The role of solvent quality, inhomogeneous polymer brush composition, grafting density and number of free chains on the viscosity, friction between surfaces, and their scaling laws

Relationship between the coefficient of friction of additive in the bulk and chain graft surface density through a diffusion process: Erucamide–stearyl erucamide mixtures in polypropylene films

“…Solving Equation (5) numerically by substituting the experimental information (Section 3.1), where the diffusion coefficient is a constant, allowed us to convert a time scale to a concentration scale (Γ). The results obtained from the surface density are comparable to the simulation results reported by Catarino‐Centeno et al [ 15 ] Subsequently, the CoF graphs as a function of Г for 50 μm PP films with 1500 ppm of erucamide and the respective mixtures were compared. The units for surface density were normalized to the maximum value (Г max ), as shown in Figure 4(A,B).…”

“…(A) Coefficient of friction (CoF) as a function of normalized surface density (Г) for a 50 μm thick PP film in five concentrations. (B) Mesoscopic simulation results with 200 free chains in a good solvent [ 15 ] [Color figure can be viewed at wileyonlinelibrary.com]…”

“…These results were obtained from the coarse‐grained simulations considering that 200 erucamide free molecules acted as lubricating agents and interacted with the polymeric brushes, as reported in previous works. [ 15 ] These free molecules fraction results were considered because they presented the best results in terms of CoF stability as a function of the surface grafting density because of the polymeric brushes' composition and the solvent's quality. The CoFs tendency in each case decreases and subsequently stabilizes at different values.…”

“…In a recent publication, Gama‐Goicochea and coworkers modeled on a mesoscopic scale the rheological properties of a mixture of two slip additives (erucamide and stearyl erucamide) forming polymeric brushes in two parallel plates as a function of chains grafting density. [ 15 ] They found that brushes made of polymer mixtures can reduce the CoF to a greater extent compared to a mono‐chain brush and that both the viscosity and the CoF obey scaling laws that depend only on the solvent's quality. Very little has been reported in the literature on slip additives diffusion, such as erucamide, oleamide, stearamide, and stearyl erucamide.…”

“…This work attempts to establish a relationship between the surface density and the bulk concentration using a diffusive process. The additive chain grafting density calculated by simulation is given as a function of CoF, [ 15 ] while the experimental CoF is evaluated as a function of time. This relationship is based on the resolution of the diffusion equation (Fick's second law) with boundary conditions close to the problem of interest.…”