Upper-bound line

The upper-bound line connects discontinuous points, but polymers exist near the bound for separations of interest. Whether these be available as membranes is a different matter. A useful membrane requires a polymer which can be fabricated into a device having an active layer around 50 nm thick. At this thickness, membrane properties may vary significantly from bulk properties, although not by a factor of 2. 

Robeson [/. Membrane Sci., 62, 165 (1991) Polymer, 35, 4970 (1994)] has determined upper-bound lines for many permeant pairs in hundreds of polymers. These lines may be drawn from Eq. (20-97) and the data included in Table 20-31. These values will give pj in... 

Figure 8.3 Oxygen/nitrogen selectivity as a function of oxygen permeability. The upper-bound line represents the point above which no better membranes are known [12]. This line shows the trade-off relationship between membrane permeability and selectivity.

The above-mentioned inverse selectivity/permeability relationship of polymers has been summarized by Robeson by means of log-log plots of the overall selectivity versus the permeability coefficient, where A is considered to be the more rapidly permeating gas. These plots were made for a variety of binary gas mixtures from the list He, H2, O2, N2, C02, and CH4, and for a large number of rubbery and glassy polymer membranes. Such representations, shown in Fig. 8 and Fig. 9 are often referred to as upper bound plots (Robeson, 1991). The upper bound lines clearly show the inverse selectivity/permeability relationship of polymer membranes. While these plots were prepared in 1991, only small advances have been made to push the upper bound higher since that time. 

Commercial polymeric membranes are cheap, but very often not sufhciently permselective. For any given gas pair, polymers typically show high selectivities with modest permeabilities, or high permeabilities coupled with reduced selectivities, so that in a selectivity vs. permeability log-log plot aU polymers fall below a so-called upper bound line [1]. On the other hand, inorganic membranes are often very permselective, easy to clean, thermally and chemically resistant, but are usually expensive, brittle, difficult to be prepared in a reproducible way, aud are typically characterized by a low surface-to-volume ratio in modules which, in turn, affects industrial applications (increased dead volume, need of larger compressors) and therefore translates into higher investment and running costs. 

Figure 2.7 Robeson plot illustrating the tradeoff between selectivity (a, ALPHA) and permeability (P) for the separation of carbon dioxide from nitrogen with polymer membranes [47]. The circles indicate all literature data considered relevant. The upper bound line is an empirical judgment of the outermost range of reliable data. Reprinted from Robeson IM. The upper bound revisited. J Membr Sci 2008 320(1—2) 390—400. Copyright (2008), with permission from Elsevier.

Fig. 8 is a plot of break load of wool fibres against the area of cross-section at the point of break. The slope of the upper bound line, which is 100 MPa, is a mea.sure of the intrinsic strength of wool at a break extension of 50 to 60%. The points below the line are due to defects of one sort or another. Some of these will be a.ssociated with localised damage, but others may have physiological causes associated with the growth of the fibres. One suggestion is that weakness in the CMC may cause cells to pull out from one another, particularly if they are shorter or thicker with a low aspect ratio. 

However, with the addition of SDS, strain recovery is almost 80-90 % at low mass fraction of gelatin (<14 %). The upper bound lines for both empirical and experiment data are closely packed and there is little difference between them. Thus, the empirical model trend-line correlates well with the experimental data providing reasonable estimation of strain recovery for gelatin content of 2—50 % and SDS content between 0 and 0.66 %. 

While Freeman (79) has developed a theory about the upper bound line depending on gas size, condensability, and an adjustable parameter, another direction was taken by Robeson et al. (78), who developed a group contribution (80) approach to predict permselectivity. The intent of the latter is to maximize the proximity to the upper bound line based on a knowledge of the permeability contribution of each specific group in a wide variety of polymers. Ideally polymers synthesized on the basis of the most permselective groups would yield the best possibility to increase selectivity. 

The chapters in this book by Langsam, Xu et aL, Hirayama et aL, Fritsch, and Maier et al focus on polymer structure modification to improve the performance of gas separation membranes relative to the upper bound tradeoff relations. Mahajan et al, describe characteristics of hybrid inorganic/organic membranes as a route to break the simple rules that result in equations 8 and 9, possibly resulting in materials with properties which are above and beyond the upper bound lines. Koval et al and Eriksen et al, describe facilitated transport membranes. They seek to strongly enhance solubility selectivity for penetrant pairs i,e, olefin/paraffin) where... 

Figure 1. Selectivity-permeability-plots of poly(ether ketone)s 9 (upper-bound lines and some literature data added for orientation)...

The P02 vs. ct O2/N2 and Ph2 vs. 0. H2/N2 plot for the modified PEK(S)-C polymers together with common polymers are presented in Figures 1 and 2. As can be seen from the plot, most of the polymers synthesized in this work are located above the upper bound line (13). 

Figure 24.5 Upper bound line of CO2 permeability and CO2/CH4 pomseiectivily (Robeson, 1991).

The following empirical equation was proposed to explain the upper-bound lines for given gas pairs ... 

These parameters determine the average lines of experimental correlations of permeabihty and selectivity and not the upper-bound lines as suggested by Robeson (1991) and Freeman (1999). They lead to the same recommendations of sorption selectivity enhancement for moving above the upper-bound lines of Robeson s correlation. Trade-off relations of gas permeability and selectivity were well correlated with data obtained at room temperature. 

Permeabilities listed in Table 5 allow calculating permeability ratios for different combinations of gases. Permeability ratios, often referred to as ideal selectivities, are good measure of the actual separation factors that can be achieved using membranes prepared from a given polymer. In 1991, Robeson compiled permeability and permeability ratio data for a variety of gases in large number of polymers. This analysis revealed the existence of an upper-bound line on permeability versus permeability ratio plots for all gas pairs, above which no data or very limited data existed [20]. Therefore, the position of the polymer relative to the upper bound line... 

It can be noticed that in case of O2/N2, CO2/CH4, H2/N2, and H2/CH4, some SPPO films fall on, or even above the respective upper-bound lines. In particular, some LMW SPPO-33.8 films [3] show an extraordinary potential for the H2/N2 and H2/CH4 separations. Unfortunately, other researchers have not investigated permeabilities of these gases through SPPO so that the extraordinary potential of SPPO for the above separations can not be confirmed. However, not all LMW SPPO-33.8 films are equally good, some of them, as shown in Figures 9d and 9f, fall considerably below the respective upper bound lines. The variation in performance of LMW SPPO-33.8 films indicates the importance of counter ion in sulfonic groups and polymer chemistry in general, which will be discussed later in this Chapter. 

Co, Cu, Ni, and Ba, respectively. The first three of them are the transition metal cations while the fourth one, Ba, is the alkaline earth metal cation. The three films, which fall below the upper bound line, correspond to Mg, Ca " and Sr, respectively, that are the alkaline earth metal cations. Therefore, the transition metal cations appear to be a better choice than... 

Figure 16 shows the plot of O2 permeability versus O2/N2 permeability ratio for HMW SPPO in comparison with the upper bound line. This figure is again an extract from Figure 9a, which shows all the literature data pertaining SPPO and this pair of gases. 

In case of SPPO-13.2, the polymer in Na form is not any closer to the upper-bound line than the polymer in protonated form. This is because an... 

Kruczek and Matsuura in their studies on characterization of gas separation properties of SPPO films have reported similar trends for permeabilities and permselectivities for O2 and N2. They have also reported CO2/CH4 permeability ratio of 43 corresponding to CO2 permeability of 11 Barrer for SPPO. The authors have conducted a detailed study on the effect of mono-, di- and trivalent cation substitutions of SPPO membranes on their gas separation performances. The thus substituted polymers were more permeable to gases than the hydrogen form of SPPO without any loss in the permeability ratios. The improved gas transport properties (separation factor for O2/N2 of 7.65 corresponding to 67.3% of O2 in the permeate when the membrane was used for oxygen enrichment of air) of SPPO with a degree of substitution of 18.5% and in the Mg " form for O2/N2 gas pair placed the polymer above the upper-bound line. 

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