Study On Generalized Expressions And Their Applications Of Chemical Potential And Gibbs-Duhem Equation With Influence Of External Fields

Thermodynamics is a discipline about the study the laws of the thermal phenomena andthermal motions. The thermodynamical research method is based on the logical deductionaccording to the basic laws summerized up from experiences, and it is universal and reliable.In the thermodynamic study, classical thermodynamics is most widely used, which mainlydeals with the equilibrium state. The chemical potential and Gibbs-Duhem equation are twoimportant concepts in thermodynamics, and they have important applications in physical,chemical thermodynamics and the other subjects.Chemical potential is an important thermodynamic property. It is defined as the partialderivative of internal energy with respect to the amount of substance in the constant-entropyand constant-volume processes, or the partial molar Gibbs function in the isothermal andconstant-pressure processes. So the physical meaning of chemical potential is the increasedinternal energy of the system when adds one mole of one kind of substances to it under thecondition that all the other quantities remain constant, or the increased Gibbs function causedby the increase of one mole substance. As a basic thermodynamic intensive property, chemicalpotential not only determines the direction and limits of mass transfer, but also directly playsthe role of criterion to estimate the phase equilibrium of a system. Some enhancementmethods were developed in recent years, while enhancement by external fields is one of themost promising methods, which becomes a hot research realm recently. From the view pointof thermodynamics, mass transfers are determined by chemical potentials, and the gradient ofchemical potential is the driving force of mass transfer, so the research on chemical potentialincluding the influences of external fields is of great significance. Gibbs-Duhem equation isone of the basic equations in Thermodynamics, which clarifies the functional relationshipbetween intensive quantity and extensive quantity describing the state of system. On the basisof Gibbs-Duhem equation, the activity of binary solution and adsorption quantity can besolved and the Gibbs adsorption formula is also deduced. The experiments show that theactivity of solution and adsorption quantity could be affected by the external field, so theGibbs-Duhem equation under the influence of the external field can give effective theoreticaldescription about the influence of solution properties and interfacial adsorption by externalfield.In this paper, starting from the fundamental definition of chemical potential and based onthe energy postulate, a generalized expression of chemical potential including the influences of external fields was derived. A variety of specific chemical potentials, such as gravitationalchemical potential, centrifugal chemical potential, electrochemical potential and the dielectricchemical potential, will be deduced from this generalized expression. The application of thedielectric chemical potential was investigated from two specific phenomena in the paper.Firstly, the vapor-liquid equilibriums of pure substances acted by electrostatic field wasinvestigated with this new chemical potential. The results show that the electric field canslightly raise the saturated vapor pressure of polar substances, which coincide with theexperimental results. Secondly, the effects of charged particle as condensation nuclei ondroplets growth were investigated with the chemical potential of dielectric in electric field.The theoretical results show that the amount of charge can strongly affect the growth ofdroplets, the critical radius of droplets becomes smaller, and a stable droplet or a dropletwhich could continue to grow up through condensation can form depending on the amount ofcharge. This analysis reveals that the chemical potential of dielectric can effectively describethe process of gas-liquid phase transition enhanced by electric field. Based on the basicprinciple of thermodynamic and Euler theorem, the generalized expression of Gibbs-Duhemequation under the environment of external field was derived using energy postulate and thegeneralized expression of chemical potential. Furthermore, the Gibbs adsorption formulaunder external field was deduced from Gibbs-Duhem equation. Conclusions were obtainedthat external field has an influence on interfacial adsorption by analyzing the Gibbs adsorptionformula. This work promotes the development of thermodynamics under the electromagneticfield, and provides a new method to investigate the transfer process enhanced by externalfields.