Negative Gaussian curvature induces significant suppression of thermal conduction in carbon crystals

Nanoscale ◽  
2017 ◽  
Vol 9 (37) ◽  
pp. 14208-14214 ◽  
Author(s):  
Zhongwei Zhang ◽  
Jie Chen ◽  
Baowen Li
Keyword(s):  
Gaussian Curvature ◽  
Thermal Conduction ◽  
Negative Curvature ◽  
Positive Curvature ◽  
Significant Suppression ◽  
Carbon Allotropes ◽  
Zero Curvature ◽  
Negative Gaussian Curvature

From the mathematic category of surface Gaussian curvature, carbon allotropes can be classified into three types: zero curvature, positive curvature, and negative curvature.

scholarly journals Chirality in curved polyaromatic systems

2017 ◽  
Vol 46 (6) ◽  
pp. 1643-1660 ◽  
Author(s):  
Michel Rickhaus ◽  
Marcel Mayor ◽  
Michal Juríček
Keyword(s):  
Gaussian Curvature ◽  
Carbon Allotrope ◽  
Carbon Allotropes ◽  
Negative Gaussian Curvature ◽  
Helical Chirality

Chiral non-planar polyaromatic systems that display zero, positive or negative Gaussian curvature are analysed and their potential to ‘encode’ chirality of larger sp2-carbon allotropes is evaluated. Shown is a hypothetical peanut-shaped carbon allotrope, where helical chirality results from the interplay of various curvature types.

scholarly journals Wrinkles and splay conspire to give positive disclinations negative curvature

2015 ◽  
Vol 112 (41) ◽  
pp. 12639-12644 ◽  
Author(s):  
Elisabetta A. Matsumoto ◽  
Daniel A. Vega ◽  
Aldo D. Pezzutti ◽  
Nicolás A. García ◽  
Paul M. Chaikin ◽  
...  
Keyword(s):  
Diblock Copolymer ◽  
Gaussian Curvature ◽  
Negative Curvature ◽  
Topological Defects ◽  
Free Standing ◽  
Columnar Phase ◽  
Negative Gaussian Curvature ◽  
Positive Gaussian Curvature

Recently, there has been renewed interest in the coupling between geometry and topological defects in crystalline and striped systems. Standard lore dictates that positive disclinations are associated with positive Gaussian curvature, whereas negative disclinations give rise to negative curvature. Here, we present a diblock copolymer system exhibiting a striped columnar phase that preferentially forms wrinkles perpendicular to the underlying stripes. In free-standing films this wrinkling behavior induces negative Gaussian curvature to form in the vicinity of positive disclinations.

2D carbon sheets with negative Gaussian curvature assembled from pentagonal carbon nanoflakes

2018 ◽  
Vol 20 (14) ◽  
pp. 9123-9129 ◽  
Author(s):  
Cunzhi Zhang ◽  
Fancy Qian Wang ◽  
Jiabing Yu ◽  
Sheng Gong ◽  
Xiaoyin Li ◽  
...  
Keyword(s):  
Gaussian Curvature ◽  
The Novel ◽  
Carbon Allotropes ◽  
Graphene Nanoflakes ◽  
Negative Gaussian Curvature ◽  
Carbon Nanoflakes

Based on the recent experimental synthesis of pentagonal graphene nanoflakes and the novel properties of penta-graphene, we report a series of 2D assembled carbon allotropes (CG568-80, CG568-180 and CG568-320) that have unusual properties.

The multifarious medical applications of carbon curvatures: A cohort review

2020 ◽  
Vol 16 ◽  
Author(s):  
Vishal Chavda ◽  
Vimal Patel
Keyword(s):  
Negative Curvature ◽  
Structural Characteristics ◽  
Short Review ◽  
Medical Applications ◽  
The Novel ◽  
Carbon Allotropes ◽  
Therapeutic Applications ◽  
Zero Curvature ◽  
Bio Imaging ◽  
Bio Material

Abstract:: Carbon curvatures are the novel therapeutic bio-material that are in research due to its multifarious applications in a variety of research aspects. All the carbon allotropes were grouped mathematically into three types based upon surface Gaussian curvatures: zero curvature (graphene), negative curvature (schwarzites), and positive curvatures (fullerenes, CNTs), because of they have physiochemical activities such as optoelectrical, chemical, thermal and magnetic properties. All these allotropes consisting sp2 hybridization with delocalized π bond electrons. Based on the types and number of aro-matic carbon rings, all have unique geometric structural characteristics, chirality, and solubility, which offers them as a po-tential candidate for biomedical and therapeutic applications. In this short review, we highlight the basic structural and phys-icochemical characteristics of carbon allotropes and their biomedical and therapeutic applications recently been studied by researchers and described the therapeutic applications of graphene and its derivatives in drug delivery, gene delivery, bio-imaging, biosensors, therapeutic diagnosis, and photo-stimulation therapies.

RELATIVE STABILITY OF SINGLE GRAPHITE SHEETS OF POSITIVE, NEGATIVE AND ZERO CURVATURE

1995 ◽  
Vol 09 (25) ◽  
pp. 3319-3332 ◽  
Author(s):  
L. N. BOURGEOIS ◽  
L. A. BURSILL
Keyword(s):  
Relative Stability ◽  
Negative Curvature ◽  
Positive Curvature ◽  
Maximum Size ◽  
Radius Of Curvature ◽  
Curvature Radius ◽  
Negatively Curved ◽  
Zero Curvature ◽  
Transmission Electron ◽  
Graphite Sheets

The relative stability of single graphite sheets of zero, positive and negative curvature is investigated through a simple model where both strain and dangling bond energy are taken into account. Although it is found that flat sheets are always more stable than negatively curved ones, calculations show that above a critical radius of curvature there is a crossover from positive to negative curvature as the more stable geometry for a single sheet. A maximum size for a negatively curved sheet is also predicted. Similarly, positive curvature is found to be energetically favored over zero curvature below some value of the curvature radius and above a certain number of atoms of the sheet. These results are discussed in view of available transmission electron microscopy observations of sp2 amorphous carbon.

Hypothetical graphite structures with negative gaussian curvature

1993 ◽  
Vol 343 (1667) ◽  
pp. 113-127 ◽  
Keyword(s):  
Constant Curvature ◽  
Gaussian Curvature ◽  
Minimal Surfaces ◽  
Hyperbolic Plane ◽  
Negative Curvature ◽  
Positive Curvature ◽  
Three Dimensions ◽  
Ring Size ◽  
Two Dimensional ◽  
Planar Lattice

We consider the geometries of hypothetical structures, derived from a graphite net by the inclusion of rings of seven or eight bonds, which may be periodic in three dimensions. Just as the positive curvature of fullerene sheets is produced by the presence of pentagons, so negative curvature appears with a mean ring size of more than six. These structures are based on coverings of periodic minimal surfaces, and surfaces parallel to these, which are known as exactly defined mathematical objects. In the same way that the cylindrical and conical structures can be generated (geometrically) by curving flat sheets so that the perimeter of a ring can be identified with a vector in the two-dimensional planar lattice, so these structures can be related to tessellations of the hyperbolic plane. The geometry of transformations at constant curvature relates various surfaces. Some of the proposed structures, which are reviewed here, promise to have lower energies than those of the convex fullerenes

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