Determination of Nonlinear Parameters Included in Rate Equations by Taylor's Differential Correction Method Intermolecular Transfer of a Fluorine Atom from UF6 to UF5

Abstract

KEYWORDS: Taylor's first order differential correction, nonlinear parameter, simultaneous differential equations, intermolecular transfer of fluorine atom, isotopic exchange, uranium hexafluoride, uranium pentafluoride, uranium isotope, laser isotope separationThe analysis of experimental data obtained in chemical observation often leads to cumbersome problems in the determination of reaction parameters included nonlinearly in the governing rate equations. When the quantities to be observed are given in explicit functional expressions of these parameters, such a nonlinear regression method as first proposed by Marquardt 1) and recently devoted to selected applications to various experiments by Rusling and Kumosinski 2) can be used to extract reliable parameters from raw experimental data. However, there are many cases where the rate equations do not have analytical solutions. In this note we discuss a stepwise, iterative approach to the least squares condition for such cases where the observed quantities must be related to their numerical solutions, taking as an example the intermolecular transfer of a fluorine atom from UF 6 to UF 5 . The discussions include also a short review of the previous researches and the possibility of a new rate equation for this reaction. Short Review on Reaction between UF 6 and UF 5Since the first observation by Grigor'ev et al., 3) particular attention [4][5][6][7][8][9][10] has been paid to the uranium isotope exchange between gaseous UF 6 and solid UF 5 expressed bybecause this reaction may be an important factor, which results in a drop in the final selectivity of molecular laser isotope separation. Grigor'ev et al.3) have pointed out the reaction may easily occur through intermolecular transfer of a fluorine atom from UF 6 to UF 5 . They have suggested also that the reaction includes two processes: one is a rather rapid process due to the reaction on the surface layer of the UF 5 particle and the other a relatively slow process due to a secondary reaction participated by underlying UF 5 molecules exposed by successive fluorine transfer reactions. Several works [4][5][6][7][8] have been done to confirm this. In these works [4][5][6] the reaction has been discussed within a framework that the number of available UF 5 molecules on the particle surface that enter into the reaction will remain unchanged. The assumption of constant number of surface UF 5 molecules has some difficulty in satisfying the condition of related isotopic mass balance. To avoid this, Yato 7,8) has introduced the assumption that the surface area of UF 5 particles increases with time. However, this assumption leads to another difficulty: if there is an increase in the UF 5 surface area, the surface energy must increase with time, while there is no way to supply the required energy to the particles under the isothermal and isobaric conditions, as pointed out by Kuga and Takeuchi. 9)Recently, Kuga and Takeuchi 10) have carried out the experiment under the condition of high concentration of UF 6 over a long time,...