If your decision making relies on analytical chemistry, then you want to be confident that the measurements are an accurate representation of the matrix that is being analyzed, and that they are of “publication” quality. But how can you know for sure if the analytical laboratory that you’ve selected is producing reliable data?

Kevin A. Schug is a Full Professor and Shimadzu Distinguished Professor of Analytical Chemistry in the Department of Chemistry & Biochemistry at The University of Texas (UT) at Arlington. He joined the faculty at UT Arlington in 2005 after completing a Ph.D. in Chemistry at Virginia Tech under the direction of Prof. Harold M. McNair and a post-doctoral fellowship at the University of Vienna under Prof. Wolfgang Lindner. Research in the Schug group spans fundamental and applied areas of separation science and mass spectrometry. Schug was named the LCGC Emerging Leader in Chromatography in 2009, and most recently has been named the 2012 American Chemical Society Division of Analytical Chemistry Young Investigator in Separation Science awardee.

This blog is a collaboration between LCGC and the American Chemical Society Analytical Division Subdivision on Chromatography and Separations Chemistry.

Those working in a technical field are always trying to innovate and increase operational efficiency to produce the most value out of any given project. This requires making data-driven decisions to identify patterns and to forecast the potential implications of specific strategic moves. As with anything, these decisions are only as good as the information that they are predicated upon, and the data are only as good as the people and processes that generate them.

If your decision making relies on analytical chemistry, then you want to be confident that the measurements are an accurate representation of the matrix that is being analyzed, and that they are of “publication” quality. This is a major feather in one’s cap, especially when litigation is involved, because the state and federal court systems regard peer-reviewed data as the gold standard.

But how can you know for sure if the analytical laboratory that you’ve selected is producing reliable data? Often, we are quick to assume that analytical data is sound and accurate based on an accreditation or certification held by the laboratory in question. These sorts of credentials are meant to indicate reliable data production, because a series of compliance training, proficiency testing, and validations is generally required to achieve such qualifications. Even so, they are not the broad-scale cloak of infallibility that many might think they are. In other words, just because a given laboratory carries a certain accreditation does not mean that the data that they generate can be trusted, without performing a deeper dive into their quality assurance and quality control protocols (QA/QC).

From our experience in the energy, environmental, agricultural, and forensic sectors, one must take accreditations at face value and ask a bounty of questions about control and surrogate retention measurements, calibrations, validations, and instrumental upkeep. Fortunately, the majority of this information is made available in a good laboratory’s QA/QC reports. Below are some suggestions regarding what to look for in QA/QC reports, so that you can secure confidence in the laboratory’s work and the data that it produces.

: The use of surrogate, “spiked,” or control measurements are a standard practice whereby laboratory operators use samples of known concentration to assess the accuracy and precision of the response of their instruments. For many inorganic constituents, such as arsenic, an accuracy threshold window of 85–115% of the known concentration is an acceptable range. For organic constituents, such as certain volatile organic compounds (VOCs), this range can be a bit broader; however, one should evaluate this quite closely in a given laboratory’s QA/QC to ensure consistency and conformity to standards.

As an example, we recently participated in an environmental assessment of an alleged case of surface-water contamination where the detection of several VOC contaminants was being evaluated within the context of federal drinking-water standards. In this particular case, the concentrations of benzene in several samples collected from the water body of interest were elevated above the Environmental Protection Agency’s 5 parts-per-billion Safe Drinking Water Act standard. However, the QA/QC report of the accredited laboratory that performed the analyses reported accuracy ranges between 50–200% as acceptable. This means that their instruments that performed the VOC analysis could yield data that is artificially low or high by a very significant amount, and that this is supposed to be acceptable for some seemingly arbitrary reason. From our perspective, this was absolutely incomprehensible when we considered the potential legal and financial implications of the reported data in this particularly litigious matter.

: Accurate instrumental calibration may singlehandedly be the most important aspect of reliable data generation in analytical chemistry. Proper calibration allows the operator of a given instrument to interpolate the concentration of a particular constituent based on the instrumental response to samples of known concentrations. This requires that one’s calibration standards and certified reference materials (CRMs) are dependable and haven’t expired, and that their serial dilution, for the preparation of a multipoint calibration curve, is performed accurately. If performed correctly, a multipoint calibration curve of five to seven points should yield a linear correlation value (r-value) >0.99. The incorporation of an internal standard is nearly always a best practice.

It’s important to keep in mind that an instrumental measurement is only reliable if the sample response signal falls within the range of the calibration curve. Attempting to quantify the concentration of a given analyte when extrapolating beyond the range of the calibration curve can lead to inaccurate measurements and unreliable data.

We’ve seen this phenomenon plague commercial laboratories in the cannabis/hemp sector, particularly with the analysis of concentrates and oil products. Depending on the state, laboratories operating in this space may not yet be guided by a specific set of analytical recommendations to guide their QA/QC practices. A problem arises when analysts may only run three calibration standards to create their calibration curve, which can then represent an artificially high (or low) calibration range. As a result, the analysis of a concentrated sample can then present a signal that is beyond the calibration range. The software then does its best to extrapolate the concentration of the constituent of interest, and you end up with an inaccurate measurement.

A particularly egregious example of this was presented on LinkedIn. A cannabis business owner was so proud to present their new concentrate product that had a delta-9-tetrahydrocannabinol (THC) concentration of 1,045 mg/g. That’s right, it was 104.5% pure – a reality-defying innovation. We attempted to shine light on this inaccuracy by inquiring about the QA/QC with the laboratory in question, but we all know how “collegial” discourse goes on the internet. Long story short, it turned out to be a calibration issue that wasn’t caught during data processing and reporting.

Furthermore, it is important to ask your laboratory of interest how frequently they calibrate their instruments. Instruments can fall out of calibration for a number of reasons, and it is important that these changes in performance are accounted for as they arise. Ideally, calibration should be performed on the same day that real samples are analyzed for their determination.

: Laboratories performing quantitative and qualitative analyses need to follow certain protocols for method validation. These are generally industry-specific but are similar in the types of the measures they prescribe in order to demonstrate that a method is fit for use and can be expected to provide reliable results. In forensics chemical analysis, we often see this lacking—it appears that much of the standard method validation guidance was provided some years after the establishment of many forensics measurements and that the industry has been slow to conform. This lack of conformity creates a great deal of uncertainty in measurement results.

As just one example, the Texas Department of Public Safety currently asserts that all of their headspace gas chromatograph instruments operated across the state are free of matrix effects during blood alcohol measurements, because this was evaluated on a couple of instruments in Austin. Many of these instruments are also from different manufacturers than those in Austin and have different headspace sampling configurations. That is akin to assuming that your Honda Civic runs well because your friend’s Ford Fiesta is running well. This is not a reliable practice. Every instrument must be individually fully validated using the prescribed procedures in order to prove that they provide reliable results.

: Analytical instruments need routine maintenance and often require major repairs after a significant amount of use. Laboratories should keep regular maintenance logs to document instrumental upkeep. Additionally, major alterations, such as the installation of new columns, require re-validation of the method according to guidelines. There should be documented re-validation of the instrument performance following major maintenance efforts.

Collectively, reviewing these QA/QC-related items can reveal a considerable amount about the veracity of the data being generated by a given laboratory. The technical fidelity of a laboratory’s QA/QC report is far more insightful than a simple recitation of standardized accreditations and certifications that may be held, which as we’ve mentioned, should be taken with a grain of salt. All of this feeds back into the simple truth that the only thing worse than no data is bad data. Given our evolving world where correlations, projections, and ultimately, data-driven decision making are the standard, it is paramount that the information that we are reliant upon is generated from a trustworthy source that exercises proper QA/QC procedures.

 is a Full Professor and the Shimadzu Distinguished Professor of Analytical Chemistry in the Department of Chemistry & Biochemistry at The University of Texas (UT) at Arlington. He is also a Partner in Medusa Analytical, LLC. Research in the Schug group at UT Arlington spans fundamental and applied areas of separation science, spectroscopy, and mass spectrometry. Schug was named the 

 Emerging Leader in Chromatography in 2009 and the 2012 American Chemical Society Division of Analytical Chemistry Young Investigator in Separation Science. He is a fellow of both the U.T. Arlington and U.T. System-Wide Academies of Distinguished Teachers.

 is a partner of Medusa Analytical. He sits on the scientific advisory board of the Collaborative Laboratories for Environmental Analysis and Remediation (CLEAR), is a director of the Curtis Mathes Corporation (OTC:TLED) and is a research professor at the University of Texas at El Paso. Hildenbrand’s research has produced more than 60 peer-reviewed scientific journal articles and textbook chapters. He is regarded as an expert in point source attribution and has participated in some of the highest profile oil and gas contamination cases across the United States. Hildenbrand has also provided consultation for several private-sector clients on various water-treatment and hydrocarbon-capturing technologies.

 and the American Chemical Society Analytical Division Subdivision on Chromatography and Separations Chemistry (ACS AD SCSC). The goals of the subdivision include

promoting chromatography and separations chemistry

organizing and sponsoring symposia on topics of interest to separations chemists

developing activities to promote the growth of separations science

increasing the professional status and the contacts between separations scientists.

For more information about the subdivision, or to get involved, please visit 

https://acsanalytical.org/subdivisions/separations/

Articles

If your decision making relies on analytical chemistry, then you want to be confident that the measurements are an accurate representation of the matrix that is being analyzed, and that they are of “publication” quality. But how can you know for sure if the analytical laboratory that you’ve selected is producing reliable data? 

The LCGC Blog: Laboratory Accreditation is Not a Cloak of Infallibility 

Join the 19th International GC×GC Symposium, May 29-June 2, 2022 in spectacular Canmore, Alberta. A beautiful location to enjoy the GC×GC award lectures and a schedule packed with scientific content from today’s and tomorrow’s leaders in the field of GC×GC. New this year is an advanced GC×GC course in addition to the popular introductory course. This meeting will have a hybrid option. 

The preliminary outline of the scientific and social program is available here: 

"On behalf of the GCxGC committee, I am excited to welcome everyone to the 19th International GCxGC Symposium to be held in beautiful Canmore, Alberta. We are planning this as a hybrid event so that we can include as many people as possible."

Prof. James Harynuk
University of Alberta
Symposium Chair


Join the 19th International GC×GC Symposium, May 29-June 2, 2022 in spectacular Canmore, Alberta. 

The 19th International GCxGC Symposium

With the increasing interest in biopharmaceuticals such as proteins, antibodies, and nucleic acids, there is a corresponding increase in the need for characterizing such components. Much effort is spent on characterization in the early drug development phases as well as during formulation development and quality control. One parameter that is commonly investigated is the size distribution of the macromolecular components to deduce if there is aggregation or degradation occurring, if conformational changes occur, or if there are interactions with excipients. While the properties of the protein drug in the buffer system or in the pharmaceutical formulation are important, possibly even more interesting are the properties of the drug once it enters the body. Size characterization of macromolecules in biological fluids has traditionally been an area hampered by the complexity of the matrix. The large amount of indigenous components can interfere with commonly applied analytical techniques for size characterization. However, the separation technique asymmetrical flow field-flow fractionation (AF4) has recently shown increasing applicability for the characterization of components in blood plasma and serum. This article reviews some aspects of applying AF4 to plasma, serum, milk, and cerebrospinal fluid in the field of analysis and characterization of proteins, biologics, and nanoparticles in biological fluids.

Alejandra Castro Nilsson is a senior scientist and CEO at Solve Research and Consultancy in Lund, where she works with the characterization of biopolymers, proteins, and nanoparticles. Alejandra holds a Ph.D. in food engineering from Lund University. She has worked with AF4, light scattering, laser diffraction, and chromatographic techniques for more than 10 years for various applications, including polysaccharides, proteins, nanoparticles, and biopolymers.


Biopharmaceuticals such as proteins, antibodies, peptides, and nucleic acids are increasingly being used in practically all branches of medicine. The market for these and other biologics has been developing at a faster rate than the market for all drugs and it will continue to grow (1). Yet, the complexity of these structures poses a significant challenge for biopharmaceutical developers and often requires an in-depth characterization to gain understanding and to ensure safety and efficacy (2). A major concern with pharmaceutical proteins is their propensity to form aggregates. These aggregates can exist as small oligomers up to large sub-visible or even visible precipitates, and are of concern because they can reduce drug efficacy and give rise to adverse toxicological and immunological responses (3,4).

While characterizing biopharmaceuticals in formulation is certainly important, it is also of interest to perform the characterization of the drug product after its administration (5). This implies the analysis of blood samples after drug administration. However, blood samples are difficult to analyze due to the complex nature of their components and their wide size range, which requires extensive sample preparation prior to analysis. Similar to blood plasma, the analysis of proteins in biological fluids such as cerebrospinal fluid (CSF) and amniotic fluid is challenging, and until recently only possible to achieve either 

The most common method for determining the size and amount of proteins and sub-visible aggregates is size-exclusion chromatography (SEC) in combination with suitable detectors. However, some complications with SEC are that it has high surface area and shear forces, which may be a problem for analysis of large-sized aggregates with the potential to adsorb to surfaces. To achieve high recovery and proper elution of analytes in SEC, the separation often uses a mobile phase that does not agree with physiological conditions with respect to ionic strength, pH, and composition. It is therefore recommended to verify SEC data with complementary orthogonal methods because SEC can give erroneous estimates of the aggregate levels (6,7,8). Analytical SEC is rarely reported to be used for the analysis of biological fluids (without extraction protocols to remove matrix components). This is presumably because samples such as blood plasma could clog the column or rapidly deteriorate its performance due to adsorption of matrix components to the column.

Asymmetrical flow field-flow fractionation (AF4), an orthogonal technique to SEC, has been used to characterize biomacromolecules and pharmaceutical molecules (9,10,11), and it has been proven to be a powerful tool to characterize proteins, antigens, and antibodies (12,13). One critical step when applying AF4 is to choose the proper detection technique and factors such as selectivity and sensitivity should be considered. The combination of AF4 with fluorescence (FL), enzyme‑linked immunosorbent assay (ELISA), surface plasmon resonance (SPR), or mass spectrometry (MS) offers the possibility of obtaining information about the size distribution of the biopharmaceutical in blood, the aggregation potential after administration, the interaction of the protein with different matrix components, and potentially applying the methodology to the study of other biological fluids.

Several methodologies exist that have the ability to selectively detect and quantify the amount of a component in a biological fluid. Commonly used techniques are ELISA, SPR, and MS. A limitation of all these techniques is that it is difficult or not possible to determine if the analyte response originates from the analyte in monomeric form or if it is from an aggregated (or conjugated) species. In some cases, there is a significant loss of signal when the analyte is present in a biological matrix. It may then be suspected that the analyte is aggregated or associated with matrix components, thereby giving a loss of signal. While such information may give valuable indications, it is often inconclusive and still does not give any information on the size of the aggregates. Furthermore, quantification is often difficult or not possible.

If the sample in the biological matrix could be size-separated and then detected it would enable more detailed information on the analyte size distribution, potentially offering answers to if the analyte is aggregated or associated with matrix components, and to what extent. An alternative methodology is AF4. In contrast to SEC, a sample passing an AF4 channel is subjected to significantly lower shear forces and exposed to much smaller surface areas. Also, clogging of the channel is no longer an issue, and AF4 generally works very well with mobile phases of physiological ionic strength and pH.

As reported elsewhere, AF4 can be applied to a variety of different biological fluids (14,15,16,17,18). Blood serum and plasma are perhaps the most obvious and interesting from a pharmaceutical point-of-view, but the methodology is equally applicable to other interesting biological matrices such as CSF and amniotic fluid (Figure 1).

In AF4 (Brownian mode), the sample components are eluted in order of increasing size. The eluted fractions can be collected and measured offline, or monitored online by an UV detector, as in the Figure 1 example.

As can be seen in Figure 1, the different fluids share some characteristics: the most intense peak (at ~4 min) corresponds well with the elution time of serum albumin reference (67 kDa), which should be the most abundant component, with the second most intense peak being dominated by IgG (150 kDa). A significant difference between the different matrices lies in the total amount of proteins, so that, for example, the lower protein content CSF gives considerably lower signals than the serum.

It is equally possible to apply the same methodology to serum and plasma from different animals (Figure 2), which can be helpful when investigating if a component behaves differently in different animal types. In the example (Figure 2), the different plasma samples all contained an active pharmaceutical ingredient (API). Fractions were collected after the AF4 size separation and analyzed by ELISA for quantification of the API. As can be noted from the four plasma fractograms in Figure 2, the general profile is similar irrespective of the source, with the difference being that protein levels, and especially antibody levels, show some variability. The different antibody levels may be related to pattern-variations of age, health, and infection history between individuals.

Biological samples and matrices can also contain very large colloidal structures such as lipoproteins, vesicles, and viruses. One example of a biological fluid with an abundance of large colloidal structures is milk (Figure 3). Due to the large size range over which AF4 is applicable, it can also be applied for the analysis and characterization of casein micelles present in milk (19,20,21).

In Figure 3, AF4 was used to investigate the impact of pasteurization of milk and reconstitution of milk powder on the size and structure of casein micelles. The most abundant component of the milk samples was confirmed to be casein micelles (elution 16–45 min, radius size range of 30–300 nm), with the difference being that the most abundant size (peak apex) depends on the milk type. In the same analysis, the first population of the fractogram consists mainly of serum (whey) proteins and other relatively small and low molar mass components of the milk (<6 nm in hydrodynamic radius and peak maximum at 2.8 min). The second population (between 6–15 min)—of which there is substantially less in the raw and pasteurized milk samples—consists partially of serum protein aggregates.

As has been shown, it is possible to size-fractionate biological fluids containing a wide variety of components, with sizes ranging from small proteins up to ~0.5 µm colloidal structures. However, some aspects of the sample and the aim of the study must be considered before starting the experiments. One must primarily consider the size range of interest—is it peptides and small proteins, or large colloids? (AF4 can, in Brownian mode, cover from ~2 nm to approximately 1000 nm hydrodynamic diameter.) Depending on the size range to be investigated, different separation conditions should be used for optimal resolution. One should also consider the sample load as many biological fluids
have a very high protein content. For example, blood serum and plasma are often in the 50–100 mg/mL protein range. To avoid overloading the AF4 channel (otherwise detrimental effects on resolution can be experienced), only small volumes of sample need to be injected or the sample needs to be diluted prior to analysis. Another consideration is that in many cases it is preferable to investigate the sample under conditions as close as possible to physiological conditions. Thus, it is suitable to use a carrier liquid that has a physiological pH and ionic strength. Some biologically active components, for example, enzymes or milk as in the earlier example, may require certain ions (Ca

) to maintain their structure or function. Such considerations may impact the choice of buffers used for both dilutions and as the carrier liquid.

Biological fluids are complex and contain millions to trillions of different components. While AF4 is able to separate a wide range of macromolecular and colloidal components, the resolution is not sufficient to resolve all of them. Thus, one of the critical steps when applying the methodology is to choose the detection technique. Due to the complexity of the sample matrix and the often low concentration of the analyte, two factors are particularly important: selectivity and sensitivity. As the analyte will be coeluting with other substances, selectivity is necessary for accurate concentration determinations. As the analyte is often present at low concentrations in body fluids, and the sample becomes further diluted during the AF4 separation, there is also demand on the detection sensitivity. The most straightforward selective detection technique is via fluorescently labelling the component of interest. This approach has the added benefit of being easily performed online. An example is presented in Figure 4: a fluorescently labelled antibody is present in CSF, making it straightforward to monitor by AF4 equipped with an online fluorescence detector.

A potential drawback with FL‑labelling is that the introduction of the chemical groups with fluorescence activity might affect how the component interacts with matrix components. From that perspective it would therefore be better to use a detection technique that is able to selectively measure an unlabelled component. Examples are immunoassays such as ELISA or SPR (Figure 5) (15). Besides the obvious benefit of not needing to go through a labelling procedure, any concerns that the methodology incurs changes in the physicochemical properties of the analyte are eliminated. However, immunoassays are not without caveats either. First, there must be an antibody against the target analyte. For late-stage pharmaceutical candidates this may be the case, but in the early stage it is not always available.

Another more fundamental consideration that should be taken into account is the detectability of the analyte if present in an aggregated state or associated with matrix components. It is not guaranteed that an immunoassay technique (such as ELISA or SPR) has the ability to give a response for an oligomer or aggregate (at least it is not certain that the detection will have the same sensitivity or response factor for an aggregate). In the example of SPR on a stressed trastuzumab, the large aggregates were detected when the stressed trastuzumab was in a buffer system. However, when the stressed trastuzumab was in a blood serum matrix, the largest aggregates were not detected (15). This may be caused by matrix components associating with the large aggregates, making them less accessible to the SPR-sensor surface.

During the separation, the sample is diluted, and the run-time of the complete process (from injection to detection or fraction collection) is at least several minutes up to an hour. For example, if a protein aggregate dissociates upon dilution and does so within seconds or minutes, such protein aggregates would not be detected or accurately quantified by the methodology. In summary, for a system where the analyte aggregates or associates rapidly and is dependent on concentration, results may be inaccurate.

AF4 fractionates by hydrodynamic size. Thus, if there are changes in an analyte that occur but that do not significantly change the hydrodynamic size of the analyte, they will not be noticed by any shift in elution time. An example would be the association of a peptide internally within a large protein structure may go undetected (although FL-labelling of the peptide or MS against the peptide would be able to detect this).

There is a renewed interest in AF4 as it may be helpful with regards to analyzing complex biological fluids. The methodology becomes especially interesting when combined with selective detection techniques, such as FL, ELISA, SPR or MS, as the combination then offers the potential to provide information on analyte behaviour in biological systems that is difficult to obtain by any other technique.

S. Berkowitz, J. Engen, J. Mazzeo, et al., 

J. den Engelsman, P. Garidel, R. Smulders, et al., 

W. Wang, S.K. Singh, N. Li, M.R. Toler, K.R. King, and S. Nema, 

R.R. Manning, R.E. Holcomb, G.A. Wilson, et al., 

J.F. Carpenter, T.W. Randolph, W. Jiskoot, et al.,

Guidance for Industry Immunogenicity Assessment for Therapeutic Protein Products

 (FDA, Rockville, Maryland, USA, 2014), pp. 1–36.

D.C. Rambaldi, P. Reschiglian, and A. Zattoni, 

M. Leeman, W.M. Albers, R. Bombera, et al., 

M. Madörin, P. Van Hoogevest, R. Hilfiker, et al., 

 J. Chromatogr. B Anal. Technol. Biomed. Life Sci.

M. Glantz, A. Håkansson, H.L. Månsson, et al., 

A. Lie-Piang, M. Leeman, A. Castro, et al., 

 is a senior scientist at Solve Research and Consultancy in Lund, Sweden, where he works with size characterization of proteins, polymers, and nanoparticles. Mats holds a Ph.D. in technical analytical chemistry from Lund University. He has been using AF4 for more than 15 years for various applications within the pharmaceutical, specialty chemicals, and biotech industries.

 is a senior scientist and CEO at Solve Research and Consultancy in Lund, where she works with the characterization of biopolymers, proteins, and nanoparticles. Alejandra holds a Ph.D. in food engineering from Lund University. She has worked with AF4, light scattering, laser diffraction, and chromatographic techniques for more than 10 years for various applications, including polysaccharides, proteins, nanoparticles, and biopolymers.

is Professor of Formulation Technology at Lund University. His research focus is on applied colloid chemistry and formulation technology as well as development and application of AF4 methodology for the separation and characterization of biomacromolecules and nanoparticles within the life sciences. His AF4 work currently focuses on the analysis and characterization of therapeutic proteins and peptides in relation to formulation aspects and biological fluids.

Aspects of applying AF4 to plasma, serum, milk, and cerebrospinal fluid in the field of analysis and characterization of proteins, biologics, and nanoparticles in biological fluids are reviewed.

Analysis of Proteins, Biologics, and Nanoparticles in Biological Fluids Using Asymmetrical Flow Field-Flow Fractionation

Some “LC Troubleshooting” topics never get old because there are some problems that persist in the practice of liquid chromatography (LC), even as instrument technology improves over time. There are many ways for things to go wrong in an LC system that ultimately manifest as deviations from the expected pressure. Developing a short list of the likely causes of these deviations can help streamline our troubleshooting experience when pressure-related problems occur.

Writing this “LC Troubleshooting” column and thinking about topics each month is interesting in the sense that there are some topics that just never get old. Whereas, in the chromatography research world, certain topics or ideas become obsolete as they are displaced by newer and better ideas, in the troubleshooting world there are certain topics that have remained relevant since the very first troubleshooting article appeared in this magazine (

 at that time) in 1983 (1). Over the last few years, I’ve focused several “LC Troubleshooting” instalments on contemporary trends (such as the relatively recent advances in our understanding of the effects of pressure on retention [2]) in liquid chromatography (LC) that are affecting the way we approach our interpretation of LC results, and approach troubleshooting with modern LC instruments. With this month’s instalment, I am starting a series focused on some of the “bread and butter” topics of LC troubleshooting—those elements that are essential for any troubleshooter, no matter the vintage of the system we are working with. The topics at the heart of this series will be highly related to the well-known “LC Troubleshooting” wallchart (3) that hangs in many laboratories. For the first instalment in this series, I’ve chosen to focus on problems related to pressure (too low, too high, or fluctuating). I hope LC users young and old will find some useful tips and reminders related to this important topic.

In the area of pressure problems, everything is possible. Sometimes pressure is unexpectedly low but stable. Other times the pressure is too low, and appears to steadily decrease. The same is true for pressures that are higher than expected. In other cases, the observed pressure may seem to be about right, but it is fluctuating more than usual. Figure 1 illustrates the idea that pressure problems appear in all kinds of different ways, and lists the specific situations that are discussed in this article. The list of pressure-related problems shown in Figure 1 is not exhaustive; in this instalment, I focus on those problems that I see most frequently in practice.

A critical step in any troubleshooting exercise —but one that I think is underappreciated—is recognizing that there is a problem to be solved. Recognizing that there is a problem usually amounts to recognizing that what is happening with the instrument is different from what is expected to happen, and our expectations are formed from theories, empirical knowledge, and experience (4).

Before getting into details about what we can expect about pressure, a few words to clarify what it is and how it is measured in LC instruments are warranted. In LC, when we say “pressure”, we are really talking about a “pressure drop” or a “pressure difference”. These more precise terms are indicated in various equations that relate pressure drop to other variables, such as flow using the symbol ΔP. Most commercially available LC systems have a single pressure readout associated with the pump that reports the pressure drop between the pump and the outlet of the system (the outlet side of a detector flow cell) that, for all practical purposes, is zero, because the atmospheric pressure of about 1 bar is usually small compared to LC operating pressures. This single pressure readout quantifies the total pressure drop across the entire flow path, but does not tell us anything about the pressure drops across individual elements of the flow path (for example, filters, different pieces of connecting tubing, and the column).

Most practical high performance liquid chromatography (HPLC) is done under conditions where flow through connecting tubing in the system is laminar. Under these conditions, the pressure drops across the different pieces of tubing can be calculated with the accuracy needed for troubleshooting purposes using Poiseulle’s Law:

where η is the dynamic viscosity of the mobile phase, 

 are the length and diameter of the tubing, respectively. Calculating the pressure drop using equation 1 is straightforward when all of the values needed are available; however, the dependence of viscosity on mobile‑phase composition and temperature is a bit complex. Fortunately, there are some freely available web‑based tools that take these factors into account (for example, see reference 5, and https://www.multidlc.org/dispersion_calculator), and provide users with quick estimates of the expected pressure drops for the tubes in their systems.


The pressure drop across the LC column itself (assuming the column is packed with particles) can be calculated using equation 2 (or similar). Like equation 1 for open tubes, the pressure drop depends on the column length, mobile-phase viscosity, and the flow rate (through the interstitial mobile phase velocity, 

).
Different in equation 2 are the Φ term that quantifies the permeability of the packed particle bed and the particle size term, 

As with equation 1, calculating the pressure drop across the column is straightforward once all of the values for length, viscosity, and other variables are in hand, but they are not all easy to come by. Once again, there are freely available simulators that can calculate the pressure drop for conditions of interest. Two such simulators that I am familiar with are the web-based LC simulator maintained by my group (https://www.multidlc.org/hplcsim), and the spreadsheet-based simulator developed more recently by Professor Davy Guillarme’s group (see [6]; https://ispso.unige.ch/labs/fanal/practical_hplc_simulator:en).

 The other elements of an LC flow path that can contribute substantially to the pressure drop measured at the pump are inline filters (and guard columns, though these can be treated like columns as above). Most inline filters sold for use in analytical LC systems are designed in a way that they will
not contribute more than a few bar to the total pressure drop under typical
conditions (that is, less than 5 mL/min). When debris begins to accumulate on the filter, the pressure drop across the filter will increase, and become highly, and sometimes nonlinearly, dependent on operating conditions (for example, flow rate and mobile-phase composition). Because it is difficult to cope with this hard-to-predict behaviour, in my laboratory we simply change the filter if the pressure drop across it exceeds about 10 bar.

Using These Numbers in Troubleshooting Practice:

 Throughout the hundreds of “LC Troubleshooting” articles John Dolan wrote, he emphasized the value of “rules of
thumb” in effective troubleshooting (7). I completely agree, and think the value of these ideas—which are informed both by theory and experience—cannot be overstated. As an example of a rule of thumb that is useful in the context of troubleshooting pressure problems, the one that we use in my group is that the pressure drop across all of the tubing(no column) in a “typical” LC system is about 30 bar under the following conditions (if the observed pressure is much lower or higher than that, this should trigger a thought that something is not right):

All tubing from injector to detector is 0.005” i.d. (120 µm); total length is about 60 cm. The capillary from pump to injector is usually larger in diameter, and does not contribute much to the total pressure drop.

Flow rate, 1 mL/min.; Temperature, ambient; mobile phase, 100% aqueous.

Situations Involving Pressure That Is Lower Than Expected

There are two main problems that lead to pressures that are lower than expected.

 There are many different ways that a leak can occur in a LC system. The most common ones I see are related to connections (for example, tubing to valve, or tubing to column). Usually, these leaks are relatively small (that is, a few microlitres per minute), and can be corrected by tightening the fitting slightly. However, be careful—forcing a metal ferrule into a connection too much can deform the port (such as a column endfitting or valve port). If you feel like the connection is already very tight, then it is better to throw the capillary away and start with a fresh one. I always tell my students that “too loose is much better than too tight”. Another way of saying this is that it is much cheaper to replace several capillaries than it is to replace a valve stator because a capillary was overtightened and deformed or stripped the threads on a valve port. Significant leaks can also occur between the pump pistons and seals. We should never be able to see liquid emerging from the pump head in the area of the piston/seal. If liquid is observed, the seals are probably leaking and should be replaced. In my experience this problem does not occur nearly as frequently as it did with pumps 20 years ago. Finally, it is possible for polyetheretherketone (PEEK) tubing to burst, even when working below the advertised pressure limit of the tubing. When this happens it usually leads to a major, obvious leak, whereas leaks with connections and pump seals tend to be more subtle.

A partially obstructed solvent inlet filter

: LC pumps rely on a free, steady flow of solvent from the solvent bottle to the inlet check valve to work properly. If the inlet filter on the end of the line in the solvent bottle becomes partially obstructed by particulates or bacterial growth, this can slow the flow to the point where the pump is “starved” of solvent, and unable to deliver flow to the column at the specified flow rate, leading to lower than expected pressure. If one suspects that this might be the problem, a quick check involves simply removing the inlet filter from the solvent line. If the pressure returns to normal after the filter is removed, then the filter needs to be cleaned at a minimum, and it is usually best to just replace it altogether.

Situations Involving Pressure That Is Higher Than Expected

Most problems involving higher than expected pressure are somehow related to accumulation of debris somewhere in the system. The origins of this debris vary; it can come from particulate matter in the injected sample, molecules that are soluble in the sample solvent but precipitate in the mobile-phase stream, polymeric material shed by pump and injector seals, and so on. The specific nature of the problem that results from this debris depends strongly on how the system is configured. Determining where the obstruction is in the system can be tricky. A systematic approach to finding out where the problem lies involves removing components from the flow path one at a time, starting from the downstream end. For example, suppose we are running at 1 mL/min, and we observe a pressure at the pump of 600 bar, which is high compared to a normal operating pressure of 250 bar. With the flow off, remove the detector from the flow path. Turn the pump back on and record the pressure. If it has only decreased by 5 bar to 595 bar, then we know that the obstruction does not lie in the detector flow path. Again, with the flow off, remove the tubing between the detector and the column outlet. Turn the flow back on and record the pressure. If it has decreased another 10 bar to 585 bar, then we know that the tubing between the column outlet and the detector is not the source of the problem. Next, remove the column, turn the flow back on, and record the pressure. There should be a significant difference between the pressure recorded with and without the column connected. Suppose in this case that the pressure is still 365 bar even without the column connected, which would be abnormal in any typical analytical LC system. Next, suppose that upon removing the inline filter installed immediately upstream from the column the pressure drops to 20 bar. This would tell us that the pressure drop over the filter itself was 345 bar (far higher than expected), indicating that the filter should be thrown away and replaced. This “one-piece‑at‑a‑time” approach can feel tedious when trying to get an instrument back on track, but it is the most reliable way to isolate the problem. The three most commonly encountered scenarios are:

: In my laboratory, partially plugged filters account for 95% of our high pressure problems. Once it is clear that a filter is obstructed, one could try backflushing them, but this solution is usually short-lived. It is far better in the long run to just replace the filter.

An obstruction in a piece of capillary tubing

: This does not happen very often if inline filters (0.2–0.5 µm porosity) are used immediately after the sample injector. If inline filters are not used, then the capillaries of the smallest diameters and the ones furthest upstream (that is, closest to the injector) are the most likely to become blocked. Reversing the flow through an obstructed capillary will occasionally be sufficient to remove the debris, but the most reliable solution is to just replace the capillary.

: This can also be largely prevented through routine use of an inline filter upstream from the column. If an increase in pressure drop across the column is observed over time, reversing the flow through the column can flush debris out of the inlet frit, but, in my experience, the reduction in pressure is usually short-lived. It is also important to note that some column manufacturers use frits with larger porosities at the column inlet; reversing the flow is then a bit risky, because some particles could go through the frit and be lost from the column (thank you to Professor Chuck Lucy for this reminder). The bottom line is that it is best to avoid problems like this with the column by protecting it, through routine use of inline filters and/or guard columns.

Situations Involving Pressure That Appears To Be Fluctuating

Most modern LC pumps are based on some variation of a reciprocating dual piston design, where the pressure variation that occurs at the end of each piston stroke can be minimized, but is difficult to eliminate entirely. The specification for modern pumps is that the pressure variation should not exceed about 1%. If the observed variation is much larger than 1%, then it is most likely because of one of two reasons.

: A typical reciprocating dual piston pump design relies on two check valves to keep the mobile-phase flow moving in the direction of the column. When solvent is being pushed out of the pump head toward the column, the inlet check valve closes so that solvent cannot travel back towards the solvent bottle. When solvent is being drawn from the solvent bottle into the pump, an outlet check valve closes to prevent solvent from flowing backwards into the pump head. When working properly, these check valves open and close multiple times per minute. If one or both of them does not open or close properly, there will be a significant interruption in the flow to the column, which in turn manifests as a change in pressure. Determining which of the two check valves is faulty can be tricky. One approach is to first replace the inlet check valve with one that is known to be functional. If this does not solve the problem, then re-install the original inlet valve, and change out the outlet check valve with one that is known to be functional. If this does not reduce the pressure fluctuation, then the problem does not lie with the check valves.

: Even a pump with properly functioning check valves can get tripped up by an air bubble. If air becomes trapped in a pump head (for example, after the pump has accidentally run dry, because an inline degasser is not working properly, or after a prolonged period without use), it can lead to severe flow or pressure fluctuations. Purging the pump at high flow rate (with the column disconnected) is often effective for dislodging the bubble and returning to normal operation. If this does not resolve the problem, purging the pump head with isopropanol is another approach that often works well.

In this first instalment on essential topics in LC troubleshooting, I have discussed situations where the observed system pressure is somehow different from what is expected or normal. Effective troubleshooting for this type of problem begins with a sense for what the expected system behaviour is, so that a deviation from those expectations is noticeable. While there are many different potential causes of pressure‑related problems (too low, too high, or fluctuation), most problems can be connected to five or six specific causes. Understanding this short list of likely causes provides a good place to start troubleshooting, but it does not capture all possibilities. Readers interested in learning about a deeper list of causes and solutions are referred to the “LCGC Troubleshooting” wallchart (3).

https://www.chromatographyonline.com/view/troubleshooting-wallchart

D. Guillarme, B. Bobaly, and J.-L. Veuthey, 

 is the editor of “LC Troubleshooting”. Stoll is a professor and the co-chair of chemistry at Gustavus Adolphus College in St. Peter, Minnesota, USA. His primary research focus is on the development of 2D-LC for both targeted and untargeted analyses. He has authored or coauthored more than 75 peer-reviewed publications and four book chapters in separation science and more than 100 conference presentations. He is also a member of

’s editorial advisory board. Direct correspondence to: amatheson@mjhlifesciences.com

Some “LC Troubleshooting” topics never get old because there are some problems that persist in the practice of LC, even as instrument technology improves over time.

Essentials of LC Troubleshooting, Part 1: Pressure Problems

In this instalment of “GC Connections”, we take a close look at Golay’s famous equation that most people view as relating height equivalent to a theoretical plate (HETP) to the carrier gas flow rate or average linear gas velocity in a capillary column. We explore the original works of Golay and Keulemans. We also look closely at the original equation, the assumptions involved with its development, and the assumptions (both good and bad) that have been applied to HETP over the years. In part two, we will explore the consequences and relevance of this theory today, with temperature programming, very long (and very short) columns, high pressure drops, and vacuum outlet detectors.

The height equivalent to a theoretical plate (HETP) is one of the most important parameters used to measure column performance. HETP is the length of column required to generate one theoretical plate, with a theoretical plate being one transfer process of an analyte molecule between the mobile phase and the stationary phase. We are all familiar with considering the number of theoretical plates in a column or the number of theoretical plates in a length of column, as these are often stated by column vendors as a measure of column quality. More theoretical plates and more theoretical plates per metre are often considered good, leading to better resolution. A 30 m column with 100,000 theoretical plates is said to have 3333 theoretical plates per metre.

We use a chromatogram to measure theoretical plates (as shown in Figure 1), using equation 1, where 

 and HETP (as discussed later) are dependent on many parameters, including temperature, carrier gas flow rate, inlet and outlet pressures, column dimensions, and the choice of carrier gas. One challenge in comparing plate numbers between different columns is that the experiments will almost always have been performed under different conditions, making true comparisons difficult.

HETP is then calculated using equation 2, where 

 is the number of theoretical plates calculated using equation 1:

, or HETP, is also defined as the rate of band broadening. As we know, the peaks or bands get wider in all chromatographic techniques as the peaks and bands traverse the length of the column. HETP provides a measure of the rate of the broadening, with a smaller HETP indicating slower band broadening, leading to sharper peaks.

How was HETP as a measure of the rate of band broadening originally defined? This definition goes back to the earliest days of gas chromatography (GC) in the 1950s and the work of A.J.P. Martin and A.T. James, the inventors of GC; J. Van Deemter, who developed the original theory of band broadening for packed columns; Golay, who developed the theory for capillary columns; and Keulemans, who provided a fundamental conceptual definition for a theoretical plate.

Keulemans presented a picture of the separation process in chromatography in a classic text, 

, published in 1959 (1). In the foreword to this short text, A.J.P. Martin described it as “an admirably clear account of all the practical and theoretical aspects of this rapidly growing method”. The clear influence of the text is seen in the highly recognized 1965 text, 

As illustrated in Table 1, Keulemans described each theoretical plate as a liquid–liquid extraction between immiscible solvents. Starting with a flask containing a solution of an analyte dissolved in a solvent, say, water. The solution is mixed with an equal volume of hexane. If the partition coefficient is 1, then equal masses of solute are present in each phase. The hexane layer is then removed and mixed with an equal volume of water in a second flask and fresh hexane is added to the first flask. Each flask now contains half of the original analyte, equally distributed between the two phases. This process can be repeated with a third, fourth, fifth, and up to any number of flasks, ultimately resulting in a distribution of analyte among all the flasks (seen in Table 1), calculated for 10 flask theoretical plates, 10,000 molecules, and a distribution constant between the two phases of one.

The numbers in Table 1 represent the number of molecules out of the 10,000 in each flask or theoretical plate. We can note immediately that as the number of flasks increases, the number of molecules in each flask decreases, analogous to the chromatographic peak becoming broader and shorter. Also note that there are still some molecules in the initial flask, even after 10 extractions, an often-unappreciated consequence of chemical equilibrium: There are always some molecules left behind.

The description provided above makes several assumptions that, although illustrative of the chromatographic process, do not account for all processes that occur in real columns. First, it assumes that each theoretical plate occurs independently and has no direct contact with the other theoretical plates. Obviously in a column with a mobile phase, this assumption cannot be true as the mobile phase is continuously transporting solutes along the column. Second, it assumes that there are no barriers to mass transfer at the phase interfaces. In a real system, of course, the kinetics of mass transfer across the phase interfaces must be considered. Finally, there is no consideration of diffusion both within and between the two phases. In a column, the solute molecules distribute throughout the mobile and stationary phases. Golay’s equation, described below, uses a description of the chromatographic process like Keulemans, and accounts for these assumptions, plus the dimensions and physical conditions observed within columns.

Golay provided a thorough description of an equation describing the rate of band broadening in the proceedings of the “Gas Chromatography 1958” symposium organized by the Hydrocarbon Research Group of the Institute of Petroleum and the Koninkiljke Nederlandse Chemische Vreniging in Amsterdam, The Netherlands, in May 1958. The symposium volume was published in 1959, edited by Desty (3). The equation for circular capillary columns is presented as equation 3:

Note that Golay also described a similar equation for rectangular capillaries. At the time, there was considerable discussion about which would be better, and clearly circular capillaries have become far more popular. Interestingly, with recent interest in columns etched into silicon wafers for “laboratory on a chip” applications, rectangular capillaries are increasing in usage and importance. This equation is popularly called the “Golay Equation”, but it combines the work of many early researchers in chromatography.

Definitions of the many variables are discussed in the “deeper dive” below. Interestingly, the proceedings volume includes commentary following the formal text of the talk, in which substantive discussion among the symposium participants was captured. The names of those participating in that discussion read like an all-star lineup of modern chromatography inventors, including Golay, A.J.P. Martin, R.P.W. Scott, I.G. McWilliam, and others. It was traditional in the past to assign scribes to record the discussions. In one especially important exchange between Golay and Martin, they appear to agree, possibly begrudgingly, to use the definition of HETP presented by Keulemans and illustrated above (4).

In the original work, several related forms of the equation are presented, relating to specific situations that may occur in the making of capillary columns; the form used here is equation 31a from that work, chosen for simplicity in discussing the basic principles and consequences. The first thing to note is that this is a differential equation relating to 

, a differential of length or distance. The terms enclosed in the parentheses provide what we term as HETP or 

, the height equivalent to a theoretical plate, so the equation could be conceptually simplified to equation 4. Interestingly, similar to the Keulemans description, the independent variable is the length of the column (

), as the differential is distance and the dependent variable is the peak width, represented by the differential of the second statistical moment (

Equation 4 shows us that the rate of band broadening as the band traverses the column is equal to HETP. As we have learned in short courses and textbooks, smaller HETP means a slower rate of band broadening and sharper peaks. In many textbooks and courses, the terms within the parentheses in equation 3 are simplified to the form shown in equation 5. As we will see in Part 2 next month, equation 5 is an oversimplification that can generate confusion and possibly lead to false directions in method development and optimization.

Note the average velocity of carrier gas (

) is usually chosen as the independent variable in equations 4 and 5, leading to the “van Deemter” or “Golay” plots often seen in discussions of column performance in the scientific literature. The three terms are often described as representing analyte diffusion in the mobile phase (the “

” term), analyte diffusion in the stationary phase (the “

” term), and analyte diffusion in the mobile phase (the “

” term). In developing equation 3, Golay noted the similarity in form to the equation of van Deemter, developed a few years earlier.

Whether we perform detailed calculations based on it or not, equation 3 provides a very useful description of the many variables and processes relating to band broadening and, ultimately, to peak widths and resolution. Some important general principles are discussed here; for a detailed description of all variables and how they are used to evaluate column performance, see these book chapters or the discussion in ChromAcademy, 

’s online chromatography learning platform (5–7). In short, to minimize HETP, the quantities in parentheses in equation 3 should be minimized.

In the first term within the parentheses, often called the “

” term using the terminology in equation 5, diffusion in the mobile phase is considered. The numerator, 

, is the diffusion coefficient of an analyte molecule in the gas phase, which for simplicity can be considered a constant for that analyte at a given temperature in a given carrier gas. Diffusion coefficients in the gas phase are mainly dependent on the identity of the analyte, the solvent gas, and the temperature. The denominator is the average carrier gas velocity in the column. Not surprisingly, this suggests an inverse relationship between HETP and average carrier gas velocity.

, relates to mass transfer, also in the mobile phase, and is the major difference between Golay’s equation for capillary columns and the original van Deemter equation for packed columns. Capillary columns usually have much larger phase ratios (volume of mobile phase divided by volume of stationary phase) than packed columns, so mass transfer in the mobile phase becomes important. Note that in this term, the same diffusion coefficient described above is now in the denominator and the average carrier gas velocity (

) is in the numerator, suggesting a proportional (linear) relationship between HETP and carrier gas velocity.

m term include the square of the column radius, 

, and a complex polynomial of the retention factor (

). Note that all of the variables, except for the column radius are temperature dependent and that the retention factor is also related to the column dimensions and average linear gas velocity.

, relates to mass transfer in the stationary phase. Similar to the 

 term is linear with the average carrier gas velocity and the square of the column radius (

 term, the denominator includes a diffusion coefficient, this time in the liquid phase, which depends on the specific analyte, liquid phase, and temperature. Additionally, the analyte partition coefficient (

) into the liquid phase is part of the denominator. The term also includes a polynomial function of the retention factor (

Taken together, the three terms of the expression describing HETP, as presented by Golay, have numerous dependencies, and many of the variables that make up the equation have their own dependencies. The column radius is fixed and appears in two of the three terms. All the other variables are dependent on temperature. The average carrier gas velocity is dependent on the choice of carrier gas, the column dimensions (length and inside diameter), and temperature. The partition coefficient depends on the chemical nature of the analyte and stationary phase, and the retention factor depends on the partition coefficient, column phase ratio, and is further related to the average carrier gas velocity.

In our next instalment, we will examine these dependencies and the assumptions upon which our traditional view of HETP, based on the “Golay Equation”, are founded. We will also discuss their relevance in today’s capillary GC. The major changes between thinking about GC from the 1950s, when these ideas were first developed, and today include: the nearly universal use of temperature programming, smaller diameter capillary columns, thinner stationary phase films, and high vacuum column outlets, as seen in GC–mass spectrometry (MS). We will see that many of the traditional views that we were all taught (and still teach) about HETP, peak broadening, and peak widths in gas chromatography deserve some new thinking.

 (Reinhold, New York, USA, 1959), pp. 106–139.

 D.H. Desty, Ed.(Butterworths, London, UK, 1958), pp. 36–55.

 D.H. Desty, Ed.(Butterworths, London, UK, 1958), pp. 65–66.

H.M. McNair, J.M. Miller, and N.H. Snow, 

, (John Wiley and Sons, New York, USA, 2019), pp. 15–36.

 C.F. Poole, Ed. (Elsevier Amsterdam, The Netherlands, 2021), pp. 48–67

’s Online Learning Platform. https://www.chromacademy.com/channels/gc-training-courses/principles/gc-band-broadening/ (accessed December 2021).

 is the Founding Endowed Professor in the Department of Chemistry and Biochemistry at Seton Hall University, and an Adjunct Professor of Medical Science. During his 30 years as a chromatographer, he has published more than 70 refereed articles and book chapters and has given more than 200 presentations and short courses. He is interested in the fundamentals and applications of separation science, especially gas chromatography, sampling, and sample preparation for chemical analysis. His research group is very active, with ongoing projects using GC, GC–MS, two-dimensional GC, and extraction methods including headspace, liquid–liquid extraction, and solid-phase microextraction. Direct correspondence to: amatheson@mjhlifesciences.com

In this instalment we take a close look at Golay’s famous equation that most people see as relating HETP (height equivalent to a theoretical plate) to the carrier gas flow rate or average linear gas velocity in a capillary column.

Is Golay’s Famous Equation for HETP Still Relevant in Capillary GC? Part 1: A Common View of HETP

Choosing a liquid chromatography (LC) column for a particular application can be a surprisingly challenging task. On the one hand, column manufacturers give us many options to choose from, including particle types, pore sizes, particle sizes, and different lengths and diameters. On the other hand, we usually do not have time to experimentally evaluate many combinations of these parameters, and sometimes we end up picking something similar to the columns that are already in the drawer. The “kinetic plot” is a powerful graphical tool that can help leverage the best available theory to help us understand how different combinations of parameters (such as particle size and length) will perform in relation to the time needed to get to a particular column efficiency (and thus resolution), and therefore make well-informed decisions when choosing columns.

Fifty years into the evolution of modern liquid chromatography (LC) we are still observing remarkable growth in the commercial offerings of LC columns. Each year, we see introductions of columns prepared with superficially porous particles (SPPs) from more manufacturers, new column formats (such as pillar array columns), more particle types suitable for bioanalysis (such as wide pore particles), and so on. From an analyst’s perspective, these developments are wonderful because they give us more choices, and increasingly they give us options that are designed with specific applications in mind (such as columns sold specifically for the purpose of characterizing monoclonal antibodies [mAbs]). However, having all these options to choose from can also make purchasing decisions complicated. How do we know which column is the “right” one? Of course, with purchase prices in the $500–$1000 range, trying a large number of them is simply not realistic. In the worst-case scenario, making the wrong choice can lead to real disappointment and sunk costs. If we choose the wrong combination of particle size and column length and diameter and pore size for a particular application, we may find that the performance we observe (as measured by analysis time, resolution, and sensitivity) is not as good as we expected, or perhaps even worse than what we were already using.

The analysis time–resolution compromise is one of the most studied topics in the history of LC research. Although the issue may have been considered settled in the late 1990s, new developments over the last 20 years, including the use of pressures greater than 400 bar, particles smaller than three micrometers, new stationary phase supports, and the surge in interest in the analysis of biopharmaceuticals, are keeping things interesting (1,2). One very powerful framework that is used to understand how all these factors influence what columns we should use for which applications is the “kinetic plot.” For this first installment in a multipart series on the construction and use of these plots in practice, I’ve asked kinetic plot expert Professor Ken Broeckhoven to join me in describing what a kinetic plot is and how it relates to the practical factors we care about most in LC—analysis time and resolution. In subsequent installments, we will go on to show how these plots can be constructed from experimental data of your own, or data accessible to you, and finally how the resulting plots can be used to guide decision making when choosing columns, and help troubleshoot situations where a particular column does not deliver the performance expected based on intuition and community conversations.

Analysis Time and Resolution Are Connected

A primary goal of most analytical separations is to achieve a certain resolution between one or more pairs of compounds in the shortest possible analysis time. More efficient columns enable realization of this resolution in shorter times. Column efficiency (plate number, 

) as defined in equation 1 makes the connection between plate number and peak width (

If we compare two separations where an analyte of interest is eluted at the same retention time (

), the separation with the higher efficiency will have narrower peaks because of the inverse relationship between 

. Because resolution is also inversely related to peak width, higher plate numbers lead to higher resolution. As soon as we start discussing analysis time, the mobile phase flow rate matters: Higher flow rates lead to shorter analysis times, and vice versa. However, the plate number also depends on the flow rate, so optimizing a separation is not as simple as using the highest possible flow rate. The conventional framework used to relate the plate height and flow rate involves the concept of the plate height (

), or height equivalent to a theoretical plate (HETP), which is related to the column length (

In rough terms, the plate height is a property of the material inside the column, but is also affected by the mobile-phase flow rate and the properties of the analyte. Increasing the diameter of the particles inside the column generally leads to larger plate heights and lower efficiencies, for a given column length. The relationship between the plate height and the mobile-phase flow rate has the characteristic shape shown in Figure 1a, and is most commonly referred to as a 

 (3,4). Although for real separations we are mostly interested in the mobile-phase flow rate, van Deemter curves are usually plotted with mobile-phase velocity on the 

-axis because the velocity is independent of the column diameter, and thus allows a comparison of the curves constructed from data obtained using different columns. The most valuable takeaway from the van Deemter curve is the realization that the smallest plate heights—and thus highest plate number and resolution—are obtained at intermediate velocities (not too low and not too high). However, the mobile-phase flow rate that produces the optimal (minimum) plate height—and thus the maximum plate number and resolution—is not necessarily the best flow rate in practice because analysis time is so heavily dependent on the flow rate.

FIGURE 1: Classical perspective on the compromise between resolution and analysis time, and the pressure requirements associated with operating columns under different conditions. (a) van Deemter curves for small molecules and three different particle sizes, based on experimental data. (b) Pressures required to operate 100 mm long columns at the flow rates needed to produce the data points shown in (a). (c–h) Simulated chromatograms for a pair of close-eluting peaks under conditions corresponding to three different points in the curve for 3.5 μm particles in (a). (f–h) are the same as (c–e), but with x-axes adjusted to focus on the elution window.

It is instructive to examine the chromatograms that we would observe in experiments conducted with flow rates corresponding to three characteristic points on the van Deemter curve: a) the low-flow region (referred to as the 

 is at its minimum); and c) the high-flow region (referred to as the 

). These three points are highlighted with purple geometric shapes in Figure 1a, and the corresponding chromatograms are shown in panels (c–e) (full timescale) and (f–h) (zoomed view). These chromatograms make clear the practically relevant tradeoffs that are encoded in the van Deemter plot, but can be difficult to appreciate without a lot of experience working with these plots. We call your attention to three main points:

Working at flow rates below the optimum flow rate (where 

 is at its minimum) is almost never a good idea. Under these conditions the analysis will take longer than necessary—compare panel (c) to (d) and (e)—and the resolution will be poorer than what can be obtained at the optimum flow rate.

The highest resolution is obtained by working at the optimum flow rate, which is clear in panels (f–h) where we see that the valley between the peaks is greatest in panel (g). The valley between the peaks is greatest in panel (g) because the peaks are narrower, which also leads to taller peaks.

Much shorter analysis times can be realized by working at flow rates above the optimum, so long as some resolution can be sacrificed in the interest of a faster analysis. The resolution in panel (h) is clearly not as good as it is in panel (g), but this is a small change compared to the 70% decrease in analysis time. This tradeoff, and the extent to which this game can be played with real separations, strongly depends on how steep the 

-term regime. This slope strongly depends on particle size (slope generally increases with particle size, see Figure 1a), and the properties of the analyte (slope generally increases with molecular weight).

At this point, we encounter a significant limitation of the use of van Deemter curves alone for optimizing a separation—the plot does not explicitly communicate anything about the pressures required to realize chromatograms like those shown in Figure 1c–h. The significance of this limitation is made dramatically clear in Figure 1b, which shows the pressures required to produce the data points plotted in Figure 1a. For example, it is true that a 100-mm column packed with 1.7-μm particles will yield a plate number at the optimum flow rate that is roughly three times higher (29,400 compared to 10,000) than that for a column of the same length packed with 5-μm particles, and it will do so in one-third the time (optimum velocity of 6 mm/s compared to 2 mm/s). However, this improvement in plate number and speed comes at the cost of a significantly higher pressure requirement for the smaller particles. The pressure at the optimum for the 1.7-μm particles is 800 bar, whereas it is only 33 bar for the 5-μm particles. We also see here that one can also achieve a plate number of about 29,000 using a 20-cm long column packed with 3.5-μm particles at the optimum velocity, which would require a longer analysis time (roughly four times longer) compared to the column with 1.7-μm particles, but only one-fourth the pressure (200 compared to 800 bar). The van Deemter plot alone cannot help us manage the compromise between resolution (plate number), analysis time, and pressure requirements. However, the kinetic plot can help with this, and this is why it is so useful as a conceptual framework for optimizing separations and choosing columns.

Although many variants of the kinetic plot have been introduced and discussed over the years, a kinetic plot, in principle, is any method of presenting data that relates plate number to analysis time (5,6). This type of representation is not new and dates back to some of the early publications of Giddings (7,8). Figure 2 shows the relationship between a van Deemter curve and a kinetic plot. To go from the van Deemter curve in panel (a) to the first type of kinetic plot in panel (b), the 

-axis is transformed from mobile phase velocity (

FIGURE 2: Illustration of the relationship between van Deemter curves (a) and kinetic plots (b,c). The curve in (a) is the same as that in red in Figure 1, and curves in (b) and (c) are for a 100-mm column packed with the same 3.5 μm particles.

The kinetic plot in panel B makes the implications of the relationship between 

 for analysis time clear. Moving to the right on the plot—which corresponds to the B-term regime discussed above—leads to longer analysis times and poor efficiencies, which is not good. On the other hand, moving to the left of the maximum in the curve leads to much shorter analysis times, albeit at a slight cost of reduced plate number. The kinetic plot in Figure 2c is a simple transformation of the plot in panel B. The axes are reversed, and each axis is presented on a logarithmic scale, which helps visualize the relationship between 

 over a time range that spans from a few seconds to tens of minutes.

Adding the Dimension of Pressure to the Kinetic Plot

The kinetic plot in Figure 2c is sometimes referred to as a “fixed length kinetic plot.” Although it does make explicit the connection between analysis time and plate number, it does not make clear how the pressure limitations of a particular LC system (or column type) influence column selection. The fixed length plot can be extended as shown in Figure 3 by adding multiple curves, each representing a different column length. On each curve, moving from the top of the plot toward the bottom corresponds to an increase in flow rate until the maximum pressure of the system is reached, where the curve terminates in “X,” and intersects the gray line. This gray line represents the “kinetic performance limit,” which defines the maximum achievable plate number for a given analysis time, or the shortest time needed to obtain a given plate number, depending on your perspective. Such families of curves can yield very instructive insights related to column selection. Consider the vertical dashed black line that intersects the curves for the 10-, 15-, and 25-cm columns. This view makes it immediately clear that there are multiple ways to obtain a plate number of 10,000 using columns of different lengths, but all packed with 3.5-μm particles. The most time-inefficient way is to use a 25-cm column and operate it at low flow rate. In this example, the column dead time would be approximately 15 min (intersection of the dashed vertical line and the green curve), which is in spite of the fact that we generally think of long columns as being more efficient. Although it is true that longer columns have the potential to produce larger plate numbers, this potential can only be realized when the column is operated the “right” way. The next best option out of those shown here is to use the 15-cm column, which would produce 10,000 plates with a dead time of about 4 min. By far, the best way is to use the 10-cm column, operated at a velocity above the optimum, where the dead time would be about 10 s, a 90-fold improvement over the use of the 25-cm column at a low flow rate. Another way to look at this is to fix the analysis time at 0.9 min (horizontal black dashed line). Using a 10-cm column, this corresponds to operation in the 

-term regime and only a little more than 10,000 plates are obtained (Note that by operating the same column length in the 

-term, the same efficiency is reached in only 10 s, as shown for the vertical line). Operating a 15 cm column at the optimum velocity, a much higher efficiency of 21,600 plates is obtained, clearly making it a better choice. However, when operating a 25-cm long column slightly above its optimum flow rate, even 33,000 plates can be obtained in 0.9 min.

Kinetic plots can help us understand how different combinations of parameters will perform in relation the time needed to acquire a particular column efficiency—and thus resolution.