Analysis of nanoindentation of soft materials with an atomic force microscope

Nanoindentation is a popular experimental technique for characterization of the mechanical properties of soft and biological materials. With its force resolution of tens of pico-Newtons, the atomic force microscope (AFM) is well-suited for performing indentation experiments on soft materials. However, nonlinear contact and adhesion complicate such experiments. This paper critically examines the application of the Johnson-Kendall-Roberts (JKR) adhesion model to nanoindentation data collected with an AFM. The use of a nonlinear least-square error-fitting algorithm to calculate reduced modulus from the nanoindentation data using the JKR model is discussed. It is found that the JKR model fits the data during loading but does not fit the data during unloading. A fracture stability analysis shows that the JKR model does not fit the data collected during unloading because of the increased stability provided by the AFM cantilever

Johnson-Kendall-Roberts theory applied to living cells

Johnson-Kendall-Roberts (JKR) theory is an accurate model for strong adhesion energies of soft slightly deformable material. Little is known about the validity of this theory on complex systems such as living cells. We have addressed this problem using a depletion controlled cell adhesion and measured the force necessary to separate the cells with a micropipette technique. We show that the cytoskeleton can provide the cells with a 3D structure that is sufficiently elastic and has a sufficiently low deformability for JKR theory to be valid. When the cytoskeleton is disrupted, JKR theory is no longer applicable

Determination of work of adhesion of biological cell under AFM bead indentation

Hertz contact theory has been widely used for the determination of cell elasticity based on AFM indentation experiments. In light of the adhesive contact between AFM tip and cell, this study applied Johnson–Kendall–Roberts (JKR) model to fit the indentation force–displacement (F–D) curves reported previously. A MIN6 cell has been modeled as first a sphere and then a flattened cell with different thicknesses. The results have shown that both basic JKR model and “generalized” JKR model can best describe the unloading force–displacement behaviors of the indentation curves. The Young׳s modulus of the cell and the work of adhesion of the cell–indenter interface are obtained. In comparison to the Hertzian contact model, the JKR model provides obviously better fitting to the experimental results, indicating that the adhesion is significant in the cell interaction

An approximate JKR solution for a general contact, including rough contacts

In the present note, we suggest a simple closed form approximate solution to the adhesive contact problem under the so-called JKR regime. The derivation is based on generalizing the original JKR energetic derivation assuming calculation of the strain energy in adhesiveless contact, and unloading at constant contact area. The underlying assumption is that the contact area distributions are the same as under adhesiveless conditions (for an appropriately increased normal load), so that in general the stress intensity factors will not be exactly equal at all contact edges. The solution is simply that the indentation is D=D1-Sqrt(2w A'/P") where w is surface energy, D1 is the adhesiveless indentation, A' is the first derivative of contact area and P" the second derivative of the load with respect to indentation. The solution only requires macroscopic quantities, and not very elaborate local distributions, and is exact in many configurations like axisymmetric contacts. It permits also an estimate of the full solution for elastic rough solids with Gaussian multiple scales of roughness, which so far was lacking, using known adhesiveless simple results. The solution turns out to depend only on rms amplitude and slopes of the surface, and in the fractal limit, slopes would grow without limit, tends to the adhesiveless result - although in this limit the JKR model is inappropriate. However, a more solid result is that the solution would also go to adhesiveless result for large rms amplitude of roughness h_{rms}, irrespective of the small scale details, and in agreement with common sense and previous models by the author.Comment: 14 page

A modelling approach towards Epidermal homoeostasis control

In order to grasp the features arising from cellular discreteness and individuality, in large parts of cell tissue modelling agent-based models are favoured. The subclass of off-lattice models allows for a physical motivation of the intercellular interaction rules. We apply an improved version of a previously introduced off-lattice agent-based model to the steady-state flow equilibrium of skin. The dynamics of cells is determined by conservative and drag forces,supplemented with delta-correlated random forces. Cellular adjacency is detected by a weighted Delaunay triangulation. The cell cycle time of keratinocytes is controlled by a diffusible substance provided by the dermis. Its concentration is calculated from a diffusion equation with time-dependent boundary conditions and varying diffusion coefficients. The dynamics of a nutrient is also taken into account by a reaction-diffusion equation. It turns out that the analysed control mechanism suffices to explain several characteristics of epidermal homoeostasis formation. In addition, we examine the question of how {\em in silico} melanoma with decreased basal adhesion manage to persist within the steady-state flow-equilibrium of the skin.Interestingly, even for melanocyte cell cycle times being substantially shorter than for keratinocytes, tiny stochastic effects can lead to completely different outcomes. The results demonstrate that the understanding of initial states of tumour growth can profit significantly from the application of off-lattice agent-based models in computer simulations.Comment: 23 pages, 7 figures, 1 table; version that is to appear in Journal of Theoretical Biolog

Models for quantitative charge imaging by atomic force microscopy

Two models are presented for quantitative charge imaging with an atomic-force microscope. The first is appropriate for noncontact mode and the second for intermittent contact (tapping) mode imaging. Different forms for the contact force are used to demonstrate that quantitative charge imaging is possible without precise knowledge of the contact interaction. From the models, estimates of the best charge sensitivity of an unbiased standard atomic-force microscope cantilever are found to be on the order of a few electrons

Nanosecond electro-optics of nematic liquid crystal with negative dielectric anisotropy

We study a nanosecond electro-optic response of a nematic liquid crystal in a geometry where an applied electric field $\textbf{E}$ modifies the tensor order parameter but does not change the orientation of the optic axis (director $\hat{\textbf{N}}$). We use a nematic with negative dielectric anisotropy with the electric field applied perpendicularly to $\hat{\textbf{N}}$. The field changes the dielectric tensor at optical frequencies (optic tensor) due to the following mechanisms: (a) nanosecond creation of the biaxial orientational order; (b) uniaxial modification of the orientational order that occurs over timescales of tens of nanoseconds, and (c) the quenching of director fluctuations with a wide range of characteristic times up to milliseconds. We develop a model to describe the dynamics of all three mechanisms. We design the experimental conditions to selectively suppress the contributions from fluctuations quenching (c) and from the biaxial order effect (a) and thus, separate the contributions of the three mechanisms in the electro-optic response. As a result, the experimental data can be well fitted with the model. The analysis provides a detailed physical picture of how the liquid crystal responds to a strong electric field on a timescale of nanoseconds. This work provides a useful guide in the current search of the biaxial nematic phase. Namely, the temperature dependence of the biaxial susceptibility allows one to estimate the temperature of the potential uniaxial-to-biaxial phase transition. An analysis of the fluctuations quenching indicates that on a timescale of nanoseconds, the classic model with constant viscoelastic material parameters might reach its limit of validity. The effect of nanosecond electric modification of the order parameter (NEMOP) can be used in applications in which one needs to achieve ultrafast (nanosecond) changes of optical characteristics.Comment: 42 pages, 13 figures, 2 appendice