Self-Consistent Field Theory and Its Applications by M. W. Matsen

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Contents 1 Self-consistent field theory and its applications (M. W. Matsen) 3 1.1 Gaussian Chain ................................. 7 1.2 Gaussian Chain in an External Field ...................... 11 1.3 Strong-Stretching Theory (SST): The Classical Path .............. 15 1.4 Analogy with Quantum/Classical Mechanics .................. 17 1.5 Mathematical Techniques and Approximations . . .............. 18 1.5.1 Spectral Method . . . . . . ...................... 18 1.5.2 Ground-State Dominance . . ...................... 20 1.5.3 Fourier Representation . . . ...................... 21 1.5.4 Random-Phase Approximation . . . .................. 23 1.6 Polymer Brushes . . . ............................. 25 1.6.1 SST for a Brush: The Parabolic Potential . .............. 26 1.6.2 Path-Integral Formalism for a Parabolic Potential . . . . ....... 28 1.6.3 Diffusion Equation for a Parabolic Potential .............. 31 1.6.4 Self-Consistent Field Theory (SCFT) for a Brush . . . . ....... 31 1.6.5 Boundary Conditions . . . . ...................... 34 1.6.6 Spectral Solution to SCFT . ...................... 36 1.7 Polymer Blends ................................. 41 1.7.1 SCFT for a Polymer Blend . ...................... 43 1.7.2 Homogeneous Phases and Macrophase Separation . . . ....... 45 1.7.3 Scattering Function for a Homogeneous Blend . . . . . ....... 47 1.7.4 SCFT for a Homopolymer Interface .................. 50 1.7.5 Interface in a Strongly-Segregated Blend . .............. 53 1.7.6 Grand-Canonical Ensemble ...................... 55 1.8 Block Copolymer Melts ............................. 57 1.8.1 SCFT for a Diblock Copolymer Melt . . . .............. 58 1.8.2 Scattering Function for the Disordered Phase . . . . . . ....... 59 1.8.3 Spectral Method for the Ordered Phases . . .............. 61 1.8.4 SST for the Ordered Phases ...................... 67 1.9 Current Track Record and Future Outlook for SCFT .............. 70 1.10 Beyond SCFT: Fluctuation Corrections . . . .................. 72 1.11 Appendix: The Calculus of Functionals . . .................. 74 Bibliography ..................................... 82
2 Contents Index 83
Page 1: Self-Consistent Field Theory and It
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Bibliography Almdal, K., Rosedale,
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BIBLIOGRAPHY 81 Matsen, M. W. and G
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Index action 17 binodal point 46 bl
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Self-Consistent Field Theory and Its Applications by M. W. Matsen

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