I have been trying to find information on the following without much luck. I'm wondering if anyone has any advice or suggestions.

It is well known that, for chromatographic applications involving packed column, smaller particle diameters are preferred as they lead to better efficiency. However, with non-chromatographic applications such as: trapping on a sorbent cartridge in SFE or for thermal desorption, there is no efficiency issue. So, in these cases one would want to be able to figure out the effect of particle diameter on the phase ratio or "stopping power" of these sorbent cartridges.

From what I understand, the mobile phase volume would not change with particle diameter (they say well packed chromatography columns have an interparticle porosity of 0.4 regardless of the diameter of the particles).

However, the mass or volume of the stationary phase would change. Presumably as the particle diameter increases the surface area would decrease. But I do not know what the exact relationship would be. It may be fairly complex given that "surface area" is a two dimensional concept, but the stationary phase on column packings have some depth which needs to be considered.

May need a mathematician for this one.

Would appreciate any help/guidance/suggestions that anyone has to offer.

Thank You
Mark A Stone

The short answer is that there is no effect of particle size on true equilibrium phase ratio under "ideal" conditions with linear isotherms. You don't have to use a chromatographic process to measure phase ratio, athough it can be a more elegant method. Without chromatography there is no diffusion limiting process (resistance to mass transfer), no carrier velocity, hence no particle size effect.

There is a much longer answer which would occupy a book chapter on the theory of non-ideal chromatography (not non-linear chromatography - overloaded peaks are not considered here). If particle size had an effect so would column diameter and length. In fact if you just measure phase ratio by the time it takes for a peak crest to get to the other end of the trap or column, particle size does have an effect, but then you would not be measuring true phase ratio. For that you must use a point that accounts for inefficiency (resistance to mass transfer) or a finite value of N the number of theoretical plates. With short traps N can be very finite indeed. What do you think N=1 looks like? It can happen in some special micropore effects at ambient temperature and high flow rates. The true phase ratio here is calculated by injecting a small pulse and talking the first statistical moment of the eluting peak, sometimes known as the centroid or peak centre of gravity. When N=1 the centroid takes about three times as long as the crest and the peak is heavily skewed.

I use this curve function to model the amplitude of skewed peaks in Excel
(1/v). [N.V/2pi.v]^0.5 exp [(-N/2) . ( (v-V)^2 )/v.V ].
where V is the fixed centroid or true retention volume or time (call it 1 for this purpose) and v is the variable volume or time. Breakthrough curves of a steady state inlet concentration will just be the integral of the above which you can calculate numerically (provided you are not going into the non-linear overloaded region).
Acknowledgments for the curve function to D. Underhill (1985), Pulse residence in short chromatographic columns, Anal Chem 57, 826-829.

The short answer is that there is no effect of particle size on true equilibrium phase ratio under "ideal" conditions with linear isotherms. You don't have to use a chromatographic process to measure phase ratio, athough it can be a more elegant method. Without chromatography there is no diffusion limiting process (resistance to mass transfer), no carrier velocity, hence no particle size effect.

There is a much longer answer which would occupy a book chapter on the theory of non-ideal chromatography (not non-linear chromatography - overloaded peaks are not considered here). If particle size had an effect so would column diameter and length. In fact if you just measure phase ratio by the time it takes for a peak crest to get to the other end of the trap or column, particle size does have an effect, but then you would not be measuring true phase ratio. For that you must use a point that accounts for inefficiency (resistance to mass transfer) or a finite value of N the number of theoretical plates. With short traps N can be very finite indeed. What do you think N=1 looks like? It can happen in some special micropore effects at ambient temperature and high flow rates. The true phase ratio here is calculated by injecting a small pulse and talking the first statistical moment of the eluting peak, sometimes known as the centroid or peak centre of gravity. When N=1 the centroid takes about three times as long as the crest and the peak is heavily skewed.

I use this curve function to model the amplitude of skewed peaks in Excel
(1/v). [N.V/2pi.v]^0.5 exp [(-N/2) . ( (v-V)^2 )/v.V ].
where V is the fixed centroid or true retention volume or time (call it 1 for this purpose) and v is the variable volume or time. Breakthrough curves of a steady state inlet concentration will just be the integral of the above which you can calculate numerically (provided you are not going into the non-linear overloaded region).
Acknowledgments for the curve function to D. Underhill (1985), Pulse residence in short chromatographic columns, Anal Chem 57, 826-829.