Size-dependence of surface thermodynamic functions of nano-Cu by dissolution kinetics

Zhang, Wenjuan; Xue, Yongqiang; Cui, Zixiang

doi:10.1016/j.colsurfa.2017.07.064

Cited by 7 publications

(5 citation statements)

References 25 publications

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“…However, partial molar surface thermodynamic properties are not equal to molar surface thermodynamic properties for the dissolution of nanoparticles with different sizes. According to the theoretical derivation of Xue et al, 58 the ratio of the partial molar surface thermodynamic functions to the molar surface thermodynamic functions of spherical nanoparticles is 2 : 3.…”

Section: Paper Pccpmentioning

confidence: 99%

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

Zhang

Tan

Zhou

et al. 2022

Phys. Chem. Chem. Phys.

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Section: Paper Pccpmentioning

confidence: 99%

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

Zhang

Tan

Zhou

et al. 2022

Phys. Chem. Chem. Phys.

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“…According to Xue’s and our previous works, ,, the molar surface thermodynamic properties of nanoparticles can be expressed as, G normalm normals = 3 2 R T ( ln ⁡ k − ln ⁡ k b ) H normalm normals = 3 2 × ( Δ r H m b o̵ − Δ r H m o̵ ) S normalm normals = H normalm normals − G normalm normals T …”

Section: Methodsmentioning

confidence: 99%

“…According to Xue’s and our previous works, ,, the molar surface thermodynamic properties of nanoparticles can be expressed as, …”

Section: Methodsmentioning

confidence: 99%

“…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).…”

Section: Processes Of Data Handling and Calculationsmentioning

confidence: 99%

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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

Zhang

Tang

Gan

et al. 2022

Ind. Eng. Chem. Res.

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Phase transition, energy storage, and other activities depend critically on the size variations of nanomaterials for their heat capacity. The size variation of the nanomaterial is also equally important to the thermodynamic properties for chemical reaction processes. Based on this, it will be fascinating to examine how the surface heat capacity of nanomaterials changes with size. Herein, we used an in situ microcalorimeter to report a general approach to obtaining the regular patterns of numerical changes in the surface heat capacity at different sizes and temperatures when the chemical reactions of cuprous oxide (Cu 2 O) take place in the liquid phase. We synthesized four Cu 2 O nanocubes with uniform size distributions, which range from 40 to 120 nm, by using the liquid-phase reduction method. Combined with the principle of thermodynamic cycle and transition state theory, the effects of size and temperature changes on the standard molar formation thermodynamic properties, surface thermodynamic properties, and specific surface thermodynamic properties of Cu 2 O nanocubes were calculated and analyzed. The calculated results are in agreement with the established thermodynamic model. It is inspiring that we find that Cu 2 O nanocubes also have a critical size in the range of 55−67 nm, and their molar surface heat capacity and specific surface heat capacity are 59.35 and 59.31 nm, respectively. This property allows them to exhibit differences in thermal resistance from bulk materials within an acceptable range of error. This work has important scientific significance and values for enriching and developing the surface physical chemistry and understanding the energy storage and other processes of nanomaterials.

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“…The calculated pre-exponential factors, as shown in Table 3, are relatively constant with the same order of magnitude. However, it significantly decreases for the nanometre-sized particles [33,34]. As the particle size decreases, the partial molar surface enthalpy and the partial molar surface entropy increase, leading to the decrease in the apparent activation energy and the pre-exponential factor [29,35].…”

Section: The Arrhenius Pre-exponential Factormentioning

confidence: 99%

The effect of the TiC particle size on the preferred oxidation temperature for self-healing of oxide ceramic matrix materials

et al. 2018

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The effect of particle size on the oxidation kinetics of TiC powders is studied. Different sizes of TiC powder ranging from nanometre to submillimetre sizes are investigated. The samples are heated at different heating rates from room temperature up to 1200°C in dry synthetic air. The Kissinger method for analysis of non-isothermal oxidation is used to estimate the activation energy for oxidation of the powders and to identify the active temperature window for efficient self-healing. The master curve plotting method is used to identify the model which best describes the oxidation of TiC powders, and the Senum and Yang method is used to approximate the value for the Arrhenius constant. The oxidation of TiC proceeds via the formation of oxycarbides, anatase and then finally the most stable form: rutile. The activation energy is found to be a strong function of the particle size for particle sizes between 50 nm and 11 lm and becomes constant at larger particle sizes. The data demonstrate how the minimal healing temperature for oxide ceramics containing TiC as healing particles can be tailored between 400 and 1000°C by selecting the right average TiC particle size.

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Size-dependence of surface thermodynamic functions of nano-Cu by dissolution kinetics

Cited by 7 publications

References 25 publications

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

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

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

The effect of the TiC particle size on the preferred oxidation temperature for self-healing of oxide ceramic matrix materials

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Size-dependence of surface thermodynamic functions of nano-Cu by dissolution kinetics

Cited by 7 publications

References 25 publications

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

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

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

The effect of the TiC particle size on the preferred oxidation temperature for self-healing of oxide ceramic matrix materials

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Product

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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