Amorphous state diffusion

There is actually no sharp distinction between the crystalline and amorphous states. Each sample of a pharmaceutical solid or other organic material exhibits an X-ray diffraction pattern of a certain sharpness or diffuseness corresponding to a certain mosaic spread, a certain content of crystal defects, and a certain degree of crystallinity. When comparing the X-ray diffuseness or mosaic spread of finely divided (powdered) solids, the particle size should exceed 1 um or should be held constant. The reason is that the X-ray diffuseness increases with decreasing particle size below about 0.1 J,m until the limit of molecular dimension is reached at 1-0.1 nm (10-1 A), when the concept of the crystal with regular repetition of the unit cell ceases to be appropriate. 

Diffusion coefficients in amorphous solids such as oxide glasses and glasslike amorphous metals can be measured using any of the methods applicable to crystals. In this way it is possible to obtain the diffusion coefficients of, say, alkah and alkaline earth metals in silicate glasses or the diffusion of metal impurities in amorphous alloys. Unlike diffusion in crystals, diffusion coefficients in amorphous solids tend to alter over time, due to relaxation of the amorphous state at the temperature of the diffusion experiment. 

In summary, there are at least four ways in which residual moisture in the amorphous state can impact on chemical reactivity. First, as a direct interaction with the drug, for example, in various hydrolytic reactions. Second, water can influence reactivity as a by-product of the reaction, by inhibiting the rate of the forward reaction, for example, in various condensation reactions, such as the Maillard reaction. Third, water acting locally as a solvent or medium facilitating a reaction, without direct participation. Finally, by virtue of its high free volume and low Tg, water can act as a plasticiser, reducing viscosity and enhancing diffusivity [28]. 

The diffusion coefficient D is inversely related to the cross-link density of vulcanized rubbers. When D is extrapolated to zero concentration of the diffusing small molecules, it is related to the distance between the cross-links. Thus, as the cross-link density increases D becomes smaller, as expected. Further, the diffusion coefficient is less for crystalline polymers in comparison with the same polymer except in the amorphous state. In fact, this can be roughly stated as follows. 

In a previous paper (7), we have illustrated that diffusion in FCC takes place in the non-steady regime and that this explains the failure of several attempts to relate laboratory measurements on FCC catalysts to theories on steady state diffusion. Apart from the diffusion aspects, Nace (13) has also indicated the limited accessibility of the zeolite portal surface area by comparing the cracking rates of various model compounds with an increasing number of naphthenic rings on zeolite and amorphous FCC catalysts, figure 2. 

Important data on the structure of the films were obtained in an analysis of electron diffraction patterns recorded directly in the transmission electron microscope. In all cases, the diffraction patterns had the form of diffuse halos, which indicate that nanoparticles are in the amorphous state [30]. The fact that the nanoparticles are amorphous is in all probability due to the exceedingly fast cooling of nanometer drops after the expansion of the plasma cloud. Estimates of the cooling rate of nanodrops at the instant of their hardening give values of up to 107K/sec. 

Using Eq. (9-24) one calculates a diffusion coefficient for the amorphous state to be ... 

Spectroscopic methods, such as FT-infrared (FTIR) and Raman spectroscopy detect changes in molecular vibrational characteristics in noncrystalline solid and supercooled liquid states. Various nuclear magnetic resonance (NMR) techniques and electron spin resonance (ESR) spectroscopy, however, are more commonly used, detecting transition-related changes in molecular rotation and diffusion (Champion et al. 2000). These methods have been used for studies of the amorphous state of a number of sugars in dehydrated and freeze-concentrated systems (Roudaut et al. 2004). 

Many polymers have the capability to crystallize. This capability basically depends on the structure and regularity of the chains and on the interactions between them. The term sernicrystalline state should be used rather than crystalline state, because regions in which the chains or part of them have an ordered and regular spatial arrangement coexist with disordered regions typical of the amorphous state. X-ray diffraction studies of samples of polymers crystallized from the melt reveal diffuse zones, char-... 

BET studies of both the commercial and laboratory scale particles discussed above indicate that there is little internal area accessible to BET adsorbate molecules. This holds for both amorphous and polycrystall ine particles. If the individual particles are composed of multiple crystalline substructures, internal defects capable of adsorption would be expected. However, the BET measurements. show that internal pore.s, if they are present, are not accessible to adsorbate gases. A possible explanation is that annealing by solid-state diffusion occuin sufftcienily rapidly al the temperatures of formation to block access of the external gas to dislocations and grain boundaries. However, the origins of the crystallites within the particles and the mechanisms of crystallization tire not understood al present. 

The transformation of the crystalline into the glassy state by solid-state reactions is extensively reviewed in its theoretical and experimental aspects. First, we give some historical background and describe the thermodynamics of metastable phase formations, adding as well the kinetic requirements for the amorphization process. Then we discuss the different experimental routes into the amorphous state hydriding, thin diffusion couples, and other driven systems. In the discussion and the summary, we close the gap between the melting phenomena and the amorphization and provide a tentative outlook. 

The details of each timescale depend very much on the experimental situation. This will be discussed in Sect. 2.2 of this article. Here we give only some general remarks concerning the timescales r1 a and ra-.2 of the solid-state amorphization reaction. For the timescale TWa, we decide between an inhomogeneous reaction (e.g., multilayers of pure elements will form an amorphous interlayer) and the homogeneous transformation into the amorphous state, where the timescale t -, decreases to very low values due to the diffusionless transition. In the first case, the timescale for the amorphization of the entire sample is obviously determined by the diffusion process of one species... 

Amorphous powder formed by mechanical alloying for 510 h at intensity 5 was further milled at intensity 7 for 25 h. The typical broad diffuse maximum of the amorphous state disappeared, and the characteristic intensity distribution of the quasicrystalline phase showed up in the X-ray diffraction pattern. Therefore, additional milling at higher intensity led to an amorphous-to-quasicrystal transition. Amorphization can also be achieved for crystalline starting powder mechanically alloyed for 206 h at intensity 9 by a further milling for 433 h at intensity 3 [3.108]. 

Figure 1.12 is a schematic illustration of a spray-dried particle in a humid air environment in which the particle would adsorb water vapor this is then followed by state changes of carrier matrices from the amorphous state to a rubbery state. The encapsulated flavors can easily move in the matrix of the carrier matrices. At the same time, the oxygen uptake into the wall matrix becomes higher and the oxidation of the encapsulated flavors progresses. The most interesting point is that around the glass transition temperature, both release and oxidation rate constants change nearly in the same trends with T- T, as shown in Figure 1.11. This implies that the flavor diffusion and the oxygen upt e can be treated as a similar behavior.

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