Control the self‐assembly of block copolymers by tailoring the packing frustration

Graphene-Assisted Electron-Based Imaging of Individual Organic and Biological Macromolecules: Structure and Transient Dynamics

Characterizing the structures, interactions, and dynamics of molecules in their native liquid state is a long-existing challenge in chemistry, molecular science, and biophysics with profound scientific significance. Advanced transmission electron microscopy (TEM)-based imaging techniques with the use of graphene emerged as promising tools, mainly due to their performance on spatial and temporal resolution. This review focuses on the various approaches to achieving high-resolution imaging of individual molecules and their transient interactions. We highlight the crucial role of graphene grids in cryogenic electron microscopy for achieving Ångstrom-level resolution for resolving molecular structures and the importance of graphene liquid cells in liquid-phase TEM for directly observing dynamics with subnanometer resolution at a frame rate of several frames per second, as well as the cross-talks of the two imaging modes. To understand the chemistry and physics encoded in these molecular movies, incorporating machine learning algorithms for image analysis provides a promising approach that further bolsters the resolution adventure. Besides reviewing the recent advances and methodologies in TEM imaging of individual molecules using graphene, this review also outlines future directions to improve these techniques and envision problems in molecular science, chemistry, and biology that could benefit from these experiments.

Assessment of Solubility Behavior of a Copolymer in Supercritical CO2 and Organic Solvents: Neural Network Prediction and Statistical Analysis

In the industrial sector, understanding the behavior of block copolymers in supercritical solvents is crucial. While qualitative agreement with polymer solubility curves has been evaluated using complex theoretical models in many cases, quantitative predictions remain challenging. This study aimed to create a rapid and accurate artificial neural network (ANN) model to predict the lower critical solubility and upper critical solubility space of an atypical block copolymer, poly(styrene-co-octafluoropentyl methacrylate) (PSOM), in different supercritical solvent systems over a wide range of temperatures (51.75-182.05 °C) and high pressure (3.28-200.86 MPa). The experimental data set used in this study included one copolymer, five supercritical solvents, one cosolvent, and one initiator. It consisted of seven unique copolymer-solvent combinations (252 cloud point pressures) used to predict the model quantitatively and qualitatively. To predict the PSOM-solvent interactions, the study considered two different input systems: a six-variable system, a five-variable system, and one target output. Initially, we used a three-layer feed-forward neural network to select the best learning algorithm (Levenberg-Marquardt) from 14 different algorithms, considering one sample PSOM-solvent system. Then, the network topology was optimized by varying hidden neuron numbers from 2 to 80 for all seven PSOM-solvent combination systems. The predicted cloud point pressures were in excellent agreement with the experimental cloud point pressures, confirming the model's accuracy. It is clear from the results of a minimum mean square error (≤1.90 × 10-27) and maximum linear regression R 2 (≥0.99) during training, validation, and testing of all the data sets. Further, the ANN model accuracy was tested by statistical analysis, confirming the model's ability to accurately capture the miscibility regions of polymers, enabling efficient processing of various polymer materials. This data-driven approach facilitates the prediction of coexistence curves for other polymers and complex macromolecular systems.

Phase Behavior of Binary Blends of Diblock Copolymers: Progress and Opportunities

The phase behavior of binary blends of diblock copolymers has been examined extensively in the past decades. Experimental and theoretical studies have demonstrated that mixing two different block copolymers provides an efficient and versatile route to regulate their self-assembled morphologies. A good understanding of the principles governing the self-assembly of block copolymer blends has been obtained from the study of A1B1/A2B2 diblock copolymer blends. The second (A2B2) diblocks could act synergistically as fillers and cosurfactants to regulate the domain size and interfacial properties, resulting in the formation of ordered phases not found in the parent (A1B1 or A2B2) diblock copolymer melts. The study of A1B1/A2B2 block copolymer blends further provides a solid foundation for future research on more complex block copolymer blends.

The impact of intramolecular polydispersity on the self-assembly of ABn miktoarm star copolymers

The self-assembly behaviors of AB_n miktoarm star copolymers as one typical type of asymmetric architecture have been studied well in the past few decades due to their deflected phase boundaries. In particular, recently, they have attracted renewed theoretical interest due to their expanded spherical phase region that stabilizes complex Frank-Kasper spherical phases. However, previous theoretical studies have never considered AB_n copolymers with unequal arm lengths, which is more or less the case for synthesized copolymers. In this work, we investigate the self-assembly behaviors of AB_n miktoarm star copolymers with unequal B-arms using self-consistent field theory. We propose an intramolecular polydispersity index (iĐ) to quantify the distribution of unequal B-blocks. Accordingly, we further propose a simple quantity of an effective arm number n_equ = n/iĐ for quantitatively comparing the phase boundaries between various AB_n copolymer samples with different arm numbers or different distributions of B-blocks. Our results indicate that different AB_n copolymers with equal n_equ exhibit similar phase diagrams. On the other hand, we also found that the phase boundaries of two different samples with same n_equ are not exactly overlapped. We speculate that the effect of spontaneous curvature may be mainly controlled by n_equ, but the packing frustration of B-blocks may also be dependent on the other quantities that are closely related to the shape of the distribution of B-arms, such as higher order polydispersity indexes.

Theoretical Study of Phase Behaviors of Symmetric Linear B1A1B2A2B3 Pentablock Copolymer

The nanostructures that are self-assembled from block copolymer systems have attracted interest. Generally, it is believed that the dominating stable spherical phase is body-centered cubic (BCC) in linear AB-type block copolymer systems. The question of how to obtain spherical phases with other arrangements, such as the face-centered cubic (FCC) phase, has become a very interesting scientific problem. In this work, the phase behaviors of a symmetric linear B₁A₁B₂A₂B₃ (f_A1 = f_A2, f_B1 = f_B3) pentablock copolymer are studied using the self-consistent field theory (SCFT), from which the influence of the relative length of the bridging B₂-block on the formation of ordered nanostructures is revealed. By calculating the free energy of the candidate ordered phases, we determine that the stability regime of the BCC phase can be replaced by the FCC phase completely by tuning the length ratio of the middle bridging B₂-block, demonstrating the key role of B₂-block in stabilizing the spherical packing phase. More interestingly, the unusual phase transitions between the BCC and FCC spherical phases, i.e., BCC → FCC → BCC → FCC → BCC, are observed as the length of the bridging B₂-block increases. Even though the topology of the phase diagrams is less affected, the phase windows of the several ordered nanostructures are dramatically changed. Specifically, the changing of the bridging B₂-block can significantly adjust the asymmetrical phase regime of the Fddd network phase.

Periodic Patchy Spheres Self-Assembled by AmBCAn' Multiblock Terpolymers

We have designed A_mBCA_n^' multiblock terpolymers and studied their self-assembly using self-consistent field theory, aiming to generate the periodically arranged patchy spheres and thus to clarify the regulation mechanism of the number of patches. A number of two-dimensional phase diagrams are constructed for three typical architectures A₂BCA₂^', A₂BCA₃^', and A₃BCA₂^'. Four kinds of stable patchy spheres with the number of patches as 2 (S₂), 4 (S₄), 5 (S₅), and 6 (S₆) are obtained. These phases follow a common transition sequence of S₂ → S₄ → S₅ → S₆ along with the increasing of the volume fraction of C-block (f_C), which forms the core sphere patched with B-domains. Moreover, the S₆ phase exhibits the widest stability window, while S₅ has the narrowest one. The increased arms of A'-blocks in A₂BCA₃^' architecture deflect the phase boundaries toward large f_C and accordingly expand the regions of these patchy spheres due to the amplified effect of spontaneous curvature. In contrast, the increased arms of A-blocks in A₃BCA₂^' remarkably expands the window of S₆ but narrows those of the other patchy spheres, which is mainly caused by increased packing frustration resulting from the reduced extension of the more divided A-blocks. The widest window of the S₆ phase reaches Δf_C ∼ 0.13, which is readily accessed by experiment. Our work not only demonstrates a self-assembly strategy to engineer the patchy spheres, but also sheds light on the regulation mechanism of the patchy number.