Quantitative measurement of indentation hardness and modulus of compliant materials by atomic force microscopy

Abstract

An atomic force microscopy (AFM) based technique is proposed for the characterization of both indentation modulus and hardness of compliant materials. A standard AFM tip is used as an indenter to record force versus indentation curves analogous to those obtained in standard indentation tests. In order to overcome the lack of information about the apex geometry, the proposed technique requires calibration using a set of reference samples whose mechanical properties have been previously characterized by means of an independent technique, such as standard indentation. Due to the selected reference samples, the technique has been demonstrated to allow reliable measurements of indentation modulus and hardness in the range of 0.3-4.0 GPa and 15-250 MPa, respectively.

Elastic modulus measurements at variable temperature: Validation of atomic force microscopy techniques

“…Briefly, at selected locations of the sample surface, the AFM cantilever deflection (d) is recorded as a function of the vertical displacement of the piezoelectric actuator (∆z) when the AFM tip is approached to and then retracted from the sample surface. The collected curves can be used to obtain a forceindentation curves which are analogous to those obtained in standard DSI, the approaching and retracting phases in I-AFM corresponding to the loading and unloading ones in DSI [22,23]. By varying the range of ∆z, different penetration depths can be achieved from a few to several tens or even a few hundreds of nanometers, which represents a key capability in the study of polymeric thin films on stiff substrates [24,25].…”

“…Conversely, in case of compliant materials the tip indents the sample surface. In this case, the indentation depth h can be calculated as h = d − ∆z, having assumed d = 0 and ∆z = 0 in correspondence of the contact (snap-in) point [22,23]. The surface elastic modulus of compliant samples can be calculated from the initial slope of the retracting curves, also referred to as the tip-sample contact stiffness k * , as the unloading phase is affected by plastic effects [26].…”

“…Analogous effects, but less marked, are observed on PC sample, too (curves not shown). To quantitatively evaluate the indentation modulus of the samples, the geometry of the tip should be calibrated using a set of reference materials [22][23][24]37]. In this work, however, indentation modulus values M at different temperatures were compared after normalization by the corresponding value at room temperature M 0 , in order to avoid the timeconsuming calibration step.…”

“…For isotropic materials, M = E/(1−ν 2 ), where E represents the Young's modulus and ν the Poisson ratio of the investigated sample. In case of samples much more compliant than the tip (M t >> M), E * ≈ M. The contact area depends on the geometry of the tip, which has to be calibrated using a set of reference materials [22].…”

Contact resonance atomic force microscopy for viscoelastic characterization of polymer-based nanocomposites at variable temperature

“…LDPE and polycarbonate (PC) sheets 1 mm thick (Goodfellow Cambridge Ltd.) were used as reference samples to verify the accuracy of CR-AFM for viscoelastic characterizations [26,27]. LDPE and PC are characterized by different glass transition temperature, i.e., about -120°C and 140°C, respectively.…”