Size-Dependent Thermodynamics and Kinetics of Adsorption on Nanoparticles: A Theoretical and Experimental Study.

Owing to their excellent adsorption properties compared with those of the corresponding bulk materials, nanoparticles have been widely applied in many fields. Their properties depend on the thermodynamics and kinetics of adsorption, which depend on the particle size. In this paper, we present universal theories of the thermodynamics and kinetics for nanoadsorption that have been developed over the past few years. Theoretically, we have derived relationships between the adsorption thermodynamic properties and the particle size, as well as those between the adsorption kinetic parameters and the particle size. Moreover, we discuss the regularities and mechanisms of influence of the particle size on the thermodynamics and kinetics of adsorption. Experimentally, taking the adsorption of methyl orange on nano-CeO in aqueous solution as a system, we have studied the size-dependent thermodynamics and kinetics of the system, and the size dependences were confirmed to be consistent with the theoretical relationships. The results indicate that particle size has a significant effect on the thermodynamic properties and kinetic parameters of adsorption: with decreasing particle size of nano-CeO, the adsorption equilibrium constant K and the adsorption rate constant k increase, while the molar Gibbs free energy of adsorption Δ G, the molar adsorption entropy Δ S, the molar adsorption enthalpy Δ H, the adsorption activation energy E, and the adsorption pre-exponential factor A all decrease. Indeed, ln K, Δ G, Δ S, Δ H, ln  k, E, and ln  A are each linearly related to the reciprocal of particle size. Furthermore, thermodynamically, Δ G and ln  K are influenced by the molar surface area and the difference in surface tensions, Δ S is influenced by the molar surface area and the difference in temperature coefficients of surface tension, and Δ H is influenced by the molar surface area, the difference in surface tensions, and the difference in temperature coefficients of surface tension. Kinetically, E is influenced by the partial molar surface enthalpy of the nanoadsorbent, ln  A is influenced by the partial molar surface entropy, and ln  k is influenced by the partial molar surface Gibbs energy. The theories can quantitatively describe adsorption behavior on nanoparticles, explain the regularities and mechanisms of influence of particle size, and provide guidance for the research and application of nanoadsorption.