Sampling frequency, response times and embedded signal filtration in fast, high efficiency liquid chromatography: A tutorial

Abstract

With increasingly efficient columns, eluite peaks are increasingly narrower. To take full advantage of this, choice of the detector response time and the data acquisition rate a.k.a. detector sampling frequency, have become increasingly important. In this work, we revisit the concept of data sampling from the theorem variously attributed to Whittaker, Nyquist, Kotelnikov, and Shannon. Focusing on time scales relevant to the current practice of high performance liquid chromatography (HPLC) and optical absorbance detection (the most commonly used method), even for very narrow simulated peaks Fourier transformation shows that theoretical minimum sampling frequency is still relatively low (<10 Hz). However, this consideration alone may not be adequate for real chromatograms when an appreciable amount of noise is present. Further, depending on the instrument, the manufacturer's choice of a particular data bunching/integration/response time condition may be integrally coupled to the sampling frequency. In any case, the exact nature of signal filtration often occurs in a manner neither transparent to nor controllable by the user. Using fast chromatography on a state-of-the-art column (38,000 plates), we evaluate the responses produced by different present generation instruments, each with their unique black box digital filters. We show that the common wisdom of sampling 20 points per peak can be inadequate for high efficiency columns and that the sampling frequency and response choices do affect the peak shape. If the sampling frequency is too low or response time is too large, the observed peak shapes will not remain as narrow as they really are - this is especially true for high efficiency and high speed separations. It is shown that both sampling frequency and digital filtering affect the retention time, noise amplitude, peak shape and width in a complex fashion. We show how a square-wave driven light emitting diode source can reveal the nature of the embedded filter. We discuss time uncertainties related to the choice of sampling frequency. Finally, we suggest steps to obtain optimum results from a given system.

Peak deconvolution to correctly assess the band broadening of chromatographic columns

“…To investigate the effect of measurement frequency [71], the peaks of the asymmetrical test case were "shrunk" in width in order to reduce the number of points per peak while keeping the same peak shape. The resulting system + column peak in this test case only had a 4-peak width of 1 s. This test case was subsequently analyzed using three different measurement frequencies (160 Hz, 80 Hz and 40 Hz).…”

Signal convolution indicates chromatographic pulse flow and open-end flow

“…Very large injection volumes produce long segments when injected into narrow pipes, and the resulting 'square distribution' of the concentration of solute molecules is pulse-like [11,25,36] rather than Gaussian shaped [11,37]. The chromatographic peak is observed not as a square signal, but as a signal that is smoothed by the response function of the detector, extra-column band broadening [38,39] and column-only band broadening [40]. Correction for extra-column band broadening was performed by Wright et al [36] who used a digital system peak with a tail and the Dirac-delta function to perform the deconvolution of the peak.…”

Wavelet transforms in separation science for denoising and peak overlap detection

“…One of the best visual ways to "see" the distorting effect of these filters is to run these filters on square waves instead of chromatographic peaks. The generation of a square wave can be easily understood as a light source that is rapidly turning on and off as shown previously [28]. These square wave patterns on an HPLC can be readily achieved by attaching a light-emitting diode on an HPLC detector flow cell as shown previously [28]; when the light is off, the "absorbance" is high, and when the light is on, the absorbance is "low."…”

“…The generation of a square wave can be easily understood as a light source that is rapidly turning on and off as shown previously [28]. These square wave patterns on an HPLC can be readily achieved by attaching a light-emitting diode on an HPLC detector flow cell as shown previously [28]; when the light is off, the "absorbance" is high, and when the light is on, the absorbance is "low." Since the manufacturers do not explicitly state the noise suppressing filters, we simulate several commonly used filters and show these effects on a perfect square wave in the absence of noise.…”

“…Most state of the art HPLC/UHPLC software use Savistky-Golay, digital RC-filter, and various varieties of moving average filters such as simple moving average, Gaussian weighted moving average, and Hamming weighted moving average [28]. From an analytical chemist's perspective, these traditional filters used in chromatography always lead to the broadening and deformation of the peak, albeit without affecting peak area.…”