A universal method to calculate the surface energy density of spherical surfaces in crystals

Wang, Jian; Bian, Jianjun; Niu, Xinrui; Wang, Gangfeng

doi:10.1007/s10409-016-0605-z

Cited by 6 publications

(6 citation statements)

References 31 publications

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“…Hence, the curvature effect will be non-negligible when the surface curvatures become larger than 1/5 nm −1 , which is in consistent with the conclusion mentioned in Ref. [ 21 ].…”

Section: Resultssupporting

confidence: 91%

“…Through extensive theoretical calculations of the surface tension of most of the liquid metals, Aqra et al used the fraction of broken bonds in liquid metals to calculate surface tension and surface energy [ 19 , 20 ]. An analytical approach is developed to estimate the surface energy density of spherical surfaces through that of planar surfaces using a geometrical analysis and the scaling law [ 21 ].…”

Section: Introductionmentioning

confidence: 99%

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Surface Energy of Curved Surface Based on Lennard-Jones Potential

Wang

Peng

et al. 2021

Nanomaterials

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Although various phenomena have confirmed that surface geometry has an impact on surface energy at micro/nano scales, determining the surface energy on micro/nano curved surfaces remains a challenge. In this paper, based on Lennard-Jones (L-J) pair potential, we study the geometrical effect on surface energy with the homogenization hypothesis. The surface energy is expressed as a function of local principle curvatures. The accuracy of curvature-based surface energy is confirmed by comparing surface energy on flat surface with experimental results. Furthermore, the surface energy for spherical geometry is investigated and verified by the numerical experiment with errors within 5%. The results show that (i) the surface energy will decrease on a convex surface and increase on a concave surface with the increasing of scales, and tend to the value on flat surface; (ii) the effect of curvatures will be obvious and exceed 5% when spherical radius becomes smaller than 5 nm; (iii) the surface energy varies with curvatures on sinusoidal surfaces, and the normalized surface energy relates with the ratio of wave height to wavelength. The curvature-based surface energy offers new insights into the geometrical and scales effect at micro/nano scales, which provides a theoretical direction for designing NEMS/MEMS.

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“…Hence, the curvature effect will be non-negligible when the surface curvatures become larger than 1/5 nm −1 , which is in consistent with the conclusion mentioned in Ref. [ 21 ].…”

Section: Resultssupporting

confidence: 91%

Section: Introductionmentioning

confidence: 99%

Surface Energy of Curved Surface Based on Lennard-Jones Potential

Wang

Peng

et al. 2021

Nanomaterials

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“…This surface energy density is highly dependent on the nanoparticles size. Two opposite trends of size-dependent surface energy density of nanomaterials have, however, been reported by different studies [19][20][21]. Yin Yao et al reported that surface energy density decreases with the increase in nanoparticles size [22].…”

Section: Hr-tem Observations Of Nanofluidsmentioning

confidence: 94%

“…Yin Yao et al reported that surface energy density decreases with the increase in nanoparticles size [22]. In another recent study by Wang et al, atomic simulations done to calculate the surface energy density of spherical nanosurfaces found that the average surface energy density almost remains constant once its radius exceeds 5 nm [21].…”

Section: Hr-tem Observations Of Nanofluidsmentioning

confidence: 99%

Nanostructuring of 1-butyl-4-methylpyridinium chloride in ionic liquid–iron oxide nanofluids

Joseph

Fal

Żyła

et al. 2018

J Therm Anal Calorim

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Understanding the behavior of ionic liquids (ILs) in ionic liquid-based nanofluids has great significance for its proper application. The phase changes and solidification observed in most ILs offer a great challenge to nanoparticles stabilization. Herein, we have synthesized and characterized a new type of IL-based iron oxide nanofluids using 1-butyl-4-methylpyridinium chloride. We have investigated the formation of dendrite-like nanostructures by 1-butyl-4-methylpyridinium chloride at the IL-nanoparticle interface. This solidification induced under high electric field was nanoparticle size dependent and may be controlled by temperature and frequency changes. Examining the rheological behavior showed that higher volume fraction of nanoparticles in this nanofluids drastically decreased the flow viscosity causing a crossover from non-Newtonian (pure IL) to Newtonian and then to shear-thinning behavior. The nanofluid stability also decreased with the increase in nanoparticle size.

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“…The coupling between γ and particle size aligns with previous reports on crystalline NPs. 33,40 Such ambiguity in evaluating γ bring difficulty is supporting continuum models of NPs evolution by atomistic simulations.…”

Section: Appendixmentioning

confidence: 99%

Mesoscale Model for Ostwald Ripening of Catalyst Nanoparticles

Bucci

Gadelrab

Carter

2021

J. Electrochem. Soc.

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A mesoscale model is proposed to characterize coarsening of platinum-based catalyst particles with the aim of understanding cathode degradation and power loss in proton exchange membrane fuel cells (PEMFC). The microstructure of a cathode catalyst layer is more complex than the ones typically described by Ostwald-ripening models, such as the Lifshitz and Slyozov and Wagner (LSW) theory or diffuse interface models. Our model captures the dissolution kinetics of the catalyst material, and the diffusivity of the ions in solution. The network structure of the model embeds the tortuosity of the microstructure and the effect of water content on Pt-ion mobility. Detailed diffusional interactions among catalyst particles are explicitly described with the aim of providing statistically averaged properties of coarsening ensembles. Through numerical tests, the scaling of coarsening kinetics is predicted as function of voltage. The effect of voltage cycling, and initial particle size distribution are also probed. The power-law exponents for the mean square radius vs time are affected by the reduced dimensionality of inter-particle diffusion, constrained by the carbon support and the surface wetting. This theoretical framework can be used to understand how material design influences the degradation pathways that are responsible for platinum surface area loss.

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A universal method to calculate the surface energy density of spherical surfaces in crystals

Cited by 6 publications

References 31 publications

Surface Energy of Curved Surface Based on Lennard-Jones Potential

Surface Energy of Curved Surface Based on Lennard-Jones Potential

Nanostructuring of 1-butyl-4-methylpyridinium chloride in ionic liquid–iron oxide nanofluids

Mesoscale Model for Ostwald Ripening of Catalyst Nanoparticles

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