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

1.9 Current Track Record and Future Outlook for SCFT 71
complex phase behavior of diblock copolymer melts several years in advance of experiment.
At the time that SCFT predicted (Matsen and Schick 1994a) the phase diagram in Fig. 1.20,
experiments had reported four stable complex phases: the double-diamond (Thomas et al.
1987), the perforated-lamellar (PL) (Hamley et al. 1993), the modulated-lamellar (Hamley
et al. 1993), and the gyroid (G) (Hajduk et al. 1994; Schulz et al. 1994). The existence
of the modulated-lamellar phase, based solely on scattering experiments, was the least certain,
and strongly conflicted with our theoretical understanding of the complex phase behavior
(Matsen 2002b; Matsen and Bates 1996b). It is now accepted and well supported by theory
(Yeung et al. 1996) that the observed scattering pattern was simply a result of anisotropic
fluctuations from the classical lamellar (L) phase. Secondly, it has become apparent that the
double-diamond phase was nothing more than a misidentified gyroid phase (Hajduk et al.
1995), attributed to the remarkable similarities of the two microstructures, coupled with the
limited resolution of scattering experiments at the time. Conversely, the perforated-lamellar
phase is most definitely observed in diblock copolymer melts, but it is now accepted to be a
metastable state that, given sufficient time, converts to the gyroid morphology (Hajduk et al.
1997). With that final realization, experiments are now in line with the SCFT prediction that
gyroid is the only stable complex phase in diblock copolymer melts. However, in more elaborate
architectures, notably ABC triblock copolymers, a zoo of complex morphologies are
possible (Bates and Fredrickson 1999), and SCFT is having equal success in resolving their
complex phase behavior (Matsen 1998; Shefelbine et al. 1999; Wickham and Shi 2001). Another
impressive accomplishment of SCFT has been the successful treatment (Matsen 1997)
of a delicate symmetry-breaking transition in the grain boundary of a lamellar morphology,
where a symmetric chevron boundary switches to an asymmetric omega boundary as the angle
between two lamellar grains increases (Gido and Thomas 1994). Arguably, the most impressive
accomplishment up to now involves the macrophase separation of chemically-equivalent
small and large diblock copolymers (Hashimoto et al. 1993). The fact that SCFT is the only
theory to correctly predict (Matsen 1995b) this effect is impressive in its own right, but the
truly stunning achievement emerged later when Papadakis et al. (1998) purposely synthesized
diblock copolymers in order to quantitatively test one of the predicted SCFT phase diagrams.
The agreement between the theoretical and experimental phase boundaries is virtually perfect,
which is particularly remarkable, given the fact that the competing theories fail to predict
any boundaries at all. With this level of success, SCFT has unequivocally emerged as the
state-of-the-art theory for structured polymeric melts.
The superb track record of SCFT can be attributed to the sound approximations upon
which it is built. Although the Gaussian chain model treats polymers as simple microscopic
elastic threads, which may seem at first to be highly artificial, it is a well-grounded model
for high-molecular-weight polymers as justified in Section 1.1. In this limit of high molecular
weight, the separation between the atomic and molecular length scales allows for the
effective treatment of the monomer-monomer interactions by the simple Flory-Huggins form,
U[ ˆφ A , ˆφ B ], in Eq. (1.192) coupled with the incompressibility constraint, ˆφ A (r)+ ˆφ B (r) =1.
Beyond these approximations in the underlying model, the only other is the saddle-point approximation,
which amounts to mean-field theory. Again, this approximation becomes increasingly
accurate for large invariant polymerization indices, N , where the individual polymers
acquire more and more contacts with their neighboring molecules. The conventional
understanding is that SCFT becomes exact in the limit of N→∞. Nevertheless, real poly-