Competing micellar and cylindrical phases in semi-dilute diblock copolymer solutions

We develop a “first principles” coarse-graining procedure based on a soft effective segment representation of an athermal AB diblock copolymer model in selective solvent, to map out the self-assembly phase diagram for several asymmetry ratios f using Monte Carlo free energy calculations. We find that the free energy per unit volume is surprisingly insensitive to the aggregation number of monodisperse cubic and cylindrical phases for a given polymer volume fraction. The cylindrical phase is found to pre-empt the cubic micellar phases for nearly symmetric (f ≃ 0.6) copolymers.

[1]  A. Shi,et al.  A Theoretical Study of Phase Behaviors for Diblock Copolymers in Selective Solvents , 2009 .

[2]  J. Hansen,et al.  Entropic self-assembly of diblock copolymers into disordered and ordered micellar phases. , 2009, The journal of physical chemistry. B.

[3]  Francisco J. Martinez-Veracoechea,et al.  Bicontinuous Phases in Diblock Copolymer/Homopolymer Blends : Simulation and Self-Consistent Field Theory , 2009 .

[4]  M. Radosz,et al.  Monte Carlo Phase Diagram of Symmetric Diblock Copolymer in Selective Solvent , 2008 .

[5]  E. Sambriski,et al.  Theoretical coarse-graining approach to bridge length scales in diblock copolymer liquids. , 2007, Physical review. E, Statistical, nonlinear, and soft matter physics.

[6]  J. Hansen,et al.  A soft effective segment representation of semidilute polymer solutions. , 2007, The Journal of chemical physics.

[7]  P. Maass,et al.  Soft particle model for block copolymers. , 2007, The Journal of chemical physics.

[8]  J. Hansen,et al.  Multiscale coarse graining of diblock copolymer self-assembly: from monomers to ordered micelles. , 2006, Physical review letters.

[9]  A. Louis,et al.  Coarse-graining diblock copolymer solutions: a macromolecular version of the Widom–Rowlinson model , 2005, cond-mat/0507360.

[10]  G. Grason.  Ordered phases of diblock copolymers in selective solvent. , 2005, The Journal of chemical physics.

[11]  M. Hillmyer,et al.  Strategies for controlling intra- and intermicellar packing in block copolymer solutions: illustrating the flexibility of the self-assembly toolbox. , 2005, Faraday discussions.

[12]  Kurt Binder,et al.  Formation of Block Copolymer Micelles in Solution: A Monte Carlo Study of Chain Length Dependence , 2001 .

[13]  A. Pelissetto,et al.  Critical phenomena and renormalization-group theory , 2000, cond-mat/0012164.

[14]  D. Frenkel,et al.  Microscopic and mesoscopic simulation of entropic micelles , 1997 .

[15]  Schick,et al.  Stable and unstable phases of a diblock copolymer melt. , 1994, Physical review letters.

[16]  J. Hansen,et al.  On the stability of polydisperse colloidal crystals , 1986 .

[17]  L. Leibler.  Theory of Microphase Separation in Block Copolymers , 1980 .

[18]  B. Widom,et al.  Some Topics in the Theory of Fluids , 1963 .

[19]  T. Lodge,et al.  On the selection of FCC and BCC lattices in poly(styrene-b-isoprene) copolymer micelles , 2008 .