Total peak shape analysis: detection and quantitation of concurrent fronting, tailing, and their effect on asymmetry measurements

Influence of theoretical and semi-empirical peak models on the efficiency calculation in chiral chromatography

Height equivalent to theoretical plate (H) equations, such as the van Deemter or Knox-Saleem equations, and other efficiency vs. linear velocity equations (u), provide kinetic insights into chromatographic separations phenomena and column performance. In enantioselective separations, the peak shape of the two enantiomers can differ significantly and are often asymmetric. The peak efficiency calculations heavily impact these efficiency-flow profiles, leading to erroneous estimations of eddy diffusion, longitudinal diffusion, and mass transfer terms. In this work, new asymmetric peak functions are employed for modeling enantiomer peaks based on the Haarhoff-Van der Linde function, its generalized variant (GHVL), once Generalized Asymmetric Gaussian (AGN), and Twice Generalized Gaussian (TGN). The new models (AGN, TGN, and GHVL) incorporate higher statistical moments besides the zeroth, first, and second moments to account for two-sided asymmetry (fronting or tailing). The fit results are compared with the traditional efficiency calculation methods endorsed by official pharmacopeia and numerical estimation of moments from the raw data. Enantiomeric separations of ibuprofen and dl-homophenylalanine were chosen as probe molecules. The results demonstrate that non-linear least squares fitted functions provide better estimations of peak efficiency data even in the presence of high noise. In particular, the generalized models consistently offered the best quality fits for various peak shapes in chiral separations. Conversely, the half-height Gaussian method greatly overpredicted skewed peak efficiencies. This investigation reveals that the commonly held assumptions of peak shape and numerical integration of raw data are highly insufficient for chiral chromatography. The impact of asymmetry on plate height should not be overlooked when accurate data from efficiency-flow rate curves is derived. We advocate for the broader adoption of these new generalized peak (AGN, TGN, GHVL) models because they provide robustness at various SNRs that account for right or left asymmetry while accurately representing peak geometry.

A new chromatographic response function with automatically adapting weight factor for automated method development

A critical factor for automated method development in chromatography is the maximization or minimization of an objective function describing the quality (and speed) of the separation. In chromatography, this function is commonly referred to as a chromatographic response function (CRF). Many CRFs have previously been introduced, but many have unfavourable properties such as featuring multiple optima, insufficient discriminatory power, and a too strong dependence on the weight factors needed to balance resolution and time penalty components. To overcome these problems, the present study introduces a new type of CRF wherein the relative weight of the time penalty term is a self-adaptive function of the separation quality. The ability to unambiguously identify the optimal gradient settings of this newly proposed CRF is compared to that of some of the most frequently used CRFs in a study covering 100 randomly composed in silico samples. Doing so, the new CRF is found to flawlessly lead to the correct solution (=linear gradient parameters providing the highest resolution in the shortest potential time) in 100 % of the cases, while the most frequently used literature CRFs were off-target for about 50 to 60 % of the samples, even when considering the availability of spectral peak shape data. Some slight alterations to the proposed CRF are introduced and discussed as well.

Enhancing enantiomeric and diastereomeric separations: A single chromatograph approach for two-dimensional heart-cut methodology

A high-performance chromatograph was adapted and reconfigured to establish a two-dimensional methodology for separations that are not easily achievable using a single enantioselective column. Allethrin, a pyrethroid used widely as a pesticide in domestic environments, was chosen as the model analyte. With three chiral centers, it has eight stereoisomers and is considered one of the more difficult chiral separations. Diastereomeric separation was achieved in the first dimension using a shape-selective stationary phase based on ultrapure porous graphitic carbon (particle diameter, 3 μm) in the reversed phase mode. Advanced asymmetric bidirectional peak functions (half-Gaussian modified Gaussian and exponentially modified Gaussian) were employed to extract overlapping peak areas. The four diastereomeric peaks were heart-cut and sent to the second dimension online using a standard six-port 2-position rotary valve. Enantiomeric separation was attained in the second dimension using an immobilized-cellulose tris(3,5-dichlorophenylcarbamate) column (3 μm) with chromatographic resolutions >2.7 for all enantiomeric pairs. The second dimension method was developed using the information from circular dichroism detection. The baseline separation of seven peaks of allethrin in a single dimension was also demonstrated using (2-hydroxypropyl)-β-cyclodextrin. The enantiomeric purity of a purified formulation of allethrin in a commercial pesticide was validated using the developed 2D approach.

Automatic peak detection algorithm based on continuous wavelet transform for complex chromatograms from multi-detector micro-scale gas chromatographs

Peak detection for chromatograms, including the detection of peak retention times, peak start locations, and peak end locations, is an important processing step for extracting peak information that is used for chemical recognition. Compared to benchtop gas chromatographs, the chromatograms generated by microscale gas chromatographs (µGCs) often contain higher noise levels, peak overlap, peak asymmetry, and both positive and negative chromatographic peaks, increasing the challenges for peak detection. This paper reports an automatic peak detection algorithm based on continuous wavelet transform (CWT) for chromatograms generated by multi-detector µGCs. The relationship between chemical retention time and peak width is leveraged to differentiate chromatographic peaks from noise and baseline drift. Special features in the CWT coefficients are leveraged to detect peak overlap and asymmetry. For certain detectors that may generate positive and negative chromatographic peaks, the peaks cannot be independently detected reliably, but the peak information can be well extracted using peak information generated by other in-line single-polarity detectors. The implemented algorithm provided a true positive rate of 97.2 % and false discovery rate of 7.8 % for chromatograms generated by a µGC with three integrated detectors, two capacitive and one photoionization. The chromatograms included complex scenarios with positive and negative chromatographic peaks, up to five consecutive overlapping peaks, peak asymmetry factor up to 24, and signal-to-noise ratios spanning 9-2800.

Direct Construction of Peaks from Free Induction Decay Curves for Gas Chromatography-Molecular Rotational Resonance Spectroscopy without Fourier Transforms

The concept of coupling gas chromatography with molecular rotational resonance spectroscopy (GC-MRR) was introduced in 2020, combining the separation capabilities of GC with the unparalleled specificity of MRR. In this study, we address the challenge of the high data throughput of MRR spectrometers, as GC-MRR spectrometers can generate thousands to millions of data points per second. In the previous GC-MRR studies, a free induction decay (FID) measurement was Fourier transformed to generate each point on the chromatogram. Such extensive calculations limit the performance, sensitivity, and speed of GC-MRR. A direct approach is proposed here to extract peak intensity from FID using the Gram-Schmidt vector orthogonalization method. First, analyte-free FIDs are used to construct a basis set representing the instrument's background noise, and then the remaining FIDs are orthogonalized to this fixed basis set. Each FID yields a single intensity value after Gram-Schmidt orthogonalization. The magnitude of the orthogonalized analyte FID is the signal intensity plotted in the chromatogram. This approach is computationally much faster (up to 10 times) than the conventional Fourier transform algorithm, is at least as sensitive as the FT algorithm, and maintains or improves the chromatographic peak shape. We compare the sensitivity, linearity, and chromatographic peak shapes for the Fourier transform and Gram-Schmidt approaches using both synthetically generated FIDs and instrumental data. This approach would allow the summed peak intensity to be displayed essentially in real-time, following which identified peaks can be further investigated to identify and quantify the species associated with each.

Implementation of design of experiments for optimization of forced degradation conditions and development of a stability-indicating high-performance liquid chromatography method for sepiwhite

Sepiwhite is a novel anti-pigmenting agent that is derived from fatty acid and phenylalanine and used for hyperpigmentation induced by light exposure or inflammation. In this study, a simple and validated high-performance liquid chromatography method for the quantitation of sepiwhite was developed. Optimized forced degradation of sepiwhite at thermal, acid/base, photolysis, oxidative, and heavy metal ions conditions were evaluated and the effect of each of them on production of specific 10%-30% degradants was studied by the approach of design of experiments. Sepiwhite accelerated study was conducted and toxicity of sepiwhite at each condition was tested. An optimized high-performance liquid chromatography method was validated by a face-centered central composition design. Ten different degradants were identified from sepiwhite and degradation behavior under different conditions was studied. Sepiwhite and its degradant products show no cytotoxicity. This optimized high-performance liquid chromatography method can be applied for quality control assay and sepiwhite degradation behavior may be considered in the manufacturing of sepiwhite products.

High efficiency functionalized hydrophilic cyclofructans as stationary phases in sub/supercritical fluid chromatography

Packed column SFC has become very popular for preparative and analytical separations due to the low cost of CO₂, its accessible critical temperature, and pressure, with the additional benefit of a low environmental burden. Currently, there is a shortage of new polar stationary phase chemistries for SFC. In this work, two new functionalized cyclofructan columns are introduced and evaluated for their performance in achiral SFC separations for the first time. Cyclofructan (CF6), a macrocyclic oligosaccharide, was covalently linked with benzoic acid (BCF6) and propyl sulfonic acid (SCF6) groups by ether bonds. Superficially porous particles (2.7 μm) bonded with modified CF6 showed markedly different selectivity than native CF6. In SFC, peak shapes of amines and basic compounds are often compromised. We show that small quantities (~5.7% v/v) of water added to the methanol modifier in CO₂ improves peak symmetries of primary, secondary, and tertiary amines. Efficiencies as high as 200,000 plates/m (reduced plate height ~ 1.8) were observed for benzamide and amitriptyline on the BCF6 column. The relative standard deviations (RSDs) of retention times on BCF6 were about 1.4%, and on SCF6 were less than 1%. Amines on the SCF6 column showed plate counts as high as 170,000 plates/m. Tetramethylammonium acetate is examined as an alternative to water in MeOH. A run time of 36 min with methanol, trifluoroacetic acid, triethylamine mobile phase was reduced to <5 min with complete baseline resolution for a set of amines. The new stationary phases allow greener approaches towards solving separation problems.

A new metric for relating macroscopic chromatograms to microscopic surface dynamics: the distribution function ratio (DFR)

Heterogeneous stationary phase chemistry causes chromatographic tailing that lowers separation efficiency and complicates optimizing mobile phase conditions. Model-free metrics are attractive for assessing optimal separation conditions due to the low quantity of information required, but often do not reveal underlying mechanisms that cause tailing, for example, heterogeneous retention modes. We report a new metric, which we call the Distribution Function Ratio (DFR), based on a graphical comparison between the chromatogram and Gaussian cumulative distribution functions, achieving correspondence to ground truth surface dynamics with a single chromatogram. Using a Monte Carlo framework, we show that the DFR can predict the prevalence of heterogeneous retention modes with high precision when the relative desorption rate between modes is known, as in during surface dynamics experiments. Ground truth comparisons reveal that the DFR outperforms both the asymmetry factor and skewness by yielding a one-to-one correspondence with heterogeneous retention mode prevalence over a broad range of experimentally realistic values. Perhaps of more value, we illustrate that the DFR, when combined with the asymmetry factor and skewness, can estimate microscopic surface dynamics, providing valuable insights into surface chemistry using existing chromatographic instrumentation. Connecting ensemble results to microscopic quantities through the lens of simulation establishes a new chemistry-driven route to measuring and advancing separations.

Low-Cost Benzene Toluene Xylene Measurement Gas System Based on the Mini Chromatographic Cartridge

Benzene, toluene and xylene (BTX) are an important part of the volatile organic compounds (VOCs) to be detected and monitored in the air, due to their toxicity towards human health. One of the most reliable technique used in BTX detection is gas chromatography (GC), which presents a high sensitivity. On the other hand, it has important drawbacks, such as high costs, the need for qualified personnel and frequent maintenance. To overcome these drawbacks, this work reports the development of a low cost and portable BTX gas detection system based on a mini chromatographic cartridge, a photo ionization detector (PID), a simple control unit (based on Arduino architecture) and a mini pump. In order to separate the BTX components, we propose the use of a cartridge 80 mm in length, composed of several commercial chromatographic column sections. To test the system performances, we have injected different amounts (from about 0.3 to 5.3 µg) of benzene, toluene and xylene and two of the most frequent possible interferents (ethanol, acetone). Experimental results have shown different retention time values (i.e., 25 ± 0.5 s, 51 ± 1.2 s and 117 ± 4 s, respectively) for benzene, toluene and xylene.

Metal-Organic Framework Stationary Phases for One- and Two-Dimensional Micro-Gas Chromatographic Separations of Light Alkanes and Polar Toxic Industrial Chemicals

Despite promising advances with metal-organic frameworks (MOFs) as stationary phases for chromatography, the application of MOFs for one- and two-dimensional micro-gas chromatography (μGC and μGC × μGC) applications has yet to be shown. We demonstrate for the first time, μGC columns coated with two different MOFs, HKUST-1 and ZIF-8, for the rapid separation of high volatility light alkane hydrocarbons (natural gas) and determined the partition coefficients for toxic industrial chemicals, using μGC and μGC × μGC systems. Complete separation of natural gas components, methane through pentane, was completed within 1 min, with sufficient resolution to discriminate n-butane from i-butane. Layer-by-layer controlled deposition cycles of the MOFs were accomplished to establish the optimal film thickness, which was validated using GC (sorption thermodynamics), quartz-crystal microbalance gravimetric analysis and scanning electron microscopy. Complete surface coverage was not observed until after ~17 deposition cycles. Propane retention factors with HKUST-1-coated μGC and a state-of-the-art polar, porous-layer open-tubular (PLOT) stationary phase were approximately the same at ~7.5. However, with polar methanol, retention factors with these two stationary phases were 748 and 59, respectively, yielding methanol-to-propane selectivity factors of ~100 and ~8, respectively, a 13-fold increase in polarity with HKUST-1. These studies advance the applications of MOFs as μGC stationary phase.

The utility of statistical moments in chromatography using trapezoidal and Simpson's rules of peak integration

Modern chromatographic data acquisition softwares often behave as black boxes where the researchers have little control over the raw data processing. One of the significant interests of separation scientists is to extract physico-chemical information from chromatographic experiments and peak parameters. In addition, column developers need the total peak shape analysis to characterize the flow profile in chromatographic beds. Statistical moments offer a robust approach for providing detailed information for peaks in terms of area, its center of gravity, variance, resolution, and its skew without assuming any peak model or shape. Despite their utility and theoretical significance, statistical moments are rarely incorporated as they often provide underestimated or overestimated results because of inappropriate choice of the integration method and selection of integration limits. The Gaussian model is universally used in most chromatography softwares to assess efficiency, resolution, and peak position. Herein we present a user-friendly, and accessible approach for calculating the zeroth, first, second, and third moments through more accurate numerical integration techniques (Trapezoidal and Simpson's rule) which provide an accurate estimate of peak parameters as compared to rectangular integration. An Excel template is also provided which can calculate the four moments in three steps with or without baseline correction.