Infinite Dilution Diffusion Coefficients Research Articles

Evaluation of different equations of state and free-volume approaches for unified modeling of diffusion and thermodiffusion coefficients

This article is a development and testing of the previously suggested theoretical approach for simultaneous thermodynamic modeling of diffusion and thermodiffusion coefficients. The new theoretical framework allows for the calculation of transport properties with the aid of the concepts of penetration distances and emission functions, which are fully determined from thermodynamic equations that relate functions of state variables, that is, equations of state (EoS). Four underlying EoS were tested in this work, 3 different cubic EoS and PC-SAFT, with the aim of investigating the effect of the thermodynamic model on the description of experimental data. We also investigated the impact of different approaches to estimating the free volume, which is an essential part of the model. The results indicate that the application of the effective co-volume provides a superior representation of the diffusion and thermodiffusion coefficients, which should be included in the parameterization procedure for the selection of the unified model parameters. We evaluated the use of infinite dilution diffusion coefficient data and molecular dynamics simulation to validate model parameters, and discussed the possible ways to improve the model, including predicting diffusion data as a function of temperature.

Diffusivities and solubilities of carbon dioxide in deep eutectic solvents

Deep eutectic solvents (DESs) have been identified as promising solvents for CO2 capture because of their low volatility and tunable properties. Detailed information on solute solubility and diffusivity is crucial for the design and operation of processes involving mixtures composed of DESs and dissolved gases. The infinite-dilution diffusion coefficients of CO2 in 33 DESs (both hydrophilic and hydrophobic) were gravimetrically determined with a magnetic suspension balance at 298.15 and 313.15 K along with the Henry’s constants of CO2 in these DESs. Interestingly, the diffusion coefficients of CO2 at infinite dilution in hydrophobic DESs were found to be much higher than those in hydrophilic DESs. In order to better understand this phenomenon, CO2 diffusion coefficients under infinite dilution conditions in traditional solvents and ionic liquids (ILs) were summarized from literature, which revealed that the CO2 diffusivity is often approximately inversely proportional to the square root of the viscosity. However, the hydrophilic DESs and some ILs/hydrophobic DESs with large molar volumes displayed a significantly different behavior. The OH group seems to hinder CO2 diffusion, while the presence of multiple long flexible alkyl chains in the DES constituents can facilitate the diffusion. Modified Wilke–Chang correlations were successfully developed to describe the infinite-dilution diffusion coefficients in the measured DESs. Tetraoctylammonium bromide - decanoic acid (1:2) was found promising for further investigation for application in CO2 capture processes with supported liquid membranes or physical absorption.

Determination of Diffusion Coefficients of Heavy Metal Ions (Ni3+, Zn2+, Ba2+, and Mn2+) at Infinite Dilution through Electrolytic Conductivity Measurements

One important parameter to examine the behavior and mass transfer properties of heavy metal ions is the diffusion coefficient. Due to the costly methods of its determination, a simple process correlating the molar conductivity data to diffusion coefficient was utilized. Molar conductivity data were determined for five (5) different dilute concentrations of the chlorides of the heavy metal ions (Ni3+, Zn2+, Ba2+, and Mn2+) and at temperatures ranging from 303.15 to 323.15 K. The infinite dilution diffusion coefficients of the heavy metals were estimated using the Nernst-Haskell equation and Nernst-Einstein equation. The molar conductivity and the diffusion coefficients values of the ions were in the order of Ba2+ > Mn2+ > Zn2+ > Ni3+ with the Ba2+ having the highest molar conductivity with a correlated infinite dilution diffusion coefficient of 1.6565 × 10-9 m2/s at 303.15 K. This study was able to predict the values of the infinite dilution diffusion coefficient of heavy metal ions and could contribute to a better understanding of the mobility of heavy metal ions in a water environment

Mutual diffusion coefficients of dimethyl carbonate + n-heptane and dimethyl carbonate + isooctane from 288.15 K to 318.15 K

The mutual diffusion coefficients of dimethyl carbonate + n-heptane and dimethyl carbonate + isooctane binary systems were measured at temperatures from 288.15 K to 318.15 K with the mass fraction of dimethyl carbonate from 0.05 to 0.95 under atmospheric pressure. All the mutual diffusion coefficients we reported are Fick diffusion coefficients, which were measured by the digital holographic interferometry. The expanded relative uncertainty for the measured mutual diffusion coefficients is estimated to 2.4% with the level of confidence of 0.95 (coverage factor k = 2). Moreover, a theoretical model (UNIDIF) of mutual diffusion coefficients for dimethyl carbonate + n-heptane and dimethyl carbonate + isooctane binary mixtures was given by fitting the experimental results, and the adjustable parameters and infinite dilution diffusion coefficients of these two solutions were given. The influences of temperature and composition on the mutual diffusion coefficients were discussed.

The influence of water on the thermophysical properties of 1-ethyl-3-methylimidazolium acetate

Recent efforts in using ionic liquids for the dissolution of wood constituents, including cellulose, concluded that 1-ethyl-3-methylimidazolium acetate ([emim][OAc]) is one of the most promising ionic liquids to dissolve cellulose. However, in order to make possible any industrial application, thermophysical properties of the pure liquid and of its mixtures with water are needed. In this study the influence of water on the thermophysical properties of [emim][OAc] is discussed. Density, speed of sound, viscosity, electrical conductivity, thermal conductivity, refractive index and infinite dilution diffusion coefficients were measured for mixtures of [emim][OAc] and water, in the temperature range 293.15–333.15 K, at 0.1 MPa, and full composition range. The rheological behaviour was also tested. The mixture was found to be completely miscible. Water free values for the properties of pure ionic liquid were extracted from mixture data, using new methodologies. Resultsshow that the mixture is highly structured, dominated by hydrogen bonding interactions between the water molecules and the ionic liquid acetate anions. The values of the properties establish a consistent and accurate data set for chemical plant cellulose dissolution and other future applications of these mixtures.

Estado del arte de correlaciones para el modelamiento del fenómeno de transferencia de masa en columnas de extracción líquido - líquido

El modelo tradicional de ecuaciones MESH no contempla los fenómenos de transferencia de masa, los cuales están presentes en operaciones de separación y, desde un punto de vista más riguroso, deben ser tenidos en cuenta para una simulación más exitosa a la hora de proponer el diseño real de un equipo de esta índole. Numerosas teorías han sido propuestas para el modelamiento de este fenómeno, de las que se han derivado ecuaciones netamente teóricas y empíricas que a la fecha no han logrado reducir el error promedio en la estimación del 20 %, según la amplia literatura consultada. En este documento se presenta el estado del arte de las correlaciones disponibles para el modelamiento del fenómeno de transferencia de masa en columnas de extracción, incluyendo modelos de difúsividad a dilución infinita en soluciones concentradas, coeficientes de transferencia de masa y cálculo de propiedades, que posteriormente pueden ser útiles para el modelamiento de columnas de extracción por ecuaciones MERSHQ

Molecular dynamics simulation of infinite dilution diffusivity of carbon dioxide in supercritical water

We apply equilibrium molecular dynamic simulations for investigating the infinite dilution diffusivity of carbon dioxide in near- and supercritical water (SCW) over the wide temperature ranging from 647 to 973 K at 115, 217, 426 and 663 kg/m3. The diffusion coefficients of SCW and infinite dilution diffusion coefficients (IDDCs) of carbon dioxide are calculated by using the Einstein mean-square displacement method. It is observed that the IDDCs of carbon dioxide in SCW are approximately 1–2 orders of magnitude higher than that in normal water. The analysis of the temperature dependence of the IDDCs of carbon dioxide reveals that they do not conform to the Arrhenius equation. In the near critical region, the IDDCs of carbon dioxide do not exhibit a monotonic change with a variation in temperature, but increase gradually with an increase in the temperature in a region far from the critical state. The anomaly of the temperature dependence of the diffusion of carbon dioxide in SCW can be explained using the microstructure features of the different states of the water. In addition, we observe that the IDDCs of oxygen are slightly larger than those of carbon dioxide under the same conditions.

Estimation of diffusion coefficients of ascorbate-based ions at infinite dilution through electrolytic conductivity measurements

Ascorbic acid is a naturally-occurring organic compound that has high water solubility. One significant parameter that can describe the mobility and transport of ascorbic acid and its mineral salts in water systems is the diffusion coefficient. Molar conductivity data were determined from electrolytic conductivity data measured at different concentrations of ascorbate-based ions (dilute region) and temperatures (293.15 to 313.15 K). From these data, the infinite dilution diffusion coefficients of the ascorbic acid and mineral salts in water were estimated using the Nernst-Haskell Equation. The Nernst-Einstein Equation was used to predict the infinite dilution self-diffusion coefficients of the representative ascorbate-based ions ([H+], [Na+], and [Ca2+]). For most temperatures and concentrations considered, the Ca2+ cation had the highest molar conductivity but the [H+] cation had the highest correlated infinite dilution self-diffusion coefficient of 11.4105 × 10−9 m2/s at 313.15 K. The [Na+] and [Ca2+] cations had values of correlated infinite dilution self-diffusion coefficient of 2.6263 × 10−9 m2/s and 2.4045 × 10−9 m2/s at 313.15 K, respectively. The molar conductivity and diffusion coefficient of the ions at infinite dilution were in the order of [H+] > [Na+] > [Ca2+]. It was found that an increase in temperature also increases the diffusion coefficient. This study was able to estimate infinite dilution diffusion coefficient data for ascorbate-based ions. Thus, the results of this study can serve as a basis and reference for future researches to have a better understanding of the fate and transport of ascorbate-based ions in the environment.

Molecular Dynamic Simulation of Diffusion Coefficients for Alkanols in Supercritical CO21

The infinite dilution diffusion coefficients (D12) of methanol, ethanol, 1-propanol, 1-butanol and 1-pentanol in supercritical CO2 (scCO2) at 313.2 K and 10–16 MPa were simulated by molecular dynamics (MD) simulation. The microscopic structure was also analyzed by calculation of the radial distribution function, coordination number (CN) between the center mass of solute and solvent molecules, and the average number of hydrogen bonding of this system. In infinite dilute solution, the probability of forming hydrogen bond between alkanol molecules is greatly reduced relative to pure alkanol fluid, and the weak hydrogen bonds formed between alkanol and CO2 molecules. In general, this work provides a reliable simulation method for transfer properties of solutes in scCO2. The prediction data were provides for the design and development of chemical processing. The results are helpful for one to deeper understand the relationship between microscopic structures of fluid and its transfer properties.

Determination of diffusion coefficients of various livestock antibiotics in water at infinite dilution

The fate of antibiotics entering the environment raised concerns on the possible effect of antimicrobial resistance bacteria. Prediction of the fate and transport of these particles are needed to be determined, significantly the diffusion coefficient of antibiotic in water at infinite dilution. A systematic determination of diffusion coefficient of antibiotic in water at infinite dilution of five different kinds of livestock antibiotics namely: Amtyl, Ciprotyl, Doxylak Forte, Trisullak, and Vetracin Gold in the 293.15 to 313.15 K temperature range are reported through the use of the method involving the electrolytic conductivity measurements. A continuous stirred tank reactor is utilized to measure the electrolytic conductivities of the considered systems. These conductivities are correlated by using the Nernst-Haskell equation to determine the infinite dilution diffusion coefficient. Determined diffusion coefficients are based on the assumption that in dilute solution, these antibiotics behave as strong electrolyte from which H+ cation dissociate from the antibiotic’s anion.

Tributyl Phosphate Aggregation in the Presence of Metals: An Assessment Using Diffusion NMR Spectroscopy.

Diffusion nuclear magnetic resonance (NMR) spectroscopy was used to find the interaggregate interactions and sizes of tributyl phosphate (TBP) aggregates containing varying concentrations of uranium or zirconium and HNO3 in an n-dodecane diluent. The average diffusion coefficients of TBP species were measured using a pulsed-field gradient stimulated echo experiment with a longitudinal eddy-current delay (STE-LED). Interaggregate interactions were determined by measuring the diffusion coefficient of TBP in a sample after a series of dilutions with n-dodecane. The interaction-independent infinite dilution diffusion coefficient was also calculated from these measurements. The sizes of TBP aggregates were calculated from the infinite dilution diffusion coefficient using the Wilke-Chang equation. Interactions between TBP aggregates were observed to correspond to a hard sphere potential with a repulsive component. Aggregate sizes found by NMR were comparable to literature values found using small-angle neutron scattering. The diffusion of TBP in heavy organic third phases indicates that the third phase may be a bicontinuous structure like that found in traditional surfactant systems.

Molecular dynamics simulation of diffusion and structure of n-alkane/n-alkanol mixtures at infinite dilution

Infinite dilute diffusion coefficients (D12) of normal alkanes (C1 to C14) in 1-octanol (C8-OH), as well as primary alkanols (C1-OH to C14-OH) in n-octane (C8) have been studied using molecular dynamics simulation in the temperature range from 298 to 374K and at atmosphere pressure. Simulated D12 values for short-chain solute molecules show a good agreement with the experimental ones taken from literature, while for the long-chain solute molecules the overestimation is large. Besides, the structures of solute molecules in above fluid mixtures are investigated by calculating radial distribution functions, radius of gyration, end-to-end distance, and root mean square fluctuation of atomic positions. These results confirm long-chain n-alkanes and n-alkanols molecules are curved and curled up, which we call it flexibility. Moreover, flexibilities for solute molecules (5≤n≤9) are symmetric but for much long-chain solute molecules like n-tetradecane (C14) and 1-tetradecanol (C14-OH) are asymmetric. We believe that strong chain-chain interactions are existed between different long-chain molecules, and it will result in the solute and solvent molecules are intertwisted. The serious overestimation of simulated D12 for long-chain solute molecules can be reasonably explained by the intertwist effect.

Measurement of solubility thermodynamic and diffusion kinetic characteristic of solvents in PDMS by inverse gas chromatography

Inverse gas chromatography is a versatile and effective method for the characterization of the solubility thermodynamics and diffusion kinetic of solvent–polymer system with the advantages of fast, low dosage of samples and large range of temperature. Polydimethylsiloxane (PDMS) is well known as an excellent polymer membrane material for its high permeability to gases and liquids and widely used in the separation and purification of bio-fermentation broth which was mainly consisted by acetone, butanol, ethanol and water. In this paper, the inverse gas chromatography method was applied to measure solubility thermodynamics parameters like the infinite dilution activity coefficient and Flory–Huggins interaction parameter between those small molecules and PDMS. The infinite dilution diffusion coefficients were calculated by Van Deemter model over a temperature range of 373.2–413.2K. The diffusion coefficient was fitted with the temperature according to the Arrhenius correlation. The data could help the selection of membrane material in pervaporation or gas separation and the analysis of mass transfer process.

A Molecular Dynamics simulation study on nitrobenzene and [rad]OH radical in supercritical water

With Molecular Dynamics simulation method, the diffusion of nitrobenzene and OH radical in supercritical water was studied at the temperature of 643.2K–843.2K and under the pressure of 23MPa–29MPa. The diffusion-controlled reaction rate constant was calculated. Thus, guidance for reaction kinetics study on the nitrobenzene oxidation in supercritical water process can be provided. Additionally, the microstructure of supercritical water-nitrobenzene system under different conditions was investigated. The deviation of the calculation results of infinite dilute diffusion coefficients obtained from the data processing method in this work is within 9%, compared with experimental values in the literatures. With MD simulation method, at the temperature of 643.2K–823.2K and under the pressure of 23MPa–29MPa, the infinite dilute diffusion coefficients of nitrobenzene and OH radical in supercritical water were obtained. Based on the infinite dilute diffusion coefficients of nitrobenzene and OH radical in supercritical water, the rate constant of the diffusion-controlled reaction was calculated.

Solution and diffusion properties of organic sulfur in poly[bis(phenoxy)phosphazene] by inverse gas chromatography

In this work, the solution and diffusion properties of n-heptane, thiophene, 2-methylthiophene, 2,5-dimethylthiophene, ethyl sulfide, butyl mercaptan in poly[bis(phenoxy)phosphazene] (PBPP) were studied by inverse gas chromatography. The infinite dilute activity coefficients and diffusion coefficients were determined. Effects of temperatures and solvent species on the activity coefficients and diffusion coefficients were investigated. The results showed that higher temperature was beneficial for both solution and diffusion process. Compared with pervaporation desulfurization performance in our previous work, the order of infinite dilute diffusion coefficients was in agreement with that of partial flux, which indicated that diffusion decided the permeability within solution–diffusion model.

Infinite Dilution Diffusion Coefficients of Chlorinated Methane in Poly(ethylene terephthalate) by Inverse Gas Chromatography

On the basis of the Van Deemter model of the chromatographic process, the infinite dilution diffusion coefficients of dichloromethane, chloroform, and carbon tetrachloride in poly(ethylene terephthalate) (PET) have been measured over a wide range of temperatures from 373.15 to 413.15 K by inverse gas chromatography. The relationships between the infinite dilution diffusion coefficients and molecular size of the solvent, as well as the temperature, were investigated. Meanwhile, the measured diffusion data were compared with the theoretical predictions by free-volume theory. The results indicated that neglecting the molecular interactions, i.e., the diffusivity energy term in the free-volume equation, may result in a poor prediction of the diffusion coefficient for PET-chlorinated methane systems because of the strong molecular interactions. The good agreement between the experimental data and the theoretical predictions by the proposed method showed that it is reasonable to take the diffusivity energy term into consideration for those systems with strong molecular interactions, and, furthermore, the infinite dilution diffusion coefficients at different temperature can be predicted accurately with this method.

Molecular dynamics simulation on the interfacial features of supercritical 1-butene/subcritical water

We studied the interfacial features of 1-butene/water and extraction process of 2-butanol by molecular dynamics (MD) simulations. The infinite dilute diffusion coefficients of 1-butene in water is larger than that of 2-butanol, and one important reason is that 2-butanol molecules can form hydrogen bonds with water molecules. 1-butene is more soluble in water under supercritical condition than that under subcritical condition. 1-butene under supercritical condition can extract more 2-butanol from aqueous solution than that under other conditions. A process of producing 2-butanol by the direct hydration of 1-butene is more competive when it operates under the supercritical conditions of 1-butene which due to a higher solubility of 1-butene in water, a larger diffusion coefficient of 1-butene and a lower 2-butanol concentration in water.

Diffusion Behavior of Water at Infinite Dilution in Hydroxypropyl Xylan Films with Sorbitol and Cellulose Nanocrystals

Inverse gas chromatography (IGC) was used to measure the infinite dilution diffusion coefficients of water in hydroxypropyl xylan (HPX) films containing sorbitol, a commonly used plasticizer, and cellulose nanocrystals (CNC) at temperatures above their glass transition temperatures (Tg). HPX forms transparent but relatively rigid films and has the potential to be used for certain food-packaging applications. Sorbitol and CNC were added to HPX films to reduce Tg and to reduce the water diffusivity, respectively. It was found that almost 40 wt % of sorbitol was needed to yield a HPX film to have the desired flexibility, as quantified by its Tg, and that addition of a small amount of CNC (1–5 wt %) while maintaining the total concentration of sorbitol and CNC at 40 wt % (39–35 wt % of sorbitol) slightly increased the Tg but significantly decreased the diffusivity of water. In particular, the infinite dilution diffusion coefficient of water for the HPX film with 35 wt % of sorbitol and 5 wt % CNC was comparable to that of the bare HPX film. The diffusion data suggest that effects of sorbitol and CNC on the water diffusivity follow the free volume theory.

Molecular dynamics simulation of diffusion coefficients and structural properties of some alkylbenzenes in supercritical carbon dioxide at infinite dilution

The binary infinite dilute diffusion coefficients, D₁₂(∞), of some alkylbenzenes (Ph-C(n), from Ph-H to Ph-C12) from 313 K to 333 K at 15 MPa in supercritical carbon dioxide (scCO2) have been studied by molecular dynamics (MD) simulation. The MD values agree well with the experimental ones, which indicate MD simulation technique is a powerful way to predict and obtain diffusion coefficients of solutes in supercritical fluids. Besides, the local structures of Ph-C(n)/CO2 fluids are further investigated by calculating radial distribution functions and coordination numbers. It qualitatively convinces that the first solvation shell of Ph-C(n) in scCO2 is significantly influenced by the structure of Ph-C(n) solute. Meanwhile, the mean end-to-end distance, the mean radius of gyration and dihedral angle distribution are calculated to gain an insight into the structural properties of Ph-C(n) in scCO2. The abnormal trends of radial distribution functions and coordination numbers can be reasonably explained in term of molecular flexibility. Moreover, the computed results of dihedral angle clarify that flexibility of long-chain Ph-C(n) is the result of internal rotation of C-C single bond (σ(c-c)) in alkyl chain. It is interesting that compared with n-alkane, because of the existence of benzene ring, the flexibility of alkyl chain in Ph-C(n) with same carbon atom number is significantly reduced, as a result, the carbon chain dependence of diffusion behaviors for long-chain n-alkane (n ≥ 5) and long-chain Ph-C(n) (n ≥ 4) in scCO2 are different.

Multiscale modelling of heterogeneously catalysed transesterification reaction process: an overview

Biodiesel is fast becoming one of the key transport fuels as the world endeavours to reduce its carbon footprint and find viable alternatives to oil derived fuels. Research in the field is currently focusing on more efficient ways to produce biodiesel, with the most promising avenue of research looking into the use of heterogeneous catalysis. This article presents a framework for kinetic reaction and diffusive transport modelling of the heterogeneously catalysed transesterification of triglycerides into fatty acid methyl esters (FAMEs), unveiled by a model system of tributyrin transesterification in the presence of MgO catalysts. In particular, the paper makes recommendations on multicomponent diffusion calculations such as the diffusion coefficients and molar fluxes from infinite dilution diffusion coefficients using the Wilke and Chang correlation, intrinsic reaction kinetic studies using the Eley–Rideal kinetic mechanism with methanol adsorption as the rate determining steps and multiscale reaction-diffusion process simulation between catalytic porous and bulk reactor scales.