A Study of Perturbations in Structure and Elastic Modulus of Bone Microconstituents Using Bimodal Amplitude Modulated-Frequency Modulated Atomic Force Microscopy

Nanomechanical Mapping of Hard Tissues by Atomic Force Microscopy: An Application to Cortical Bone

Force mapping of biological tissues via atomic force microscopy (AFM) probes the mechanical properties of samples within a given topography, revealing the interplay between tissue organization and nanometer-level composition. Despite considerable attention to soft biological samples, constructing elasticity maps on hard tissues is not routine for standard AFM equipment due to the difficulty of interpreting nanoindentation data in light of the available models of surface deformation. To tackle this issue, we proposed a protocol to construct elasticity maps of surfaces up to several GPa in moduli by AFM nanoindentation using standard experimental conditions (air operation, nanometrically sharp spherical tips, and cantilever stiffness below 30 N/m). We showed how to process both elastic and inelastic sample deformations simultaneously and independently and quantify the degree of elasticity of the sample to decide which regime is more suitable for moduli calculation. Afterwards, we used the frequency distributions of Young's moduli to quantitatively assess differences between sample regions different for structure and composition, and to evaluate the presence of mechanical inhomogeneities. We tested our method on histological sections of sheep cortical bone, measuring the mechanical response of different osseous districts, and mapped the surface down to the single collagen fibril level.

Accurate Wide-Modulus-Range Nanomechanical Mapping of Ultrathin Interfaces with Bimodal Atomic Force Microscopy

The nanoscale determination of the mechanical properties of interfaces is of paramount relevance in materials science and cell biology. Bimodal atomic force microscopy (AFM) is arguably the most advanced nanoscale method for mapping the elastic modulus of interfaces. Simulations, theory, and experiments have validated bimodal AFM measurements on thick samples (from micrometer to millimeter). However, the bottom-effect artifact, this is, the influence of the rigid support on the determination of the Young's modulus, questions its accuracy for ultrathin materials and interfaces (1-15 nm). Here we develop a bottom-effect correction method that yields the intrinsic Young's modulus value of a material independent of its thickness. Experiments and numerical simulations validate the accuracy of the method for a wide range of materials (1 MPa to 100 GPa). Otherwise, the Young's modulus of an ultrathin material might be overestimated by a 10-fold factor.

Ordered Fibril Arrays in Osteons Promote the Multidirectional Nanodeflection of Cracks: In Situ AFM Imaging

The high fracture resistance of cortical bone is not completely understood across its complex hierarchical structure, especially on micro- and nanolevels. Here, a novel in situ bending test combined with atomic force microscopy (AFM) is utilized to assess the micro-/nanoscale failure behavior of cortical bone under the external load. Unlike the smoother crack path in the transverse direction, the multilevel composite material model endows the longitudinal direction to show multilevel Y-shaped cracks with more failure interfaces for enhancing the fracture resistance. In the lamellae, the nanocracks originating from the interfibrillar nanointerface deflect multidirectionally at certain angles related to the periodic ordered arrangement of the mineralized collagen fibril (MCF) arrays. The ordered MCF arrays in the lamellae may use the nanodeflection of the dendritic nanocracks to adjust the direction of the crack tip, which subsequently reaches the interlamellae to sharply deflect and finally form a zigzag path. This work provides an insight into the relationship between the structure and the function of bone at a multilevel under load, specifically the role of the ordered MCF arrays in the lamellar structure.

Quantitative mapping of magnetic properties at the nanoscale with bimodal AFM

We demonstrate that a force microscope operated in a bimodal configuration enables the mapping of magnetic interactions with high quantitative accuracy and high-spatial resolution (∼30 nm). Bimodal AFM operation doubles the number of observables with respect to conventional magnetic force microscopy methods which enables to determine quantitatively in a single processing step several magnetic properties. The theory of bimodal AFM provides analytical expressions for different magnetic force models, in particular those characterized by power-law and exponential distance dependences. Bimodal AFM provides a self-evaluation protocol to test the accuracy of the measurements. The agreement obtained between the experiments and theory for two different magnetic samples support the application of bimodal AFM to map quantitatively long-range magnetic interactions.

Nanomechanical mapping of soft materials with the atomic force microscope: methods, theory and applications

Fast, high-resolution, non-destructive and quantitative characterization methods are needed to develop materials with tailored properties at the nanoscale or to understand the relationship between mechanical properties and cell physiology. This review introduces the state-of-the-art force microscope-based methods to map at high-spatial resolution the elastic and viscoelastic properties of soft materials. The experimental methods are explained in terms of the theories that enable the transformation of observables into material properties. Several applications in materials science, molecular biology and mechanobiology illustrate the scope, impact and potential of nanomechanical mapping methods.

Fast, quantitative and high resolution mapping of viscoelastic properties with bimodal AFM

Quantitative mapping of viscoelastic properties of soft matter with a nanoscale spatial resolution is an active and relevant research topic in atomic force microscopy (AFM) and nanoscale science characterization. The AFM has demonstrated its accuracy to measure the energy dissipated on a sample surface with an atomic-scale resolution. However, the transformation of energy dissipation values associated with viscoelastic interactions to a material property remains very challenging. A key issue is to establish the relationship between the AFM observables and some material properties such as viscosity coefficient or relaxation time. Another relevant issue is to determine the accuracy of the measurements. We demonstrate that bimodal atomic force microscopy enables the accurate measurement of several viscoelastic parameters such as the Young's modulus, viscosity coefficient, retardation time or loss tangent. The parameters mentioned above are measured at the same time that the true topography. We demonstrate that the loss tangent is proportional to the viscosity coefficient. We show that the mapping of viscoelastic properties neither degrades the spatial resolution nor the imaging speed of AFM. The results are presented for homogeneous polymer and block co-polymer samples with Young's modulus, viscosity and retardation times ranging from 100 MPa to 3 GPa, 10 to 400 Pa s and 50 to 400 ns, respectively. Numerical simulations validate the accuracy of bimodal AFM to determine the viscoelastic parameters.