Penetrant size

In addition to temperature and concentration, diffusion in polymers can be influenced by the penetrant size, polymer molecular weight, and polymer morphology factors such as crystallinity and cross-linking density. These factors render the prediction of the penetrant diffusion coefficient a rather complex task. However, in simpler systems such as non-cross-linked amorphous polymers, theories have been developed to predict the mutual diffusion coefficient with various degrees of success [12-19], Among these, the most notable are the free volume theories [12,17], In the following subsection, these free volume based theories are introduced to illustrate the principles involved. 

For the period from around 1840 to the early 1970s paper was usually made in an acidic environment at pHs of around 4-5. This was because many grades required the use of rosin and aluminium sulfate for the control of water penetration (sizing), and solutions of aluminium sulfate exhibit a pH of around 4.5. Aluminium sulfate has also been popular with paper makers because it assists the flocculation of colloidal particles and therefore behaves as a mildly... 

TABLE II Characteristic Penetrant Size (Diameter) Spectrum for Nonpermeating Species... 

For many years, molecular orientation and crystallinity have been observed to improve the barrier properties of polymers (1-3). In extreme cases, drawing of semicrystalline polymers has been shown to reduce permeability by as much as two orders of magnitude. A crude understanding of the dependence of the transport parameters on penetrant size and chain packing can be... 

It is probably a function of both effective crystal surface area and penetrant size. It was noted, however, that the concept of chain immobilization loses its significance as the rigidity of the polymer backbone increases (22.). ... 

A few final remarks are necessary concerning the dependence of D and of the experimental activation energy Ea for diffusion on penetrant size. Some experimental results [29-31] on PVC and on rubbery polymers suggest that, contrary to the arguments made and the references provided in the discussion above, D may sometimes decrease less rapidly, and Ea may sometimes increase less rapidly, with increasing penetrant size. Three possible sources can be identified for such apparent discrepancies ... 

The difference in dimensions between molecular diameter (d), cross-sectional area (proportional to d ), and van der Waals (vdW) volume (proportional to d ), each one of which has been used as an indicator of penetrant size by different authors. For example, if the rate of increase of Ea were proportional to the cross-sectional area of the penetrant, Ea would increase much faster than linearly if plotted against d, but much slower than linearly if plotted against the vdW volume. 

Thermodynamics of Solubility Mathematics of Diffusion Factors Affecting Solubility and Transport Crystallinity, Fillers, and Morphology Temperature and Transitions Penetrant Size... 

Figure 6. Effect of penetrant size, expresssed as van der Waals volume, on diffusion coefficient in poly(vinyl chloride) at 30 °C. (Reproduced with permission from Reference 20.)...

The latter was recently further elaborated by Rowe et al. in order to correlate permeability directly to o-Ps lifetime from PALS analysis [44]. Freeman discussed the physical basis for the Robeson upper bound, closely related to the fractional free volume and to penetrant size ratio [45]. 

In the present work the van der Waals volumes were calculated as a measure of the penetrant size. The values of the different vapour species are listed in Table 4.4. The... 

CO2 separation by using a membrane prepared from a rubbery polymer is based on high solubility selectivity, while diffusivity selectivity should be maintained or even increased. The CO2/H2 permselectivity is increased (due to the inaeased EO units), which is a consequence of solubility selectivity increase. The strategy of increasing the solubility plays an important role, because of the unfavourable diffusivity selectivity. Incorporation of PEG increases the permselectivity of the pair CO2/H2 to 13. However, the CO2/N2 and CO2/CH4 permselectivities are maintained almost constant due to the similar penetrants size. 

Aerosol removal processes that oceur when a bubble rises through a suppression pool vary in efficiency with particle size. As with sprays, very fine and very large particles are efficiently removed. There is a partiele size that is minimally affeeted by the deeontamination processes. Aerosols that emerge from a suppression pool have sizes narrowly distributed around the minimally affected particle size (also called the maximum penetration size). These residual aerosols also resist removal by many other deeontamination proeesses so they can be quite persistent in the atmosphere. 

The diffusion and permeabihty are closely interconnected with the solubility of a polymer. The permeation of the permeants through polymeric membrane film occurs in three stages (1) Sorption includes the initial adsorption, absorption, penetration, and dispersal of penetrant into the voids of the polymer membrane surface and cluster formation. The distribution of permeant in the membrane may depend on penetrant size, concentration, temperature, and swelling of the matrix as well as on time. The extent to which permeant molecules are sorbed and their mode of sorption in the polymer depends upon the enthalpy and entropy of permeant-polymer mixing, i.e., upon the activity of the permeant within the polymer at equilibrium. When both polymer-permeant and permeant-permeant interactions are weak relative to polymer-polymer interactions, i.e., dilute solution occurs, Henry s law is obeyed. The solubihty coefficient S is a constant independent of sorbed concentration at a given temperature. (2) Diffusion includes the transfer of the penetrant through the polymer membrane which depends on penetrant concentration that leads to a plasticization effect, penetrant size and shape, polymer Tg, time, and temperature. The diffusion coefficient is determined by Pick s first law of diffusion. (3) Desorption includes release of the penetrant from the opposite side of the membrane face. 

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