Volume 79, Number 5, September 2007
|Number of page(s)||6|
|Section||Condensed Matter: Structural, Mechanical and Thermal Properties|
|Published online||06 August 2007|
Helical, angular and radial ordering in narrow capillaries
Moscow State University - Moscow 119992 Russia
2 Institute Charles Sadron - 6 rue Boussingault, 67083 Strasbourg Cedex, France
Accepted: 16 July 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 , where R is the cylinder radius and 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.
PACS: 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
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.