چكيده لاتين
In complex chemical systems, accurately determining equilibrium constants is crucial for understanding molecular processes and drug design. However, the calculation of equilibrium constants is often challenged by the correlation between these constants, which is influenced by various chemical parameters, such as the concentrations of the components in the system under study. One of the commonly used methods to determine equilibrium constants and their correlations in chemical systems is acid-base titrations combined with spectrophotometry, which is employed to record the necessary data for multivariate analysis. In this method, the concentration of the titrant and analyte significantly affects the accuracy and precision of the equilibrium constant calculations.
This study investigates the interactions of several organic acids (HA), including ibuprofen, aspirin, acetaminophen, and benzoic acid, with β-cyclodextrin (D) using spectrophotometric titration. The equilibrium constants in these systems include Kf (HA), Kf (DHA), and Kf (DA). The primary objective of this research was to identify conditions that minimize uncertainty and the correlation between the equilibrium constants. Initially, simulations were performed to analyze the concentration profiles of these complexes, providing valuable information about the systemsʹ behavior under different conditions. Subsequently, experimental design methods were used to identify optimal conditions for the simulated data that reduce uncertainty and correlation between the equilibrium constants of the components in the system. The optimal concentration conditions of the components in the system were found to be C(H+) > C(HA) > C(D).
Under these conditions, the correlation between Kf(HA) and Kf(DHA) ranged from 0.752 for acetaminophen to 0.967 for aspirin, the correlation between Kf(HA) and Kf(DA) ranged from 0.198 for aspirin to 0.619 for ibuprofen, and the correlation between Kf(DHA) and Kf(DA) ranged from 0.054 for aspirin to 0.922 for acetaminophen. Based on the model provided by experimental design, experimental tests were conducted under the optimal conditions. Additionally, experiments were carried out under non-optimal conditions for comparison and model evaluation. The results showed that conducting experiments under optimal conditions reduced the correlation between the equilibrium constants and minimized uncertainty in the calculations.
Since the optimal conditions obtained through the initial experimental design spanned a broad range of component concentrations, a further experimental design was carried out at limited concentration levels, considering the condition C(H+) > C(HA) > C(D).
An important finding of this study is that for complexes with lower formation constants, higher concentrations of the organic acids are required compared to β-cyclodextrin. This is due to the decreased affinity of the compound for cyclodextrin under such conditions. Furthermore, an appropriate amount of H⁺ is necessary to ensure that the acids are fully present in the HA form, facilitating the formation of stable complexes with β-cyclodextrin. The results indicate that designing experimental setups using simulations, experimental design, and multivariate data analysis is a powerful tool for improving accuracy and reducing errors in the analysis of chemical equilibrium systems. These findings could contribute to the development of novel methods in drug delivery system design and enhance the precision of equilibrium constant calculations.
