Conductivity vs TOC for detecting organic contaminants

Published in June 2024, by Ryan Olf, PhD and the Trisk team.

Total organic carbon (TOC) and conductivity measurements are the well-known dynamic duo of water purity, a complementary one-two punch of highly-sensitive and highly-available assays through which few (relevant) contaminants can pass in pharmaceutically meaningful quantities. USP 1231 tells the story of their early heroics, wherein a zoo of chemical requirements (that hitherto required an army of specific tests) was knocked out by this potent pair of compendial tests.

A wide range of compounds and potential contaminants used in pharmaceutical and (especially) bioprocesses contain organic matter, and so TOC levels — both in the form of direct surface samples and indirect rinse samples — have become a common and accepted means of gauging the performance and effectiveness of cleaning operations. For biologics, where pharmacological inactivation by hydrolyzing chemicals like hot sodium hydroxide is effectively complete, acceptable post-cleaning carryover may be defined primarily in the non-specific terms of TOC. In our dynamic duo, at least from a cleaning perspective, TOC is definitely Batman to conductivity’s Robin.

But TOC measurements, especially online ones, are often built on top of conductivity measurements — conductivity with extra steps — and are correspondingly slower, more expensive, and more easily biased by the specifics of the measurement technique. So while TOC is clearly ultimately indispensable (there are definitely many low- and no-charge organic molecules that are invisible to conductivity), we’ve wondered whether conductivity alone can do a good enough job detecting the kinds of soils we care most about — protein fragments and DNA — in the background we care about — WFI-grade water.

We will ultimately want and need the range, sensitivity, and robustness of TOC to complement conductivity, but how much does it really give us now? Can Robin strike out on his own… at least for now?

Backstory: conductivity

In the analysis that follows, it’s helpful to understand the origin of conductivity in pure water and its close relationship with pH.

Liquid water, $\text{H}_2\text{O}$, invariably carries in it some $\text{H}^+$ and $\text{OH}^-$ ions owing to the chemical dissociation equilibrium $\text{H}_2\text{O} \xrightleftharpoons{} \text{H}^+ + \text{OH}^-$. The equilibrium constant for this reaction is called the water dissociation constant and takes the well-known value $10^{-14}$ at 25°C (assume everything is at this temperature from now on). This means (roughly) the product of the concentrations of the ions $[\text{H}^+]$ and $[\text{OH}^-]$ (expressed in mol/L) is always $10^{-14}$, which is the origin of the rule $\text{pH} = -\log_{10}([\text{H}^+]) = 14 -\log_{10}([\text{OH}^-]) = 14 - \text{pOH}$.

These ions give pure water some conductivity, and unsurprisingly the conductivity due to these ions is minimal (roughly) when there are fewest of them, which is at pH 7 ($1\cdot10^{-7}$ mol/L each). You can lookup the limiting ion conductivity of $\text{H}^+$ and $\text{OH}^-$ and calculate the conductivity of pure water using the concentration of each ion, and you’ll get the accepted answer — 0.05 µS/cm.

At any other pH, the water is no longer absolutely pure in the Platonic sense, but it can certainly be pure enough. WFI, for example, doesn’t have an explicit pH limit, but it can theoretically pass the compendial conductivity test with a pH anywhere between at most 5 and at least 8.5 (estimating the theoretical lower and upper limit pH for WFI could be the subject of a future, related blog post). For pure enough water, the pH and conductivity typically track together because the dominant source of mobile charge tends to be the excess $\text{H}^+$ and $\text{OH}^-$, which have limiting ion conductivities several times larger than typical counter ions thanks to the Grotthuss mechanism.

For example, water at pH 8 has a lower-bound conductivity due to $10^{-6}$ mol/L of $\text{OH}^-$ (the $10^{-8}$ mol/L of $\text{H}^+$ is negligible) of about 0.2 µS/cm, i.e. roughly 5x the conductivity at pH 7, as there are roughly 5x as many combined $\text{H}^+$ and $\text{OH}^-$ ions. Of course, we can’t have pH 8 water without a positive counter ion for the excess $\text{OH}^-$. If we take the counter ion as $\text{Na}^+$, e.g. from NaOH, the theoretical minimum conductivity rises only slightly to 0.25 µS/cm.

Of course, realistically, compendial waters such as WFI will generally have higher than this minimum conductivity — exposure to air results in the conversion of atmospheric CO2 into dissolved carbonic acid, which readily dissociates at neutral pH — and low levels of other ions are permitted. In fact, WFI that has equilibrated with the atmosphere can have a conductivity as high as 4.6 µS/cm at pH 7 (though only 2.1 µS/cm at pH 6.6) and still meet the USP and EP requirements!

Conductivity and TOC vs The Usual Suspects

Organic compounds that solvate into mobile charges will obviously contribute to conductivity, but how much? Will this make them sufficiently visible to conductivity? Can Robin give Batman a night off?

To explore this, let’s imagine we’re gauging the effectiveness of our cleaning process by looking at rinse water (of course this isn’t sufficient to show cleanliness) and comparing it to WFI. We’ll take an organic molecule and see how much would need to be present in the rinse to take WFI out of its compendial limits, assuming the WFI is initially ultra-pure (so we can ignore the effects of bicarbonate buffering — a worthy topic for a future post). For these purposes we’ll use the WFI limits for on-line conductivity at 25°C (1.3 µS/cm — roughly 25x that of pure water) and TOC (0.5 ppm).

Let’s consider acetic acid ($\text{CH}_3\text{COOH}$) as a baseline. Small amounts of acetic acid added to pure neutral water would be expected to completely dissociate into $\text{CH}_3\text{COO}^-$ (acetate) and $\text{H}^+$. To get our limit amount of 25x the conductivity of pure water, we’d need to add about $25\times 2\cdot10^{-7} = 5\cdot10^{-6}$ mol/L of acetic acid. Acetic acid carries two carbons (24 g/mol), so the TOC of this acetic acid is $24 \times 5\cdot10^{-6} = 1.2\cdot10^{-4}$ g/L, or 0.12 ppm — about a quarter of the limit amount. In this case, conductivity is the more stringent limit. A point for Robin! But don’t send Batman home just yet.

Acetic acid should be among the easiest organic molecules to detect by conductivity as it provides a relatively large amount of charge (1 charge) per carbon (2 carbons). This is not typical for the sorts of organic molecules we’re mostly concerned with. Notoriously charged DNA contributes one charge to solution for every 9 or 10 carbons — so against our easiest realistic adversary, Robin just yields his edge, though is still competitive. Unfortunately, proteins will be his true downfall.

Amino acids may be positively charged, negatively charged, or uncharged at neutral pH, so it’s not obvious a priori what the typical charge of a protein should be. Helpfully, some folks have looked at the net charge of proteins in a minimal proteome, and their figure with key results is copied below.

We can see that at roughly neutral pH, many proteins have very little net charge for their size, which corresponds to very little net addition of $\text{H}^+$ and $\text{OH}^-$ ions. Consider a small-ish 25 kDa protein with a large-ish charge of +20. This protein will have 1000+ carbon atoms, so the carbon/charge ratio is worse than 50:1. Most of the proteins in that database would seem to have higher ratios than that, and in the case of the nearly neutral proteins, much much higher. Furthermore, when our solution contains a mixture of proteins, the positively and negatively charged ones can effectively cancel out: the most mobile ions are largely redistributed among them, the pH remains close to neutral, and the conductivity should remain correspondingly low. (At higher concentrations, the much-less-mobile charged proteins themselves can become relevant, but that’s not germane here.)

Of course, most pertinent to our cleaning work are protein fragments left over from hydrolysis, but with an expected mass of fragments near 10 kDa, this doesn’t move the needle on the charge-per-carbon scale. TOC is going to be orders of magnitude more sensitive.

The final boss: robustness

In all of this analysis we’ve assumed the sampled water to be very pure and essentially devoid of any pH buffer, which could largely mute the effect on conductivity of any charged organic contaminants. This seems reasonable, but it is not trivial to achieve in practice given that interaction with atmospheric air naturally induces a weak bicarbonate buffer system. In our analysis we determined that 5 µM acetic acid in pure water would lead to a notable deviation from our on-line WFI limit of 1.2 µS/cm. However, otherwise pure water at equilibrium with atmosphere (400 ppm $\text{CO}_2$) already has roughly 5 µM bicarbonate concentration with 1.2 µS/cm conductivity as a baseline, and addition of 5 µM acetic acid will not double the conductivity like it would absent any buffering effect — theoretically it would go up by roughly the golden ratio, 1.6. And, of course, the presence of other ions from either the system or WFI source only further complicates the interpretation and reproducibility of conductivity readings.

Given all this, it’s clear why TOC complements conductivity in the standard for WFI, and why TOC is essential for detecting non-specific organic contaminants or residues.