The coil-globule transition for a polymer chain confined in a tube: A Monte Carlo simulation

The behavior of a grafted polymer chain confined in a tube is investigated within a scaling theory substantiated with biased Monte Carlo simulations o f a self-avoiding walk (SAW) on a cubic lattice. All the statistical and th ermodynamic properties of the chain follow from the knowledge of the joint distribution P(z,m) giving the probability to observe a length z and a numb er of contacts m, in a model where the energy of the chain in a given confi guration is proportional to m. The analysis is based on the factorization o f P(z,m) into the a priori distribution P(z) and the conditional probabilit y P(m\z) of finding m contacts given that the chain length is z. P(m\z) is well-approximated by a Gaussian distribution. Taking the variance [m(2)]-(m ) over bar (2) of this distribution into account, we obtain a nonmean-field expression for the free energy of the confined chain. We show that the coi l-globule transition of the confined chain is independent of its size but d epends on the pore diameter. Contrary to free, unconfined chains, it is alw ays a continuous transition. (C) 2000 American Institute of Physics. [S0021 -9606(00)50540-6].