Method Development using "Linear" Buffer Systems

[freemab222]

Having worked for a company that did not encourage publishing by us hoi polloi, I never published the following tidbit, or even checked whether it was already published. For those working in method development, it could speed the optimization of mobile phase pH considerably, as it did for me.

Anyone who has done buffer calculations is probably aware of the "sigmoid" curve titration plot (volume reagent added versus pH). I don't believe it is commonly appreciated that this plot need not be sigmoid, but can be linear. That is to say, within a specified region of pH, it is possible to have a linear relationship between titrant and pH.

More to the point with respect to HPLC mobile phases, it is possible to have two stocks of buffer reagents, and linear change from one to the other will, within a wide range, give a linear and predictable buffer pH. (Note always that when buffer is combined with organic solvent, the apparent pH as measured by the glass electrode will shift. I am speaking of the pH before addition of any organic solvent.)

The "magic" involves in choosing a series of pKa's that are approximately 1.5 pH units apart. (I have no intention of proving this here. I have and can prove it mathematically, but more importantly, I have demonstrated it experimentally. What is important is that this is a calculated result that has been confirmed experimentally, and those calculations can be confirmed by anyone with a slide rule or computer, and those experimental confirmations can be reproduced by anyone who has an analytical balance and a pH meter.)

Curiously, citric acid is a perfect polyacid for this use, as its three pKa's differ by almost exactly 1.5 pH units. (Note that some published values for the pKa's of citric acid include one wrong value -- I forget which. I discovered this when I couldn't confirm the published pKa's, and later found other published values that agreed with my calculations.)

Hence, if you make, for example, 100 mM trisodium citrate solution, and 100 mM citric acid solution, you will find that across the midrange of possible mixtures, the pH will vary linearly with the volume fraction of the former in the mixture (or inverse linearly with the volume of the latter). At the extremes, the linearity is lost, but this still gives a wide range of pH control BY VOLUMETRIC MEANS.

(Note that citric acid can be corrosive to stainless steel and other metals. If using citric acid in HPLC systems, purge after use to prevent the mobile phase from attacking the metal. This is also true of other chelating agents and of chloride ion.)

There is no reason that a single polyacid is needed. Any series of acids or bases (so long as they don't react, precipitate, etc.) can be employed for this purpose. So, for example, one could choose three bases with pKa's of 7.5, 9, & 10.5 and create a two-component buffer system that would range linearly from about (I'm guessing here) pH 6.5 to pH 11.5. You can calibrate this if you wish, so you know the relationship between volume and pH, but it isn't necessary to do so, as it's simpler just to measure the pH of the buffer system that works best for you. This is to say that the importance of linear variation in pH is not that it's predictable, but that it is gradual and reproducible, so you can come back later and determine the exact pH you found to work best on the basis of the volume mixture you used during the chromatography.

So, how is this useful for method development? Well, ternary mixers are common. Consider reversed-phase HPLC (e.g., C18 column). Devote A to methanol, B to acetonitrile, C to 100 mM citric acid and D to 100 mM trisodium citrate. Start with some level of A, with the balance 50:50 C & D, and vary the level of A across a few chromatograms. Next use something less of B (as acetontrile is a "stronger" solvent than methanol), with the balance 50:50 C & D, and vary the level of B across a few chromatograms. A few such tests will tell what the organic can do for you, and might suggest whether a mixture of methanol and acetonitrile will be beneficial (possible, but rare in my experience). Now start with some results that look promising and vary the C-to-D ratio, while leaving the organic alone. This alters pH only, and in a linear way. If pH matters in your separation (which it may if you're dealing with acids and bases, but probably won't if you're not), then you'll see changes of interest.

Find some "optimal" results, but don't spend a lot of time on them because the next thing you'll do is to change the buffer system entirely. (As mentioned, citric acid is a poor choice as buffer due to corrosion effects. Or, if you're using a mixture of other acids or bases, you might not need all these in the final mobile phase.) Determine the ratio of C to D you prefer, pump this w/o organic until you've collected maybe 50 mL, then take it to a pH meter and read the actual pH.

Once you know the pH you need, choose a buffer that will provide this pH -- namely, one that has a pKa within one pH unit of the desired pH. (Also note that the effective buffer strength of a buffer at a pH equal to it's pKa is ten times that of the same buffer at a pH titrated to a pH 1 pH unit away from it's pKa, etc. Buffer strength is usually not critical in HPLC, but it can be critical, so don't neglect it.)

I've probably neglected to mention something important here, but I'll be happy to field questions. If I don't respond quickly, it's because I don't monitor this site often.

(If indeed this is the first time this information has been "published", I expect that might be because chemists are not generally taught pH calculations, at least not for multi-pKa systems. I learned to do such calculations in my studies of biochemistry.)

[HW Mueller]

There have been extensive discussions, here, involving pH.
It seems that your proposition depends on what you define as linear. In any case, if one used different acids or bases one would not only shift the pH, but also the type of material doing the buffering. One may not want that.
There are those here, me included, who would argue that weighing components (see, for instance, http://www.liv.ac.uk/buffers/buffercalc.html ) is more accurate than using a pH meter for generating a desired pH.
Also, corrosion has been discussed intensively. In my hands Cl- has not been among the chemicals doing this, only HCL (Cl- at suffucient conc. of H+).

[lmh]

There's a huge literature on how to make interesting buffers for interesting purposes, but much of it is pre-electronic and hard to find. My all-time favourite is:

Ellis KJ, Morrison JF (1982) Buffers of constant ionic strength for studying pH-dependent processes. Methods Enzymol 87: 405-426

This describes how to make multi-pKa buffers containing multiple components chosen such that the buffer has good buffer-strength over a wide range of pH, but its ionic strength remains constant over the wide range. It was originally designed for experiments to determine the pH optimum of an enzyme, but I've mentioned it here as it's a useful tool to have in the box...

[freemab]

To H.W. Mueller:

I am not sure what to make of your posting. I had posted a suggestion, with explanation, of how to make a wide-range buffer that I myself found quite useful when investigating pH effects during method development. You responded with a posting that is of questionable import and tends to cast doubt on my statements.

Perhaps English is not your native language and didn't realize it, but your comments in that posting come across negative. As such, they contribute nothing and don't belong in this forum. (On the other hand, if English [i]isn't[/i] your native language, I must thank you for participating in this forum in my language -- as I could not participate in a foreign language.)

For example, your "...what you define as linear" suggests that I don't know what a straight line is. That might not have been what you intended to say, but it is the implication harbored within your words. Let me reassure you and all readers that, by "linear," I mean a mathematically straight line, one that follows the general equation y=mx+b. That is about as simply as I can state it.

As I mentioned, this straight line does not hold true throughout the range, but rather there is a deviation at either end. By avoiding those ends, one has linear buffer control. Also, strictly speaking, there may be some small deviation from linearity, depending upon exact the pKa's of the buffer components, which is why I suggest components that differ by 1.5 pH units, and happen to give quite linear pH plots. However, even with these deviations at their worst, the buffer system is useful because the pH changes predictably, and the actual pH of any given mix can easily be determined.

If anyone doesn't believe me about these buffer systems then I suggest they try it themselves in the laboratory, or do the math (but be forewarned that some publications list one erroneous value among the three pKa's of citric acid). For chemists not tutored in such calculations, I suggest you pick up a basic biochemistry textbook, e.g., "Biochemical Calculations" by Irwin H. Segal, J.Wiley, c. 1968.

As to your comment that weighing components is more accurate, I happen to agree. But that comment is completely irrelevant to the subject of my posting. In all probability I prepared my "acid" and "salt" buffers by weight. However, unless a system is used in which prepared buffers are mixed to yield the working buffer, it is quite tedious to prepare the number of buffers needed to empirically investigate the effects of pH. (This is not news. I believe there's a table of buffer preparation predicated on this concept in my CRC handbook from ~1970 -- and the table was probably quite old even then.)

It was precisely to avoid having to mix up numerous individual buffers during method development that led me to this concept of a linear buffer. In a few automatic experiments ("chaining methods") on a modern, computerized HPLC, I was able to investigate the effect of pH on the numerous components in my sample mixture with no muss, no fuss, and no time wasted mixing numerous buffers. When I found a pH region that looked promising, only then did I replace my "linear buffer" mix with a single target buffer, so that all chemical effects and ionic strength effects of the buffer could be properly accounted for in the final method.

As to your comment about chloride ion, which is [i]only [/i]relevant because I brought up the subject -- that's very interesting that HCl is the corrosive agent, not Cl-. But since most reversed-phase HPLC methods are run below pH 7, then some level of HCl would be present in such mobile phases were chloride included in the mixture.

Note particularly that, when I brought up the point about chloride, I was really pointing out that citrate and some other chelating agents are corrosive to metals -- a point that was not generally understood by my younger colleagues. This is one of many reasons that an HPLC system should be flushed with a wash solvent mixture before being shut down between uses. This wash solvent mixture generally should be free of additives and should contain enough organic solvent to prevent growth of microorganisms.

[HW Mueller]

What I am saying is that I don´t see a reason for adopting your method. Are you trying to tell me that I should agree with you or shut up?
With the phrase "what you define as linear" I obviously was referring to what standard deviation you accept (or whatever other statistical parameters you use to define linearity). Or in other words, I tried to point out that what you consider as linear I might not. To define linearity was probably the main reason for introducing statistics to chemical analysis.

[SIELC_Tech]

Freemab/freemab22
Statements about "English is not your first language" really offend me, people use it when they don't know how to argue their point of view. I am sure that a lot of people on this board are not native speakers, but they know 100 times more than you. HWM is one of people with knowledge. Just compare how much he posted compare to "freemab". In addition to this, chromforum is a public board and people are entitled to their opinions.

[fandaga]

I found the original post useful. I'm going to try a variation by substituting volatile buffers for LC-MS when I do a pH screen tomorrow. I think this will save a lot of time.

Thanks!

[freemab]

Fandanga -- Thanks for your posting. It's nice to know that someone appreciated my posting for its content. If you have any trouble with the technique, please let me know if I can help you. You might consider starting your development work with non-volatile buffer components (with the MS out of the loop), and only switch to volatile buffers when the effect of pH on your analytes is understood. (Obviously, this suggestion won't work if the MS is essential for detection.)

SIELC_Tech -- Exactly which of my statements about "English is not your first language" really offended you? The one where I thanked people whose primary language is NOT English for participating in this forum in what, to them, is a foreign language? Or the one in which I allowed that Mueller's apparently offensive and out-of-place comments might be innocent consequences of a less-than-perfect understanding of English?

HW Mueller -- If you don't see any reason for adopting the method, then don't adopt the method. But don't bad-mouth it without trying it first.

As to the standard deviation of the pH vs. titrant line, I really don't care in the least what it might be. All that matters is that the plot is a straight line. Statistical measures of linearity are of no consequence whatsoever to the matter.

You seem to have missed the fact that the linearity of the titration plot is a completely different matter from the linearity of a calibration plot, upon which analytical results depend.

But perhaps my original posting was insufficiently clear, so I'll review my suggestion in hopes that additional detail will make the technique accessible to a wider audience.

To review: For the purpose of method development (only), I suggest using a programmable HPLC with a quaternary pump, and provided with two buffer solution components instead of a single buffer -- one such as citric acid, the other such as trisodium citrate, of equal molar strength. Mix these and you get a buffer of intermediate pH to the two. Vary the mixture and you vary the pH -- in a manner "strictly increasing" (or decreasing) and linear. (The citric acid and trisodium citrate buffer system is suggested, but is by no means the only possible buffer system suitable to the technique.) Once you find a mixture that works for you, you can determine the pH of the buffer preparing the same relative mixture of the two buffer component solutions OFF the HPLC, and directly measuring the pH.

At this point, it should be clear that the degree of the linearity of the pH vs. titrant plot is of no consequence whatsoever in the application of this method-development technique, as the pH of any given mixture can be measured before or after the fact. Even so, it becomes profoundly less a concern because one next switches to a "true" buffer system -- the nature of which is not to vary in pH significantly.

However, further thought will make it clear that, for the two-buffer-component system, if the pH vs. titrant plot is not "strictly increasing" (or decreasing), two problems arise: (1) buffer strength (not to be confused with molarity of the buffer, nor with ionic strength) may vary excessively across the range (being greater near the pKa's and considerably less between them), and (2) the pH may either plateau or become excessively steep (as it does in the classic sigmoid curve titration plot near the pKa and far from it, respectively), giving regions in which the pH does not vary with titrant in a manner useful to this technique. Hence, it is the strictly increasing (or decreasing) change in pH with titrant that is required for the implementation of this trick of method development -- not the linearity. (For this reason, a phorsphoric acid / trisodium phosphate system, without other buffer components, will not produce a system of much use to this technique.) The linearity of the relationship is a bonus that one accrues by using buffers which differ in pKa by ~1.5 pH units. This choice of spacings of pKa also minimizes the changes in buffer strength.

If you doubt the linearity of the titration plot, then go to the lab, mix up a citric acid stock and a trisodium citrate stock, run the titration, and plot the results. It's as simple as that. I have already done this experimental work, plotted the results, and concluded by inspection that the plot was linear. No statistics needed for the aforementioned reasons.

Feel free to do all the statistical analyses on your data that you wish, but, unless you plan to report assay results based directly upon pH measurements, such statistics are irrelevant and misapplied. If you wish to challenge the statistical linearity of the titration plot, you are free to do so -- in a manner that does not denigrate a method development technique for which it is irrelevant. I suggest a separate thread.

If empirical evidence doesn't impress you, then do the buffer calculations. I have also done these and have examined various combinations of pKa's before concluding that 1.5 pH units is the "magic" differential between pKa's. The calculations have the great advantage of independence from real-world values of pKa (i.e., available buffer chemicals), as well as from the need for the accurate knowledge of pKa of any given chemical.

I did not mention in the first posting that once the desired organic solvent component is known and fixed, the quaternary pump can be fitted with water, organic solvent, and the two buffer component solutions. This enables one to test buffer concentration as well as buffer pH in a single series of experiments -- taking advantage of the empirical fact that pH varies little with buffer concentration. For those not familiar with such experimental techniques, the value of this sort of approach is that the analyst can set up a series of experiments to be run automatically overnight by the computerized instrument, and in the morning he need only review the results and decide upon his next approach. With the advent of very rapid UPLC separations, such overnight runs may decrease in importance, but I suspect there will always be a place for them.

All the objections to this technique for reasons of undesirable chemistry, etc., are quite correct, which is why the next step is to remove the two buffer components from the system and use instead a single buffer at the pH determined while using the mixture of the two buffer components. What I suggest (and have done myself) is to isolate the determination of the effect of pH from much of the other steps in optimization of the mobile phase.

Erratum: In my original posting, I notice I stated "ternary mixers are common" when I meant to say "quaternary mixers are common". I trust this error left no one irredeemably puzzled as I launched into a description of mixing four solvent on a "ternary" mixer.

Note: I experienced a glitch in my connection to ChromForum while composing this post, which required me to log in a second time. If a double posting resulted, then the one with this note should be considered the complete one. (I should have learned by now never to compose using these on-line editors!)

[HW Mueller]

"As to the standard deviation of the pH vs. titrant line, I really don't care in the least what it might be. All that matters is that the plot is a straight line. Statistical measures of linearity are of no consequence whatsoever to the matter."
This is what I suspected: That you don´t care about accuracy and that´s the reason for my first reply. I suspected that also from examples of plots in a book on chemical equilibrium, no need for me to spend any more time with this.

"You seem to have missed the fact that the linearity of the titration plot is a completely different matter from the linearity of a calibration plot, upon which analytical results depend."
Disagree emphatically, I could make an evaluation of what you should do, like the ones you suggested to me, but I prefer to decline.

"It's as simple as that. I have already done this experimental work, plotted the results, and concluded by inspection that the plot was linear. No statistics needed for the aforementioned reasons."
Again: One important reason for introducing statistics in analytical chemistry is just to prevent that anybody inspect their data, then introduce arbitrariness in their interpretation even of mathematical aspects.

[tom jupille]

Time to take this discussion off-line, guys.