Amontons’ classical friction law states that the resistive force against the motion of a sliding macroscopic object on a surface is proportional to the applied external normal force. Recent advances in nanotribology and single-molecule experiments have revealed that at nanoscopic scales, conventional laws do not apply due to the adhesive forces and thermal fluctuations, and these laws should be reviewed. This work focuses on the friction dynamics of nano-soft matter, which plays an important role in the biological machinery and is accessible by single-molecule experiments. In the first part of this work, the friction of laterally pulled single peptides over planar H-terminated non-polar and hydroxylated polar substrates are put under investigation in the presence of water using extended Molecular Dynamics (MD) simulations and the stochastic Fokker-Planck equation. Since the stiffness of the surface-peptide matrix affects the hydrogen bonding, we also discuss the friction experienced by a peptide in a peptide bundle as a function of a confinement parameter, which is the number of neighbouring chains in the bundle. We show that the friction of hydrogen-bonded matter obeys a simple equation in the biologically relevant low-velocity viscous regime: The friction force is proportional to the number of hydrogen bonds, the sliding velocity, and a friction coefficient per hydrogen bond γHB. The value of γHB is extrapolated from simulations by mapping on the stochastic model. The γHB turns out to span a range from γHB = 10-11 kg/s, for parallel or perpendicular pairs of polyglycines, to γHB = 10-6 kg/s,, for a denser bundle of 7 polyglycines. At the polar surfaces, γHB = 10-8 kg/s, which coincides with that in a bundle of 5 peptides. Our findings can explain the confinement dependent slowing observed in single-molecule experiments.
To interpret these experiments precisely, hydrodynamic friction, which is particularly important in experiments utilizing nano-scale beads or nanowires, should be considered. Hence, in a related project, the transient compressible Navier-Stokes equation is solved analytically to obtain the frequency-dependent friction response functions for spherical, cylindrical and planar geometries in an unbounded fluid, with finite slip length. For high driving frequencies, the flow pattern is dominated by the diffusion of vorticity and compression. On the other hand, for low frequencies, the compression propagates in the form of sound waves which are exponentially damped at a screening length larger than the sound wave length. In the propagative regime, the hydrodynamic-friction response of spheres and cylinders exhibits a high-frequency resonance when the particle size is of the order of the sound wave length. A distinct low-frequency resonance occurs at the boundary between the propagative and diffusive regimes.