We present a quantitative method for determining the viscoelastic properties of materials with nanometer spatial resolution. The approach is based on the atomic force acoustic microscopy technique that involves the resonant frequencies of the atomic force microscopy cantilever when its tip is in contact with a sample surface. We derive expressions for the viscoelastic properties of the sample in terms of the cantilever frequency response and damping loss. We demonstrate the approach by obtaining experimental values for the storage and loss moduli of a poly͑methyl methacrylate͒ film using a polystyrene sample as a reference material. Experimental techniques and system calibration methods to perform material property measurements are also presented.

We demonstrate the accurate nanoscale mapping of near-surface loss and storage moduli on a polystyrene-polypropylene blend with contact resonance force microscopy (CR-FM). These viscoelastic properties are extracted from spatially resolved maps of the contact resonance frequency and quality factor of the AFM cantilever. We consider two methods of data acquisition: (i) discrete stepping between mapping points and (ii) continuous scanning. For point mapping and low-speed scanning, the values of the relative loss and storage modulus are in good agreement with the time-temperature superposition of low-frequency dynamic mechanical analysis measurements to the high frequencies probed by CR-FM.

Resonant properties of a nonlinear dissipative layer excited by a vibrating boundary: Q-factor and frequency responseContact resonance AFM characterization techniques rely on the dynamics of the cantilever as it vibrates while in contact with the sample. In this article, the dependence of the quality factor of the vibration modes on the sample properties is shown to be a complex combination of beam and sample properties as well as the applied static tip force. Here the tip-sample interaction is represented as a linear spring and viscous dashpot as a model for sample (or contact) stiffness and damping. It is shown that the quality factor alone cannot be used to infer the damping directly. Experimental results for polystyrene and polypropylene are found to be in good agreement with predictions from the model developed. These results form the basis for mapping viscoelastic properties with nanoscale resolution.

Postmenopausal osteoporosis in women is characterized by an increase in bone fragility and risk of fracture. In addition to transmenopausal decline in three-dimensional trabecular bone architecture, changes in intrinsic material properties (local stiffness, damping, and hardness) may contribute to increased bone fragility. In this study, nanoindentation was used to quantify transmenopausal changes in the intrinsic properties of trabecular bone. Paired transilial biopsy specimens were used from a previously reported study in which bone biopsies were obtained from women prior to menopause (premenopausal, age 49.0 ± 1.9) and at 12 months past the last menstrual period (postmenopausal, age 54.6 ± 2.2). Elastic and viscoelastic material properties of the trabecular bone were measured using quasi-static and dynamic nanoindentation techniques, respectively. Paired Student's t tests (n = 15) were performed to assess the significance of the measured intrinsic properties. Trabecular bone microarchitecture is compromised in postmenopausal women, and although this loss is associated with a trend toward reduction in some intrinsic properties (storage modulus), we found no statistically significant changes in bone intrinsic properties between healthy pre- and postmenopausal biopsies in the quasi-static results and frequency-averaged dynamic results.