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Advances in Colloid and Interface Science (v.118, #1-3)
Application of the extended RSA models in studies of particle deposition at partially covered surfaces by Paweł Weroński (pp. 1-24).
This paper reviews the application of the extended random sequential adsorption (RSA) approaches to the modeling of colloid-particle deposition (irreversible adsorption) on surfaces precovered with smaller particles. Hard (noninteracting) particle systems are discussed first. We report on the numerical simulations we performed to determine the available surface function, jamming coverage, and pair-correlation function of the larger particles. We demonstrate the effect of the particle size ratio and the small particle surface coverage. We found that the numerical results were in reasonable agreement with the formula stemming from the scaled-particle theory in 2D with a modification for the sphere geometry. Next, we discuss three approximate models of adsorption allowing electrostatic interaction of colloid particles at a charged interface, employing a many-body superposition approximation. We describe two approaches of the effective hard-particle approximation next. We demonstrate the application of the effective hard-particle concept to the bimodal systems and present the effect of electrolyte concentration on the effective particle size ratio. We present the numerical results obtained from the theoretical models of soft-particle adsorption at precovered surfaces. We used the effective hard-particle approximation to determine the corresponding simpler systems of particles, namely the system of hard spheres and the system of hard discs at equilibrium. We performed numerical computations to determine the effective minimum particle surface-to-surface distance, available surface function, jamming coverage, and pair-correlation function of the larger particles at various electrolyte ionic strengths and particle size ratios. The numerical results obtained in the low-surface coverage limit were in good agreement with the formula stemming from the scaled-particle theory with a modification for the sphere geometry and electrostatic interaction. We compared the results of numerical computations of the effective minimum particle surface-to-surface distance obtained using the 2D, 3D, and curvilinear trajectory model. The results obtained with the 3D and curvilinear trajectory models indicate that large-particle/substrate attractive interaction significantly reduces the kinetic barrier to large, charged-particle adsorption at a surface precovered with small, like-charged particles. The available surface function and jamming-coverage values predicted using the simplified 3D and the more sophisticated curvilinear trajectory models are similar, while the results obtained with the 2D model differ significantly. The pair-correlation function suggests different structures of monolayers obtained with the three models. Unlike the three models of the electrostatic interaction, both effective hard-particle approximations give almost identical results. Results of this research clearly suggest that the extended RSA approaches can fruitfully be exploited for numerical simulations of colloid-particle adsorption at precovered surfaces, allowing the investigation of both hard and soft-particle systems.
Keywords: Adsorption of colloid particles; Particle electrostatic interaction; Colloid deposition; Monte Carlo simulation; Random sequential adsorption; RSA model
Irreversible adsorption of particles on heterogeneous surfaces by Zbigniew Adamczyk; Katarzyna Jaszczółt; Aneta Michna; Barbara Siwek; Lilianna Szyk-Warszyńska; Maria Zembala (pp. 25-42).
Methods of theoretical and experimental evaluation of irreversible adsorption of particles, e.g., colloids and globular proteins at heterogeneous surfaces were reviewed. The theoretical models were based on the generalized random sequential adsorption (RSA) approach. Within the scope of these models, localized adsorption of particles occurring as a result of short-ranged attractive interactions with discrete adsorption sites was analyzed. Monte-Carlo type simulations performed according to this model enabled one to determine the initial flux, adsorption kinetics, jamming coverage and the structure of the particle monolayer as a function of the site coverage and the particle/site size ratio, denoted by λ. It was revealed that the initial flux increased significantly with the site coverage Θs and the λ parameter. This behavior was quantitatively interpreted in terms of the scaled particle theory. It also was demonstrated that particle adsorption kinetics and the jamming coverage increased significantly, at fixed site coverage, when the λ parameter increased. Practically, for α= λ2 Θs>1 the jamming coverage at the heterogeneous surfaces attained the value pertinent to continuous surfaces. The results obtained prove unequivocally that spherically shaped sites were more efficient in binding particles in comparison with disk-shaped sites. It also was predicted that for particle size ratio λ<4 the site multiplicity effect plays a dominant role, affecting significantly the structure of particle monolayers and the jamming coverage. Experimental results validating main aspects of these theoretical predictions also have been reviewed. These results were derived by using monodisperse latex particles adsorbing on substrates produced by covering uniform surface by adsorption sites of a desired size, coverage and surface charge. Particle deposition occurred under diffusion-controlled transport conditions and their coverage was evaluated by direct particle counting using the optical and electron microscopy. Adsorption kinetics was quantitatively interpreted in terms of numerical solutions of the governing diffusion equation with the non-linear boundary condition derived from Monte-Carlo simulations. It was proven that for site coverage as low as a few percent the initial flux at heterogeneous surfaces attained the maximum value pertinent to homogeneous surfaces. It also was demonstrated that the structure of larger particle monolayers, characterized in terms of the pair correlation function, showed much more short-range ordering than predicted for homogeneous surface monolayers at the same coverage. The last part of this review was devoted to detection of polyelectrolyte multilayers on various substrates via particle deposition experiments.
Keywords: Adsorption of colloids; Colloid adsorption; Heterogeneous surface adsorption; Irreversible adsorption; Kinetics of particle adsorption; Protein adsorption; Random site adsorption
Influence of cell-model boundary conditions on the conductivity and electrophoretic mobility of concentrated suspensions by F. Carrique; J. Cuquejo; F.J. Arroyo; M.L. Jiménez; A.V. Delgado (pp. 43-50).
In the last few years, different theoretical models and analytical approximations have been developed addressing the problem of the electrical conductivity of a concentrated colloidal suspension. Most of them are based on the cell model concept, and coincide in using Kuwabara's hydrodynamic boundary conditions, but there are different possible approaches to the electrostatic boundary conditions. We will call them Levine–Neale's (LN, they are Neumann type, that is they specify the gradient of the electrical potential at the boundary), and Shilov–Zharkikh's (SZ, Dirichlet type). The important point in our paper is that we show by direct numerical calculation that both approaches lead to identical evaluations of the conductivity of the suspensions if each of them is associated to its corresponding evaluation of the macroscopic electric field. The same agreement between the two calculations is reached for the case of electrophoretic mobility. Interestingly, there is no way to reach such identity if two possible choices are considered for the boundary conditions imposed to the field-induced perturbations in ionic concentrations on the cell boundary ( r= b), δn i ( r= b). It is demonstrated that the conditions δn i( b)=0 lead to consistently larger conductivities and mobilities. A qualitative explanation is offered to this fact, based on the plausibility of counter-ion diffusion fluxes favoring both the electrical conduction and the motion of the particles.
Keywords: Electrical conductivity; Concentrated suspensions; Kuwabara cell model; Shilov-Zharkikh's boundary condition; Levine-Neale's boundary condition
Recent developments in the kinetic theory of nucleation by E. Ruckenstein; Y.S. Djikaev (pp. 51-72).
A review of recent progress in the kinetics of nucleation is presented. In the conventional approach to the kinetic theory of nucleation, it is necessary to know the free energy of formation of a new-phase particle as a function of its independent variables at least for near-critical particles. Thus the conventional kinetic theory of nucleation is based on the thermodynamics of the process. The thermodynamics of nucleation can be examined by using various approaches, such as the capillarity approximation, density functional theory, and molecular simulation, each of which has its own advantages and drawbacks. Relatively recently a new approach to the kinetics of nucleation was proposed [Ruckenstein E, Nowakowski B. J Colloid Interface Sci 1990;137:583; Nowakowski B, Ruckenstein E. J Chem Phys 1991;94:8487], which is based on molecular interactions and does not employ the traditional thermodynamics, thus avoiding such a controversial notion as the surface tension of tiny clusters involved in nucleation. In the new kinetic theory the rate of emission of molecules by a new-phase particle is determined with the help of a mean first passage time analysis. This time is calculated by solving the single-molecule master equation for the probability distribution function of a surface layer molecule moving in a potential field created by the rest of the cluster. The new theory was developed for both liquid-to-solid and vapor-to-liquid phase transitions. In the former case the single-molecule master equation is the Fokker–Planck equation in the phase space which can be reduced to the Smoluchowski equation owing to the hierarchy of characteristic time scales. In the latter case, the starting master equation is a Fokker–Planck equation for the probability distribution function of a surface layer molecule with respect to both its energy and phase coordinates. Unlike the case of liquid-to-solid nucleation, this Fokker–Planck equation cannot be reduced to the Smoluchowski equation, but the hierarchy of time scales does allow one to reduce it to the Fokker–Plank equation in the energy space. The new theory provides an equation for the critical radius of a new-phase particle which in the limit of large clusters (low supersaturations) yields the Kelvin equation and hence an expression for the macroscopic surface tension. The theory was illustrated with numerical calculations for a molecular pair interaction potential combining the dispersive attraction with the hard-sphere repulsion. The results for the liquid-to-solid nucleation clearly show that at given supersaturation the nucleation rate depends on the cluster structure (for three cluster structures considered-amorphous, fcc, and icosahedral). For both the liquid-to-solid and vapor-to-liquid nucleation, the predictions of the theory are consistent with the results of classical nucleation theory (CNT) in the limit of large critical clusters (low supersaturations). For small critical clusters the new theory provides higher nucleation rates than CNT. This can be accounted for by the fact that CNT uses the macroscopic interfacial tension which presumably overpredicts the surface tension of small clusters, and hence underpredicts nucleation rates.
Keywords: Kinetics of nucleation; Molecular interactions; Rate of emission of molecules; Mean-passage-time based theory; Fokker–Planck equation
Nature and properties of ionomer assemblies. II by Ignác Capek (pp. 73-112).
The principle subject in the current paper is to summarize and characterize the ionomers based on polymers and copolymers such as polystyrene (PSt), polyisoprene (PIP), polybutadiene (PB), poly(styrene- b-isobutylene- b-styrene) (PSt-PIB-PSt), poly(butadiene-styrene) (PB-PSt), poly(ethylene terephthalate) (PET), poly(butylene adipate) (PBA), poly(butylene succinate) (PBSi), poly(dimethylcarbosiloxanes), polyurethane, etc. The self-assembly of ionomers, models concerning ionomer morphologies, physical and rheological properties of ionomer phase and percolation behavior of ionomers were discussed. The ionomer phase materials and dispersions have been characterized by differential scanning calorimetry (DSC), small-angle X-ray catering (SAXS), small-angle neutron scattering (SANS), Fourier transform infrared (FTIR) spectroscopy, transmission electron microscopy (TEM), etc. The wide range of compositions, molecular architectures, and morphologies present in ionomeric disperse systems are of great interest. The research is particularly devoted to the potential application of these materials and an understanding of the fundamental principles of the ionomers. They are extremely complex systems, sensitive to changes in structure and composition, and therefore not easily amenable to modeling and to the derivation of general patterns of behavior. The reviewed data indicate that a large number of parameters are important in influencing multiplet formation and clustering in random ionomers. Among these are the ion content, size of the polyion and counterion, dielectric constant of the host, Tg of the polymer, rigidity or persistence length of the backbone, position of the ion pair relative to the backbone, steric constraints, amount and nature of added additive (plasticizer), thermal history, etc.
Keywords: Ionomers; Assembly of ionomers; Percolation and physical properties
Adsorption model for retention in normal-phase liquid chromatography with ternary mobile phases by Małgorzata Borówko; Barbara Ościk-Mendyk (pp. 113-124).
The review gives a link between the theory of adsorption from multicomponent solutions and liquid chromatography. The article surveys the methods developed to describe the retention in normal-phase chromatography with ternary mobile phases with emphasis on the results of the authors. In the model used the driving force for the separation is the difference in adsorption of a solute and all solvents onto the solid surface. The general equation generates a series of simple linear relationships to predict the retention factor in ternary mobile phase for which certain parameters remain fixed. Theoretical concepts are tested by comparison with experimental data. The correlations between parameters characterizing retention in ternary, binary and pure solvents are discussed.
Keywords: Retention mechanism; Ternary mobile phase; Liquid–solid chromatography
Unusual properties of water at hydrophilic/hydrophobic interfaces by V.M. Gun'ko; V.V. Turov; V.M. Bogatyrev; V.I. Zarko; R. Leboda; E.V. Goncharuk; A.A. Novza; A.V. Turov; A.A. Chuiko (pp. 125-172).
The behaviour of water at mosaic hydrophilic/hydrophobic surfaces of different silicas and in biosystems (biomacromolecules, yeast cells, wheat seeds, bone and muscular tissues) was studied in different dispersion media over wide temperature range using1H NMR spectroscopy with layer-by-layer freezing-out of bulk water (close to 273 K) and interfacial water (180< T<273 K), thermally stimulated depolarization current (TSDC) (90< T<270 K), infrared (IR) spectroscopy, and quantum chemical methods. Bulk water and water bound to hydrophilic/hydrophobic interfaces can be assigned to different structural types. There are (i) weakly associated interfacial water (1H NMR chemical shift δH=1.1–1.7 ppm) that can be assigned to high-density water (HDW) with collapsed structure (CS), representing individual molecules in hydrophobic pockets, small clusters and interstitial water with strongly distorted hydrogen bonds or without them, and (ii) strongly associated interfacial water ( δH=4–5 ppm) with larger clusters, nano- and microdomains, and continuous interfacial layer with both HDW and low-density water (LDW). The molecular mobility of weakly associated bound water is higher (because hydrogen bonds are distorted and weakened and their number is smaller than that for strongly associated water) than that of strongly associated bound water (with strong hydrogen bonds but nevertheless weaker than that in ice Ih) that results in the difference in the temperature dependences of the1H NMR spectra at T<273 K. These different waters are also appear in changes in the IR and TSDC spectra.
Keywords: Interfacial water; Fumed silica; Silica gel; Silochrome; Mosaic hydrophilic/hydrophobic interfaces; Modified silica; HSA; Yeast cells; Wheat seeds; Bone tissue; Dried muscular tissue; Collagen; 1; H NMR; Layer-by-layer freezing-out of water; TSDC; FTIR; Adsorption; Structural characteristics; Interfacial water relaxation; Pore size distribution
Thermodynamic modeling of contact angles on rough, heterogeneous surfaces by J. Long; M.N. Hyder; R.Y.M. Huang; P. Chen (pp. 173-190).
Theoretical modelling for contact angle hysteresis carried out to date has been mostly limited to several idealized surface configurations, either rough or heterogeneous surfaces. This paper presents a preliminary study on the thermodynamics of contact angles on rough and heterogeneous surfaces by employing the principle of minimum free energy and the concept of liquid front. Based on a two-dimensional regular model surface, a set of relations were obtained, which correlate advancing, receding and system equilibrium contact angles to surface topography, roughness and heterogeneity. It was found that system equilibrium contact angles ( θES) can be expressed as a function of surface roughness factor ( δ) and the Cassie contact angle ( θC): cos θES= δcos θC. This expression can be reduced to the classical Wenzel equation.: θES= θW for rough but homogeneous surfaces, and the classical Cassie equation θES= θC for heterogeneous but smooth surfaces. A non-dimensional parameter called surface feature factor ( ω) was proposed to classify surfaces into three categories (types): roughness-dominated, heterogeneity-dominated and mixed-rough-heterogeneous. The prediction of advancing and receding contact angles of a surface is dependent on which category the surface belongs to. The thermodynamic analysis of contact angle hysteresis was further extended from the regular model surface to irregular surfaces; consistent results were obtained. The current model not only agrees well with the models previously studied by other researchers for idealized surfaces, but also explores more possibilities to explain the reported experimental results/observations that most existing theories could not explain.
Keywords: Contact angle hysteresis; Surface modelling; Rough heterogeneous surface; Surafce free energy; Surface thermodynamics