Additive diffusion coefficient

Brandsch, J. Mercea, P. Piringer, O. Modeling of Additive Diffusion Coefficients in Polymers. New Developments in the Chemistry of Packaging Materials ACS Symposium Series, ACS, Washington, D.C. 1999. 

J. Brandsch, P. Mercea, O. Piringer. Modeling of additive diffusion coefficients in polyolefins. Food Packaging Testing Methods and Applications, S.J. Risch editor, pp. 27-36, ACS Symposium Series Washington DC, 753 (2000). 

In ulttafUttation, the flux,/ through the membrane is large and the diffusion coefficient, D, is small, so the ratio cjcan teach a value of 10—100 or mote. The concentration of retained solute at the membrane surface, may then exceed the solubility limit of the solute, and a precipitated semisohd gel forms on the surface of the membrane. This gel layer is an additional battier to flow through the membrane. 

Water Transport. Two methods of measuring water-vapor transmission rates (WVTR) ate commonly used. The newer method uses a Permatran-W (Modem Controls, Inc.). In this method a film sample is clamped over a saturated salt solution, which generates the desired humidity. Dry air sweeps past the other side of the film and past an infrared detector, which measures the water concentration in the gas. For a caUbrated flow rate of air, the rate of water addition can be calculated from the observed concentration in the sweep gas. From the steady-state rate, the WVTR can be calculated. In principle, the diffusion coefficient could be deterrnined by the method outlined in the previous section. However, only the steady-state region of the response is serviceable. Many different salt solutions can be used to make measurements at selected humidity differences however, in practice,... 

The advantage of the simulations compared to the experiments is that the correspondence between the tracer diffusion coefficient and the internal states of the chains can be investigated without additional assumptions. In order to perform a more complete analysis of the data one has to look at the quench-rate and chain-length dependence of the glass transition temperature for a given density [43]. A detailed discussion of these effects is far beyond the scope of this review. Here we just want to discuss a characteristic quantity which one can analyze in this context. 

The measurement of transport numbers by the above electrochemical methods entails a significant amount of experimental effort to generate high-quality data. In addition, the methods do not appear applicable to many of the newer non-haloalu-minate ionic liquid systems. An interesting alternative to the above method utilizes the NMR-generated self-diffusion coefficient data discussed above. If both the cation (Dr+) and anion (Dx ) self-diffusion coefficients are measured, then both the cation (tR+) and anion (tx ) transport numbers can be determined by using the following Equations (3.6-6) and (3.6-7) [41, 44] ... 

In addition, it was concluded that the liquid-phase diffusion coefficient is the major factor influencing the value of the mass-transfer coefficient per unit area. Inasmuch as agitators operate poorly in gas-liquid dispersions, it is impractical to induce turbulence by mechanical means that exceeds gravitational forces. They conclude, therefore, that heat- and mass-transfer coefficients per unit area in gas dispersions are almost completely unaffected by the mechanical power dissipated in the system. Consequently, the total mass-transfer rate in agitated gas-liquid contacting is changed almost entirely in accordance with the interfacial area—a function of the power input. 

In Table 3 we have listed the results of a basis set and correlation study for the hyperpolarizability dispersion coefficients. In a previous investigation of the basis set effects on the dispersion coefficients for the first hyperpolarizability (3 of ammonia [22] we found quite different trends for the static hyperpolarizability and for the dispersion coefficients. While the static hyperpolarizability was very sensitive to the inclusion of diffuse functions, the dispersion coefficients remained almost unchanged on augmentation of the basis set with additional diffuse functions, but the results obtained with the CC2 and CCSD models, which include dynamic electron correlation, showed large changes with an increase of the... 

This equation is identical to the Maxwell [236,237] solution originally derived for electrical conductivity in a dilute suspension of spheres. Hashin and Shtrikman [149] using variational theory showed that Maxwell s equation is in fact an upper bound for the relative diffusion coefficients in isotropic medium for any concentration of suspended spheres and even for cases where the solid portions of the medium are not spheres. However, they also noted that a reduced upper bound may be obtained if one includes additional statistical descriptions of the medium other than the void fraction. Weissberg [419] demonstrated that this was indeed true when additional geometrical parameters are included in the calculations. Batchelor and O Brien [34] further extended the Maxwell approach. 

In addition to the environmentally benign attributes and the easily tunable solvent properties, other important characteristics such as low interfacial tension, excellent wetting behavior, and high diffusion coefficients also make SCCO2 a superior medium for the synthesis of nanoscale materials [2]. Previous works on w/c RMs showed that conventional hydrocarbon surfactants such as AOT do not form RMs in scCOi [3] AOT is completely insoluble in CO2 due to the poor miscibility of the alkyl chains with CO2, restricting the utilization of this medium. Recently, we had demonstrated that the commonly used surfactant,... 

It is important to note that the dilfnsion-layer thickness depends not only on hydro-dynamic factors but also (through the diffusion coefficient) on the nature of the diffusing species. This dependence is minor, of course, since the values of Dj differ little among the various substances, and in addition are raised to the power one-third in Eq. (4.37). 

We have applied FCS to the measurement of local temperature in a small area in solution under laser trapping conditions. The translational diffusion coefficient of a solute molecule is dependent on the temperature of the solution. The diffusion coefficient determined by FCS can provide the temperature in the small area. This method needs no contact of the solution and the extremely dilute concentration of dye does not disturb the sample. In addition, the FCS optical set-up allows spatial resolution less than 400 nm in a plane orthogonal to the optical axis. In the following, we will present the experimental set-up, principle of the measurement, and one of the applications of this method to the quantitative evaluation of temperature elevation accompanying optical tweezers. 

The mobilities of alkylpyridines were modeled and predicted in capillary zone electrophoresis.35 The model predicted that compounds adopt a preferred orientation, and additionally predicted mobilities of structural isomers to within 4%, a higher degree of accuracy than can be obtained from simple considerations of van der Waal s radius. Quantitative prediction of the mobilities of some pyridines, such as alkenylpyridines, was not possible. Mobilities of small solutes in capillaries filled with oligomers of ethylene glycol were related to solution viscosity and the diffusion coefficient.36... 

---