Kinetic Pathways of Block Copolymer Directed Self-Assembly: Insights from Efficient Continuum Modeling

Inference of Onsager coefficient from microscopic simulations by machine learning

Dynamic density functional theory (DDFT) is a fruitful approach for modeling polymer dynamics, benefiting from its multiscale and hybrid nature. However, the Onsager coefficient, the only free parameter in DDFT, is primarily derived empirically, limiting the accuracy and broad application of DDFT. Herein, we propose a machine learning-based, bottom-up workflow to directly extract the Onsager coefficient from molecular simulations, circumventing partly heuristic assumptions in traditional approaches. In this workflow, the Onsager coefficient is derived from the proposed DDFT-informed ordinary differential equation network, trained to replicate density evolution observed in Brownian dynamics (BD) simulations. We validate our method by studying the lamellar transition in symmetric diblock copolymer melts, where the DDFT model with the extracted Onsager coefficient precisely reproduces both the density evolution and interface narrowing predicted by BD simulations, thereby demonstrating the reliability of the present scheme. Meanwhile, our studies reveal the strong relevance of the Onsager coefficient with dynamic processes and identify the explicit connection between dynamic correlations, characterized by the correlation strength and correlation length, and the system parameters, e.g., the Flory-Huggins interaction parameter. We found that far from the transition point, the correlation that transmits the thermodynamic force into a density current is localized and strong, while close to the transition point, it becomes long-ranged but weak. Our approach aims to develop a more generalized framework to bridge more refined particle-based simulations to more coarse-grained field-based calculations, and the insights gained by using our approach could be extended to other non-equilibrium systems in polymer sciences.

Reaction-driven assembly: controlling changes in membrane topology by reaction cycles

Chemical reaction cycles are prototypical examples how to drive systems out of equilibrium and introduce novel, life-like properties into soft-matter systems. We report simulations of amphiphilic molecules in aqueous solution. The molecule's head group is permanently hydrophilic, whereas the reaction cycle switches the molecule's tail from hydrophilic (precursor) to hydrophobic (amphiphile) and vice versa. The reaction cycle leads to an arrest in coalescence and results in uniform vesicle sizes that can be controlled by the reaction rate. Using a continuum description and particle-based simulation, we study the scaling of the vesicle size with the reaction rate. The chemically active vesicles are inflated by precursor, imparting tension onto the membrane and, for specific parameters, stabilize pores.

Temperature-Controlled Pathway Complexity in Self-Assembly of Perylene Diimide-Polydiacetylene Supramolecule

Self-assembly process represents one of the most powerful and efficient methods for designing functional nanomaterials. For generating optimal functional materials, understanding the pathway complexity during self-assembly is essential, which involves the aggregation of molecules into thermodynamically or kinetically favored pathways. Herein, a functional perylene diimide (PDI) derivative by introducing diacetylene (DA) chains (PDI-DA) is designed. Temperature control pathway complexity with the evolution of distinct morphology for the kinetic and thermodynamic product of PDI-DA is investigated in detail. A facile strategy of UV-induced polymerization is adopted to trap and capture metastable kinetic intermediates to understand the self-assembly mechanism. PDI-DA showed two kinetic intermediates having the morphology of nanosheets and nanoparticles before transforming into the thermodynamic product having fibrous morphology. Spectroscopic studies revealed the existence of distinct H- and J-aggregates for kinetic and thermodynamic products respectively. The polymerized fibrous PDI-DA displayed reversible switching between J-aggregate and H-aggregate.

Complex-tensor theory of simple smectics

Matter self-assembling into layers generates unique properties, including structures of stacked surfaces, directed transport, and compact area maximization that can be highly functionalized in biology and technology. Smectics represent the paradigm of such lamellar materials - they are a state between fluids and solids, characterized by both orientational and partial positional ordering in one layering direction, making them notoriously difficult to model, particularly in confining geometries. We propose a complex tensor order parameter to describe the local degree of lamellar ordering, layer displacement and orientation of the layers for simple, lamellar smectics. The theory accounts for both dislocations and disclinations, by regularizing singularities within defect cores and so remaining continuous everywhere. The ability to describe disclinations and dislocation allows this theory to simulate arrested configurations and inclusion-induced local ordering. This tensorial theory for simple smectics considerably simplifies numerics, facilitating studies on the mesoscopic structure of topologically complex systems.

Perspective: New directions in dynamical density functional theory

Classical dynamical density functional theory (DDFT) has become one of the central modeling approaches in nonequilibrium soft matter physics. Recent years have seen the emergence of novel and interesting fields of application for DDFT. In particular, there has been a remarkable growth in the amount of work related to chemistry. Moreover, DDFT has stimulated research on other theories such as phase field crystal models and power functional theory. In this perspective, we summarize the latest developments in the field of DDFT and discuss a variety of possible directions for future research.

Nonequilibrium Processes in Polymer Membrane Formation: Theory and Experiment

Porous polymer and copolymer membranes are useful for ultrafiltration of functional macromolecules, colloids, and water purification. In particular, block copolymer membranes offer a bottom-up approach to form isoporous membranes. To optimize permeability, selectivity, longevity, and cost, and to rationally design fabrication processes, direct insights into the spatiotemporal structure evolution are necessary. Because of a multitude of nonequilibrium processes in polymer membrane formation, theoretical predictions via continuum models and particle simulations remain a challenge. We compiled experimental observations and theoretical approaches for homo- and block copolymer membranes prepared by nonsolvent-induced phase separation and highlight the interplay of multiple nonequilibrium processes─evaporation, solvent-nonsolvent exchange, diffusion, hydrodynamic flow, viscoelasticity, macro- and microphase separation, and dynamic arrest─that dictates the complex structure of the membrane on different scales.

Solvent Vapor Annealing, Defect Analysis, and Optimization of Self-Assembly of Block Copolymers Using Machine Learning Approaches

Self-assembly of block copolymers (BCPs) is an alternative patterning technique that promises high resolution and density multiplication with lower costs. The defectivity of the resulting nanopatterns remains too high for many applications in microelectronics and is exacerbated by small variations of processing parameters, such as film thickness, and fluctuations of solvent vapor pressure and temperature, among others. In this work, a solvent vapor annealing (SVA) flow-controlled system is combined with design of experiments (DOE) and machine learning (ML) approaches. The SVA flow-controlled system enables precise optimization of the conditions of self-assembly of the high Flory-Huggins interaction parameter (χ) hexagonal dot-array forming BCP, poly(styrene-b-dimethylsiloxane) (PS-b-PDMS). The defects within the resulting patterns at various length scales are then characterized and quantified. The results show that the defectivity of the resulting nanopatterned surfaces is highly dependent upon very small variations of the initial film thicknesses of the BCP, as well as the degree of swelling under the SVA conditions. These parameters also significantly contribute to the quality of the resulting pattern with respect to grain coarsening, as well as the formation of different macroscale phases (single and double layers and wetting layers). The results of qualitative and quantitative defect analyses are then compiled into a single figure of merit (FOM) and are mapped across the experimental parameter space using ML approaches, which enable the identification of the narrow region of optimum conditions for SVA for a given BCP. The result of these analyses is a faster and less resource intensive route toward the production of low-defectivity BCP dot arrays via rational determination of the ideal combination of processing factors. The DOE and machine learning-enabled approach is generalizable to the scale-up of self-assembly-based nanopatterning for applications in electronic microfabrication.

Introducing Memory in Coarse-Grained Molecular Simulations

Preserving the correct dynamics at the coarse-grained (CG) level is a pressing problem in the development of systematic CG models in soft matter simulation. Starting from the seminal idea of simple time-scale mapping, there have been many efforts over the years toward establishing a meticulous connection between the CG and fine-grained (FG) dynamics based on fundamental statistical mechanics approaches. One of the most successful attempts in this context has been the development of CG models based on the Mori-Zwanzig (MZ) theory, where the resulting equation of motion has the form of a generalized Langevin equation (GLE) and closely preserves the underlying FG dynamics. In this Review, we describe some of the recent studies in this regard. We focus on the construction and simulation of dynamically consistent systematic CG models based on the GLE, both in the simple Markovian limit and the non-Markovian case. Some recent studies of physical effects of memory are also discussed. The Review is aimed at summarizing recent developments in the field while highlighting the major challenges and possible future directions.

Dynamic coarse-graining of polymer systems using mobility functions

We propose a dynamic coarse-graining (CG) scheme for mapping heterogeneous polymer fluids onto extremely CG models in a dynamically consistent manner. The idea is to use as target function for the mapping a wave-vector dependent mobility function derived from the single-chain dynamic structure factor, which is calculated in the microscopic reference system. In previous work, we have shown that dynamic density functional calculations based on this mobility function can accurately reproduce the order/disorder kinetics in polymer melts, thus it is a suitable starting point for dynamic mapping. To enable the mapping over a range of relevant wave vectors, we propose to modify the CG dynamics by introducing internal friction parameters that slow down the CG monomer dynamics on local scales, without affecting the static equilibrium structure of the system. We illustrate and discuss the method using the example of infinitely long linear Rouse polymers mapped onto ultrashort CG chains. We show that our method can be used to construct dynamically consistent CG models for homopolymers with CG chain lengthN= 4, whereas for copolymers, longer CG chain lengths are necessary.