### High Accuracy Chromatographic Peak Fitting for System Suitability and QC of Columns and Flow Systems

When you want to know with certainty the state of a column’s health, you need to measure the theoretical plates of just the column’s separation, not artifacts of injectors, detector cells, or changes in the fluid flow path.

PeakLab fits chromatographic peaks to near perfect goodness of fit values. In the above UHPLC C18 peak fit, the 0.59 ppm unaccounted variance equates to a r^{2} goodness of fit greater than 0.999999, allowing separation of the column peak from all instrumental distortions. In the fit above, the blue is the observed peak, the red is the peak specific to the column separation minus all instrumental effects. The FWHM traditional Gaussian estimate of N uses only the magenta half-width and produces an N=20,671. The moment method accounts the full blue peak, but that includes the instrumental effects and tailing, and this results in N=13,234. The red deconvolved peak consists of only the column separation minus the instrumental distortions, N=26,905.

PeakLab goes one step further offering a model-based N which removes higher moment differences. such as those which can arise from the packing variation in narrow diameter columns and other nonidealities. For the above peak, the model-based N=35,137, the value that would be seen if the packing and interphase mass transfer were perfectly uniform.

Quantifying the instrument response function (IRF) parameters has value as well. The IRF parameters will catch aging injectors, flow path changes, and differences in detectors. Identifying the IRF also assists in designing preps that minimize these instrumental distortions, such as the differences in mobile phase solvents.

### High Accuracy Chromatographic Modeling of Overlapping Peaks – Don’t Reconfigure or Reformulate!

PeakLab introduces two model-based innovations to realize close to perfect fits of real-world chromatographic peaks. The first is the convolution integral fitting of IRFs, and the second is advanced HVL-based models with higher moment statistical generalizations. Both expertly manage the real-world non-idealities of chromatographic peaks.

The above separation represents an optimal separation of the BDMC region in a curcuminoid analysis. In most published studies, only a single peak is seen at this location. In this optimized separation, there are three additional components and little prospect for realizing baseline resolved peaks, gradient or isocratic. Despite sharing the tailing-fronting factor and third moment asymmetry across all four peaks, the peak fit above produced an unaccounted variance error of just 1.52 ppm, and accurate estimates of the areas of the four components. PeakLab was also able to process the 3D DAD data to extract and confirm different UV-VIS curcuminoid spectra for the four components. For chromatographic researchers where baseline resolved peaks are not always an option, PeakLab is an indispensable analytical tool.

The new PeakLab modeling of chromatographic peaks is so accurate, you can fit overlapping peaks with separate widths for each peak if just the upper 30% of a peak’s amplitude is exposed on each side, and you can successfully fit any set of overlapping peaks with shared widths and tailing-fronting factors if the second derivative method can simply detect the peak’s presence in the data.

For R&D work, there is no need to reformulate or redesign a separation in order to get baseline-resolved peaks and their conventional integrated areas. As in the example above, highly accurate areas are possible with overlapping peaks.

### Gradient UHPLC Reverse-Phase C_{18} Chromatographic Separations

Gradient UHPLC and HPLC separations add one more tier of complexity to the peak shape. While a third moment adjustment of the underlying density is generally needed for isocratic analytic peaks, gradient peaks require both third and fourth moment adjustments for truly effective modeling as well as an estimate of the aggregate gradient that is present during the analyte’s overall transit through the column.

While a well-crafted gradient can sometimes cancel most of the tailing of the IRF, the compressed shape of a gradient peak still requires this additional fourth moment level of modeling with respect to peak shape. Further, simply because a gradient can cancel much of an IRF, doesn’t mean that this will occur for even a single peak, and it will definitely not occur for peaks which partially or fully transit during an isocratic hold. The IRF will also still be present if a slower gradient is used or if the flow path has a strong IRF that cannot be fully offset by the gradient.

The above gradient peaks consist of near coeluting beta and alpha turmerones. A twice-generalized HVL model with third and fourth moment adjustments and also fitting the non-cancelled portion of the IRF produces a 0.75 ppm unaccounted variance goodness of fit. The modeling was able to fit the peaks to an accuracy which would match that seen with integrating baseline-resolved peaks.

### Thermal Gradient GC

Thermal gradient GC peaks often span a large portion of the region of nonlinear-chromatographic shapes, and can vary from close to symmetric peaks at low concentrations to sharply left and right triangular tailed and fronted shapes at high concentrations. Overlapping peaks are often encountered, especially with natural materials with many components.

While the thermal gradient will generally offset the IRF tailing common to conventional GC, these are gradient peaks which require the third and fourth adjustments of a twice-generalized HVL model as well as fitting that is capable of successfully processing small concentration peaks independently. PeakLab has a number of intelligent fit strategies that make even these difficult fits quite easy to realize.

In the above fit of the peaks in the turmerone elution regime of turmeric, the colors in the upper plot represent different data regions in the baseline segments option. This procedure is used to isolate the baseline resolved regions of the elution and independently fit the different overlapping peaks in each segments In each of these fits, the individual peaks in an overlap feature are further fitted individually to better realize the global or optimal fit. In the 62 ppm error fit shown above, PeakLab fit the individual regions separately, each segment sharing the width but varying the tailing-fronting factor. If you look closely, you will see small, close to symmetric peaks in the left tail of the sharply fronted first and third principal turmerone peaks.

### Preparative Chromatography

Preparative separations often operate at or beyond the level of column overload. In such a case, you will want to closely monitor the health of the columns.

In the above IC preparative separation, the overload state within the column is apparent. The blue curve is the peak as registered by the instrument, the red curve is the peak that would be seen if there were no instrumental distortions, and the green curve is the pure HVL that would be seen if there were no higher moment nonidealities and if the column’s capacity had been such no overload occurred. For the peak as registered by the instrument, the blue curve, the N by the Gaussian FWHM was 125, and the N by moments was 150. For the parametric model where the overload state was deconvolved, the green curve, the separation that would be seen in the column had infinite capacity, N=6518, essentially the value one would expect to see in an analytic separation.

### High Speed, Small Column Diameter Separations

If you are working with fast separations using small diameter columns, you are likely to see overlapping peaks, prominent IRFs, and a considerable third moment skew and possibly significant fourth moment dilation.

In the above research chromatogram, only one of the eight peaks is baseline resolved where one would see an accurate quantification using conventional integration. PeakLab’s fitting not only accurately determines the areas and center of mass locations of all eight peaks, but it also quantifies the IRF of the instrument as well as the higher moment nonidealities in the separation. When you see peaks such as the above, the brief time required for a PeakLab analysis will give you more analytic information than you would see in an elaborate optimization of the separation where all peaks were baseline resolved.

### Chemometric Predictive Modeling of Chromatography with Spectroscopy Data

Chromatographic measurements can be time consuming and costly, and for certain lower accuracy, high-speed screening applications, it may be of value to build a predictive model based on mapping chromatographic analysis values to UV/VIS, IR, FTIR, FTNIR, or other rapid spectroscopic measurements.

PeakLab introduces an innovative chemometric modeling solution that is an attractive alternative to traditional PLS and PCR modeling. These are direct spectral models that outperform the PLS and PCR ‘unscrambling’ algorithms for predictive accuracy and web-based computational performance.