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 of a self-avoiding walk (SAW) on a cubic lattice. All the statistical and thermodynamic 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 number of contacts m, in a model where the energy of the chain in a given configuration is proportional to m. The analysis is based on the factorization of P(z,m) into the a priori distribution P(z) and the conditional probability 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 〈m2〉−m̄2 of this distribution into account, we obtain a nonmean-field expression for the free energy of the confined chain. We show that the coil–globule transition of the confined chain is independent of its size but depends on the pore diameter. Contrary to free, unconfined chains, it is always a continuous transition.