Monte Carlo simulation of a grafted polymer chain confined in a tube

We study a grafted polymer chain confined in a tube by Monte Carlo simulations of a self-avoiding walk on a cubic lattice. We measure the probability distribution of the one-dimensional gyration radius r∥ and of the length of tube z occupied by the chain. We use a biased Monte Carlo algorithm in order to sample a large interval of r∥ or z. A simple scaling law is proposed for the length of tube z occupied by the chain, in the regime where the chain behaves as a linear, one-dimensional packing of units submitted to excluded-volume (blobs). A simple scaling law is also proposed for the number of contacts as a function of z. A model expression for the free energy of the confined chain is then deduced. It has a scaling structure similar to that of a free self-avoiding walk, with a different exponent of z in the small z regime.