含义Meaning
超速离心中沉降系数与摩尔质量的关系。沉降系数单位为斯韦德贝里 S（\(10^{-13}\) s），如核糖体 70S、80S。
Links the sedimentation coefficient in ultracentrifugation to molar mass; unit svedberg S = \(10^{-13}\) s (e.g. 70S, 80S ribosomes).
符号说明Symbols
| 符号Symbol | 含义 Meaning | 单位 Unit |
|---|---|---|
| \(s\) | 沉降系数sedimentation coefficient | s |
| \(\omega\) | 角速度angular velocity | rad·s⁻¹ |
| \(\bar v\) | 偏比容partial specific volume | mL·g⁻¹ |
| \(\rho\) | 溶剂密度solvent density | g·mL⁻¹ |
| \(f\) | 摩擦系数frictional coefficient | kg·s⁻¹ |
| \(D\) | 扩散系数diffusion coefficient | m²·s⁻¹ |
推导Derivation
粒子匀速沉降时离心力 − 浮力 = 摩擦力：\(m\omega^2r - m\bar v\rho\,\omega^2 r = fv\)。
At terminal velocity, centrifugal minus buoyant force equals friction: \(m\omega^2r(1-\bar v\rho) = fv\).
定义 \(s = v/(\omega^2r) = m(1 - \bar v\rho)/f\)，以 \(m = M/N_A\) 代入。
Define \(s = v/(\omega^2r)\) and use \(m = M/N_A\).
由爱因斯坦关系 \(D = k_\mathrm{B}T/f\) 消去 f，得 \(M = sRT/[D(1-\bar v\rho)]\)。
Eliminate f with Einstein’s \(D = k_\mathrm{B}T/f\).
适用条件与局限Assumptions & limitations
s 不可加和（70S 核糖体 = 50S + 30S），因为 s 还取决于形状。
s values are not additive (70S = 50S + 30S) because shape matters.
应外推到无限稀释并换算到 20 °C 水中（\(s_{20,w}^0\)）。
Extrapolate to infinite dilution and correct to water at 20 °C.