Efficiency is said to be roughly related to column length, particle size by the equation:
The operant word in there is "roughly"
.
If memory serves, the "random walk" model of peak broadening suggests that the plate height at the optimum flow rate
for a perfectly packed column should be about twice the particle diameter. For small molecules on columns with small particles (say, in the 3-micron range or below), the C-term is fairly small, so the Knox (or VanDeemter) plots are fairly flat, which means that the plate height at "typical" flow rates is not that much worse than at the optimum flow (maybe 10% or so).
In practice, what we see is the net effect of the column plus "extra-column" band broadening, so reduced plate heights are typically > 2. That said, I've seen reduced plate heights down around 1.2 - 1.5 published for some of the 2.x-micron "superficially porous" material. It looks to my eye like the C-term is about what you'd expect, with the improved efficiency resulting from an anomalously small A term -- which goes to show that "the theory is not the reality"!
As a
very rough approximation I've used:
N = 3000 x dp / L
where dp is the particle diameter in microns and L is the column length in cm. Yes, I know the units don't cancel; this has no theoretical validity whatever, but it does seem to indicate what we can expect from a good column on a good day (usually around 10k plates from a typical column).