Theoretical consideration of the anomalous temperature dependence of the surface tension of pure liquid gallium

The surface tension of pure liquid gallium in the temperature range 303-503 K (303 K is the melting point) was previously measured using the noninvasive method of capillary wave spectroscopy (CWS). The result of this experiment showed that the value of surface tension increases from 303 to 345 K indicating a negative surface excess entropy (S-sigma), and decreases linearly from similar to 345 to 503 K confirming a negative slope, and thus a positive S-sigma. This unusual behavior of Ga is not known for other liquid metals such as Bi, Pb, Hg, Sn and Al. The reported experimental behavior is modeled here. A theoretical equation for calculating the surface tension of liquid Ga, based upon formulating a proper partition function that includes the rotational part, is derived and described. The theory predicted no maximum in the temperature-dependence of the surface tension, as seen in the experiment, where the analysis was done over a large temperature range (325-503 K). The value obtained from this mathematical expression indicates that the temperature variation of surface tension has no positive slope within the temperature range 303-345 K. At T > 345 K, the surface tension shows the usual linear temperature-dependence with a negative slope. Therefore, the equation is only applicable for the latter temperature range. A comparison between the theoretical and experimental values of surface tension of liquid Ga is discussed.