Predictive correlation of binary diffusion and self-diffusion coefficients under supercritical and liquid conditions

The hydrodynamic equation D/T = αη^β, where D is the infinite dilution binary diffusion or self-diffusion coefficient, T is the temperature, η is the fluid viscosity, and α and β are constants, were demonstrated to be effective for predicting both binary diffusion and self-diffusion coefficients in high density fluids, i.e. liquid and supercritical states. When a solute was specified, the correlation well represented both binary diffusion and self-diffusion coefficients, irrespective of solvent over a wide solvent viscosity range. The solute-dependent constants α and β were determined for 12 solutes with average absolute deviation of 6.2% for 1006 data points.     

Prediction of binary diffusion coefficients in supercritical CO2 with improved behavior near the critical point

In this work, a predictive model for binary diffusivities at infinite dilution (D₁₂) in SC-CO₂ is proposed. It combines two terms – background and singular – with the objective to represent D₁₂ accurately not only far but also near the critical point, where critical enhancement is always observed. The model provides an average error of 6.20% for a large database including 149 systems and 4469 data points over wide ranges of temperature and pressure. The models selected for comparison (Wilke–Chang, Scheibel, Lusis–Ratcliff, Lai–Tan, Tyn–Calus and Reddy–Doraiswamy) achieve scattered and biased results, with average errors from 11.62% to 75.17%. In the whole, the new model exhibits an excellent performance for any kind of molecules in terms of size, molecular weight, polarity and sphericity, in all critical region. In order to help interested readers, a spreadsheet for the calculation of D₁₂ is given in Supplementary data. The input data is: temperature, pressure, CO₂ viscosity, and solute properties (acentric factor, critical constants, molar volume at normal boiling point, and molecular weight – given in this paper for the systems studied).     

Preparative-scale supercritical fluid extraction/supercritical fluid chromatography of corn bran

A preparative-scale supercritical fluid extraction/supercritical fluid chromatography (SFE/SFC) procedure has been developed for the removal of oil from corn bran to obtain fractions enriched with free sterols and ferulate-phytosterol esters (FPE). Operational parameters from an analytical-scale supercritical fluid fractionation technique were translated to and optimized on a home-built, preparatory-scale SFE/SFC apparatus. SFE was performed at 34.5 MPa and 40°C using supercritical carbon dioxide. These conditions did not result in exhaustive extraction of the corn bran, but yielded about 96% of the available oil. SFC was conducted in three steps, followed by reconditioning of the sorbent bed. Preparative-scale SFE/SFC of corn bran produced a fraction enriched greater than fourfold in free sterols and 10-fold in FPE, suggesting that such a scheme could be used industrially to produce a functional food ingredient.     

Distribution of solutes between polymer and supercritical fluid by inverse supercritical fluid chromatography

Two methods of inverse supercritical fluid chromatography (ISFC), frontal analysis supercritical fluid chromatography (SFC) and elution SFC, have been compared for the determination of distribution coefficients of solutes between a polymer and a supercritical CO₂. The logarithm of the distribution coefficient showed monotonic decrease with the density of the supercritical fluid (SF). The abnormal-maximum behavior of solute sorption in the polymer phase was explained by the fluid and solute properties, ϕ₂P/P ₂ ^sat . Interesting open-elliptic shapes of sorption and volume-fraction curves were obtained and explained with the fugacity coefficient. Correction to the capacity factor was employed to eliminate the retention due to the adsorption on the surface of the silica support. A model based on the Flory equation and the Peng-Robinson equation of state (EOS) successfully predicted the phase behavior of the ternary solutesupercritical fluid-polymer systems using only interaction parameters obtained from the binary systems. The solute distribution coefficient at infinite dilution was used to calculate the phase equilibrium at finite concentration using a ternary-phase diagram.     

Onsager coefficients for binary mixture diffusion in nanopores

This paper presents a critical appraisal of current estimation methods for the Onsager coefficients L₁₁, L₂₂, and L₁₂ for binary mixture diffusion inside nanopores using pure component diffusivity data inputs. The appraisal is based on extensive sets of molecular dynamics (MD) simulation data on L_ij for a variety of mixtures in zeolites (MFI, AFI, TON, FAU, CHA, DDR, MOR, and LTA), carbon nanotubes (CNTs: armchair and zig-zag configurations), titanosilicates (ETS-4), and metal-organic frameworks (IRMOF-1, CuBTC). The success of the L_ij predictions is crucially dependent on the estimates of the degree of correlations in molecular jumps for different guest-host combinations; these correlations are captured in Maxwell-Stefan approach by the exchange coefficients ?_ij. Three limiting scenarios for correlation effects have been distinguished; for each of these scenarios appropriate expressions for the L_ij are presented. For CNTs, correlation effects are dominant and the interaction factor, defined by , is close to unity. For cage-type zeolites such as LTA, CHA, and DDR with narrow windows separating cages, correlation effects are often, but not always, negligibly small and the assumption of uncoupled diffusion, i.e., α₁₂=0, is a reasonable approximation provided the occupancies are not too high. In other cases such as zeolites with one-dimensional channel structures (AFI, TON), intersecting channels (MFI), cage-type zeolite with large windows (FAU), ETS-4, CuBTC, and in IRMOF-1, it is essential to have a reliable estimation of the ?_ij; MD simulations underline the wide variety of factors that influence the ?_ij.We also highlight two situations where estimations of the L_ij fail completely; in both cases the failure is caused due to segregated adsorption. In adsorption of CO₂-bearing mixtures in LTA and DDR zeolites, CO₂ is preferentially lodged at the narrow window regions and this hinders the diffusion of partner molecules between cages. The second situation arises in MOR zeolite that has one-dimensional channels connected to side pockets. Some molecules such as methane, get preferentially lodged in the side pockets and do not freely participate in the molecular thoroughfare. Current phenomenological models do not cater for segregation effects on mixture diffusion.     

Determination of sudan dyes in food samples using supercritical fluid extraction-capillary liquid chromatography

Determination of sudan dyes (Sudan I, Sudan II, Sudan III and Sudan IV) in food samples has been developed by several and different methods. However, sample treatment continues being the most important problem to determine these compounds in real samples. A rapid, sensitive and selective method for the extraction, separation and quantification of sudan dyes in commercial food samples has been developed. The method is based on the combination of a supercritical fluid extraction (SFE) procedure, followed by the analysis of the extracted plug by capillary liquid chromatography (CLC) with diode array detection (DAD). The entire procedure was optimized for the extraction of the samples, separation and detection of the analytes. For the SFE, the effect of CO₂ flow rate, extraction pressure, extraction temperature, equilibration and extraction time and methanol modifier content were studied. Linear responses in the range from 50 to 1000 ng mL⁻¹ with average relative standard deviation lower than 11.6, and detection limits ranging from 23.2 to 42.0 ng mL⁻¹ were obtained for the different sudan dyes. The recoveries were in the range of 91-109% for dyes powder samples.     

Determination of vernolic acid content in the oil ofEuphorbia lagascae by gas and supercritical fluid chromatography

Determination of the content of vernolic acid (12,13-epoxy-9c-octadecenoic) in the oil ofEuphorbia lagascae has been performed by gas chromatography of the fatty acid methyl ester derivatives of the triacylglycerols in the oil and by supercritical fluid chromatography (SFC) of the raw oil and the fatty acid derivatives of the oil. The content of vernolic acid was found to be 55 wt%. The three methods were compared, and SFC analysis of the fatty acid derivatives was found to be the most accurate method.     

Determination of diffusion coefficients with a pipe wall electrode

A flow cell electrode has been designed to measure diffusion coefficients in electrochemical solutions. Potassium ferri-ferrocyanide solutions containing different amounts of sodium carboxymethylcellulose were studied. The diffusion coefficient of ferricyanide ion and the rheological properties of these solutions were measured at various temperatures.     

Measurement and prediction of diffusion coefficients of supercritical CO2 in molten polymers

The solubility and diffusivity of supercritical carbon dioxide (sc‐CO₂) in low‐density polyethylene (LDPE), high‐density polyethylene (HDPE), polypropylene (PP), ethylene‐ethylacrylate copolymer (EEA) and polystyrene (PS) were measured at temperatures from 150°C to 200°C and pressures up to 12 MPa by using the Magnetic Suspension Balance (MSB), a gravimetric technique for gas sorption measurements. The solubility of CO₂ in each polymer was expressed by Henry's constant. The interaction parameter between CO₂ and polymer could be obtained from the solubility data, and it was used to estimate the Pressure‐Volume‐Temperature relationship and the specific free volume of polymer/CO₂ mixtures. The diffusion coefficients were also measured by the MSB for each polymer. The resulting diffusion coefficients were correlated with the estimated free volume of polymer/CO₂ mixture. Combining Fujita's and Maeda and Paul's diffusion models, a model was newly developed in order to predict diffusion coefficients for the polymers studied. Polym. Eng. Sci. 44:1915–1924, 2004. © 2004 Society of Plastics Engineers.     

Determination of the infinite dilution diffusion and activity coefficients of alkanes in polypropylene by inverse gas chromatography

Infinite dilution diffusion and activity coefficients of n‐hexane, n‐heptane, and n‐decane in polypropylene were measured from 373.15 to 393.15 K by inverse gas chromatography. The influences of small molecule solvent and temperature on the infinite dilution diffusion and activity coefficients were investigated. The results showed that the infinite dilution diffusion coefficient decreased but the infinite dilution activity coefficient increased with an increasing number of CH₂ group in the aliphatic solvents. The temperature increase resulted in the increase in the infinite dilution diffusion coefficient and the decrease in the infinite dilution activity coefficient. The graphs plotted according to the results of the infinite dilution diffusion coefficient versus temperature were in agreement with the Arrhenius equation. Diffusion constant and activation energy were obtained from the Arrhenius equation. Also, the interdependence on the infinite dilute activity coefficient and temperature accorded with Gibbs‐Helmholtz equation. From the temperature dependence of the limiting activity coefficients partial molar excess enthalpy at infinite dilution H^E,∞ was obtained. © 2006 Wiley Periodicals, Inc. J Appl Polym Sci 101: 1925–1930, 2006     

茄尼醇的SFC制备色谱分离工艺

采用ZORBAX SB-C18(250 mm×9.4 mm I.D.,5 μm)色谱柱为固定相,SC-CO2/甲醇为流动相,考察了超临界流体色谱分离提纯烟草萃取物中茄尼醇的工艺条件、流动相流速和改性剂含量对分离度的影响,以及温度和压力对茄尼醇容量因子、茄尼醇与相邻色谱峰组分分离度和选择性因子的影响.通过采用选定SFC分离工艺条件,茄尼醇产品纯度达到94.9%.     

Determination of solid fat content (SFC) of binary fat blends and use of these data to predict SFC of selected ternary fat blends containing low-erucic rapeseed oil

Several oils and fats often used for the industrial preparation of European shortenings were blended in binary systems. The equilibrium (after 48 h at 15°C) solid fat contents (SFC; determined by pulsed NMR spectroscopy) were measured and plotted against blend composition. SFC of the blends resulted from the SFC of each fat for the considered temperature as well as the type of interaction existing between those fats (namely, ideal behavior, monotectic interaction, eutectic interaction, and so on). The type of relationship fitted was dependent on the kind of interaction: Linear relationships were found for total compatibility between fats, and polynomial-type (order 2) relationships were found for fats exhibiting incompatibility. Some corresponding ternary oils and fats blends were also prepared and analyzed. Selected relationships (regression equations of the fitted curves) obtained for binary blends were combined in order to calculate the SFC of the corresponding ternary blends. Experimental values were generally close to predicted ones. The representation of SFC as a function of composition is interesting as it allows one to determine rapidly and easily the type of molecular interaction between two fats and also to determine equations that can be combined to calculate easily the SFC of corresponding ternary blends crystallized in the same way with a good accuracy. The texture (hardness) of several binary and ternary blends was also measured. The combination of the results obtained for SFC with the results obtained for the hardness of binary blends allows the prediction of the hardness of a corresponding ternary blend under the same conditions.     

Partition coefficients for fatty acid esters in supercritical fluid CO2 with and without ethanol

The complex nature of fish oils was exploited to study the dependence of structural factors upon fatty acid ester solubility in supercritical fluid carbon dioxide (SCF-CO₂). Partition coefficients were determined for a number of components present in two mixtures of fatty cid ethyl esters derived from menhaden oil in SCF-CO₂ at 60°C and 125 bar. Analogous data also were obtained for SCF-CO₂ with 5% (w/w) ethanol added. The addition of ethanol was found to increase partition coefficients for all species, but resulted in a decrease of fluid selectivity. Aside from the chain length of a component, both the degree and position of unsaturation were found to be structural factors that affect the value of the partition coefficient.     

Quantitative analysis of ethoxylated alcohols by supercritical fluid chromatography

This work was undertaken to develop a relatively simple, rapid, reproducible and accurate method for measuring the ethylene oxide distribution, overall ethylene oxide ratio, and percent free alcohol in ethoxylated alcohols. Using single isomer ethoxylate standards comprised of from one to eight ethylene oxide units per alcohol, a response factor correlation for the flame ionization detector on a supercritical fluid Chromatograph was established. Response factors for ethoxylates with higher than eight ethylene oxide units were estimated by extrapolation of this correlation. Supercritical fluid Chromatographic separation of ethoxylates was accomplished using a density-programmed carbon dioxide mobile phase and a poly (dimethylsiloxane) coated open tubular column. The validity and accuracy of this method was demonstrated by comparing its results for unreacted alcohol levels, ethylene oxide-to-alcohol average ratios, and weights of samples injected relative to internal standards with values measured independently by standard methods. In addition, supercritical fluid Chromatographic determinations of ethylene oxide molar distributions are in agreement with theoretical Weibull-Nycander distributions. Presented in part at the AOCS Annual Meeting in PHoenix, AZ, in May 1988.     

Argentation supercritical fluid chromatography for quantitative analysis of triacylglycerols

A method for quantitative analysis of neutral lipids has been developed. Four different techniques have been combined for this purpose—supercritical fluid chromatography (SFC), silver ion chromatography, packed microcolumns and miniaturized evaporative light-scattering detection (ELSD). The development and optimization of the method are discussed. The separation of a series of vegetable, fish and hydrogenated oils was demonstrated. Application of eluent composition programming resulted in excellent separation of complex samples. Packed microcolumn argentation SFC provides at least as high a separation power as corresponding high-performance liquid chromatography methods. The combination of packed microcolumn SFC and miniaturized ELSD constitutes a powerful analytical system for the quantitative analysis of triacylglycerols.     

Steady microfluidic measurements of mutual diffusion coefficients of liquid binary mixtures

We present a microfluidic method leading to accurate measurements of the mutual diffusion coefficient of a liquid binary mixture over the whole solute concentration range in a single experiment. This method fully exploits solvent pervaporation through a poly(dimethylsiloxane) (PDMS) membrane to obtain a steady concentration gradient within a microfluidic channel. Our method is applicable for solutes which cannot permeate through PDMS, and requires the activity and the density over the full concentration range as input parameters. We demonstrate the accuracy of our methodology by measuring the mutual diffusion coefficient of the water (1) + glycerol (2) mixture, from measurements of the concentration gradient using Raman confocal spectroscopy and the pervaporation‐induced flow using particle tracking velocimetry. © 2017 American Institute of Chemical Engineers AIChE J, 63: 358–366, 2018     

Analysis of tocopherols by capillary supercritical fluid chromatography and mass spectrometry

Tocopherol-containing mixtures were analyzed by gas chromatography (GC) and capillary supercritical fluid chromatography (SFC). GC analysis of tocopherols required the formation of the silyl derivatives, while SFC analysis of the tocopherol-containing mixtures was accomplished on neat samples. SFC analysis conditions were optimized with respect to column type and density/pressure programming. Enhanced resolution of many components was achieved by using inverse temperature programming during the SFC analyses. Both SFC and GC analyses permitted the separation and quantitation of alpha-, beta-, gamma- and delta-tocopherols. In addition, SFC proved particularly applicable for characterizing the composition of a deodorizer distillate and commercial antioxidant formulation. Coupling of a quadrapole mass spectrometer with a supercritical fluid chromatograph was also achieved; the mass spectrometer provided electron impact mass spectra on the underivatized tocopherol and sterol moieties. Both SFC and SFC/mass spectrometry proved effective for the analysis of complex lipid-containing mixtures, requiring minimal sample preparation prior to analysis. Presented at the 82nd Annual Meeting of the American Oil Chemists’ Society, Chicago, IL, May 12–15, 1991.     

Purification of polyunsaturated fatty acid esters from tuna oil with supercritical fluid chromatography

The technical and economic feasibility of producing docosahexaenoic acid (DHA)- and eicosapentaenoic acid (EPA)-ethyl ester concentrates from transesterified tuna oil using supercritical fluid chromatography (SFC) was studied. A systematic experimental procedure was used to find the optimal values for process parameters and the maximal production rate. DHA ester concentrates up to 95 wt% purity were obtained in one chromatographic step with SFC, using CO₂ as the mobile phase at 65°C and 145 bar and octadecyl silane-type reversed-phase silica as the stationary phase. DHA ester, 0.85 g/(kg stationary phase · h) and 0.23 g EPA ester/(kg stationary phase · h) can be simutaneously produced at the respective purities of 90 and 50 wt%. The process for producing 1,000 kg DHA concentrate and 410 kg EPA concentrate per year requires 160 kg stationary phase and 2.6 tons/h carbon dioxide eluant recycle. The SFC operating cost is U.S. $550/kg DHA and EPA ethyl ester concentrate.     

Determination of diffusion coefficients of water in cellulose acetate membranes

The determination of the diffusion coefficient for water in various porosity cellulose acetate membranes by a gravimetric method, using a humidified carrier gas, is described. It was found to be impossible to obtain meaningful results for very porous membranes, although dense membranes gave limiting values of diffusion coefficient at high carrier gas velocities. This phenomenon is explained in terms of the dissipation of the heat of sorption by the forced convection provided by the carrier gas. The variation of diffusion coefficient with concentration of water in dense cellulose acetate is explained in terms of clustering of water molecules in the polymer at high concentration.     

Calculations of diffusion coefficients of cyclic poly(dimethylsiloxanes)

The Kirkwood equation and a Monte-Carlo technique which employs Metropolis sampling have been used to calculate diffusion coefficients (D) for low molar mass cyclic poly(dimethylsiloxanes). Correlations between calculated and experimental values of D show that the effective segment size is larger for cyclic than for linear PDMS. Thus, free-draining flow is reduced for the cyclic species consistent with its greater segment density. The cyclic molecules also show enhanced diffusion coefficients at very low molar masses which may be associated with the rigid toroidal shapes of these molecules.