Melting point depression of high surface to volume ratio materials results from this effect. For the same reason, surfaces of nano materials 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. Where: TMB = Bulk Melting temperature σsl = solid–liquid interface energy Hf = Bulk heat of fusion ρs = density of solid d = particle diameter A normalized Gibbs–Thomson Equation for gold nanoparticles is plotted in Figure 1, and the shape of the curve is in general agreement with those obtained through experiment. Semiconductor/covalent nanoparticles Equation 2 gives the general relation between the melting point of a metal nanoparticle and its diameter. However, recent work indicates the melting point of semiconductor and covalently bonded nanoparticles may have a different dependence on particle size. The covalent character of the bonds changes the melting physics of these materials. Researchers have demonstrated that Equation 3 more accurately models melting point depression in covalently bonded materials. Where: TMB=Bulk Melting temperature c=materials constant d=particle diameter Equation 3 indicates that melting point depression is less pronounced in covalent nanoparticles due to the quadratic nature of particle size dependence in the melting Equation. Proposed mechanisms The specific melting process for nanoparticles is currently unknown. The scientific community currently accepts several mechanisms as possible models of nanoparticle melting. Each of the corresponding models effectively match experimental data for melting of nanoparticles. Three of the four models detailed below derive the melting temperature in a similar form using different approaches based on classical thermodynamics. Liquid drop model The liquid drop model (LDM) assumes that an entire nanoparticle transitions from solid to liquid at a single temperature. This feature distinguishes the model, as the other models predict melting of the nanoparticle surface prior to the bulk atoms. If the LDM is true, a solid nanoparticle should function over a greater temperature range than other models predict. The LDM assumes that the surface atoms of a nanoparticle dominate the properties of all atoms in the particle. The cohesive energy of the particle is identical for all atoms in the nanoparticle. The LDM represents the binding energy of a nanoparticles as function of the free energies of the volume and surface. Equation 4 gives the normalized, size dependent melting temperature of a material according to the