Permeation and diffusion

Diffusion, however, is only one part of permeation. First, the permeating substance has to infiltrate the surface of the membrane it has to be absorbed by the membrane. Similarly, the permeating substance has to be desorbed on the opposite side of the membrane. Combining eqn. (2.110) and (2.111), we can calculate the sorption equilibrium using 

Equation (2.113) does not take into account the influence of pressure on the permeability of the material and is only valid for dilute solutions. The Henry-Langmuir model takes into account the influence of pressure and works very well for amorphous thermoplastics. It is written as 

In the case of multi-layered films commonly used as packaging material, we can calculate the permeation coefficient PC for the composite membrane using 

Sorption, diffusion, and permeation are processes activated by heat and, as expected, follow an Arrhenius type behavior. Thus, we can write 

The diffusion activation energy ED depends on the temperature, the size of the gas molecule d, and the glass transition temperature of the polymer. This relationship is well represented in Fig. 2.61 [62] with the size of nitrogen molecules, d 2 as a reference. Table 2.17 contains values of the effective cross section size of important gas molecules. 

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Diffusion and Permeation Testing 23.4.4.1 Kinetics of Liquid Diffusion Tests... 

Mitragotri, S., Johnson, M. E., Blankschtein, D. and Langer, R. (1999). An analysis of size selectivity of solute partitioning, diffusion, and permeation across lipid bilayers, Biophys. J., 77, 1268-1283. 

Because no single homogeneous phase could fulfill these conflicting needs simultaneously, CLs require composite morphologies that consist of several interpenefrafing phases. A minimum of fwo distinct phases is needed, including a solid phase of nanoparticle catalyst (Pt) and electronically conducting substrate (carbon) and a liquid water phase in the void spaces of the substrate for diffusion and permeation of protons, water, and reactant molecules. 

In order to predict correctly the fluxes of multicomponent mixtures in porous membranes, simplified models based solely on Fields law should be used with care [28]. Often, combinations of several mechanisms control the fluxes, and more sophisticated models are required. A well-known example is the Dusty Gas Model which takes into account contributions of molecular diffusion, Knudsen diffusion, and permeation [29]. This model describes the coupled fluxes of N gaseous components, Ji, as a function of the pressure and total pressure gradients with the following equation ... 

The second gas law states that there cannot be unequally distributed partial pressures in any system. Thus, the greater the vacuum, the greater the rate of desorption, diffusion, and permeation to overcome the differences in concentration as nature abhorring a vacuum tries to equalize the system. 

Rogers, C. E., V. Stannett and M. Szwarc The sorption, diffusion, and permeation of organic vapors in polyethylene. J. Polymer Sci. 45, 61 (I960). 

Finally, even the activation energies of diffusion and permeation can be estimated in this way, as was already quantitatively described by the relationship Ed oc a1. We may conclude that if two of the three quantities D, S and P are known (or can be estimated) for nitrogen in a given polymer, those for the other gases can be estimated very quickly and rather accurately. 

The constitutive equations of transport in porous media comprise both physical properties of components and pairs of components and simplifying assumptions about the geometrical characteristics of the porous medium. Two advanced effective-scale (i.e., space-averaged) models are commonly applied for description of combined bulk diffusion, Knudsen diffusion and permeation transport of multicomponent gas mixtures—Mean Transport-Pore Model (MTPM)—and Dusty Gas Model (DGM) cf. Mason and Malinauskas (1983), Schneider and Gelbin (1984), and Krishna and Wesseling (1997). The molar flux intensity of the z th component A) is the sum of the diffusion Nc- and permeation N contributions,... 

Shan, C. et al.. Behaviour of diffusion and permeation of tritium through 316L stainless steel with coating of TiC and TiN -i- TiC, Journal of Nuclear Materials, 191-194, 221 (1992). 

The temperature dependence of the polarographic current is deduced from that of the oxygen diffusion and permeation coefficients and of the oxygen solubility in the membrane and media. With increasing temperature the polarographic current rises and the response time becomes shorter. 

A theory of gas diffusion and permeation has recently been proposed [56] for the interpretation of experimental data concerning molecular-sieve porous glass membranes. Other researchers [57,58], on the basis of experimental evidences, pointed out that a Stefan-Maxwell approach has to be preferred over a simple Pick one for the modeling of mass transfer through zeolite membranes. 

Nominating a beneficial conceptual pore structure like that in Fig. 30 does not immediately tell us how it could be achieved. However, this nested pore networks in networks concept gives a strong incentive to seek fabrication procedures that will deliver nonrandom structured pore designs, tailored to combine diffusion and permeation to improve catalyst particle reactivity. 

The models most frequently used to describe the concentration dependence of diffusion and permeability coefficients of gases and vapors, including hydrocarbons, are transport model of dual-mode sorption (which is usually used to describe diffusion and permeation in polymer glasses) as well as its various modifications molecular models analyzing the relation of diffusion coefficients to the movement of penetrant molecules and the effect of intermolecular forces on these processes and free volume models describing the relation of diffusion coefficients and fractional free volume of the system. Molecular models and free volume models are commonly used to describe diffusion in rubbery polymers. However, some versions of these models that fall into both classification groups have been used for both mbbery and glassy polymers. These are the models by Pace-Datyner and Duda-Vrentas [7,29,30]. 

The aim of this study is to eompare pore structure characteristics of two industrial catalysts determined by standard methods of textural analysis (physical adsorption of nitrogen and mercury porosimetry) and selected methods for obtaining parameters relevant to transport processes (multicomponent diffusion and permeation of gases). 

The Mean Transport Pore Model (MTPM) described diffusion and permeation the model (represented as a boundary value problem for a set of ordinary differential equations) are based on Maxwell-Stefan diffusion equation and Weber permeation law. Parameters of MTPM are material constants of the porous solid and, thus, do not dependent on conditions under which the transport proeesses take place. 

Both catalysts were mono- or bidispersed with mean pore radii about 70 and 2000 run diffusion and permeation measurements were performed with four inert gases (H2, He, N2 and Ar). 

The relevance of the second approach stems from the possibility to use the same pore-structure model as used in description of the process in question (counter-current (isobaric) diffusion of simple gases, permeation of simple gases under steady-state or dynamic conditions, combined diffusion and permeation of gases under dynamic conditions, etc.). 

Today two models are available for description of combined (diffusion and permeation) transport of multicomponent gas mixtures the Mean Transport-Pore Model (MTPM)[21,22] and the Dusty Gas Model (DGM)[23,24]. Both models enable in future to connect multicomponent process simultaneously with process as catalytic reaction, gas-solid reaction or adsorption to porous medium. These models are based on the modified Stefan-Maxwell description of multicomponent diffusion in pores and on Darcy (DGM) or Weber (MTPM) equation for permeation. For mass transport due to composition differences (i.e. pure diffusion) both models are represented by an identical set of differential equation with two parameters (transport parameters) which characterise the pore structure. Because both models drastically simplify the real pore structure the transport parameters have to be determined experimentally. 

Two non-standard transport processes (counter-current isobaric ternary diffusion and permeation of simple gases were chosen for obtaining pore-structure transport characteristics. MTPM was used for evaluation of transport parameters. 

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