| The unique physical and chemical properties of nanomaterials are closely related to their “nano-effect”,and the major factor for “nano-effect” is the size of nanoparticles.Size will significantly affect the application values of nanomaterials.In addition,nowadays,most literatures have reported the size dependence of thermodynamic properties during the dissolution of nanoparticle.However,there are still not many research reports on the size dependence of the kinetic properties for nanoparticles during dissolution,and there are still have contradictions and conflicts between the conclusions of these existing reports.On the other hand,there are too many methods for determination of surface energy（including surface Gibbs free energy,surface enthalpy,surface entropy and surface heat capacity）and surface tension on solid substance.However,most of them are not suitable for determining the surface energy and surface tension of nanoscale materials.There are also not many laws and explanations about the research on interfacial thermodynamic properties（including surface tension,interfacial enthalpy,interfacial entropy and interfacial heat capacity）and size dependence of it.So far,it can be seen that the above-mentioned basic physical and chemical properties of nanomaterials are not perfect,which greatly hinders their subsequent development and application values.Therefore,based on these aspects,this paper proposes to use solubility technology to solve the size-dependent problems of thermodynamics,kinetics,surface thermodynamics and interfacial thermodynamic properties of nanomaterials during the dissolution processes.（1）Preparation of spherical nano-cadmium sulfide with different particle sizesIn this paper,the solvothermal method was used to prepare spherical nano-cadmium sulfide with different particle sizes via two methods,which is I.cadmium acetate and TAA as reactants,oleic acid as solvent and surfactant.II. cadmium nitrate and thiourea with PVP K-40 as surfactant and ethylene glycol as solvent.At the same time,bulk-cadmium sulfide was prepared by aging method.The phase,morphology,size and specific surface area of the products were characterized by using X-ray powder diffractometer,transmission electron microscope and specific surface area and porosity analyzer.（2）Size-dependent studies of dissolution thermodynamics and surface thermodynamic properties（surface energy）By designing the thermodynamic cycle in the theoretical derivation part and introducing the interface variable parameters,the complete theoretical derivation of the dissolution thermodynamics and surface thermodynamic properties of spherical nanoparticles is carried out.The size-dependent laws of dissolution mechanics and surface thermodynamic properties were systematically calculated in the experiments by using the solubility technique combined with the principle of electrochemical equilibrium method,and the physical and chemical parameters of bulk-cadmium sulfide.The results indicate:（a）For the dissolution system of spherical nano-cadmium sulfide,there is an obvious curved or linear relationship between the dissolution thermodynamic properties and the reciprocal of particle size.The values of standard molar dissolution Gibbs free energy,standard molar dissolution entropy and standard molar dissolution enthalpy also increases with the gradually increasing particle size.However,the values of the logarithm of standard dissolution equilibrium constant,the values of molar surface Gibbs free energy,the values of molar surface enthalpy and the values of molar surface entropy are decreasing with the gradually increasing particle size.（b）There is an obvious critical size effect on the molar surface heat capacity of nano-cadmium sulfide,and the value of critical size is between 8.1 nm and 15.1 nm,which is 9.3 nm.（3）Size-dependent studies of dissolution kinetic propertiesIn the theoretical derivation part,the transition state theory is combined to carry out a complete theoretical derivation of dissolution kinetic properties for spherical nanoparticles by introducing interface variable parameters.The size-dependent laws of dissolution kinetic properties were systematically calculated in the experiments by using the solubility technique combined with the principle of electrochemical equilibrium method,and the physical and chemical parameters of bulk-cadmium sulfide.The results indicate:（a）For the dissolution processes of spherical nano-cadmium sulfide,there is an obvious linear or curved relationship between the dissolution kinetics and the particle size（or the reciprocal of particle size）,and the dissolution processes follow the Arrhenius law.The values of dissolution molar activation Gibbs free energy,the values of dissolution molar activation entropy,the values of dissolution molar activation enthalpy,the values of apparent activation energy and the values of logarithm of the pre-exponential factor all gradually increase with the gradually increasing particle size,while the values of logarithm of the dissolution rate constant and the values of the dissolution order are gradually decreasing.（b）By comparing the molar surface thermodynamic properties derived from the dissolution thermodynamic properties and the dissolution kinetic properties,it is found that calculated by the dissolution kinetic properties for the values of molar surface Gibbs free energy,the values of molar surface enthalpy and the values of molar surface entropy are too large,which may be due to the ideal assumptions of transition state theory.（4）Size-dependent studies of interfacial thermodynamic propertiesIn the theoretical derivation part,the single molecular layer model and the Gibbs–Tolman–Kening–Buff equation were combined to conduct a complete theoretical derivation of the interfacial mechanical properties of spherical nanoparticles.The size-dependent laws of interfacial thermodynamic properties were systematically calculated in the experiments by using the solubility technique combined with the molar surface thermodynamic properties of nano-and bulkcadmium sulfide（molar surface Gibbs free energy,molar surface enthalpy,and molar surface entropy）and the values of specific surface areas.The results indicate:（a）For spherical nano-cadmium sulfide,the values of surface tension,the values of interfacial enthalpy and the values of interfacial entropy gradually increase with increasing particle size.（b）The interfacial heat capacity of nano-cadmium sulfide also has an obvious critical size effect,and the value of critical size is between 8.1 nm and 15.1 nm,which is 8.7 nm.There is a controllable error of 0.6 nm between the molar surface heat capacity.The solubility technique used in this study combined with the complete theoretical derivation is used to solve the size–dependent problems of dissolution thermodynamics（including surface thermodynamic properties）,kinetics and interfacial thermodynamic properties during the dissolution of nanoparticles.It has important guiding significance and reference values,the calculated surface tension can solve the difficult problem of measuring the surface tension for nanomaterials and provide a general new way for it.In addition,the critical size effect of the surface heat capacity of nano-cadmium sulfide is valuable to understand the energy storage process of nanomaterials. |
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