By Anonymous on Tuesday, June 29, 2004 - 03:14 am:

I wonder if anyone can help me.

I have calculated resolution between two peaks using the half width method i.e. 1.18*(Rt2-Rt1)/(W1+W2)

Can anyone tell me what the values resulting from this calculation mean, that is, at what value can the peak be defined as 100% resolved?

All the searchs I have conducted about resolution refer to the following equation: ¼ [k’ / (1 + k’)] N½ (a - 1), where a resolution of greater than 1.5 = 100% separation.

My resolution values of greater than 2 are obviously not well separated.

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By DR on Tuesday, June 29, 2004 - 06:22 am:

You have it a bit backwards - more resolution is indicated by higher values. At ~1.5, you have baseline resolution. Beyond 2, you have peaks that you could toss a cat through - maybe it is time to consider shortening your run time by modifying your % organic, gradient profile etc. if your lowest resolution is >2...

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By MAS on Tuesday, June 29, 2004 - 08:08 am:

I can think of 2 reasons why your separation might not be as good as your calculated resolution suggests. One is if you have tailing. This, of couse, causes peaks to be wider at the base but may not have that much of an effect on the peak width at the half-height point.

The second thing is the way the baseline is constructed. For example if you have 2 peaks that are not resolved but you have contructed the baselines so they connect to the valley point (instead of using a drop line) the calculated resolution will be better than the true resolution.

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By tom jupille on Tuesday, June 29, 2004 - 10:08 am:

To elaborate a bit on MAS's post:

The "textbook" definition of resolution uses *baseline* resolution:

Rs = 2*(Rt2-Rt1)/(W1+W2)

The "equivalent" formula you used is based on the assumption that the baseline width is 1.7 times the width-at-half-height. This assumption is strictly true *only* for a perfectly symmetrical, Gaussian peak.

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By BB on Thursday, July 1, 2004 - 07:38 am:

Guys I'm new to this thing...how do you measure the width at half hight? Or do the software provide that? and are all the units in min?
Thanks?
BB

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By Rob Burgess on Thursday, July 1, 2004 - 08:22 am:

I have a thing about Rs calculations and what you actually see iin the chromatogram. DR has stated above that with a Rs of 2.0 you can throw a cat through it. However, as the first poster says, his measuremnt of Rs is greater than 2 but he still visibly cannot see baseline spearation. One common situation where RS's > 2 do not visbly give you baseline Rs is when the opposing peak height ratios are very different (ofeten the case for impurity dterminations). when this is the case Then more stringent Rs numbered criteria need to be employed. This is all explained in the bible text Practical HPLC methoid development, where I actually learned about this phenomena.

I have a further question if a there is a peak height ratio of 100:1, with a calcualted Rs of 1.2, would you even see the smaller peak? the reason I'm asking is that our validation guideline states that this is the minimum that we acan accept. however, for accurate and precise quantification shouldn't this number be increased to 4 or higher to achieve baseline Rs.

At the end of the day instead of just dealing with fanciful calculations and numbers, one can very easily see by the naked eye whther Rs is acceptable for a Rs in case.

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By tom jupille on Thursday, July 1, 2004 - 09:08 am:

To BB: most data systems will report width at half-height. If your data system does not, manual measurement is easy from a printout of the chromatogram: it's the distance between the back and the front of the peak measured at a 50% of the maximum peak height.

Units can be distance, time, or volume (if you know the chart scale, you can convert distance to time, and if you know the flow rate, you can convert time to volume). You just have to use the same units for both retention and width.

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By BB on Thursday, July 1, 2004 - 09:15 am:

Thanks a lot Tom!

BB

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By tom jupille on Thursday, July 1, 2004 - 10:07 am:

To Rob Burgess: This gets to be a big topic when we do our Advanced HPLC Method Development course. To answer the specific question, if both peaks are "ideal" (Gaussian, no tailing), then you will indeed see a 1% peak at Rs=1.2.

If you want to play with things, I've posted a quick-and-dirty Excel worksheet here:
http://www.sepsci.com/temp/GAUSSIAN.xls
(note that if you type this address in to your browser, it is case-sensitive).
This displays the two peaks individually and summed, and lets you change heights, widths, and retention times.

The catch is that real peaks are almost never ideal, so that additional resolution is required to compensate for tailing. Unfortunately, the measurement(s) used for tailing (Asymmetry Factor @ 10% or Tailing Factor @ 5%) are miserably uninformative in that two peaks can have the same Tailing Factor and differ significantly in the details of the distribution. This makes it virtually impossible to set quantitative rules for the resolution required. {by the way, if someone wants to contradict me on this, I'd be delighted!}

The "naked eye" (to borrow your phrase) approach is not good science, but it's what we have to live with.

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By Anonymous on Thursday, July 1, 2004 - 10:22 am:

I had resolution greater than 6 between active and impurity, with impurity eluting later. Impurity was at approximately 0.1%. Management thought the separation was inadequate since the "naked eye" could see that the impurity was eluting on the tail of the active when chromat was really expanded. Agree with Tom that tailing factors tell you next to nothing about what is going on at the bottom 0.1% of your peak.

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By DR on Wednesday, July 7, 2004 - 08:46 am:

Agreed - tailing problems can and do frequently compound resolution problems that are already tricky when dealing with height ratios that are far from 1:1. In the case of a small peak that is obviously eluting on the tail of a much larger peak, there is frequently little one can do (in a reasonable HPLC method time frame) except integrate properly (commonly tangent skim in the case of reasonable resolution on a protracted tail), and also provide an exponential skim as a 'worst case' integration. Show both to management and tell them that further resolution between the peaks will come only if they are willing to wait a long time between injections. Hope that they will see reason when confronted with physics...
GL