The Effect Of Particle Size And Shape On The Thermodynamic Properties: A Theoretical Study And Quantum Chemistry Calculation

As we all know, the materials have many differences in chemical reaction equilibrium,reaction kinetics, phase change, adsorption, electrochemistry and catalysis due to surfaceeffect and small size effect when their dimension reaches nanoscale, and these changes mainlyattribute to the change in thermodynamic properties. Therefore, it is become very importantand imperative to study the effect of particle size and morphology on the thermodynamicproperties of nanomaterials. At present, the effect of particle size on the thermodynamicproperties of nanomaterials is rarely reported, the influence regularity of particle size on thethermodynamic properties is unclear, the theoretic study of thermodynamic properties ofspherical nanoparticles is imperfect, and the theoretic study of thermodynamic properties ofother morphologies has not been reported.In this paper, interface variables were introduced to the Gibbs function of nanoparticles,and the surface thermodynamic properties of different morphologies (spherical, cubic, rodlikeand schistose) and the relations between thermodynamic properties, respectively, and particlesize were systematically deduced, including the molar surface Gibbs free energy, the molarsurface enthalpy, the molar enthalpy, the molar surface entropy, the molar entropy, the molarinternal energy, the molar surface heat capacity and molar heat capacity at constant pressure,then the additional pressure of solid nanoparticles was deduced by applying theYoung-Laplace equation to solid nanoparticles for the first time, then the molar surface energy,the molar internal energy, the molar surface heat capacity and molar heat capacity at constantvolume were further deduced.Then, according to the single crystal cell parameters of Fe and Ag, the VB source program calculating coordinate of atom clusters was wrote, and a series of nano-Ag clustersand nano-Fe clusters models with different sizes and morphologies were constructed. Themolar Gibbs energy, the molar enthalpy, the molar entropy, the molar internal energy, and themolar heat capacity at constant volume of nano-Ag clusters and nano-Fe clusters werecalculated by using semi-empirical method PM6of the quantum chemistry method inGaussian09software. Then the effect of particle size and morphology on the thermodynamicproperties was discussed. At last, the Tolman length and expansion coefficient of nano-Fewere further estimated.The results show that the thermodynamic properties are related to the size, the surfacetension, and the temperature coefficient and expansion coefficient of surface tension. For theinfluence regularity of particle size on the thermodynamic properties of nanoparticles, thequantum chemistry calculation results agree with the thermodynamic theory; with the particlesize decreasing, the molar Gibbs energy, the molar enthalpy, the molar entropy and the molarinternal energy increase, while the molar heat capacity at constant volume has little change,but shows a downward tendency. For the nanoparticles with different morphologies, thethermodynamic properties have few differences if the atom numbers are the same. In addition,In addition, the Tolman lengths of nano-Fe clusters is0.1and its expansion coefficient isnegative.The thermodynamic theory of nanoparticle and influence regularity of nanoparticle sizeon the thermodynamic properties can provide important and significant guidance on thestudies and applications of nanoparticles in the chemical reaction, phase change, adsorption,electrochemistry and catalysis..