Re-evaluating uncertainty in modern instruments B. Falgueras-Vallbona, K. Duthie, Q. Hanley Department of Chemistry and Forensics, School of Science and Technology, United Kingdom Relationships between scale and uncertainty in chemical measurement have been noted since at least the early 1970s 1 but explanations have remained mostly empirical. Here, we looked at modern instruments (FTIR, ICP-MS, and UV-Vis) toward a goal of understanding the fundamentals of uncertainty functions in these systems. A range of studies and a reasonably general theory of limiting uncertainty in spectrophotometers has been available for some time based on Poisson statistics and the intensity of light. 2,3 Previous work has tended to treat individual instruments using wavelengths in isolation and limited studies are available extending to the IR. 2,4,5 In a review of the literature, we did not find definitive studies for ICP-MS. The instruments were assessed by challenging them with samples spanning a range of concentrations to create plots to document the scale dependence of uncertainty. In the case of UV-Vis, a dye mixture of E102, E124, E133 and E155 was engineered to try to assess the full spectrum. Ga was selected for the ICP-MS to minimize the impact of contamination. The ICP-MS had near zero background in the absence of sample and its scaling exponent approached a value consistent with a Poisson distribution. Of the instruments, FTIR was closest to homoscedastic due to the multiplexed processing of the interferograms. Most difficult were the UV-Vis Spectrophotometers which exhibited a complicated response due to the processing required to convert intensities to absorbance values. Previous theoretical work regarding maximum absorbances and optimal absorbance for minimizing uncertainty do not apply in modern instruments and vary within a spectrum. For example, a Poisson noise limited system has a minimum relative standard deviation at an absorbance of 0.86 au while a thermal noise limited system has a minimum at ~0.43 au. 6 Our modern UV-Vis instruments had minima ranging between 0.48 and 0.61 au depending on the wavelength. Full theoretical understanding of UV-Vis instruments is hampered by the tradition of considering absorbance values as raw data. In the absence of the intensity data, direct connection to theory becomes an ill- posed problem. References 1. Thompson, M. Uncertainty Functions, a Compact Way of Summarising or Specifying the Behaviour of Analytical Systems. TrAC Trends Anal. Chem. 2011 , 30 (7), 1168–1175. 2. Rothman1, L. D.; Crouch, S. R.; Ingle, J. D. Theoretical and Experimental Investigation of Factors Affecting Precision in Molecular Absorption Spectrophotometry. Anal. Chem. 1975 , 47 (8), 1226–1233. 3. Ratzlaff, K. L.; Natusch, D. F. S. Theoretical Assessment of Precision in Dual Wavelength Spectrophotometric Measurement. Anal. Chem. 1977 , 49 (14), 2170–2176. 4. Galbán, J.; De Marcos, S.; Sanz, I.; Ubide, C.; Zuriarrain, J. Uncertainty in Modern Spectrophotometers. Analytical Chemistry . 2007, 79 (13), 4763–4767. 5. Xu, Z.; Larsen, D. W. Development of Ultra-Low-Noise Spectrophotometry for Analytical Applications. Anal. Chem. 2005 , 77 (19), 6463–6468. 6. Laqua, K.; Melhuish, W. H.; Zander, M. Molecular Absorption Spectoscopy, Ultraviolet and Visible (UV/Vis). Pure Appl. Chem. 1988 , 60 (9), 1449–1460.
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