Measuring the viscoelastic creep of soft samples by step response AFM

Abstract

We have measured the creep response of soft gels and cells after applying a step in loading force with atomic force microscopy (AFM). By analysing the creep response data using the standard linear solid model, we can quantify the viscous and elastic properties of these soft samples independently. Cells, in comparison with gels of similar softness, are much more viscous, as has been qualitatively observed in conventional force curve data before. Here, we quantify the spring constant and the viscous damping coefficient from the creep response data. We propose two different modes for applying a force step: (1) indirectly by increasing the sample height or (2) directly by employing magnetic cantilevers. Both lead to similar results, whereas the latter seems to be better defined since it resembles closely a constant strain mode. The former is easier to implement in most instruments, and thus may be preferable from a practical point of view. Creep analysis by step response is much more appropriate to analyse the viscoelastic response of soft samples like cells than the usually used force curve analysis.

Load-dependent surface nanomechanical properties of poly-HEMA hydrogels in aqueous medium

“…As an alternative, one may choose to probe the local creep response 16 and stress relaxation [17][18][19] of soft samples by AFM based methods. Here, the tip rests on the surface of the sample, and then either the change in tip deflection with time or the change in force required to keep the deflection constant with time is monitored.…”

Modeling and Measuring Viscoelasticity with Dynamic Atomic Force Microscopy

“…The Hertz model [22] gives a repulsive contact force. Assuming an axially symmetric rigid tip, one can parameterize the tip profile in terms of a power m ∈ [1,2] and a length scale [23], to express the contact force as a function of tip indentation z 0 − z, where z is the position of the tip and z 0 is the equilibrium position of the surface (see fig. 1a).…”

The effect of cortical elasticity and active tension on cell adhesion mechanics

“…The physical properties of the cell's internal structures are complex, and models that capture its mechanical behavior are often dependent on the timescale of interest. At fast timescales ( 1 s), indented cells show a viscoelastic creep response, which might be attributed to Maxwell fluid behavior of the cell's internal structures (16). Hence, the assumption in our analyses was that experiments were at least slow enough to relax any deviatoric stresses.…”