W. Richard Bowen and Nidal Hilal 4

216 7. MICRO/NANOENgINEERINg ANd AFM FOR CELLULAR SENSINg
(a)
On glass
On nucleus
On filopodia
0.0
–1400 –1200 –1000 –800 –600 –400 –200 0 200
Piezo-displacement (nm)
(b)
angle of the tip (�, only for a conical tip) and Poisson’s ratio (v, normally
assumed to be 0.5 as cells are virtually incompressible). Young’s
modulus can then be calculated by taking � and F at a single point or
by fitting to the contact region of a force distance (F–�) curve. In the
single-point method, a significant uncertainty comes from the accuracy
of determining the point where the tip first contacts the surface with zero
force (contact point). This can be extremely difficult, and so it is normally
recommended to fit the data in the contact region.
δ
d
0.4
0.3
0.2
0.1
δ
Force (nN)
δ
Contact point
δ + d
FIgurE 7.10 Schematic diagram showing indentation of a soft substrate by an AFM tip
and cantilever (a). Contact point between the tip and substrate with no load or indentation
of the sample (left image). Tip indenting the sample by a distance �, with a load caused by
the cantilever deflection d, the total displacement of the tip–sample separation is given by
� � d (right image). Examples of force curves generated on a solid glass substrate (no indentation),
a cell nucleus region and a filopodia region (b). Note the heterogeneity of the cell.
The indentation distance into the sample (�) can be corrected by subtracting the cantilever
deflection (d) from the piezo-displacement.