Experimental studies on the applicability of the Kelvin equation to highly curved concave menisci

The thermodynamic properties of liquids trapped in microscopic pores are described in theory by the Kelvin equation, which relates the equilibrium meniscus curvature to the relative vapor pressure. We report here two series of experiments designed to test the validity of the Kelvin equation by direct measurement of the mean radius of curvature of the surface of cyclohexane condensed between crossed mica cylinders. In one series of experiments, the relative vapor pressure of the volatile cyclohexane was controlled by mixing it with a relatively involatile solute (n-dodecane or n-hexadecane). We found that the mean radius of curvature rapidly reached that predicted by the Kelvin equation at each relative vapor pressure of the volatile liquid, but that there was also a slow, but continuous, accumulation of the “involatile” solute at the point of condensation as the system approached true equilibrium. Such accumulation of very low vapor pressure materials may be one factor responsible for the discordant results reported by earlier workers. We find that the process of impurity buildup is complex, and suggest that studies of real porous systems may be affected by accumulation of “involatile” impurities through the vapor phase and by surface diffusion. The other series of experiments was designed to eliminate the impurity problem by maintaining the vapor pressure by temperature control of the pure liquid. The results from this series of experiments were not time dependent, and no evidence of contamination was found. The measured radii were within ±6% of those predicted by the Kelvin equation, for radii in the range 4–20 nm. We conclude that the thermodynamic basis of the Kelvin equation is valid in principle for menisci with radii as low as 4 nm.