Athermal solutions (from dilute to concentrated) of semiflexible macromolecules confined in a film of thickness D between two hard walls are studied by means of grand-canonical lattice Monte Carlo simulation using the bond fluctuation model. This system exhibits two phase transitions as a function of the thickness of the film and polymer volume fraction. One of them is the bulk isotropic-nematic first-order transition, which ends in a critical point on decreasing the film thickness. The chemical potential at this transition decreases with decreasing film thickness ("capillary nematization"). The other transition is a continuous (or very weakly first-order) transition in the layers adjacent to the hard planar walls from the disordered phase, where the bond vectors of the macromolecules show local ordering (i.e., "preferential orientation" along the x or y axes of the simple cubic lattice, but no long-range orientational order occurs), to a quasi-two-dimensional nematic phase (with the director at each wall being oriented along either the x or y axis), while the bulk of the film is still disordered. When the chemical potential or monomer density increase, respectively, the thickness of these surface-induced nematic layers grows, causing the disappearance of the disordered region in the center of the film.
The osmotic equation of state for the athermal bond fluctuation model on the simple cubic lattice is obtained from extensive Monte Carlo simulations. For short macromolecules (chain length N=20) we study the influence of various choices for the chain stiffness on the equation of state. Three techniques are applied and compared in order to critically assess their efficiency and accuracy: the "repulsive wall" method, the thermodynamic integration method (which rests on the feasibility of simulations in the grand canonical ensemble), and the recently advocated sedimentation equilibrium method, which records the density profile in an external (e.g. gravitation-like) field and infers, via a local density approximation, the equation of state from the hydrostatic equilibrium condition. We confirm the conclusion that the latter technique is far more efficient than the repulsive wall method, but we find that the thermodynamic integration method is similarly efficient as the sedimentation equilibrium method. For very stiff chains the onset of nematic order enforces the formation of an isotropic-nematic interface in the sedimentation equilibrium method leading to strong rounding effects and deviations from the true equation of state in the transition regime.
We study the effect of the bending potential on the stability of toroidal and rodlike globules which are typical collapsed conformations of a single stiff-chain macromolecule. We perform numerical calculations in the framework of the bead-stick model of a polymer chain. The intrinsic structure of globules is also analyzed. It was shown that the bending potential affects the packing geometry of bundles in a toroidal globule in the ground state. This potential also influences the bends at the ends of a rodlike globule: both the shape of the loops and the number of bonds in each loop have been investigated numerically as well as by Monte Carlo computer simulations performed for a separate loop. Our main results are (1) the shape of the bending potential could be possibly seen from the geometry of a globule; (2) toroidal globules are always more favorable than the rodlike ones.
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