Conformational Scaling Relations of Two-Dimensional Macromolecular Graphene Oxide in Solution

Dynamics of a self-interacting sheet in shear flow

Solution processing of 2D materials such as graphene is important for applications thereof, yet a complete fundamental understanding of how 2D materials behave dynamically in solution is lacking. Here, we extend previous work by Silmore et al., Soft Matter, 2021, 17(18), 4707-4718 by adding short-ranged Lennard-Jones interactions to 2D sheets in shear flow. We find that the addition of these interactions allows for a rich landscape of conformations which depend on the balance between shear strength, bending rigidity, and interaction strength as well as the initial configuration of the sheet. We explore this conformational space and classify sheets as flat, tumbling, 1D folded, or 2D folded based on their conformational properties. We use kinetic and energetic arguments to explain why sheets adopt certain conformations within the folded regime. Finally, we calculate the stresslet and find that, even in the absence of thermal fluctuations and multiple sheet interactions, shear-thinning followed by shear-thickening behavior can appear.

Falling-Leaves Stacking Aggregation of Two-Dimensional Macromolecular Graphene Oxide in Solution

Understanding the dynamical behaviors of two-dimensional (2D) macromolecules is of fundamental importance for the precise modulation of their assembled structures and material performances. However, considerably less is known about how discrete macromolecular sheets aggregate into extended macroscopic assemblies in solutions. The absence of a quantitative description of the assembly process limits the precise structural control of assemblies. Here, we investigated the aggregation thermodynamic transition and kinetic behavior of 2D macromolecules in the model of single layer graphene oxide (GO). Combining Flory-Huggins theory with experimental observations, we unveiled the critical thermodynamic transition of GO to correlate with the solvent property. We proposed a theoretical falling-leaf model to quantitatively describe the kinetic aggregation process of 2D GO sheets. Experimental analysis validated the theoretical prediction that the thickness of GO aggregates has a power law relation with the poor solvent content. Our work provides a fundamental understanding of phase separation of 2D macromolecules and offers an insight into modulating the aggregated structures of their assembled materials.

Crumpling Defective Graphene Sheets

Upon crumpling, graphene sheets yield intriguing hierarchical structures with high resistance to compression and aggregation, garnering a great deal of attention in recent years for their remarkable potential in a variety of applications. Here, we aim to understand the effect of Stone-Wales (SW) defects, i.e., a typical topological defect of graphene, on the crumpling behavior of graphene sheets at a fundamental level. By employing atomistically informed coarse-grained molecular dynamics (CG-MD) simulations, we find that SW defects strongly influence the sheet conformation as manifested by the change in size scaling laws and weaken the self-adhesion of the sheet during the crumpling process. Remarkably, the analyses of the internal structures (i.e., local curvatures, stresses, and cross-section patterns) of crumpled graphene emphasize the enhanced mechanical heterogeneity and "glass-like" amorphous state elicited by SW defects. Our findings pave the way for understanding and exploring the tailored design of crumpled structure via defect engineering.

Wide-Range Size Fractionation of Graphene Oxide by Flow Field-Flow Fractionation

Many interesting properties of 2D materials and their assembled structures are strongly dependent on the lateral size and size distribution of 2D materials. Accordingly, effective size separation of polydisperse 2D sheets is critical for desirable applications. Here, we introduce flow field-flow fractionation (FlFFF) for a wide-range size fractionation of graphene oxide (GO) up to 100 μm. Two different separation mechanisms are identified for FlFFF, including normal mode and steric/hyperlayer mode, to size fractionate wide size-distributed GOs while employing a crossflow field for either diffusion or size-controlled migration of GO. Obviously, the 2D GO sheet reveals size separation behavior distinctive from typical spherical particles arising from its innate planar geometry. We also investigate 2D sheet size-dependent mechanical and electrical properties of three different graphene fibers produced from size-fractionated GOs. This FlFFF-based size selection methodology can be used as a generic approach for effective wide-range size separation for 2D materials, including rGO, TMDs, and MXene.

Unraveling the morphological complexity of two-dimensional macromolecules

2D macromolecules, such as graphene and graphene oxide, possess a rich spectrum of conformational phases. However, their morphological classification has only been discussed by visual inspection, where the physics of deformation and surface contact cannot be resolved. We employ machine learning methods to address this problem by exploring samples generated by molecular simulations. Features such as metric changes, curvature, conformational anisotropy and surface contact are extracted. Unsupervised learning classifies the morphologies into the quasi-flat, folded, crumpled phases and interphases using geometrical and topological labels or the principal features of the 2D energy map. The results are fed into subsequent supervised learning for phase characterization. The performance of data-driven models is improved notably by integrating the physics of geometrical deformation and topological contact. The classification and feature extraction characterize the microstructures of their condensed phases and the molecular processes of adsorption and transport, comprehending the processing-microstructures-performance relation in applications.

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Morphology of 2D macromolecules are classified into four phases

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Data-driven models capture physics and topology beyond the geometry

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Condensed-phase properties are understood by the features extracted

Resolving morphological complexity of macromolecules is the stepping stone to the design and fabrication of high-performance, multi-functional materials and to understanding the soft matter behaviors in biology and engineering. To extract the physics of lattice distortion and surface contact beyond the conformation is critical, yet challenging. Here, we show that, by labeling the simulation data using the 2D map of potential energies, the 3D geometry, and the topology of contact, morphological classification can be achieved with high accuracy. The well-trained model can be used to decipher the microstructural complexity using simulation or experimental data, which may include the geometrical representation only. This data-driven approach extracts the key geometrical and topological features of 2D macromolecules that are directly responsible for the material performance in relevant applications and can be extended to study other complex surfaces such as red blood cells and the brain.

Thermally fluctuating, semiflexible sheets in simple shear flow

We perform Brownian dynamics simulations of semiflexible colloidal sheets with hydrodynamic interactions and thermal fluctuations in shear flow. As a function of the ratio of bending rigidity to shear energy (a dimensionless quantity we denote S) and the ratio of bending rigidity to thermal energy, we observe a dynamical transition from stochastic flipping to crumpling and continuous tumbling. This dynamical transition is broadened by thermal fluctuations, and the value of S at which it occurs is consistent with the onset of chaotic dynamics found for athermal sheets. The effects of different dynamical conformations on rheological properties such as viscosity and normal stress differences are also quantified. Namely, the viscosity in a dilute dispersion of sheets is found to decrease with increasing shear rate (shear-thinning) up until the dynamical crumpling transition, at which point it increases again (shear-thickening), and non-zero first normal stress differences are found that exhibit a local maximum with respect to temperature at large S (small shear rate). These results shed light on the dynamical behavior of fluctuating 2D materials dispersed in fluids and should greatly inform the design of associated solution processing methods.

Revisiting the Molar Mass and Conformation of Derivatized Fractionated Softwood Kraft Lignin

The limited utilization of reliable tools and standards for determination of the softwood kraft lignin molar mass and the corresponding molecular conformation hampers elucidation of the structure-property relationships of lignin. At issue, conventional size exclusion chromatography (SEC) is unable to robustly measure the molar mass because of a lack of calibration standards with a similar structure to lignin. In the present work, the determination of the absolute molar mass of acetylated technical lignin was revisited utilizing SEC combined with multi-angle light scattering with a band pass filter to suppress the fluorescence. Fractionated lignin isolated using sequential techniques of solvent and membrane methods was used to enhance the clarity of light-scattering profiles by narrowing the molar mass distribution of lignin fractions. Further information on the molecular conformation of derivatized samples was studied utilizing a differential viscometer, and chemical structures were identified by NMR spectroscopy analysis. Through the help of fractionation, intrinsic viscosity values were determined for the different fractions as a function of molecular weight cut-off membranes. The derivatized acetone-soluble lignin was found to possess a lower molecular weight and an extremely compact structure relative to the derivatized acetone-insoluble fraction based on a significantly lower "α" value in the Mark-Houwink-Sakurada plot (0.15 acetone-soluble vs 0.33 acetone-insoluble). The differences in geometry were supported by the linkage analysis from NMR showing the acetone-soluble part containing fewer native linkages. In both of these examples, kraft lignin behaved like a solid sphere, limiting the ability to provide entanglements between molecular chains. From this standpoint, macroscopic properties of lignin are justified with this knowledge of a dense and extremely compact structure.

Multi-Scale Structure-Mechanical Property Relations of Graphene-Based Layer Materials

Pristine graphene is one of the strongest materials known in the world, and may play important roles in structural and functional materials. In order to utilize the extraordinary mechanical properties in practical engineering structures, graphene should be assembled into macroscopic structures such as graphene-based papers, fibers, foams, etc. However, the mechanical properties of graphene-based materials such as Young’s modulus and strength are 1–2 orders lower than those of pristine monolayer graphene. Many efforts have been made to unveil the multi-scale structure–property relations of graphene-based materials with hierarchical structures spanning the nanoscale to macroscale, and significant achievements have been obtained to improve the mechanical performance of graphene-based materials through composition and structure optimization across multi-scale. This review aims at summarizing the currently theoretical, simulation, and experimental efforts devoted to the multi-scale structure–property relation of graphene-based layer materials including defective monolayer graphene, nacre-like and laminar nanostructures of multilayer graphene, graphene-based papers, fibers, aerogels, and graphene/polymer composites. The mechanisms of mechanical property degradation across the multi-scale are discussed, based on which some multi-scale optimization strategies are presented to further improve the mechanical properties of graphene-based layer materials. We expect that this review can provide useful insights into the continuous improvement of mechanical properties of graphene-based layer materials.

Understanding the Role of Self-Adhesion in Crumpling Behaviors of Sheet Macromolecules

Understanding the crumpling behavior of two-dimensional (2D) macromolecular sheet materials is of fundamental importance in engineering and technological applications. Among the various properties of these sheets, interfacial adhesion critically contributes to the formation of crumpled structures. Here, we present a coarse-grained molecular dynamics (CG-MD) simulation study to explore the fundamental role of self-adhesion in the crumpling behaviors of macromolecular sheets having varying masses or sizes. By evaluating the potential energy evolution, our results show that the self-adhesion plays a dominant role in the crumpling behavior of the sheets compared to in-plane and out-of-plane stiffnesses. The macromolecular sheets with higher adhesion tend to form a self-folding planar structure at the quasi-equilibrium state of the crumpling and exhibit a lower packing efficiency as evaluated by the fractal dimension of the system. Notably, during the crumpling process, both the radius of gyration R_g and the hydrodynamic radius R_h of the macromolecular sheet can be quantitatively described by the power-law scaling relationships associated with adhesion. The evaluation of the shape descriptors indicates that the overall crumpling behavior of macromolecular sheets can be characterized by three regimes, i.e., the less bent, intermediate, and highly crumpled regimes, dominated by edge-bending, self-adhesion, and further compression, respectively. The internal structural analysis further reveals that the sheet transforms from the initially ordered state to the disordered glassy state upon crumpling, which can be facilitated by greater self-adhesion. Our study provides fundamental insights into the adhesion-dependent structural behavior of macromolecular sheets under crumpling, which is essential for establishing the structure-processing-property relationships for crumpled macromolecular sheets.

The Origin of the Sheet Size Predicament in Graphene Macroscopic Papers

The larger size of graphene sheets should intuitively generate higher overall properties of their macroscopic materials. However, this intuitive notion still remains ambiguous. Here, we uncover that the wrinkle formation causes the counterintuitive size predicament of graphene sheets in their macroscopic materials. In the model of graphene oxide assembled papers, we reveal that the giant size of graphene oxide sheets aggravates the formation of larger wrinkles and more microvoids, causing the negative size effect in mechanical strength. A major microscopic origin of the size predicament is the skin wrinkling in the drying process, and the wrinkling behavior follows a general rule of deformation of an elastic thin plate. We use a wrinkle-engineering strategy to depress the spontaneously formed large wrinkles and succeed in the resolution of the size predicament. After wrinkle modulation, an authentically positive size effect reversely appears in which giant graphene sheets generate ultrahigh mechanical strength and superior functionalities of graphene papers. The origin of the size predicament reminds us of the hidden importance of modulating wrinkles for graphene macroscopic materials and provides a guidance of wrinkle engineering for graphene materials with advanced performances.