Critical size effect for the surface heat capacities of nano-CdS: theoretical and experimental studies

Abstract

The unique physical and chemical properties of nanomaterials are closely related to their surface thermodynamic functions which mainly depend on their sizes. In this study, the thermodynamic properties of nano-cadmium...

Theoretical and Experimental Studies on the Critical Size Effect on Surface Heat Capacity Using In Situ Microcalorimetry: During the Solid–Liquid Reactions of Cu2O Nanocubes

“…It can be seen from Table S7 and Figure that the values of σ g–s , H s , and S s for Cu 2 O nanocubes decrease with decreasing size when the temperature is the same. This is consistent with the research results of our previous work and some literature. , This may be due to the morphology of synthesized nano-Cu 2 O, which is a regular cube. Surface atoms per unit area may be in a stable state with decreasing size, thus leading to a decrease in the values of σ g–s , H s , and S s for nano-Cu 2 O with decreasing size.…”

“…All the isotherms belong to the typical type IV isotherm mode (based on the IUPAC classification). 34 Furthermore, we can find that all the type IV adsorption isotherms of four Cu 2 O nanocubes have no hysteresis loop. (In the part of middle pressure, that is, when the partial pressure ratio of N 2 is about 0.2−0.3, there will be no hysteresis loop in the isotherm adsorption line, although there is a large adsorption capacity.)…”

“…The relationship between the reaction rate constant and the standard molar reaction Gibbs free energy is obtained according to eq 14 in conjunction with the transition state theory, 74 which can be expressed as, (17) The standard molar formation Gibbs free energy of nano-Cu 2 O is obtained by combining eqs 14 and 17, which can be expressed as, (18) According to our previous work 46 and the classical thermodynamic equation, Δ r G m o̵ = Δ r H m o̵ − TΔ r S m o̵ , as well as in conjunction with eq 17, the standard molar entropy of nano-Cu 2 O can be expressed as, (19) According to Xue's and our previous works, 34,75,76 the molar surface thermodynamic properties of nanoparticles can be expressed as, Referring to our previous research work, 34 the specific surface thermodynamic functions can be abbreviated as the following series of equations, since the BET specific surface area data of bulk-Cu 2 O is very small and can be ignored, Figure 5 shows the N 2 adsorption−desorption isotherms and the corresponding linear fit of Cu 2 O nanocubes with different sizes. All the isotherms belong to the typical type IV isotherm mode (based on the IUPAC classification).…”

“…In the year 2002, Eroshenko and Stoudenets 33 defined the heat capacity of a heterogeneous nanosystem as the sum of the bulk and surface phases, and they found that the heat capacity of the surface phase showed negative values after studying organic nanodroplets, which was consistent with the values of the surface heat capacity obtained from our previous research work. 34 They believed that the interfacial area increases sharply when the size of the organic nanodroplets decreases, thus resulting in the decrease in the values of total heat capacity for the heterogeneous nanosystem. In the year 2004, Navrotsky et al 35 measured the surface energy of nano-CoO crystals using a calorimeter.…”

“…Furthermore, the standard molar formation thermodynamic functions, surface thermodynamic functions, and specific surface thermodynamic functions of Cu 2 O nanocubes were calculated based on the principle of thermodynamic cycle and basic thermodynamic theory, and then the effects of particle size and temperature on them are discussed. However, so far, to our knowledge, besides our previous work, 34,48 there has been no research reported on the critical size effect on the surface heat capacity with the cubic morphology of nanomaterials except for the spherical nanocadmium sulfide and octahedral cadmium molybdate.…”