Size-dependent elastic properties of spherical nanoparticles: a nonlocality-emerged surface model

doi:10.1007/s10483-025-3323-6

Abstract

Abstract:

The incomplete understanding of nanoscale surface interactions arising from underlying atomistic long-range forces limits our ability to simulate and design their performance. In this paper, the surface elasticity is constructed from underlying atomistic nonlocal interactions in spherical nanoparticles. By introducing an intrinsic length scale, we quantify the surface region thickness, and demonstrate the progressive elastic modulus transition caused by asymmetric atomistic nonlocal interactions. The universal surface scaling law, relating the intrinsic length scale to the particle dimensions, is established, and a surface-dominated criterion is developed for quantifying the transition to the surface-dominated behaviors. The model is thoroughly validated through the molecular static simulations and experimental data with the material-specific intrinsic length constants.

Key words: nonlocal elasticity theory, nanoparticle, size-dependent, elastic modulus, intrinsic length

2010 MSC Number:

O343

Ruozhen ZHANG, Li LI. Size-dependent elastic properties of spherical nanoparticles: a nonlocality-emerged surface model. Applied Mathematics and Mechanics (English Edition), 2025, 46(12): 2281-2296.

TrendMD

Figures/Tables 10

Fig. 1

Fig. 2

Fig. 3

Fig. 4

Fig. 5

Fig. 6

Fig. 7

Fig. 8

Table 1

Material parameters"

Material	$λ$	$ρ b$ /(g·cm^-3)	$A r$	Mass of $12 C$ /g	$M a$ /g
Au	1.659	19.32	197	$1.66 × 10 − 24$	$3.270 × 10 − 22$
Pt	1.659	21.45	195	$1.66 × 10 − 24$	$3.237 × 10 − 22$
Al	1.659	2.70	27	$1.66 × 10 − 24$	$4.482 × 10 − 23$
Ag	1.659	10.49	108	$1.66 × 10 − 24$	$1.793 × 10 − 22$
Fe	1.659	7.86	56	$1.66 × 10 − 24$	$9.296 × 10 − 23$
Cu	1.659	8.96	64	$1.66 × 10 − 24$	$10.620 × 10 − 22$

Table 1

Fig. 9

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