含义Meaning
溶质在表面的过剩量与表面张力随浓度变化的关系。使表面张力降低的物质（表面活性剂）在表面富集（Γ > 0）；无机盐使 γ 略增，表面贫化。
Relates surface excess to how surface tension changes with concentration. Substances that lower γ (surfactants) accumulate at the surface (Γ > 0); inorganic salts raise γ slightly and are depleted.
符号说明Symbols
| 符号Symbol | 含义 Meaning | 单位 Unit |
|---|---|---|
| \(\Gamma_2\) | 溶质表面过剩量surface excess of solute | mol·m⁻² |
| \(a_2\) | 溶质活度solute activity | 1 |
推导Derivation
表面相的吉布斯–杜亥姆关系：\(d\gamma = -\sum_i\Gamma_i\,d\mu_i\)（恒温）。
Surface Gibbs–Duhem: \(d\gamma = -\sum\Gamma_i\,d\mu_i\).
选择分界面使溶剂过剩量为零（\(\Gamma_1 = 0\)），且 \(d\mu_2 = RT\,d\ln a_2\)。
Choose the dividing surface with Γ₁ = 0 and use \(d\mu_2 = RT\,d\ln a_2\).
于是 \(\Gamma_2 = -(1/RT)\,\partial\gamma/\partial\ln a_2\)。离子型表面活性剂（含反离子）还需乘以 1/2。
For ionic surfactants a factor ½ appears.
适用条件与局限Assumptions & limitations
稀溶液近似用浓度代活度；临界胶束浓度以上 γ 几乎不变，公式不再给出表面量。
Uses concentration for activity; above the CMC γ stops changing.
例题Worked example
十二烷基硫酸钠在 CMC（8 mmol/L）以下 γ–lg c 斜率给出 Γ ≈ 3×10⁻⁶ mol/m²，即每个分子约占 0.5 nm²。
SDS below its CMC gives Γ ≈ 3×10⁻⁶ mol m⁻² (~0.5 nm² per molecule).