Brushes shear effects

In this article I review some of the simulation work addressed specifically to branched polymers. The brushes will be described here in terms of their common characteristics with those of individual branched chains. Therefore, other aspects that do not correlate easily with these characteristics will be omitted. Explicitly, there will be no mention of adsorption kinetics, absorbing or laterally inhomogeneous surfaces, polyelectrolyte brushes, or brushes under the effect of a shear. With the purpose of giving a comprehensive description of these applications, Sect. 2 includes a summary of the theoretical background, including the approximations employed to treat the equifibrium structure of the chains as well as their hydrodynamic behavior in dilute solution and their dynamics. In Sect. 3, the different numerical simulation methods that are appHcable to branched polymer systems are specified, in relation to the problems sketched in Sect. 2. Finally, in Sect. 4, the appHcations of these methods to the different types of branched structures are given in detail. 

This idea that the solvent flow field can be approximated by the Brinkman equation has been used in several recent simulations of a polymer brush in simple shear flow. In these simulations, the solvent is not included explicitly but it s effect is modeled using the Brinkman equation. Lai and Binder [65] and Lai and Lai [66], using a bond fluctuation lattice model, and Miao et al. [67], using a continuum model, studied the properties of a dense polymer brush in a flow field by modifying the standard Metropolis Monte Carlo transition probability to take into account the effective force acting upon the brush chains by the moving sol-... 

Finally, there also remains the possibility that the extra normal force observed by Klein et al. [16] may arise for other reasons than an increase in the brush height. Since the experiments are in an open system, solvent entering and leaving the gap between the two curved surfaces may contribute to the observed extra normal force. This could explain the fact that there is a critical shear rate for the extra normal force to appear. Sufficed to say, the origin of the excess normal force under an oscillatory shear remains an open issue. Further experiments and simulations are needed to clarify the origin of this effect. 

Carbopol ETD 2823 is used in this formulation to cost effectively thicken the surfactant system into a gel form - which can be applied to the fabric by brush or sprayed on due to CarbopoVs shear thinning nature. 

When D < 2Lh, the brushes apparently interpenetrate (but see below when shearing motion is discussed), relative motion of polymer and solvent occurs and solvent molecules experience increased drag. Assuming that for these cases the concentration of polymer is uniform, the flow of solvent was analysed by the treatment used for flow in porous media (Brinckman 1947). In this approximation j/o in equation (3.4.13) is replaced by an effective viscosity, for which a scaling relation was obtained ... 

For the brushes, the degree of interpenetration is small. Within this interpenetration zone the concentration can be viewed as semi-dilute, and the effective viscosity is that of chains which have the dimensions of the correlation length (i). As a result the additional shear force over that of the pure... 

The extremely low friction achieved on PLL(20)-g[2.9]-PEG(5) films in SFA experiments is not a unique property of this specific copolymer but has also been observed for other grafted poly(ethylene glycol) films as well as for other polymer-brush systems in a good solvent, such as grafted polystyrene in toluene. The osmotic pressure, which leads to strong repulsive forces as the polymer brushes are compressed, effectively prevents the direct contact of the solid surfaces. At comparable solid surface separations, thin films of water or aqueous salt solutions have been shown to retain a shear fluidity characteristic of the bulk liquid. In a control experiment, this was also observed in 10 mM HEPES buffer solution (data not shown). 

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