Analytic formulas for basic shapes

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• Analytic formulas for basic shapes
• Numerical calculations with volume elements for
  realistic tip or particle shapes and roughness.

Principle K. Cooper et. al. J. Colloid Interface
Sci. 234 (2001)
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• AFM image of the real
• SiO2 surface

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• AFM image of the real
• SiO2 surface
• Align tip randomly,
• optionally allow to relax
• Calculate the adhesion force

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• Without relaxation poor results

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• With relaxation the deviations usually match
  nicely with experiments

• Without relaxation poor results

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• With relaxation the deviations usually match
  nicely with experiments

• Without relaxation poor results

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• Capillary force arises from the pressure
  difference, caused by surface tension, in the
  water meniscus between two bodies. The meniscus
  condenses from ambient humidity.
• Also a direct surface tension component in the
  force.

• Present if humidity exceeds 10-20
• The strength of the force is dependent on
  shapes, sizes and materials of the bodies.

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• The experimental humidity dependence

SiO2 sphere on TiO2 and SiO2 surfaces
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• Code solving the exact (non-circular) meniscus
  profile numerically from the Kelvin equation has
  been developed.
• Line elements are arranged so that
• the meniscus has the correct surface
• curvature at each point
• Any axially symmetric particle shape
• can be studied
• The capillary force can be calculated
• from the profile using the
• Young-Laplace equation.

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• The capillary force becomes humidity dependent
  for nanoscale objects
• - standard approximation
• for spheres fails

• Increasing tip-sample separation induces a
  non-zero offset humidity, below which the
  meniscus does not form.

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• The capillary force becomes humidity dependent
  for nanoscale objects
• - standard approximation
• for spheres fails

• Increasing tip-sample separation induces a
  non-zero offset humidity, below which the
  meniscus does not form.

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• The capillary force humidity dependence has been
  studied for different tip profiles and tip-sample
  separations.
• Tip profile determines the maximum force humidity.

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• Also two different models of pull-off have been
  studied.
• The models are found to produce very different
  predictions of the capillary force.

• Equilibrium approximation
• is valid in most processes.
• (Shown by MD-simulations,
• D. Seveno, J. De Coninck,
• Langmuir 20 (2004) 737)

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