Percolation and jamming in structures built through sequential deposition of particles

The strength of attractive interaction among particles on a surface, which was studied in our previous work, leads to different degrees of clustering and ordering. A growing structure percolates when all clusters connect and become one and finally the structure is jammed when there is no space large enough to accommodate one more particle. The lowest jamming limit reported is for structures from the random sequential adsorption. We studied here, by means of Monte Carlo simulation, structures built through sequential deposition of particles, into which surface diffusion and various degrees of attractive forces are incorporated and reported jamming limits along with the percolation thresholds. The higher the strength of attractive interactions, the larger the percolation densities and jamming limits are. These results were shown in a diagram as a function of temperature (or equivalently the strength of attractive interaction), ranging from very low temperature to very high temperature (RSA limit).     

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.     

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).     

Mechanisms of fibrinogen adsorption at solid substrates

Adsorption of fibrinogen, modeled as a linear chain of touching beads of various sizes, was theoretically studied using the random sequential adsorption (RSA) model. The adsorption process was assumed to consist of two steps: (i) formation of an irreversibly bound fibrinogen monolayer under the side-on orientation, which is independent of the bulk protein concentration and (ii) formation of the reversibly bound, end-on monolayer, whose coverage was dependent on the bulk concentration. Calculation based on the RSA model showed that the maximum surface concentration of the end-on (reversible) monolayer equals N(⊥∞) = 6.13 × 10(3) μm(-2) which is much larger than the previously found value for the side-on (irreversible) monolayer, equal to N(∞) = 2.27 × 10(3) μm(-2). Hence, the maximum surface concentration of fibrinogen in both orientations is determined to be 8.40 × 10(3) μm(-2) corresponding to the protein coverage of 5.70 mg m(-2) assuming 20% hydration. Additionally, the surface blocking function (ASF) was determined for the end-on fibrinogen adsorption, approximated for the entire range of coverage by the interpolating polynomial. For the coverage approaching the jamming limit, the surface blocking function (ASF) was shown to vanish proportionally to (θ(⊥∞) - θ(⊥))(2). These calculation allowed one to theoretically predict adsorption isotherms for the end-on regime of fibrinogen and adsorption kinetics under various transport conditions (diffusion and convection). Using these theoretical results, a quantitative interpretation of experimental data obtained by TIRF and ellipsometry was successfully performed. The equilibrium adsorption constant for the end-on adsorption regime was found to be 8.04 × 10(-3) m. On the basis of this value, the depth of the adsorption energy minimum, equal to -17.4 kT, was predicted, which corresponds to ΔG = -41.8 kJ mol(-1). This is in accordance with adsorption energy derived as the sum of the van der Waals and electrostatic interactions. Besides having significance for predicting fibrinogen adsorption, theoretical results derived in this work also have implications for basic science providing information on mechanisms of anisotropic protein molecule adsorption on heterogeneous surfaces.     

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.     

Fibronectin adsorption on gold, Ti-, and Ta-oxide investigated by QCM-D and RSA modelling

The adsorption of fibronectin on gold, Ti-, and Ta-oxide surfaces is investigated by means of the quartz crystal microbalance with dissipation (QCM-D) technique. The surface chemistry (gold, Ti-, and Ta-oxide) is found to influence the frequency shift observed during adsorption of the fibronectin layer with the magnitude being Delta f Au>Delta f Ti-oxide approximately Delta f Ta-oxide. Corresponding variations in the dissipation change normalised to frequency change (Delta D/Delta f) for the layer are observed. The QCM-D data are further analyzed by the random sequential adsorption (RSA) model, and adsorption rate parameter ka and footprint (a) determined, which supported the trend seen in the Delta f and Delta D/Delta f values. The value of ka found by the RSA modelling of the QCM-D resonance frequency data is found to match the ratio between the mass measured by QCM-D and the mass reported by optical techniques in literature. We conclude that comparison of the adsorption rate parameter (ka) obtained by RSA modelling of the QCM-D data with ka values obtained from RSA modelling of data obtained using optical techniques can be a route to determine the degree of hydration of the adsorbed protein layer.     

Random sequential adsorption kinetics of dimers and trimers on geometrically disordered substrates

A study is made by means of Monte Carlo (MC) simulations of the kinetics of random sequential adsorption (RSA) of dimers and linear and bent trimers on some geometrically disordered substrates. The MC data are explained by a semiempirical equation whose parameters interpret the jamming fraction of the process and some geometric characteristics of the systems studied.     

Water monomer interaction with gold nanoclusters from van der Waals density functional theory

We investigate the interaction between water molecules and gold nanoclusters Au(n) through a systematic density functional theory study within both the generalized gradient approximation and the nonlocal van der Waals (vdW) density functional theory. Both planar (n = 6-12) and three-dimensional (3D) clusters (n = 17-20) are studied. We find that applying vdW density functional theory leads to an increase in the Au-Au bond length and a decrease in the cohesive energy for all clusters studied. We classify water adsorption on nanoclusters according to the corner, edge, and surface adsorption geometries. In both corner and edge adsorptions, water molecule approaches the cluster through the O atom. For planar clusters, surface adsorption occurs in a O-up/H-down geometry with water plane oriented nearly perpendicular to the cluster. For 3D clusters, water instead favors a near-flat surface adsorption geometry with the water O atom sitting nearly atop a surface Au atom, in agreement with previous study on bulk surfaces. Including vdW interaction increases the adsorption energy for the weak surface adsorption but reduces the adsorption energy for the strong corner adsorption due to increased water-cluster bond length. By analyzing the adsorption induced charge rearrangement through Bader's charge partitioning and electron density difference and the orbital interaction through the projected density of states, we conclude that the bonding between water and gold nanocluster is determined by an interplay between electrostatic interaction and covalent interaction involving both the water lone-pair and in-plane orbitals and the gold 5d and 6s orbitals. Including vdW interaction does not change qualitatively the physical picture but does change quantitatively the adsorption structure due to the fluxionality of gold nanoclusters.     

Irreversible adsorption of particles on heterogeneous surfaces

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 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 = lambda2theta(s) > 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 lambda < 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.     

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.     

Computational study of the self-organization of bidisperse nanoparticles

We study computationally the self-organization of bidisperse mixtures of thiol-stabilized gold particles in two dimensions through random sequential adsorption (RSA) coupled with the Metropolis algorithm for determining surface diffusion. It was previously shown [Doty et al. Phys. Rev. E 2002, 65, 061503] that ordered lattices of bidisperse particles cannot form with hard sphere interactions. Here we include the effects of interparticle forces. Osmotic and steric interactions provide a repulsive force at close distances, while at longer ranges the van der Waals interaction leads to attraction. Two size ratios (sigma) of 0.375 and 0.577, determined experimentally to form LS (the two-dimensional NaCl analogue) and LS2 (the two-dimensional AlB2 analogue) lattices, were studied. The calculated jamming limits for RSA fall well below the minimum surface coverage necessary for stable ordering as determined by melting simulations. Uniform compression of the particles' positions, as a model of the convection and lateral capillary forces that would be experienced during solvent evaporation, allowed this critical surface coverage to be achieved, and LS lattice formation was observed for sigma = 0.375. No LS2 lattice formation was observed for sigma = 0.577 with compression. The melting coverage of the LS2 lattice far exceeds the coverage observed experimentally and so is not observed.     

A revisit to the Gibbs dividing surfaces and helium adsorption

This paper addresses the long-standing problem of the so-called Gibbs dividing surface and the use of helium as a “non-adsorbing” gas for the determination of the “helium”-void volume and thence the Gibbs excess. Using helium is subject to some uncertainty because helium does adsorb (to call it a non-adsorbing gas is misleading) and it is able to access pore spaces that other larger adsorbates cannot. On the other hand, even helium atoms can not physically probe all the space described by the helium-void volume. To avoid these difficulties, we suggest an alternative to the formulation of the Gibbs dividing surface and the definition of the excess amount. We illustrate this with the two common tools to study adsorption—the volumetric and gravimetric techniques, and justify our new analysis with a computer simulation of a number of model adsorption systems. Furthermore, we also show that by using the correct accessible volume and inaccessible volume the excess amount obtained from a volumetric experiment is exactly the same as that obtained from a gravimetric experiment.     

A.C. Polarography and faradaic impedance of strongly adsorbed electroactive species: Part III. Theoretical complex plane analysis for a surface redox reaction

The complex plane analysis of a cell impedance in the case of a surface redox system (strong adsorption of both O and R) is treated theoretically. The adsorption rate does not control the kinetics of the system. These systems present the general property that the equation of the curves obtained does not depend on the isotherm when the angular frequency is varied. When the concentration or the potential is varied, on the contrary, the curves differ according to the isotherm; either a Langmuir or a Frumkin isotherm is considered. The use of certain representations for the characterization of adsorption is discussed.     

Formation of multilayered structures in the layer by layer deposition of colloid particles

Theoretical calculations of particle film formation in the layer by layer (LbL) self-assembling processes have been performed according to the generalized random sequential adsorption (RSA) scheme. The first (precursor) layer was generated using the standard RSA scheme pertinent to homogeneous surface. Formation of the consecutive layers (up to twenty) was simulated for two kinds of particles of equal size. The interaction of two particles of different kind resulted in irreversible and localized adsorption upon contact, whereas particles of the same kind were assumed to interact via the hard potential (no adsorption possible). Using this algorithm particle coverage (2D density) and volume fraction (3D density) were calculated as well as the film thickness as a function of the number of layers. Additionally, the structure of the film was quantitatively characterized in terms of the 2D and 3D pair correlation functions. The simulations revealed that particle concentration distribution in the film was more uniform for low precursor layer density than for higher density, where well-defined layers of closely packed particles appeared. It was also predicted theoretically that the averaged value of particle volume fraction in the uniform film region was rho(LbL)=0.42, which is very close to the maximum packing density equal to 0.382 predicted from the 3D RSA model. On the other hand, the roughness of the film was the lowest at the highest precursor layer density. It was shown that for low precursor layer density the film thickness increased with the number of layers in a nonlinear way. However, for high precursor layer density, the film thickness increased linearly with the number of layers and the average layer thickness was close to the hexagonal layer thickness equal to 1.73a p. It was concluded that our theoretical results can be effectively exploited for interpretation of the LbL processes involving colloid particles and polyelectrolytes.     

Adsorption of model surfactantlike copolymers on nanopatterned surfaces

The adsorption of polymers, copolymers, surfactants, and biopolymers is often used to engineer surfaces. Towards improving our understanding of polymer adsorption we report simulation results for the adsorption of model copolymers, resembling surfactants, on nanoscale patterned hydrophobic surfaces at infinitely dilute concentrations. The surfactants are composed by a hydrophobic tail and a hydrophilic head. Surfactant adsorption on the hydrophobic surface occurs in the tail-down configuration in which the tail segments are in contact with the surface. We investigate how the presence of a solid hard mask, used to create the nanoscale pattern on the underlying hydrophobic surface, affects the surfactant adsorption. We find that surfactant adsorption on the underlying hydrophobic surface is prevented when the characteristic dimensions of the solid hard mask are less than twice the radius of gyration. We also show that details about mask-surfactant head effective interactions have the potential to alter the characteristics of adsorption. When the mask repels the head segments, the surfactants hardly adsorb on the underlying hydrophobic surface. When the mask strongly attracts the surfactant heads, the surfactants may preferentially adsorb on the mask rather than on the underlying hydrophobic surface. Under these latter circumstances the adsorbed surfactants in some cases assume a head-down configuration in which the head segments are in contact with the mask and the tail segments extend towards the bulk solution. We explain our results in terms of enthalpy and entropy of adsorption and discuss practical implications.     

Adsorption of microstructured particles at liquid-liquid interfaces

The solid particles are adsorbed at interfaces and form self-assembled structures when the particles have suitable wettability to both liquids. Here, we show theoretically how the microstructure on the particle surface affects their adsorption properties. The physical properties of the interface adsorbing a particle will be described by taking into account the surface roughness due to the microstructure. The microstructure on the surface changes drastically the wettability and the equilibrium position of the adsorbed particle. Therefore, the contact angle of the particle at the three-phase contact line shifts with the particle surface area, because the surface roughness enhances the interfacial properties of the particle surface. Moreover, the range of the interfacial tensions at which the particle is adsorbed becomes narrower with the increase of the surface roughness. The effect of the particle shape on the adsorption properties is also studied. In the case of disk-shaped particles, the energy changes discontinuously when the plane surface of the particle contacts the liquid-liquid interface. The adsorbing position does not change with the surface roughness. The orientation of a parallelepiped particle at the liquid-liquid interface is governed by the aspect ratio and the surface area of the particle. On the other hand, the particle which is partially covered with the microstructured surface is adsorbed firmly at the interface in an oriented state. We should consider not only the interfacial tensions but also the surface structure and the particle shape to control the adsorption behavior of the particle.     

High physisorption affinity of water molecules to the hydroxylated aluminum oxide (001) surface

The adsorption mechanism of water on the hydroxylated (001) plane of α-Al(2)O(3) was studied by measuring adsorption isotherms and GCMC simulations. The experimental adsorption isotherms for three α-Al(2)O(3) samples from different sources are typical type II, in which adsorption starts sharply at low pressures, suggesting a high affinity of water to the Al(2)O(3) surface. Water molecules are adsorbed in two registered forms (bilayer structure). In the first form, water is registered at the center of three surface hydroxyl groups by directing a proton of the water. In the second form, a water molecule is adsorbed by bridging two of the first-layer water molecules through hydrogen bonding, by which a hexagonal ring network is constructed over the hydroxylated surface. The network domains are spread over the surface, and their size decreases as the temperature increases. The simulated adsorption isotherms present a characteristic two-dimensional (2D) phase diagram including a 2D critical point at 365K, which is higher than that on the hydroxylated Cr(2)O(3) surface (319 K). This fact substantiates the high affinity of water molecules to the α-Al(2)O(3) surfaces, which enhances the adsorbability originating from higher heat of adsorption. The higher affinity of water molecules to the α-Al(2)O(3) (001) plane is ascribed to the high compatibility of the crystal plane to form a hexagonal ring network of (001) plane of ice Ih.     

Acetone adsorption on ice investigated by X-ray spectroscopy and density functional theory

Using a combination of X-ray photoemission and near-edge X-ray absorption spectroscopy (NEXAFS) as well as density-functional theory (DFT), we have investigated the adsorption of acetone on ice in the temperature range from 218 to 245 K. The adsorption enthalpy determined from experiment (45 kJ mol(-1)) agrees well with the adsorption energy predicted by theory (41 to 44 kJ mol(-1)). Oxygen K-edge NEXAFS spectra indicate that the presence of acetone at the ice surface does not induce the formation of a pre-melted layer at temperatures up to 243 K. DFT calculations show that the energetically most favored adsorption geometry for acetone on ice is with the molecular plane almost parallel to the surface.