Classical dynamical density functional theory (DDFT) is one of the cornerstones of modern statistical mechanics. It is an extension of the highly successful method of classical density functional theory (DFT) to nonequilibrium systems. Originally developed for the treatment of simple and complex fluids, DDFT is now applied in fields as diverse as hydrodynamics, materials science, chemistry, biology, and plasma physics. In this review, we give a broad overview over classical DDFT. We explain its theoretical foundations and the ways in which it can be derived. The relations between the different forms of deterministic and stochastic DDFT as well as between DDFT and related theories, such as quantum-mechanical time-dependent DFT, mode coupling theory, and phase field crystal models, are clarified. Moreover, we discuss the wide spectrum of extensions of DDFT, which covers methods with additional order parameters (like extended DDFT), exact approaches (like power functional theory), and systems with more complex dynamics (like active matter). Finally, the large variety of applications, ranging from fluid mechanics and polymer physics to solidification, pattern formation, biophysics, and electrochemistry, is presented.

Classical dynamical density functional theory: from fundamentals to applications

Investigations on monolayered transition metal dichalcogenides (TMDs) and TMD heterostructures have been steadily increasing over the past years due to their potential application in a wide variety of fields such as microelectronics, sensors, batteries, solar cells, and supercapacitors, among others. The present work focuses on the characterization of TMDs using transmission electron microscopy, which allows not only static atomic resolution but also investigations into the dynamic behavior of atoms within such materials. Herein, we present a body of recent research from the various techniques available in the transmission electron microscope to structurally and analytically characterize layered TMDs and briefly compare the advantages of TEM with other characterization techniques. Whereas both static and dynamic aspects are presented, special emphasis is given to studies on the electron-driven in situ dynamic aspects of these materials while under investigation in a transmission electron microscope. The c...

Electron-Driven In Situ Transmission Electron Microscopy of 2D Transition Metal Dichalcogenides and Their 2D Heterostructures.

Low-angle grain boundaries generally exist in the form of dislocation arrays, while high-angle grain boundaries (misorientation angle $g15\ifmmode^\circ\else\textdegree\fi{}$) exist in the form of structural units in bulk metals. Here, through in situ atomic resolution aberration corrected electron microscopy observations, we report size-dependent grain-boundary structures improving both stabilities of electrical conductivity and mechanical properties in sub-10-nm-sized gold crystals. With the diameter of a nanocrystal decreasing below 10 nm, the high-angle grain boundary in the crystal exists as an array of dislocations. This size effect may be of importance to a new generation of interconnects applications.

Size-Dependent Grain-Boundary Structure with Improved Conductive and Mechanical Stabilities in Sub-10-nm Gold Crystals.

Scientific Literacy And The Myth Of The Scientific Method

A key challenge in large-scale graphene fabrication and application is controlling the grain boundaries (GBs) in polycrystalline graphene grown by chemical vapor deposition (CVD). Here, we adopt a phase field crystal (PFC) model to predict the equilibrium structures as well as dynamic formation of GBs in CVD-grown graphene. The results demonstrate that GBs consisting of clustered 5|7|5|7 dislocation dipoles, as constructed by the conventional coincidence site lattice (CSL) theory, are not energetically favorable, and should be replaced by dispersed 5|7 dislocations, as predicted from the PFC model, when constructing GBs’ atomistic structures for theoretical and numerical investigations. The PFC modeling also demonstrates possible routes of engineering GBs in two-dimensional (2D) materials by controlling grain orientations in pre-patterned growing seeds and suggests a simple geometric rule that explains the predominant existence of curved grain boundaries in graphene. As a prominent example of potential applications of our method, we show how to grow triple-junction-free polycrystalline graphene that exhibits enhanced mechanical strength and defy the traditional Hall–Petch relation.

Phase field crystal modeling of grain boundary structures and growth in polycrystalline graphene

Understanding and controlling the properties and dynamics of topological defects is a lasting challenge in the study of two-dimensional materials, and is crucial to achieve high-quality films required for technological applications. Here grain boundary structures, energies, and dynamics of binary two-dimensional materials are investigated through the development of a phase field crystal model that is parametrized to match the ordering, symmetry, energy, and length scales of hexagonal boron nitride. Our studies reveal some new dislocation core structures for various symmetrically and asymmetrically tilted grain boundaries, in addition to those obtained in previous experiments and first-principles calculations. We also identify a defect-mediated growth dynamics for inversion domains governed by the collective atomic migration and defect core transformation at grain boundaries and junctions, a process that is related to inversion symmetry breaking in binary lattice.

Grain Boundary Structures and Collective Dynamics of Inversion Domains in Binary Two-Dimensional Materials.

TRIOBP is an actin-bundling protein. Mutations of TRIOBP are associated with human deafness DFNB28. In vitro, TRIOBP isoform 4 (TRIOBP-4) forms dense F-actin bundles resembling the inner ear hair c...

R1 motif is the major actin-binding domain of TRIOBP-4.

The formation and dynamics of a wide variety of binary two-dimensional ordered structures and superlattices are investigated through a phase field crystal model with sublattice ordering. Various types of binary ordered phases, the phase diagrams, and the grain growth dynamics and structural transformation processes, including the emergence of topological defects, are examined. The results are compared to the ordering and assembly of two-component colloidal systems. Two factors governing the binary phase ordering are identified, the coupling and competition between the length scales of two sublattices and the selection of average particle densities of two components. The control and variation of these two factors lead to the prediction of various complex binary ordered patterns, with different types of sublattice ordering for integer vs. noninteger ratios of sublattice length scales. These findings will enable further systematic studies of complex ordering and assembly processes of binary systems particularly binary colloidal crystals.

Phase ordering, transformation, and grain growth of two-dimensional binary colloidal crystals: A phase field crystal modeling

The formation and dynamics of a wide variety of binary two-dimensional ordered structures and superlattices are investigated through a phase field crystal model with sublattice ordering. Various types of binary ordered phases, the phase diagrams, and the grain growth dynamics and structural transformation processes, including the emergence of topological defects, are examined. The results are compared to the ordering and assembly of two-component colloidal systems. Two factors governing the binary phase ordering are identified, namely the coupling and competition between the length scales of two sublattices, and the selection of average particle densities of two components. The control and variation of these two factors lead to the prediction of various complex binary ordered patterns, with different types of sublattice ordering for integer versus noninteger ratios of sublattice length scales. These findings will enable further systematic studies of complex ordering and assembly processes of binary systems, particularly binary colloidal crystals.

Influence of Misorientation on Graphene Moir\'{e} Patterns

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Papers

Grain Boundary Structures and Collective Dynamics of Inversion Domains in Binary Two-Dimensional Materials.

R1 motif is the major actin-binding domain of TRIOBP-4.

Phase ordering, transformation, and grain growth of two-dimensional binary colloidal crystals: A phase field crystal modeling

Phase ordering, transformation, and grain growth of two-dimensional binary colloidal crystals: A phase field crystal modeling

Influence of Misorientation on Graphene Moir\'{e} Patterns