Collapse transitions of a periodic hydrophilic hydrophobic chain

Short title: Transitions of a periodic hydrophilic hydrophobic chain 1 We study a single self avoiding hydrophilic hydrophobic polymer chain, through Monte Carlo lattice simulations. The affinity of monomer i for water is characterized by a (scalar) charge λ i , and the monomer-water interaction is short-ranged. Assuming incompressibility yields an effective short ranged interaction between monomer pairs (i, j), proportional to (λ i + λ j). In this article, we take λ i = +1 (resp. (λ i = −1)) for hydrophilic (resp. hydropho-bic) monomers and consider a chain with (i) an equal number of hydro-philic and-phobic monomers (ii) a periodic distribution of the λ i along the chain, with periodicity 2p. The simulations are done for various chain lengths N , in d = 2 (square lattice) and d = 3 (cubic lattice). There is a critical value p c (d, N) of the periodicity, which distinguishes between different low temperature structures. For p > p c , the ground state corresponds to a macroscopic phase separation between a dense hydrophobic core and hydrophilic loops. For p < p c (but not too small), one gets a microscopic (finite scale) phase separation, and the ground state corresponds to a chain or network of hydro-phobic droplets, coated by hydrophilic monomers. We restrict our study to two extreme cases, p ∼ O(N) and p ∼ O(1) to illustrate the physics of the various phase transitions. A tentative variational approach is also presented.