## Optimization of Polymer Permeation Properties

Table 1 illustrates the range of oxygen permeability and oxygen/nitrogen permselectivity for some

Table 3 Structure-property relationships in polymer membranes

Polymer

Structure

PMDA-ODA

PMDA-mDA

PMDA-IPA

6FDA-ODA

6FDA-mDA

6FDA-IPA

DMPSF

TMPSF

common polymers. Permeability spans a wide range: seven orders of magnitude. Further, as the permeability of polymers increases, their ability to differentiate between gases, the permselectivity, decreases. This correlation is valid for nearly all polymeric membranes and has been the subject of research. While long recognized, this observation was first formalized by Robeson in 1991. Working with a database of over 200 polymers, the selectivity of several gas pairs, plotted on a log-log scale against the permeability of the faster gas, exhibits a characteristic upper bound defining the combinations of permeability and perm-selectivity simultaneously achievable with polymeric materials (Figure 7). Upper bound performance can be described by eqn [9]:

where the values of k and n, tabulated in Table 2, are calculated from the upper bound relationship for specific gas pairs. The parameter n is related to the difference in kinetic diameters of the penetrant gas pair Adj as shown in Figure 8. This empirical treatment implies that the upper bound is a natural result of the sieving characteristic of stiff chain glassy polymers. A fundamental theory was later developed by Freeman in which the constants could be related to gas size and gas condensability and invoked just a single adjustable parameter f:

ln a„ = - X„ ln D# + {ln (S,/S,) — jb -f(1- a)/RT)}

where Xj = [(d,/d;)2 — 1] and d{ is the kinetic diameter; S/Sj = N(s/k — £j/k), where k is the Boltzmann constant and s is the potential energy well depth in the Lennard-Jones potential energy function. The constants a and b are derived from linear free energy relationships and are independent of gas type. Moreover a is independent of polymer and has a universal value of 0.64; b has a value of 11.5 for glassy polymers and 9.2 for rubbery polymers. The solubility selectivity among polymers is largely constant; consequently diffusivity considerations dominate upper bound permselectivity.

The optimization of polymer structure to obtain upper bound properties comprises the lion's share of polymer membrane research in the last 20 years and the reader is referred to the Further Reading section. Researchers have heuristically developed the understanding gained via the upper bound analysis. The permselectivity for gases i and j is given by eqns [4] and [5] as:

Groups are defined volume of atoms within shaded areas 1000

i 10

0J LUXJjjjjJLJ^UJJJJJJJJ^JJJ^^

34-56 789 10 11

Groups are defined by volume of atoms between lines

Groups are defined by volume of atoms between lines

(B) barrers experimental

Figure 10 Structure-property relationship: (A) FFV model (Paul). (B) Robeson model.

(B) barrers experimental

Figure 10 Structure-property relationship: (A) FFV model (Paul). (B) Robeson model.

The solubility selectivity (S,/S;) is nearly constant across a wide variety of polymers and for O2/N2 is about 2. Selectivity in glassy polymers is therefore dominated by the diffusive selectivity which in turn results from the sieving properties of the imperfectly packed polymer chains. The best trade-off in permeability properties within a polymer family is obtained when both main chain mobility is limited and intersegmental packing of polymer chains is

i 10

Figure 12 Cross-section of an asymmetric membrane.

inhibited. This behaviour is illustrated (Table 3) for a family of pyromellitic dianhydride (PMDA) and hexafiuoro-isopropylidene dianhydride (6FDA)-based polyimides. Changes in the functionality lead to different packing arrangements as measured by density and X-ray d-spacings (average distance between polymer chains). Very small changes in chain packing result in significant changes in both permeability and selectivity. Further, groups such as 6FDA are particularly desired because they can increase permeability without a large loss of selectivity. A further example is that of ortho, di- versus tetra-substitution patterns on aromatic polymers. It is widely recognized that incorporation of bulky substituents leads to an increase in permeability, usually at a loss of selectivity. However, it is also noted that ortho di-substitution patterns result in lower permeability and higher selectivity than the symmetrically tetra-substituted analogue. Using this intuitive approach a great many new polymers were synthesized and characterized between 1990 and 1993 and as a result the empirically determined upper bound has been shifted upperwards and its slope has changed (Figure 9), with many polymers lying at or near the upper bound.

## Solar Panel Basics

Global warming is a huge problem which will significantly affect every country in the world. Many people all over the world are trying to do whatever they can to help combat the effects of global warming. One of the ways that people can fight global warming is to reduce their dependence on non-renewable energy sources like oil and petroleum based products.

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