Amorphous phase solute diffusivity

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. 

Most polymers that have been of interest as membrane materials for gas or vapor separations are amorphous and have a single phase structure. Such polymers are converted into membranes that have a very thin dense layer or skin since pores or defects severely compromise selectivity. Permeation through this dense layer, which ideally is defect free, occurs by a solution-diffusion mechanism, which can lead to useful levels of selectivity. Each component in the gas or vapor feed dissolves in the membrane polymer at its upstream surface, much like gases dissolve in liquids, then diffuse through the polymer layer along a concentration gradient to the opposite surface where they evaporate into the downstream gas phase. In ideal cases, the sorption and diffusion process of one gas component does not alter that of another component, that is, the species permeate independently. 

Here Dv is the volume diffusion coefficient of the solute atoms and C, is the solute content of the residual amorphous phase (C, C0 at an early stage of primary crystallization). Here, dr/df is proportional to f1/2 and the growth rate decreases progressively with time. An in-situ time-resolved x-ray... 

Water permeates a flawless polymer film through the amorphous phase via solution-diffusion mechanisms. Therefore, water permeability is inversely proportional to the volume fraction of the crystalline phase (crystallinity). Water molecules are first dissolved into the polymer matrix at the interface the dissolved water molecules diffuse through the polymer according to the chemical potential... 

It seems likely that, amorphous phase formation by mechanical alloying of the mixture of elemental metal powders occurs in four stages (i) formation of very fine composite powder whereby particles my be understood as diffusion couples (ii) formation of solid solution (ii) collapse of supersaturated solution to the amorphous phase and (iv) gradual dissolution of residual crystallites (dispersoids) into the amorphous matrix. 

The method of soluble anode has also been used to produce nanoparticles [369-371, 378]. Based on the Ritz method [379], authors [371] obtained the magnetite nanoparticles of 8.3 nm in size of the soluble iron electrode. The aqueous solution of dimethylformamide (DMF) and cationic surfactants has been chosen as electrolyte. The particle size was under control by variation of the current density in the system. The as-prepared nanoparticles gave a diffuse X-ray diffraction peak similar to that from the amorphous phase. Using Raman spectroscopy, it was found that the obtained phase was magnetite. The same technique has been used for other oxide phases fabrication, namely the method called electrochemical deposition under... 

What is phase competition in the process of a solid-state reaction. Consider a diffusion couple of two mutually soluble components A/B, which diffuse into each other forming intermediate phases and, possibly, a solid solution, beta binary system A-B have three stable intermediate phases 1, 2, 3, a metastable compound 4, and an amorphous phase 5. The dependence of the Gibbs free energy on the composition of these phases is given in Figure 4.1. 

This process of gas transport through a membrane is called permeation, and the mechanism has been identified as solution-diffusion. Gas species i dissolves at the feed-membrane interface (z = 0) by molecular diffusion, the dissolved gas molecules move through the membrane and are finally desorbed into the product gas phase at the product-membrane interface (z = dm). Under the simplest of conditions, each species in a mixture diffuses independently of the others according to flux expression (3.4.72). The nature of the dependence of Di on the effective diameter of the gas molecules, the temperature and the polymer for an activated diffusion is iliustrated in Section 4.3.3 for an amorphous polymer. 

In fact, studies of guest desorption kinetics [111,138] and of gas transport [97,144,145] on SPS films have shown that the guest solubility can be much higher in the crystalline phase (mainly for low-solute activities) while the solute diffusivity is generally much higher in the amorphous phase. This offers the opportunity to prepare and characterize samples including low-molecular-mass molecules essentially only as guests of the host crystalline phase. 

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