Demonstrates that Gaussian regression accurately represents deviations from Beer’s Law in optical absorbance, indicating the need for revised analytical methods.
Except under extremely deviant conditions, the “standard curve” regressional relationship between optical absorbance and absorbent concentration is shown to exhibit an S-shaped profile of progressively increasing slope up to an inflexion followed by a region of progressively decreasing slope. Applied to this profile, a Gaussian regression procedure is shown to deliver i) a versatile, accurate representation of these sigmoid deviations from the Beer’s Law proportional relationship between absorbance (A) and absorbent concentration (C), namely Ar = a exp[ – {(C – b) / c}2 + d in which a, b, c and d are experimentally determined constants ii) an explicit inversion of this regressional relationship C = b + c sqrt[ ln{ a / (Ar – d)}] which is required to determine the absorbent concentration corresponding to an observed value of absorbance, and iii) an expression for the slope of the regressional relationship dAr / dC = – 2(a / c2) (C – b) exp[ – (C – b)2 / c2 ] as a measure of the sensitivity of the experimental procedure.
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John C. O’C.Young (2015) studied this question.
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