Citation: DAI Chaozheng, XU Xiaoping. Unified form of liquid chromatography plate height equation[J]. Chinese Journal of Chromatography, 2020, 38(5): 581-586. doi: 10.3724/SP.J.1123.2019.08024
液相色谱塔板高度方程的统一形式
H=2γDm/u+2λdpu1/3/u1/3+ω（Dm/dp）1/3+2ku/（1+k）2（1+κ0）kd+θ（κ0+κ0k+k）2dp2u/30Dmκ0（1+κ0）2（1+k）2+κi（κ0+κ0k+k）2dp5/3u2/3/3κ0ΩDm2/3（1+κ0）2（1+k）2+r02（κ0+κ0k+k）u/4Dr（1+k）exp（-Kr02α）
该方程概括了高效液相色谱（HPLC）、超高效液相色谱（UPLC）、毛细管电色谱（CEC）和消滞留层液相色谱（ESFLC）塔板高度与各种因素的关系。方程最后一项代表了径向扩散和柱发热对塔板高度的贡献。当流动相线速度较低且柱内径较细时，流动相摩擦生热和径向扩散对塔板高度的贡献趋近于零，塔板高度方程还原成Horvath和Lin的方程；当流动相线速度较高时，由于流动相摩擦生热，柱轴心与边缘温差增加，导致流动相线速度径向分布差异，使得柱效率降低。柱轴心与边缘的温差与流动相线速度平方成正比。该文指出，在流动相高线速度情况下，液相色谱的柱效率与柱内径密切相关，采用细内径柱有利于实现高速与高效率；过高的流动相线速度将导致色谱柱效率崩溃。
English
Unified form of liquid chromatography plate height equation
H=2γDm/u+2λdpu1/3/u1/3+ω(Dm/dp)1/3+2ku/(1+k)2(1+κ0)kd+θ(κ0+κ0k+k)2dp2u/30Dmκ0(1+κ0)2(1+k)2+κi(κ0+κ0k+k)2dp5/3u2/3/3κ0ΩDm2/3(1+κ0)2(1+k)2+r02(κ0+κ0k+k)u/4Dr(1+k)exp(-Kr02α)
This equation summarized the relationship between plate heights for high performance liquid chromatography (HPLC), ultra performance liquid chromatography (UPLC), capillary electrochromatography (CEC), and eliminate stagnant fluid layer chromatography (ESFLC) and various factors. The last term in the equation represented the contribution of radial diffusion and column heating to the plate height. When the linear velocity of the mobile phase was low and the column diameter was fine, the contribution of the frictional heat generation of the mobile phase to the plate height approached zero, and the plate height equation reduced to the Horvath and Lin equation. When the linear velocity of the mobile phase was too high, friction heat was generated in the column system. The temperature difference between the axis and the edge of the column increased, resulting in a decrease in the column efficiency. The temperature difference between the axis and the edge of the column was proportional to the square of the velocity of the mobile phase. The authors clearly point out that the column efficiency in liquid chromatography is closely related to the inner diameter of the column. The use of a column with a small inner diameter is conducive to high analytical speed and high efficiency, a very high mobile phase line velocity would serious degrade the column efficiency.
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