Size-dependent melting of nanoparticles: Hundred years of thermodynamic model

Thermodynamic model first published in 1909, is being used extensively to understand the size-dependent melting of nanoparticles. Pawlow deduced an expression for the size-dependent melting temperature of small particles based on the thermodynamic model which was then modified and applied to different nanostructures such as nanowires, prism-shaped nanoparticles, etc. The model has also been modified to understand the melting of supported nanoparticles and superheating of embedded nanoparticles. In this article, we have reviewed the melting behaviour of nanostructures reported in the literature since 1909. This article is dedicated to Indian Institute of Science which is also celebrating its centenary this year.     

Molecular dynamics simulations on the melting of gold nanoparticles

Molecular dynamics is employed to study the melting of bulk gold and gold nanoparticles. PCFF, Sutton-Chen and COMPASS force fields are adopted to study the melting point of bulk gold and we find out that the Sutton-Chen force field is the most accurate model in predicting the melting point of bulk gold. Consequently, the Sutton-Chen force field is applied to study the melting points of spherical gold nanoparticles with different diameters. Variations of diffusion coefficient, potential energy and translational order parameter with temperature are analyzed. The simulated melting points of gold nanoparticles are between 615～1115 K, which are much lower than that of bulk gold (1336 K). As the diameter of gold nanoparticle drops, the melting point also descends. The melting mechanism is also analyzed for gold nanoparticles.     

Modeling the cohesive energy and melting point of nanoparticles by their average coordination number

We present a relation between the average coordination number and the cohesive energy for nanoparticles that shows that the ratio of nanoparticles cohesive energy to the bulk value is equal to the ratio of the nanoparticles average coordination number to that of the bulk. We consider the effect of lattice and surface packing factors on the average coordination numbers of the atoms in the nanoparticle. The melting temperature of nanoparticles has been calculated from the obtained relation for cohesive energy, and predictions for the cohesive energy and melting temperature of the nanoparticles have been compared with other theoretical models and available experimental data and the results of molecular dynamics simulations.     

Superheating and solid-liquid phase coexistence in nanoparticles with nonmelting surfaces

We present a phenomenological model of melting in nanoparticles with facets that are only partially wet by their liquid phase. We show that in this model, as the solid nanoparticle seeks to avoid coexistence with the liquid, the microcanonical melting temperature can exceed the bulk melting point and that the onset of coexistence is a first-order transition. We show that these results are consistent with molecular dynamics simulations of aluminum nanoparticles which remain solid above the bulk melting temperature.     

Compaction of agglomerates of aerosol nanoparticles: A compilation of experimental data

The compacting behavior of agglomerated aerosol nanoparticles in the size range between 7 and 150 nm was investigated using available literature data. We observed a characteristic behavior, which can be described by three separate steps. When comparing the first step, the compaction from agglomerates into spherules, differences could be observed for nanoparticles of different materials. It is seen from the available data that smaller particles compact at lower temperatures. For most materials where data available (Ag, Au, Fe, W, PbS and SnO₂), the compaction temperatures were found to lie in a temperature interval, between 1/3 and 1/2 of the bulk melting temperature. For the data available on TiO₂, on the other hand, the compaction temperature corresponds to about 2/3 of the bulk melting temperature. Thus, a fundamental difference might exist in the sintering behavior of titania as compared with other materials. This difference may be attributed to a lower degree of cleanliness of the titania particles.     

The origin of the redshift in Brillouin spectra of silica films containing tin nanoparticles

The abrupt change of velocity in surface acoustic waves in thin films of amorphous SiO_x containing nanometre scale -Sn crystals is shown to be directly associated with the size-dependent melting of the nanoparticles, confirming preliminary experiments. High resolution thin film powder diffraction using synchrotron radiation shows that the abrupt redshift in the Brillouin spectra satellites occurs at the same temperature as the melting of the nanoparticles, evident for the loss of the Bragg peaks. Effective medium theory is used to explain the origin of the anomaly. A central peak in the Brillouin spectrum, the intensity of which shows a maximum at the melting temperature, can be interpreted in terms of overdamped fluctuations in the dielectric function. The melting temperature as a function of particle size is in agreement with theoretical predictions. No evidence for strain could be found on the X-ray diffraction profiles; the a- and c-axis thermal expansion coefficients are the same as those in bulk tin. Received 30 March 2000 and Received in final form 24 July 2000     

Effects of iron oxide nanoparticles on polyvinyl alcohol: interfacial layer and bulk nanocomposites thin film

Iron oxide (α-phase) nanoparticles with coercivity larger than 300 Oe have been fabricated at a mild temperature by an environmentally benign method. The economic sodium chloride has been found to effectively serve as a solid spacer to disperse the iron precursor and to prevent the nanoparticles from agglomeration. Higher ratios of sodium chloride to iron nitrate result in smaller nanoparticles (19 nm for 20:1 and 14 nm for 50:1). The presence of polyvinyl alcohol (PVA) limits the particle growth (15 nm for 20:1 and 13 nm for 50:1) and favors nanoparticle dispersion in polymer matrices. Obvious physicochemical property changes have been observed with PVA attached to the nanoparticle surface. With PVA attached to the nanoparticle surface, the nanoparticles are found not only to increase the PVA cross-linking with an increase in melting temperature but also to enhance the thermal stability of the PVA. The nanoparticles are observed to be uniformly dispersed in the polymer matrix. Scanning electron microscopy (SEM) microstructure also shows an intermediate phase with a strong interaction between the nanoparticles and the polymer matrices, arising from the hydrogen bonding between the PVA and hydroxyl groups on the nanoparticle surface. The addition of nanoparticles favors the cross-linkage of the bulk PVA matrices, resulting in a higher melting temperature, and an enhanced thermal stability of the polymer matrix.     

Phase transitions and kinetic properties of gold nanoparticles confined between two-layer graphene nanosheets

The thermodynamic and kinetic behaviors of gold nanoparticles confined between two-layer graphene nanosheets (two-layer-GNSs) are examined and investigated during heating and cooling processes via molecular dynamics (MD) simulation technique. An EAM potential is applied to represent the gold–gold interactions while a Lennard–Jones (L–J) potential is used to describe the gold–GNS interactions. The MD melting temperature of 1345 K for bulk gold is close to the experimental value (1337 K), confirming that the EAM potential used to describe gold–gold interactions is reliable. On the other hand, the melting temperatures of gold clusters supported on graphite bilayer are corrected to the corresponding experimental values by adjusting the ε_Au–C value. Therefore, the subsequent results from current work are reliable. The gold nanoparticles confined within two-layer GNSs exhibit face center cubic structures, which is similar to those of free gold clusters and bulk gold. The melting points, heats of fusion, and heat capacities of the confined gold nanoparticles are predicted based on the plots of total energies against temperature. The density distribution perpendicular to GNS suggests that the freezing of confined gold nanoparticles starts from outermost layers. The confined gold clusters exhibit layering phenomenon even in liquid state. The transition of order–disorder in each layer is an essential characteristic in structure for the freezing phase transition of the confined gold clusters. Additionally, some vital kinetic data are obtained in terms of classical nucleation theory.     

Higher surface energy of free nanoparticles

We present an accurate online method for the study of size-dependent evaporation of free nanoparticles allowing us to detect a size change of 0.1 nm. This method is applied to Ag nanoparticles. The linear relation between the onset temperature of evaporation and the inverse of the particle size verifies the Kelvin effect and predicts a surface energy of 7.2 J/m(2) for free Ag nanoparticles. The surface energy of nanoparticles is significantly higher as compared to that of the bulk and is essential for processes such as melting, coalescence, evaporation, growth, etc., of nanoparticles.     

Size and composition dependence of melting temperature of binary nanoparticles

Based on the ideal solution approximation, the model for size-dependent melting temperature of pure metal nanoparticles is extended to binary alloy systems. The developed model, free of any adjustable parameter, demonstrates that the melting temperature is related to the size and composition of alloy nanoparticles. The melting temperature of CuNi, PbBi and SnIn binary alloy nanocrystals is found to be consistent with the experiments and molecular dynamics simulations. The research reveals that alloy nanocry...     

铝纳米颗粒的热物性及相变行为的分子动力学模拟

采用分子动力学方法模拟了纳米金属铝在粒径为0.8-3.2 nm 时的熔点、密度和声子热导率的变化, 研究了粒径为1.6 nm的铝纳米颗粒的密度、比热和声子热导率随温度的变化. 采用原子嵌入势较好地模拟了纳米金属铝的热物性及相变行为, 根据能量-温度曲线和比热容-温度曲线对铝纳米颗粒的相变温度进行了研究, 并利用表面能理论、尺寸效应理论对铝纳米颗粒熔点的变化进行了分析. 随着纳米粒径的不断增大, 铝纳米颗粒的熔点呈递增状态, 当粒径在2.2-3.2 nm时, 熔点的增幅减缓, 但仍处于递增趋势. 随着纳米粒径的增大, 铝纳米颗粒的密度呈单调递减, 热导率则呈线性单调递增, 且热导率的变化情况符合声子理论. 随着温度的升高, 粒径为1.6 nm的铝纳米颗粒的密度、热导率均减小. 该模拟从微观原子角度对纳米材料的热物性进行了研究, 对设计基于铝纳米颗粒的相变材料具有指导意义.     

The melting mechanism in binary Pd0.25Ni0.75 nanoparticles: molecular dynamics simulations

The melting mechanism for Pd_0.25Ni_0.75 alloy nanoparticles (NPs) was investigated using molecular dynamics (MD) simulations with quantum Sutton-Chen many-body potentials. NPs of six different sizes ranging from 682 to 22,242 atoms were studied to observe the effect of size on the melting point. The melting temperatures of the NPs were estimated by following the changes in both the thermodynamic and structural quantities such as the total energy, heat capacity and Lindemann index. We also used a thermodynamics model to better estimate the melting point and to check the accuracy of MD simulations. We observed that the melting points of the NPs decreased as their sizes decreased. Although the MD simulations for the bulk system yielded higher melting temperatures because of the lack of a seed for the liquid phase, the melting temperatures determined for both the bulk material and the NPs are in good agreement with those predicted from the thermodynamics model. The melting mechanism proceeds in two steps: firstly, a liquid-like shell is formed in the outer regions of the NP with increasing temperature. The thickness of the liquid-like shell increases with increasing temperature until the shell reaches a critical thickness. Then, the entire Pd–Ni NP including core-related solid-like regions melts at once.     

Superheating and induced melting at semiconductor interfaces

We present ab initio density-functional simulations of the state of several semiconductor surfaces at temperatures near the bulk melting temperatures. We find that the solid-liquid phase-transition temperature at the surface can be altered via a microscopic (single-monolayer) coating with a different lattice-matched semiconducting material. Our results show that a single-monolayer GaAs coating on a Ge(110) surface above the Ge melting temperature can dramatically reduce the diffusion coefficient of the germanium atoms, going so far as to prevent melting of the bulk layers on the 10 ps time scale. In contrast, a single-monolayer coating of Ge on a GaAs(110) surface introduces defects into the bulk and induces melting of the top layer of GaAs atoms 300 K below the GaAs melting point. To our knowledge, these calculations represent the first ab initio investigation of the superheating and induced melting phenomena.     

Disorder effect on heat capacity,self-diffusion coefficient,and choosing best potential model for melting temperature,in gold–copper bimetallic nanocluster with 55 atoms

Molecular dynamics simulation has been implemented for doping effect on melting temperature, heat capacity, self-diffusion coefficient of gold–copper bimetallic nanostructure with 55 total gold and copper atom numbers and its bulk alloy. Trend of melting temperature for gold–copper bimetallic nanocluster is not same as melting temperature copper–gold bulk alloy. Molecular dynamics simulation of our result regarding bulk melting temperature is consistence with available experimental data. Molecular dynamics simulation shows that melting temperature of gold–copper bimetallic nanocluster increases with copper atom fraction. Semi-empirical potential model and quantum Sutton–Chen potential models do not change melting temperature trend with copper doping of gold–copper bimetallic nanocluster. Self-diffusion coefficient of copper atom is greater than gold atom in gold–copper bimetallic nanocluster. Semi-empirical potential within the tight-binding second moment approximation as new application potential model for melting temperature of gold–copper bulk structure shows better result in comparison with EAM, Sutton–Chen potential, and quantum Sutton–Chen potential models.     

Effect of pressure on melting and solidification of metal nanoparticles

A thermodynamic model was developed to clarify the dependence of melting temperature on hydrostatic pressure in the nanoscopic scale. It is based on the classic Clausius-Clapeyron relation and the size dependence of the melting entropy. The melting of nanoparticles in matrix with coherent and incoherent boundaries was also under consideration. It was shown that external hydrostatic pressure leads to the appearance of extrema of the melting temperature that was considered as a function of the characteristic size of nanoparticles.     

Solid clusters above the bulk melting point

The fact that the melting points of nanoparticles are always lower than those of the corresponding bulk material is a paradigm supported by extensive experimental data for a large number of systems and by numerous calculations. Here we demonstrate that tin cluster ions with 10-30 atoms remain solid at approximately 50 K above the melting point of bulk tin. This behavior is possibly related to the fact that the structure of the clusters is completely different from that of the bulk element.     

Computer study of the temperature dependence of physical properties of noncrystalline silicon nanoparticles

Variations in the structure and kinetic properties of vitreous and amorphous Si₄₀₀ nanoparticles upon heating from 300 to 1700 K are studied by molecular dynamics. The nanoparticle density increases with temperature and approaches the density of bulk solid silicon. A transition from a unimodal to a bimodal distribution of bond lengths is observed upon heating. This transition is more pronounced in the case of the vitreous nanoparticle. The average bond length in the amorphous nanoparticle is, as a rule, larger than that in the vitreous one, and the average number of bonds per atom is lower than that in the vitreous nanoparticle for nearly all studied temperatures. Negative values of the excess potential energy correspond to middle concentric layers of nanoparticles. Liquid layers form in the surface region of nanoparticles in the vicinity of the melting transition. A kinetic test indicating the beginning of nanoparticle melting is formulated.     

Can Nano-Particle Melt below the Melting Temperature of Its Free Surface Partner?

The phonon thermal contribution to the melting temperature of nano-particles is inspected. The discrete summation of phonon states and its corresponding integration form as an approximation for a nano-particle or for a bulk system have been analyzed. The discrete phonon energy levels of pure size effect and the wave-vector shifts of boundary conditions are investigated in detail. Unlike in macroscopic thermodynamics, the integration volume of zero-mode of phonon for a nano-particle is not zero, and it plays an important role in pure size effect and boundary condition effect. We find that a nano-particle will have a rising melting temperature due to purely finite size effect; a lower melting temperature bound exists for a nano-particle in various environments, and the melting temperature of a nano-particle with free boundary condition reaches this lower bound. We suggest an easy procedure to estimation the melting temperature, in which the zero-mode contribution will be excluded, and only several bulk quantities will be used as input. We would like to emphasize that the quantum effect of discrete energy levels in nano-particles, which is not present in early thermodynamic studies on finite size corrections to melting temperature in small systems, should be included in future researches.     

Size‐Dependence of the Melting Temperature of Individual Au Nanoparticles

Nanoparticles have an immense importance in various fields, such as medicine, catalysis, and various technological applications. Nanoparticles exhibit a significant depression in melting point as their size goes below ≈10 nm. However, nanoparticles are frequently used in high temperature applications such as catalysis where temperatures often exceed several 100 degrees which makes it interesting to study not only the melting temperature depression, but also how the melting progresses through the particle. Using high‐resolution transmission electron microscopy, the melting process of gold nanoparticles in the size range of 2–20 nm Au nanoparticles combined with molecular dynamics studies is investigated. A linear dependence of the melting temperature on the inverse particle size is confirmed; electron microscopy imaging reveals that the particles start melting at the surface and the liquid shell formed then rapidly expands to the particle core.     

Nuclear magnetic resonance investigation of metallic sodium nanoparticles in porous glass

Sodium nanoparticles embedded in porous glass have been studied by NMR. The measurements have been carried out on pulse spectrometers in magnetic fields of 9.4 and 17.6 T in a wide temperature range. Changes in the magnitude and temperature dependence of the ²³Na Knight shift with respect to those in bulk sodium have been discovered. An additional component of the NMR line shifted to high frequencies has been observed in the temperature range from 240 to 100 K. Investigation of the specific heat has revealed a considerable decrease in the melting and crystallization temperatures of sodium under nanoconfinement, which were not accompanied by abrupt changes in the Knight shift.