Thermodynamically and kinetically controlled products

Abstract

Parallel irreversible and reversible reactions, thermodynamic aspects and the effect of temperature.

Cellular automata models of kinetically and thermodynamically controlled reactions

“…Because of the tenfold increase in the number of cells monitored, these curves are seen to be significantly smoother than those from the single trial run shown in Figure 1. The crossing point for [B] ϭ [C] was found to occur at 492 (Ϯ21, standard deviation) iterations for the ten trials, a value fairly close to that reported for the equation-based model [6]. The maximum of the B concentration occurred at 132 Ϯ 15 iterations, and the average concentration at was 0.309 Ϯ [B] max 0.003 in this instance, a value significantly different from the 0.5 value suggested by Brown et al [6].…”

“…The crossing point for [B] ϭ [C] was found to occur at 492 (Ϯ21, standard deviation) iterations for the ten trials, a value fairly close to that reported for the equation-based model [6]. The maximum of the B concentration occurred at 132 Ϯ 15 iterations, and the average concentration at was 0.309 Ϯ [B] max 0.003 in this instance, a value significantly different from the 0.5 value suggested by Brown et al [6]. Moreover, our data do not exhibit the highly peaked behavior for the concentration of species B reported in their study.…”

“…The "noise" or slight raggedness seen in the plots of the populations is due to the relatively small number of ingredients being monitored. The crossing point at which [B] ϭ [C] occurs for this trial at 477 iterations, which is to be compared with the value of approximately 470 s obtained by Brown et al [6]. The maximum value of [B] occurred near 130 iterations, and our value for this single trial corresponds to a [B] max concentration of 0.301, a value different from the 0.5 value given by Brown et al [6].…”

“…In order to compare the results of our cellular automata models with the results of the traditional approach utilizing differential rate equations, we have selected for examination two examples (cases 3 and 6) from the study of Brown et al [6]. For the transition probabilities P t (i,j) between the species we have used the rate constants employed for each case by Brown et al The transition probabilities can thus be represented by the transition probability matrix.…”

“…Analytical forms for the solutions can be found, al-though they are typically complicated functions of the rate constants and the initial conditions [4,5]. Using the common assumptions that and [A] ϭ [A] 0 Brown et al [6] have illustrated the…”