Effect of Surface Roughness on the Interaction Energy between a Colloidal Sphere and a Flat Plate

Suresh, Lakkapragada; Walz, John Y.

doi:10.1006/jcis.1996.0535

Cited by 261 publications

(240 citation statements)

References 10 publications

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“…The expressions for pyramidal and more complex tips are given by Suresh and Walz (1996), Touhari et al (1998), and Zanette et al (2000). Calculation of the van der Waals contribution to the total tip-surface force requires only knowledge of ␥, R, and H. ␥ and R depend only on the tip shape, and this can be estimated from experimental studies of NC-SFM tip properties (see Sec.…”

Section: Van Der Waals Forcesmentioning

confidence: 99%

Theories of scanning probe microscopes at the atomic scale

2003

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Significant progress has been made both in experimentation and in theoretical modeling of scanning probe microscopy. The theoretical models used to analyze and interpret experimental scanning probe microscope (SPM) images and spectroscopic data now provide information not only about the surface, but also the probe tip and physical changes occurring during the scanning process. The aim of this review is to discuss and compare the present status of computational modeling of two of the most popular SPM methods-scanning tunneling microscopy and scanning force microscopy-in conjunction with their applications to studies of surface structure and properties with atomic resolution. In the context of these atomic-scale applications, for the scanning force microscope (SFM), this review focuses primarily on recent noncontact SFM (NC-SFM) results. After a brief introduction to the experimental techniques and the main factors determining image formation, the authors consider the theoretical models developed for the scanning tunneling microscope (STM) and the SFM. Both techniques are treated from the same general perspective of a sharp tip interacting with the surface-the only difference being that the control parameter in the STM is the tunneling current and in the SFM it is the force. The existing methods for calculating STM and SFM images are described and illustrated using numerous examples, primarily from the authors' own simulations, but also from the literature. Theoretical and practical aspects of the techniques applied in STM and SFM modeling are compared. Finally, the authors discuss modeling as it relates to SPM applications in studying surface properties, such as adsorption, point defects, spin manipulation, and phonon excitation. CONTENTS

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Section: Van Der Waals Forcesmentioning

confidence: 99%

Theories of scanning probe microscopes at the atomic scale

2003

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“…The value of A was reported to be −1.2 × 10 −20 J for a bubble-silica system [28] and R was chosen as 200 µm in this work. For electrostatic interaction, a linear approximation of the Poisson-Boltzmann equation was used, and the hemispherical-asperity-bubble-plane interaction was approximated as a sphere interacting with a bubble plane [26]. Thus, the double-layer potential energy per unit area, E A e , between the hemispherical-asperity-coated silica sphere and air bubble surface can be expressed as:…”

Section: Theoretical Modelmentioning

confidence: 99%

“…It should also be noted that we assumed the asperities coated on the silica sphere to be composed of silica for simplification. Therefore, the total van der Waals energy between the hemispherical-asperity-coated silica sphere and air bubble surface is given as [26]:…”

Section: Theoretical Modelmentioning

confidence: 99%

“…The theoretical model used in this work was derived based on the model proposed by Suresh and Walz [26,27], who considered the effect of roughness on the interaction energy between a rough sphere and a flat plate. The van der Waals potential was calculated using a pairwise additivity approach, while the electrostatic double-layer potential was assumed equal to the sum of the asperity-flat plate and sphere-flat plate potentials.…”

Section: Theoretical Modelmentioning

confidence: 99%

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Role of Collectors and Depressants in Mineral Flotation: A Theoretical Analysis Based on Extended DLVO Theory

et al. 2017

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A theoretical analysis was conducted to study the role of collectors and depressants in flotation, based on the extended Derjaguin-Landau-Verwey-Overbeek (DLVO) theory, where the hydrophobic force is considered. The collector-coated hydrophilic particle and the depressant-coated hydrophobic particle are simplified to a sphere uniformly covered with respectively hydrophobic and hydrophilic nanometer-sized hemispherical asperities of identical radius. Results show that the role of a collector in bubble-particle attachment is to create an attractive hydrophobic force and thus overcome the repulsive van der Waals and electrostatic forces. Moreover, increasing the length of the hydrophobic part of the collector molecule is a more effective way to enhance flotation recovery, compared to increasing the collector concentration. For a depressant, however, its function mechanism is to create a strong electrostatic double-layer force, while the suppression of the hydrophobic force plays a secondary role in decreasing the bubble-particle attachment barrier. The depressant molecule length is also a dominant parameter in designing a powerful depressant.

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“…38,39 The effect of regular (non-random) roughness has been considered through contact of hemispherical asperities. 40 Other studies have introduced a statistical description of roughness into calculation of the van der Waals interaction. [41][42][43][44] Advanced statistical analysis of asperity contact has been performed 44,45 but requires detailed knowledge of the surface roughness, not routinely available, and not in combination with roughened noncontact forces.…”

Section: Introductionmentioning

confidence: 99%

Surface forces: Surface roughness in theory and experiment

Parsons

Walsh

Craig

2014

The Journal of Chemical Physics

119

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A method of incorporating surface roughness into theoretical calculations of surface forces is presented. The model contains two chief elements. First, surface roughness is represented as a probability distribution of surface heights around an average surface height. A roughness-averaged force is determined by taking an average of the classic flat-surface force, weighing all possible separation distances against the probability distributions of surface heights. Second the model adds a repulsive contact force due to the elastic contact of asperities. We derive a simple analytic expression for the contact force. The general impact of roughness is to amplify the long range behaviour of noncontact (DLVO) forces. The impact of the elastic contact force is to provide a repulsive wall which is felt at a separation between surfaces that scales with the root-mean-square (RMS) roughness of the surfaces. The model therefore provides a means of distinguishing between "true zero," where the separation between the average centres of each surface is zero, and "apparent zero," defined by the onset of the repulsive contact wall. A normal distribution may be assumed for the surface probability distribution, characterised by the RMS roughness measured by atomic force microscopy (AFM). Alternatively the probability distribution may be defined by the histogram of heights measured by AFM. Both methods of treating surface roughness are compared against the classic smooth surface calculation and experimental AFM measurement.

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Effect of Surface Roughness on the Interaction Energy between a Colloidal Sphere and a Flat Plate

Cited by 261 publications

References 10 publications

Theories of scanning probe microscopes at the atomic scale

Theories of scanning probe microscopes at the atomic scale

Role of Collectors and Depressants in Mineral Flotation: A Theoretical Analysis Based on Extended DLVO Theory

Surface forces: Surface roughness in theory and experiment

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