Solubility-diffusion mechanism transport

In dense membranes, no pore space is available for diffusion. Transport in these membranes is achieved by the solution diffusion mechanism. Gases are to a certain extent soluble in the membrane matrix and dissolve. Due to a concentration gradient the dissolved species diffuses through the matrix. Due to differences in solubility and diffusivity of gases in the membrane, separation occurs. The selectivities of these separations can be very high, but the permeability is typically quite low, in comparison to that in porous membranes, primarily due to the low values of diffusion coefficients in the solid membrane phase. 

As explained in Chapter 5, the transport mechanism in dense crystalline materials is generally made up of incessant displacements of mobile atoms because of the so-called vacancy or interstitial mechanisms. In this sense, the solution-diffusion mechanism is the most commonly used physical model to describe gas transport through dense membranes. The solution-diffusion separation mechanism is based on both solubility and mobility of one species in an effective solid barrier [23-25], This mechanism can be described as follows first, a gas molecule is adsorbed, and in some cases dissociated, on the surface of one side of the membrane, it then dissolves in the membrane material, and thereafter diffuses through the membrane. Finally, in some cases it is associated and desorbs, and in other cases, it only desorbs on the other side of the membrane. For example, for hydrogen transport through a dense metal such as Pd, the H2 molecule has to split up after adsorption, and, thereafter, recombine after diffusing through the membrane on the other side (see Section 5.6.1). 

Transport through nonporous membranes follows the solution-diffusion mechanism, and separation is achieved either by differences in solubility or diffusivity. Therefore,... 

In this equation, the first term on the right-hand side is the flux contributed by the solution-diffusion mechanism, while the second term is due to the facilitated transport mechanism. The nonreacting gases, like H2, N2, and CO, do not have chemical association with carriers and therefore can only be transported by diffusion, which is limited by their low solubility in the highly polar sites in the membranes.16... 

POLYMER MEMBRANES. The transport of gases through dense (nonporous) polymer membranes occurs by a solution-diffusion mechanism. The gas dissolves in the polymer at the high-pressure side of the membranes, diffuses through the polymer phase, and desorbs or evaporates at the low-pressure side. The rate of mass transfer depends on the concentration gradient in the membrane, which is proportional to the pressure gradient across the membrane if the solubility is proportional to the pressure. Typical gradients for a binary mixture are shown in Fig. 26.2. Henry s law is assumed to apply for each gas, and equilibrium is assumed... 

Pervaporation, vapor permeation and gas permeation are very closely related processes. In aU three cases the driving force for the transport of matter through the membrane is a gradient in the chemical potential that can best be described by a gradient in partial vapor pressure of the components. The separation is governed by the physical-chemical affinity between the membrane material and the species to be passed through and thus by sorption and solubility phenomena. The transport through the membrane is affected by diffusion and the differences in the diffiisivities of the different components in the membrane can play an important role for the separation efficiency, too. All three processes are best described by the solution-diffusion mechanism , their main differences are determined by the phase state and the thermodynamic conditions of the feed mixture and the condensability of the permeate. 

For diffusion of liquid through rubbery polymer composites, Fickian and non-Fickian diffusion theories are frequently used to describe the mechanism of transport, but for gas or vapour, other models have been developed to fit experimental data of diffusion profiles. The models of gas transport include Maxwell s model," free volume increase mechanism," solubility increase mechanism," nanogap hypothesis," Nielsen model, " " Bharadwaj model, ° Cussler model " " and Gusev and Lusti model, " etc. 

Gas transport in nonporous polymer membranes typically proceeds by a solution-diffusion mechanism in which the permeability (P) is given by. xD, where S and D denote the solubility and diffusivity of the permeating species, respectively. The solubility provides a measure of interaction between the polymer matrix and penetrant molecules, whereas the diffusivity describes molecule mobility, which is normally governed by the size of the penetrant molecule as it winds its way through the permanent and transient voids afforded by the free volume of the membrane [42], Therefore gas transport has to be strongly dependent on the amount of free volume in the polymer matrix. 

The transport can be described by solution-diffusion mechanism and the selectivity is determined by selective sorption and/or selective diffusion. The permeability (P) of a specific compound i from a mixture i, j can be expressed as a function of the diffusivity (D) and solubility (5), which are strongly dependent on the feed composition. 

Nonporous membranes are used to perform separations on a molecular level. However, rather than molecular weight or molecular size, the chemical nature and morphology of the polymeric membrane and the extent of interaction between the polymer and the permeants are the important factors to consider. Transport through nonporous membranes occurs by a solution-diffusion mechanism and separation is achieved ei er by differences in solubility and/or diffusivity. Hence such membranes cannot be characterised by the methods described in the previous section, where the techniques involved mainly characterised the pore size and pore size distribution in the membranes. The determination of the physical properties related to the chemical structure is now more important and in this respect the following methods will be described ... 

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