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How densely objects, particles, atoms, and molecules can be packed is intimately related to the properties of the corresponding hosts and macrosystems. We present results from extensive Monte Carlo simulations on maximally compressed packings of linear, freely-jointed chains of tangent hard spheres of uniform size in films whose thickness is equal to the monomer diameter. We demonstrate that fully flexible chains of hard spheres can be packed as efficiently as monomeric analogs, within a statistical tolerance of less than 1%. The resulting ordered polymer morphology corresponds to an almost perfect hexagonal (TRI) crystal of the p6m wallpaper group, whose sites are occupied by the chain monomers. The Flory scaling exponent, that corresponds to the maximally dense polymer packing in 2-D, has a value of n = 0.62, which lies between the limits of 0.50 (compact and collapsed state) and 0.75 (self-avoiding random walk).

We study, at the atomic level, the behaviour of athermal, linear semiflexible polymers of tangent spheres in thin films of one-layer thickness (2-D systems) and bulk 3-D systems. We employ extensive Monte Carlo simulations [1] at progressively increased concentrations adopting the hard-sphere model to represent interactions between monomers. Extreme, plate-like confinement for thin films is realized through the presence of flat, parallel walls in one dimension with the inter-wall distance being equal to the diameter of the spherical monomers. Chain stiffness is controlled by a tuneable potential for the bending angles whose intensity dictates the rigidity of the polymer backbone. At very high values of bending intensity, the polymer model approaches that of freely-rotated chains and bending angles sample the whole range from acute to obtuse angles, reaching the limit of rod-like polymers. We study how packing density, chain length and stiffness affect the entropy-driven phase transition from initially disordered (random) to ordered (crystal) local and global structures in dense polymer packings in 2-D and 3-D systems and compare against fully flexible chains and monomeric counterparts [2]. To gauge local order, we employ the characteristic crystallographic element (CCE) norm, a descriptor, which can detect and quantify, with high precision, similarity to reference crystals in general atomic and particulate systems [3,4]. In all cases, we identify the critical volume fraction for the phase transition and gauge the established crystal morphologies.

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