Biomedical Engineering Reference
In-Depth Information
very well in cases of compliant spheres on stiff substrates ( e.g ., polymers
on glass) and the logarithmic potential is correct, if of limited use. The
Mie potential is probably of the broadest applicability, if only because of
the generalized empirical nature of its formulation, and incorporates the
possibility of snap-on, quiescent, indentation, and pull-off phenomena
along with an implicit surface energy, but has the disadvantage of lack of
closed-form solutions. In all these cases, the central physics of adhesive
indentation contact is the same; the net stiffness field in which the tip
moves, set by surface interactions and elastic deformations, determined
what is observed outside the system by the indenter. Indentation without
apparent adhesion is possible if the probe spring is very stiff. Adhesion
without apparent indentation is possible if the probe spring is very
compliant. Both adhesion and indentation with no loss of energy are
possible during a single contact event if the probe spring is stiff enough
(a supercritical probe). Adhesion and indentation with both adhesive
(snap-on) and separation (pull-off ) instabilities are possible if the probe
spring is compliant enough (a sub-critical probe). Indentation of
biological materials with either compliant nanoindenters or atomic force
microscopes will nearly always fall into this last category, in which the
energies involved with deforming (indenting) the surface will be
comparable to those involved with deforming the probe spring and with
interactions between the tip and surface. The ideas laid out here in
Chapters 2 and 4 provide a framework for interpreting adhesive
indentation measurements of biological materials and optimizing
instrument configurations for measurement of both surface interaction
and material deformation properties.
References
1. B. I. Bleaney and B. Bleaney, Electricity and Magnetism, Third Edition . Oxford
University Press (1976).
2. J. S. Rowlinson, Cohesion , Cambridge University Press (2002).
3. K. L. Johnson, Contact Mechanics , Cambridge University Press (1985).
4. K. L. Johnson, K. Kendall and A. D. Roberts, Proc. Roy. Soc. A 324 , 301 (1971).
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