Universal version of density-functional theory for polymers with complex architecture

Abstract

We propose a density-functional theory for inhomogeneous polyatomic fluids with complex architecture by introducing a different representation for the polymers. This representation gives an efficient hierarchical algorithm to calculate the direct bonding connectivity integral for polymers with complex architecture, such as linear, star, branched, and dendritic structures. A comparison with the available simulated data for linear and star polymers confirms the accuracy of the present theory in reproducing the density profiles of the two types of polymer in the slits. By using the proposed algorithm, we also explore partitioning coefficients of polymers of different architectures in a slit, and find that the partitioning coefficients of branched, star, and dendrimer forms of 22-mers decrease to a minimum at extremely low packing fraction, and then increase monotonically with packing fraction. Moreover, it is found that it is more difficult for a linear polymer of 22-mers to enter the slit than for branched, star, and dendritic polymers. In addition, we also investigate the self-assembly of diblock copolymers with different tails in a slit. It is found that the linear copolymer self-assembles into a trilayer film structure, while copolymers with branched and dendritic tails self-assemble into a five-layer film structure. Interestingly, the copolymer with a star tail self-assembles into a trilayer film structure, and then the trilayer structure evolves into a five-layer structure with increase of the bulk packing fraction in the case studied.