This article deals with melting/freezing point depression due to very small particle size. For depression due to the mixture of another compound, see freezing-point depression. Melting-point depression is the phenomenon of reduction of the melting point of a material with a reduction of its size. This phenomenon is very prominent in nanoscale materials, which melt at temperatures hundreds of degrees lower than bulk materials.
Introduction The melting temperature of a bulk material is not dependent on its size. However, as the dimensions of a material decrease towards the atomic scale, the melting temperature scales with the material dimensions. The decrease in melting temperature can be on the order of tens to hundreds of degrees for metals with nanometer dimensions. Melting-point depression is most evident in nanowires, nanotubes, and nanoparticles, which all melt at lower temperatures than bulk amounts of the same material. Changes in melting point occur because nanoscale materials have a much larger surface-to-volume ratio than bulk materials, drastically altering their thermodynamic and thermal properties. Melting-point depression was mostly studied for nanoparticles, owing to their ease of fabrication and theoretical modeling. The melting temperature of a nanoparticle decreases sharply as the particle reaches critical diameter, usually < 50 nm for common engineering metals.
Melting point depression is a very important issue for applications involving nanoparticles, as it decreases the functional range of the solid phase. Nanoparticles are currently used or proposed for prominent roles in catalyst, sensor, medicinal, optical, magnetic, thermal, electronic, and alternative energy applications. Nanoparticles must be in a solid state to function at elevated temperatures in several of these applications.
Measurement techniques Two techniques allow measurement of the melting point of the nanoparticle. The electron beam of a transmission electron microscope (TEM) can be used to melt nanoparticles. The melting temperature is estimated from the beam intensity, while changes in the diffraction conditions to indicate phase transition from solid to liquid. This method allows direct viewing of nanoparticles as they melt, making it possible to test and characterize samples with a wider distribution of particle sizes. The TEM limits the pressure range at which melting point depression can be tested. More recently, researchers developed nanocalorimeters that directly measure the enthalpy and melting temperature of nanoparticles. Nanocalorimeters provide the same data as bulk calorimeters, however, additional calculations must account for the presence of the substrate supporting the particles. A narrow size distribution of nanoparticles is required since the procedure does not allow users to view the sample during the melting process. There is no way to characterize the exact size of melted particles during the experiment.
History Melting point depression was predicted in 1909 by Pawlow. It was directly observed inside an electron microscope in the 1960s–70s for nanoparticles of Pb, Au, and In.
Physics Nanoparticles have a much greater surface-to-volume ratio than bulk materials. The increased surface-to-volume ratio means surface atoms have a much greater effect on the chemical and physical properties of a nanoparticle. Surface atoms bind in the solid phase with less cohesive energy because they have fewer neighboring atoms in close proximity compared to atoms in the bulk of the solid. Each chemical bond an atom shares with a neighboring atom provides cohesive energy, so atoms with fewer bonds and neighboring atoms have lower cohesive energy. The cohesive energy of the nanoparticle has been theoretically calculated as a function of particle size according to Equation 1.
E = E B ( 1 − d D ) {\displaystyle E=E_{B}\left(1-{\frac {d}{D}}\right)}
Where: D = nanoparticle size
d = atomic size Eb = cohesive energy of bulk As Equation 1 shows, the effective cohesive energy of a nanoparticle approaches that of the bulk material as the material extends beyond the atomic size range (D>>d). Atoms located at or near the surface of the nanoparticle have reduced cohesive energy due to a reduced number of cohesive bonds. An atom experiences an attractive force with all nearby atoms according to the Lennard-Jones potential.
The cohesive energy of an atom is directly related to the thermal energy required to free the atom from the solid. According to Lindemann's criterion, the melting temperature of a material is proportional to its cohesive energy, av (TM=Cav). Since atoms near the surface have fewer bonds and reduced cohesive energy, they require less energy to free from the solid phase. Melting point depression of high surface-to-volume ratio materials results from this effect. For the same reason, surfaces of nanomaterials can melt at lower temperatures than the bulk material. The theoretical size-dependent melting point of a material can be calculated through classical thermodynamic analysis. The result is the Gibbs–Thomson equation shown in Equation 2.
T M ( d ) = T M B ( 1 − 4 σ s l H f ρ s d ) {\displaystyle T_{M}(d)=T_{MB}\left(1-{\frac {4\sigma \,_{sl}}{H_{f}\rho \,_{s}d}}\right)}
Where: TMB = bulk melting temperature
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