Field-Theoretic Simulations for Block Copolymer Melts Using the Partial Saddle-Point Approximation

Abstract

Field-theoretic simulations (FTS) provide an efficient technique for investigating fluctuation effects in block copolymer melts with numerous advantages over traditional particle-based simulations. For systems involving two components (i.e., A and B), the field-based Hamiltonian, Hf[W−,W+], depends on a composition field, W−(r), that controls the segregation of the unlike components and a pressure field, W+(r), that enforces incompressibility. This review introduces researchers to a promising variant of FTS, in which W−(r) fluctuates while W+(r) tracks its mean-field value. The method is described in detail for melts of AB diblock copolymer, covering its theoretical foundation through to its numerical implementation. We then illustrate its application for neat AB diblock copolymer melts, as well as ternary blends of AB diblock copolymer with its A- and B-type parent homopolymers. The review concludes by discussing the future outlook. To help researchers adopt the method, open-source code is provided that can be run on either central processing units (CPUs) or graphics processing units (GPUs).

Disordered Micelle Regime in a Conformationally Asymmetric Diblock Copolymer Melt

“…The recent advances in accelerating this class of field-theoretic simulations may render such a calculation feasible but still expensive. 33,34,49 The results obtained here further emphasize the importance of finite N̅ on the emergence of Frank−Kasper phases, in particular, for thermal processing routes that produce the C14 and C15 Laves phases. 16 As noted in the Introduction section, Frank−Kasper phases are predicted by SCFT to emerge at equilibrium as a consequence of conformational asymmetry 18−20 and thus do not require access to a disordered micelle regime to promote nonequilibrium emergence of those phases.…”

“…We recognize that this is a tentative conclusion, drawn from results at a single value of f A and N̅ , and a considerable amount of additional work is required to draw a firm conclusion. The recent advances in accelerating this class of field-theoretic simulations may render such a calculation feasible but still expensive. ,, …”

Order-to-Disorder Transition of Cylinder-Forming Block Copolymer Films Confined within Neutral Interfaces

“…where w + is the pressure field at the saddle point, and the Hamiltonian becomes a real-valued function. 1,21,22,24,33 In this partial saddle point approximation method, only the exchange field W − fluctuates and it does not suffer from severe instability, which is problematic for the CL-FTS.…”

“…For the purpose of effectively finding w + , DL and the Anderson mixing method 21,33,36 were employed. The pressure field was initially guessed by the NN, and then we started iterations.…”

Direct calculation of the functional inverse of realistic interatomic potentials in field-theoretic simulations

“…[1][2][3] They are particularly suited for capturing structural features of high molecular weight polymers on scales from nanometers to micrometers. Typical examples include block copolymer melts, [4][5][6] bottlebrush polymers, 7,8 complex coacervates, [9][10][11] polymer nanocomposites, 12,13 template-guided self-assembly and pattern formation, 14,15 polymer solutions, 16 the calculation of free energies for classical fluids and polymers, 17 the morphology of multi-component polymer systems, 18 and even the design of liquid-crystalline foods. 19 In combination with deep learning, in particular, 20 they hold the promise of accelerating polymer design or expanding the spectrum of properties to be addressed.…”