Colloid particle adsorption at random site (heterogeneous) surfaces

Irreversible adsorption of colloid particles and globular proteins at heterogeneous surfaces was studied theoretically. The substrate surface was created by covering a uniform surface by coupling sites (active centers) of a desired coverage. In contrast to previous studies concerned with disks, in our simulations the centers were modeled by spheres having a size smaller than that of the adsorbing particles. Adsorption was assumed to occur due to short-ranged attractive interactions if the colloid particle contacted the center. The Monte-Carlo-type simulations 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 lambda. It was revealed that the initial flux increased significantly with the site coverage theta(s) and the lambda 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 lambda parameter increased. Practically, for alpha=lambda(2)theta(s)>1 the jamming coverage at the heterogeneous surfaces attained the value pertinent to continuous surfaces. The results obtained prove unequivocally that the spherically shaped sites are much more effective in binding particles than the disk-shaped sites considered previously.     

Colloid Particle Adsorption on Partially Covered (Random) Surfaces

The random sequential adsorption (RSA) approach was used to model irreversible adsorption of colloid particles at surfaces precovered with smaller particles having the same sign of surface charge. Numerical simulations were performed to determine the initial flux of larger particles as a function of surface coverage of smaller particles θ(s) at various size ratios lambda=a(l)/a(s). These numerical results were described by an analytical formula derived from scaled particle theory. Simulations of the long-time adsorption kinetics of larger particles have also been performed. This allowed one to determine upon extrapolation the jamming coverage θ(l)(infinity) as a function of the lambda parameter at fixed smaller particle coverage θ(s). It was found that the jamming coverage θ(l)(infinity) was very sensitive to particle size ratios exceeding 4. Besides yielding θ(l)(infinity), the numerical simulations allowed one to determine the structure of large particle monolayers at the jamming state which deviated significantly from that observed for monodisperse systems. The theoretical predictions suggested that surface heterogeneity, e.g., the presence of smaller sized contaminants or smaller particles invisible under microscope, can be quantitatively characterized by studying larger colloid particle adsorption kinetics and structure of the monolayer. Copyright 2001 Academic Press.     

Irreversible adsorption of particles at random-site surfaces

Irreversible adsorption of negatively charged polystyrene latex particles (averaged diameter 0.9 microm) at heterogeneous surfaces was studied experimentally. The substrate bearing a controlled number of adsorption sites was produced by precovering mica sheets by positively charged polystyrene latex (averaged diameter of 0.45 microm). Positive latex (site) deposition was carried out under diffusion-controlled transport conditions and its coverage was determined by direct particle counting using the optical microscopy. Deposition kinetics of larger latex particles (averaged diameter 0.9 microm) at heterogeneous surfaces produced in this way was studied by direct optical microscope observations in the diffusion cell (under no-convection transport conditions). It was demonstrated that the structure of larger particle monolayers, characterized in terms of the pair correlation function, showed much more short-range ordering than it was predicted for homogeneous surface monolayers at the same coverage. This was found in agreement with theoretical predictions derived from the Monte Carlo simulations. On the other hand, particle adsorption kinetics was quantitatively interpreted in terms of numerical solutions of the governing diffusion equation with the nonlinear boundary condition derived from Monte Carlo simulations. From these kinetic measurements maximum (jamming) coverage of particles was determined in an accurate way by extrapolation. It was concluded that both the monolayer structure and jamming coverage were strongly influenced by the site multiplicity (coordination) effect.     

Kinetics of Diffusion-Controlled Adsorption of Colloid Particles and Proteins

A theoretical model was developed for describing localized adsorption kinetics of proteins and colloid particles at solid/liquid interfaces. In contrast to previous approaches the adsorption and desorption rate constants as well as the surface blocking function were evaluated explicitly without using empirical parameters. It was also predicted that irreversible adsorption kinetics can unequivocally be characterized in terms of the adsorption rate constant k(a) and the maximum (jamming) coverage Theta(mx) known for various particle shapes from previous Monte-Carlo simulations. The dimensionless constant k(a) was shown to be inversely proportional to the concentration of particles which is usually very low for protein and colloid adsorption measurements. From the theoretical model it was also deduced that in this case the asymptotic adsorption law for large dimensionless time tau can be expressed as Theta(mx)-Theta approximately 1/tau(1/(n-1)) (where n=3 for spheres, n=4 for side-on adsorption of spheroids, n=5 for randomly oriented spheroid adsorption). It was also shown that this limiting adsorption regime occurs for proteins at surface coverage Theta(l) very close to the jamming value Theta(mx), becoming therefore difficult to detect due to limited experimental accuracy. These analytical predictions were found to be in agreement with numerical calculations performed by using the finite-difference scheme, valid for an arbitrary range of adsorption time. Moreover, it was demonstrated that these numerical results adequately reflected the experimental results of Johnson and Lenhoff who determined the kinetics of colloid particle adsorption using atomic force microscopy. Previously used approaches assuming that particle adsorption flux is reduced by the factor B(Theta) were found to be inadequate. It was also demonstrated that due to the similarity of underlying parameters the results obtained for colloid systems can be exploited as well-defined reference data for estimating the adsorption kinetics of proteins. Copyright 2000 Academic Press.     

Surface clusters of colloid particles produced by deposition on sites

The possibility of producing surface clusters of well-defined structure formed by colloid particles was analyzed theoretically and experimentally. Theoretical results were derived by performing Monte Carlo-type simulations according to the generalized random sequential adsorption (RSA) mechanism. In these simulations, the jamming coverage of particles adsorbing irreversibly on spherical sites was determined as a function of the particle-to-site size ratio lambda. It was revealed that, by properly choosing lambda, a targeted site coordination can be achieved; for example, there can be one, two, three, and so forth particles attached to one site. The structure of the heterogeneous clusters produced in this way was described in terms of the pair correlation function. It was predicted that the extent of ordering within surface clusters was diminished as the concentration of sites increased. These theoretical predictions were checked by performing deposition experiments of negatively charged polystyrene latex particles (average diameter 0.9 mum) under the diffusion-controlled transport regime. Mica sheets precovered by positively charged polystyrene latex (average diameters 0.45 and 0.95 microm) were used as the substrate surface in these experiments. Positive latex (site) deposition was also carried out under diffusion-controlled transport conditions. The concentration of the sites and the adsorbed particles was determined by direct particle counting using optical microscopy. It was found, in quantitative agreement with theoretical simulations, that the structure of surface clusters produced in this way exhibits a significant degree of short-range ordering. It also was proven experimentally that clusters containing a targeted number of colloid particles (e.g., 2 and 4) could be produced by the deposition procedure.     

Particle adsorption and deposition: role of electrostatic interactions

This work demonstrates how electrostatic interactions, described in terms of the classical DLVO theory, influence colloid particle deposition phenomena at solid/liquid interfaces. Electrostatic interactions governing particle adsorption in both non-polar and polar media (screened interactions) are discussed. Exact and approximate methods for calculating the interaction energy of spherical and non-spherical (anisotropic) particles are presented, including the Derjaguin method. Phenomenological transport equations governing particle deposition under the linear regime are discussed with the limiting analytical expressions for calculating initial flux. Non-linear adsorption regimes appearing for higher coverage of adsorbed particles are analysed. Various theoretical approaches are exposed, aimed at calculating blocking effects appearing due to the presence of adsorbed particles. The significant role of coupling between bulk transport and surface blocking is demonstrated. Experimental data obtained under well-defined transport conditions, such as diffusion and forced convection (impinging-jet cells), are reviewed. Various experimental techniques for detecting particles at interfaces are discussed, such as reflectometry, ellipsometry, streaming potential, atomic force microscopy, electron and optical microscopy, etc. The influence of ionic strength and flow rate on the initial particle deposition rate (limiting flux) is presented. The essential role of electrostatic interactions in particle deposition on heterogeneous surfaces is demonstrated. Experimental data pertinent to the high-coverage adsorption regime are also presented, especially the dependence of the maximum coverage of particles and proteins on the ionic strength. The influence of lateral electrostatic interactions on the structure of particle monolayers is elucidated, and the links between colloid and molecular systems are pointed out.     

Particle assembly on surface features (patterned surfaces)

Irreversible adsorption (deposition) of spherical particles on surface features of various shapes (collectors) was studied using the random sequential adsorption (RSA) model. The collectors in the form of linear line segments, semicircles, and circles were considered. Numerical simulation of the Monte Carlo type enabled one to determine particle configurations, the jamming coverage, and the end to end length of particle monolayers for various collector length (L) to particle size (d) ratio L = L/d. It was revealed that the jamming coverage for linear collectors Theta'(infinity) increases for L > 2 according to a linear dependence with respect to 1/L. For 2 > L > 1, a parabolic dependence of Theta'(infinity) on 1/L was predicted, characterized by the maximum value of Theta'(infinity) = 1.125 for L = 4/3. These dependencies allowed one to formulate an equation determining the length of nanostructures on surfaces if the averaged number of adsorbed particles is known. It was also predicted that the end to end length of the monolayer on a linear collector /L increased linearly with 1/L for L > 2. For 2 > L > 1 the dependence of /L on L was approximated by a polynomial expression, exhibiting a maximum of /L = 1.17 for L = 1.45. In the case of circular collectors, the jamming coverage was found to be substantially smaller for the same value of 1/L. It was demonstrated that the theoretical results are in agreement with our preliminary experimental data obtained for latex particles adsorbing on polyelectrolyte modified mica and on patterned surfaces obtained by a polymer-on-polymer stamping technique of gold covered silicon (Zheng et al. Langmuir 2002, 18, 4505).     

Deposition of colloid particles on protein layers: fibrinogen on mica

Colloid particle deposition was applied to characterize fibrinogen (Fb) monolayers on mica, which were produced by controlled adsorption under diffusion transport. By adjusting the time of adsorption and the bulk Fb concentration, monolayers of desired surface concentration were obtained. The surface concentration of Fb was determined directly by AFM enumeration of single molecules adsorbed over the substrate surface. It was proven that Fb adsorbed irreversibly on mica both at pH 3.5 and at pH 7.4 with the rate governed by bulk transport. The electrokinetic properties of Fb monolayers produced in this way were studied using the streaming potential method. The dependence of the apparent zeta potential of Fb monolayers was determined as a function of the coverage. It was shown that for pH 3.5 the initial negative zeta potential of the mica substrate was converted to positive for Fb coverage exceeding 0.16. On the other hand, for pH 7.4, the zeta potential of a Fb-covered mica remained negative for the entire coverage range. The charge distribution in Fb monolayers was additionally studied using the colloid deposition method, in which negatively and positively charged polystyrene latex particles (ca. 800 nm in diameter) were used. An anomalous deposition of negative latex particles on substrates exhibiting a negative zeta potential was observed. Results of these experiments were quantitatively interpreted in terms of the fluctuation theory assuming that adsorption sites consisted of two and three Fb molecules, for pH 3.5 and 7.4, respectively. These results suggested that for pH 7.4, the distribution of charge on Fb molecules was heterogeneous, characterized by the presence of positive patches, whereas the average zeta potential was negative, equal to -19 mV. The utility of the colloid deposition method for studying Fb monolayers was further demonstrated in deposition experiments involving positive latex particles. It was shown that for a rather broad range of fibrinogen coverage, both the positive and the negative latex particles can adsorb on surfaces covered by Fb, which behaved, therefore, as superadsorbing surfaces. It was also concluded that the colloid deposition method can be used to determine the Fb bulk concentration for the range inaccessible for other methods.     

Colloid particle and protein deposition - electrokinetic studies

Recent developments in the electrokinetic determination of particle, polyelectrolyte and protein deposition at solid/electrolyte interfaces, are reviewed. In the first section basic theoretical results are discussed enabling a quantitative interpretation of the streaming current/potential and microelectrophoretic measurements. Experimental results are presented, pertinent to electrokinetic characteristics of simple (homogeneous) surfaces such as mica, silica and various polymeric surfaces used in protein studies. The influence of the ionic strength, background electrolyte composition and pH is discussed, and the effective (electrokientic) charge of these interfaces is evaluated. In the next section, experimental data obtained by streaming potential measurements for colloid particle mono- and bilayers are presented and interpreted successfully in terms of available theoretical approaches. These results, obtained for model systems of monodisperse colloid particles are used as reference data for discussion of more complicated experiments performed for polyelectrolyte and protein covered surfaces. Results are discussed, obtained for cationic polyelectrolytes (PEI, PAH) and fibrinogen adsorbing on mica, interpreted quantitatively in terms of the theoretical approach postulating a heterogeneous 3D charge distribution. The Gouy-Chapman model, based on the continuous charge distribution proved inadequate. Interesting experimental data are also discussed, obtained by electrophoretic methods in the case of protein adsorption on colloid latex particles. In the last section, supplementary results on particle deposition on heterogeneous surfaces produced by controlled protein adsorption are discussed. Quantitative relationships between the amount of adsorbed protein, zeta potential of the interface and the particle coverage are specified. Possibility of evaluating the heterogeneity of protein charge distribution is pointed out. The anomalous deposition of colloid particles on protein molecules bearing the same sign of zeta potential, which contradicts classical DLVO theory, is interpreted in terms of the fluctuation theory. It is concluded that theoretical and experimental results obtained for model colloid systems and flat interfaces can be effectively used for interpretation of protein adsorption phenomena, studied by electrophoresis. In this way the universality of electrokinetic phenomena is underlined.     

Application of the extended RSA models in studies of particle deposition at partially covered surfaces

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.     

Characterization of poly(ethylene imine) layers on mica by the streaming potential and particle deposition methods

Deposition kinetics of polystyrene latex (averaged particle size of 0.66 microm) on mica covered by poly(ethylene imine) (PEI), a cationic polyelectrolyte having an average molecular mass of 75,000 g mol(-1), was studied using the impinging-jet method. The hydrodynamic radius of PEI, determined by PCS measurements, was 5.3 nm. The electrophoretic mobility of PEI was measured as a function of pH for ionic strengths of 10(-3) and 10 (-2) M, which made it possible one to determine the amount of electrokinetic charge of the molecule and its zeta potential. Formation of the polyelectrolyte layer on mica was followed by measuring the streaming potential in the parallel-plate channel. From these measurements, the dependence of the apparent zeta potential of mica on the surface coverage of PEI was determined. The amount of adsorbed PEI on mica was calculated from the convective diffusion theory. These results were quantitatively interpreted in terms of the theoretical model postulating a particle-like adsorption mechanism for PEI with not too significant shape deformation upon adsorption. On the other hand, the Gouy-Chapman model postulating the adsorption in the form of flat disks was proved inappropriate. After the surface was fully characterized, particle deposition experiments were carried out with the aim of finding the correlation between the polymer coverage and the initial rate of latex particle deposition. In the range of small polyelectrolyte coverage, a monotonic relation between the polymer coverage and the initial deposition rate of particles, as well as the jamming coverage, was found. For Theta(PEI)>0.25, the initial particle deposition rate attained the value predicted from the convective diffusion theory for homogeneous surfaces. These results were interpreted theoretically by postulating that an effective immobilization of colloid particles occurred on local polyelectrolyte assemblages containing between two and three PEI molecules.     

Particle assembly on patterned surfaces bearing circular (dots) and rectangular (stripes) surface features

Irreversible and localized adsorption of spherical particles on surface features of various shapes (collectors) was studied using the random sequential adsorption (RSA) model. Collectors in the form of dots and rectangles were considered, including the two limiting cases of squares and stripes. Numerical simulation of the Monte Carlo type enabled one to determine particle configurations, average coverage of particles, and the distribution for various collector length to particle size ratios L = L/d and collector width to particle size ratios B = b/d. It was predicted that particle coverage under the jamming state was highly nonuniform, exhibiting a maximum at the center and at the periphery of the collectors. The averaged number of particles Np adsorbed at the jamming state was also determined as a function of the L and B parameters, as well as the averaged number of particles per unit length in the case of stripes. It was revealed that Np was the highest for the circular and square collectors (for a fixed value of L). On the other hand, for L > 5, our numerical results could be well approximated by the analytical expressions Np = thetainfinityL2 for circles, Np = 4thetainfinityL2/pi for squares, Np = 4thetainfinityBL/pi for rectangles, and Np = 4thetainfinityB/pi for stripes (per unit length). It was demonstrated that the theoretical results are in agreement with experimental data obtained for latex particles adsorbing on patterned surfaces obtained by a polymer-on-polymer stamping technique of gold covered silicon and on photolitographically patterned silane layers on silica.     

Polyelectrolyte adsorption layers studied by streaming potential and particle deposition

Adsorption of a cationic polyelectrolyte, polyallylamine hydrochloride (PAH), having a molecular weight of 70,000 on mica was characterized by the streaming potential method and by deposition of negative polystyrene latex particles. Formation of PAH layers was followed by determining the apparent zeta potential of surface zeta as function of bulk PAH concentration. The zeta potential was calculated from the streaming potential measured in the parallel-plate channel formed by two mica plates precovered by the polyelectrolyte. The experimental data were expressed as the dependence of the reduced zeta potential zeta/zeta0 on the PAH coverage Theta(PAH), calculated using the convective diffusion theory. It was found that for the ionic strength of 10(-2) M, the dependence of zeta/zeta0 on Theta(PAH) can be reflected by the theoretical model formulated previously for surfaces covered by colloid particles. The electrokinetic measurements were complemented by particle deposition experiments on PAH-covered mica surfaces. A direct correlation between the polymer coverage and the initial deposition rate of particles, as well as the jamming coverage, was found. For ThetaPAH > 0.3 the initial deposition rate attained the value predicted from the convective diffusion theory for homogeneous surfaces. The initial deposition rates for surfaces modified by PAH were compared with previous experimental and theoretical results obtained for heterogeneous surfaces formed by preadsorption of colloid particles. It was revealed that negative latex deposition occurred at surfaces exhibiting negative apparent zeta potential, which explained the anomalous deposition of particles observed in previous works. It was suggested that the combined electrokinetic and particle deposition methods can be used for detecting adsorbed polyelectrolytes at surfaces for coverage range of a percent. This enables one to measure bulk polyelectrolyte concentrations at the level of 0.05 ppm.     

Modeling adsorption of colloids and proteins

Recent developments in the modeling of particle and protein adsorption kinetics on solid surfaces are discussed. Emphasis is focused on the coarse-grained methods, where protein molecules are treated as particles having a regular shape (spheres, spheroids) or a system of spherical beads of various sizes. Using such approaches hydrodynamic radii and diffusion coefficients of protein molecules are calculated in an exact way using the linear Stokes equation. Additionally, the surface blocking functions and jamming coverages for such molecule shapes are determined using the random sequential adsorption simulations. Theoretical results obtained in this way for various molecule shapes, including the bead models of fibrinogen are discussed. Knowing the jamming coverage and blocking functions one can formulate boundary conditions for bulk transport equations. Solutions of these equations for the convection and diffusion-controlled transport are presented. These theoretical predictions proved adequate for interpreting experimental data obtained for fibrinogen using AFM, ellipsometry and fluorescence methods. It is, therefore, concluded that these coarse grained approaches combined with solutions of the continuity equation can be efficiently used for quantitatively predicting protein adsorption kinetics for the time scale met under practical situations.     

High density silver nanoparticle monolayers produced by colloid self-assembly on polyelectrolyte supporting layers

A stable silver nanoparticle suspension was synthesized via the reduction of silver nitrate using sodium borohydride and sodium citrate. The particle's shape and size distribution were measured by various methods. The electrophoretic mobility measurements revealed that the zeta potential of particles was highly negative, increasing slightly with the ionic strength, from -52 mV for I=10(-5) M to -35 mV for I=3×10(-2) M (for pH=5.5). The zeta potential of mica modified by the adsorption of cationic polyelectrolytes: PEI and PAH was also determined using the streaming potential measurements. The modified mica sheets were used as substrates for particle monolayers formed via colloid self assembly. The kinetics of this process, proceeding under diffusion-controlled transport conditions, was quantitatively evaluated by a direct enumeration of particles using the AFM and SEM techniques. Both the kinetics of particle deposition and the maximum surface concentration were determined. From the slope of the initial deposition rates, the equivalent diameter of particles was determined to be 16 nm, in agreement with previous measurements. Based on this finding, an efficient method of determining particle size in suspension was proposed. It was also demonstrated that for higher ionic strengths, the maximum coverage of particle monolayers on PAH modified mica exceeded 0.39. The kinetic data were quantitatively interpreted in terms of the random sequential adsorption (RSA) model using the effective hard particle concept.     

Kinetics of localized adsorption of colloid particles

Methods of analyzing localized adsorption of colloid particles at solid/liquid interfaces were extensively reviewed. First, the initial adsorption fluxes calculated using the Levich-Smoluchowski approximation were discussed. The uniformly, and nonuniformly accessible interfaces were distinguished and the superiority of the former in experimental studies was pointed out. A criterion was introduced for estimating the relative significance of the bulk transfer and surface adsorption steps. It was shown that for the majority of experimental and practical situations the surface mass balance equation can be decoupled from the bulk continuity equation. Thus, in due course attention was focused on theoretical and experimental methods of determining the surface blocking parameter B. It was shown that for low and moderate surface concentration range the statistical mechanic approach can be effectively used for predicting B. By introducing the equivalent hard sphere radius r¹ it became possible to analyze quantitatively blocking effects of interacting as well as nonspherical particles. The analytical solutions were compared with numerical simulation methods valid for the entire range of surface concentrations. The Monte-Carlo algorithm based on the random sequential adsorption (RSA) concept was compared with the sequential Brownian-Dynamics (SBD) method. Theoretical results obtained using these approaches were extensively discussed especially the role of repulsive electrostatic interaction among adsorbing particles. It was shown that these interactions diminish profoundly both the particle adsorption rate and the maximum surface concentration of particles forming “random” monolayers. When the electrostatic forces were operating (lower ionic strength) two distinctive adsorption regimes were predicted (i) fast Langmuir-type adsorption for short times and then (ii) very slow RSA-type approach to the maximum surface concentrations. As discussed such long lasting transient adsorption states could erroneously be interpreted as equilibrium adsorption isotherms. Then, the indirect and direct experimental methods aimed at a quantitative determination of particle adsorption kinetics were described. Illustrative experimental results performed for model latex suspensions were evoked. A satisfactory agreement with theoretical predictions was found for a variety of important physicochemical parameters studied. The RSA approach was found useful for describing particle adsorption kinetics for low and moderate surface concentrations in the case when the flow induced effects could be neglected. On the other hand, the SBD method was found of general validity especially in describing the hydrodynamic scattering effect observed experimentally for higher shear rates. Finally, the theoretical and experimental results concerning structure formation in adsorption processes were presented. The experimentally measured two-dimensional (2D) pair correlation function g12 of adsorbed particles suggested a liquid-like short range ordering occurring for larger surface concentrations. The extent of the 2D ordering was influenced by the adsorption mechanisms of particles, especially the presence of external field of forces.     

Zeta potential of particle bilayers on mica: a streaming potential study

The streaming potential of mica covered by bilayers of latex particles was measured using the parallel-plate channel cell. The size of the first latex (A500) bearing amidine charged groups was 503 nm and the second latex (L800) bearing sulfonate groups was 810 nm (at pH 5.5 and an ionic strength of 10(-2)M). The A500 latex exhibited an isoelectric point at pH 10.5, whereas the L800 latex was strongly negative at all pH. Mica sheets were precovered first by the A500 latex particles under diffusion transport conditions. The coverage of this supporting layer was regulated between 0.02 and 0.5 by changing the bulk concentration of latex and the deposition time. Then, the second layer of the L800 latex of regulated coverage up to 0.55 was deposited under the diffusion transport. The coverage of particles and their distributions in both layers were determined by a direct enumeration of particles by optical microscopy under wet conditions and by AFM. It was shown that the structure of the L800 particle layers and the maximum coverage were in accordance with theoretical simulations performed according to the random sequential adsorption (RSA) model. After forming bilayers of desired composition and structure, streaming potential measurements were carried out. The influence of the mica substrate, the supporting layer coverage, and its zeta potential on the apparent zeta potential of bilayers was systematically studied. It was established that for a bilayer coverage exceeding 0.20, the net zeta potential became independent of the substrate and the supporting layer zeta potentials. Then, the asymptotic values of the zeta potential of the bilayer approach 1/√2=0.71 of the bulk zeta potential of the particles forming the external (second) layer. This behavior was interpreted theoretically in terms of the electrokinetic model derived previously for monolayers. It was also concluded that results obtained in this work can be exploited for interpretation of polyelectrolyte film formation in the layer by layer (LbL) processes and protein adsorption pertinent to the antigen/antibody interactions.     

Salt-regulated attraction and repulsion of spherical polyelectrolyte brushes towards polyelectrolyte multilayers

Adsorption of colloidal particles presents an interesting alternative to the modification of surfaces using covalent coupling or physisorption of molecules. However, to tailor the properties of these materials full control over the effective particle-substrate interactions is required. We present a systematic investigation of the adsorption of spherical polyelectrolyte brushes (SPB) onto polyelectrolyte multilayers (PEM). A brush layer grafted from colloidal particles allows the incorporation of various functional moieties as well as the precise adjustment of their adsorption behaviour. In the presence of oppositely charged surfaces the amount of adsorbed SPB monotonically increases with the ionic strength, whereas equally charged substrates efficiently prevent colloidal attachment below a threshold salt concentration. We found that the transition from the osmotic to the salted brush regime at approximately 100 mM coincided with a complete loss of substrate selectivity. In this regime of high ionic strength, attractive secondary interactions become dominant over electrosteric repulsion. Due to the soft polyelectrolyte corona a surface coverage exceeding the theoretical jamming limit could be realized. Both the adsorption kinetics and the resulting thin film morphologies are discussed. Our study opens avenues for the production of two-dimensional arrays and three-dimensional multilayered structures of SPB particles.     

Fibrinogen adsorption on mica studied by AFM and in situ streaming potential measurements

Adsorption of fibrinogen from aqueous solutions on mica was studied using AFM and in situ streaming potential measurements. In the first stage, bulk physicochemical properties of fibrinogen and the mica substrate were characterized for various ionic strength and pH. The zeta potential and number of uncompensated (electrokinetic) charges on the protein surfaces were determined from microelectrophoretic measurements. Analogously, using streaming potential measurements, the electrokinetic charge density of mica was determined for pH range 3-10 and the NaCl background electrolyte concentration of 10(-3) and 10(-2) M. Next, the kinetics of fibrinogen adsorption at pH 3.5 and 7.4 in the diffusion cell was studied using a direct AFM determination of the number of molecules per unit area of the mica substrate. Then, streaming potential measurements were performed to determine the apparent zeta potential of fibrinogen-covered mica for different pH and ionic strength in terms of its surface concentration. A quantitative interpretation of these streaming potential measurements was achieved in terms of the theoretical model postulating a side-on adsorption of fibrinogen molecules as discrete particles. On the basis of these results, the maximum coverage of fibrinogen Θ close to 0.29 was predicted, in accordance with previous theoretical predictions. It was also suggested that anomalous adsorption for pH 7.4, where fibrinogen and the mica substrate were both negatively charged, can be explained in terms of a heterogeneous charge distribution on fibrinogen molecules. It was estimated that the positive charge was 12 e (for NaCl concentration of 10(-2) M and pH 7.4) compared with the net charge of fibrinogen at this pH, equal to -21 e. Results obtained in this work proved that the coverage of fibrinogen can be quantitatively determined using the streaming potential method, especially for Θ < 0.2, where other experimental methods become less accurate.