Measurements and correlation of diffusion coefficients of ibuprofen in both liquid and supercritical fluids

Influence of Ethanol Parametrization on Diffusion Coefficients Using OPLS-AA Force Field

Molecular dynamics simulations employing the all-atom optimized potential for liquid simulations (OPLS-AA) force field were performed for determining self-diffusion coefficients (D11) of ethanol and tracer diffusion coefficients (D12) of solutes in ethanol at several temperature and pressure conditions. For simulations employing the original OPLS-AA diameter of ethanol's oxygen atom (σOH), calculated and experimental diffusivities of protic solutes differed by more than 25%. To correct this behavior, the σOH was reoptimized using the experimental D12 of quercetin and of gallic acid in liquid ethanol as benchmarks. A substantial improvement of the calculated diffusivities was found by changing σOH from its original value (0.312 nm) to 0.306 nm, with average absolute relative deviations (AARD) of 3.71% and 4.59% for quercetin and gallic acid, respectively. The new σOH value was further tested by computing D12 of ibuprofen and butan-1-ol in liquid ethanol with AARDs of 1.55% and 4.81%, respectively. A significant improvement was also obtained for the D11 of ethanol with AARD = 3.51%. It was also demonstrated that in the case of diffusion coefficients of non-polar solutes in ethanol, the original σOH=0.312 nm should be used for better agreement with experiment. If equilibrium properties such as enthalpy of vaporization and density are estimated, the original diameter should be once again adopted.

Modeling Tracer Diffusion Coefficients of Any Type of Solutes in Polar and Non-Polar Dense Solvents

In this work, a simple two-parameters correlation based on the Rice and Gray, Lennard-Jones, and Stockmayer theories was devised for the calculation of binary diffusion coefficients (D12) of any type of solutes at infinite dilution in polar and non-polar solvents. This equation can be relevant for systems with polar solvents, since most models in the literature fail when strong intermolecular forces predominate in solution. The new correlation embodies the Stockmayer potential without requiring the dipole moments of any component, which significantly enlarges its application. It was validated with the largest D12 database of polar and non-polar dense systems, with 8812 data points (NDP) spanning 553 systems, of which 133 have water as solvent (NDP = 1266), 89 contain polar solvents excluding water (NDP = 1405), 177 have supercritical carbon dioxide (SC-CO2) as solvent (NDP = 5028), and 154 have non-polar or weakly polar solvents excluding SC-CO2 (NDP = 1113). Overall, the model achieved an average deviation of only 3.43%, with accurate and unbiased behavior even for polar systems.

FTIR as a Powerful Tool for Measurements of Diffusion in Supercritical Carbon Dioxide Using Taylor Dispersion Method

A new experimental high-pressure setup for measuring diffusion coefficients in supercritical fluids, based on Taylor dispersion method, and using an FTIR detector to operate up to 25.0 MPa was designed and optimized. Tracer diffusivities, D12, of toluene and benzene in supercritical carbon dioxide were measured in the temperature range of 306.15–320.15 K, and pressure range of 7.5–17 MPa to evaluate the setup and experimental protocol. The effects of flow velocity, volume of the cell, absorbance at different wavenumbers on the diffusion coefficient as well as all parameters respecting the Taylor dispersion method have been analyzed. The obtained diffusion coefficients are in excellent agreement with the available literature data. The dependence of D12 on temperature, pressure, and solvent density were examined. Some correlation models based on the hydrodynamic theory were used to estimate the diffusion coefficients in supercritical carbon dioxide, which is the best agreement obtained for an improved version of the Wilke–Chang model.

Predictive Models for the Binary Diffusion Coefficient at Infinite Dilution in Polar and Nonpolar Fluids

Experimental diffusivities are scarcely available, though their knowledge is essential to model rate-controlled processes. In this work various machine learning models to estimate diffusivities in polar and nonpolar solvents (except water and supercritical CO₂) were developed. Such models were trained on a database of 90 polar systems (1431 points) and 154 nonpolar systems (1129 points) with data on 20 properties. Five machine learning algorithms were evaluated: multilinear regression, k-nearest neighbors, decision tree, and two ensemble methods (random forest and gradient boosted). For both polar and nonpolar data, the best results were found using the gradient boosted algorithm. The model for polar systems contains 6 variables/parameters (temperature, solvent viscosity, solute molar mass, solute critical pressure, solvent molar mass, and solvent Lennard-Jones energy constant) and showed an average deviation (AARD) of 5.07%. The nonpolar model requires five variables/parameters (the same of polar systems except the Lennard-Jones constant) and presents AARD = 5.86%. These results were compared with four classic models, including the 2-parameter correlation of Magalhães et al. (AARD = 5.19/6.19% for polar/nonpolar) and the predictive Wilke-Chang equation (AARD = 40.92/29.19%). Nonetheless Magalhães et al. requires two parameters per system that must be previously fitted to data. The developed models are coded and provided as command line program.