Cyclic motion and inversion of surface flow direction in a dense polymer brush under shear

Using molecular simulations, we study the properties of a polymer brush in contact with an explicit solvent under Couette and Poiseuille flow. The solvent is comprised of chemically identical chains. We present evidence that individual, unentangled chains in the dense brush exhibit cyclic, tumbling motion and non-Gaussian fluctuations of the molecular orientations similar to the behaviour of isolated tethered chains in shear flow. The collective molecular motion gives rise to an inversion of hydrodynamic flow direction in the vicinity of the brush-coated surface. Utilising Couette and Poiseuille flow, we investigate to what extend the effect of a brush-coated surface can be described by a Navier slip condition. Introduction. – Grafting polymers onto surfaces is a versatile and stable method for controlling wettability, lubrication, adhesion and surface interactions [1]. Brush coatings are utilised for biocompatibilisation or as antifouling coatings in microfluidic devices. They are employed to stabilise colloids or, in form of interfacial layers of copolymers, to prevent coalescence of droplets in polymer blends. 1 Dense polymer brushes give rise to fascinating dynamical properties like a dramatic reduction of friction between two brushes sliding past each other [2], incompletely understood collective dynamics [3], additional dissipation mechanisms of droplets moving on brushes due to the the deformability of the soft elastic surface [4], and large effective slip lengths [5]. Simulations of dense polymer brushes with an explicit solvent [6–9] are computationally very demanding and previous studies of brushes in shear flow [10–14] conceived the brush as a porous medium [15] utilising Brinkman’s equation [16] to quantify the penetration of the solvent flow into the brush. They observed that density profiles normal to the surface are not strongly affected by shear flow but the average molecular conformations are tilted towards and stretched along the direction of the flow. (a)E-mail:[email protected] 1Copolymers at interfaces in blends can laterally move, but the ends of grafted chains in a brush are immobile. Isolated grafted chains in shear flow already exhibit intriguing dynamics [17–20]: Thermal fluctuations away from the surface expose the non-grafted chain end to a faster flow and lead to an elongation of the chain in the flow direction. The stretched chain rotates back towards the grafting surface and contracts. Related effects have also been reported for the chain ends in swollen brushes under strong shear and they have been attributed to the non-linear elasticity of the macromolecules [14]. One hallmark of this dynamic behaviour of isolated chains are strongly non-Gaussian distribution functions of angular orientations [18, 20]. Explicit hydrodynamic interactions [19, 20] appear not to be crucial for this cyclic tumbling motion. Using Single-Chain-in-Mean-Field (SCMF) simulations and Molecular Dynamics (MD) simulations of a brush in contact with an explicit solvent of identical chain molecules we demonstrate that the tumbling motion observed for isolated chains persist as one increases the grafting density and that the individual motion of the tethered molecules results in the inversion of the collective flow direction at the surface. The effect of the brush cannot be described by a Navier slip condition [21–23]. Model and simulation technique. – Brush and melt polymers are represented by a bead-spring model