Helical, angular and radial ordering in narrow capillariesI. Erukhimovich1 and A. Johner2
1 Moscow State University - Moscow 119992 Russia
2 Institute Charles Sadron - 6 rue Boussingault, 67083 Strasbourg Cedex, France
received 2 May 2007; accepted in final form 16 July 2007; published September 2007
published online 6 August 2007
To enlighten the nature of the order-disorder and order-order transitions in block copolymer melts confined in narrow capillaries we analyze peculiarities of the conventional Landau weak crystallization theory of systems confined to cylindrical geometry. This phenomenological approach provides a quantitative classification of the cylindrical ordered morphologies by expansion of the order parameter spatial distribution into the eigenfunctions of the Laplace operator. The symmetry of the resulting ordered morphologies is shown to strongly depend both on the boundary conditions (wall preference) and dimensionless parameter q*R, where R is the cylinder radius and q* is the wave number of the critical order parameter fluctuations, which determine the bulk ordering of the system under consideration. In particular, occurrence of the helical morphologies is a rather general consequence of the imposed cylindrical symmetry for narrow enough capillaries. We discuss also the ODT and OOT involving some other simplest morphologies. The presented results are relevant also to other ordering systems as charge-density waves appearing under addition of an ionic solute to a solvent in its critical region, weakly charged polyelectrolyte solutions in poor solvent, microemulsions etc.
64.70.-p - Specific phase transitions .
64.70.Nd - Structural transitions in nanoscale materials .
82.35.Jk - Copolymers, phase transitions, structure .
© Europhysics Letters Association 2007