Correction of random surface roughness on colloidal probes in measuring adhesion

Atomic force microscopes (AFM) are commonly used to measure adhesion at nanoscale between two surfaces. To avoid uncertainties in the contact areas between the tip and the surface, colloidal probes have been used for adhesion measurements. We measured adhesion between glass spheres and silicon (100) surface using colloidal probes of different radii under controlled conditions (relative humidity of < 3%, temperature of 25 +/- 1 degrees C). Results showed that the adhesion forces did not correlate with the radii of the spheres as suggested by elastic contact mechanics theories. Surface roughness and random surface features were found on the surfaces of the colloidal probes. We evaluated various roughness parameters, Rumpf and Rabinovich models, and a load-bearing area correction model in an attempt to correct for the roughness effects on adhesion, but the results were unsatisfactory. We developed a new multiscale contact model taking into account elastic as well as plastic deformation in a successive contacting mode. The new model was able to correct for most of the surface roughness features except for surface ridges with sharp angular features, limited by the spherical asperity assumption made in the model.     

Hydrodynamic interactions between spheres in a viscous fluid with a flat free surface or hard wall

Hydrodynamic interactions between spheres immersed in a low-Reynolds-number fluid flow close to a flat free surface or hard wall are investigated. The spheres may have different or equal radii, and may be separated from the boundary or at contact with the free surface. A simple and useful expression is derived for the propagator (Green operator) connecting centers of two spheres. In the derivation, the method of images and the displacement theorems are used. Symmetry of the displacement operators is explicitly shown. The significance of these results in efficient Stokesian and Brownian dynamics simulations is outlined. An example of an application is shown.     

An MS Xα study of the electronic structure of osmium tetroxide

Multiple scattering Xα calculations of the electronic structure of OsO₄ are performed using various sets of atomic spheres radii. It is shown that the use of overlapping atomic spheres leads to a good agreement with photoelectron and electronic absorption spectra.     

Molar volume and adsorption isotherm dependence of capillary forces in nanoasperity contacts

The magnitude of the capillary force at any given temperature and adsorbate partial pressure depends primarily on four factors: the surface tension of the adsorbate, its liquid molar volume, its isothermal behavior, and the contact geometry. At large contacting radii, the adsorbate surface tension and the contact geometry are dominating. This is the case of surface force apparatus measurements and atomic force microscopy (AFM) experiments with micrometer-size spheres. However, as the size of contacting asperities decreases to the nanoscale as in AFM experiments with sharp tips, the molar volume and isotherm of the adsorbate become very important to capillary formation as well as capillary adhesion. This effect is experimentally and theoretically explored with simple alcohol molecules (ethanol, 1-butanol, and 1-pentanol) which have comparable surface tensions but differing liquid molar volumes. Adsorption isotherms for these alcohols on silicon oxide are also reported.     

An algorithm for three-dimensional Voronoi S-network

The paper presents an algorithm for calculating the three-dimensional Voronoi-Delaunay tessellation for an ensemble of spheres of different radii (additively-weighted Voronoi diagram). Data structure and output of the algorithm is oriented toward the exploration of the voids between the spheres. The main geometric construct that we develop is the Voronoi S-network (the network of vertices and edges of the Voronoi regions determined in relation to the surfaces of the spheres). General scheme of the algorithm and the key points of its realization are discussed. The principle of the algorithm is that for each determined site of the network we find its neighbor sites. Thus, starting from a known site of the network, we sequentially find the whole network. The starting site of the network is easily determined based on certain considerations. Geometric properties of ensembles of spheres of different radii are discussed, the conditions of applicability and limitations of the algorithm are indicated. The algorithm is capable of working with a wide variety of physical models, which may be represented as sets of spheres, including computer models of complex molecular systems. Emphasis was placed on the issue of increasing the efficiency of algorithm to work with large models (tens of thousands of atoms). It was demonstrated that the experimental CPU time increases linearly with the number of atoms in the system, O(n).     

Formation of Iron Macro-Spheres in Plasma

In this paper the formation mechanism of iron macro-spheres in a plasma medium is dealt with, including the conditions under which such spheres are formed. The geometry of the spheres referred to above depends on the main technological parameters involved in the production of pores. Conditions under which pores occur within macro-spheres are also established. The radii of these pores are sensitive to the velocity distribution within the plasma jet section     

Simulations of the gyroid phase in diblock copolymers with the Gaussian disphere model

Pure melts of asymmetric diblock copolymers are studied by means of the off-lattice Gaussian disphere model with Monte-Carlo kinetics. In this model, a diblock copolymer chain is mapped onto two soft repulsive spheres with fluctuating radii of gyration and distance between centers of mass of the spheres. Microscopic input quantities of the model such as the combined probability distribution for the radii of gyration and the distance between the spheres as well as conditional monomer number densities assigned to each block were derived in the previous work of F. Eurich and P. Maass [J. Chem. Phys. 114, 7655 (2001)] within an underlying Gaussian chain model. The polymerization degree of the whole chain as well as those of the individual blocks are freely tunable parameters thus enabling a precise determination of the regions of stability of various phases. The model neglects entanglement effects which are irrelevant for the formation of ordered structures in diblock copolymers and which would otherwise unnecessarily increase the equilibration time of the system. The gyroid phase was reproduced in between the cylindrical and lamellar phases in systems with box sizes being commensurate with the size of the unit cell of the gyroid morphology. The region of stability of the gyroid phase was studied in detail and found to be consistent with the prediction of the mean-field theory. Packing frustration was observed in the form of increased radii of gyration of both blocks of the chains located close to the gyroid nodes.     

Calculations of the Gibbs Energy of Formation of Cavities in Water

The Gibbs energy Δ_cav G of formation of cavities in water was calculated by thermodynamic integration. The cavities corresponded to organic molecules of various volumes and shapes with characteristic radii of 3–7 Å and spheres of radii 3–6 Å. Statistical integrals were calculated by the Monte Carlo simulation of an ensemble of water molecules with periodic boundary conditions at 25°C and pressure 1 atm. Interaction between water molecules was described by the TIP4P four-point nonpolarizable model. It was found that the proportionality of Δ_cav G to cavity volume V obtained earlier for spheres with radii not exceeding 5 Å remained valid for cavities corresponding to organic molecules of different volumes and shapes, including cavities with the characteristic radii exceeding 5 Å. A possible explanation of the retention of the Δ_cav G ∞ V dependence at large characteristic radii was suggested in terms of the two-peak binomial model of the cavitation effect. The conclusion was drawn that the Δ_cav G = αV dependence could be used for calculating the nonpolar part of the Gibbs energy of solvation in implicit water models.     

In situ determination of the size and polydispersity of concentrated emulsions

Droplet size distributions of concentrated, polydisperse oil-in-water emulsions have been measured using ultra small angle neutron scattering (USANS). The mean radii calculated by fitting a model for polydisperse hard spheres with excluded volume interactions to the USANS data were consistent with those derived from electroacoustics on diluted emulsions after correction for conductance behind the shear plane. The Porod radii measured by USANS were similarly consistent with the mean surface-area-weighted radii derived from electroacoustics, irrespective of the drop concentration or polydispersity.     

Diffusion of spherical micronetworks in polymer diluent systems and melts studied by dynamic light scattering techniques

Spherical polystyrene (PS) micronetworks can be prepared in microemulsion with bulk radii of 5–60 nm and different cross-linking densities. The diffusion of these PS spheres has been studied in polymer diluent systems ranging from dilute solutions to plasticized melts by using forced Rayleigh scattering and photon correlation spectroscopy. On increasing the PS concentration, a colloid glass transition is observed at a volume fraction Φ_C ≈ 0.64 of the swollen spheres. At higher concentration inside the “colloid glass” state the sphere diffusion is slowed down and becomes very complex but can be observed up to the limit of a melt of collapsed spheres.     

A “phantom bubble” model for the distribution of free volume in polymers

A new approach to investigate free volume in atomistic simulation was devised. The atoms in the structure are represented by hard spheres. A phantom bubble is defined as an empty sphere, which contacts four or more hard spheres of atoms simultaneously in 3 dimensional space and does not overlap with any atom in the structure. Phantom bubbles are only allowed to overlap with other phantom bubbles. For the purpose of illustration, phantom bubbles were constructed in a fully atomistic structure. An amorphous polyethylene was prepared in a periodic box having the dimension of 28.2×28.2×28.2 Å at 293 K and a density of 0.83 g/cm³. There were two fully atomistic polymeric chains (each C₄₀₀H₈₀₂) in the box. All the atoms in the system were assumed to be hard spheres, usually with 89% of their van der Waals radii. Larger and smaller radii were also considered. The size distribution of phantom bubbles in this system was calculated and the bubbles had a median radius of 0.8 Å. Small changes in the radii used for the atoms have little effect on the shape of the distribution function.     

Nodoids and toroids: comparison of two geometries for the meniscus profile of a wetting liquid between two touching isolated spheres and extensions to the model of a collection of packed spheres

In the mid 1960s the present authors published two papers dealing with penetration of nonwetting liquids such as mercury into the interstitial void spaces using the model of uniform packed spheres. A circular arc was used to approximate the liquid-vapor interface in both papers. However, our circular arc-toroid values for the pressure-volume relationship in the pendular ring which exists between two touching spheres was criticized. The authors concluded that our approximation led to unacceptably large differences compared to the values calculated from the exact nodoid shape. This incorrect conclusion was never rebutted and has, in fact, been misinterpreted by subsequent workers to include values calculated for the shape of the access opening and the associated pressure for penetration into the void space of a collection of spheres. This leaves a cloud of uncertainty, not only over our original work on nonwetting fluids, but on the application of our procedures to the field of wetting fluids. The contrast in the geometrical shapes of the toroid and nodoid is depicted and the pressure values are compared at equal volumes. In contrast to the claim of excessive error, we show the toroid geometry, in conjunction with a pressure-volume work derivation, to have a maximum error of 0.06% as compared to the nodoid at all liquid-solid contact angles. The toroid also has the advantage of using a readily derived work versus surface free energy balance rather than requiring the use of incomplete elliptic integrals to evaluate the nodoid. Attempts to use radii of curvature to evaluate the toroid shape are shown to give extremely poor approximations of the exact values for the pressure. Values reported for access to the interior void space of a collection of spheres still need adjustment for the effect of contact angles between 0 degrees and 180 degrees for characterizing assemblies of real solids by computing "equivalent spherical" particle size from porosity and mercury penetration data. However, there is no anticipation that use of the circular arc will introduce large errors in the results. This gives confidence to us and others working with wetting media to test the potential applicability of the packed sphere model to various diverse fields.     

Molecular dynamics simulation of the association of nonpolar spheres in water

We apply molecular dynamics (MD) simulations to the study of the association of nonpolar spheres of effective radii between 1.6 and 6.1 A dissolved in water. The constrained MD method is used to calculate the potential of mean force (PMF) of the interaction between spheres. The depth of the potential of mean force increases with increasing radius of the nonpolar sphere. Our results suggest that the PMF is largely governed by size or entropic effects, and that energetic effects associated with the breaking or distortion of hydrogen bonds are of minor importance.     

Behavior of double emulsions in a cross-type optical separation system

The behavior of double emulsions in a cross-type optical particle separation system was studied for different combinations of refractive indices and different inner and outer layer radii. The radii and refractive indices of the double emulsions were easily adjusted by taking advantage of the coflowing geometry of a cross-type optical particle separation device. An analytical expression of the optical forces on a pair of concentric spheres was derived using the photon stream method in the ray optics regime. The predicted trajectories of the double emulsions by the optical force agreed well with the experimental data. This work has potential uses in cell separation by morphometry, drug delivery vehicle, and emulsion-based biomedical applications.     

Polymers as compressible soft spheres

We consider a coarse-grained model in which polymers under good-solvent conditions are represented by soft spheres whose radii, which should be identified with the polymer radii of gyrations, are allowed to fluctuate. The corresponding pair potential depends on the sphere radii. This model is a single-sphere version of the one proposed in Vettorel et al. [Soft Matter 6, 2282 (2010)], and it is sufficiently simple to allow us to determine all potentials accurately from full-monomer simulations of two isolated polymers (zero-density potentials). We find that in the dilute regime (which is the expected validity range of single-sphere coarse-grained models based on zero-density potentials) this model correctly reproduces the density dependence of the radius of gyration. However, for the thermodynamics and the intermolecular structure, the model is largely equivalent to the simpler one in which the sphere radii are fixed to the average value of the radius of gyration and radii-independent potentials are used: for the thermodynamics there is no advantage in considering a fluctuating sphere size.     

The theory of non-Cottrellian diffusion on the surface of a sphere or truncated sphere.

A method is developed whereby spherical and other particles can be derivatised with electroactive species on their surface and then immobilised on the surface of an electrode. The chronoamperometric and voltammetric responses in the limit of reversible electrode kinetics are modelled using a theory of charge movement over the surface of the spheres where this movement is considered as a diffusional process. The model is extended to include different distributions of sphere radii and to model the scenario of truncated spheres resting on the electrode surface. It is found that a good estimation of the truncation angle can be found by fitting the experimental data with theoretical predictions.     

Mean spherical model approximation for the primitive model of sodium chloride

A calculation of the excess internal energy and the osmotic coefficient for a mixture of charged hard spheres of diameters equal to the ionic radii of NaCl, is done in the mean spherical approximation. The results are compared to the best available data, provided by the hypernetted chain theory. The agreement is better for the osmotic coefficient than for the internal energy, and improves at higher concentrations.     

Adhesive Contact of Elastically Deformable Spheres: A Computational Study of Pull-Off Force and Contact Radius

Elastic spheres in contact deform around the contact region, due to intermolecular interaction forces. The deformed contacting surfaces change the distance between interacting molecules that in turn alters the force of interaction. Thus, the contact behavior of elastic spheres constitutes a nonlinear mathematical problem that defies the traditional analytical methods for general solution. Efficient computational techniques have enabled a detailed study of adhesive contact behavior of elastically deformable spheres with self-consistent solutions of a nonlinear integral governing equation. The present work extends the previous computational analysis to the quantities of practical interests such as the pull-off force and the radius of contact area. Trends of variations in the pull-off force as physical properties change are examined. Computationally determined radial positions as stress condition indicators suggest that the concept of contact radius is not clearly defined in the literature and can be confusing. It seems that some contact mechanics models would be consistent with the definition of the edge of contact area as the radial position for the local surface stress to change from compression to tension, whereas others would rather assume the contact radius as the radial position for the local tensile stress to reach its peak. The substantial quantitative deviation of self-consistently computed contact radius from the DMT model prediction suggests that models based on the assumption of a well-defined contact area having a constant gap may not be appropriate when describing cases of small values of Tabor's parameter. Copyright 2001 Academic Press.     

Freezing of hard spheres confined in narrow cylindrical pores

Monte Carlo simulations for the equation of state and phase behavior of hard spheres confined inside very narrow hard tubes are presented. For pores whose radii are greater than 1.1 hard sphere diameters, a sudden change in the density and the microscopic structure of the fluid is neatly observed, indicating the onset of freezing. In the high-density structure the particles rearrange in such a way that groups of three particles fit in sections across the pore.     

Depletion potential between large spheres immersed in a multicomponent mixture of small spheres

We analyze the depletion potential between large spheres in a multicomponent mixture of dense small spheres (up to seven components) using the integral equation theory (IET), in which semiempirical bridge functions are incorporated, and the insertion approach within the framework of density functional theory (DFT). The diameters of the small spheres considered are in the range of d(S)-5d(S). The results from the IET and DFT are in close agreement with each other. The depletion potential in the mixture is substantially different from that in a one-component system of dense small spheres with diameter d(S). In comparison with the latter, the former possesses in general a less pronounced oscillatory structure, and the free-energy barrier for large spheres to overcome before reaching the contact is significantly reduced. This tendency can be enhanced as the number of components increases. In a several-component mixture of small spheres whose diameters are suitably chosen and in which the packing fractions of the components share the same value, the depletion potential is essentially short ranged and attractive and possesses a sufficiently large, negative value at the contact.