Penetrant molecules permeate

Three factors play key roles in determining the relative permeabilities of different polymers to a given penetrant molecule permeating by the solution-diffusion mechanism. The "free volume" available for molecule to traverse the polymer plays a major role, especially in the diffusivity. The cohesive forces between the polymer chains (i.e., how tightly the chains are held together) are also crucial. Finally, the solubility can be affected very significantly by the strength of the interactions between the penetrant molecule and the structural units in the polymer chains, i.e., by the "compatibility" of the polymer and the penetrant with each other. 

Diffusion of small molecular penetrants in polymers often assumes Fickian characteristics at temperatures above Tg of the system. As such, classical diffusion theory is sufficient for describing the mass transport, and a mutual diffusion coefficient can be determined unambiguously by sorption and permeation methods. For a penetrant molecule of a size comparable to that of the monomeric unit of a polymer, diffusion requires cooperative movement of several monomeric units. The mobility of the polymer chains thus controls the rate of diffusion, and factors affecting the chain mobility will also influence the diffusion coefficient. The key factors here are temperature and concentration. Increasing temperature enhances the Brownian motion of the polymer segments the effect is to weaken the interaction between chains and thus increase the interchain distance. A similar effect can be expected upon the addition of a small molecular penetrant. 

Permeation (and absorption) are both conditions that only apply when the penetrating molecule is much smaller than the molecules of the wall material. A molecule of any size can be involved in adsorption. 

Until now we have considered the simplest case of more or less ideal permeation behaviour Henry s law for sorption (sorbed penetrant randomly dispersed within the polymer) and Fick s first law for diffusion (diffusion coefficient independent of the concentration of the sorbed penetrant). This ideal behaviour is observed in practice only when "permanent gases" are the penetrants and if the gas pressure is nearly atmospheric. In this case there are no strong polymer-penetrant interactions and no specific interactions between the penetrant molecules. 

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 free aperture of the main 100 channels in Y-type zeolite is 0.74 nm [7] and is much larger than the diameter of CO2 and N2 molecules. If the concentrations of CO2 and N2 in the micropores of the Y-type zeolite membrane are equal to those in the outside gas phase, these molecules permeate through the membrane at a low CO2/N2 selectivity. However, this was not the case. Carbon dioxide molecules adsorbed on the outside of the membrane migrate into micropores by surface diffusion. Nitrogen molecules, which are not adsorptive, penetrate into micropores by translation-collision mechanism from the outside gas phase. 

The stationary phase consists of materials with different pore sizes and the molecules permeate the phase as they elute. The mobile phase solely serves as a carrier for the analyte as it does not induce any chemical interaction. In SEC, small molecules penetrate the porous structure more easily than large... 

Ep Activation energy for permeation of small penetrant molecules through polymers. 

Permeation of small molecules through polymers usually occurs by the solution-diffusion mechanism, which has two key steps. The penetrant molecule is first "sorbed" by the polymer, i.e., dissolves in the polymer. It then crosses the specimen by a succession of diffusive "jumps". P is therefore equal to the product of the diffusivity (or diffusion coefficient) D and solubility S ... 

The principle of microscopic reversibility states that a given penetrant molecule is equally likely to make a diffusive jump towards either surface of a specimen at any given instant. A net diffusion and thus permeation of molecules from one surface to the other surface only occurs if... 

The sizes and shapes of the penetrant molecules, and their solubilities, are the key properties determining their relative permeabilities in a given polymer, i.e., the selectivities of polymers between them, when permeation occurs by the solution-diffusion mechanism. For example, the activation energy for diffusion typically increases with increasing size of penetrant molecules of identical shape permeating through a given polymer. 

Copolymers of vinylidene chloride and vinyl chloride have been used as test cases. Permeation of penetrant molecules is generally believed to occur through the amorphous regions of these semicrystalline polymers. Their study is, however, complicated by the necessity to understand the effects of the presence of the crystallites in addition to the amorphous regions. 

Small molecules can penetrate and permeate through polymers. Beeause of this property, polymers have found widespread use in separation technology, protection coating, and controlled delivery [53]. The key issue in these applications is the selective permeability of the polymer, which is determined by the diffusivity and the solubility of a given set of low-molecular-weight compounds. The diffusion of a small penetrant oeeiu s as a series of jitmps... 

As with the predictions of mechanical behavior, predictions of permeability by different models require additional experimental verification to determine the limitations of the expressions proposed. Another interesting point—and one which complicates the quantitative application of permeability expressions— is the possible role of filler-polymer interactions (see also Section 12.3). The mechanism of permeation in polymers is believed to depend upon the ability of segments to move in such a way as to create a hole which can accommodate a penetrant molecule. Thus any restriction or enhancement of mobility would be expected to alter the permeability (Crank and Park, 1969), just as such effects are known to alter the relaxation behavior and hence the glass temperature of a polymer. 

The Nielsen model has been a popular theory, originally used to explain polymer lay nanocomposites. This model is used to describe the tortuosity effect of plate-like particulates of filled rubber polymer composite on the gas permeation. An increase in barrier properties of gas permeation of rubber polymer nanocomposites is a result of the impermeable nature of filler particles which creates a long path of penetrant molecule by directing them around the particle. 

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 most important characteristic of membranes is their ability to separate different chemical species in view of the different permeation rate they can reach across the selective layer. The different penetrant rates are obtained on the basis of their kinetics, their thermodynamic properties, and the interactions established with the membrane matrix. The driving force of the process is the concentration gradient and, as shown in Fig. 7.1, when this is established across the membrane, the penetrant molecules start to move from the high to the low concentration side according to their ability to diffuse within the matrix. In this view, the thickness of the selective layer also plays a relevant role for the determination of the penetrant flux, because the thinner the layer the lower the distance that must be covered by the molecules within the membrane matrix and the larger the permeation rate. 

In addition to the solution-diffusion mechanism, which is based only on physical interactions between the polymeric layer and the penetrant molecules, a reaction-based mechanism has been proposed when moieties with specific reactivity toward a target component are present within the membrane matrix, called the facilitated transport mechanism. High performances in terms of permeability and selectivity can be achieved in this case because the permeation of the target compound can count on a physical and chemical contribution, whereas all of the other penetrants diffuse through the matrix only because of the physical solution-diffusion contribution. An example of this mechanism is reported in Fig. 7.11 for the case of amine-based polymeric membranes in CO2 separation applications. 

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