Interfacial mechanism friction theory

Computational techniques have extensively been used to stu(fy the interfacial mechanics and nature of bonding in CNT-polymer composites. The computational studies can be broadly classified as atomistic simulations and continuum methods. The atomistic simulations are primarily based onMD simulations and DFT [105-110], The main focus of these techniques was to understand and stndy the effect of bonding between the polymer and nanotube (covalent, electrostatic or vdW forces) and the effect of friction on the interface. The continuum methods extend the continuum theories of microme-chanics modeling and fiber-reinforced composites (elaborated in the next section) to CNT-polymer composites [111-114] and explain the behavior of the composite from a mechanics point of view. 

Apart from pinch-offs detachment, fiow may also speed up the pull-out of copolymers from the interface and their subsequent dispersion as micelles in the continuous blend phase. This pull-out mechanism depends on the frictional shear force exerted on the interfacial copolymer chains, which is determined by the thermodynamical interaction of the interfacial copolymer chain with the blend chains at each phase and by the molecular weight and structure of the copolymer chains [77[. The experimental studies of Inoue et al. [77-79] corroborate the frictional theory and show that the pull-out tendency depends on the structure of the interfacial copolymer, on its molecular weight, and on the intensity of shear stress during fiow ... 

Dutrowski [5] in 1969, and Johnson and coworkers [6] in 1971, independently, observed that relatively small particles, when in contact with each other or with a flat surface, deform, and these deformations are larger than those predicted by the Hertz theory. Johnson and coworkers [6] recognized that the excess deformation was due to the interfacial attractive forces, and modified the original Hertz theory to account for these interfacial forces. This led to the development of a new theory of contact mechanics, widely referred to as the JKR theory. Over the past two decades or so, the contact mechanics principles and the JKR theory have been employed extensively to study the adhesion and friction behavior of a variety of materials. 

In recent years it has been demonstrated that also adhesion (or adhesion hysteresis) plays an important role in friction. Israelachvili and coworkers could show that friction and adhesion hystereses are, in general, directly correlated if certain assumptions are fulfilled. These authors have proposed models based on data obtained by surface forces apparatus (SFA) experiments, e. g. the cobblestone model of interfacial friction (4). In addition, several groups described the application of continuum contact mechanics (e.g. Johnson-Kendall-Roberts (JKR) theory (5)) to describe friction data measured between flat surfaces and nanometer sized contacts (d). 

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