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Field-theoretic simulations are numerical treatments of polymer field theory models that go beyond the mean-field self-consistent field theory level and have successfully captured a range of mesoscopic phenomena. Inherent in molecularly-based field theories is a “sign problem” associated with complex-valued Hamiltonian functionals. One route to field-theoretic simulations utilizes the complex Langevin (CL) method to importance sample complex-valued field configurations to bypass the sign problem. Although CL is exact in principle, it can be difficult to stabilize in strongly fluctuating systems. An alternate approach for blends or block copolymers with two segment species is to make a “partial saddle point approximation” (PSPA) in which the stiff pressure-like field is constrained to its mean-field value, eliminating the sign problem in the remaining field theory, allowing for traditional (real) sampling methods. The consequences of the PSPA are relatively unknown, and direct comparisons between the two methods are limited. Here, we quantitatively compare thermodynamic observables, order-disorder transitions, and periodic domain sizes predicted by the two approaches for a weakly compressible model of AB diblock copolymers. Using Gaussian fluctuation analysis, we validate our simulation observations, finding that the PSPA incorrectly captures trends in fluctuation corrections to certain thermodynamic observables, microdomain spacing, and location of order-disorder transitions. For incompressible models with contact interactions, we find similar discrepancies between the predictions of CL and PSPA, but these can be minimized by regularization procedures such as Morse calibration. These findings mandate caution in applying the PSPA to broader classes of soft-matter models and systems.
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This content will become publicly available on January 14, 2026
Polymer Field Theory for Multimonomer Incompressible Models: Symmetric Formulation and ABC Systems
We present a symmetric formulation of polymer field theory for incompressible systems containing any number M of monomer types, in which all monomers are treated on an equal footing. This is proposed as an alternative to the multispecies exchange formulation, which imposes incompressibility by eliminating one monomer type. The symmetric formulation is shown to correspond to the incompressible limit of a corresponding compressible model, and to reduce in the case M = 2 to the usual formulation of field theory for incompressible AB systems. An analysis of ABC systems (M = 3) identifies ranges of interaction parameter values in which a fully fluctuating field theory requires one, two or three imaginary-valued fields. ABC systems with parameters that satisfy the Hildebrand solubility parameter approximation are shown to require only one imaginary pressure-like field, much like AB systems. Generalization of the partial saddle-point approximation to M > 2 is discussed.
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- Award ID(s):
- 2103627
- PAR ID:
- 10629288
- Publisher / Repository:
- American Chemical Society
- Date Published:
- Journal Name:
- Macromolecules
- Volume:
- 58
- Issue:
- 1
- ISSN:
- 0024-9297
- Page Range / eLocation ID:
- 816-825
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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