Large-Scale Models of Radiation Chemistry and the Principle of Detailed Balancing

Abstract

Large-scale kinetic models containing more than 50 homogeneous reaction steps have been developed to help understand the behavior of actinide solutions in various circumstances. One specific objective is to understand the behaviors in nitrate solutions as such solutions are used in actinide separations. A challenge arises in developing these large-scale models while ensuring compliance with the principle of detailed balancing because it can be very difficult to identify all embedded reaction loops. These loops can violate the principle of detailed balancing either by consisting of reversible steps that do not meet Wegscheider’s condition or by having unopposed irreversible steps that cause illegality. Here we report the development of DETBAL, which is a software code that systematically identifies a basis of reversible loops and a basis of all loops within the model, and then automatically checks for illegal loops. We apply DETBAL to two recent large-scale models of the radiation of nitrate solutions, show that these models violate the principle of detailed balancing in many ways, provide potential solutions to these violations, and demonstrate the effect of some of these modifications.

The principle of detailed balancing, the iron-catalyzed disproportionation of hydrogen peroxide, and the Fenton reaction

“…When the equilibrium constant for eqn (42) (eqn (1.19) in Table 1) is combined with the forward rate constant cited above, a reverse rate constant of 3 × 10 3 M −1 s −1 is calculated for eqn (42). This latter result seems quite plausible and suggests that eqn (42) could be the first step leading to eqn (41). It has been proposed that eqn (42) itself is not an elementary step but proceeds through intermediate formation of [Fe(H 2 O 2 )] 2+ .…”

“…40 Subsequently we devised a computer software method, DETBAL, that greatly simplifies and automates the process. 41 It is not uncommon for mechanisms to have loops that are linked by shared steps; in such cases the complete set of loops is generated by linear combinations of a basis set, and there is no unique basis set. Thus, DETBAL reveals a basis of loops in the mechanism but other loops can be possible.…”

“…In this Perspective we assume that OH • is the product. This reaction tends to be written as eqn (41):…”

“…Sychev and Isak's 1995 review cites 15 literature values for its rate constant ranging from 41.7 to 79 M −1 s −1 . 9 If this rate constant is combined with the equilibrium constant (eqn (1.18) in Table 1), a reverse rate constant of 2 × 10 15 M −2 s −1 is calculated for this reaction; this value greatly exceeds the diffusion limit for a termolecular reaction, which implies that eqn (41) must not be an elementary step.…”

“…The principle of detailed balancing has been the topic of several of the author's recent publications, [39][40][41][42] but its history extends back almost a century. It is a fundamental principle of chemical kinetics that has both qualitative and quantitative implications.…”