Determination of Interfacial Tension of Nanomaterials and the Effect of Particle Size on Interfacial Tension.

The unique physical and chemical properties and performances of nanomaterials are closely related to the interfacial tension. However, there is no method to accurately measure the interfacial tension of nanomaterials. In addition, the effect of particle size on the interfacial tension of nanoparticles is unclear, and there exist conflicting conclusions about the value and sign of Tolman length. In this paper, a novel method of determining the interfacial tension (solid-liquid and solid-gas interfaces), temperature coefficient of interfacial tension, and Tolman lengths of nanomaterials by adsorption thermodynamics and kinetics was presented. The interfacial tension and its temperature coefficient of the solid-liquid interface of nano cadmium sulfide before adsorption were obtained, and further, the Tolman length was also obtained. The experimental results show that the particle size of nanoparticles has significant effects on the interfacial tension and its temperature coefficient. When the radius is larger than 10 nm, the interfacial tension and its temperature coefficient are almost constant with the decrease of the radius. When the radius is less than 10 nm, the interfacial tension decreases sharply and the temperature coefficient increases sharply with the decrease of the radius, and the temperature coefficient of the interfacial tension is negative. The Tolman length of the solid-liquid interface of nanoparticles is proved to be positive, and the particle size also has a significant effect on the Tolman length. The Tolman length decreases with the decrease of particle size. However, the effects of particle size on the Tolman length become significant only when the particle radius approach or reach the order of magnitudes of molecular (or atomic) radius. The effects of particle size on interfacial tension and Tolman length of nano cadmium sulfide obtained in this paper can provide significant references for the research and applications of interface thermodynamics of other nanomaterials.

Size-dependent melting thermodynamics of nanorods in theory and experiment.

Compared with other morphological nanomaterials, nanorods have many unique properties that are closely related to their thermal stability. However, current studies on melting thermodynamic theory of nanorods are still not perfect, and the mechanism and the quantitative regularities of the effect of size of nanorods on melting thermodynamics still remain unclear. Herein, we proposed a melting model of nanorods, derived the thermodynamic relations (free of any adjustable parameters) between the melting temperature, melting enthalpy, and melting entropy, respectively, and the radius of nanorods, and discussed the mechanism of the effect of nanorods and the size dependences of melting thermodynamic properties. Experimentally, taking the melting of Se nanorods as an experimental system, Se nanorods with different diameters were prepared by a Na2SeSO3 disproportionation method, and then the melting temperature and melting thermodynamic properties were determined by differential scanning calorimetry. The effects of the diameter of Se nanorods on the melting temperature and the melting thermodynamic properties were obtained. The experimental results are consistent with the theoretical relations. Both theoretical and experimental results demonstrate that the radius and length of nanorods have significant effects on the melting temperature and the melting thermodynamic properties; for nanorods with a large aspect ratio, the main factors of influence are interfacial tension and radius. Compared with spherical nanoparticles with the same radius, the reduced values of the melting temperature and the thermodynamic properties of nanorods are just half of those corresponding to spherical nanoparticles; the melting temperature, the melting enthalpy, and the melting entropy decrease with the decrease in the radius, and when the radius exceeds 10 nm, these physical quantities are all linearly related to the reciprocal of the radius. The theory can describe the quantitative size-dependent melting thermodynamic properties of nanorods, explain and predict the melting behaviors of nanorods.

Size and shape dependences of the adsorption kinetics of malachite green on nano-MgO: a theoretical and experimental study.

Compared with bulk materials, there is a considerable difference in the adsorption kinetics of nanoparticles, which mainly depend on particle size and shape. Herein, by introducing the shape factor, we have derived the relations between the kinetic parameters of adsorption and the particle size of nanoparticles of different shapes. Then, the influence of the regularities and mechanisms of particle size and shape on the kinetic parameters of adsorption were discussed. In the experiment, spherical nano-MgO and cubic nano-MgO of different particle sizes were synthesized via a sol-gel method, the kinetic parameters of the adsorption of malachite green on nano-MgO were determined, and the influence of the regularities of particle size and shape on the adsorption kinetic parameters were obtained. The experimental results show that shape and particle size may significantly influence the kinetic parameters of adsorption. For the adsorption of nano-MgO with the same equivalent particle diameter, compared to spherical shapes, the rate constant of adsorption k for cubic shapes is larger, while the apparent activation energy Ea and the pre-exponential factor A are smaller. For the adsorption of spherical or cubic nano-MgO, k increases with decreasing particle size, while Ea and A decrease, and there exist good linear relationships between ln k, Ea, ln A and the reciprocal of particle size. The experimental results are well in agreement with the theoretical relations. Furthermore, k is influenced by the shape factor, Ea by the shape factor and the specific surface enthalpy, and A by the shape factor and the temperature coefficient of surface tension. The kinetic theory of adsorption can quantitatively describe the influence of the regularities and mechanisms of particle size and shape on the adsorption kinetics of nanoparticles and provide significant guidance for the research and the application of nano-adsorptions in the related fields.

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-CeO2 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-CeO2, the adsorption equilibrium constant K⊖ and the adsorption rate constant k increase, while the molar Gibbs free energy of adsorption Δads Gm⊖, the molar adsorption entropy Δads Sm⊖, the molar adsorption enthalpy Δads Hm⊖, the adsorption activation energy Ea, and the adsorption pre-exponential factor A all decrease. Indeed, ln K⊖, Δads Gm⊖, Δads Sm⊖, Δads Hm⊖, ln  k, Ea, and ln  A are each linearly related to the reciprocal of particle size. Furthermore, thermodynamically, Δads Gm⊖ and ln  K⊖ are influenced by the molar surface area and the difference in surface tensions, Δads Sm⊖ is influenced by the molar surface area and the difference in temperature coefficients of surface tension, and Δads Hm⊖ is influenced by the molar surface area, the difference in surface tensions, and the difference in temperature coefficients of surface tension. Kinetically, Ea 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.

Determination Method and Size Dependence of Interfacial Tension between Nanoparticles and a Solution.

Interfacial tension plays an important role in the processes of preparation, research, and application of nanomaterials. Because the interfacial tension is fairly difficult to be determined by experiments, it is still unclear about the effect of particle size on interfacial tension. In this paper, we proposed a method to determine the interfacial tensions and its temperature coefficients by determining the electrode potential of the nanoparticle electrode. Nano-Au with different radii (from 0.9 to 37.4 nm) in an aqueous solution was taken as a research system; we determined the interfacial tension and its temperature coefficient of the interface and discussed the size dependence. At the same time, we found surprisingly that this method can also be applied to determine the Tolman length and the atomic radius. The results show that the particle size of nano-Au has remarkable influences on the interfacial tension and its temperature coefficient. As the particle size decreases, the interfacial tension and the absolute value of its temperature coefficient increase. With the decrease of radius, the influences of the particle size on the interfacial tension and its temperature coefficient become more significant, whereas the influences can be neglected when the radius exceeds 10 nm. In addition, the results also show that the Tolman length is a negative value, and temperature has little effect on the Tolman length. This research can provide a new method to conveniently and reliably determine the interfacial tension on interfaces between nanoparticles and solutions, the temperature coefficients, the Tolman lengths, and the atomic radii; and the size dependences can provide important references for preparation, research, and application of nanomaterials.

Shape dependence of thermodynamics of adsorption on nanoparticles: a theoretical and experimental study.

Nanomaterials have excellent adsorption performance, which mainly depends on the adsorption thermodynamics that is related to the shape of the nanoparticles that make up the nanomaterial, but the effects of shape on the thermodynamics of adsorption are not fully clear. In this paper, theoretically, the general formulae of adsorption thermodynamic properties for nanoparticles with different shapes and different sizes were derived, and the influencing regularities and mechanisms on adsorption thermodynamic properties were discussed. Experimentally, the influences of the shape and size of nano-CeO2 on the thermodynamics of adsorption were studied in aqueous solution. The experiment results showed that the shape has significant influences on the thermodynamics of adsorption, and the smaller the particle size, the more significant the effects of shape on the thermodynamics. For the adsorption of nano-CeO2 with different shapes and the same equivalent particle size, compared with the sphere, the equilibrium constant of adsorption for the octahedron is larger, while the molar Gibbs free energy of adsorption , the molar adsorption enthalpy of adsorption and the molar adsorption entropy of adsorption are smaller. For the adsorption of nano-CeO2 with the same shape, with the decreasing particle size, increases, while , and decrease; and , , and are each linearly related to the reciprocal of particle size. The experimental results are consistent with the theoretical relations. The theories can quantitatively describe the adsorption behavior on nanoparticles, explain the regularities and mechanisms of influence of shape, and provide guidance for the research and application of nanoadsorption.

Inside-out regulation of MnO toward fast reaction kinetics in aqueous zinc ion batteries.

An "inside-out regulation" strategy is proposed to improve the Zn2+ storage of MnO by Ni doping into the lattice and graphene wrapping outside the nanoparticles. The as-prepared Ni-MnO@rGO exhibits 112 mA h g-1 at 2.0 A g-1 over 800 cycles, due to the improved transport of electrons and ions from the synergistical function of intrinsic doping and external graphene encapsulation.

The effect of microdroplet size on the surface tension and Tolman length.

A monomolecular layer model of the surface phase of microdroplets was proposed, and the exact expression for Tolman length was derived in this paper. The Tolman lengths of water, n-pentane, and n-heptane were calculated by the expression, and the values are quite in agreement with the experimental values. By use of the Gibbs-Tolman-Kening-Buff equation, the exact relationship between the microdroplet surface tension and the radius is obtained, and the predicted values agree well with the simulated values. The results show that there is an obvious effect of the size of microdroplets (or nanoparticles) on the surface tension, and the surface tension decreases with decreasing droplet size. For the microdroplets of general liquid, only if their radius approaches or reaches 10(-9) m does the effect become significant.