Canonical-Ensemble SCFT Derivation for an Linear Incompressible AB Diblock Melt (Density Explicit Formalism)
Published:
Summary
This note summarizes a canonical-ensemble self-consistent field theory (SCFT) derivation for an linear incompressible AB diblock copolymer melt.
The derivation starts from a microscopic polymer model with:
- Gaussian-chain model
- Flory-Huggins A-B contact interaction
- A incompressibility constraint
It then introduces collective density fields and auxiliary conjugate fields through functional delta identities and Fourier representations. This converts the many-chain partition function into a field-theoretic form and defines an effective Hamiltonian.
At the mean-field saddle point, the SCFT equations are obtained, including:
- Forward/backward chain propagator equations
- Segment-density expressions from propagators
- Incompressibility condition
- Self-consistent relations between fields and densities
Finally, the derivation is recast into the common real-field and volume-fraction form, and interpreted through the free-energy decomposition into:
- Interaction enthalpy
- Field-coupling/incompressibility contribution
- Conformational entropy contribution
Full Derivation (PDF)
The full derivation with complete equations is provided below.
References
- Sides SW, Fredrickson GH. Parallel algorithm for numerical self-consistent field theory simulations of block copolymer structure. Polymer. 2003 Sep 1;44(19):5859-66.
- Gadelrab KR. Block copolymer self-assembly-a computational approach towards novel morphologies (Doctoral dissertation, Massachusetts Institute of Technology).
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