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Unconventional ordering behavior of semi-flexible polymers in dense brushes under compression

Using a coarse-grained bead-spring model for semi-flexible macromolecules forming a polymer brush, structure and dynamics of the polymers is investigated, varying chain stiffness and grafting density. The anchoring condition for the grafted chains is chosen such that their first bonds are oriented along the normal to the substrate plane. Compression of such a semi-flexible brush by a planar piston is observed to be a two-stage process: for small compressions the chains contract by "buckling" deformation whereas for larger compression the chains exhibit a collective (almost uniform) bending deformation. Thus, the stiff polymer brush undergoes a 2-nd order phase transition of collective bond reorientation. The pressure, required to keep the stiff brush at a given degree of compression, is thereby significantly smaller than for an otherwise identical brush made of entirely flexible polymer chains! While both the brush height and the chain linear dimension in the z-direction perpendicular to the substrate increase monotonically with increasing chain stiffness, lateral (xy) chain linear dimensions exhibit a maximum at intermediate chain stiffness. Increasing the grafting density leads to a strong decrease of these lateral dimensions, compatible with an exponential decay. Also the recovery kinetics after removal of the compressing piston is studied, and found to follow a power-law / exponential decay with time. A simple mean-field theoretical consideration, accounting for the buckling/bending behavior of semi-flexible polymer brushes under compression, is suggested.