Interfacial friction coefficient

The shppage at the interface between a thin film of density Amf and the substrate is usually described in terms of an interfacial friction coefficient ( coefficient of shding friction ), x- This coefficient determines the stress acting between the film and the substrate, which move at different velocities. An infinite value of x implies that the non-sHp (sticking) boundary condition is applicable. When the interfacial friction coefficient equals zero, the film is free to slide with no energy dissipation. 

The effect of slippage at a substrate-film interface can also be described in terms of sbp time [39]. To understand the physical meaning of the slip time, one can consider an adsorbate film on a substrate, moving at constant velocity. If the substrate stops, the velocity and momentum of the film decay exponentially, and the time constant of this process is the slip time. If this process is very rapid, i.e., we have a rigidly adsorbed film, the time constant will be close to zero, and there will be no noticeable shp. The shp time is related to the interfacial friction coefficient through the equation [39] ... 

The molecular meaning of b is best seen from the second or third equality of Eq. (3). In other words, b is explicitly related to the steady shear melt viscosity q and depends on the chain-chain interactions near the melt/wall interface as quantified by the friction coefficient p. In the limit of no polymer adsorption or in absence of interfacial chain entanglements due to the coil-stretch transition, P involves an interfacial viscosity q , which is as small as the viscosity of a monomeric liquid and independent of the molecular weight Mw p=qj/a, where a is a molecular length. Thus at the stick-slip transition, the molecular weight dependence of b arises entirely from q in Eq. (3). 

A study carried out by Masao Uemura and colleagues was specifically designed to distinguish between the occurrence of cleavage, shear and interfacial slip (which they referred to as intercrystalline slip.) They concluded that cleavage took place when surface material was not fully oriented parallel to the basal planes, and that the friction coefficient was then of the order of 0.1. When shear was taking place the coefficient of friction was about 0.06, whereas when interfacial slip between fully basal-plane oriented surfaces was occurring the coefficient of friction was as low as 0.025. 

Sokhan and Quirke434 devise a method of computing interfacial friction and the Maxwell slip coefficients (a) by equilibrium MD, in which a is computed from the relaxation time, which itself can be estimated by an exponential fit to the collective velocity autocorrelation function. Their equilibrium method is compared to an NEMD method devised by the authors previously and excellent agreement is found. They study the density dependence of the slip... 

The Cooper-Mann theory of monolayer transport was based on the model of a sharply localized interfacial region in which ellipsoidal molecules were constrained to move. The surfactant molecules were assumed to be massive compared with the solvent molecules that made up the substrate and a proportionate part of the interfacial region. It was assumed that the surfactant molecules had many collisions with solvent molecules for each collision between surfactant molecules. A Boltzmann equation for the singlet distribution function of the surfactant molecules was proposed in which the interactions between the massive surfactant molecules and the substrate molecules were included in a Fokker-Planck term that involved a friction coefficient. This two-dimensional Boltzmann equation was solved using the documented techniques of kinetic theory. Surface viscosities were then calculated as a function of the relevant molecular parameters of the surfactant and the friction coefficient. Clearly the formalism considers the effect of collisions on the momentum transport of the surfactant molecules. 

Thus, the interfacial friction can be evaluated from measurement of AT and A/. This procedure has been applied to a number of systems in which weak physical adsorption occurs, such as the adsorption of Xe, Kr, N2 on Au, and of H2O and CeH on Ag [34-38]. In all the above cases slippage was observed, and the ratio of the coefficient of sliding friction to the mass density was of the order x/Amf = (10 - 10 )s As an example, the frictional stress acting on the monolayer Xe film sliding on a Ag(lll) surface at a velocity v = 1 cms F = xv, equals about 10Nm [40]. It is much smaller than typical shear stresses involved in sliding of a steel block on a steel surface under boundary lubrication condition (Eq. 6), which is of order 10 Nm 2 [39]. 

T. Fujii, H. Honda, and S. Nozu, Condensation of Fluorocarbon Refrigerants Inside a Horizontal Tube—Proposals of Semi-Empirical Expressions for the Local Heat Transfer Coefficient and the Interfacial Friction Factor, Refrigeration, 55(627), pp. 3-19,1980 (in Japanese). 

We are interested in the following questions How does a polymer move or flow on its own monolayer, or more generally, how do macromolecules slide past each other What are the consequences of the autophobic behavior between grafted and free polymers for dewetting What is the value of the friction coefficient at such polymer-polymer interfaces After a brief description of our experimental conditions, we present the experimental results, which are discussed in light of the theory described above. Finally, we show what we can learn about molecular parameters controlling interfacial properties. 

The interfacial interaction coefficient depends on the density Pj, the volume fraction 0 of a continuous medium, and the friction coefficient C ... 

Block copolymer coatings for tuning the interfacial properties of PDMS surfaces also play an important role in biomaterials science because PDMS surfaces are often employed in biomedical devices [126]. Iwasaki et al. reported the functionalization of pretreated PDMS films with well-defined triblock copolymers by spin coating [127]. The polymers were prepared using RAFT polymerization. Hydrophobic PDMS-based polymers were copolymerized with 2-methacryloyloxyethyl phospho-rylcholine (MPC). The polymeric coating material was spin-coated on thin PDMS films and chemically immobilized via hydrosilylation. The block copolymers were very effective in reducing the surface friction coefficient and improving wettability. 

For both PDMSs, for both substrates, and for all friction speeds, a great effect of normal force is observed. The higher friction coefficient observed at low normal force could be explained by the role of adhesion, which is magnified at low load (where the bulk contribution is lower). The contribution of interfacial interactions (or adhesive contact) is then magnified. These interfacial interactions will activate viscoelastic dissipation mechanisms, increasing the friction resistance. 

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