Non-Conventional Structural Phase Transitions and Amphiphobic Matter
  The aim of this paper is two-fold. First, via a phenomenological consideration I show that, equally with the conventional phases (body-centred cubic, hexagonal planar and lamellar), such non-conventional phases as simple cubic, face-centered cubic, well known double gyroid as well as some other phases could be stable in a vicinity of the critical point in the systems undergoing the order-disorder and order-order transition. A general phase diagram indicating the strength of so-called angle dependence of the forth vertex necessary for existence of these non-conventional phases is presented. Next, I demonstrate via a direct Leibler-like microscopic consideration of the ternary ABC block and graft copolymers that these real systems do reveal these nonconventional phases even close to the critical point. In particular, the ternary ABC block copolymers with a long middle block non-selective with respect to both side blocks are especially inclined to form the gyroid phase. A new cubic non-centrosymmetric phase and some other cubic phases are also first predicted to exist as the most stable low temperature phase instead of the lamellar one. Such a phase behavior is suggested to be common for a new class of materials we propose to call amphiphobic since their (macro)molecules consist al least of three mutually incompatible types of monomers. 
Igor Erukhimovich