Solution diffusion mechanism

Ultrafiltration separations range from ca 1 to 100 nm. Above ca 50 nm, the process is often known as microfiltration. Transport through ultrafiltration and microfiltration membranes is described by pore-flow models. Below ca 2 nm, interactions between the membrane material and the solute and solvent become significant. That process, called reverse osmosis or hyperfiltration, is best described by solution—diffusion mechanisms. 

Basic Principles of Operation RO and NF are pressure-driven processes where the solvent is forced through the membrane by pressure, and the undesired coproducts frequently pass through the membrane by diffusion. The major processes are rate processes, and the relative rates of solvent and sohite passage determine the quality of the product. The general consensus is that the solution-diffusion mechanism describes the fundamental mechanism of RO membranes, but a minority disagrees. Fortunately, the equations presented below describe the obseiwed phenomena and predict experimental outcomes regardless of mechanism. 

Some of the polymeric membranes are suitable for bulk separation of hydrogen from impurities to enrich a dilute hydrogen stream. Dense polymers permeate gases by solution diffusion mechanism. The permeation rate of a gas species through a polymer membrane... 

In pulsed vacuum immersion, a phenomenological model would be difficult to develop as solution filtration and solute diffusion mechanisms have to be considered. The main problem to be solved concerning this aspect... 

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. 

Transport through the membrane can be considered to occur by a solution-diffusion mechanism under the influence of a chemical potential driving force [48, 49]. The primary benefit of using PV systems is that they are essentially independent of the vapor-liquid equihbrium of solvent mixtures. Therefore PV can be used to overcome the separation barriers created by many azeotropic mixtures [48, 50]. 

Additionally in pervaporation separation follows the solution-diffusion mechanism. Therefore the molecular size of the permeating molecules becomes very important to characterize the permeation behavior [43], It is known that acetic acid has larger molecular size (0.40 nm) than water molecules (0.28 nm). As the amount of acetic acid increases in the feed mixture it becomes difficult for acetic acid molecules to diffuse through the less swollen membrane, so separation factor increases at high acid concentrations. 

Figure 2.1 Molecular transport through membranes can be described by a flow through permanent pores or by the solution-diffusion mechanism...

The second assumption concerns the pressure and concentration gradients in the membrane. The solution-diffusion model assumes that when pressure is applied across a dense membrane, the pressure throughout the membrane is constant at the highest value. This assumes, in effect, that solution-diffusion membranes transmit pressure in the same way as liquids. Consequently, the solution-diffusion model assumes that the pressure within a membrane is uniform and that the chemical potential gradient across the membrane is expressed only as a concentration gradient [5,10]. The consequences of these two assumptions are illustrated in Figure 2.5, which shows pressure-driven permeation of a one-component solution through a membrane by the solution-diffusion mechanism. 

Although these microporous membranes are topics of considerable research interest, all current commercial gas separations are based on the dense polymer membrane shown in Figure 8.2. Separation through dense polymer films occurs by a solution-diffusion mechanism. 

The most important characteristic of nonporous membranes is that they are hydrophobic and contain no pores in the polymeric structure. This means that these membranes not only selectively act as a barrier to particles and polar species, but they also provide unique selectivity and specificity for the permeation and transport of a specific group of compounds that can readily solubilize and diffuse in the membrane material. The analyte extraction rate (permeability) in a nonporous membrane separation process is governed by the solution-diffusion mechanism, as commented on earlier. 

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. 

Thus, we can use Equation 4.3 as representative of the solution-diffusion mechanism where S and D may not be constants but depend on the external conditions in the gas phases. With this in mind for a pair of gases A and B, we can construct the following useful relationship... 

Micro-ultrafiltration and reverse osmosis are mature technologies for separations based on molecular exclusion and solution-diffusion mechanisms, respectively. Cleaning and maintenance procedures able to control fouling to an acceptable extent have made these processes commercially suitable. 

Membrane-reservoir systems based on solution-diffusion mechanism have been utilized in different forms for the controlled delivery of therapeutic agents. These systems including membrane devices, microcapsules, liposomes, and hollow fibres have been applied to a number of areas ranging from birth control, transdermal delivery, to cancer therapy. Various polymeric materials including silicone rubber, ethylene vinylacetate copolymers, polyurethanes, and hydrogels have been employed in the fabrication of such membrane-reservoir systems (13). 

Such an osmotic delivery system is capable of providing not only a prolonged zero-order release but also a delivery rate much higher than that achievable by the solution-diffusion mechanism. 

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). 

Hydrogen separation through a Pd-based him takes place via a solution-diffusion mechanism. Then, the equation for the hydrogen flux is written in terms of Sievert s law [33,34] (see Figure 5.11)... 

Table 4.2 Polymers used for fabrication of reservoir systems Polymers providing solution-diffusion mechanism...

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... 

In the latter case (nonporous membrane), the space in which the transport occurs is not fixed in size and location. The free volume is the volume that is not occupied by the polymer molecules in the solid phase, and its size and location fluctuate with time at a given temperature. Accordingly, the transport through such a membrane is completely different from the transport through fixed pores, and can be expressed by the solution-diffusion mechanism. The permeant is first dissolved in the membrane phase, and the dissolved permeant diffuses through the membrane following the chemical potential gradient. 

Liquid water on one side of a silicone contact lens permeates through the lens by a solution-diffusion mechanism and evaporates on the other side quickly according to the permeability of water, whereas the solubility of water in silicone polymer is low [1]. The high water vapor permeability was speculated to be one of the reasons causing the suction cup effect that makes the lens stationary on one spot and tenaciously stick to the cornea this may damage the corneal epithelium and result in other complications. However, the high permeability per se cannot be the reason for the suction cup effect if the exterior surface is covered by the tear film, i.e., if there is no driving force for water permeation. 

Membrane catalysts are structures with permeable walls between passages. The membrane walls exhibit selectivity in transport rates for the various components present. A slow radial mass transport can occur, driven by diffusion or solution/ diffusion mechanisms in the permeable walls. 

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