含义Meaning
小液滴的饱和蒸气压高于平面液体，凹液面（毛细孔中）的蒸气压则低于平面。解释了过饱和、奥斯特瓦尔德熟化、毛细凝聚，以及小晶粒溶解度较大。
Small droplets have higher vapour pressure than a flat liquid, while concave menisci (in pores) have lower. It explains supersaturation, Ostwald ripening, capillary condensation and the higher solubility of small crystals.
符号说明Symbols
| 符号Symbol | 含义 Meaning | 单位 Unit |
|---|---|---|
| \(p_r\) | 曲率半径 r 处的蒸气压vapour pressure over curvature r | Pa |
| \(p_0\) | 平面液体蒸气压flat-surface vapour pressure | Pa |
| \(V_m\) | 液体摩尔体积molar volume of liquid | m³·mol⁻¹ |
推导Derivation
液滴内液体受附加压力 \(\Delta p = 2\gamma/r\)，其化学势升高 \(V_m\Delta p\)。
The Laplace pressure raises the liquid’s chemical potential by \(V_m\Delta p\).
与蒸气平衡：\(RT\ln(p_r/p_0) = V_m\cdot 2\gamma/r\)。
Equilibrium with vapour gives the result.
凹面取 r < 0，蒸气压降低 → 多孔材料中蒸气在 \(p < p_0\) 时即凝聚（可由此求孔径分布）。
For concave menisci r < 0: condensation below p₀ (pore-size analysis).
适用条件与局限Assumptions & limitations
假设液体不可压缩、γ 与尺寸无关；r 小于约 1 nm 时不可靠。
Assumes incompressible liquid and size-independent γ.
例题Worked example
20 °C 半径 10 nm 的水滴：ln(p/p₀) = 2×0.0728×1.8×10⁻⁵/(10⁻⁸×8.314×293) = 0.108 → 蒸气压高 11%。
A 10 nm water droplet at 20 °C has 11 % higher vapour pressure.