Theoretical analysis of factors affecting the formation and stability of multilayered colloidal dispersions

A mathematical analysis of the major factors influencing the formation and stability of colloidal dispersions containing spherical particles surrounded by multilayered polymeric interfacial membranes formed by the layer-by-layer electrostatic deposition technique is carried out. The mathematical model assumes that (i) the colloidal dispersion initially consists of a mixture of electrically charged monodisperse spherical particles and oppositely charged polymer molecules, (ii) the adsorption of polymer molecules to the particle surfaces is diffusion-limited, and (iii) the dominant particle-particle collision mechanism is Brownian motion. This approach was used to produce stability maps that highlight conditions under which bridging flocculation, multilayer formation, or depletion flocculation occurs. The stability maps are derived from calculations of the critical polymer concentrations required to (i) saturate the particle surfaces (C(Sat)), (ii) ensure that polymer adsorption is faster than particle collisions (C(Ads)), and (iii) promote depletion flocculation (C(Dep)). In addition, the influence of interfacial properties on the stability of multilayer colloidal dispersions was assessed by calculating the colloidal interactions between the coated particles (i.e., van der Waals, electrostatic, steric, and depletion). These calculations indicated that the major factors are the interfacial charge and composition rather than the interfacial thickness. This article provides useful insights into the factors affecting the formation of stable multilayer colloidal dispersions.     

Viscosity behavior of silica suspensions flocculated by associating polymers

Associating polymers are hydrophilic long-chain molecules containing a small number of hydrophobic groups, and act as flocculants in aqueous suspensions. The effects of associating and nonassociating polymers on viscosity behavior are studied for silica suspensions. Since flocculation is induced by polymer bridging, the viscosity behavior is converted from Newtonian to shear-thinning profiles. The additions of surfactant cause an increase in viscosity for suspensions prepared with associating polymer, whereas the flow behavior of suspensions with nonassociating polymer is not significantly influenced. In adsorption of associating polymers onto silica particles, the chain may adopt a conformation with a water-soluble backbone attached to the particle surfaces. The hydrophobic groups extending from the chains adsorbed onto different particles can form a micelle by association with surfactant. Therefore, the bridging flocculation is enhanced by surfactant. The cooperative micellar formation between associating polymer and surfactant is responsible for viscosity increase in suspensions.     

Mathematical modeling of polymer-induced flocculation by charge neutralization

A detailed mathematical model for flocculation of colloidal suspensions in presence of salts and polymers is described and validated. In former case, the classical DLVO theory, which accounts for relevant variables such as pH and salt concentration, is incorporated into a geometrically sectioned discrete population balance model. For processes involving polymers, flocculation via simple charge neutralization is modeled using a modified DLVO theory in which the effect of adsorbed polymer layers on van der Waals attraction is included. The fractal dimension of aggregates is obtained by dynamic scaling of experimental data for time evolution of mean aggregate size. The particle surface potential is assumed to be approximately equal to the zeta potential. The model predictions are in close agreement with experimental results for flocculation of colloidal hematite suspensions in the presence of KCl and polyacrylic acid at different concentrations. In particular, given values of model parameters, e.g., Hamaker constant, fractal dimension, surface potential, and thickness of adsorbed polymer layer, the model can realistically describe the kinetics of flocculation by a simple charge neutralization mechanism and track the evolution of floc size distribution. Representative examples of sensitivity of the flocculation model to perturbations in surface potential and fractal dimension and to modification in the DLVO theory for polymer-coated particles are included.     

Monte Carlo simulation of structure and nanoscale interactions in polymer nanocomposites

Off-lattice Monte Carlo simulations in the canonical ensemble are used to study polymer-particle interactions in nanocomposite materials. Specifically, nanoscale interactions between long polymer chains (N=550) and strongly adsorbing colloidal particles of comparable size to the polymer coils are quantified and their influence on nanocomposite structure and dynamics investigated. In this work, polymer-particle interactions are computed from the integrated force-distance curve on a pair of particles approaching each other in an isotropic polymer medium. Two distinct contributions to the polymer-particle interaction potential are identified: a damped oscillatory component that is due to chain density fluctuations and a steric repulsive component that arises from polymer confinement between the surfaces of approaching particles. Significantly, in systems where particles are in a dense polymer melt, the latter effect is found to be much stronger than the attractive polymer bridging effect. The polymer-particle interaction potential and the van der Waals potential between particles determine the equilibrium particle structure. Under thermodynamic equilibrium, particle aggregation is observed and there exists a fully developed polymer-particle network at a particle volume fraction of 11.3%. Near-surface polymer chain configurations deduced from our simulations are in good agreement with results from previous simulation studies.     

Collapse transitions of a supersized neutral chain due to irreversibly adsorbed small colloidal particles

 We performed Monte Carlo simulations to study the destabilization processes of large neutral and flexible polymer chains due to irreversibly adsorbed colloidal particles attached to the chains like beads on a necklace. The particles are modeled as charged spherical units which interact with each other via repulsive electrostatic and attractive van der Waals (vdW) potentials. The usual Monte Carlo search procedure is extended and carefully checked to completely sample the chain conformational space and achieve dense conformations in the limit of both strong attractive and repulsive interaction potentials. Configurational properties, such as the radius of gyration, the end-to-end length, and the Kuhn length, are calculated as a function of the intensity of the vdW interactions and ionic strength values. It is observed that chains exhibit a new range of possible conformations compared to the classical random walk and self avoiding walk chains or polyelectrolytes. In the limit of low salt concentration, by gradually increasing vdW interactions, chains undergo a cascade of transitions from extended structures to dumbbells, from dumbbells to pearl necklaces, and from pearl necklaces to collapsed coils. Because of strong competition between the vdW and electrostatic forces, the distance along the chain between the interacting particles, and the sampling limitations, these transitions are found to sample metastable domains and to depend on the initial conformations. To gain insight into the spatial organization of the collapsed conformations, the pair correlation functions of both monomers and particles are calculated. It is shown that collapsed conformations which are the result of strong particle–particle interactions exhibit two distinct parts: a hard core mainly composed of particles and a surrounding polymeric shell composed of loops and tails. Possible effects of such a collapsed transition on the kinetics of flocculation of a mixture containing large flexible chains and small adsorbing colloidal particles are discussed. Received: 26 July 1999 Accepted in revised form: 9 November 1999     

The interaction between triton X series surfactants and poly (ethylene glycol) in aqueous solutions

 A series of Triton X surfactants with different ethylene oxide chain length and poly(ethylene glycols) with different molecular weight were used, to find the effects of polymer chain length and size of the micelles on the cloud point of the surfactants. Two possible models are considered on the basis of cloud point changes of the solutions, to describe the polymer–surfactant interactions. One model considers that intra-chain micelles of polysoap are formed among the surfactant monomers and long polymer chains. The bridging attraction between two intra-chain micelles in such structures can enhance the collisions among the micelles, due to the exchange of amphiphilic monomers among the neighboring micelles. The other model suggests that flocculation depletion for the polymer chains exists between two regular micelles. This provides the driving force for the neighboring micelles to approach each other and destabilize the colloidal system. The flocculation effect is more significant for polymer with a long chain. Polymers with a shorter chain block the approach of the micelles, since there is no typical polymer–surfactant association formed but just simple small molecule associations in which the steric and solvation effects of the polymer chains make the inter-micelle interactions repulsive. Received: 19 August 1997 Accepted: 11 December 1997     

Flocculation of hematite particles by a comparatively large rigid polysaccharide: schizophyllan

We studied the flocculation kinetics and structure of hematite aggregates induced by a large rigid extracellular polysaccharide, schizophyllan. Transmission electron microscopy (TEM), atomic force microscopy (AFM), photon correlation spectroscopy (PCS), and static light scattering (SLS) were used to characterize hematite particles, schizophyllan chains, and their flocs, to follow the time evolution of floc sizes, and to determine floc fractal dimensions. A maximum flocculation rate was found at a certain schizophyllan/hematite ratio. The maximum rate was considerably smaller than the rate of diffusion-limited aggregation (DLA) of hematite particles induced by simple electrolytes. To interpret the experimental results and to reveal various factors affecting the optimal dosage, Monte Carlo simulations were performed on the flocculation of small colloidal particles by relatively long, monodisperse linear polymers. The existence of the maximum flocculation rate was confirmed by computer simulation. However, a higher optimal dosage of schizophyllan was obtained in the experiments. The difference in the optimal dosage can be attributed mostly to the higher adsorption affinity of the hematite on schizophyllan aggregates present in the initial solution and the presence of a large fraction of free polymer chains which do not participate in the flocculation process. Both experiments and computer simulations demonstrated the fractal nature of the schizophyllan-hematite flocs. The fractal dimensions of the flocs at the optimal dosage were determined. A higher fractal dimension was obtained from experiments than from computer simulations, suggesting a reconstruction of the floc structure. Finally, a two-stage flocculation mechanism for hematite particles in the presence of a relatively long schizophyllan polymer was proposed. In the first flocculation stage, the hematite particles are preferentially adsorbed onto the schizophyllan aggregates in solution. The second stage consists of the association of these reactive entities with each other and also with naked chains to form fractal flocs by a bridging mechanism, where the hematite particles play the role of ligands.     

THE EFFECT OF POLYMER ON THE CLOUD POINT OF A SERIES OF TRIBLOCK NONIONIC SURFACTANTS IN AQUEOUS SOLUTION

A series of triblock nonionic surfactants with different Propylene oxide and ethylene oxide chain lengths were synthesized. The triblock nonionic surfactants and poly(ethylene glycols) with different molecular weight were used, to find the effects of polymer chain length and size of the micelles on the cloud point of the surfactants. Two possible models are considered on the basis of cloud point changes of the solutions, to describe the polymer- surfactant interactions. One model suggests that flocculation depletion for the polymer chains exist between two regular micelles. This provides the driving force for the neighboring micelles to approach each other and destabilize the colloidal system. The flocculation effect is more important for polymers with a shorter chain block the approach of the micelles, since there is no typical polymer-surfactant association formed but just simple small molecule associations in which the steric and solvation effects of the polymer chains make the inter-micelles interactions repulsive. The other model considers that intra-chain micelles of polysoap are formed among the surfactant monomers and long polymer chains. The bridging attraction between two intra-chain micelles in such structures can enhance the collisions among the micelles, due to the exchange of amphiphilic monomers among the neighboring micelles.     

Rheological behavior of silica suspensions in aqueous solutions of associating polymer

Associating polymers are hydrophilic long-chain molecules containing a small amount of hydrophobic groups. The aqueous solutions show viscoelastic responses above some critical concentrations because a three-dimensional structure is formed by association of hydrophobic groups. When the associating polymers are added to silica suspensions at low concentrations, the flocculation is induced by bridging mechanisms, and the flow of suspensions become shear-thinning. For suspensions prepared with polymer solutions in which the associating network is developed, the viscosity decreases, shows a minimum, and then increases with increasing particle concentration. The viscosity decrease may arise from the breakdown of associating network due to adsorption of polymer chains onto the silica surfaces. As the particle concentration is increased, the polymer concentration in solution is decreased, and finally, all polymer chains are adsorbed on the surfaces. Beyond this point, the partial coverage of particle surfaces takes place and strong interactions are generated between particles by polymer bridging. Since the stable suspensions are converted to highly flocculated systems, the viscosity is increased and the flow becomes shear-thinning. The concentration effect of silica particles on the viscosity behavior of suspensions can be explained by a combination of viscosity decrease in solution due to polymer adsorption and viscosity increase due to flocculation.     

A kinetic investigation of the flocculation of alumina with polyacrylic acid

Using a model colloidal system of alumina and polyacrylic acid (PAA), the kinetics of flocculation was investigated at low polymer concentrations and short durations (on the order of seconds). The polymer-induced flocculation processes obeyed Von Smoluchowski's bimolecular rate equation. Increases in the concentration of the polymer resulted in higher rate constants for the flocculation process. At a fixed concentration (say 50 ppb, parts per billion), the rate constant values showed a maximum value for 250,000 g mol(-1) polyacrylic acid. At this polymer concentration, calculations of the surface coverage of alumina by PAA molecules of different molecular weights show that for all the cases the coverage is nearly the same, approximately 1x10(-3), but the flocculation response and the rates are significantly different. This trend in flocculation characteristics is attributed to the critical polymer number density requirement for effective flocculation (at least partial charge neutralization and initiation of flocculation). The mechanism governing the flocculation at ultralow concentrations (50 ppb) is the synergistic effect of partial patch neutralization and bridging.     

The use of dielectric spectroscopy for the characterization of polymer-induced flocculation of polystyrene particles

The flocculation of colloidal suspensions is an important unit operation in many industries, as it greatly improves the performance of solid separation processes. The number of available techniques for evaluating flocculation processes on line is limited, and most of these are only functional in dilute suspensions. Thus, techniques usable for flocculation characterization in high-solids suspensions are desirable. This study investigates the use of dielectric spectroscopy to monitor the flocculation of polystyrene particles with a cationic polymer. The frequency-dependent permittivity is modeled and the model parameters are used to describe the particle aggregation. The results show a peak in the modeled time constants of the dielectric relaxation at the onset of flocculation. Further, the adsorption of polymeric flocculant onto the particle surface results in a reduction in particle charge, evident as a decrease in the magnitude of the dielectric dispersion. The use of dielectric spectroscopy is found to be valuable for assessing flocculation processes in high-solids suspensions, as changes in parameters such as floc size and charge can be detected.     

On the origin of colloidal particles in the dispersion polymerization of aniline

When aniline is oxidized in an aqueous medium in the presence of a steric stabilizer, colloidal polyaniline (PANI) dispersions are obtained. The generally accepted model of the stabilization assumes that the macromolecules of the water-soluble steric stabilizer are adsorbed at the polymer, precipitating during the dispersion polymerization, and provide steric protection against further aggregation. An alternative mechanism of conducting-polymer particle formation is proposed in the present study. We suggest that the steric stabilizer provides a site for adsorption of oligoaniline initiation centers; subsequent polymerization from anchored centers yields particle nuclei that grow to produce colloidal PANI particles. This hypothesis is based on the observation that the colloidal particles are obtained only in the case where the steric stabilizer is introduced in the early stages of polymerization when aniline oligomers are present in the reaction mixture. If the stabilizer had been added during the growth of PANI chains, colloidal dispersions would not have been produced. The process of particle growth is completely analogous to the formation of conducting PANI films on the surface of microparticles and various materials. There, the polymerization of aniline at the surfaces is preferred to the same process proceeding in the bulk of the reaction mixture. While the films grow at the interfaces with the reaction mixture, the dispersion particles similarly emanate from the stabilizer chains. The particle size, the formation of nonspherical morphologies, the importance of the chemical nature of the stabilizer chains, and the general relation between the conducting-polymer film and particle growth are discussed in the light of the proposed model.     

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.     

Flocculation of kaolin particles by two typical polyelectrolytes: A comparative study on the kinetics and floc structures

The flocculation kinetics of kaolin particles induced by two polyelectrolytes is studied by using small-angle laser light scattering (SALLS). Two different methods, image analysis and SALLS, are used to calculated the fractal dimensions of flocs formed under different flocculation mechanisms. For a high charge density of polydiallyldimethylammonium chloride (PDADMAC), the initially flocculation rates are slow due to the quite low molecular weight. Smaller and more compact flocs are in the particle–particle connections, and restructuring of the flocs occurs in the flocculation process. With cationic polyacrylamide C498 of very high molecular weight and low charge density, however, the initially flocculation rates are much higher due to its rapid adsorption on kaolin particles, but it will take the adsorbed polymer a much longer time to reach equilibrium due to re-conformation. High potentialities of adsorption prevent the particles from entering the interior of the floc structure or rearrangement, which results in a more open floc structure. Different underlying flocculation mechanisms are evident for these two kinds of polyelectrolytes, in which charge neutralization is mainly involved for the low molecular weight and high charge density polymer of PDADMAC while polymer bridging is suggested to be the dominant mechanism for the high molecular weight polyelectrolyte of C498.     

Effect of temperature on the reentrant condensation in polyelectrolyte-liposome complexation

Interactions of oppositely charged macroions in aqueous solution give rise to intriguing aggregation phenomena, resulting in finite-size, long-lived clusters, characterized by a quite narrow size distribution. Particularly, the adsorption of highly charged linear polyelectrolytes on oppositely charged colloidal particles is strongly correlated and some short-range order arises from competing electrostatic interactions between like-charged polymer chains (repulsion) and between polymer chains and particle surface (attraction). In these systems, in an interval of concentrations around the isoelectric point, relatively large clusters of polyelectrolyte-decorated particles form. However, the mechanisms that drive the aggregation and stabilize, at the different polymer/particle ratios, a well-defined size of the aggregates are not completely understood. Nor is clear the role that the correlated polyion adsorption plays in the aggregation, although the importance of "patchy interactions" has been stressed as the possible source of attractive interaction term between colloidal particles. Different models have been proposed to explain the formation of the observed cluster phase. However, a central question still remains unanswered, i.e., whether the clusters are true equilibrium or metastable aggregates. To elucidate this point, in this work, we have investigated the effect of the temperature on the cluster formation. We employed liposomes built up by DOTAP lipids interacting with a simple anionic polyion, polyacrylate sodium salt, over an extended concentration range below and above the isoelectric condition. Our results show that the aggregation process can be described by a thermally activated mechanism.     

Interaction between small colloidal particles and molecular chains with selectively adsorbing groups: computer simulation study

Using the Monte Carlo simulation technique and the method of simulated annealing, we study interactions between small (nanometric) particles and flexible‐chain polymers with sticker groups which selectively adsorb on the particles and also can strongly attract each other. For the chains with two end stickers (telechelic polymers), we find that the colloidal particles adsorbing on the polymers play the role of junction points (locks) which bind together the ends of different chains. This direct or indirect binding leads to the formation of a web‐like structure throughout the sample: colloidal particles and chain stickers group into mixed clusters – “drops of a fog” – which are wrapped by polymer chains and connected by bridges. Analyzing static structure factors, we show that the selectively adsorbing telechelic polymers can affect the equilibrium spatially homogeneous distribution of colloidal particles that results in the appearance of a quasiregular structure on the intermediate scale related to the average intercluster distance. At sufficiently strong attraction between particles and chain end‐groups, most of the telechelic chains (>90%) adopt either a loop‐like or a stretched bridge‐like conformation, the most typical morphology of the system being a combination of these two structural elements. In the mixed clusters, the colloidal particles and the chain ends pack locally on a binary grid corresponding to a local crystal‐like arrangement. For the chains without attracting end‐groups, we observe the formation of elongated, rugby‐ball‐like clusters having alternate layers of particles and adsorbing chain groups.     

扩散模型和凝聚模型耦合作用下胶体凝聚动力学的Monte Carlo模拟研究

以扩散模型(Ds(γ)=D0×sγ)和凝聚模型(Pij(σ)=P0×(i×j)σ)为基础,对胶体体系随时间的演变、团簇大小分布及其标度关系、团簇的重均大小S(t)的变化规律以及模型对最终分形维数的影响四个角度进行了比较研究,发现扩散指数γ0和凝聚概率指数σ0对胶体的凝聚动力学过程有相似的影响.本文在较宽的γ和σ取值范围内,对胶体的凝聚动力学进行了模拟研究,对慢速凝聚向快速凝聚的转化机理作了定量分析,并进一步分析了在团簇-团簇凝聚(CCA)模型下,得到类似扩散置限凝聚(DLA)模型的凝聚体的物理意义,结果表明:(1)γ0代表了体系中团簇或单粒做"定向运动"而非无规则的布朗运动的情况.这种"定向运动"的推动力可能来自于大团簇产生的强"长程范德华力"、"电场力"等,或来自于体系边界处的外力场的作用.(2)当σ0时,体系成为先快后慢的慢速凝聚,这可能对应大团簇为一排斥中心,即胶体颗粒存在"排斥力场"的现象.(3)证实了团簇的重均大小在凝聚过程的早期按指数规律增长,而后期按幂函数规律增长的实验现象.模拟研究还表明,胶体体系的凝聚动力学过程,在σ0时是一个存在正反馈机制的非线性动力学过程,而在σ0时则体现出负反馈的特征.     

The role of polymer adsorption kinetics in flocculation

The adsorption of polymeric flocculants on the surfaces of suspended solid particles is a non-equilibrium process. It is postulated that the process is controlled by an irreversible attachment between polymer molecules and solid particles. The frequency of such collisions determines the kinetics of adsorption and the distribution of adsorbed polymer on individual particle surfaces. A simplified model is presented in which polymer–particle collision frequencies determine the distribution of adsorbed polymer, and therefore, the adhesion efficiency of the particle–particle collisions that lead to flocculation. The implications of the model with regard to the effects of process variables, such as polymer molecular weight, particle size distribution, solids concentration and mixing conditions, are discussed at length. The critical importance of initial dispersion stability on polymer dosage requirements and overall process performance is demonstrated. The model provides considerable insight into the mechanisms involved in the use of progressive polymer addition to control adsorption and enhance flocculation efficiency.     

Flocculation kinetics of precipitated calcium carbonate

When the percentage of filler in paper is increased, the optical properties are improved and the production cost lowered. However, fillers weaken paper strength by decreasing the fibre–fibre bonded area. Little is known about the optimum filler floc size or filler floc properties to allow developing optimum paper characteristics. Consequently, the kinetics of aggregation of scalenohedral precipitated calcium carbonate (PCC) filler was studied using various polymers (flocculants, coagulants and dry strength agents). The sodium salt of partially hydrolysed polyvinyl formamide copolymerized with acrylic acid (PVFA/NaAA) or C-starch lead to floc sizes, less sensitive to dosage within a certain range. Results from stability ratios correlate with PCC particle size. The change in particle size measured by photometric dispersion analysis (PDA) correlates well with the change in PCC particle size measured by light scattering/diffraction. Kinetic calculations show the orthokinetic aggregation times to be consistent with the experimental PDA results. The main uncertainty in the orthokinetic times is estimating the effective shear rate. It is proposed that the bridging surface area of PCC particles, the area which can form bonds between PCC particles or aggregates, should be used to study the kinetics of PCC aggregation, and not the total or projected surface area. In polymer induced aggregation, the PCC particle size increases to a plateau value with increasing polymer dosage. Two regions are most pronounced for C-PAM, PVFA/NaAA and A-starch. Region I corresponds to bridging flocculation. Region II is where the particle size reaches a plateau, and not the expected maximum predicted by classical polymer bridging theory or charge neutralisation theory, likely because of a competition between particle aggregation and polymer adsorption.