Surface energy and shrinkage of a nanocavity

Ouyang, Gang; Tan, Xin; Cai, Maoqi; Yang, Guo

doi:10.1063/1.2374808

Cited by 29 publications

(44 citation statements)

References 28 publications

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“…The large inner‐surface energy can lead to the effective elastic modulus of the surface with a negative curvature being larger than that of the plane case 16. Importantly, the inner skin of nanocavities will undergo local hardening owing to the local bond stiffening around nanocavities when the void size becomes small 16–17. However, there are not any quantitative theories to predict the mechanical responses of nanoporous structures when the cylindrical pore size is in the range of several nanometers 2.…”

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confidence: 99%

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Nanoporous Structures: Smaller is Stronger

Ouyang

Yang

Sun

et al. 2008

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Nanoporous structures have become the focus of intensive research in recent years owing to their unique applications in mesoscopic physics and chemistry, and potential technological applications, including sensing, catalysis, DNA translocation, and as templates for nanostructure self-assembly. [1][2][3][4][5][6] The study of nanoporous structures such as nanopore-, nanocavity-, and nanochannel-array materials can afford a deep understanding of the new scientific results in such good systems with negative curvature surface. As the number of atoms near the inner surface of nanoporous structures is very large relative to the total number of atoms, the surface effects on the physical and chemical properties can be dominant. It is well known that many physical properties of nanomaterials and nanostructures such as melting temperature, surface free energy, elastic modulus, and cohesive energy show strong size effects. [7][8][9] Nanoporous materials with large internal surface area have been more extensively employed than other nanomaterials as good host materials in nanotechnology. [10] For example, nanoporous structures and nanocavities show a novel sink effect to capture molecules, and the effect can be controlled by tuning the pore size and porosity. [2] Since the lower coordination of atoms of nanoporous structures can lead to the redistribution of electronic charge and change the cohesive energy of single atoms in a matrix, the mechanical responses differ from those of atoms in the bulk counterpart. Additionally, the mechanical applications of nanoporous structures are currently an important subject of much research. Thus, numerous expressions about the porosity dependence of the isotropic elastic modulus have been developed by effective medium theory. [11][12] The effective elastic modulus is suitable for describing the mechanical properties of nanoporous structures. In general, the effective elastic modulus of porous material is expressed as the elastic module of the matrix and the porosity inclusion in the materials. [13] However, the surface elasticity of nanostructures is different from the bulk, which is generalized by the Young-Laplace equation based on the mechanical equilibrium principle. [14] Dual et al. pointed out that the stiffness of nanoporous materials may be made to exceed those of the nonporous counterpart bulk by satisfying certain surface modifications. [15] In fact, nanoporous structures are similar with nanocavities with negative curvature of inner surface in matrix.Sentence ambiguous. Please rephrase. The large innersurface energy can lead to the effective elastic modulus of the surface with a negative curvature being larger than that of the plane case. [16] Importantly, the inner skin of nanocavities will undergo local hardening owing to the local bond stiffening around nanocavities when the void size becomes small. [16][17] However, there are not any quantitative theories to predict the mechanical responses of nanoporous structures when the cylindrical pore size is in the range of several ...

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confidence: 99%

“…Similarly, the density of the elastic strain energy increases as the cylindrical pore size decreases. Thus, according to our previous considerations,8, 17 the inner‐surface free energy ( γ ) of a cylindrical pore of nanoporous structures can be written as Equation (1): …”

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confidence: 99%

Nanoporous Structures: Smaller is Stronger

Ouyang

Yang

Sun

et al. 2008

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“…Since the structural portion of the surface energy density due to surface relaxation has a minor effect on the size-dependent behavior of a nanostructure's surface energy density, 9,13 we take the total Helmholtz free energy per unit volume as c = c chem where c chem represents the chemical portion of the excess surface free energy density, 9,13 and…”

Section: Continuum-based Frameworkmentioning

confidence: 99%

“…[4][5][6][7][8][9][10][11] Furthermore, thermodynamic models based on density functional theory (DFT) calculations and theoretical approaches also show that the surface energy reduces with decreasing size of a nanostructure. 1,9,[12][13][14][15] In particular, Ouyang et al 13 and Liang et al 5 have developed thermodynamic models by dividing the surface energy into the chemical and structural parts related to surface dangling bond energy and surface strain energy, respectively, and predicted that the size-dependent behaviour of the surface energy is dominated by its chemical part. By just considering the chemical part of the surface energy, Xiong et al 9 have developed a model based on the bond broken rule and the relaxation of bonds to predict the size-dependent surface energy of nanoparticles.…”

Section: Introductionmentioning

confidence: 99%

A continuum state variable theory to model the size-dependent surface energy of nanostructures

Jamshidian

Thamburaja

Rabczuk

2015

Phys. Chem. Chem. Phys.

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We propose a continuum-based state variable theory to quantify the excess surface free energy density throughout a nanostructure. The size-dependent effect exhibited by nanoplates and spherical nanoparticles i.e. the reduction of surface energy with reducing nanostructure size is well-captured by our continuum state variable theory. Our constitutive theory is also able to predict the reducing energetic difference between the surface and interior (bulk) portions of a nanostructure with decreasing nanostructure size.

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“…These empty cavities, due to their negative curvatures, contain high density of dangling bonds that exhibit high affinity for metallic contaminants and can act as impurity gettering sites [55]. Gettering of oxygen impurity atoms and structural defects in GaN by helium implantation has been reported [55][56][57]. [66].…”

Section: X-ray Diffraction (Xrd)mentioning

confidence: 99%