Diffusion amorphous phase

Appropriately, this was called the Folded Chain Theory and is illustrated in Fig. A.ll. There are several proposals to account for the co-existence of crystalline and amorphous regions in the latter theory. In one case, the structure is considered to be a totally crystalline phase with defects. These defects which include such features as dislocations, loose chain ends, imperfect folds, chain entanglements etc, are regarded as the diffuse (amorphous) regions viewed in X-ray diffraction studies. As an alternative it has been suggested that crystalline... 

The existence of the amorphous phase of the fiber is confirmed in x-ray examination by the occurrence of a distinct intensity maximum of the radiation scattered diffusively at 2Q = 21.6 . The fraction of the amorphous phase in the fiber depends on manufacturing conditions and a possible further refining treatment. It is estimated to vary from 0.25 to 0.60. With an increase of the draw ratio and following the thermal treatment of the fiber, the proportion of the amorphous phase only reaches the lower values of this interval,... 

The amorphous orientation is considered a very important parameter of the microstructure of the fiber. It has a quantitative and qualitative effect on the fiber de-formability when mechanical forces are involved. It significantly influences the fatigue strength and sorptive properties (water, dyes), as well as transport phenomena inside the fiber (migration of electric charge carriers, diffusion of liquid). The importance of the amorphous phase makes its quantification essential. Indirect and direct methods currently are used for the quantitative assessment of the amorphous phase. 

The nature of the solidification process in these cements has received little attention. Rather, attention has focussed on the crystalline components that form in cements which have been allowed to equilibrate for some considerable time the nature of such phases is now quite well understood. Gelation is reasonably rapid for these cements and occurs within a significantly shorter time than does development of crystalline phases. The conclusion may be drawn that initial cementition is not the same as crystallization, but must occur with the development of an essentially amorphous phase. Reactions can continue in the amorphous gelled phase, but are presumably limited in speed by the low diffusion rates possible through such a structure. However, reactions are able to proceed substantially to completion, since in many cases X-ray diffraction has demonstrated almost quantitative conversion of the parent compounds to complex crystalline mixed salts, though several days or weeks of equilibration are required to bring this about. 

The use of Equation (22) is very general, but it is also possible, with accurate measurements and data treatment, to perform the quantitative phase analysis in semi-crystalline materials without using any internal standard. This procedure is possible only if the chemical compositions of all the phases, including the amorphous one, are known. If the composition of the amorphous phase is unknown, the quantitative analysis without using any internal standard can still be used provided that the chemical composition of the whole sample is available [51]. This approach, until now, has been developed only for the XRD with Bragg-Brentano geometry that is one of the most diffused techniques in powder diffraction laboratories. 

Oxygen diffuses inside the amorphous phase of amorphous crystalline polymers. The diffusion coefficient can be expressed for such polymers in the form [68]... 

Diffusion of dioxygen occurs 102 105 times more slowly with the diffusion coefficient D 10 7 10 10 cm2 s 1 Carbon-centered atom of P changes its orbital hybridization in this reaction and changes the C—C bond angles from 120° to 109°. Since P is macroradical and is surrounded by segments of macromolecules, this process occurs with an activation energy Solubility of dioxygen in the amorphous phase of polymer is about 3 x 10 4-2 x 10 3 mol L 1 atm-1... 

The papers of Mallon and Ray [98, 123] can be regarded as the state of the art in understanding and modelling solid-state polycondensation. They assumed that chain ends, catalysts and by-products exist solely in the amorphous phase of the polymer. Because of the very low mobility of functional groups in the crystalline phase, the chemical reactions are modelled as occurring only in the amorphous phase. Additionally, the diffusion of by-products is hindered by the presence of crystallites. The diffusivity of small molecules was assumed to be proportional to the amorphous fraction. Figure 2.32 shows the diffusion coefficients for the diffusion of EG and water in solid PET. 

Diffusion Rate Controlled Process If the rate of chemical reaction is much faster than the diffusion of water and EG through the solid amorphous phase, then the reaction can be considered to be at equilibrium throughout the pellet [21], The reaction rate is dependent upon the pellet size, the diffusivity of both water and EG, the starting molecular weight, and the equilibrium constants Ki and K5. In addition, the pellet can be expected to have a radial viscosity profile due to a by-product concentration profile through the pellet with the molecular weight increasing as the by-product concentrations decreases in the direction of the pellet surface [22-24],... 

Said this, we can let the reader to recall Fig. 1.15, where we depicted amorphous-like phase regions at grain boundaries as the pathways open for preferential diffusion of hydrogen atoms. Apparently, an alloy can benefit from some fraction of amorphous phase to improve kinetics of hydrogen absorption, but complete amorphization of crystalline lattice lowers capacity for storing hydrogen [156]. Mechanochemical activation is therefore a complex process where kinetic and thermodynamic effects must be firstly well understood, and then optimized. 

In another model, Harland and Peppas [159] considered the diffusion of solutes through semicrystalline hydrogel membranes. These types of membranes were assumed to consist of a crosslinked, swollen (amorphous) phase through which solute diffusion occurred and an impermeable, crystalline phase. A simplified form of the model assumes uniform amorphous regions. With this assumption, the diffusion coefficient through a semi-crystalline membrane, Dc, was written as... 

Here, Da is diffusion coefficient in the amorphous phase alone, oc is the volume fraction of crystalline polymer, and t is a scalar quantity that denotes the tortuosity of diffusional path of the solute. The value of Da may be estimated by the Peppas-Reinhart model if the amorphous regions of the polymer are highly swollen. This substitution yields... 

In both equations, Dw is the solute diffusion coefficient in pure water, rs is the molecular radius of the solute, ls is its characteristic size, Vw is the water free volume, Mc is the molecular weight between crosslinks in the amorphous phase, Mn is the number average molecular weight of the polymer before crosslinking, M is the minimum value of Mc below which the solute cannot diffuse, 4>(V) is the free volume function mentioned earlier, and k3 is a constant. 

Because experimental study of the structure of crystal/liquid interfaces has been difficult due to the buried nature of the interface and rapid structural fluctuations in the liquid, it has been investigated by computer simulation and theory. Figure B.3 provides several views of crystal/liquid (or amorphous phase) interfaces, which must be classified as diffuse interfaces because the phases adjoining the interface are perturbed significantly over distances of several atomic layers. 

On the other hand, a diffuse interface possesses a significantly wider core that extends over a number of atomic distances. A diffuse crystalline/amorphous phase interface is shown in Fig. B.3. Similar structures exist in crystal/liquid interfaces [5]. 

Improved catalytic performance, selectivity and resistance to fusion, over bismuth molybdate catalysts was reported by McClellan (90) for catalysts obtained by chemically combining bismuth, molybdenum, phosphorus, and silica. After calcination at 450°C, the bismuth phosphomolybdate-on-silica catalyst showed an X-ray pattern of mainly crystalline Bi2(Mo04)3 which subsequently was converted to a new, substantially amorphous, phase after calcination at 800°C. Substantially morphous meant that the X-ray diffraction lines were broad diffuse bands of low intensity. The pattern of lines for this novel phase indicated a scheelite structure. A special interaction of silica with bismuth molybdate was also suggested by Callahan et al. (91). 

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