Search for: All records

Complex fluids in confined geometries are found in numerous applications, including membranes, lubricants, and microelectronics. However, current computational approaches for studying these systems have a variety of shortcomings. Particle-based simulations are limited in accessible length and time scales, while the interaction parameters in field-theoretic approaches have no direct connections to specific chemistries. Here, we extend a multiscale framework that we earlier developed for bulk systems to address these challenges in confined polymer formulations. The methodology uses atomistic molecular dynamics simulations to parameterize coarse-grained field-theoretic models of confined fluids, which subsequently enable fast equilibration and the ability to surmount length scales inaccessible to particle-based simulation methods. We first use this workflow to study a model system consisting of a confined Gaussian fluid to validate and determine best practices for the coarse-graining methodology. Next, we demonstrate this methodology by applying it to an alkyl acrylic diblock copolymer and dodecane solution confined between α-iron oxide surfaces and examining the effect of diblock concentration and length on the structure of the adsorbed film. This approach has the potential to expedite the study of complex fluids in confined environments, bridging atomistic detail and mesoscale modeling with broad implications for materials design. 

Abstract A general algorithm is introduced to compute single‐chain partition functions in field‐theoretic simulations of polymers with nested tree‐like topologies, including self‐consistent field theory simulations that invoke the mean‐field approximation. The algorithm is an extension of a method used in a number of recent studies on the phase behavior of bottlebrush block copolymers. In those studies, the computational cost of computing single‐chain partition functions is reduced by aggregating the statistical weight of degenerate side arms. By extending this method to chains with arbitrary degrees of branching, the computational cost is reduced to scale with the total length of unique segments in the chain instead of the total length/mass of the entire chain. The method is first validated on a model dendrimer system by comparing results to coarse‐grained molecular dynamics simulations and also demonstrate its advantage over more conventional approaches to compute single‐chain partition functions. The algorithm is subsequently used to analyze the phase behavior of a molecularly informed field‐theoretic model of poly(butyl acrylate)‐graft‐poly(dodecyl acrylate) (pBA‐graft‐pDDA) copolymers in a dodecane solvent. The methodology can help advance field‐theoretic investigations of branched polymers by leveraging degeneracy in the chain to reduce computational cost and avoid the need to develop architecture‐specific algorithms. 

Understanding the phase behavior and dynamics of multi-component polymeric systems is essential for designing materials used in applications ranging from biopharmaceuticals to consumer products. While computational tools for understanding the equilibrium properties of such systems are relatively mature, simulation platforms for investigating non-equilibrium behavior are comparatively less developed. Dynamic self-consistent field theory (DSCFT) is a method that retains essential microscopic thermodynamics while enabling a continuum-level understanding of multi-component, multi-phase diffusive transport. A challenge with DSCFT is its high computational complexity and cost, along with the difficulty of incorporating thermal fluctuations. External potential dynamics (EPD) offers a more efficient approach to studying inhomogeneous polymers out of equilibrium, providing similar accuracy to DSCFT but with significantly lower computational cost. In this work, we introduce an extension of EPD to enable efficient and stable simulations of multi-species, multi-component polymer systems while embedding thermodynamically consistent noise. We validate this framework through simulations of a triblock copolymer melt and spinodally decomposing binary and ternary polymer blends, demonstrating its capability to capture key features of phase separation and domain growth. Furthermore, we highlight the role of thermal fluctuations in early stage coarsening. This study provides new insights into the interplay between stochastic and deterministic effects in the dynamic evolution of polymeric fluids, with the EPD framework offering a robust and scalable approach for investigating the complex dynamics of multi-component polymeric materials. 

Field-theoretic simulations are numerical methods for polymer field theory, which include fluctuation corrections beyond the mean-field level, successfully capturing various mesoscopic phenomena. Most field-theoretic simulations of polymeric fluids use the auxiliary field (AF) theory framework, which employs Hubbard–Stratonovich transformations for the particle-to-field conversion. Nonetheless, the Hubbard–Stratonovich transformation imposes significant limitations on the functional form of the non-bonded potentials. Removing this restriction on the non-bonded potentials will enable studies of a wide range of systems that require multi-body or more complex potentials. An alternative representation is the hybrid density-explicit auxiliary field theory (DE-AF), which retains both a density field and a conjugate auxiliary field for each species. While the DE-AF representation is not new, density-explicit field-theoretic simulations have yet to be developed. A major challenge is preserving the real and non-negative nature of the density field during stochastic evolution. To address this, we introduce positivity-preserving schemes that enable the first stable and efficient density-explicit field-theoretic simulations (DE-AF FTS). By applying the new method to a simple fluid, we find thermodynamically correct results at high densities, but the algorithm fails in the dilute regime. Nonetheless, DE-AF FTS is shown to be broadly applicable to dense fluid systems including a simple fluid with a three-body non-bonded potential, a homopolymer solution, and a diblock copolymer melt. 

Block copolymer self-assembly in conjunction with nonsolvent-induced phase separation (SNIPS) has been increasingly leveraged to fabricate integral-asymmetric membranes. The large number of formulation and processing parameters associated with SNIPS, however, has prevented the reliable construction of high performance membranes. In this study, we apply dynamical self-consistent field theory to model the SNIPS process and investigate the effect of various parameters on the membrane morphology: solvent selectivity, nonsolvent selectivity, initial film composition, and glass transition composition. We examine how solvent selectivity and concentration of polymers in the film impact the structure of micelles that connect to form the membrane matrix. In particular, we find that preserving the order in the surface layer and forming a connection between the supporting and surface layer are nontrivial and sensitive to each parameter studied. The effect of each parameter is discussed, and suggestions are made for successfully fabricating viable block copolymer membranes. 

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. 

The critical micelle concentration (CMC) is a crucial parameter in understanding the self-assembly behavior of surfactants. In this study, we combine simulation and experiment to demonstrate the predictive capability of molecularly informed field theories in estimating the CMC of biologically based protein surfactants. Our simulation approach combines the relative entropy coarse-graining of small-scale atomistic simulations with large-scale field-theoretic simulations, allowing us to efficiently compute the free energy of micelle formation necessary for the CMC calculation while preserving chemistry-specific information about the underlying surfactant building blocks. We apply this methodology to a unique intrinsically disordered protein platform capable of a wide variety of tailored sequences that enable tunable micelle self-assembly. The computational predictions of the CMC closely match experimental measurements, demonstrating the potential of molecularly informed field theories as a valuable tool to investigate self-assembly in bio-based macromolecules systematically.