\[R_s = \frac{2(t_{R2} - t_{R1})}{w_{b1} + w_{b2}} = \frac{\sqrt N}{4}\cdot\frac{\alpha - 1}{\alpha}\cdot\frac{k_2}{1 + k_2}\]
含义Meaning
两峰分开的程度。R_s = 1.5 时两等高高斯峰基线分离（重叠约 0.15%）。珀内尔方程把分离度分解为柱效、选择性和保留三项，指明优化方向。
How well two peaks are separated; R_s = 1.5 gives baseline separation (~0.15 % overlap). The Purnell equation factors resolution into efficiency, selectivity and retention terms, showing what to optimise.
符号说明Symbols
| 符号Symbol | 含义 Meaning | 单位 Unit |
|---|---|---|
| \(R_s\) | 分离度resolution | 1 |
| \(N\) | 理论塔板数plate number | 1 |
| \(\alpha\) | 选择性因子selectivity factor | 1 |
| \(k_2\) | 后出峰的保留因子retention factor of the later peak | 1 |
推导Derivation
按定义：峰间距除以平均峰底宽。
By definition: peak spacing over average base width.
设两峰宽近似相等 \(w = 4t_{R2}/\sqrt N\)，\(t_R = t_M(1 + k)\)。
Assume equal widths \(w = 4t_{R2}/\sqrt N\) and \(t_R = t_M(1+k)\).
代入整理得珀内尔方程。由于 \(R_s \propto \sqrt N\)，分离度加倍需要柱长增加 4 倍；而稍增大 α 效果更显著。
Since R_s ∝ √N, doubling it needs a 4× longer column; a small rise in α helps far more.
适用条件与局限Assumptions & limitations
近似式；峰宽相差大或峰不对称时用定义式计算。
Approximate; use the definition for unequal or asymmetric peaks.