Abstract
Surface tension is a key parameter for understanding nucleation in the very initial stage of phase transformation. Although surface tension has been predicted to vary with the curvature of the liquid-vapor interface, particularly at the large curvature of, e.g., the subnanometric critical nucleus, experimental study still remains challenging due to inaccessibility to such a small cluster. Here, by directly measuring the critical size of a single capillary-condensed nanomeniscus using atomic force microscopy, we address the curvature dependence of surface tension of alcohols and observe that the surface tension is doubled for ethanol and n-propanol with a radius-of-curvature of ∼-0.46 nm. We also find that the interface of larger negative (positive) curvature exhibits larger (smaller) surface tension, which evidently governs nucleation at the ∼1 nm scale and below, indicating more facilitated nucleation than normally expected. Such well characterized curvature effects contribute to better understanding and accurate analysis of nucleation occurring in various fields including materials science and atmospheric science.
Highlights
Surface tension is a key parameter for understanding nucleation in the very initial stage of phase transformation
Surface-force apparatus (SFA) experiments showed the validity of constant surface tension for a cyclohexane meniscus with a mean radius-of-curvature down to −4 nm.[20]
The researchers directly measured the distance between two mica surfaces where the meniscus is formed upon contact, they could not clarify further the curvature-dependent change in surface tension due to the experimental limit of distance measurement
Summary
When characterizing phase transitions including such nucleation processes, surface tension is an important thermodynamic parameter.[10,11,12] It determines the energy barrier to overcome to form a cluster of new phase and provides the equilibrium criteria for the critical nucleus, the very first stage of nucleation. Surface-force apparatus (SFA) experiments showed the validity of constant surface tension for a cyclohexane meniscus with a mean radius-of-curvature down to −4 nm.[20] the researchers directly measured the distance between two mica surfaces where the meniscus is formed upon contact, they could not clarify further the curvature-dependent change in surface tension due to the experimental limit of distance measurement. SFA experiments provided the adhesion force measurement for capillary-condensed cyclohexane in the contact zone down to the molecular. We measure the surface tension of ethanol and n-propanol at the nanoscale by direct size measurement of a single critical nucleus, capillary-condensed between two surfaces, which enables the identification of the unambiguous increase of surface tension. Since the experiment is conducted at unsaturated low vapor pressure ( p/p0 < 0.5), a nanomeniscus with large negative curvature is formed (Fig. 1(d)), which is (meta-) stable in equilibrium, minimizing the typical systematic errors in size characterization, in contrast to the supersaturated case.[25,26,27] Note that the curvature dependent change in surface tension for nucleation systems that have either sign of curvature (Fig. 1(b)–(d)) is closely interrelated.[28]
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