where wa is Dupre's work of adhesion and K is the bulk modulus, which is related to the
elastic modulus, E, by Poisson's ratio, v, by the following:
E
K=
3(1-2v)
At greater thickness where t >> a, the relationship between the pull-off force and
the elastic modulus is given by
P 8Ew 2
PC =)\ -
The implication of this equation is that stiffer materials improve strength of adhesion.[5]
One of the assumptions to this equation is that the attached surface is rigid, while for a
cell, this is not the case. As discussed earlier with the low modulus wrinkling elastomers,
a cell has the ability to create its own forces and change them depending on the substrate
on which it is adhering. If a focal adhesion is modeled as a rigid body, then the equation
can hold validity. If we imagine a cell applying traction forces on the substrate it is
adhering to, then it is possible that a cell in equilibrium might exert forces just under the
critical force in equal directions. Chicurel et al. concluded in their review of focal
adhesion literature that a cell will continually contract on a substrate until the forces come
into balance, much like a bow and a bowstring.[103] By that reasoning, for higher
modulus materials the critical force is greater and thereby the traction forces applied.
Since the ridges and grooves select the direction for a cell to align by directing its
cytoskeleton, these increased forces would travel along the ridge and result in increasing
the elongation of the cell, and the effect of contact guidance.