Kinetic diameters, penetrants

The permeability of polymers decreases with the increase in their glass transition temperature. This dependence becomes more pronounced with increasing kinetic diameter of penetrant molecules (Figure 9.9). 

FIGURE 9.14 Dependence of the diffusion activation energy of carbon dioxide, methane, and propane in organosihcon polymers on the kinetic diameter of the penetrant molecules (designations of polymers are the same as in Figure 9.9). (From analysis of results presented in Semenova, S.I., J. Membr. Sci., 231, 189, 2004. With permission.)... 

Figure 6. Correlation of the average diffusion coefficient, D, and the kinetic diameters of several penetrants in a number of glassy polymers at 35 °C for an upstream penetrant pressure of 20 atm polycarbonate,...

Another problem that is still under discussion concerns the size of the guest molecule. Researchers mostly use the kinetic diameters for guidance (see Table 2.22). However, it has been remarked (574,580) that the kinetic diameter is not the best criterion for the molecular dimension. The flexibility and the shape of the molecule in relation to the shape of the pore openings should be taken into account. Consideration of these properties explains some results that indicated penetration of relatively large molecules into smaller pores. Armaroh et al. (331) observed differing behavior of m-xylene and 2,6-lutidine (similar in size) in accessing the ZSM-5 pores and su ested that chemical effects also play a role for accessibihty. 

Figure 5. Relative permeability of HIQ-40 to several gases and acetone at 35 C (24), The numbers in parentheses are the penetrant kinetic diameters.

It is known that glassy polymer membranes can have a considerable size-sieving character, reflected mainly in the diffusive term of the transport equation. Many studies have therefore attempted to correlate the diffusion coefficient and the membrane permeability with the size of the penetrant molecules, for instance expressed in terms of the kinetic diameter, Lennard-Jones diameter or critical volume [40]. Since the transport takes place through the available free volume in the material, a correlation between the free volume fraction and transport properties should also exist. Through the years, authors have proposed different equations to correlate transport and FFV, starting with the historical model of Cohen and Turnbull for self diffusion [41], later adapted by Fujita for polymer systans [42]. Park and Paul adopted a somewhat simpler form of this equation to correlate the permeability coefficient with fractional free volume [43] ... 

The window apertures quoted here are the free diameters calculated from structural models assuming a diameter of 1.4 A for the oxygens. Due to the effects of vibration of both the diffusing molecule and the crystal lattice, these windows may be penetrated by molecules with critical kinetic diameters which are somewhat greater than the nominal aperture. The effective diameters of the unobstructed 8-, 10-, and 12-ring sieves are therefore approximately 4.5, 6.0, and 8.5 A. 

In equations 9 and 10, de and dA are the kinetic diameters of the larger and smaller penetrants, respectively. The parameters a and b in equation 11 are from the linear free energy relation between activation energy of diffiision,, and, the front... 

The kinetic diameter of penetrant molecules used in the gas permeation study are of the order CO2 (3.3 A) < CO (3.76 A) < CH4 (3.8 A). The selectivities of pure PDMS 2vol% Au/PDMS 3 vol% Au/PDMS are reported in Table. 1. As expected the pure polymer shows permeation to gas molecules in the order of their kinetic diameter, i.e., selectivity is based on the size exclusion of gas molecules or diffusion selective. Thus CO2 is more permeable in pure polymer and the selectivity of CH4 and CO is close to unity, which shows they are equally permeable. But when the filler loading of 2 3 vol% of Au NPs in PDMS, there is a reverse selective phenomenon of CO2, i.e., now CO2 is less permeable compared to higher kinetic diameter counterparts CO CH4. This could be CO2 has a quadrupole moment and the inter-connectivity of free volume elements enabled by Au NPS must have restricted CO2 movement. Also CO2 is expected to be more soluble in polymer with polar group, but the interaction of PDMS and Au NPs could have reduced the polarity of hybrid membrane. 

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