Microscopic friction

In the previous section, we learned that the important processes of friction occur at microcontacts. Thus, to get a better understanding of friction phenomena, one should study friction at the micro- and nanoscale. This field of micro- and nanotribology evolved with the availability of suitable experimental techniques namely FFM, SFA, and QCM (reviews are Refs. [474,475]). The first measurement of friction with atomic resolution using friction force 

The validity of Coulomb s law has been verified also on the nanoscale Zworner et al. [484] showed that, for different carbon compound surfaces, friction does not depend on sliding velocity in the range between 0.1 /xm/s and up to 24 /xm/s. At low speeds, a weak (logarithmic) dependence of friction on speed was observed by Gnecco et al. [485] on a NaCl(lOO) surface and by Bennewitz et al. [486] on a Cu (111) surface. This can be modeled when taking into account thermal activation of the irreversible jumps in atomic stick-slip [487], 

In experiments with friction force microscopy, the tip forms a contact of a few nanometers in diameter with the substrate, a so-called nanocontact. In reality, friction of macroscopic bodies is determined by the interaction via m/crocontacts. One possibility of extending the method of friction force microscopy to larger contact areas is the use of the colloidal probe technique, where a small sphere is attached to the end of an atomic force microscope cantilever (see Section 6.4). Even for microcontacts, the proportionality between the true area of contact and the friction force was observed (see example 11.1). 

The reduction of friction by lubricants was a prerequisite for the industrial revolution. Lubrication helps to reduce energy consumption and increase the lifetime of machines by minimizing wear. Without lubricants, almost no machine made of metal would work. It is not surprising that the phenomenon of friction and lubrication was of interest since ancient times. We know that the Egyptians wetted the sand on which they transported their stones, to reduce friction [493], 

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The relation between the microscopic friction acting on a molecule during its motion in a solvent enviromnent and macroscopic bulk solvent viscosity is a key problem affecting the rates of many reactions in condensed phase. The sequence of steps leading from friction to diflfiision coefficient to viscosity is based on the general validity of the Stokes-Einstein relation and the concept of describing friction by hydrodynamic as opposed to microscopic models involving local solvent structure. In the hydrodynamic limit the effect of solvent friction on, for example, rotational relaxation times of a solute molecule is [ ]... 

Another microscopic approach to the viscosity problem was developed by Gierer and Wirtz (1953) and it is worthwhile describing the main aspects of this theory, which is of interest because it takes account of the finite thickness of the solvent layers and the existence of holes in the solvent (free volume). The Stokes-Einstein law can be modified using a microscopic friction coefficient ci micro... 

In Fig. 6.22 the results of a viscosity scahng by f— fxT/rj (T) of the relaxation data are shown. Such a scaling is motivated by the Rouse model and should hold for the a-relaxation. The pure PPO data (right) behave according to this expectation in contrast the PP0-IiC104 curves deviate considerably. This indicates that the coupling factor between microscopic friction and viscosity depends on temperature, possibly due to transient cross-linking via Li-ions. 

Microscopic Friction and Solvation in Barrier Crossing Isomerization of Stilbene in Size-Selected Hexane Clusters, A. A. Heikal, S. H. Chong, J. S. Baskin, and A. H. Zewail, Chem. Phys. Lett. 242, 380 (1995). 

Pioneering contact mode AFM studies by Meiners et ai. (1995) show that chemical sensitivity at the surface of thin polymer films can be achieved by measuring the microscopic friction and stiffness for glassy block copolymers. This provides invaluable information to complement topography on the nature of the block at the surface. 

Interestingly, this microscopic friction behaves much the way our macroscopic intuitions predict that it should. The manner in which the... 

The earliest attempts to explain Amontons s laws were based on the idea that macroscopic peaks or asperities on one surface interlocked with valleys on the opposing surface [1]. As illustrated in Fig. la, the bottom surface then forms a ramp that the top surface must be lifted up over in order to slide. If the typical angle of the ramp is 9, and there is no microscopic friction between the surfaces. 

To what extent does macroscopic friction , as indicated by solvent viscosity or by inverse self-diffusion coefficient, really reflects the microscopic friction experienced by the reaction coordinate ... 

Throughout our analyses, macroscopic solvent shear viscosity tj has been assumed to be proportional to the microscopic friction between the reactant and the solvent... 

The viscosity which yields the maximum reaction rate, shifts to a lower value with increasing temperature in GTA. In KF-54, however, the maximum viscosity stays almost constant. This behavior suggests the existence of a factor which affects the reaction rate but does not contribute to the macroscopic viscosity. If this second contribution to the microscopic friction decreases with increasing temperature, the behavior shown in Fig. 3.28 is to be expected. This second factor may be related to local segmental rotation of the siloxane chain. However, further experiments are necessary for detailed analysis. 

Perhaps though the most severe criticism of the whole theory is that, to date, applications and breakthroughs with respect to experimental observations have not been plentiful. The original introduction of memory friction by Grote and Hynes was useful conceptually and some experimental results have been analyzed in terms of non-Mar-kovian spectral densities, see for example Ref. 123. However, beyond a parametrization, there is to date no general good theory for microscopic friction. Application of VTST to simulations of realistic reactions in liquids is perhaps a first step but has not yet really clarified this issue. 

The total velocity of the solute molecule is given hy v = Vi + Vi- Because the friction coefficient is the ratio of the viscous force to the velocity = F/v), the microscopic friction coefficient c micro consists of two parts ... 

Paige, M. F. 2003. A comparison of atomic force microscope friction and phase imaging for the characterization of an immiscible polystyrene/polyfmethyl methacrylate) blend film. Polymer 44, 6345-6352. 

An assumption that the microscopic friction y(/), exerted by the solvent on the solute reaction coordinate, can be approximated by the viscosity of the bulk fluid, T],... 

Here we alternate single convective steps with single diffusive steps. In general, the time sequence of convective and diffusive steps could follow any regular or random distribution. Different choices of the convective-diffusive sequence, as well as different values of the microscopic friction coefficients F, lead to variations in dynamic be-... 

The friction depends on the microscopic details of the substrate and its interaction with the polymer on the atomistic scale," - but some universal aspects of the slip of polymer over substrates have been considered. " In order to incorporate microscopic friction in a continuum description, for example, a hydrodynamic description in terms of a Navier-Stokes equation, one routinely employs a boundary condition devised by Navier in 1823 ... 

In this article we investigate atomic force microscope friction (AFM) measurements at the Si02/Si02 interface. We use two approaches which differ in the way in which the surfaces are driven relative to each other in contact. The silicon tip of the AFM is driven at constant velocity or harmonically. The resulting response corresponds to either the tribological or the rheological properties at the contact. Here we bridge the gap between the two approaches which do not always lead to the same conclusions. 

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