Influence of the Diameter of Sections on Electrochemical Thermodynamics of Nanorod Electrodes: Theoretical and Experimental Research Studies

Abstract

Nanorods have been widely applied in the electrochemistry field due to their excellent electrochemical properties. However, thermodynamic theory of nanorod electrodes still remains a blank, and the effect of the section diameter on the electrochemical thermodynamics of nanorod electrodes has not been clear. In this paper, theoretically, according to the thermodynamic definition of chemical potential, the expression of the surface chemical potential of nanorods was derived; then, the thermodynamic relations of the electrode potential, its temperature coefficient, reaction Gibbs energy, equilibrium constant, reaction enthalpy, reaction entropy, and reversible reaction heat of nanorod electrodes with the section diameter were derived based on the second law of thermodynamics; finally, the influencing regularities and mechanisms of the section diameter on these electrochemical quantities were discussed. Experimentally, the electrode reaction of rod-like nano-SnO2 was taken as an example, the solvothermal method was applied to prepare SnO2 nanorods with different section diameters, and a potentiometer was used to determine the electrode potentials of the nanorod electrodes. On this basis, we further obtained the standard electrode potentials and their temperature coefficients, reaction Gibbs energies, equilibrium constants, reaction enthalpies, reaction entropies, and reversible reaction heats of nanorod electrodes with different section diameters and discussed the influencing regularities of the section diameter on these electrochemical quantities. The experimental results are in agreement with the above theoretical relations. Both theoretical and experimental results show that the section diameter has a remarkable influence on electrochemical thermodynamics of nanorod electrodes. When the nanorods act as a reactant of an electrode reaction, with the decrease in section diameter, the standard electrode potential and the equilibrium constant of the electrode reaction increase, while the temperature coefficient of the standard electrode potential, the reaction Gibbs energy, the reaction entropy, the reaction enthalpy, and the reversible reaction heat decrease. When the nanorods act as a product of an electrode reaction, the effects of the section diameter on the electrochemical quantities are just reverse. Furthermore, when the section diameter exceeds 20 nm, the logarithm of the equilibrium constant and other electrochemical quantities are linearly related to the reciprocal of the section diameter. Besides, we also found that the additional electrode potential (i.e., surface electrode potential) of a nanorod electrode is exactly half that of the corresponding spherical nanoparticle electrode if the diameters are the same. The theory proposed in this paper can quantitatively describe the influencing regularities and mechanisms of the section diameter on electrochemical quantities of nanorod electrodes and can provide a foundation and guidance for the design, preparation, research, and applications of nanorod electrodes.