A detailed study on the selection of borderline features for accurate mechanism description of the adsorption of different pesticide molecules under different temperature ranges

Mathematical models play a crucial role in data acquisition by boosting the capacity to interpret and group the gathered information. However, the challenge lies in choosing the most accurate model to represent data sets with very slight nuances, as it occurs in the validation of adsorption processes considering molecules with different properties but similar structural attributes. Due to these very small variations, there is a high chance of excessive adaption to specific patterns created by the distributions, statistically blindsiding the decision-making. In this work, we used statistical physics (sta-phy) modeling and thermodynamic calculations of the three different pesticides 2,4-dichlorophenoxyacetic acid (2,4-D), dicamba (DCB), and mecoprop (MCPP) on a woody based activated carbon (WBAC) to demonstrate these patterns while also unveiling the mechanisms involved. We demonstrate that the statistical criteria alone do not provide enough clarity in these cases, and we propose using the physical meaning of each estimated parameter as a way out. Thus, in this work, we prove in detail that using sta-phy models requires absolute mastering of the subjects to ensure reliable results by understanding the relationships between the adsorption parameters and the system properties instead of a simple read of the determination coefficients.