Size And Shape Dependent Thermodynamic Properties Of Nanoparticles: A Theoretical And Experimental Study

Numerous thermodynamic problems of nanoparticles are involved in the preparations,researches and applications of nanomaterials.The own thermodynamic properties,the melting thermodynamic properties and the electrochemical thermodynamic properties of nanoparticles present notable differences compared with their bulk counterparts which depend on particle size and shape.The own thermodynamic properties of nanoparticles consist of two parts: the thermodynamic properties of the surface and bulk phases;however,due to the size and shape dependent surface thermodynamic properties remains unclear and the differences of the thermodynamic properties between the bulk phase and the massive substances have not been reported yet,there are serious defects in the current theories of nanothermodynamics.And the rationality and quantitative application scopes of different melting models and the influence regularities and mechanisms of particle size and shape on the melting enthalpy and entropy are still ambiguous.In addition,the size and shape dependence of the electrochemical thermodynamic properties of nano-sized electrodes are not entirely clear.Because the thermodynamic problems severely restrict the preparations,researches and applications of nanomaterials,the purpose of this subject is to investigate them in theory and experiment.(1)Study on the own thermodynamic properties of nanoparticlesFirstly,based on the basic equations of thermodynamics and the molar surface Gibbs energy derived from surface tension and specific area,the relations of surface thermodynamic properties to size of nanoparticles with different shapes(sphere,regular polyhedrons,rod,wire,sheet and film)were obtained.Then,expressions of size dependent thermodynamic properties of bulk phase were derived through designing a thermochemical cycle and combining Laplace and Tolman equations.Subsequently,the completed and universal expressions of the own thermodynamic properties of nanoparticles were gotten,and combining theoretical calcultions,the influence regularities and mechanisms of particle size and shape on these properties were discussed.The thermodynamic theory of bulk phase of nanoparticles was preliminarily established,and the theory of surface thermodynamics was improved,and thus the theoretical foundation of nanothermodynamics was laid.The results indicate that: the thermodynamic properties of bulk phase of nanoparticles differ from those of bulk counterparts,and the differences are determined by the volume change factor(?)and surface tension(?).If r < 10 nm,with size decreasing,? and ? present dramatic variations,and so do the differences;for larger nanoparticles(r > 10 nm),size effect on the thermodynamic properties of bulk phase can be neglected,and the ? can be regarded as a constant,and the surface thermodynamic properties are directly proportional to specific surface area,and therefore the own thermodynamic properties of nanoparticles present linear variations with inverse particle size.For nanoparticles with different shapes but identical volume(all the dimensions are nano-sized,the same below),if the surface tensions are approximately equal,the more the shape deviates from sphere,the larger the own thermodynamic properties are.(2)Study on the melting thermodynamic properties of nanoparticlesTheoretically,by the employment of the strict criterion for phase equilibrium,the corresponding relations were derived to describe the change of melting temperature with particle size of nanoparticles based on different melting models.Then by the comparison of the results of theoretical calculation and literatures,it was found that Reiss and Rie models are rational,and the former applies to the stage from initial melting to critical thickness of liquid layer and the latter from the critical thickness to final melting.Furthermore,relations of the melting enthalpy and entropy to size of nanoparticles with different shapes were derived based on Reiss model,and combining theoretical calcultions,the influence regularities and mechanisms of size and shape on the melting thermodynamic properties were discussed.A systematic melting thermodynamic theory of nanopartilces was established.Experimentally,the melting of nano-Ag and nano-Sn was chosen as the research systems.Nano-Ag(sphere,wire and cube)and nano-Sn(sphere)with different sizes were prepared by chemical reduction methods.The influence factors and influence regularities on size and shape were analysed and summarized.Then the melting temperatures,melting enthalpies and entropies of nano-Ag and nano-Sn were determined by differential scanning calorimeter (DSC),and the influence regularities of size and shape on the melting thermodynamic properties were obtained.The experimental results agree with the theoretical relations.The results reveal that: the melting thermodynamic properties decrease with particle size reducing,and the smaller the particle size,the more dramatic the depression of the melting thermodynamic properties;for larger nanoparticles,these properties linearly vary with inverse particle size.For nanoparticles with different shapes but identical volume,if the surface tensions are approximately equal,the more the shape deviates from sphere,the smaller the melting thermodynamic properties are.(3)Study on the electrochemical thermodynamics of nanoparticlesTheoretically,based on the derived relation of molar reaction Gibbs energy of nanoelectrode to size of nanoparticles with different shapes and combined the second law and basic equations of thermodynamics,the relations to describe the variations of electrode potential,temperature coefficient of electrode potential,equilibrium constant,thermodynamic properties of reaction and reversible reaction heat with size and shape were obtained,and the influence regularities and mechanisms of particle size and shape on the electrochemical properties were discussed.The electrochemical thermodynamic theory of nanoparticles was improved.Experimentally,nano-Ag electrodes constituted by nano-Ag with different sizes and shapes were prepared.By determining the electrode potentials of the nonoelectrodes at different temperatures and combining the basic equations of thermodynamics,the temperature coefficients of electrode potential,the reaction equilibrium constants,the thermody-namic properties of reaction and the reversible reaction heat were calculated.Then the influence regularities of size and shape on the electrochemical properties were gotten.The experimental results agree with the theoretical relations.The results demonstrate that: as the product of the electrode reaction,as particle size of nano-Ag decreases,the electrode potential and the equilibrium constant decrease,while the temperature coefficient of electrode potential,the thermodynamic properties of reaction and the reversible reaction heat increase.If the nanoparticle is the reactant of the electrode reaction,the influence regularities of size and shape on these electrochemical properties are opposite.Moreover,these electrochemical properties linearly valy with inverse particle size for larger nanoparticles.For nanoparticles with different shapes but identical volume,if surface tensions are approximately equal,the more the shape deviates from sphere,the more significant change the electrochemical properties are.The thermodynamic theory of bulk phase of nanoparticles was established,and the theories of surface thermodynamics,melting thermo-dynamics and electrochemical thermodynamics were improved.These thermodynamic theories can quantitatively describe influence regularities of size and shape on the thermodynamic properties of nanoparticles involved in various chemical processes,and accurately predict and explain the size and shape dependent thermodynamic behaviors,and provide valuable theoretical guidance for the thermodynamic problems involved in the preparations,researches and applications of nanomaterials.