Determination of diffusion coefficients for supercritical fluids

Decoupling of rotation and translation at the colloidal glass transition

In dense particle systems, the coupling of rotation and translation motion becomes intricate. Here, we report the results of confocal fluorescence microscopy where simultaneous recording of translational and rotational particle trajectories from a bidisperse colloidal dispersion is achieved by spiking the samples with rotational probe particles. The latter consist of colloidal particles containing two fluorescently labeled cores suited for tracking the particle's orientation. A comparison of the experimental data with event driven Brownian simulations gives insights into the system's structure and dynamics close to the glass transition and sheds new light onto the translation-rotation coupling. The data show that with increasing volume fractions, translational dynamics slows down drastically, whereas rotational dynamics changes very little. We find convincing agreement between simulation and experiments, even though the simulations neglect far-field hydrodynamic interactions. An additional analysis of the glass transition following mode coupling theory works well for the structural dynamics but indicates a decoupling of the diffusion of the smaller particle species. Shear stress correlations do not decorrelate in the simulated glass states and are not affected by rotational motion.

Measurement of the molecular diffusion coefficient and the effective longitudinal diffusion under supercritical fluid chromatography conditions in packed bed columns

The improvement of supercritical fluid chromatography (SFC) instrumentation enhanced its reliability and utility over the past decade. The further development of high speed and high resolution separations is however obstructed by the lack of accurate models for axial dispersion in SFC. This work is a first step to tackle this by developing more reliable methods to measure molecular (D_mol) and longitudinal diffusion (D_eff) in SFC, as these affect all aspects of separation efficiency. In the present contribution, we report on an improved method, to enable more flexible, reliable and accurate measurements of D_mol in SFC using commercial instrumentation. A two-column variant of the stopped-flow experiment is proposed as an adapted set-up for measuring the effective longitudinal diffusion coefficient D_eff in SFC-conditions. Using the set-ups for a number of test-compounds, it has been found that D_eff, and the coefficients describing its constituent sub-processes (cf. particle diffusion D_part and surface diffusion γ_sD_s), all vary in a linearly proportional way with the bulk diffusion coefficient D_mol within a high degree of accuracy. It has also been found that D_eff decreases much more sharply with increasing retention factor compared to LC. By applying the effective medium theory, it was found that the relative surface diffusion coefficient γ_sD_s/D_mol decreases strongly with retention factor for the investigated solutes and column, in contrary to what is typically observed in reversed phase liquid chromatography. Results indicate that this might be related to a change in retention behavior of the analytes. Obviously, more analytes and conditions need to be explored to complete this picture and the extend range of applicability of these observations.

Diffusion coefficients of an extensive set of pharmaceutical compounds in supercritical fluid chromatography over a wide range of mobile phase compositions

Diffusion data are essential for adequate analysis of the kinetic separation performance of any chromatographic system. Unfortunately, for Supercritical Fluid Chromatography (SFC), very little data is available of the diffusion coefficients in mobile phases typically used in contemporary methods, i.e. with a non-negligible amount of polar modifier such as methanol. In this work, a relative simple method which only requires minor modifications to a standard commercially available SFC instrument is used to determine the diffusion coefficient of an extensive set of pharmaceutical compounds in the range of 10-50 vol% of modifier (methanol) in CO₂. By using a traditional SFC column, the solute is first separated from the sample solvent plug, before entering a long capillary, where the band broadening can be linked to its diffusion coefficient using the Taylor-Aris equation. By using two UV-detectors, before and after the capillary, the effect of the dispersion in the column can be eliminated and the true volumetric flow rate determined. It was found that in the investigated range of conditions, the change in mobile phase viscosity in a first approximation allows to predict the variation in diffusion coefficient. Chemical structure and more particularly functional groups can however have a significant effect on the diffusion coefficient.

Quasi-equilibrium phase coexistence in single component supercritical fluids

In their supercritical state simple fluids are generally thought to assume a homogeneous phase throughout all combinations of pressures and temperatures, although various response functions or transport properties may exhibit anomalous behavior, characterizing a state point as either more gas-like or liquid-like, respectively. While a large body of results has been compiled in the last two decades regarding the details of the supercritical phase in thermodynamic equilibrium, far less studies have been dedicated to out-of-equilibrium situations that nevertheless occur along with the handling of substances such as carbon dioxide or Argon. Here we consider successive compression-expansion cycles of equal amounts of Argon injected into a high-pressure chamber, traversing the critical pressure at two times the critical temperature. Due to expansion cooling, the fluid temporarily becomes sub-critical, and light scattering experiments show the formation of sub-micron-sized droplets and nanometer-scale clusters, both of which are distinct from spontaneous density fluctuations of the supercritical background and persist for a surprisingly long time. A kinetic rate model of the exchange of liquid droplets with the smaller clusters can explain this behavior. Our results indicate non-equilibrium aspects of supercritical fluids that may prove important for their processing in industrial applications.

In their supercritical state simple fluids are generally thought to assume a homogeneous phase throughout. Lee et al. find that liquid droplets temporarily formed in a supercritical background after sub-critical injection can survive for a surprisingly long time.

Aerogels in drug delivery: From design to application

Aerogels are the lightest processed solid materials on Earth and with the largest empty volume fraction in their structure. Composition versatility, modularity, and feasibility of industrial scale manufacturing are behind the fast emergence of aerogels in the drug delivery field. Compared to other 3D materials, the high porosity (interconnected mesopores) and high specific surface area of aerogels may allow faster loading of small-molecule drugs, less constrained access to inner regions of the matrix, and more efficient interactions of the biological milieu with the polymer matrix. Processing in supercritical CO₂ medium for both aerogel production (drying) and drug loading (impregnation) has remarkable advantages such as absence of an oxidizing environment, clean manufacture, and easiness for the scale-up under good manufacturing practices. The aerogel solid skeleton dictates the chemical affinity to the different drugs, which in turn determines the loading efficiency and the release pattern. Aerogels can be used to increase the solubility of BCS Class II and IV drugs because the drug can be deposited in amorphous state onto the large surface area of the skeleton, which facilitates a rapid contact with the body fluids, dissolution, and release. Conversely, tuning the aerogel structure by functionalization with drug-binding moieties or stimuli-responsive components, application of coatings and incorporation of drug-loaded aerogels into other matrices may enable site-specific, stimuli-responsive, or prolonged drug release. The present review deals with last decade advances in aerogels for drug delivery. An special focus is paid first on the loading efficiency of active ingredients and release kinetics under biorelevant conditions. Subsequent sections deal with aerogels intended to address specific therapeutic demands. In addition to oral delivery, the physical properties of the aerogels appear to be very advantageous for mucosal administration routes, such as pulmonary, nasal, or transdermal. A specific section devoted to recent achievements in gene therapy and theranostics is also included. In the last section, scale up strategies and life cycle assessment are comprehensively addressed.

Photosensitizing Furocoumarins: Content in Plant Matrices and Kinetics of Supercritical Carbon Dioxide Extraction

Furocoumarins are a group of plant phytoalexins exhibiting various bioactive properties; the most important of which are photosensitization and alteration of P450 cytochrome activity. Supercritical fluid extraction with carbon dioxide has been proposed as a green alternative for an organic solvent extraction of the furocoumarins. Four plant matrices rich in furocoumarins were extracted with CO₂ at a temperature of 80 °C and pressure of 40 MPa, as these conditions were characterized by the highest solubility of furocoumarins. The extracts collected were analyzed using the HPLC method and the results obtained were used for the mathematical modeling of the observed phenomena. The total content of the furocoumarins in the matrices was 4.03–26.45 mg g⁻¹ of dry weight. The impact of the process parameters on the solubility was consistent with the Chrastil equation. The broken plus intact cell model proved to be suitable to describe extraction curves obtained. The research proved the possibility of supercritical carbon dioxide utilization for the extraction of the furocoumarins from plant material and provided valuable data for prospective industrial-scale experiments.

Radioprotection and cross-linking of allograft bone in the presence of vitamin E

Bone allografts are the preferred method for bone augmentation in over 500,000 orthopedic surgical procedures in the US. Sterilization by ionizing radiation is the most effective method of minimizing the bioburden of bone allografts; however, radiation causes chain scission of collagen, resulting in the reduction of the allografts' mechanical strength. In this study, we doped bone allografts with vitamin E as radioprotectant using a novel two-step process to protect the collagen architecture against radiation damage and to preserve the mechanical strength of the construct. In addition, combining the radioprotectant with a cross-linking agent further minimized collagen degradation and further preserved the mechanical strength of the allografts. Both vitamin E and combined vitamin E/genipin-treated allograft were less cytotoxic to both osteoblasts and osteoclasts when compared to irradiated-only allografts. Host bone-allograft unionization was faster in a rat calvaria defect model with vitamin E-treated and combined vitamin E and genipin-treated allograft when compare to irradiated-only allografts. This method can enable the efficient and uniform radioprotective treatment of bone allograft of desired shapes for sterilization with improved mechanical strength and biointegration.

Distribution, Ecological Risk Assessment, and Bioavailability of Cadmium in Soil from Nansha, Pearl River Delta, China

Background: Cadmium (Cd) pollution poses a threat to human health. Examination of the spatial distribution of Cd in soils can be used to assess the risks posed to humans and the environment. Objective: This study determined the enrichment rules and factors influencing Cd pollution in Nansha, and evaluated the pollution characteristics and bioavailability of Cd in quaternary sediments through 7 deep soil profiles (0-200 cm), 4 boreholes, and 348 topsoil (0-20 cm) samples. Methods: The geo-accumulation index (Igeo) and the potential ecological risk index (Er) were used to assess ecological risk, and bioavailability was determined using multivariate, spatial distribution, and correlation matrix analyses. Results: From the Er, 52% of Nansha was classed as being at very high risk of Cd pollution; a further 36% was classed as dangerous. Cadmium was more abundant in clay soils than in sandy soils. Bioavailable Cd in quaternary sediments was significantly affected by the total Cd, and labile Cd accounted for more than half of the total Cd. Changes in pH mainly affected bioavailable Cd rather than total Cd, affecting the overall bioavailability of Cd. Conclusions: Nansha soils are commonly and seriously contaminated with Cd. An appropriate remediation treatment approach should be used to reduce Cd bioavailability. Furthermore, planting structures in farmland should be adjusted to avoid the impact of heavy metals on human health.

Diffusion of methane in supercritical carbon dioxide across the Widom line

Diffusion of methane diluted in supercritical carbon dioxide is studied by experiment and molecular simulation in the temperature range from 292.55 to 332.85 K along the isobars 9.0, 12.5 and 14.7 MPa. Measurements of the Fick diffusion coefficient are carried out with the Taylor dispersion technique. Molecular dynamics simulation and the Green-Kubo formalism are employed to obtain Fick, Maxwell-Stefan and intradiffusion coefficients as well as shear viscosity. The obtained diffusion coefficients are on the order of 10-8 m2/s. The composition, temperature and density dependence of diffusion is analyzed. The Fick diffusion coefficient of methane in carbon dioxide shows an anomaly in the near-critical region. This behavior can be attributed to the crossing of the so-called Widom line, where the supercritical fluid goes through a transition between liquid-like and gas-like states. Further, several classical equations are tested on their ability to predict this behavior and it is found that equations that explicitly include the density are better suited to predict the sharp variation of the diffusion coefficient near the critical region predicted by molecular simulation.

Self-diffusion of water-cyclohexane mixtures in supercritical conditions as studied by NMR and molecular dynamics simulation

The self-diffusion coefficients of water (D_w) and cyclohexane (D_ch) in their binary mixtures were determined using the proton pulsed field gradient spin-echo method from medium to low densities in subcritical and supercritical conditions. The density (ρ), temperature (T), and water mole fraction (x_w) are studied in the ranges 0.62-6.35 M (M = mol dm^-3), 250-400 °C, and 0.109-0.994, respectively. A polynomial fitting function was developed for a scaled value of Ξ = ρDT^-1/2 with ρ, T, and x_w as variables in combination with a comprehensive molecular dynamics (MD) simulation. The NMR and MD results agree within 5% for water and 6% for cyclohexane, on average. The differences between D_w and D_ch in the dependence on ρ, T, and x_w are characterized by the activation energy E_a and the activation volume ΔV_Ξ ^‡ expressed by the scaled fitting function. The decrease in the ratio D_w/D_ch and the increase in the E_a of water with increasing x_w are related to the increase in the number of hydrogen bonds (HBs). The D_w value for a solitary water molecule at a low x_w is controlled by the solvation shell, most of which is occupied by nonpolar cyclohexane molecules that provide less friction as a result of weaker interactions with water. A microscopic diffusion mechanism is discussed based on an analysis of the HB number as well as the first-peak height of the radial distribution functions that are taken as measures of the potential of the mean field controlling self-diffusion.

Kinetics of Supercritical Drying of Gels

Supercritical drying of gels is considered as the most important step of aerogel production since it enables preservation of the three-dimensional pore structure which lead to unique material properties such as high porosity, low density, and large surface area. An understanding of the kinetics of supercritical drying is necessary to provide insight into material development, scale-up, and optimization of the aerogel manufacturing process. Thus, investigation of supercritical drying is gaining increased attention in recent years. This review paper covers the experimental considerations and techniques to study the kinetics of supercritical drying, fundamental mass transfer mechanisms during the drying process and modeling efforts to predict the drying kinetics for varying operating conditions and gel properties. Transport phenomena involving diffusion, convection, spillage by volume expansion, and axial dispersion are discussed by providing the fundamental equations and empirical correlations to predict transfer coefficients. A detailed review of literature covering experimental and theoretical studies on kinetics of supercritical drying is presented.

Numerical Modeling of Bubble Growth in Microcellular Polypropylene Produced in a Core-Back Injection Process Using Chemical Blowing Agents

A core-back polypropylene foaming injection process using chemical blowing agents (CBA) has been studied. First, injection tests were carried out with two different CBAs and the different morphologies of the obtained samples have been analyzed. Structural parameters such as cell density and average radius size were calculated. Then, a bubble growth model was developed to predict the foaming development during the process, controlled by the depressurization of the mold cavity during the short core-back opening coupled with the evolution of the temperature during core-back and subsequent cooling. A good agreement is found between theoretical predictions and experimental results.

Perspectives on DNP-enhanced NMR spectroscopy in solutions

More than 60 years after the seminal work of Albert Overhauser on dynamic nuclear polarization by dynamic cross relaxation of coupled electron-nuclear spin systems, the quest for sensitivity enhancement in NMR spectroscopy is as pressing as ever. In this contribution we will review the status and perspectives for dynamic nuclear polarization in the liquid state. An appealing approach seems to be the use of supercritical solvents that may allow an extension of the Overhauser mechanism towards common high magnetic fields. A complementary approach is the use of solid state DNP on frozen solutions, followed by a rapid dissolution or in-situ melting step and NMR detection with substantially enhanced polarization levels in the liquid state. We will review recent developments in the field and discuss perspectives for the near future.