Complete Theoretical Treatment of the Transmittance Ratio Ultraviolet/Visible Spectrophotometric Stray Radiant Energy Test Method

Abstract

This paper develops the theoretical basis behind the transmittance ratio test method for determining the relative stray radiant energy level in a double-beam dispersive spectrophotometer so as to allow for the non-transparency of a test solution towards the stray radiant energy for all sample beam-to-reference beam cuvette path length ratios. Non-transparency is defined as the transmittance of the reference beam solution, whose monochromatic absorbance is unity, towards stray radiant energy. The proposed method has the same concentration absorbing sample placed in the beams of the scanning spectrophotometer, the sample-beam cuvette being a known factor longer than the reference-beam cuvette. While scanning towards shorter wavelengths, an apparent differential absorbance Mielenz peak is recorded. An exact formula is derived in this paper relating the relative stray radiant energy level to the Mielenz peak absorbance, to the known cuvette path length ratio, to the observed monochromatic absorbance of the test sample at the Mielenz peak wavelength, and to the sample transmittance towards the stray radiant energy. Sample transmittance towards stray radiant energy cannot be determined experimentally. However, the derived formula only allows the other experimental quantities to tie in together for a single numerically calculated value for the sample-transmittance towards stray radiant energy. The formulae are tedious to derive and cumbersome to handle, but their application is facilitated greatly by a Microsoft Office Excel 2007 spreadsheet. The test method was applied to an ultraviolet–visible (UV/VIS) scanning spectrophotometer at nine wavelengths in the range 713 < γ (nm) >; 649 for a sample beam-to-reference beam cuvette path length ratio of 10 mm/5 mm and using blue food dye (E123) as the test material. Sample transparency to stray radiant energy fluctuated in wavelength between 0.819 and 0.948, while the relative stray radiant energy level fluctuated between 1.283 × 10⁻³ and 2.516 × 10⁻³. The investigation was repeated at 665.6 nm for all fifteen sample beam-to-reference beam cuvette path length ratios, which it was possible to establish using combinations of quartz-glass cuvettes with path lengths of 100, 50, 20, 10, 5, 2, and 1 mm. The sample transparency to stray radiant energy at 665.6 nm was 0.95 ± 0.5, while the relative stray radiant energy was (1.5 ± 0.33) × 10⁻³.