Water nucleation: A comparison between some phenomenological theories and experiment

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.

Curvature Dependence of the Liquid-Vapor Surface Tension beyond the Tolman Approximation

Surface tension is a macroscopic manifestation of the cohesion of matter, and its value σ_{∞} is readily measured for a flat liquid-vapor interface. For interfaces with a small radius of curvature R, the surface tension might differ from σ_{∞}. The Tolman equation, σ(R)=σ_{∞}/(1+2δ/R), with δ a constant length, is commonly used to describe nanoscale phenomena such as nucleation. Here we report experiments on nucleation of bubbles in ethanol and n-heptane, and their analysis in combination with their counterparts for the nucleation of droplets in supersaturated vapors, and with water data. We show that neither a constant surface tension nor the Tolman equation can consistently describe the data. We also investigate a model including 1/R and 1/R^{2} terms in σ(R). We describe a general procedure to obtain the coefficients of these terms from detailed nucleation experiments. This work explains the conflicting values obtained for the Tolman length in previous analyses, and suggests directions for future work.

Size-Dependent Surface Free Energy and Tolman-Corrected Droplet Nucleation of TIP4P/2005 Water

Classical nucleation theory is notoriously inaccurate when using the macroscopic surface free energy for a planar interface. We examine the size dependence of the surface free energy for TIP4P/2005 water nanodroplets (radii ranging from 0.7 to 1.6 nm) at 300 K with the mitosis method, that is, by reversibly splitting the droplets into two subclusters. We calculate the Tolman length to be -0.56 ± 0.09 Å, which indicates that the surface free energy of water droplets that we investigated is 5-11 mJ/m(2) greater than the planar surface free energy. We incorporate the computed Tolman length into a modified classical nucleation theory (δ-CNT) and obtain modified expressions for the critical nucleus size and barrier height. δ-CNT leads to excellent agreement with independently measured nucleation kinetics.