Surface energy of nanoparticles – influence of particle size and structure

Dieter Vollath, Franz Dieter Fischer and David Holec

Beilstein J. Nanotechnol. 2018, 9, 2265–2276. https://doi.org/10.3762/bjnano.9.211

Cite the Following Article

Dieter Vollath, Franz Dieter Fischer and David Holec

Beilstein J. Nanotechnol. 2018, 9, 2265–2276. https://doi.org/10.3762/bjnano.9.211

How to Cite

Vollath, D.; Fischer, F. D.; Holec, D. Beilstein J. Nanotechnol. 2018, 9, 2265–2276. doi:10.3762/bjnano.9.211

Download Citation

Citation data can be downloaded as file using the "Download" button or used for copy/paste from the text window below.
Citation data in RIS format can be imported by all major citation management software, including EndNote, ProCite, RefWorks, and Zotero.

File format:

RIS

BibTeX

Include:

Citation for the article above

Citation and complete reference list for the article above

Download

TY  - JOUR
A1  - Vollath, Dieter
A1  - Fischer, Franz Dieter
A1  - Holec, David
T1  - Surface energy of nanoparticles – influence of particle size and structure
JF  - Beilstein Journal of Nanotechnology
PY  - 2018///
VL  - 9
SP  - 2265
EP  - 2276
SN  - 2190-4286
DO  - 10.3762/bjnano.9.211
PB  - Beilstein-Institut
JA  - Beilstein J. Nanotechnol.
UR  - https://doi.org/10.3762/bjnano.9.211
KW  - ab initio calculations
KW  - classical thermodynamics
KW  - molecular dynamics simulation
KW  - surface energy
KW  - surface layer
N2  - The surface energy, particularly for nanoparticles, is one of the most important quantities in understanding the thermodynamics of particles. Therefore, it is astonishing that there is still great uncertainty about its value. The uncertainty increases if one questions its dependence on particle size. Different approaches, such as classical thermodynamics calculations, molecular dynamics simulations, and ab initio calculations, exist to predict this quantity. Generally, considerations based on classical thermodynamics lead to the prediction of decreasing values of the surface energy with decreasing particle size. This phenomenon is caused by the reduced number of next neighbors of surface atoms with decreasing particle size, a phenomenon that is partly compensated by the reduction of the binding energy between the atoms with decreasing particle size. Furthermore, this compensating effect may be expected by the formation of a disordered or quasi-liquid layer at the surface. The atomistic approach, based either on molecular dynamics simulations or ab initio calculations, generally leads to values with an opposite tendency. However, it is shown that this result is based on an insufficient definition of the particle size. A more realistic definition of the particle size is possible only by a detailed analysis of the electronic structure obtained from initio calculations. Except for minor variations caused by changes in the structure, only a minor dependence of the surface energy on the particle size is found. The main conclusion of this work is that surface energy values for the equivalent bulk materials should be used if detailed data for nanoparticles are not available.
ER  -

Presentation Graphic

Picture with graphical abstract, title and authors for social media postings and presentations.
Format: PNG	Size: 353.3 KB	Download

Citations to This Article

Up to 20 of the most recent references are displayed here.

Scholarly Works

Liu, P.; Ma, S.; Zhang, J.; Huang, Y.; Liu, Y.; Wang, Z. Formation of ultra-stable Au nanoparticles in Au–ZrO2 nanocomposites. Journal of Materials Science & Technology 2025, 217, 104–115. doi:10.1016/j.jmst.2024.08.007
Pajzderska, A.; González, M. A.; Jarek, M.; Mielcarek, J.; Wąsicki, J. Physical Stability and Molecular Mobility of Resveratrol in a Polyvinylpyrrolidone Matrix. Molecules 2025, 30, 1909. doi:10.3390/molecules30091909
Bocquet, H.; Kleibert, A.; Derlet, P. M. Impact of Planar Defects on the Reversal Time of Single Magnetic Domain Nanoparticles. Physical review letters 2025, 134, 136702. doi:10.1103/physrevlett.134.136702
Xu, X.; Li, P.; Wu, J.; Li, Y.; Zhang, D.; Qiu, S. Preparation, microstructure and properties of solar thermal storage Nano-ZrO2-corundum-mullite composite ceramics. Ceramics International 2025, 51, 11914–11927. doi:10.1016/j.ceramint.2025.01.043
Ding, R.; Martini, A.; Jacobs, T. D. Mechanical Behavior and Size–Dependent Strength of Small Noble-Metal Nanoparticles. Acta Materialia 2025, 121092. doi:10.1016/j.actamat.2025.121092
Tummino, M. L.; Liotta, L. F.; Lo Faro, M.; Campagna Zignani, S.; Deganello, F. Effects of B‐site doping and stoichiometry on strontium ferrate Sr0.85Ce0.15FexCoyO3 perovskites as electrocatalysts. Journal of the American Ceramic Society 2025, 108. doi:10.1111/jace.20528
Rajapantulu, A.; Bandyopadhyaya, R. Role of Hydrazine and Size-Tuning Parameter in Gold Nanoparticle Synthesis by Water-in-Oil Microemulsion: Experiment and Simulation. Langmuir : the ACS journal of surfaces and colloids 2025, 41, 8049–8059. doi:10.1021/acs.langmuir.4c04174
Cao, Y.; Ding, C.; Han, H.; Ma, T.; Zhong, W.; Ye, H.; Chen, L.; Guo, M.; He, W.; Guo, K. The self-assembly stacked ladder-like CoFe2O4 in the peroxymonosulfate activation for antibiotic degradation. Chemical Engineering Science 2025, 311, 121582. doi:10.1016/j.ces.2025.121582
Khalaf, S. F.; AL-Rashid, S. N. T. Size-dependent cohesive energy, melting temperature, and debye temperature of Ag and Au nanoparticles: a theoretical and comparative study. Journal of Nanoparticle Research 2025, 27. doi:10.1007/s11051-025-06267-5
Lee, S.; Jeon, J. Particle-Size Distribution and Light-Extinction Characteristics of Smoke Generated from Plastics (PMMA, PC) under Radiative Heat Flux. Fire Science and Engineering 2025, 39, 9–21. doi:10.7731/kifse.5b619761
Vollath, D. Simulation of Agglomeration Processes Using Stochastic Processes—Case of Limited Space in a Box. Micro 2025, 5, 8. doi:10.3390/micro5010008
Pant, S.; Pathak, R. K.; Singh, D. B.; Kim, J.-M. Applications of Nano-bioinformatics in Livestock Research. Bioinformatics in Veterinary Science; Springer Nature Singapore, 2025; pp 471–494. doi:10.1007/978-981-97-7395-4_19
Chen, Y.-J.; Chang, T.-L.; Wu, Q.-X.; Ke, K.-C.; Chiu, P.-S.; Chen, C.-T. Investigation and predictive multi-modeling of PVA/PVP-blended nanofiber diameter in electrospinning. The International Journal of Advanced Manufacturing Technology 2025, 136, 2445–2453. doi:10.1007/s00170-024-14948-z
Sherbini, A. E.; Aboulfotouh, A.; Sherbini, T. E. On the Similarity and Differences Between Nano-Enhanced Laser-Induced Breakdown Spectroscopy and Nano-Enhanced Laser-Induced Plasma Spectroscopy in Laser-Induced Nanomaterials Plasma. Quantum Beam Science 2024, 9, 1. doi:10.3390/qubs9010001
Ghareeb, A.; Fouda, A.; Kishk, R. M.; El Kazzaz, W. M. Unlocking the potential of titanium dioxide nanoparticles: an insight into green synthesis, optimizations, characterizations, and multifunctional applications. Microbial cell factories 2024, 23, 341. doi:10.1186/s12934-024-02609-5
Sico, G.; Guarino, V.; Borriello, C.; Montanino, M. Studies on Morphological Evolution of Gravure-Printed ZnO Thin Films Induced by Low-Temperature Vapor Post-Treatment. Nanomaterials (Basel, Switzerland) 2024, 14, 2006. doi:10.3390/nano14242006
Khurshid, F.; Muthu, J.; Wang, Y.-Y.; Wang, Y.-W.; Shih, M.-C.; Chen, D.-R.; Lu, Y.-J.; Austin, D.; Glavin, N.; Plšek, J.; Kalbáč, M.; Hsieh, Y.-P.; Hofmann, M. The Importance of Catalytic Effects in Hot-Electron-Driven Chemical Reactions. ACS nano 2024, 18, 34332–34340. doi:10.1021/acsnano.4c12923
Katheras, A. S.; Karalis, K.; Krack, M.; Scheinost, A. C.; Churakov, S. V. Computational Study on the Octahedral Surfaces of Magnetite Nanoparticles and Their Solvent Interaction. Environmental science & technology 2024, 58, 21068–21076. doi:10.1021/acs.est.4c06531
Mustak, M. H.; Islam, K. S.; Alam, M. S.; Karim, M. M.; Khan, G. M. A. Revalorization of Coconut Husk Lignin Through ZnO Nanoparticles Synthesis: Antibacterial Assay and Photocatalytic Activities. Waste and Biomass Valorization 2024, 16, 1839–1853. doi:10.1007/s12649-024-02773-0
Nie, S.; Wu, L.; Liu, Q.; Wang, X. Entropy-Derived Synthesis of the CuPd Sub-1nm Alloy for CO2-to-acetate Electroreduction. Journal of the American Chemical Society 2024, 146, 29364–29372. doi:10.1021/jacs.4c07711

Explore citations to this article at

Back To Article

Other Beilstein-Institut Open Science Activities

aromatic	the word “aromatic”
aromatic aldehyde	the word “aromatic” OR “aldehyde”
+aromatic +aldehyde	both words “aromatic” AND “aldehyde”
+aromatic -aldehyde	the word “aromatic” but NOT “aldehyde”
“aromatic aldehyde”	the exact phrase “aromatic aldehyde”
benz*	words which begin with “benz”, such as “benzene” or “benzyl”
benz*yl	words that begin with “benz” and end with “yl”, such as “benzyl” or “benzoyl”
benzyl~	words that are close to the word “benzyl”, such as “benzoyl” (i.e., fuzzy search)