Temperature coefficient diffusion

This is shown as a black circle in Fig. 19. One can draw further inferences if one is willing to apply (20) with the D+ given by the solid line in Fig. 16, i.e., the room-temperature value of Seager and Anderson (1988), interpolated toward the high-temperature diffusion coefficient of Van Wieringen... 

This is the first instance in which solid-state-like diffusion coefficients have been estimated from STM images. Thus, it seems likely that room temperature diffusion coefficients might be obtained with STM for well characterized systems in the future (87). 

Not only does anion-1 differ from the molecular anions of acetonitrile in its absorption properties, but its dynamic properties are also anomalous. While anion-2 has normal mobility, anion-1 is a high-mobility anion whose room temperature diffusion coefficient is more than three times higher than that of solute ions and anion-2 [30]. The activation energy for this migration is just 3.2 kJ/mol while the value for normal ions (including anion-2) is 7.6 kJ/mol [30]. Electron-transfer reactions that involve anion-1... 

One can conclude from equation (4.2.33) that the correction SR to the effective radius due to tunnelling (the second term) decreases with both the decrease of parameters ao, tq characterizing tunnelling strength, and the increase of temperature (diffusion coefficient). Since this correction makes the contribution to the rate constant, SK = AitDSR, independent on D, the... 

In order to develop an intuition for the theory of flames it is helpful to be able to obtain analytical solutions to the flame equations. With such solutions, it is possible to show trends in the behavior of flame velocity and the profiles when activation energy, flame temperature, diffusion coefficients, or other parameters are varied. This is possible if one simplifies the kinetics so that an exact solution of the equation is obtained or if an approximate solution to the complete equations is determined. In recent years Boys and Corner (B4), Adams (Al), Wilde (W5), von K rman and Penner (V3), Spalding (S4), Hirschfelder (H2), de Sendagorta (Dl), and Rosen (Rl) have developed methods for approximating the solution to a single reaction flame. The approximations are usually based on the simplification of the set of two equations [(4) and (5)] into one equation by setting all of the diffusion coefficients equal to X/cpp. In this model, Xi becomes a linear function of temperature (the constant enthalpy case), and the following equation is obtained ... 

There are different criterion of how to classify solid-solid interfaces. One is the sharpness of the boundary. It could be abrupt on an atomic scale as, for example, in III-IV semiconductor heterostructures prepared by molecular beam epitaxy. In contrast, interdiffusion can create broad transitions. Surface reactions can lead to the formation of a thin layer of a new compound. The interfacial structure and composition will therefore depend on temperature, diffusion coefficient, miscibility, and reactivity of the components. Another criterion is the crystallinity of the interface. The interface may be crystalline-crystalline, crystalline-amorphous, or completely amorphous. Even when both solids are crystalline, the interface may be disturbed and exhibit a high density of defects. 

Ziegleder, G., C. Moser, and J. Geier-Greguska, Kinetics of Fat Migration in Chocolate Products, Part II Effects of Temperature, Diffusion Coefficient, and Fat Content, Ibid. 98 253-256 (19%). 

Plant Raw Particle Size Temperature Diffusion Coefficient... 

Figure 7. Histograms of diffusion coefficients of Sample C(II) in KCl buffer at different temperatures. Diffusion coefficients corrected to the viscosity of water at 30°C D c,3o = Duci.t X t)Kci/Ti X 303/ qxo.SO.

For small molecule solutes in common solvents at room temperature, diffusion coefficients = 1 — 4 x... 

Trajectories of center-of-mass for the surface and inner chains were calculated at every picosecond interval to analyze the diffusion coefficient at a temperature. Diffusion coefficients in the surface and inner chains were computed from mean-square displacement (MSD) [194,209,210]. The average mean-square displacement of center-of-mass for the chains can be determined. 

Many diffusion coefficients for gases are on the order of 10 cm Vs. Diffusion coefficients can also be defined for liquid and solid phases. Although the kinetic theory of gases does not apply directly to these phases, there are some conceptual similarities. However, diffusion coefficients for condensed phases are much lower than for gases, especially for solids at normal temperatures. Diffusion coefficients for solids are typically in the range of 10 to 10 cmVs. 

The moisture diffusion coefficient D is of order 10 mm /s, which for composites and polymers is about 6 and 7 orders of magnitudes smaller, respectively, than the temperature diffusion coefficient. The above processes can thus be decoupled. 

Figure 7.2 shows that the diffusion coefficient is a linear function of temperature. Diffusion coefficient of erucamide obeys an Anhenius law ... 

The extremely small silica particles made compacts which showed a sharp increase in densification rate with temperature increase in the range 1100°-1250°C. The rate increased 73 times with the 150°C increase in temperature. Diffusion coefficients were not available for a calculation of the rates expected from volume diffusion. 

Diffusion of erucamide in linear low density polyethylene, LLDPE, also shows that diffusion coefficient of erucamide increases with temperature. Diffusion coefficient was found to increase with temperature for erucamide in polypropylene and ethylene propylene copolymer." Thickness of a film in which diffusion process occurs was found an important variable in terms of time required to attain equilibrium concentrations throughout the film. This can be illustrated by the data in Figure 7.3 which show that concentration of amide on surface of vinyl acetate copolymer grows until it reaches certain equilibrium determined by polymer, additive and temperature. Amide diffusion was also found to increase with increase in its concentration in bulk. ... 

Before we begin, we should list the guidelines that tend to stick in everyone s mind. Diffusion coefficients in gases, which can be estimated theoretically, are about 0.1 cm / sec. Diffusion coefficients in liquids, which cannot be as reliably estimated, cluster around 10 cm /sec. Diffusion coefficients in solids are slower still, 10 cm /sec, and they vary strongly with temperature. Diffusion coefficients in polymers and glasses lie between liquid and solid values, say about 10 cm /sec, and these values can be strong functions of solute concentration. 

---