journal article·2020-01

Determination of particle size distributions and transformation enthalpies from the temperature course of a phase transformation

Dieter Vollath

Journal of Nanoparticle Research· Volume 22· Issue 1
Publisher page

Abstract

The presented analysis of the temperature course of a phase transformation of nanoparticles offers a powerful tool to obtain data for the particle size distribution and the enthalpy of transformation. The analysis starts with the temperature distribution within an ensemble of nanoparticles and a functional relation between particle size and transformation temperature. In contrast to the Maxwell-Boltzmann distribution, in case of nanoparticles, the distribution of the temperature of the particles follows a normal distribution. Finally a reliable characterization of the specimen and the transformation in question are presented. These results, particularly the particle size distribution, represent – in many cases – a statistically more significant result as compared to the outcome, obtained by evaluation of electron micrographs. Looking at the problems of microcalorimetric determination of reaction enthalpies, one may realize comparable problems. By comparison of the experimental data with the calculated ones, one may obtain additional information about the interaction of the particles within the ensemble.
Source: openaire · Quality: candidate unverified · Source record ↗

Research context

OpenAlex topics: nanoparticles nucleation surface interactions · thermodynamics and calorimetric analyses · Material Dynamics and Properties

SciVX discovery tags are terminology-based. OpenAlex topics are source-provided classifications.

References (22)

Show source-provided references
1. Arblaster JW (2016) Thermodynamic properties of gold. JPEDAV 37:229–24510.1007/s11669-016-0449-z ↗
2. Bostanjoglo O, Röhkel K (1972) Superferromagnetism in gadolinium films. Phys Status Solidi A 11:161–16610.1002/pssa.2210110117 ↗
3. Clusius K, Schachinger L (1952) Ergebnisse der Tieftemperaturforschung IX. Die Atomwärme des Kobalts zwischen 15° und 270° K., L, Z. Naturforsch A 7:185–19110.1515/zna-1952-0209 ↗
4. Horowitz M, Silvidi AA, Malaker SF, Daunt JG (1952) The specific heat of lead in the temperature range 1 K to 75 K. Phys Rev 88:1182–118610.1103/PhysRev.88.1182 ↗
5. http://hyperphysics.phy-astr.gsu.edu/hbase/Solids/chrlen.html. Accessed September 23,2019.
6. Jaynes ET (1965) Gibbs vs Boltzmann entropies. Am J Phys 33:391–39810.1119/1.1971557 ↗
7. Li WH, Yang CC, Tsao FC, Lee KC (2003) Quantum size effects on the superconducting parameters of zero-dimensional Pb nanoparticles. Phys Rev B 68(184507):1–6
8. London H (1940) The high-frequency resistance of superconducting tin. Proc R Soc Lond A 176:522–53310.1098/rspa.1940.0105 ↗
9. Meschede D (2004) Gehrtsen Physik. Springer, Berlin Heidelberg pp 883–888
10. Mørup S, Madsen MB, Franck J, Villadsen J, Koch CJW (1983) A new interpretation of Mössbauer spectra of microcrystalline goethite: "super-ferromagnetism" or "super-spin-glass" behavior? J Magn Magn Mater 40:163–17410.1016/0304-8853(83)90024-0 ↗
11. Neeleshwar S, Chen YY, Wang CR, Ou MN, Huang PH (2004) Superconductivity in aluminum nanoparticles. Physica C 408–410:209–21010.1016/j.physc.2004.02.081 ↗
12. Pawlow PN (1909) Über die Abhängigkeit des Schmelzpunktes von der Oberflächenenergie eines festen Körpers. Z Phys Chem 65:545–54810.1515/zpch-1909-6532 ↗
13. Rupp J, Birringer R (1987) Enhanced specific-heat-capacity (cp) measurements (150–300 K) of nanometer-sized crystalline materials. Phys Rev B 36:7888–789010.1103/PhysRevB.36.7888 ↗
14. Shan J, Chen Nuopponen M, Tenhu H (2004) Two phase transitions of poly(N-isopropylacrylamide) brushes bound to gold nanoparticles. Langmuir 20:4671–467610.1021/la0363938 ↗
15. Tinkham M (2000) Limits on superconductivity in nanoparticles and nanowires. J Supercond Nov Magn 13:801–80410.1023/A:1007847122807 ↗
16. Vojta G, Vojta M (2000) Teubner Taschernbuch der statistischen Physik. B.G. Teubner, Stuttgart, pp 161–16310.1007/978-3-322-80009-1 ↗
17. Vollath D (2011) Estimation of particle size distributions obtained by gas phase processes. J Nanopart Res 13:3899–390910.1007/s11051-011-0343-x ↗
18. Vollath D (2019) Energy distribution in an ensemble of nanoparticles and its consequences. Beilstein J Nanotechnol 10:1452–145710.3762/bjnano.10.143 ↗
19. Vollath D, Fischer F-D, Holec D (2018) Surface energy of nanoparticles – influence of particle size and structure. Beilstein J Nanotechnol 9:2265–227610.3762/bjnano.9.211 ↗
20. von Delft J (2001) Superconductivity in ultrasmall metallic grains. Ann Phys (Leipzig) 10(3):219–27610.1002/1521-3889(200103)10:3<219::AID-ANDP219>3.0.CO;2-I ↗
21. Woods SI, Kirtley JR, Sun S, Koch RH (2001) Direct investigation of superparamagnetism in Co nanoparticle films. Phys Rev Lett 87(137205):1–4
22. Zhu M-Q, Wang L-Q, Exarhos GJ, Li ADQ (2004) Thermosensitive gold nanoparticles. J Am Chem Soc 126:2656–265710.1021/ja038544z ↗