How to think about the retention factor

[Deoxyribonucleon]

I'm a visual thinker so I have to be able to visualise concepts to think about them. I'm struggling a bit with the concept of retention factor aka capacity factor. I keep coming across explanations like this:

The capacity factor is the ratio of the mass of the compound in the stationary phase relative to the mass of the compound in the mobile phase. The capacity factor is a unitless measure of the column's retention of a compound.

which make no sense to me. The mathematical formula for retention factor is:

so its basically the amount of time that the analyte spends in the mobile phase divided by the time it takes the mobile phase itself to elute (the void time). How does that have anything to do with the time the analyte spends in the mobile phase? I can see that the value of the retention factor is directly proportional to the extent to which an analyte is retained by the mobile phase so thats how I like to think about this retention factor concept but these explanations are getting me confused. Any other visual thinkers here who can suggest a way to visualise this concept?

EDIT: Also, another thing that throws me off is the fact that I first came across the term retention factor in TLC. Its clearly not the same concept. TLC retention factor is inversely proportional to the extent to which the analyte is retained by the stationary phase. Is there a reason why the TLC retention factor is inverted or is this just one of those historical mistakes that never got rectified?

[unmgvar]

the basic concept with K that we like and so I prefer to use it instead of Retention Time for SST settings
is that it takes out the extra column volumes out, and these differ from system to system.

also this allows you to see if you have any type of good retention of the compound on your column
less than 2 and the compound is not retained enough in the column and so you can expect instability of it's behavior in the robustness of the method in the long run
these days since we do a lot of method transfer from HPLC to UHPLC, again a method with K is easier to move then a method with RT for QA and QC

but basically think of it as if the T0/ TR is the first wave of the mobile phase after injection. this is the physical time the first wave of mobile phase moves along the column, based on speed, and linear velocity. anything longer than that that stays in the column is doing some sort of interaction with the chemistry of the column and is delayed.

[tom jupille]

The k' (LC or GC) and Rf (TLC) values are defined that way for convenience (historical accident if you will). In TLC the migration time is (more or less) constant, and migration distance is easy to measure. In the column techniques, the migration distance is (more or less) constant and migration time is easy to measure. The terminology *is* confusing, but usually clear in context; if somebody uses the term "retention factor" in GC or LC, they are probably talking about k' whereas if they are doing TLC they are probably talking about Rf.

so its basically the amount of time that the analyte spends in the mobile phase divided by the time it takes the mobile phase itself to elute (the void time)

You actually have that part of it wrong. The retention time is the *sum* of the time the molecule spends in *both* phases.

Do a little algebra and try thinking of it this way: you can rearrange the formula to
k' = tR/tm + 1
tm is the amount of time it takes flush one column volume of mobile phase through the system, so k' is the number of column volumes of juice that it takes to wash a compound through the system minus (you can't count the first one, because it's already in the column when you make the injection!).

It would be more convenient to define k' as simply tR/tm (the number of column volumes required for elution), but the standard definition allows a nice relationship to the distribution coefficient, k. k' is the product of the distribution coefficient and the phase ratio.

[Deoxyribonucleon]

the basic concept with K that we like and so I prefer to use it instead of Retention Time for SST settings
is that it takes out the extra column volumes out, and these differ from system to system.

Ah yeah, I didn't think of that. Thanks a lot!

these days since we do a lot of method transfer from HPLC to UHPLC, again a method with K is easier to move then a method with RT for QA and QC

Yeah I see it now. The retention and void times vary depending on the column length and volume but the proportion is independent of the volume variable. I'm only beginning to learn this concept of proportions of variables being constant. I see how this principle is used to overcome the inability of an injector to inject identical volumes of sample each time using the internal standard method.

You actually have that part of it wrong. The retention time is the *sum* of the time the molecule spends in *both* phases.

Do a little algebra and try thinking of it this way: you can rearrange the formula to
k' = tR/tm + 1
tm is the amount of time it takes flush one column volume of mobile phase through the system, so k' is the number of column volumes of juice that it takes to wash a compound through the system minus (you can't count the first one, because it's already in the column when you make the injection!).

It would be more convenient to define k' as simply tR/tm (the number of column volumes required for elution), but the standard definition allows a nice relationship to the distribution coefficient, k. k' is the product of the distribution coefficient and the phase ratio.

I'm starting to get the idea now. I don't like the terminology, I think retention time should be called elution time (since its the time it takes for the sample to elute) and the corrected retention time should just be called the retention time (since its the amount of time the sample spends being retained by the stationary phase). Nothing I can do about the terminology though so I might as well just accept it. Nice one, I'm attempting to visualise what you said about k' being the number of column volumes of liquid that it takes to wash the sample through the system and a bigger picture is starting to emerge. Thanks for the info, I didn't know about that relationship between retention factor, distribution constant and phase ratio.

EDIT: What you proposed about thinking of k' as the number of column volumes it takes to wash the sample through works for me. Thanks a lot! Thats exactly what I was looking for. This mental image also illustrates why k' is independent of column volume.