# Advances in Colloid and Interface Science (v.112, #1-3)

Dispersions of polymer ionomers: I by Ignác Capek

*(1-29)*. The principle subject discussed in the current paper is the effect of ionic functional groups in polymers on the formation of nontraditional polymer materials, polymer blends or polymer dispersions. Ionomers are polymers that have a small amount of ionic groups distributed along a nonionic hydrocarbon chain. Specific interactions between components in a polymer blend can induce miscibility of two or more otherwise immiscible polymers. Such interactions include hydrogen bonding, ion–dipole interactions, acid–base interactions or transition metal complexation. Ion-containing polymers provide a means of modifying properties of polymer dispersions by controlling molecular structure through the utilization of ionic interactions. Ionomers having a relatively small number of ionic groups distributed usually along nonionic organic backbone chains can agglomerate into the following structures: (1) multiplets, consisting of a small number of tightly packed ion pairs; and (2) ionic clusters, larger aggregates than multiplets. Ionomers exhibit unique solid-state properties as a result of strong associations among ionic groups attached to the polymer chains. An important potential application of ionomers is in the area of thermoplastic elastomers, where the associations constitute thermally reversible cross-links. The ionic (anionic, cationic or polar) groups are spaced more or less randomly along the polymer chain. Because in this type of ionomer an anionic group falls along the interior of the chain, it trails two hydrocarbon chain segments, and these must be accommodated sterically within any domain structure into which the ionic group enters. The primary effects of ionic functionalization of a polymer are to increase the glass transition temperature, the melt viscosity and the characteristic relaxation times. The polymer microstructure is also affected, and it is generally agreed that in most ionomers, microphase-separated, ion-rich aggregates form as a result of strong ion–dipole attractions. As a consequence of this new phase, additional relaxation processes are often observed in the viscoelastic behavior of ionomers. Light functionalization of polymers can increase the glass transition temperature and gives rise to two new features in viscoelastic behavior: (1) a rubbery plateau above

*T*_{g}and (2) a second loss process at elevated temperatures. The rubbery plateau was due to the formation of a physical network. The major effect of the ionic aggregate was to increase the longer time relaxation processes. This in turn increases the melt viscosity and is responsible for the network-like behavior of ionomers above the glass transition temperature. Ionomers rich in polar groups can fulfill the criteria for the self-assembly formation. The reported phenomenon of surface micelle formation has been found to be very general for these materials.**Keywords:**Polymer blends; Solid dispersions; Ionomers; Functionalization; Interaction;

Interpretation of negative values of the interaction parameter in the adsorption equation through the effects of surface layer heterogeneity by Stoyan Karakashev; Emil Manev; Anh Nguyen

*(31-36)*. The problem of the negative values of the interaction parameter in the equation of Frumkin has been analyzed with respect to the adsorption of nonionic molecules on energetically homogeneous surface.For this purpose, the adsorption states of a homologue series of ethoxylated nonionic surfactants on air/water interface have been determined using four different models and literature data (surface tension isotherms). The results obtained with the Frumkin adsorption isotherm imply repulsion between the adsorbed species (corresponding to negative values of the interaction parameter), while the classical lattice theory for energetically homogeneous surface (e.g., water/air) admits attraction alone. It appears that this serious contradiction can be overcome by assuming heterogeneity in the adsorption layer, that is, effects of partial condensation (formation of aggregates) on the surface. Such a phenomenon is suggested in the Fainerman–Lucassen–Reynders–Miller (FLM) ‘Aggregation model’. Despite the limitations of the latter model (e.g., monodispersity of the aggregates), we have been able to estimate the sign and the order of magnitude of Frumkin's interaction parameter and the range of the aggregation numbers of the surface species.

**Keywords:**Adsorption; Interactions; Surface heterogeneity; Aggregation;

The bridging force between two plates by polyelectrolyte chains by Haohao Huang; Eli Ruckenstein

*(37-47)*. The interaction between particles in a colloidal system can be significantly affected by their bridging by polyelectrolyte chains. In this paper, the bridging is investigated by using a self-consistent field approach which takes into account the van der Waals interactions between the segments of the polyelectrolyte molecules and the plates, as well as the electrostatic and volume exclusion interactions. A positive contribution to the force between two plates is generated by the van der Waals interactions between the segments and the plates. This positive (repulsive) contribution plays an important role in the force when the distances between the plates are small. With increasing van der Waals interaction strength between segments and plates, the force between the plates becomes more repulsive at small distances and more attractive at large distances. When the surfaces of the plates have a constant surface electrical potential and a charge sign opposite to that of the polyelectrolyte chains, the force between the two plates becomes less attractive as the bulk polyelectrolyte concentration increases. This behavior is due to a higher bulk counterion concentration dissociated from the polyelectrolyte molecules. At short distances, the force between plates is more repulsive for stiffer chains. A comparison between theoretical and experimental results regarding the contraction of the interlayer separation between the platelets of vermiculite clays against the concentration of poly(vinyl methyl ether) was made.

**Keywords:**Bridging interaction; Polyelectrolyte; Self-consistent field theory; van der Waals interactions; Repulsive force;

Prediction of three-dimensional fractal dimensions using the two-dimensional properties of fractal aggregates by Chunwoo Lee; Timothy A. Kramer

*(49-57)*. Fractal dimension analysis using an optical imaging analysis technique is a powerful tool in obtaining morphological information of particulate aggregates formed in coagulation processes. However, as image analysis uses two-dimensional projected images of the aggregates, it is only applicable to one and two-dimensional fractal analyses. In this study, three-dimensional fractal dimensions are estimated from image analysis by characterizing relationships between three-dimensional fractal dimensions (

*D*_{3}) and one (*D*_{1}) and two-dimensional fractal dimensions (*D*_{2}and*D*_{pf}). The characterization of these fractal dimensions were achieved by creating populations of aggregates based on the pre-defined radius of gyration while varying the number of primary particles in an aggregate and three-dimensional fractal dimensions. Approximately 2000 simulated aggregates were grouped into 33 populations based on the radius of gyration of each aggregate class. Each population included from 15 to 115 aggregates and the number of primary particles in an aggregate varied from 10 to 1000. Characterization of the fractal dimensions demonstrated that the one-dimensional fractal dimensions could not be used to estimate two- and three-dimensional fractal dimensions. However, two-dimensional fractal dimensions obtained statistically, well-characterized relationships with aggregates of a three-dimensional fractal characterization. Three-dimensional fractal dimensions obtained in this study were compared with previously published experimental values where both two-dimensional fractal and three-dimensional fractal data were given. In the case of inorganic aggregates, when experimentally obtained three-dimensional fractal dimensions were 1.75, 1.86, 1.83±0.07, 2.24±0.22, and 1.72±0.13, computed three-dimensional fractal dimensions using two-dimensional fractal dimensions were 1.75, 1.76, 1.77±0.04, 2.11±0.09, and 1.76±0.03, respectively. However, when primary particles were biological colloids, experimentally obtained three-dimensional fractal dimensions were 1.99±0.08 and 2.14±0.04, and computed values were both 1.79±0.08. Analysis of the three-dimensional fractal dimensions with the imaging analysis technique was comparable to the conventional methods of both light scattering and electrical sensing when primary particles are inorganic colloids.**Keywords:**Fractal aggregates; Three-dimensional fractal; Two-dimensional fractal; One-dimensional fractal; Image analysis;

Electrokinetics of heterogeneous interfaces by Maria Zembala

*(59-92)*. The influence of surface heterogeneity of various types on electrokinetic parameters is reviewed. The scope of the paper covers classical electrokinetic phenomena characterized by linear dependence of electrokinetic parameters vs. related driving forces. Neither non-linear effects nor the effects of non-equilibrium electric double layer are considered.A historical description of hydrodynamic aspect of electrokinetic phenomena exploiting the slip plane idea is briefly outlined. Attempts to estimate the slip plane location by comparing the diffuse layer and zeta potential values for some model systems are presented.The surface heterogeneity was divided into three categories. Heterogeneity of the first type was related to geometrical morphology of an interfacial region characterized by a considerable surface development producing a three-dimensional interfacial region. The effects of solid roughness, hairy surface, dense polymer layers and gel-like layers are discussed here. The very high surface conductivity detected for such interfaces seems to be a good indicator of the presence of structured layers of this type.Heterogeneous interfaces of the second class cover systems exhibiting non-uniform distribution of surface charge. The non-uniform surface charge distribution can be either of a molecular (discrete charges) or of a microscale (two-dimensional micropatches or three-dimensional structures formed by polyelectrolyte multilayers).The last class of systems examined includes interfaces composed of charged substrate covered by charged bulky objects (particles). In comparison to the homogeneous surfaces, adsorbed charged particles modify both hydrodynamic flow and the electrostatic field significantly altering the electrokinetic parameters. The new description of electrokinetics of composed interfaces presented here takes into account both hydrodynamic and electric field modification and is free of the previously assumed slip plane shift caused by adsorbed objects. This theoretical approach verified by experiments performed on well defined model systems can be successfully applied to the interpretation of experimental data obtained for surfaces covered by objects difficult to detect.

**Keywords:**Heterogeneous surfaces; Composed surfaces; Electrokinetics; Streaming potential; Zeta potential;

High ionic strength electrokinetics by Marek Kosmulski; Jarl B. Rosenholm

*(93-107)*. The electrokinetic potentials at high ionic strengths can be measured by means of electroacoustic method. The reported values are surprisingly high: up to 25 mV in 1 mol dm

^{−3}1:1 electrolyte solution. The IEP of metal oxides in concentrated solutions of 1:1 electrolytes shifts to substantially higher pH values with respect to the pristine value, although these electrolytes are inert at low concentration. The shift in the IEP is salt-specific, and it is correlated with the hard–soft character of the anion and of the cation.**Keywords:**Isoelectric point; Zeta potential; Electric sonic amplitude; Colloid vibration current; Concentrated electrolyte solutions;

The polarization model for hydration/double layer interactions: the role of the electrolyte ions by Marian Manciu; Eli Ruckenstein

*(109-128)*. The interactions between hydrophilic surfaces in water cannot be always explained on the basis of the traditional Derjaguin–Landau–Verwey–Overbeek (DLVO) theory, and an additional repulsion, the “hydration force” is required to accommodate the experimental data. While this force is in general associated with the organization of water in the vicinity of the surface, different models for the hydration were typically required to explain different experiments. In this article, it is shown that the polarization-model for the double layer/hydration proposed by the authors can explain both (i) the repulsion between neutral lipid bilayers, with a short decay length (∼2 Å), which is almost independent of the electrolyte concentration, and, at the same time, (ii) the repulsion between weakly charged mica surfaces, with a longer decay length (∼10 Å), exhibiting not only a dependence on the ionic strength, but also strong ion-specific effects. The model, which was previously employed to explain the restabilization of protein-covered latex particles at high ionic strengths and the existence of a long-range repulsion between the apoferritin molecules at moderate ionic strengths, is extended to account for the additional interactions between ions and surfaces, not included in the mean field electrical potential. The effect of the disorder in the water structure on the dipole correlation length is examined and the conditions under which the results of the polarization model are qualitatively similar to those obtained by the traditional theory via parameter fitting are emphasized. However, there are conditions under which the polarization model predicts results that cannot be recovered by the traditional theory via parameter fitting.

**Keywords:**Polarization model; Hydration forces; Double layer interaction; Ion-specific effects; Restabilization;

Interparticle interactions in concentrate water–oil emulsions by N.A. Mishchuk; A. Sanfeld; A. Steinchen

*(129-157)*. The present investigation is based on the description of electrostatic interaction in concentrated disperse systems proposed 45 years ago by Albers and Overbeek. Starting from their model, we developed a stability theory of concentrated Brownian W/O emulsions in which nondeformed droplets undergo electrostatic and Van der Waals interactions.While the droplets in dilute emulsion may be described by pair interaction, in dense emulsions, every droplet is closely surrounded by other droplets, and when two of them come together, not only the energy of their pair interaction, but also their interaction with surrounding droplets change. Unlike in dilute emulsion, for which the reference energy of the pair is the energy at infinity (taken equal to zero), in concentrate emulsion, the reference energy is not zero but is the energy of interaction with averaged ensemble of nearest droplets. The larger the volume fraction, the higher the reference energy and, thus, the lower the energy barrier between two coagulating droplets, which enhances the coagulation. In dense packing of drops, the energy of interaction and the reference energy coincide, therefore, the height of energy barrier vanishes.In contrast with dense emulsion, at medium volume fraction, when two coagulating droplets interact only with a few nearest neighbors, our analysis shows that the energy barrier may also increase, which extends thus the domain of stability.Because in W/O emulsion, the thickness of the electric double layer is of the same order or larger than the size of droplets, the electrostatic energy was calculated with a correction factor

*β*that accounts for the deviation of double layers from sphericity. A more complete van der Waals interaction with account of screening of interaction by electrolyte has been used. Both factors promote the decrease of energy barrier between coagulating droplets and enhance the coagulation.Our model introduces two critical volume fractions. The first one,*φ*_{c1}, is the volume fraction depending on the characteristics of system (size of drops, thickness of double layer, surface potential, dielectric permittivity of medium) that limits the validity of the pair interaction model. The second one,*φ*_{c2}, is a volume fraction that limits the applicability of the simplified model of interaction of three or more double layers.By comparing the energies of barrier height and of Brownian motion, a critical volume fraction*φ*_{c3}is defined, which determines the starting point of rapid coagulation.Finally, the influence of drop interaction on gravitational coagulation is also briefly presented. It is shown that the probability of coagulation between fixed in space and sedimenting droplets is larger than with only Brownian coagulation. Unlike at free sedimentation of two identical drops, the gravitation cannot accelerate their aggregation. The surface potential, which leads to the equilibration of surface forces, gravitational and Archimedes forces for a given volume fraction, is then obtained.**Keywords:**Concentrate emulsions; Coagulation; Electrostatic interaction; Energy barrier; van der Waals interaction: Water–oil emulsion;

Brownian Dynamics, Molecular Dynamics, and Monte Carlo modeling of colloidal systems by Jim C. Chen; Albert S. Kim

*(159-173)*. This paper serves as an introductory review of Brownian Dynamics (BD), Molecular Dynamics (MD), and Monte Carlo (MC) modeling techniques. These three simulation methods have proven to be exceptional investigative solutions for probing discrete molecular, ionic, and colloidal motions at their basic microscopic levels. The review offers a general study of the classical theories and algorithms that are foundational to Brownian Dynamics, Molecular Dynamics, and Monte Carlo simulations. Important topics of interest include fundamental theories that govern Brownian motion, the Langevin equation, the Verlet algorithm, and the Metropolis method. Brownian Dynamics demonstrates advantages over Molecular Dynamics as pertaining to the issue of time-scale separation. Monte Carlo methods exhibit strengths in terms of ease of implementation. Hybrid techniques that combine these methods and draw from these efficacies are also presented. With their rigorous microscopic approach, Brownian Dynamics, Molecular Dynamics, and Monte Carlo methods prove to be especially viable modeling methods for problems with challenging complexities such as high-level particle concentration and multiple particle interactions. These methods hold promising potential for effective modeling of transport in colloidal systems.

**Keywords:**Brownian Dynamics; Molecular Dynamics; Monte Carlo; Inter-particle interaction; Diffusivity; Stochastic force; Verlet algorithm; Langevin equation; Metropolis method;