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

Arrhenius Crossover Temperature of Glass-Forming Liquids Predicted by an Artificial Neural Network

The Arrhenius crossover temperature, TA, corresponds to a thermodynamic state wherein the atomistic dynamics of a liquid becomes heterogeneous and cooperative; and the activation barrier of diffusion dynamics becomes temperature-dependent at temperatures below TA. The theoretical estimation of this temperature is difficult for some types of materials, especially silicates and borates. In these materials, self-diffusion as a function of the temperature T is reproduced by the Arrhenius law, where the activation barrier practically independent on the temperature T. The purpose of the present work was to establish the relationship between the Arrhenius crossover temperature TA and the physical properties of liquids directly related to their glass-forming ability. Using a machine learning model, the crossover temperature TA was calculated for silicates, borates, organic compounds and metal melts of various compositions. The empirical values of the glass transition temperature Tg, the melting temperature Tm, the ratio of these temperatures Tg/Tm and the fragility index m were applied as input parameters. It has been established that the temperatures Tg and Tm are significant parameters, whereas their ratio Tg/Tm and the fragility index m do not correlate much with the temperature TA. An important result of the present work is the analytical equation relating the temperatures Tg, Tm and TA, and that, from the algebraic point of view, is the equation for a second-order curved surface. It was shown that this equation allows one to correctly estimate the temperature TA for a large class of materials, regardless of their compositions and glass-forming abilities.

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.

Diffusion of Squalene in Nonaqueous Solvents

Capillary flow techniques have been used to determine the translational diffusion constant, D, of squalene in seven alkanes and five cyclohexanes. The alkanes are n-hexane, n-octane, n-decane, n-dodecane, n-tetradecane, 2,2,4,4,6,8,8-heptamethylnonane (isocetane), and 2,6,10,14-tetramethylpentadecane (pristane). The cyclohexanes are cyclohexane, n-butylcyclohexane, n-hexylcyclohexane, n-octylcyclohexane, and n-dodecylcyclohexane. When combined with published data in CD₂Cl₂, ethyl acetate, n-hexadecane, squalane, n-octane-squalane mixtures, and supercritical CO₂, the 35 diffusion constants and viscosities, η, vary by factors of ∼230 and ∼500, respectively. A fit to the modified Stokes-Einstein equation (MSE, D/T = A _SE/η ^p ) gives an average absolute percentage difference (AAPD) of 7.72% between the experimental and calculated D values where p and A _SE are constants, T is the absolute temperature, and the AAPD is the average value of (10²) (|D _calcd - D _exptl|/D _exptl). Two other MSE fits using subsets of the 35 diffusion constants may be useful for (a) estimating the viscosity of the hydrophobic core of lipid droplets, where squalene is a naturally occurring component, and (b) providing estimates of the D values needed to design extraction processes by which squalene is obtained from plant oils. The Wilke-Chang equation also was considered and found to give larger AAPDs than the corresponding MSE fits.

A Theoretical Analysis on a Multi-Bed Pervaporation Membrane Reactor during Levulinic Acid Esterification Using the Computational Fluid Dynamic Method

Pervaporation is a peculiar membrane separation process, which is considered for integration with a variety of reactions in promising new applications. Pervaporation membrane reactors have some specific uses in sustainable chemistry, such as the esterification processes. This theoretical study based on the computational fluid dynamics method aims to evaluate the performance of a multi-bed pervaporation membrane reactor (including poly (vinyl alcohol) membrane) to produce ethyl levulinate as a significant fuel additive, coming from the esterification of levulinic acid. For comparison, an equivalent multi-bed traditional reactor is also studied at the same operating conditions of the aforementioned pervaporation membrane reactor. A computational fluid dynamics model was developed and validated by experimental literature data. The effects of reaction temperature, catalyst loading, feed molar ratio, and feed flow rate on the reactor’s performance in terms of levulinic acid conversion and water removal were hence studied. The simulations indicated that the multi-bed pervaporation membrane reactor results to be the best solution over the multi-bed traditional reactor, presenting the best simulation results at 343 K, 2 bar, catalyst loading 8.6 g, feed flow rate 7 mm³/s, and feed molar ratio 3 with levulinic acid conversion equal to 95.3% and 91.1% water removal.