Extended diffusion

From a mathematical perspective either of the two cases (correlated or non-correlated) considerably simplifies the situation [26]. Thus, it is not surprising that all non-adiabatic theories of rotational and orientational relaxation in gases are subdivided into two classes according to the type of collisions. Sack s model A [26], referred to as Langevin model in subsequent papers, falls into the first class (correlated or weak collisions process) [29, 30, 12]. The second class includes Gordon s extended diffusion model [8], [22] and Sack s model B [26], later considered as a non-correlated or strong collision process [29, 31, 32],... 

Fig. 6.8. The dependence of rj2 on x) by the Ivanov model (I) and friction model (F) in comparison with predictions of the extended. /-diffusion (ED) and Langevin (L) models for linear molecules. The line (H) corresponds to the Hubbard inverse proportionality between xgj and xj at very high densities. Experimental data from [81] are in rectangles around line G with the length of their vertical and horizontal sides being equal, correspondingly, to the experimental errors in x el and rj measurements. Experimental data from [270] (J) are shown both in original position and shifted down by a factor of four (broken line).

The function Z kR,) is a power series with the two limiting forms, for extended diffuse layers ... 

A critical comparison by van Konyenberg and Steele [230] and Jones et al. [231] of extended diffusion models with Brownian motion and other continuum models strongly favours the former treatment. More detailed analysis is given by Berne and Pecora [232]. 

Concentration grating Due to the Ludwig-Soret effect, the temperature grating is the driving force for a secondary concentration grating, which starts to build up and is superimposed upon the thermal one. Its temporal and spatial evolution is obtained from the one-dimensional form of the extended diffusion equation... 

In the first period, which ended with a review [18], the complex susceptibility x (0)) was expressed through the law of motion of the particles perturbed by a.c. external field E(t). The results of these calculations rigorously coincide with those obtained, for example, in Refs. 22 and 23, respectively, for the planar and spatial extended diffusion model (compare with our Ref. 18, pp. 65 and 68). The most important results of this period are (i) the planar confined rotator model [ 17, p. 70 20], which has found a number of applications in our and other [24—31] works (ii) the composite so-called confined rotator-extended diffusion model. However, this approach had no perspectives because of troublesome calculations of the susceptibility x ( )-... 

R-band characteristic for H20. Thus, it was suggested [47] that the confined rotator-extended diffusion model is capable of qualitatively describing the wideband spectra of water. 

Edge diffusion — The diffusion edge is the fictional boundary between the diffusion layer and the bulk. It is a convenient concept when an extending diffusion later reaches an object to react, e.g., at a pair electrode and a -> scanning electrochemical microscope [i]. Ref. [i] Bard AJ, Faulkner LR (2001) Electrochemical methods, 2nd edn. Wiley, New York, p 669... 

Figure 9. Full lines D(t) plotted as a function of yt for 8 — 0.5 and for bath temperatures T — 0. kT — liy/ln. kT — In/n [at T = 0, D(t) is not an extended diffusion coefficient, but characterizes the relaxation of Aj3(t) toward its finite limit value Ax2(oo)]. Dashed fines The...

If the polyurethane molecule is allowed to form a three-dimensional structure, it becomes insoluble and neither wet nor dry spinning processes can be used. A chemical spinning process must be used in this case. The trick is to spin the isocyanate-terminated prepolymer at a stage where it forms a viscous melt, and with the jets produced in an environment that contains a chain extender. This chain extender diffuses into the fibers and reacts to couple the prepolymer molecules (Couper, 1985). 

Table 3. Comparison of T2K values calculated using extended-diffusion models (J- and M-diffiision) with the values measured for D2O molecules in CH3CN, CHCI3, and at atmospheric (0.1 MPa) and high (300 MPa) pressures.

When the sweep rate v is sufficiently high that the concentration in the middle of the drop (r = 0) remains at at the completion of the scan, then the behavior is essentially that of semi-infinite diffusion and the basic treatment of Section 6.2 applies (75). Correction must be made for the sphericity of the drop [see (6.2.23)]. In this case the spherical correction term must be subtracted from the planar term, since the concentration gradient builds up inside the drop and the area of the extended diffusion field decreases with time. Thus, the equations that apply for a reversible stripping reaction at the HMDE are (75)... 

Fig. 4. Variation of diffusion coefficient with volume, reduced by Batchinski-Hildebrand Vq in each case, for various simulated and actual fluids, (a) Extended diffusivity range (MD systems only), (h) Lower D range, (expanded scale), showing nonhnear volume dependence characteristic of glass-forming molecular liquids.

Gordon (1966) has proposed what he calls extended diffusion models to take into account the effect of collisions. The <(F2(u(0) u(/))> calculated from these models cannot be expressed in simple analytical form, and we must content ourselves here with a description of the assumptions in the model and a description of results for a few particular systems. 

Comparisons of the extended diffusion model with experimental spectra on small molecules have been performed by Steele, who concludes that the model, although not very successful, is still superior to any other model studied (van Koynenberg and Steele, 1974 Jones, 1974). 

The extended diffusion model has been solved for linear molecules (Gordon, 1966), spherical top molecules (McClung, 1969, Fixman and Rider, 1969), and symmetric top molecules (Fixman and Rider, 1969). 

The existence of the extended diffuse layer in dilute solutions is also of crucial importance in colloidal systems formed by particles whose size is comparable to the wavelength of Kght, that is, about 1 pm. For example, electrophoresis, the movement of colloidal particles with respect to the solution under the influence of an external electric field, originates from the displacement of the particle and the mobile part of its EDL in the opposite directions under the action of this field, since these components of the system possess charges of opposite signs. A related phenomenon occurs if the solid particles move with respect... 

Extended diffuse filaments on edge of infrared complex 1015 (DEN 189). 

Space charge refers to the extended diffuse charge in an electrical double layer, which is passing a superlimiting current. 

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