(317g) Overcoming Challenges in Self-Assembly Control: Experimental Validation of an Integrated Framework with a Thermosensitive System

Self-assembly is a process where molecules interact to form complex morphologies. For many years, researchers have been striving to control self-assemblies to create organized nanostructures [1,2]. These resulting structures can be used for various purposes, including light harvesting materials, photonics, materials for energy storage, and nanocircuit elements [3]. However, controlling self-assemblies requires a detailed understanding of the associated pathways that molecules self-assemble and the impact of environment variables or actuators on these variables [4]. To achieve this, a model is required to capture the effect of these actuators on the self-assembly trajectories of the molecules. Subsequently, model-based control systems can be implemented to control these self-assembling species. However, this approach poses several challenges.

The first challenge is the kinetic trapping of self-assemblies to a particular configuration. These kinetic traps are metastable states, and it is challenging to drive the system out of them once the system enters these states [5]. The second challenge arises due to the high dimensionality of the molecular model, making it computationally intractable to develop and implement a model-based optimal control strategy. The third challenge is due to the system's stochastic nature, primarily due to the Brownian motion of the system.

Recent studies have attempted to overcome these challenges by controlling self-assemblies using Markov state models (MSMs) [6]. By breaking the self-assembling pathways using memoryless metastable states, the use of the MSMs can reduce the system’s dimensionality [7]. This approach allows us to compute the transition probabilities between the metastable states and capture the inherently stochastic nature of these self-assembling systems [8]. However, these studies have attempted to drive the system towards thermodynamic equilibrium through an out-of-equilibrium approach by driving the system through the metastable states. A limitation of this approach is that driving the system out of the metastable states may lead to irreversible changes to the self-assembling monomers and a complete disintegration of the complex nanostructures. Furthermore, driving the system towards thermodynamic equilibrium may not be desirable due to tight product specifications.

Motivated by the challenges and limitations of existing approaches, we propose an integrated framework to drive the self-assembling system to target morphologies while avoiding kinetic traps. In this framework, we first develop a mesoscale molecular model for the self-assembly of the monomers, then develop a reduced order model using the MSMs and formulate a stochastic optimal control problem. We then solve it using the dynamic programming (DP) approach [9]. Dissipative particle dynamic (DPD) is utilized in developing mesoscale models for self-assembly [10]. Coarse-grained molecular dynamics (MD) simulations are not used due to the time scales required for the formation of the desirable nanostructure being in the order of milliseconds, while the time scales attained by these simulations are in the order of a few microseconds, which do not serve the purpose of this study. The parameters of the DPD simulations are obtained by matching the water octanol partition coefficients attained using the all-atom MD simulations. The non-bonded repulsion parameters are specifically determined by matching the all-atom simulations with DPD simulation results. Multiple simulations are performed with varying input profiles to collect data for the self-assembling trajectories, which are used to make the MSM. The radius of gyration and the packing fraction are chosen as the set of order parameters for building the MSM. After developing the MSM, a stochastic optimal control problem is formulated by assigning rewards to the states in the MSMs and maximizing the expected sum of rewards. DP determines the optimal control policy by maximizing the expected sum of rewards. It is to be noted that the optimal control policy assigns maximum rewards to the system closer to the target morphologies, and a value iteration algorithm is used to calculate the optimal control policy associated with each state offline. This approach allows us to handle the high dimensionality of the system by avoiding the need to solve the optimization problem online. To demonstrate the effectiveness of our proposed framework, we apply it to a thermosensitive self-assembly system resulting from dynamic binary complexes (DBCs). We validate our model predictions by comparing them to experimental results from the scanning electron microscope (SEM). Our framework enables us to develop an optimal control policy to drive the system to a target morphology that satisfies the desired product properties.

References.

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