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We present a Monte Carlo simulation of the bond-fluctuation lattice model, using a Hamiltonian which introduces a change in the conformational statistics of the polymer chains from Gaussian behavior at high temperatures to rigid rod behavior at low temperatures. We do not introduce any attractive interaction between the chains. Upon cooling, the aspect ratio of the chains increases above the critical value for the density employed in the simulation, and we observe an entropically driven phase transition into a nematic phase. We examine this transition quantitatively by a careful finite size scaling study using an optimized cumulant intersection method, and show that the transition is of first order.

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The diffusion of penetrant particles in frozen polymer matrices is investigated by means of Monte Carlo simulations of the bond fluctuation model. By applying finite-size scaling to data obtained from very large systems it is demonstrated that the diffusion process takes place on a percolating free volume cluster describable by a correlated site percolation model which falls into the same universality class as random percolation. The diverging correlation length entails a pronounced dependence of the diffusion constant on the size of the simulated system. It is shown that this dependence is appreciable for a wide range of parameters around the transition. ͓S1063-651X͑96͒05810-2͔

Relying on Monte Carlo simulations, we investigate the hard-disk melting transition. The finite-size scaled values of the bond-orientational order parameter moments are obtained with the block analysis technique. The behaviour of Binder's cumulant and the susceptibility favour an interpretation in terms of a first-order transition.