Phase transitions of confined lattice homopolymers

The effect of confinement on the phase behavior of lattice homopolymers has been studied using grand canonical Monte Carlo simulations in conjunction with multihistogram reweighting. The scaling of critical parameters and chain dimensions with chain length was determined for lattice homopolymers of up to 1024 beads in strictly 2D and quasi-2D (slab) geometries. The inverse critical temperature scales linearly with the Shultz-Flory parameter for quasi-2D geometries, as it does for the bulk system. The critical volume fraction scales as a power law for all systems, with exponents 0.110 +/- 0.024 and 0.129 +/- 0.004 for the strictly 2D and slab geometries, respectively. The influence of confinement on critical behavior persists even in a thick slab due to the diverging correlation length of density fluctuations. The scaling of the radius of gyration with chain length in the quasi-2D system increasingly resembles the scaling in the strictly 2D system as the chain length increases. At the extrapolated infinite chain critical temperature, the radius of gyration of the 2D system scales with chain length with exponent 0.56 +/- 0.01 similar or equal to (4/7), in agreement with theoretical predictions.