Direct Determination Of Diffusion Coefficient Research Articles

Mathematical modeling of mass transfer in multicomponent gas mixture across the synthesized composite polymeric membrane

This study presents a new mathematical model to investigate the ternary gas mixture permeation across a synthesized composite PDMS/PA membrane. A novel algorithm is introduced for direct determination of diffusion coefficients. It pertains to study gas permeation through concentration dependent systems and comparing with traditional time lag method confirms the precision of this approach. Feature is that this method does not require physical properties of the membrane. Accordingly, it can be used as a general comprehensive model. In addition, molecular pair and molecular trio interactions were taken into account and in order to investigate the deviation of gas mixture from ideality, fugacities were calculated. The results showed that permeabilites of H2 and CH4 increase with increasing feed temperature and fugacity, while that of C3H8 decreases. Moreover, increasing C3H8 concentration improved permeation properties of all components. The results demonstrated that considering the concentration dependent system (CDS) leads to the small deviation of about less than 10%, while the deviation of 50–100% by the concentration independent system (CIS) was acquired. Additionally the results indicated that permeability of the lighter gases is specially affected by diffusivity, while solubility is dominant on permeability of the heavier gases.

Direct determination of concentration-dependent diffusion coefficient in polymeric membranes based on the Frisch method

In addition to gas permeation simulation in polymeric membranes, much progress has been attained on the theories whereby the mechanisms of transport are described. In this way, numerous studies are assigned to achieve methods for determination of diffusion coefficient. Consequently, some correlated equations are obtained which consider diffusivity dependency on concentration, position or time, or any conjunction of them. Compared to the traditional time lag, a comprehensive approach developed by Frisch gives a general mathematical procedure for achieving the concentration dependent diffusion coefficient, disregarding the effect of membrane physical properties. In this study, a comprehensive algorithm is presented for direct determination of diffusion coefficient. It determines diffusion coefficient by two approaches: first, through the traditional time lag method, and second, considering the concentration dependent system. A comprehensive mathematical model was developed and solved for CO 2 gas permeation through a nonporous polymeric membrane. The results showed that considering the concentration dependent system (CDS) for diffusion coefficient led to the small deviation of about 13%, while the deviation of 360% by the concentration independent system (CIS) was acquired. Finally, a reasonable conformity between the predicted values based on concentration dependant method and experimental data was perceived.

Controlled release of functional proteins through designer self-assembling peptide nanofiber hydrogel scaffold

The release kinetics for a variety of proteins of a wide range of molecular mass, hydrodynamic radii, and isoelectric points through a nanofiber hydrogel scaffold consisting of designer self-assembling peptides were studied by using single-molecule fluorescence correlation spectroscopy (FCS). In contrast to classical diffusion experiments, the single-molecule approach allowed for the direct determination of diffusion coefficients for lysozyme, trypsin inhibitor, BSA, and IgG both inside the hydrogel and after being released into the solution. The results of the FCS analyses and the calculated pristine in-gel diffusion coefficients were compared with the values obtained from the Stokes-Einstein equation, Fickian diffusion models, and the literature. The release kinetics suggested that protein diffusion through nanofiber hydrogels depended primarily on the size of the protein. Protein diffusivities decreased, with increasing hydrogel nanofiber density providing a means of controlling the release kinetics. Secondary and tertiary structure analyses and biological assays of the released proteins showed that encapsulation and release did not affect the protein conformation and functionality. Our results show that this biocompatible and injectable designer self-assembling peptide hydrogel system may be useful as a carrier for therapeutic proteins for sustained release applications.

Direct determination of diffusion coefficient for borohydride anions in alkaline solutions using chronoamperometry with spherical Au electrodes

Chronoamperometry is carried out with a spherical Au electrode fused at the tip of a glass tube. The slope and intercept of the linear region of the current versus reciprocal square root of time are used to deduce the diffusion coefficient ( D) without the need for the concentration of BH 4 - and the electron number involved in the oxidation of the anion. The D (in cm 2 s −1) of BH 4 - thus determined in NaOH solutions ranging 0.5–6 M at 30 °C can be described by a polynomial function 2.01 × 10 −5 − 3.65 × 10 −6 x + 2.25 × 10 −7 x 2, where x is the concentration of NaOH. The change of D with NaOH concentration is found approximately in parallel with the change of the reciprocal viscosity of the solution. In 2 M NaOH, the temperature dependence of D is describable by D 0 exp(− E a/RT) with an activation energy E a = 15.2 kJ/mol and D 0 = 5.57 × 10 −3 cm 2 s −1. After correction for the surface fraction sealed by the glass tip for the spherical electrode, the number of electrons involved in BH 4 - oxidation at the Au electrode is deduced from the above-mentioned D and independently determined BH 4 - concentration and is found to be 7.9 ± 0.1, very close to the theoretically expected value 8.

Direct determination of diffusion coefficients of substrate and product by chronoamperometric techniques at microelectrodes for any level of ionic support.

A new method for the determination of the diffusion coefficients of both the substrate, DS, and the product, DP, of an electrode process has been developed. The method proposed is based on the analysis of the transient currents and can be applied to some reactions of the type SzS = PzP + ne and, in contrast to the concept based on the steady-state current, to any ratio of the concentrations of supporting electrolyte and substrate. The diffusion coefficients can be evaluated sequentially from the two parts of the double-potential step chronoamperogram, since the magnitude of the normalized chronoamperometric current of the first step depends on the DS value, while that of the second step is controlled by both DS and DP values. The corresponding, easy-to-use equations and procedures are given in the paper. The equations were derived on the basis of the numerical simulation data. The proposed methods of determination of diffusion coefficients for the substrates and products have been examined experimentally with the charged and uncharged ferrocene derivatives under diffusional and mixed diffusion-migration conditions. Only the chronoamperometric DS values obtained for the substrates could be compared to those determined from the steady-state diffusional current. It was found that for the systems investigated the agreement between these two methods was good. In this limited comparison, the standard deviations for the transient techniques were slightly larger than those obtained for the excess supporting electrolyte steady-state voltammetry.

Brownian deposition kinetics of latex particles onto glass and polystyrene

There has been a large body of work on the deposition of colloidal particles onto many different kinds and shapes of surfaces. Nearly all work in the past has involved flowing systems in which a well-defined hydrodynamic layer exists at the collector surface with certain advantages and disadvantages. We have chosen a still system in which transport of particles to the collector surface occurs solely by diffusion. Both particles and surfaces were negatively charged, so that deposition was driven by dispersion forces. A photomicroscopic technique has been used to determine absolute values of initial rates of deposition. Three monodisperse polystyrene colloids of various particle sizes and surface charge densities were synthesized. Their zeta potentials were determined by microelectrophoresis in Ba(NO 3) 2 solutions. Collector surfaces were glass and glass coated with polystyrene. Their zeta potentials were determined from their streaming potentials in various concentrations of electrolyte. Direct determination of diffusion coefficients indicate that the particles behave normally. Initial deposition rates exhibit strong dependence on ionic strength, indicating large electrical double layer effects. Like the work of others, rates of deposition fell off with time, perhaps due to the presence of `hot spots', i.e. highly localized areas of greater reactivity. The most regular behavior occurred in deposition on polystyrene-coated glass, presumably because roughness and highly reactive sites on the glass surface were largely eliminated. Absolute rates were several times theoretical for fastest deposition. It is speculated that the hydrophobic effect plays a significant role in accelerating particles towards the collector. Plots of log (initial rate constant) vs. log (ionic strength) were linear and generally in the order anticipated by Reerink–Overbeek theory.

Dynamic light scattering during shear: measurements of diffusion coefficients

A method for determining diffusion coefficients during shear by dynamic light scattering is presented. The direct determination of diffusion coefficient during flow is hampered by the domination of the convection terms over the diffusion terms except in a very narrow azimuthal scattering angle range that is impossible to reach experimentally. The method described here offers the advantage to remove this constraint. The technique is based on a double measurement of homodyne spectrum of light scattered from small scatterers immersed in a medium subjected to a simple shear flow. This can be applied to polymer solutions. Verification is provided using suspensions of polystyrene spheres in Newtonian media and a transparent rheometer.

Determination of Diffusion Coefficients of Proteins by Flow Injection Analysis and Its Application to Estimation of Molecular Masses of Proteins

A Flow Injection Analysis (FIA) method for determination of molecular diffusion coefficients (Dm) of proteins, in a helically coiled tube, was reported. The coiling effect of the tube that causes secondary flow was avoided through using a Taylor-Aris and Golay's dispersion equation, modified by the velocity profile factor, K, and the modified equation was used for direct determination of diffusion coefficients. The experimental values of Dm were comparable with the literature values. The linear relationship between the Relative Molecular Mass (RMM, Mr) and the Molecular Diffusion Coefficient (Dm) was verified and a two-point calibration FIA method for estimation of Relative Molecular masses of proteins was suggested. Relative Molecular masses of two protein samples, hemoglobin and glucose oxidase were then estimated by this method. The values of RMM were 6.88x104 for hemoglobin and 16.0x104 for glucose oxidase.

Direct determination of diffusion coefficients by chronoamperometry at microdisk electrodes

The chronoamperometric response at a microdisk is used for the direct determination of the diffusion coefficient of an electroactive species. The method does not require knowledge of the bulk concentration and the number of electrons participating in the electrode reaction, and requires only a value for the disk radius. Subsequent determination of the number of electrons ( n) for an electrode reaction or the concentration of electroactive species is also possible. This approach is demonstrated with the evaluation of the diffusion coefficient of Fe(CN) 6 4− in KCl and that of borohydride ion in NaOH. In both cases, the values of n found remained constant over a wide time range and correspond to those expected for these processes.