Polarizability and complex conductivity of dilute suspensions of spherical colloidal particles with uncharged (neutral) polymer coatings

The polarizability of polymer-coated colloidal particles, as measured via dielectric relaxation spectroscopy, reflects on the degree to which convection, diffusion, and electromigration deform the equilibrium double layer. With a polymer coating, convection and electro-osmosis are resisted by hydrodynamic drag on the polymer segments. The electro-osmotic flow near the underlying bare surface is therefore diminished. Characteristics of the particles and the adsorbed polymer can, in principle, be inferred by measuring the frequency-dependent polarizability. In this work, "exact" numerical solutions of the electrokinetic equations are used to examine how adsorbed polymer changes the particle polarizability and, hence, the conductivity and dielectric constant increments of dilute suspensions. For neutral polymer coatings, the conductivity and dielectric constant increments are found to be very similar to those of the underlying bare particles, so the response depends mostly on the underlying bare particles. These observations suggest that dielectric spectroscopy is best used to determine the underlying surface charge, with characteristics of the coating inferred from the electrophoretic or dynamic mobility, together with the hydrodynamic radius obtained from sedimentation or dynamic light scattering. Addressed briefly are the effects of added counterions and nonspecific adsorption. The electrokinetic model explored in this work can be used to guide experiments (frequency and ionic strength, for example) to either minimize or maximize the sensitivity of the complex conductivity to the coating thickness or permeability.     

Density-functional theory of spherical electric double layers and zeta potentials of colloidal particles in restricted-primitive-model electrolyte solutions

A density-functional theory is proposed to describe the density profiles of small ions around an isolated colloidal particle in the framework of the restricted primitive model where the small ions have uniform size and the solvent is represented by a dielectric continuum. The excess Helmholtz energy functional is derived from a modified fundamental measure theory for the hard-sphere repulsion and a quadratic functional Taylor expansion for the electrostatic interactions. The theoretical predictions are in good agreement with the results from Monte Carlo simulations and from previous investigations using integral-equation theory for the ionic density profiles and the zeta potentials of spherical particles at a variety of solution conditions. Like the integral-equation approaches, the density-functional theory is able to capture the oscillatory density profiles of small ions and the charge inversion (overcharging) phenomena for particles with elevated charge density. In particular, our density-functional theory predicts the formation of a second counterion layer near the surface of highly charged spherical particle. Conversely, the nonlinear Poisson-Boltzmann theory and its variations are unable to represent the oscillatory behavior of small ion distributions and charge inversion. Finally, our density-functional theory predicts charge inversion even in a 1:1 electrolyte solution as long as the salt concentration is sufficiently high.     

Parameter identifiability in application of soft particle electrokinetic theory to determine polymer and polyelectrolyte coating thicknesses on colloids

Soft particle electrokinetic models have been used to determine adsorbed nonionic polymer and polyelectrolyte layer properties on nanoparticles or colloids by fitting electrophoretic mobility data. Ohshima first established the formalism for these models and provided analytical approximations ( Ohshima, H. Adv. Colloid Interface Sci.1995, 62, 189 ). More recently, exact numerical solutions have been developed, which account for polarization and relaxation effects and require fewer assumptions on the particle and soft layer properties. This paper characterizes statistical uncertainty in the polyelectrolyte layer charge density, layer thickness, and permeability (Brinkman screening length) obtained from fitting data to either the analytical or numerical electrokinetic models. Various combinations of particle core and polymer layer properties are investigated to determine the range of systems for which this analysis can provide a solution with reasonably small uncertainty bounds, particularly for layer thickness. Identifiability of layer thickness in the analytical model ranges from poor confidence for cases with thick, highly charged coatings, to good confidence for cases with thin, low-charged coatings. Identifiability is similar for the numerical model, except that sensitivity is improved at very high charge and permeability, where polarization and relaxation effects are significant. For some poorly identifiable cases, parameter reduction can reduce collinearity to improve identifiability. Analysis of experimental data yielded results consistent with expectations from the simulated theoretical cases. Identifiability of layer charge density and permeability is also evaluated. Guidelines are suggested for evaluation of statistical confidence in polymer and polyelectrolyte layer parameters determined by application of the soft particle electrokinetic theory.     

Towards a modellisation of the solvation energy in multi-component solvents. The interesting case of a charged solute imbedded in a polymer-containing electrolyte solution

In this paper we propose a mean-field theory to calculate the solvation free energy of a charged solute imbedded in a complex multi-component solvent. We considered a solvent made up of a mixture of small (electrolyte solution) and large (polymer) components. The presence of macromolecules ensures reduced mixing entropy among the different solvent components, an effect due to polymer connectivity. The reduced entropy favours strong preferential distribution of a particular solvent even in the presence of weak preferential solute–solvent interactions. In addition, two energy terms must be considered: (a) the interaction between the solute electrostatic potential and the electrolyte solution and (b) the formation of a polymer–solute interface. Because of the different dielectric permittivity of the solvent components, the electrolyte and polymer distribution functions are strongly coupled: ions, indeed, are more solvated in regions of higher local dielectric permittivity arising from the inhomogeneous mixing of solvent and polymer. We combined together the different energy terms in the framework of the de Gennes free energy functional for polymer solutions along with a generalised Poisson–Boltzmann equation developed for inhomogeneous dielectric media. Moreover, the preferential electrolyte solvation in regions of greater polarity was considered by an extension of the Born equation. Setting the polymer dielectric permittivity smaller than the solvent one and making null the specific polymer–solute interactions, we calculated enhanced electrolyte concentration and reduced polymer concentration near the solute surface on raising the solute surface charge density. The theory shows also the breakdown of the widely used separation between electrostatic and surface tension-dependent contributions to solvation energy when non-ideal mixed solvents are considered. In fact, according to the model, the surface tension of such mixed solvents strongly depends on the solute surface charge density: at high potentials the interfacial tension may increase rather than decrease on raising the polymer volume fraction. The theoretical results have been compared with experimental data on polymer+electrolyte solution surface tension and with solubility data of colloidal particles. The comparison evidences the complex behaviour of multi-component solvents going well beyond the trivial weighted average of the dielectric permittivity and surface tension of the isolated chemical components. Deviations from the simple behaviour predicted by an average picture of multi-component solvents could be understood by developing more sophisticated, but still simple, approaches like that proposed in this paper.Contribution to the Jacopo Tomasi Honorary Issue. This paper is dedicated to Jacopo Tomasi. I learned much of the difficult art of transforming complex problems into simple models after reading his early works on solvation energy.     

Surface properties of bottle-brush polyelectrolytes on mica: effects of side chain and charge densities

Surface properties of a series of cationic bottle-brush polyelectrolytes with 45-unit-long poly(ethylene oxide) side chains were investigated by phase modulated ellipsometry and surface force measurements. The evaluation of the adsorbed mass of polymer on mica by means of ellipsometry is complex due to the transparency of mica and its birefringence and low dielectric constant. We therefore employed a new method to overcome these difficulties. The charge and the poly(ethylene oxide) side chain density of the bottle-brush polymers were varied from zero charge density and one side chain per segment to one charge per segment and no side chains, thus spanning the realm from a neutral bottle-brush polymer, via a partly charged brush polyelectrolyte, to a linear fully charged polyelectrolyte. The adsorption properties depend crucially on the polymer architecture. A minimum charge density of the polymer is required to facilitate adsorption to the oppositely charged surface. The maximum adsorbed amount and the maximum side chain density at the surface are obtained for the polymer with 50% charged segments and the remaining 50% of the segments carrying poly(ethylene oxide) side chains. It is found that brushlike layers are formed when 25-50% of the segments carry poly(ethylene oxide) side chains. In this paper, we argue that the repulsion between the side chains results in an adsorbed layer that is non-homogeneous on the molecular level. As a result, not all side chains will contribute equally to the steric repulsion but some will be stretched along the surface rather than perpendicular to it. By comparison with linear polyelectrolytes, it will be shown that the presence of the side chains counteracts adsorption. This is due to the entropic penalty of confining the side chains to the surface region.     

Aggregation phenomena in the suspension polymerization of VCM

In the suspension polymerization of VCM, insoluble polymer particles are formed inside the monomer droplets. The growth and aggregation of these particles are responsible for important polymer properties, such as porosity. It is well established that the most characteristic polymer particles, the primary particles, are of a narrow distribution with a size (diameter) ranging from 0.10–0.20 m. This work studied the formation of primary particles based on the aggregation phenomena that take place inside a monomer droplet. This was done by formulating a population balance equation, which was based on the following considerations: a) polymerization occurs in both the monomer and the polymer phases; b) there is continuous formation of the basic particles in the monomer phase; c) the growth of the polymer particles occurs as a result of both polymerization in the polymer phase and aggregation of the particles; d) the colloidal properties of the particles that are responsible for the aggregation phenomena were considered to be the net result of attraction and repulsion energies.It was shown that for particles carrying a constant charge it was not possible to predict the formation of primary particles of size 0.10–0.20 m. The particle size distribution had a mode diameter equal to the diameter of the basic particles. Consequently, the particle charge was allowed to vary in a way proportional to the particle radius raised to a power coefficient. For values of the coefficient greater than zero, i. e., when the particle charge increased during polymerization, the aggregation of the basic particles was efficient enough to result in the formation of large primary particles.     

SEGMENT DENSITY PROFILES OF COMPACT POLYMER CHAINS CONFINED BETWEEN TWO PARALLEL PLANE WALLS

We use the pruned-enriched Rosenbluth method to investigate systematically the segment density profiles of compact polymer chains confined between two parallel plane walls.The non-adsorption case of adsorption interaction energyε=0 and the weak adsorption case ofε=-1 are considered for the compact polymer chains with different chain lengths N and different separation distances between two walls D.Several special entropy effects on the confined compact polymer chains,such as a damped oscillation in the segment density profile for the large separation distance D,are observed and discussed for different separation distances D in the non-adsorption case.In the weak adsorption case,investigations on the segment density profiles indicate that the competition between the entropy and adsorption effects results in an obvious depletion layer.Moreover,the scaling laws of the damped oscillation period T_d and the depletion layer width L_d are obtained for the confined compact chains.Most of these results are obtained for the first time so far as we know,which are expected to understand the properties of the confined compact polymer chains more completely.     

Intercalation of solvent and polymer in galleries of mobile clay platelets by a Monte Carlo simulation

The intercalation of solvent particles and polymer chains of concentration C_w = 0.2 and C_p = 0.2, respectively, in a layer of (4) clay platelets is studied by a Monte Carlo simulation on a cubic lattice. Polymer chains and platelets are modeled by bond fluctuations. Besides the excluded volume, a set of polymer-clay (cs) and solvent-clay (ws) interactions with (i) cs = 1, ws = −2, (ii) cs = −2, ws = 1 and (iii) cs = ws = −2 are considered. The global dynamics of platelets is constrained due to the presence of three components, i.e., solvent, polymer, and platelets, which retain their interstitial spacing with well-defined galleries. Intercalation of solvent particles and polymer chains (low molecular weight) occurs with their attractive interaction with the platelets, which further reinforces the layered clay morphology. The density profiles of the solvent particles are similar to previous studies with platelets in a mobile solvent. The density profile of polymer chains differs considerably from the platelets in a polymer matrix alone, particularly with its attractive interaction (ii). For the same attractive interaction of solvent and polymer chains with the clay platelets (iii), the solvent particles (the smallest constituents) intercalate the fastest in the clay galleries, whereas the intercalation of polymer chains decreases with their molecular weight. The polymer density profiles, both longitudinal (x) and transverse (y), show maxima peaks around outer platelets (surface) of the layer and decay sharply both in the adjacent galleries and in the bulk. The amplitude of oscillation in the transverse density profiles, a measure of the degree of intercalation, decreases with increasing molecular weight of the polymer. The intercalation of the polymer is driven by its attractive interaction at the low molecular weight, but reduces considerably at high molecular weight because of both entanglement and larger radius of gyration. Variations of the gyration radius of the diffusing polymer chains with molecular weight and interaction with the clay are consistent with the results of their corresponding density profiles. © 2009 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 47: 2487–2500, 2009     

Small-angle neutron scattering study of structural changes in temperature sensitive microgel colloids

The structure of temperature-sensitive poly(N-isopropylacrylamide) microgels in dilute suspension was investigated by means of small-angle neutron scattering. A direct modeling expression for the scattering intensity distribution was derived which describes very well the experimental data at all temperatures over an extensive q range. The overall particle form as well as the internal structure of the microgel network is described by the model. The influence of temperature, cross-linking density, and particle size on the structure was revealed by radial density profiles and clearly showed that the segment density in the swollen state is not homogeneous, but gradually decays at the surface. The density profile reveals a box profile only when the particles are collapsed at elevated temperatures. An increase of the cross-linking density resulted in both an increase of the polymer volume fraction in the inner region of the particle and a reduction of the smearing of the surface. The polymer volume fraction inside the colloid decreased with increasing particle size. The structural changes are in good agreement with the kinetics of the emulsion copolymerization used to prepare the microgel colloids.     

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.     

Structure of Conducting Polymer Films Prepared on the Surface and in the Pores of Poly(ethylene terephthalate) Track Membranes by Template Synthesis

The results of a structural study of conducting polymer coatings deposited onto poly(ethylene terephthalate) (PET) track membranes by template synthesis are reported. The following aspects of the quality of polymer coatings were studied: the ratio between film and granular polymers, the polymer distribution over the surface of track membranes, and the thickness of polymer layers on the opposite sides of track membranes. The fraction of granular polypyrrole (PPy) on the surface and in the pores of a film increased with pore diameter. A decrease in the polymerization temperature decreased the amount of granular PPy on the surface of membranes, whereas the effect of granular PPy on the water permeability of track membranes remained unchanged. A more homogeneous distribution of PPy over the surface of track membranes can be obtained by density equalization of reacting solutions; however, the fraction of granular PPy on the membrane surface increased in this case. It was found that polymer coatings on the two sides of the surface of a membrane template had different thicknesses. Poly(N-methylpyrrole) completely covered only one side of a track membrane facing a monomer solution.     

Structure of spherical electric double layers: a density functional approach

A density functional theory is presented for the structure of spherical electric double layers within the restricted primitive model, where the macroion is considered as a hard sphere having uniform surface charge density, the small ions as charged hard spheres, and the solvent is taken as a dielectric continuum. The theory is partially perturbative as the hard-sphere contribution to the one-particle correlation function is evaluated using suitably averaged weighted density and the ionic part is obtained through a second-order functional Taylor expansion around the uniform fluid. The theory is in quantitative agreement with Monte Carlo simulation for the density profiles and the zeta potentials over a wide range of macroion sizes and electrolyte concentrations. The theory is able to provide interesting insights about the layering and the charge inversion phenomena occurring at the interface.     

Why like-charged particles of dielectric materials can be attracted to one another

Calculations of surface charge density provide evidence of the physical effects responsible for particles of a dielectric material carrying the same sign of charge being attracted to one another. The results show that attraction requires a mutual polarisation of charge leading to regions of negative and positive surface density close to the point where the particles make contact. These results emphasise the significance of using charged particle models where the surface charge is non-stationary.     

STUDY ON THE FORMATION MECHANISM OF MONODISPERSE PARTICLES IN THE EMULSIFIER-FREE EMULSION POLYMEAIZATION OF METHYL METHACRYLATE AND BUTYL ACRYLATE

The formation mechanism of monodisperse polymer latex particles in the emulsifier-free emulsion polymerizationof methyl methacrylate and butyl acrylate with potassium persulfate as initiator was investigated. A multi-step formationmechanism for the monodisperse polymer particles was proposed. The nucleation mechanism is considered to be thecoagulation of the precursor particles by homogeneous nucleation when the primary particles reach a critical size with highsurface charge density and sufficient stability. It had been proved by a special experiment that the early latex particles formedby the coagulation were stable. The primary particles grow by absorbing monomers and radicals in the polymerization systemand then become colloidally unstable again due to the understandable decrease of particle surface charge density, which leadsto the aggregation of the growing particles and the formation of larger latex pedicles therefrom. Aner the nucleation period,the preferential aggregation of the smaller particles in the propagation process leads to the change of the particles towards auniform size and narrower particle size distribution. The coexistence and competition of homogeneous nucleation,coagulation, propagation and aggregation result in the increase of the polydispersity index (U = D_(43)/D_(10)) in the first Stage,then its decrease in the later stage because of the competition of propagation and aggregation, and the gradual formation ofthe monodisperse particles.     

Investigation on the dielectric relaxation properties of PVC with small amounts of additives: Thermally stimulated depolarization current analysis of PVC with lead sulphate

From relaxation investigations on the electric charge of the electrically polarized polymer, physical aspects of the effect of tri-basic lead sulphate, as a stabilizer, on the dielectric relaxation properties of PVC are considered. The results correlate with the established fact that tri-basic lead sulphate as a dispersion additive has a marked influence on the process of structure formation, changing the dielectric relaxation properties of the polymer.     

Effect of a surface charge on the halfwidth and peak position of cluster plasmons in colloidal metal particles

The optical response of colloidal particles depends on a variety of properties of the cluster, e.g., shape, size, size distribution and particle material. Since particles often are charged, also the surface charge may be a parameter which influences their optical properties. In this paper the effect of a surface charge on optical properties of spherical colloidal particles is studied and its magnitude is estimated by extended computations for silver clusters with surface plasmon in aqueous suspension. Two models are presented and discussed. The first model is based on the electrodynamic solution by Bohren and Hunt (Can. J. Phys. 55, 1930 (1977)), where a surface conductivity _S for a free surface charge yield an additional contribution _S to the dielectric constant of the particle material. In the second model, the surface charge contributes to the number density of free electrons in the cluster. Both models lead to a shift of the cluster plasmon peak, while an increase of the plasmon halfwidth could not be derived. The effect is quite small and limited on very small clusters.PACS 61.46+w 73.20.Mf 78.20.Dj     

Aggregation and dispersion of small hydrophobic particles in aqueous electrolyte solutions

The effect of salts on the solvent-induced interactions between hydrophobic particles dispersed in explicit aqueous solution is investigated as a function of the salt's ionic charge density by molecular dynamics simulations. We demonstrate that aggregates of the hydrophobic particles can be formed or dissolved in response to changes in the charge density of the ions. Ions with high charge density increase the propensity of the hydrophobic particles to aggregate. This corresponds to stronger hydrophobic interactions and a decrease in the solubility (salting-out) of the hydrophobic particles. Ions with low charge density can either increase or decrease the propensity for aggregation depending on whether the concentration of the salt is low or high, respectively. At low concentrations of low charge density ions, the aggregate forms a "micelle-like" structure in which the ions are preferentially adsorbed at the surface of the aggregate. These "micelle-like" structures can be soluble in water so that the electrolyte can both increase the solubility and increase aggregation at the same time. We also find, that at the concentration of the hydrophobic particles studied (approximately 0.75 m), the aggregation process resembles a first-order transition in finite systems.     

Effect of soluble polymer binder on particle distribution in a drying particulate coating

Soluble polymer is frequently added to inorganic particle suspensions to provide mechanical strength and adhesiveness to particulate coatings. To engineer coating microstructure, it is essential to understand how drying conditions and dispersion composition influence particle and polymer distribution in a drying coating. Here, a 1D model revealing the transient concentration profiles of particles and soluble polymer in a drying suspension is proposed. Sedimentation, evaporation and diffusion govern particle movement with the presence of soluble polymer influencing the evaporation rate and solution viscosity. Results are summarized in drying regime maps that predict particle accumulation at the free surface or near the substrate as conditions vary. Calculations and experiments based on a model system of poly(vinyl alcohol) (PVA), silica particles and water reveal that the addition of PVA slows the sedimentation and diffusion of the particles during drying such that accumulation of particles at the free surface is more likely.     

Colloidal Properties of Polychlorotrifluoroethylene-Based Multicomponent Dispersions

A polychlorotrifluoroethylene-based multicomponent dispersion in dimethylformamide (DMF) was used to prepare protective polymer coatings by the electrodeposition method. The properties of the fluoroplastic coatings were modified by the addition of a cationic polyelectrolyte and pigments of different natures to the dispersion, the pigments being codeposited on a cathode together with the fluoroplastic particles. The optimal composition of the dispersion was determined. It was found that all dispersion components were wetted by DMF; the surface properties of the coatings depended on the concentration of the polyelectrolyte added to the dispersion. The polyelectrolyte adsorption on F-3 and pigment particles was estimated by the UV spectroscopy; the electrokinetic potential of the particles was measured. The charge on a particle surface increased the dispersion stability, thus facilitating the formation of a more uniform electrodeposited layer, i.e., the coating.