Diffusivity ionic porosity

It has been observed that in some phases, the diffusivity is smaller, and in other phases the diffusivity is larger. One explanation is that the diffusivity is larger if there is more "free" volume in a structure (Dowty, 1980b Fortier and Giletti, 1989). The "free" volume in a structure is quantified by ionic porosity, defined as... 

Although the correlation between ionic porosity and diffusivity is imperfect, there is a rough trend that oxygen diffusivity in the minerals increases with increasing IP. The trend is useful in qualitative estimation of closure temperature (among other applications). Extending the relation to metallic systems, one prediction is that diffusion in face-centered cubic structure (25.95% free space) is slower that that in body-centered structure (31.98% free space) of the same metal composition. To avoid the issue of anisotropy, it would be worthwhile to reexamine the relations between diffusivity and ionic porosity using only isometric minerals. 

The dependence of diffusivity in silicate melts on composition is related to how melt structure (including degree of polymerization and ionic porosity) depends on composition. One the one hand, as Si02 concentration increases, the melt becomes more polymerized and the viscosity increases. Hence, diffusivity of most structural components, such as Si02 and AI2O3, decreases from basalt to rhyolite. On the other hand, as Si02 content increases, the ionic porosity increases. The increasing He diffusivity from basalt to rhyolite to silica, opposite to the viscosity... 

Table 3-2 Diffusion coefficients of noble gases in aqueous solutions Table 3-3 Ionic porosity of some minerals Table 4-1 Steps for phase transformations Table 4-2 Measured crystal growth rates of substances in their own melt...

Fortier and Giletti (1989) compared oxygen diffusion data from silicates reacted with H2O at 100 MPa with ionic porosities corrected for thermal expansion at 500 and 800°C. The straight-line fits to data at each temperature were reasonably good, from which they proposed an overall empirical equation that describes diffusion in select silicates at 100 MPa given as... 

Nordstrom DK, Munoz L (1985) Geochemical thermodynamics. Benjamin-Cumming Publ Co, London Nuccio P, Paonita A (2000) Investigation of the noble gas solubility in H2O-CO2 bearing silicate liquids at moderate pressure II the extended ionic porosity (EIP) model. Earth Planet Sci Lett 183 499-512 Ohsumi T, Horibe Y (1984) Diffusivity of He and Ar in deep-sea sediments. Earth Planet Sci Lett 70 61-68... 

Electrokinetic Transport in Soil Remediation, Table 1 Diffusion, ionic mobility, and effective ionic mobility for selected cationic and anionic species. Effective mobility was calculated for porosity n = 0.6 and tortuosity t = 0.35 [1]... 

Meade (1966) shows that claystones have a porosity decreasing to 0% at 1 Km depths and sandstones, 20% porosity at the same depth. Manheim (1970) shows that ionic diffusion rates in sediments are 1/2 to 1/20 that of free solutions when the sediments have porosities between 100 - 20%. It is evident that the burial of sediments creates a very different physical environment than that of sedimentation. As a result of reduced ionic mobility in the solutions, a different set of silicate-solution equilibria will most certainly come into effect with the onset of burial. The activity of ions in solution will become more dependent upon the chemistry of the silicates as porosity decreases and the system will change from one of perfectly mobile components in the open sea to one approaching a "closed" type where ionic activity in solution is entirely dictated by the mass of the material present in the sediment-fluid system. Although this description is probably not entirely valid even in rocks with measured zero porosity, for practical purposes, the pelitic or clayey sediments must certainly rapidly approach the situation of a closed system upon burial. 

Now, to explain the operation of the PFIEBR, it is proposed that the interdiffusion in the adhering liquid thin layer is the rate-determining step, then, it is possible to consider that n = 1 in Equation 7.33, since for this transport process the diffusion rate, k, is proportional to concentration [38], This approach is based on the assumption that states that the rate-determining process during the dynamic ionic exchange in zeolite columns determines the diffusion in the zeolite secondary porosity, that is, the transport process in the macro- and mesoporosities formed by the matrix inserted between zeolite crystals and the diffusion in the zeolite primary porosity, that is, in the cavities and channels which constitute the zeolite framework [38], This fact is experimentally justified later. With the help of Equations 7.33 through 7.35, we obtain ... 

Figure 3.5.13 (A) Equilibrium times for diffusion on macroscopic (1 mm) and nanoscopic (10 nm) length scales. (B) Illustration of ionic and electronic wiring, with hierarchical porosity as Li+ distribution network and a carbon second-phase e- distribution network. Reprinted from [58] with permission, copyright 2007 John Wiley Sons.

Polymerization of styrene in microemulsions has produced porous solid materials with interesting morphology and thermal properties. The morphology, porosity and thermal properties are affected by the type and concentration of surfactant and cosurfactant. The polymers obtained from anionic microemulsions exhibit Tg higher than normal polystyrene, whereas the polymers from nonionic microemulsions exhibit a lower Tg. This is due to the role of electrostatic interactions between the SDS ions and polystyrene. Transport properties of the polymers obtained from microemulsions were also determine. Gas phase permeability and diffusion coefficients of different gases in the polymers are reported. The polymers exhibit some ionic conductivity. 

Way, Noble and Bateman (49) review the historical development of immobilized liquid membranes and propose a number of structural and chemical guidelines for the selection of support materials. Structural factors to be considered include membrane geometry (to maximize surface area per unit volume), membrane thickness (<100 pm), porosity (>50 volume Z), mean pore size (<0.1)jm), pore size distribution (narrow) and tortuosity. The amount of liquid membrane phase available for transport In a membrane module Is proportional to membrane porosity, thickness and geometry. The length of the diffusion path, and therefore membrane productivity, is directly related to membrane thickness and tortuosity. The maximum operating pressure Is directly related to the minimum pore size and the ability of the liquid phase to wet the polymeric support material. Chemically the support must be Inert to all of the liquids which It encounters. Of course, final support selection also depends on the physical state of the mixture to be separated (liquid or gas), the chemical nature of the components to be separated (inert, ionic, polar, dispersive, etc.) as well as the operating conditions of the separation process (temperature and pressure). The discussions in this chapter by Way, Noble and Bateman should be applicable the development of immobilized or supported gas membranes (50). 

Concentration gradients can exist within the resin pore structure. Ion diffusion is complex since the resin porosity is low and this leads to steric hindrance effects and tortuous diffusion paths. Also, ion diffusion is coupled to the fixed ionic groups and the mobility of each ion within the resin due to charge balance. This coupled diffusion is present in both boundary layer and pore transport. Also, the forward and reverse rates of ion exchange can be affected by the different mobilities of the ions. 

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