Nucleation of stable cylinders from a metastable lamellar phase in a diblock copolymer melt

The nucleation of a droplet of stable cylinder phase from a metastable lamellar phase is examined within the single-mode approximation to the mean-field Landau–Brazovskii model for diblock copolymer melts. By employing a variational ansatz for the droplet interfacial profile, an analytic expression for the interfacial free energy of an interface of arbitrary orientation between cylinders and lamellae is found. The interfacial free energy is anisotropic and is lower when the cylinder axis is perpendicular to the interface than when the cylinders lie along the interface. Consequently, the droplet shape computed via the Wulff construction is lens like, being flattened along the axis of the cylinders. The size of the critical droplet and the nucleation barrier are determined within classical nucleation theory. Near the lamellar–cylinder phase boundary, where classical nucleation theory is applicable, critical droplets of size 30–400 cylinders across with aspect ratios of 4–10 and nucleation barriers of (30–40)kBT are typically found. The general trend is to larger critical droplets, higher aspect ratios, and smaller nucleation barriers as the mean-field critical point is approached.

[1]  Anisotropy of lamellar block copolymer grains. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[2]  M. Schick,et al.  Theory of T junctions and symmetric tilt grain boundaries in pure and mixed polymer systems , 2002 .

[3]  Long-Qing Chen.  Phase-Field Models for Microstructure Evolution , 2002 .

[4]  Zhen‐Gang Wang.  Concentration fluctuation in binary polymer blends: Χ parameter, spinodal and Ginzburg criterion , 2002 .

[5]  Zhen‐Gang Wang,et al.  Nucleation in binary polymer blends: A self-consistent field study , 2002 .

[6]  M. Matsen.  The standard Gaussian model for block copolymer melts , 2002 .

[7]  D. Boyer,et al.  Grain boundary pinning and glassy dynamics in stripe phases. , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.

[8]  Takao Ohta,et al.  Kinetics of morphological transitions between mesophases , 2001 .

[9]  M. Matsen.  Cylinder↔sphere epitaxial transitions in block copolymer melts , 2001 .

[10]  M. Schick,et al.  Self-consistent field theory of twist grain boundaries in block copolymers , 2000, cond-mat/0005429.

[11]  U. Wiesner,et al.  Nucleation and growth in order-to-order transitions of a block copolymer , 2000 .

[12]  An-Chang Shi,et al.  Nature of anisotropic fluctuation modes in ordered systems , 1999 .

[13]  T. Lodge,et al.  FLUCTUATIONS WITH CUBIC SYMMETRY IN A HEXAGONAL COPOLYMER MICROSTRUCTURE , 1998 .

[14]  Evolution of microstructure in the liquid and crystal directions in a quenched block copolymer melt , 1998 .

[15]  Zhen‐Gang Wang,et al.  Weakly segregated block copolymers : anisotropic fluctuations and kinetics of order-order and order-disorder transitions , 1998 .

[16]  B. A. Garetz,et al.  Identification of the Molecular Parameters that Govern Ordering Kinetics in a Block Copolymer Melt , 1998 .

[17]  M. Matsen.  CYLINDER GYROID EPITAXIAL TRANSITIONS IN COMPLEX POLYMERIC LIQUIDS , 1998 .

[18]  M. Matsen.  Kink grain boundaries in a block copolymer lamellar phase , 1997 .

[19]  M. Schick,et al.  Interfaces of modulated phases , 1997, cond-mat/9803260.

[20]  Zhen‐Gang Wang,et al.  On the nature of the perforated layer phase in undiluted diblock copolymers , 1997 .

[21]  S. Milner,et al.  Dynamics of the Lamellar-Cylindrical Transition in Weakly Segregated Diblock Copolymer Melts , 1997 .

[22]  J. Noolandi,et al.  Stability of Ordered Phases in Weakly Segregated Diblock Copolymer Systems , 1997 .

[23]  N. Maurits,et al.  The dynamic mean-field density functional method and its application to the mesoscopic dynamics of quenched block copolymer melts , 1997 .

[24]  Garetz,et al.  Grain Growth and Defect Annihilation in Block Copolymers. , 1996, Physical review letters.

[25]  I. Hamley,et al.  Landau- $$Brazovski\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\smile}$}}{\imath } $$ theory for the $$Ia\bar 3d$$ structure , 1996 .

[26]  Qi,et al.  Kinetic pathways of order-disorder and order-order transitions in weakly segregated microstructured systems. , 1996, Physical review letters.

[27]  T. Lubensky,et al.  Principles of condensed matter physics , 1995 .

[28]  Hohenberg Pc,et al.  Metastability in fluctuation-driven first-order transitions: Nucleation of lamellar phases. , 1995 .

[29]  T. Hashimoto,et al.  Nucleation and Anisotropic Growth of Lamellar Microdomains in Block Copolymers , 1995 .

[30]  Desai,et al.  Ostwald ripening in systems with competing interactions. , 1995, Physical review letters.

[31]  M. Seul,et al.  Domain Shapes and Patterns: The Phenomenology of Modulated Phases , 1995, Science.

[32]  T. Hashimoto,et al.  Ordered Structures of Block Copolymer/Homopolymer Mixtures. 5. Interplay of Macro- and Microphase Transitions , 1994 .

[33]  M. S. Turner,et al.  Surface-Induced Lamellar Ordering in a Hexagonal Phase of Diblock Copolymers , 1994 .

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

[35]  E. Thomas,et al.  Observation of a Reversible Thermotropic Order–Order Transition in a Diblock Copolymer , 1994 .

[36]  E. Kats,et al.  Weak crystallization theory , 1993 .

[37]  T. Hashimoto,et al.  Morphology transition from cylindrical to lamellar microdomains of block copolymers , 1993 .

[38]  M. Schick,et al.  Copolymers as amphiphiles in ternary mixtures: An analysis employing disorder, equimaxima, and Lifshitz lines , 1992 .

[39]  Oono,et al.  Cell dynamical system approach to block copolymers. , 1990, Physical review. A, Atomic, molecular, and optical physics.

[40]  K. Binder,et al.  Kinetics of metastable states in block copolymer melts , 1989 .

[41]  E. Helfand,et al.  Fluctuation effects in the theory of microphase separation in block copolymers , 1987 .

[42]  K. Kawasaki,et al.  Equilibrium morphology of block copolymer melts , 1986 .

[43]  K. Binder.  Nucleation barriers, spinodals, and the Ginzburg criterion , 1984 .

[44]  C. Rottman,et al.  Statistical mechanics of equilibrium crystal shapes: Interfacial phase diagrams and phase transitions , 1984 .

[45]  John S. Rowlinson,et al.  Molecular Theory of Capillarity , 1983 .

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

[47]  L. Garrido,et al.  Systems far from equilibrium , 1980 .

[48]  J. Swift,et al.  Hydrodynamic fluctuations at the convective instability , 1977 .

[49]  S. Shtrikman,et al.  Critical Behavior at the Onset of k --> -Space Instability on the lamda Line , 1975 .

[50]  John E. Hilliard,et al.  Free Energy of a Nonuniform System. III. Nucleation in a Two‐Component Incompressible Fluid , 1959 .

[51]  C. Tanford.  Macromolecules , 1994, Nature.