  We report an experimental and a theoretical study of the radial elasticity of
multi-walled carbon nanotubes as a function of external radius. We use atomic
force microscopy and apply small indentation amplitudes in order to stay in the
linear elasticity regime. The number of layers for a given tube radius is
inferred from transmission electron microscopy, revealing constant ratios of
external to internal radii. This enables a comparison with molecular dynamics
results, which also shed some light onto the applicability of Hertz theory in
this context. Using this theory, we find a radial Young modulus strongly
decreasing with increasing radius and reaching an asymptotic value of 30 +/- 10
GPa.
