双语化学辞典Chem Lexicon
概念 · 表面化学 · 胶体与界面 Surface chemistry · Colloids and interfaces

临界胶束浓度Critical micelle concentration

拼音Pinyin lín jiè jiāo shù nóng dù 别名Also CMC;CMC

定义Definition

临界胶束浓度是表面活性剂在溶液中开始大量形成胶束时的浓度。在 CMC 附近,溶液的表面张力、电导率、渗透压、增溶能力和光散射等性质会发生突变。

The critical micelle concentration is the surfactant concentration at which micelles begin to form in large numbers. Near the CMC, surface tension, conductivity, osmotic pressure, solubilising power and light scattering all change abruptly.

原理Principle

低浓度时表面活性剂分子主要吸附在气-液界面,表面张力随浓度增加而迅速下降;当表面吸附趋于饱和、浓度达到 CMC 后,继续加入的分子在溶液内部自发缔合成胶束(疏水尾朝内、亲水头朝外,通常含 50–100 个分子),表面张力几乎不再下降。胶束化由疏水效应驱动,主要是熵增:疏水链离开水后,原先围绕其排列有序的水分子获得自由。

At low concentration surfactant molecules adsorb mainly at the air–water interface and surface tension falls quickly with concentration; once the surface is nearly saturated at the CMC, further molecules associate spontaneously in solution into micelles (tails in, heads out, typically 50–100 molecules), and surface tension barely falls further. Micellisation is driven by the hydrophobic effect, chiefly an entropy gain: when the chains leave the water, the ordered water molecules that surrounded them are freed.

影响因素与测定Factors and measurement

疏水链越长,CMC 越低(每增加一个 CH₂,离子型 CMC 约降为原来的一半);非离子型表面活性剂的 CMC 一般远低于离子型;加入电解质会降低离子型表面活性剂的 CMC。测定方法包括表面张力法(曲线拐点)、电导率法(仅适用于离子型)、荧光探针法(芘的 I₁/I₃ 比值)和光散射法。

Longer hydrophobic chains lower the CMC (each added CH₂ roughly halves it for ionic surfactants); non-ionic surfactants have much lower CMCs than ionic ones; and added electrolyte lowers the CMC of ionic surfactants. It is measured from the break in surface-tension or conductivity curves (the latter for ionic surfactants only), with fluorescent probes such as pyrene's I₁/I₃ ratio, or by light scattering.

意义Significance

1913 年麦克贝恩研究肥皂溶液的电导时提出胶束概念。CMC 是表面活性剂的重要指标:洗涤剂有效浓度需在 CMC 以上;药物制剂中利用胶束增溶难溶药物;生物化学中常用 CMC 较高的去污剂(如胆酸盐)溶解膜蛋白,便于透析除去。

McBain proposed micelles in 1913 while studying the conductivity of soap solutions. The CMC is a key surfactant parameter: detergents work above it, drug formulations use micelles to solubilise poorly soluble drugs, and biochemists solubilise membrane proteins with high-CMC detergents such as cholates, which are easy to remove by dialysis.

反应Reactions

n S ⇌ Sₙ胶束ΔG°_mic ≈ RT·ln(CMC)n S ⇌ Sₙ; ΔG°_mic ≈ RT·ln(CMC)

非离子型表面活性剂的近似关系(CMC 用摩尔分数表示)。

Approximate relation for non-ionic surfactants, with CMC as a mole fraction.

SDS:CMC = 8.2 mmol/L十四烷基硫酸钠:约 2.1 mmol/LSDS: CMC = 8.2 mmol/L; AlkylSulfuric acid: ≈ 2.1 mmol/L

链长增加两个碳,CMC 约降为 1/4

Two more carbons cut the CMC to about a quarter

年表Timeline

  • 1913

    麦克贝恩提出胶束概念

    McBain proposes the micelle

  • 1936

    哈特利提出球形胶束模型

    Hartley proposes the spherical micelle model

  • 1976

    以色列奇维利等提出临界堆积参数

    Israelachvili and others introduce the critical packing parameter

相关公式Formulas

吉布斯吸附等温式 Gibbs adsorption isotherm→
\[\Gamma_2 = -\frac{1}{RT}\left(\frac{\partial\gamma}{\partial\ln a_2}\right)_T \approx -\frac{c}{RT}\frac{d\gamma}{dc}\]
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).