column format design

[jiangds06]

if I want specific peak capacity (for example 100), what kinds of column formats (particle size 5micron) and flow rate I need in order to use the least solvent consumption. do I need to look at kinetic plot? could anyone give me some literature on this aspect?Thanks so much.

[tom jupille]

Basically the plate number (which determines peak capacity) is related to linear velocity. That, in turn, is a function of the flow rate and the square of the column diameter. For small molecules, the column diameter effect dwarfs everything else, so the short answer is to use a packed capillary column. If you drop from a 4.6mm conventional column to a 500 micron packed capillary, your solvent consumption will drop almost 100 fold (all other things being equal). The catch, of course, is that you can run into hardware limitations in terms of flow rate, injection volume, detector cell volume (extra-column band broadening generally).

Beyond that, perhaps counterintuitively, larger particle sizes (in a longer column) will consume less solvent because the optimum flow rate tends to be inversely related to particle size (they give fewer plates/meter, hence the need for a longer column). Solvent viscosity, analyte molecular weight, temperature, stationary phase pore size distribution, and bondedd-phase chain length also play a role, but that's waaaay outside the scope of a Forum post.

If you want to get into the underlying theory, get a copy of Giddings' book Dynamics of Chromatography. Here's a link to it on Amazon:
http://tinyurl.com/3eztknc

[jiangds06]

Really thanks for your reply. This is very helpful. i know my question is really difficult.
some confusions here, are you suggesting optimum plate count means optimum peak capacity?
and for larger particle size with longer column, why less optimum flow rate can mean less solvent consumption. As I understand, longer column(4.6*500, 10micron) give the same plate count per unit of solvent consumption as small particle size and short column (for example, 4.6*250, 5micron).
Thanks so much!

Basically the plate number (which determines peak capacity) is related to linear velocity. That, in turn, is a function of the flow rate and the square of the column diameter. For small molecules, the column diameter effect dwarfs everything else, so the short answer is to use a packed capillary column. If you drop from a 4.6mm conventional column to a 500 micron packed capillary, your solvent consumption will drop almost 100 fold (all other things being equal). The catch, of course, is that you can run into hardware limitations in terms of flow rate, injection volume, detector cell volume (extra-column band broadening generally).

Beyond that, perhaps counterintuitively, larger particle sizes (in a longer column) will consume less solvent because the optimum flow rate tends to be inversely related to particle size (they give fewer plates/meter, hence the need for a longer column). Solvent viscosity, analyte molecular weight, temperature, stationary phase pore size distribution, and bondedd-phase chain length also play a role, but that's waaaay outside the scope of a Forum post.

If you want to get into the underlying theory, get a copy of Giddings' book Dynamics of Chromatography. Here's a link to it on Amazon:
http://tinyurl.com/3eztknc

[tom jupille]

are you suggesting optimum plate count means optimum peak capacity?

"Peak capacity" is just what it sounds like: the number of peaks that you can fit in a chromatogram. As such, it is the range of retention divided by the average width of a peak. The average width of a peak is a function of the square root of the plate number. Sooooo, for a given retention range, the higher the plate number, the higher the peak capacity.

less optimum flow rate can mean less solvent consumption

Plate number is not related to flow rate as such; it's related to linear velocity. The relationship between plate number and linear velocity is generally given by the Knox equation (for LC) or the Van Deemter equation (for GC). As you decrease particle size, the optimum plate number and the optimum linear velocity both increase (i.e., for smaller particles, you get more plates at a higher velocity). In most cases, optimization is done with respect to run time (we want the fastest separation possible), so the trend is toward smaller particles + higher velocity (and higher pressure, of course). Optimizing solvent consumption goes the other way: what you want is a lower velocity, which means larger particles. That decreases the plate count, but you can get the plates back by going to a longer column.

Now, linear velocity and flow are related by the cross-sectional area. No matter how *long* you make the column, the optimum flow for a given particle size will be the same.

To a certain extent, all of this is hair-splitting (we're talking a factor of maybe 2 - 10). The largest effect is diameter. Going from a "conventional" 4.6-mm id column to a "microbore" 0.25 mm id column drops solvent consumption by a factor of almost 400.

[sepscientologist]

Absolutely. From Giddings later book "Unified Separation Science" Peak Capacity is proportional to sq rt of plate count
and plate count is inversely proportional to particle size. Ignoring practical limitations you might just go to a 2 um
capillary column for the ultimate in high plates/low flows.

[jiangds06]

Really appreciate your help. for solvent consumption argument, I think you have a assumption that elution time are the same for both separations.
But if retention range are the same for both separation, then solvent consumption will be very similar. For example, if goes from 5micron to 10micron, plate counts drop to a half at their respective optimum linear velocity. And optimum linear velocity would also drop to a half. In order to get the plates back, length of 10 micron column needs to be double. Then in order to maintain the same retention range, your run time need also to be double in 10micron column because of column length. So after all, you have the very similar solvent consumption. Am I right? Or we have different assumptions here.

are you suggesting optimum plate count means optimum peak capacity?

"Peak capacity" is just what it sounds like: the number of peaks that you can fit in a chromatogram. As such, it is the range of retention divided by the average width of a peak. The average width of a peak is a function of the square root of the plate number. Sooooo, for a given retention range, the higher the plate number, the higher the peak capacity.

less optimum flow rate can mean less solvent consumption

Plate number is not related to flow rate as such; it's related to linear velocity. The relationship between plate number and linear velocity is generally given by the Knox equation (for LC) or the Van Deemter equation (for GC). As you decrease particle size, the optimum plate number and the optimum linear velocity both increase (i.e., for smaller particles, you get more plates at a higher velocity). In most cases, optimization is done with respect to run time (we want the fastest separation possible), so the trend is toward smaller particles + higher velocity (and higher pressure, of course). Optimizing solvent consumption goes the other way: what you want is a lower velocity, which means larger particles. That decreases the plate count, but you can get the plates back by going to a longer column.

Now, linear velocity and flow are related by the cross-sectional area. No matter how *long* you make the column, the optimum flow for a given particle size will be the same.

To a certain extent, all of this is hair-splitting (we're talking a factor of maybe 2 - 10). The largest effect is diameter. Going from a "conventional" 4.6-mm id column to a "microbore" 0.25 mm id column drops solvent consumption by a factor of almost 400.