On the anisotropy of lattice polymers

We quantified the anisotropy of various lattice models used in polymer simulations based on two quantities: the Fourier transform of the normalized Boltzmann factor of allowable bonds on a lattice (which is the central quantity for describing lattice chain conformations) and the bulk lamellar period at the mean-field order-disorder transition (ODT) of symmetric diblock copolymers on a lattice (which is pertinent to the study of microphase separation). This allowed us to compare the anisotropy of different lattices and to design new lattice models that minimize the quantified anisotropy. A lattice field theory based on the same Hamiltonian used in the newly proposed fast lattice Monte Carlo simulations [Q. Wang, Soft Matter 5, 4564 (2009)] is also presented, along with some mean-field results on the ODT of symmetric diblock copolymers on these lattices obtained under the random-phase approximation.