Novel phase behaviour of a confined fluid or Ising magnet

Fundamentals of Phase Separation in Polymer Blend Thin Films

“…the average magnetisation is zero) despite the lack of symmetry which would otherwise suggest there might be some ordering towards the most preferred (least not-preferred) spins, so only at T = T W (D) < T W (∞) is there symmetry breaking and a finite magnetisation [44]. The results are exactly in analogy with the 'interface-localisation transition' of Parry and Evans [38,40].…”

“…The change in local concentration at point r due to a weakly perturbing potential W (r ) at point r is 40) where the index m represents segment m such that W m is the perturbing potential acting on segment m, and S nm is a response function that relates how the perturbation on segment m at r affects segment n at r. Thus we see that all perturbations on all segments have been included. Since we are considering an isotropic system, the response function may only depend on the separation r − r , so we switch to Fourier space to simplify the treatment…”

“…Parry and Evans built upon their previous work to investigate a 'soft-mode' existing for T W < T < T cb , (T cb is the critical temperature for a bulk system), using a phase portrait approach to investigate the phase equilibria of the system [40]. The soft-mode is characterised by an interface between layers rich in one component of the blend, each phase rich one component of the blend, such that each phase coats the surface that prefers that component (so the soft-mode has the freely fluctuating interface discussed above).…”

“…Once again, transitions from one equilibrium state to another could be easily visualised using phase portraits. Parry and Evans studied the phase behaviour of a simple fluid or Ising magnet confined between two confining walls that exerted opposing surface fields, finding that wetting and coexistence phenomena were very different than for the same systems confined between two walls that exerted the same surface fields [40]. Although they didn't use phase portraits, they did utilise a graphical method in a similar vein as the aforementioned work above.…”

“…The reason for this focus is that the symmetries of both the blend and the walls greatly simplifies the study of phase equilibria: without an explicit consideration of material conservation (requiring that the profiles satisfyφ (z) =φ, the composition of the blend) the equilibrium profiles naturally conserve the blend ratiō φ = 1/2 for a symmetric blend, and laterally coexisting equilibria of A-rich and B-rich phases are mirror images of each other (having equal heights and equal ex-cess surface free energies [40,45]). These conveniences vanish for a polymer-blend (whether symmetric or otherwise) confined between asymmetric walls.…”