Size-effects Of Melting,electrochemical And Interfacial Thermodynamics Of Nanoparticles

Due to nano-effect,nanomaterials usually exhibit unique physicochemical properties that are different from the corresponding bulk materials,which are decided by the particle size of nanomaterials.However,the actual melting process has not been described accurately by the current thermodynamic theories about the melting of nanoparticles.As well as the degree and the range of size-dependent melting,electrochemical and interfacial thermodynamic properities are not clear.These problems severely restrict the research,development and application of nanomaterials.Therefore,in this paper,the size-effects of melting,electrochemical and interfacial thermodynamics of nanoparticles were researched by combining the theories and the experiments.(1)Size-effect of melting thermodynamics of nanoparticlesIn theory,the thermodynamic integral relationships of melting enthalpy and melting entropy of nanoparticles with the particle size were derived by designing a thermochemical cycle,respectively.And the size-dependences of melting thermodynamic properties of nanoparticles were discussed.In experiment,nano-Au particles(0.9 nm ~ 37.4 nm)and nano-Ag particles(1.4 nm ~ 39.1 nm)with different average particle sizes were prepared by liquid phase reduction method,the influencing regularities of reaction conditions on the size of nanoparticles were explored.X-ray diffractometer(XRD)and transmission electron microscope(TEM)were applied to characterize the crystal structure,morphology and particle size.The melting temperature,melting enthalpy and melting entropy of these nanoparticles were determined by differential scanning calorimeter(DSC).The influencing regularities,mechanism,degree and range of particle size on above melting thermodynamic properties were discussed by correlating the experimental results with the theoretical relationships.The results show that there are significant effects of the particle size on the melting temperature,melting enthalpy and melting entropy of nanoparticles,and they decrease with the particle size decreasing.Partial molar interfacial area and interfacial tension are the major influencing factors for melting temperature,molar interfacial area and interfacial tension are for integral melting enthalpy,as well as molar interfacial area and temperature coefficient of interfacial tension are for integral melting entropy.(2)Size-effect of electrochemical thermodynamics of nanoparticlesIn theory,the size-dependences of the standard electrode potential,the temperature coefficient of nanoparticle electrodes and the thermodynamic properties of electrode reactions were analyzed.In experiment,nano-Au and nano-Ag with different particle sizes were prepared as electrodes,and the corresponding galvanic cells were formed with the saturated calomel electrode,respectively.The electromotive forces of the galvanic cells at different temperatures were measured by potentiometer,and then the standard electrode potential and its temperature coefficient of the electrodes,equilibrium constant,Gibbs energy,enthalpy,entropy and reversible heat of the electrode reactions were obtained.The influencing regularities,mechanism,degree and range of particle size on above electrochemical thermodynamic properties were discussed by correlating the experimental results with the theoretical relationships.The results show that the particle size has a significant influence on the standard electrode potential,the temperature coefficient of nanoparticle electrodes and the thermodynamic properties of electrode reactions.If nanoparticles act as the reactants in electrode reactions,the standard electrode potential and the standard reaction equilibrium constant increase with the particle size decreasing,while the temperature coefficient of standard electrode potential,Gibbs energy,enthalpy,entropy and reversible heat of electrode reactions decrease.If nanoparticles act as the products in electrode reactions,there exist the reverse regularities.Partial molar interfacial area and interfacial tension are the major influencing factors for the standard electrode potential of nanoparticle electrodes,equilibrium constant,Gibbs energy and enthalpy of electrode reactions,as well as partial molar interfacial area and temperature coefficient of interfacial tension are for the temperature coefficient of standard electrode potential,entropy and reversible heat of electrode reactions.(3)Size-effect of interfacial thermodynamics of nanoparticlesIn theory,the size-dependences of the interfacial tension and interfacial thermodynamic properties of the interfaces between nanoparticles and solutions were analyzed.In experiment,the interfacial tension and interfacial thermodynamic properties of the interfaces of nano-Au and nano-Ag with different particle sizes,respectively,and their corresponding electrolyte solutions were calculated by the experimental results of electrochemistry.The influencing regularities of particle size on interfacial tension,as well as the influencing regularities,mechanism,degree and range of particle size on interfacial thermodynamic properties were derived by correlating the experimental results with the theoretical relationships.In addition,an electrochemical method for the determination of Tolman length and atomic radius of nanoparticles was built by the thermodynamic relationships of interfacial tension and particle size.The results show that there are significant effects of the particle size on the interfacial tension and its temperature coefficient.With the decrease of particle size,the interfacial tension increases,but its temperature coefficient decreases.When the radius is larger than 10 nm,the interfacial tension and its temperature coefficient are approaching constants.When the radius is less than 10 nm,the interfacial tension and its temperature coefficient change sharply with the decrease of particle size.In addition,there are significant effects of the particle size on the interfacial thermodynamic properites.Interfacial Gibbs energy,interfacial enthalpy,interfacial entropy and interfacial internal energy increase with the particle size decreasing.Molar interfacial area and interfacial tension are the major influencing factors for the interfacial Gibbs energy,interfacial enthalpy and interfacial internal energy,as well as molar interfacial area and temperature coefficient of interfacial tension are for the interfacial entropy.Besides,the Tolman lengths of nano-Au and nano-Ag were negative values,which were less affected by temperature;and the atomic radii determined by the electrochemical method are basically consistent with the literature values.Furthermore,the influencing degree and range of particle size on the melting,electrochemical and interfacial thermodynamic properties can be summarized as follows.When the radius is greater than 10 nm,the partial molar interfacial area(or molar interfacial area)is the major influencing factor for above thermodynamic properties.There are linear relations between the above thermodynamic properties and the reciprocal of radius,respectively.And when the radius is less than 10 nm,both partial molar interfacial area(or molar interfacial area)and interfacial tension(or its temperature coefficient)influence the above thermodynamic properties,and the relations of above thermodynamic properties and the reciprocal of radius deviate from the linear relations,and the smaller the particle size,the more obvious the deviation.Meanwhile,with the decrease of the particle size,the effect of interfacial tension(or its temperature coefficient)on above thermodynamic properites gradually increases.When the particle size reduced to a certain range(for nano-Au and nano-Ag,the range of radius is 1.0 nm ~ 2.5 nm),the effect of partial molar interfacial area(or molar interfacial area)is equal to that of interfacial tension(or its temperature coefficient);and when the particle size continues to decrease,the effect of interfacial tension(or its temperature coefficient)will hold the main position.The melting thermodynamics theory proposed in this paper can accurately and quantitatively describe the size-effect of nano-system in the real melting process,which can provide important theoretical guidance for the relative researches on the melting process.The influencing regularities,mechanism,degree and range of size on the melting,electrochemical and interfacial thermodynamic properties of nanoparticles are universal,which can provide important references for the design,research and application of nanomaterials.The established electrochemical method for the determination of Tolman length and atomic radius can provide a new approach for the study of interfacial thermodynamics of nano-systems.