Assembling two-dimensional(2D)sheets into macroscopic three-dimensional(3D)forms has created a promising material family with rich functionalities.Multiscale wrinkles are intrinsic features of 2D sheets in their 3D as...Assembling two-dimensional(2D)sheets into macroscopic three-dimensional(3D)forms has created a promising material family with rich functionalities.Multiscale wrinkles are intrinsic features of 2D sheets in their 3D assembles.Therefore,the precise wrinkling modulation optimizes the transition of outstanding properties of 2D sheets to expected performances of assembled materials and dominates their fabrication process.The wrinkling evolution of 2D sheets assembling onto flat surfaces has been extensively understood,however,the wrinkling behaviors on the more generally curved surface still remain unclear.Here,we investigate the wrinkling behaviors of graphene oxide sheets assembled onto curved surfaces and reveal the selection rule of wrinkling modes that determined by the curvature mismatch between 2D sheets and target surfaces.We uncover that three wrinkling modes including isotropic cracked land,labyrinth,and anisotropic curtain phases,respectively emerge on flat,spherical,and cylindrical surfaces.A favorable description paradigm is offered to quantitatively measure the complex wrinkling patterns and assess the curvature mismatch constraint underlying the wrinkling mode selection.This research provides a general and quantitative description framework of wrinkling modulation of 2D materials such as high performance graphene fibers,and guides the precise fabrication of particles and functional coatings.展开更多
In this paper,we give the classification of the singularities of hyperbolic Darboux image and rectifying Gaussian surface of nonlightlike curve in Minkowski 3-space.We establish the relationship between the singularit...In this paper,we give the classification of the singularities of hyperbolic Darboux image and rectifying Gaussian surface of nonlightlike curve in Minkowski 3-space.We establish the relationship between the singularities and the geometric invariants of curves which are deeply related to its order of contact with helices.展开更多
基金supported by the National Natural Science Foundation of China(Nos.52122301,51973191,52090030,and 51533008)Hundred Talents Program of Zhejiang University(No.188020*194231701/113)+2 种基金Key Research and Development Plan of Zhejiang Province(No.2018C01049)Shanxi-Zheda Institute of New Materials and Chemical Engineering(No.2012SZ-FR004)the Fundamental Research Funds for the Central Universities(Nos.K20200060,2017QNA4036,and 2017XZZX001-04).
文摘Assembling two-dimensional(2D)sheets into macroscopic three-dimensional(3D)forms has created a promising material family with rich functionalities.Multiscale wrinkles are intrinsic features of 2D sheets in their 3D assembles.Therefore,the precise wrinkling modulation optimizes the transition of outstanding properties of 2D sheets to expected performances of assembled materials and dominates their fabrication process.The wrinkling evolution of 2D sheets assembling onto flat surfaces has been extensively understood,however,the wrinkling behaviors on the more generally curved surface still remain unclear.Here,we investigate the wrinkling behaviors of graphene oxide sheets assembled onto curved surfaces and reveal the selection rule of wrinkling modes that determined by the curvature mismatch between 2D sheets and target surfaces.We uncover that three wrinkling modes including isotropic cracked land,labyrinth,and anisotropic curtain phases,respectively emerge on flat,spherical,and cylindrical surfaces.A favorable description paradigm is offered to quantitatively measure the complex wrinkling patterns and assess the curvature mismatch constraint underlying the wrinkling mode selection.This research provides a general and quantitative description framework of wrinkling modulation of 2D materials such as high performance graphene fibers,and guides the precise fabrication of particles and functional coatings.
基金the National Natural Science Foundation of China （No. 10471020） the Program for New Century Excellent Talents in University of China （No. 05-0319）.
文摘In this paper,we give the classification of the singularities of hyperbolic Darboux image and rectifying Gaussian surface of nonlightlike curve in Minkowski 3-space.We establish the relationship between the singularities and the geometric invariants of curves which are deeply related to its order of contact with helices.
