Diffusional jump

When (DEB), is much smaller than unity, the polymer relaxation is relatively rapid compared to diffusion. In this case, conformational changes take place instantaneously and equilibrium is attained after each diffusional jump. This is the type of diffusion encountered ordinarily and is called viscous diffusion. Therefore, the transport will obey classical theories of diffusion. When (DEB), is much larger than unity, the molecular relaxation is very slow compared to diffusion and there are no conformational changes of the medium within the diffusion time scale. In this case, Fick s law is generally valid, but no concentration dependence of the diffusion coefficient is expected. This is termed elastic diffusion. When (DEB), is in the neighborhood of unity, molecular rearrangment... 

One of earliest approaches of estimating the diffusion coefficient through a polymer carrier is that of Eyring (1936). In this theory, diffusion of a solute through a medium is presented as a series of jumps instead of a continuous process. Therefore, in Eq. (18) in Table I, which comes from the Eyring analysis, X is the diffusional jump of the drug in the polymer and v is the frequency of jumping. 

Peppas and Reinhart have also proposed a model to describe the transport of solutes through highly swollen nonporous polymer membranes [155], In highly swollen networks, one may assume that the diffusional jump length of a solute molecule in the membrane is approximately the same as that in pure solvent. Their model relates the diffusion coefficient in the membrane to solute size as well as to structural parameters such as the degree of swelling and the molecular weight between crosslinks. The final form of the equation by Peppas and Reinhart is... 

As mentioned, the Peppas-Reinhart theory is valid in the case of highly swollen membranes. Additional work by Peppas and Moynihan [158] resulted in a theory for the case of moderately swollen networks. This theory was derived much like the Peppas-Reinhart theory with the exceptions that in a moderately swollen network, one may not assume that the diffusional jump length of the solute in the membrane, X2, i3, is equal to the diffusional jump length of the solute in pure solvent, X2, i and, also, one may not assume that the free volume of the polymer/solvent system is equal to the free volume of the solvent. The initial... 

T2(b) refers to the case (real) of rapidly rotating SFq molecules in a lattice which is pure with respect to paramagnetic impurities. T2(a) refers to the case (real) of ISO ppm of Fe or the case (hypothetical) of SF6 molecules which rotate only upon a diffusional jump... 

Let us regard a binary A-B system that has been quenched sufficiently fast from the / -phase field into the two phase region (a + / ) (see, for example, Fig. 6-2). If the cooling did not change the state of order by activated atomic jumps, the crystal is now supersaturated with respect to component B. When further diffusional jumping is frozen, some crystals then undergo a diffusionless first-order phase transition, / ->/ , into a different crystal structure. This is called a martensitic transformation and the product of the transformation is martensite. 

Such transformations have been extensively studied in quenched steels, but they can also be found in nonferrous alloys, ceramics, minerals, and polymers. They have been studied mainly for technical reasons, since the transformed material often has useful mechanical properties (hard, stiff, high damping (internal friction), shape memory). Martensitic transformations can occur at rather low temperature ( 100 K) where diffusional jumps of atoms are definitely frozen, but also at much higher temperature. Since they occur without transport of matter, they are not of central interest to solid state kinetics. However, in view of the crystallographic as well as the elastic and even plastic implications, diffusionless transformations may inform us about the principles involved in the structural part of heterogeneous solid state reactions, and for this reason we will discuss them. 

By assuming an Arrhenius type temperature relation for both the diffusional jumps and r, we can use the asymptotic behavior of /(to) and T, as a function of temperature to determine the activation energy of motion (an example is given in the next section). We furthermore note that the interpretation of an NMR experiment in terms of diffusional motion requires the assumption of a defined microscopic model of atomic motion (migration) in order to obtain the correct relationships between the ensemble average of the molecular motion of the nuclear magnetic dipoles and both the spectral density and the spin-lattice relaxation time Tt. There are other relaxation times, such as the spin-spin relaxation time T2, which describes the... 

Solution. When mobile interstitials diffuse across a plane in the F-frame, the material left behind shrinks, due to the loss of the dilational fields of the interstitials. This establishes a bulk flow in the diffusion zone toward the side losing interstitials and causes a compensating flow (influx) of the large host atoms toward that side even though they are not making any diffusional jumps in the crystal. 

In some cases, particularly in the growth of aerosol particles, the assumption of equilibrium at the interface must be modified. Frisch and Collins (F8) consider the diffusion equation, neglecting the convective term, and the form of the boundary condition when the diffusional jump length (mean free path) becomes comparable to the radius of the particle. One limiting case is the boundary condition proposed by Smoluchowski (S7), C(R, t) = 0, which presumes that all molecules colliding with the interface are absorbed there (equivalent to zero vapor pressure). A more realistic boundary condition for the case when the diffusion jump length, (z) R, has been shown by Collins and Kimball (Cll) and Collins (CIO) to be... 

Polymers, because of their long chemical structure cohere as solids even when discrete section of the chain are undergoing Brownian motions moving by diffusional jump processes from place to place. This is the main difference between elastic solids and polymers [1-7]. 

Diffusion of atoms from the point at which they dissociate on a metal surface to the edge of the metal crystallite is one of the component steps of hydrogen spillover. Quasielastic neutron scattering experiments have produced direct evidence for the diffusion coefficients of hydrogen on the surface of catalysts. The mean time between diffusional jumps for hydrogen on a Raney Ni surface has been found to be 2.7 0.5 x 10 9s at 150°C.72 For H on the surface of Pt crystals dispersed within a Y type zeolite the mean time between surface jumps was found73 to lie between 3.0 and 8 x 10-9s at 100 °C. 

Swift and Sayne used concepts similar to those of Bockris and Saluja if a molecule stays associated with an ion for more than the time needed for a diffusional jump, it counts as a primary hydration number. This approach yields approximately 4 solvation molecules for and Ca ", and 5 for Ba and Sr", whereas nonspectroscopic methods for these systems yield values that are two to three times larger. Does NMR measure only water arranged in a first, octahedral layer in the first shell near the ion and is it insensitive to the rest of the water structure near an ion ... 

The activation energy, E, can be interpreted as the previously mentioned thermal energy that must be concentrated in the polymer adjacent to a penetrant to open a passage of sufficient volume to allow the penetrant to execute a diffusional jump. 

Experimentally, it is much easier to measure the viscosity t] of an undercooled liquid than it is to measure u. It is therefore useful to relate the nucleation rate to the viscosity, which is done as follows Given the similarity between the elementary jump shown in Fig. 9.3 and a diffusional jump, the two can be assumed to be related by... 

Indeed ( ), between 0 = 0.7 and 0 1, increases from 10 to 14 kcal mole and then it decreases for 14 to 12 kcal mole in going from 0 1 to 0 1.3. The molecular area of methanol on the Xerogel and Aerogel surfaces is about 25.5 A at 0 1. If this value is considered as the quadratic diffusional jump distance < > and if the surface diffusion coefficient is... 

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