FBX dosimeter - a theoretical approach for interpretation and optimisation

Chemical dosimetry exploiting solutions of xylenol orange (XO), benzoic acid, and ferrous sulphate (FBX) is widely used in various applications. The method is based on spectrophotometric detection of XO/Fe³⁺ion complexes generated upon irradiation. There is, however, a discrepancy between the results obtained in the previous studies. We developed, therefore, a theoretical approach for interpretation of FBX dosimeter behaviour. We assumed the formation of two types of (XO)/Fe³⁺ion complexes with stoichiometric ratios of 1:1 and 2:1. The relationship between concentrations of free XO, complexes and Fe³⁺ions and their dose response was described on basis of the binding equilibrium between these species. Spectrophotometric titration of XO solution with Fe³⁺ions and FBX solution X-ray irradiation experiments were conducted for testing the approach. Spectrophotometric titration data allowed deconvolution of the spectra of individual complexes and calculation of binding dissociation constants. We obtained values for peak molar extinction coefficients as 0.0288 μM^-1 cm^-1 at 571 nm and 0.0356 μM^-1 cm^-1 at 456 nm for XOFe³⁺ and XO₂Fe³⁺complexes, respectively. Dose response for concentrations of Fe³⁺ions and complexes were calculated from the spectral analysis of the FBX solutions exposed to doses up to 45 Gy. These results indicated that generally a non-linear net OD calibration curve is expected. At a certain wavelength, however, a linear calibration curve can be obtained, and we suggested a theoretical justification for this observation and a method to find the optimal wavelength for linearity. Our study provided an insight into the processes underlying the behaviour of the FBX dosimeter and guidelines for optimisation of measurements.