Polydispersity-driven topological defects as order-restoring excitations

Abstract

The engineering of defects in crystalline matter has been extensively exploited to modify the mechanical and electrical properties of many materials. Recent experiments on manipulating extended defects in graphene, for example, show that defects direct the flow of electric charges. The fascinating possibilities offered by defects in two dimensions, known as topological defects, to control material properties provide great motivation to perform fundamental investigations to uncover their role in various systems. Previous studies mostly focus on topological defects in 2D crystals on curved surfaces. On flat geometries, topological defects can be introduced via density inhomogeneities. We investigate here topological defects due to size polydispersity on flat surfaces. Size polydispersity is usually an inevitable feature of a large variety of systems. In this work, simulations show well-organized induced topological defects around an impurity particle of a wrong size. These patterns are not found in systems of identical particles. Our work demonstrates that in polydispersed systems topological defects play the role of restoring order. The simulations show a perfect hexagonal lattice beyond a small defective region around the impurity particle. Elasticity theory has demonstrated an analogy between the elementary topological defects named disclinations to electric charges by associating a charge to a disclination, whose sign depends on the number of its nearest neighbors. Size polydispersity is shown numerically here to be an essential ingredient to understand short-range attractions between like-charge disclinations. Our study suggests that size polydispersity has a promising potential to engineer defects in various systems including nanoparticles and colloidal crystals.crystallography | geometric frustration | soft particles | dislocation

Strain and the optoelectronic properties of nonplanar phosphorene monolayers

“…Phosphorene | Discrete differential geometry | Two-dimensional materials Abbreviations: DDG, discrete differential geometry; 2-D, two-dimensional -20] are discrete surfaces that are embedded on a three-dimensional space. Graphene [1,2] develops an effective Dirac-like dispersion on the sublattice degree of freedom and other 2-D atomic materials exhibit remarkable plasmonic, polariton, and spin behaviors too [18][19][20].The properties of 2-D materials are influenced by their local geometry [12][13][14][15][16][17][21][22][23][24][25][26][27][28][29], making a discussion of the shape of two-dimensional lattices a timely and fundamental endeavor [24,30,31,32]. A dedicated discussion of the shape of 2-D materials is given here within the context of nets.…”

“…The properties of 2-D materials are influenced by their local geometry [12][13][14][15][16][17][21][22][23][24][25][26][27][28][29], making a discussion of the shape of two-dimensional lattices a timely and fundamental endeavor [24,30,31,32]. A dedicated discussion of the shape of 2-D materials is given here within the context of nets.…”

Highly Ordered and Highly Aligned Two‐Dimensional Binary Superlattice of a SWNT/Cylindrical‐Micellar System

“…Whereas the configurational entropy of the binary mixture is decreased by the formation of the superlattice, the free‐volume entropy of particles can be maximized by the formation of the superlattice (which provides more space for local motions of particles) and may compensate the decrease in the configurational entropy 30–32. The formation of the intercalated hexagonal structure may be considered from the point of view of elastic distortion 33. Since the diameter of a p‐SWNT is larger than that of a C 12 E 5 cylinder, p‐SWNTs (which replace some of the hexagonally packed C 12 E 5 cylinders) may act as impurity particles and induce the formation of stressed regions in their vicinity.…”

Highly Ordered and Highly Aligned Two‐Dimensional Binary Superlattice of a SWNT/Cylindrical‐Micellar System

“…[16a,b, 31] As the observed intercalated hexagonal binary superlattice is a two-dimensional analogy of the AB 2 structure of binary spherical particles (an alternate stacking of hexagonal A planes and honeycomb B planes), the formation of the intercalated hexagonal binary superlattice may be attributed to the entropy-driven particlepacking phenomenon. [33] Since the diameter of a p-SWNT is larger than that of a C 12 E 5 cylinder, p-SWNTs (which replace some of the hexagonally packed C 12 E 5 cylinders) may act as impurity particles and induce the formation of stressed regions in their vicinity. [30][31][32] The formation of the intercalated hexagonal structure may be considered from the point of view of elastic distortion.…”

“…[30][31][32] The formation of the intercalated hexagonal structure may be considered from the point of view of elastic distortion. [33] Since the diameter of a p-SWNT is larger than that of a C 12 E 5 cylinder, p-SWNTs (which replace some of the hexagonally packed C 12 E 5 cylinders) may act as impurity particles and induce the formation of stressed regions in their vicinity. The minimization of the energy cost due to the insertion of p-SWNTs may also contribute to the formation of the intercalated hexagonal superlattice.…”