Using the Diffusion Coefficient

The diffusion of polystyrene of various molecular weights in high-molecular-weight polystyrene (M , = 2 x 10 g/mol) was measured by Mills et al. (Bl) using forward recoil spectrometry. At 170°C, the diffusion coefficient was found to depend on the weight-average molecular weight as 

If the concentration gradient of the diffusing species is given in concentration per unit distance, the unit 

Consider a polymer having a weight-average molecular weight of 1 x 10 g/mol. With a density of 1.05 g/cm , a bulk concentration of about 1 x 10 mol/cm is obtained. Consider a diffusion over a 100-A distance, or 1 x 10 cm from the bulk concentration to a zero concentration. In 1 sec, 8 x 10 = 1 X 10 mol will diffuse through a 1-cm area. This is a significant part of the polymer that is lying on the surface of the hypothetical 1 cm under consideration. 

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In the Goldman equation use the diffusion coefficients in question 1 in place of permeation coefficients. The rate of permeation is -D(dc/dx). The dx is essentially the membrane thickness and its neglect will cancel out of the equation (cf. the Goldman equation), (c) Is this flux consistent with actual radiotracer measurements of the movement concerned (In the Hodgkin-Huxley and Katz work, arbitrary values were used for the P s to ensure that the equation replicated the experiment. This, of course, makes it difficult to check its validity. Assume the starting concentration of ions on either side of the membrane is that shown in the text. The average internal diameter of a squid axon is about 1 mm.)... 

Mass transfer from the water phase to the microdroplet under stationary conditions quickly reaches the steady-state because of spherical diffusion. When the extraction of X is diffusion-limited in the water phase. Equation (3) is obtained using the diffusion coefficient of X in the water phase (Z w) [18]. 

Although the functional form of c given by Equation 1.5 is only one particular solution to Fick s second law (Eq. 1.4) and is restricted to the case of constant Z)y, it nevertheless is an extremely useful expression for understanding diffusion. It relates the distance a substance diffuses to the time necessary to reach that distance. The expression uses the diffusion coefficient of species/, Z)y, which can be determined experimentally. In fact, Equation 1.5 is often used to determine a particular Z)y. 

The speed of a reaction between molecules in a film and those in the underlying solution depends on the rate of approach of the latter to the interface. There are two ways of exactly evaluating the latter, one depending, as we have seen in Section II, on the use of the gas laws and the other using the diffusion coefficient of the molecules in solution. The former method w as suggested by Fosbinder and Rideal (16), who used the Hertz expression,... 

Recently, Boyer et al. (2o) used the diffusion coefficient to detect the presence of a liquid-liquid transition temperature above Tg. Arrhenius-type plots of log D against 1/T appear to result in two straight lines. The temperature at the intersection point compares favorably with... 

The P subunit sedimented as a single sharp band with S20fW= 3.54 +/- 1.9% (not shown). Using the diffusion coefficient and partial specific volume calculated for R.rubrum, a molecular weight of 45,000 was calculated which suggests that the P subunit (molecular weight 54,000) exists as a monomer in solution. This is supported by the fact that P coeluted with BSA (molecular weight 66,700) after gel filtration. 

Here, n is an integer which depends on the nature of the solute-dislocation interaction mechanism. For the size effects, n = 1 was used. The diffusion coefficient, D, for yttrium atoms in YCSZ may be expressed, as is usually done, in Eq. (4.17) ... 

Several models/ (Eq. (3)) for the diffusion coefficient are assumed. The parameters are estimated using the diffusion coefficients from Eq. (5) and the measured mole fractions. Since both quantities contain errors this is an error-in-variables problem ... 

Steam (lAPWS) website (www.iapws.org). Alternatively, one can use the diffusion coefficient of a solute in ambient water Z>298 and the temperature dependence of Du o-... 

The stationary potential ( stat) of vanadium in NaCl-KCl equimolar mixture is equal to -1.955, -1.934, and -1.920 V at 698,771, and 859 C, respectively. Taking into account that vanadium(II) ions are formed as a result of metal corrosion [11] and using the diffusion coefficients (see below) and the approximate thickness of diffusion layer 5 = 0.01 cm, we estimated the corrosion currents (/con-) frooi Equation 4.5.1 ... 

The longer a plastic part is exposed to moisture, the deeper moisture will penetrate inside the material. The greater the difference between maximum and minimum humidity, the higher the stresses are. The penetration depth of these stresses depends on the frequency of moisture change. It can be calculated down to several tenths of a millimeter using the diffusion coefficients of most plastics that are on the order of 10 cmVs [68]. 

Gartland [19] made an attempt to use corrected ionic mobility coefficients he used the diffusion coefficients collected by Bemhardsson [4] regardless of the solution concentrations but, to calculate the ion mobility coefficient, he introduced in the Nemst-Einstein equation an ionic strength-dependent correction factor based on a limited set of experimental data. 

Neither the equation using the mass transfer coefficient k nor that using the diffusion coefficient D is always successful. This is because of the assumptions made in their development. For example, the flux may not be proportional to the concentration difference if the capillary is very thin or if the two gases react. In the same way, Ohm s law is not always valid at very high voltages. But these cases are exceptions both diffusion equations work well in most practical situations, just as Ohm s law does. 

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