In this article, the effects of size and confinement at the nanometre size scale on both the melting temperature, Tm, and the glass transition temperature, Tg, are reviewed. Although there is an accepted thermodynamic model (the Gibbs–Thomson equation) for explaining the shift in the first-order transition, Tm, for confined materials, the depression of the melting point is still not fully understood and clearly requires further investigation. However, the main thrust of the work is a review of the field of confinement and size effects on the glass transition temperature. We present in detail the dynamic, thermodynamic and pseudo-thermodynamic measurements reported for the glass transition in confined geometries for both small molecules confined in nanopores and for ultrathin polymer films. We survey the observations that show that the glass transition temperature decreases, increases, remains the same or even disappears depending upon details of the experimental (or molecular simulation) conditions. Indeed, different behaviours have been observed for the same material depending on the experimental methods used. It seems that the existing theories of Tg are unable to explain the range of behaviours seen at the nanometre size scale, in part because the glass transition phenomenon itself is not fully understood. Importantly, here we conclude that the vast majority of the experiments have been carried out carefully and the results are reproducible. What is currently lacking appears to be an overall view, which accounts for the range of observations. The field seems to be experimentally and empirically driven rather than responding to major theoretical developments.

https://iopscience.iop.org/article/10.1088/0953-8984/17/15/R01/pdf

Effects of confinement on material behaviour at the nanometre size scale

Size dependence of nanostructures: Impact of bond order deficiency

Empirical relations are established between the cohesive energy, surface tension, and melting temperature of different bulk solids. An expression for the size-dependent melting for low-dimensional systems is derived on the basis of an analogy with the liquid-drop model and these empirical relations, and compared with other theoretical models as well as the available experimental data in the literature. The model is then extended to understand (i) the effect of substrate temperature on the size of the deposited cluster and (ii) the superheating of nanoparticles embedded in a matrix. It is argued that the exponential increase in particle size with the increase in deposition temperature can be understood by using the expression for the size-dependent melting of nanoparticles. Superheating is possible when nanoparticles with a lower surface energy are embedded in a matrix with a material of higher surface energy in which case the melting temperature depends on the amount of epitaxy between the nanoparticles and the embedding matrix. The predictions of the model show good agreement with the experimental results. A scaling for the size-dependent melting point suppression is also proposed.

Liquid-drop model for the size-dependent melting of low-dimensional systems

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 $7.2\text{ }\text{ }\mathrm{J}/{\mathrm{m}}^{2}$ 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.

Higher Surface Energy of Free Nanoparticles

Real-time observations were made of the shape change from pyramids to domes during the growth of germanium-silicon islands on silicon (001). Small islands are pyramidal in shape, whereas larger islands are dome-shaped. During growth, the transition from pyramids to domes occurs through a series of asymmetric transition states with increasing numbers of highly inclined facets. Postgrowth annealing of pyramids results in a similar shape change process. The transition shapes are temperature dependent and transform reversibly to the final dome shape during cooling. These results are consistent with an anomalous coarsening model for island growth.

Transition states between pyramids and domes during Ge/Si island growth

An effective mass approximation (EMA) with finite-depth square-well potential is used to investigate the size-dependent band gap (BG) of PbS and CuBr nanoparticles embedded in different matrices. These two materials are interesting from the theoretical point of view as PbS is a low-BG material with smaller effective masses and larger dielectric constants, whereas CuBr is a wide-BG material with larger effective masses and smaller dielectric constants. Comparing the experimental BGs with our theoretical calculations, it is shown that EMA provides a better description of the experimental data, especially for CuBr, when the Coulomb interaction having the size-dependent dielectric constant is included in the calculation. Further, comparing the change in the BG of spherical nanoparticle, nanowire and thin film, it is predicted that the effective dimensionality of semiconductor nanoparticles can be increased by embedding them in another semiconducting matrix.

Effective mass approximation for two extreme semiconductors: Band gap of PbS and CuBr nanoparticles

Raman scattering measurements were performed on nanostructured II–VI semiconductor CdS prepared by a chemical route. The Raman spectrum shows a low-frequency wing at 295 cm −1 besides the characteristic first-order longitudinal optical phonon (1LO) mode at 305 cm −1 when excited with a laser of wavelength 457.9 nm. The observed variation of the Raman shifts, widths and intensities of these two lines with the size of the nanoparticles is consistent with the interpretation that the low-frequency peak is a surface phonon (SP) mode. Increasing the wavelength of the exciting laser lowers the intensity of the LO mode, while shifting the lower-frequency SP mode to the higher-frequency side and simultaneously increases its width. This anomalous behavior is attributed to the possible electron hole excitation by the SP due to the presence of a continuum of localized and acceptor states within CdS band gap. The effect of temperature, on these modes, is also studied and discussed.

Raman spectroscopy of CdS nanocrystalline semiconductors

The size dependence of lattice contraction can be understood by assuming the nanoparticles to be a liquid drop and that there exists a pressure difference (?p) between the inside and outside of the liquid drop. The analysis of the experimental data of Yu et al on the lattice contraction reveals that the isothermal compressibility is different for different orientations of the lattice plane, which is in good agreement with earlier reported data.

http://iopscience.iop.org/article/10.1088/0953-8984/13/12/401/pdf

The lattice contraction of nanometre-sized Sn and Bi particles produced by an electrohydrodynamic technique

The change in specific heat by the application of magnetic field (Ba∼1 T) in the case of the high-Tc superconductors is examined phenomenologically by the Ginzburg-Landau theory of anisotropic type-II superconductors. The observed large reduction of specific heat anomaly just below the superconducting transition is explained quantitatively. We have obtained the expression for the change in specific heat in a magnetic field (ΔC) for any general orientation of Ba with respect to the crystallographic c-axis. We also present the result for a polycrystalline sample. ΔC is shown to be linear in ( B a T c ) [ t (1 −t) ] for temperatures slightly below T c , where t= T T c . The slope of this linear behaviour is found to be related to the anisotropy of the effective mass.

S. N. Behera

Papers

Liquid-drop model for the size-dependent melting of low-dimensional systems

Effective mass approximation for two extreme semiconductors: Band gap of PbS and CuBr nanoparticles

Raman spectroscopy of CdS nanocrystalline semiconductors

The lattice contraction of nanometre-sized Sn and Bi particles produced by an electrohydrodynamic technique

Ginzburg-Landau theory of specific heat anomaly of high-Tc superconductors in magnetic field