Surface forces: surface roughness in theory and experiment

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 de...

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Bibliographic Details
Published in:The Journal of chemical physics 2014-04, Vol.140 (16), p.164701-164701
Main Authors: Parsons, Drew F, Walsh, Rick B, Craig, Vincent S J
Format: Article
Language:English
Subjects:
ATOMIC FORCE MICROSCOPY
Contact force
DISTRIBUTION
Histograms
INORGANIC, ORGANIC, PHYSICAL AND ANALYTICAL CHEMISTRY
Mathematical models
Normal distribution
Physics
PROBABILITY
Probability distribution
Separation
Statistical analysis
SURFACE FORCES
Surface roughness
SURFACES
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Summary: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.
ISSN:0021-9606
1089-7690
DOI:10.1063/1.4871412