The application of Johnson–Kendall–Roberts (JKR) contact mechanics model in manipulation of a biological cell (DNA) using AFM will be studied in both air and liquid environments. Using JKR model in liquid environment requires adding interaction forces to its external force and applying equivalent adhesion energy to equations. These changes modify the adhesion force and the deformation in liquid environment. To discover the process of biological cell deformation owing to applied load by AFM, results will be compared with the results of a gold nanoparticle in the same condition, and theoretical and experimental data for mouse embryonic stem cell. Comparisons show that to have the same deformation for DNA and a gold nanoparticle, different forces are needed owing to different elasticity modulus. Sensitivity analysis of JKR deformation to elasticity modulus proved this claim. Although contact area for DNA is larger than a gold nanoparticle, less applied force is needed to have the same deformation.

This article has dealt with the development and modeling of various contact theories for biological nanoparticles shaped as cylinders and circular crowned rollers for application in the manipulation of different biological micro/nanoparticles based on Atomic Force Microscope. First, the effective contact forces were simulated, and their impact on contact mechanics simulation was investigated. In the next step, the Hertz contact model was simulated and compared for gold and DNA nanoparticles with the three types of spherical, cylindrical, and circular crowned roller type contact geometries. Then by reducing the length of the cylindrical section in the circular crowned roller geometry, the geometry of the body was made to approach that of a sphere, and the results were compared for DNA nanoparticles. To anticipatory validate the developed theories, the results of the cylindrical and the circular crowned roller contacts were compared with the results of the existing spherical contact simulations. Following the development of these contact models for the manipulation of various biological micro/nanoparticles, the cylindrical and the circular crowned roller type contact theories were modeled based on the theories of Lundberg, Dowson, Nikpur, Heoprich, and Hertz for the manipulation of biological micro/nanoparticles. Then, for a more accurate validation, the results obtained from the simulations were compared with those obtained by the finite element method and with the experimental results available in previous articles. The previous research works on the simulation of nanomanipulation have mainly investigated the contact theories used in the manipulation of spherical micro/nanoparticles. However since in real biomanipulation situations, biological micro/nanoparticles of more complex shapes need to be displaced in biological environments, this article therefore has modeled and compared, for the first time, different contact theories for use in the biomanipulation of cylindrical and circular crowned roller shaped micro/nanoparticles. The results of models indicate that the contact model of Hertz achieves the largest amount of deformation for the DNA nanoparticle in cylindrical form and the contact model of Heoprich achieves the largest deformation for the circular crowned roller shaped DNA. Of course, this finding is not always true for the other nanoparticles; and considering the mechanical and environmental characteristics, different results can be obtained. Also, by comparing the deformations of different types of nanoparticles, it was determined that the platelet type nanoparticles display the highest degree of deformation in all the considered models, due to their particular mechanical characteristics.

In this paper, the process of pushing rough cylindrical micro/nanoparticles on a surface with an atomic force microscope (AFM) probe is investigated. For this purpose, the mechanics of contact involving adhesion are studied first. Then, a method is presented for estimating the real area of contact between a rough cylindrical particle (whose surface roughness is described by the Rumpf and Rabinovich models) and a smooth surface. A dynamic model is then obtained for the pushing of rough cylindrical particles on a surface with an AFM probe. Afterwards, the process is simulated for different particle sizes and various roughness dimensions. Finally, by reducing the length of the cylindrical particle, the simulation condition is brought closer to the manipulation condition of a smooth spherical particle on a rough substrate, and the simulation results of the two cases are compared. Based on the simulation results, the critical force and time of manipulation diminish for rough particles relative to smooth ones. Reduction in the aspect ratio at a constant cross-section radius and the radius of asperities (height of asperities based on the Rabinovich model) results in an increase in critical force and time of manipulation.