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