A method for modeling the interactions of parallel flat plate systems with surface features

High density single-molecule-bead arrays for parallel single molecule force spectroscopy

The assembly of a highly parallel force spectroscopy tool requires careful placement of single-molecule targets on the substrate and the deliberate manipulation of a multitude of force probes. Since the probe must approach the target biomolecule for covalent attachment, while avoiding irreversible adhesion to the substrate, the use of polymer microspheres as force probes to create the tethered bead array poses a problem. Therefore, the interactions between the force probe and the surface must be repulsive at very short distances (<5 nm) and attractive at long distances. To achieve this balance, the chemistry of the substrate, force probe, and solution must be tailored to control the probe-surface interactions. In addition to an appropriately designed chemistry, it is necessary to control the surface density of the target molecule in order to ensure that only one molecule is interrogated by a single force probe. We used gold-thiol chemistry to control both the substrate's surface chemistry and the spacing of the studied molecules, through binding of the thiol-terminated DNA and an inert thiol forming a blocking layer. For our single molecule array, we modeled the forces between the probe and the substrate using DLVO theory and measured their magnitude and direction with colloidal probe microscopy. The practicality of each system was tested using a probe binding assay to evaluate the proportion of the beads remaining adhered to the surface after application of force. We have translated the results specific for our system to general guiding principles for preparation of tethered bead arrays and demonstrated the ability of this system to produce a high yield of active force spectroscopy probes in a microwell substrate. This study outlines the characteristics of the chemistry needed to create such a force spectroscopy array.

Electrostatic interactions between diffuse soft multi-layered (bio)particles: beyond Debye-Hückel approximation and Deryagin formulation

We report a steady-state theory for the evaluation of electrostatic interactions between identical or dissimilar spherical soft multi-layered (bio)particles, e.g. microgels or microorganisms. These generally consist of a rigid core surrounded by concentric ion-permeable layers that may differ in thickness, soft material density, chemical composition and degree of dissociation for the ionogenic groups. The formalism allows the account of diffuse interphases where distributions of ionogenic groups from one layer to the other are position-dependent. The model is valid for any number of ion-permeable layers around the core of the interacting soft particles and covers all limiting situations in terms of nature of interacting particles, i.e. homo- and hetero-interactions between hard, soft or entirely porous colloids. The theory is based on a rigorous numerical solution of the non-linearized Poisson-Boltzmann equation including radial and angular distortions of the electric field distribution within and outside the interacting soft particles in approach. The Gibbs energy of electrostatic interaction is obtained from a general expression derived following the method by Verwey and Overbeek based on appropriate electric double layer charging mechanisms. Original analytical solutions are provided here for cases where interaction takes place between soft multi-layered particles whose size and charge density are in line with Deryagin treatment and Debye-Hückel approximation. These situations include interactions between hard and soft particles, hard plate and soft particle or soft plate and soft particle. The flexibility of the formalism is highlighted by the discussion of few situations which clearly illustrate that electrostatic interaction between multi-layered particles may be partly or predominantly governed by potential distribution within the most internal layers. A major consequence is that both amplitude and sign of Gibbs electrostatic interaction energy may dramatically change depending on the interplay between characteristic Debye length, thickness of ion-permeable layers and their respective protolytic features (e.g. location, magnitude and sign of charge density). This formalism extends a recent model by Ohshima which is strictly limited to interaction between soft mono-shell particles within Deryagin and Debye-Hückel approximations under conditions where ionizable sites are completely dissociated.

A modeling approach to describe the adhesion of rough, asymmetric particles to surfaces

A combined theoretical and experimental study of the adhesion of alumina particles and polystyrene latex spheres to silicon dioxide surfaces was performed. A boundary element technique was used to model electrostatic interactions between micron-scale particles and planar surfaces when the particles and surfaces were in contact. This method allows quantitative evaluation of the effects of particle geometry and surface roughness on the electrostatic interaction. The electrostatic interactions are combined with a previously developed model for van der Waals forces in particle adhesion. The combined model accounts for the effects of particle and substrate geometry, surface roughness and asperity deformation on the adhesion force. Predictions from the combined model are compared with experimental measurements made with an atomic force microscope. Measurements are made in aqueous solutions of varying ionic strength and solution pH. While van der Waals forces are generally dominant when particles are in contact with surfaces, results obtained here indicate that electrostatic interactions contribute to the overall adhesion force in certain cases. Specifically, alumina particles with complex geometries were found to adhere to surfaces due to both electrostatic and van der Waals interactions, while polystyrene latex spheres were not affected by electrostatic forces when in contact with various surfaces.

Electrostatic interactions between double layers: influence of surface roughness, regulation, and chemical heterogeneities

Electrostatic interactions between two surfaces as measured by atomic force microscopy (AFM) are usually analyzed in terms of DLVO theory. The discrepancies often observed between the experimental and theoretical behavior are usually ascribed to the occurrence of chemical regulation processes and/or to the presence of surface chemical or morphological heterogeneities (roughness). In this paper, a two-gradient mean-field lattice analysis is elaborated to quantifying double layer interactions between nonplanar surfaces. It allows for the implementation of the aforementioned sources of deviation from DLVO predictions. Two types of ion-surface interaction ensure the adjustment of charges and potentials upon double layer overlap, i.e., specific ionic adsorption at the surfaces and/or the presence of charge-determining ions for the surfaces considered. Upon double layer overlap, charges and potentials are adjusted via reequilibrium of the different ion adsorption processes. Roughness is modeled by grafting asperities on supporting planar surfaces, with their respective positions, shapes, and chemical properties being assigned at will. Local potential and charge distributions are derived by numerically solving the nonlinear Poisson-Boltzmann equation under the boundary conditions imposed by the surface profiles and regulation mechanism chosen. Finite size of the ions is taken into account. A number of characteristic situations are briefly discussed. It is shown how the surface irregularities are reflected in the Gibbs energy of interaction.

A Parallel-Plate Flow Chamber to Study Initial Cell Adhesion on a Nanofeatured Surface

Cells in the human body come across many types of information, which they respond to. Both material chemistry and topography of the surface where they adhere have an effect on cell shape, proliferation, migration, and gene expression. It is possible to create surfaces with topography at the nanometric scale to allow observation of cell-topography interactions. Previous work has shown that 100-nm-diameter pits on a 300-nm pitch can have a marked effect in reducing the adhesion of rat fibroblasts in static cultures. In the present study, a flow of cell suspension was used to investigate cell adhesion onto nanopits in dynamic conditions, by means of a parallel-plate flow chamber. A flow chamber with inner nanotopography has been designed, which allows real-time observation of the flow over the nanopits. A nanopitted pattern was successfully embossed into polymethylmethacrylate to meet the required shape of the chamber. Dynamic cell adhesion after 1 h has been quantified and compared on flat and nanopitted polymethylmethacrylate substrates. The nanopits were seen to be significantly less adhesive than the flat substrates (p < 0.001), which is coherent with previous observations of static cultures.

Effect of ionic sizes on the stability ratio of a dispersion of particles with a charge-regulated surface

The influence of the ionic sizes on the stability of a dispersion of particles, which have an amphoteric, charged-regulated surface, is discussed. A modified Poisson-Boltzmann equation, which takes into account the sizes of ionic species, is adopted to describe the electrical field. An extended DLVO theory, which takes into account the electrical, the van der Waals, and the hydration energies, is used to estimate the stability of a colloidal dispersion. The effects of the key parameters, including ionic strength, pH, and density of surface sites, on the behavior of problem under consideration are examined. The results obtained are qualitatively consistent with experimental findings in the literature.

Cation-induced collapse of low-molecular-weight polyacrylic acid in the dispersion of barium titanate

Observations on the steric layers formed by the adsorption of low-molecular-weight polyacrylic acid (PAA) were taken using the colloidal probe method in an atomic force microscope. The effects of divalent barium ions and of monovalent potassium ions at varying concentrations were observed on the repulsive interaction profiles. High ionic concentrations screened double-layer forces to small distances, whereby the acting forces were reduced to steric interactions. De Gennes scaling theory was used to model the effect of electrolyte on an aqueous barium titanate system, which was stabilized with PAA. The brush model was found to represent the force curves better than the mushroom model. The collapse of PAA layers with increasing salt approximated a grafted polymer brush in monovalent electrolyte, but the addition of barium ions caused markedly less steric collapse. It is suggested that the formation of a Ba(2+)-PAA complex in the adsorbed layer increases its compressibility parameter.

Simulation of the Adhesion of Particles to Surfaces

The removal of micrometer and submicrometer particles from dielectric and metal films represents a challenge in postchemical mechanical polishing cleaning. Proper modeling of the adhesive force between contaminant particles and these films is needed to develop optimal solutions to postchemical mechanical polishing cleaning. We have previously developed and experimentally validated a model to describe the adhesion between spherical particles and thin films. This simulation expands previous models to characterize the adhesive interaction between asymmetrical particles, characteristic of a polishing slurry, and various films. Our simulation accounts for the contact area between particles and substrates, as well as the morphology of the surfaces. Previous models fail to accurately describe the contact of asymmetrical particles interacting with surfaces. By properly accounting for nonideal and geometry and morphology, the simulation predicts a more accurate adhesive force than predictions based upon an ideal van der Waals model. The simulation is compared to experimental data taken for both semi-ideal particle-substrate systems (polystyrene latex spheres in contact with silicon films) and asymmetrical systems (alumina particles in contact with various films). Copyright 2001 Academic Press.

A Model for Calculating Electrostatic Interactions between Colloidal Particles of Arbitrary Surface Topology

A numerical model for calculating the electrostatic interaction between two particles of arbitrary shape and topology is described. A key feature of the model is a generalized discretization program, capable of simulating any desired analytical shape as a set of flat, triangular elements. The relative sizes of the elements are adjusted using a density function to better match the desired shape and the spatial variation of the electrical surface properties on each particle. The distribution of either surface potential or surface charge density is then calculated using a boundary element approach to solve the linearized Poisson-Boltzmann equation. Example interaction energy profiles are calculated for three different types of roughness-bumps, pits, and surface waves. It is found that the interaction energy between rough particles remains different from that between two equivalent smooth spheres at all separations, even for gap widths much larger than either the solution Debye length or the characteristic roughness size. This behavior at large gap widths arises from the nature of the decay of the electric potential away from each particle. In addition, the magnitude of the roughness effect is found to depend greatly on the size and shape of the nonuniformity as well as the electrostatic boundary conditions. For example, for a sphere containing asperities of height equal to 0.2 times the particle radius, the interaction energy can be as much as 50% greater than that between two equivalent spheres under the condition of constant surface potential. At constant surface charge density, the ratio of the interaction energies between rough and smooth spheres was found to either diverge or become zero as contact between the two particles is approached, depending on the nature of the roughness. Changes of this magnitude could clearly have a substantial impact on the stability behavior of a dispersion of such particles. Copyright 2001 Academic Press.

Investigation by atomic force microscopy of forces at the origin of cement cohesion

In cement paste, the cohesion results of the interactions between calcium silicate hydrate (CSH) surfaces in an interstitial ionic solution. (N, V, T) Monte Carlo simulations show that the interactions are due to the ion correlation forces influenced by the surface charge density, the ionic concentration and the ion valence. This paper deals with the direct measurement in solutions by atomic force microscopy (AFM) of the forces and the interaction ranges between a probe and an atomically smooth substrate covered by CSH nanoparticles. Different electrolytic solutions (Ca(OH)2, CaCl2, NaCl, NaOH) have been used in order to determine influent parameters permitting to identify the nature of acting forces. Investigations have been rendered possible by selecting appropriate experimental setup and solutions. The selected probe and substrate on which CSH nanoparticles have previously grown are neutral regarding the reactivity during experiments permitting the exchange of solutions. Results show that a force originates from electrostatic nature and differs from Derjaguin-Landau-Verwey-Overbeek (DLVO) theory. Agreement is found between experiments and (N,V,T) Monte Carlo simulations of ionic correlation forces. These forces are at the origin of the cohesion of cement paste.

Part II: Theoretical Analysis

Three phenomena involved in the perikinetic coagulation process were studied with regard to their ability to account for the influence of gravity on the coagulation rate: (1) surface charge effects on the pressure in the gap between two approaching particles, through the streaming potential generated by the squeezing flow; (2) free convection induced by temperature changes in the surroundings; (3) surface roughness and hydration force effects on the interaction force between two particles. In a separate paper flow interactions between two identical spheres are shown to be insufficient to explain the influence of gravity on coagulation rate. Of these phenomena studied, a combination of surface roughness and free convection can explain the influence of gravity on coagulation. Copyright 1998 Academic Press.