[Unified form of liquid chromatography plate height equation]

The effects of radial diffusion and mobile phase heating on the column efficiency during chromatographic separation were investigated. Starting from the heat transfer equation, an equation of plate height for liquid chromatography was derived using the principle of chromatographic dynamics, with consideration of the mobile phase friction and electric heat generation:H=2γD/u+2λdu^1/3/u^1/3+ω(D/d)^1/3+2ku/(1+k)²(1+κ₀)k+θ(κ₀+κ₀k+k)²d²u/30Dκ₀(1+κ₀)²(1+k)²+κ(κ₀+κ₀k+k)²d^5/3u^2/3/3κ₀ΩD^2/3(1+κ₀)²(1+k)²+r₀²(κ₀+κ₀k+k)u/4D(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.