.

Effective charges of colloidal particles obtained from collective diffusion experiments.

In this work, the collective diffusion coefficient of highly charged colloidal particles in dilute dispersions has been measured by means of dynamic light scattering. The possibility of obtaining valuable information about the particle charge from these data is looked into with the help of electrophoresis experiments. Our results suggest that this is possible in the case of slight or moderately interacting particles as long as experimental data are properly treated. For highly interacting colloids, however, such information could not be so reliable, presumably due to certain shortcomings of the experimental technique at low angle. The role of charge renormalization is also discussed in this work.

Clustering under short-range finite interactions.

In this paper the aggregation of surface modified colloidal particles is presented, paying special attention to the cluster structure and growth. The surface was modified by adsorbing bovine serum albumin (BSA). The interaction potential develops a minimum of restricted depth, weakening the clusters which subsequently restructure and form more compact morphologies. This minimum is responsible for the reversibility of the aggregation processes (this is an important difference between diffusion-limited cluster aggregation and reaction-limited cluster aggregation). The energy minimum is associated with the presence of a steric term in the energy balance, which depends on the size of the adsorbed molecules. BSA molecules with different sizes were employed to test this point. In addition, the short-range interaction seems not to affect significantly the paths of approximating particles, since the aggregation of the clusters at long times is independent of the size of these particles. The long-time kinetics was interpreted in the frame of dynamic scaling concepts. A kinetics model, including surface-surface, protein-surface, and protein-protein aggregation, is used to determine the dominant mechanism controlling the aggregation.

Constant bond breakup probability model for reversible aggregation processes.

Reversible aggregation processes were simulated for systems of freely diffusing sticky particles. Reversibility was introduced by allowing that all bonds in the system may break with a given probability per time interval. In order to describe the kinetics of such aggregation-fragmentation processes, a fragmentation kernel was developed and then used together with the Brownian aggregation kernel for solving the corresponding kinetic master equation. The deduced fragmentation kernel considers a single characteristic lifetime for all bonds and accounts for the cluster morphology by averaging over all possible configurations for clusters of a given size. It became evident that the simulated cluster-size distributions could be described only when an additional fragmentation effectiveness was considered. Doing so, the stochastic solutions were in good agreement with the simulated data.

Interaction potentials, structural ordering and effective charges in dispersions of charged colloidal particles.

As colloidal dispersions of charged particles exhibit a wide variety of commercial, technological and scientific applications, a considerable theoretical effort has been devoted to finding an effective interaction potential from primitive models. The forces derived from this potential should justify the spatial ordering experimentally observed under certain conditions. This paper reviews the advances in these theoretical studies as well as some experiments (based on the mentioned order) that try to corroborate them. Special attention has been paid to the Derjaguin-Landau-Verwey-Overbeek (DLVO) potential. Nowadays, many of these theoretical investigations suggest that it could be applied if some of its parameters are renormalized. Nevertheless, to achieve a renormalization procedure in a strict way (from a primitive model) is a difficult task as a result of the size and charge asymmetries between small ions and macroions. Thus, several procedures for computing renormalized charges in a simple way have been developed. However, the notion of effective charge has also been widely used (as a adjustable parameter) in order to justify results found for several kinds of colloids (like solid particle dispersions or micellar systems) by means of quite different experimental techniques. Renormalization (as well as ion condensation) approaches, experiments and the controversial relationship between theoretical and phenomenological effective charges are also reviewed in this work.