Robeson plots, selectivity permeability

State of the Art A desirable gas membrane has high separating power (ot) and high permeability to the fast gas, in addition to critical requirements discussed below. The search for an ideal membrane produced copious data on many polymers, neatly summarized by Robeson [J. Membrane ScL, 62, 165 (1991)]. Plotting log permeability versus log selectivity (ot), an upper bound is found (see Fig. 22-73) which all the many hundreds of data points fit. The data were taken between 20-50°C, generally at 25 or 35°C. 

Figure 8.11 Robeson plot of CO2/CH4 selectivity versus membrane permeability and permeance [12]. The points shown are based on low-pressure, pure-gas measurements. The performance of commercial membranes when used to separate carbon dioxide from high-pressure natural gas is shown on the same figure for comparison.

The problem with use of polymeric membranes in this application is plasticization, leading to much lower selectivities with gas mixtures than the simple ratio of pure-gas permeabilities would suggest. For this type of separation, a Robeson plot based on the ratio of pure-gas permeabilities has no predictive value. Although membranes with pure-gas propylene/propane selectivities of 20 or more have been reported [43, 44], only a handful of membranes have been able to achieve selectivities of 5 to 10 under realistic operating conditions, and these membranes have low permeances of 10 gpu or less for the fast component (propylene). This may be one of the few gas-separation applications where ceramic or carbon membranes have an industrial future. 

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. 

FIGURE 4.1 Selectivity for the gas pair O2-N2 as a function of O2 permeability. Properties of materials like molecular sieves and mixed matrix are expected to be found in the upper right comer (hatched area modified Robeson plot). (From Singh A., Koros W.J., Ind. Eng. Chem. Res., 35, 1231, 1996. With permission.)... 

Fig. 14 Robeson plot showing high separation selectivities for PIM-1 and PIM-7, (a) [77], Relation between CO permeability and COj/CH selectivity of theimally rearranged polyimides, (b) [78]...

FIGURE 7.1 Selectivity for the gas pair CO2/CH4 as a function of CO2 permeability and the Robeson plots (squares for CMS membranes, solid circles for TR polymers, triangles for FSC membranes, and solid diamonds for PIMs). (Robeson plots from Ref. [5] data from Refs. [8-13].)... 

Although these rules can lead to increased permeability and selectivity, an extensive compilation of the data in the literature by Robeson suggests an upper bound exists on transport properties - increases in permeability eventually lead to a decrease in selectivity and vice versa [38]. Figure 10 illustrates the upper bounds that exist for a number of gas pairs such plots of selectivity versus permeability are referred as Robeson plots . As one might expect, a similar upper bound exists for pervaporation membranes used to separate benzene-cyclohexane mixtures [39]. 

Mehta and Zydney [41] show a similar relationship exists for ultrafiltration membranes where transport through the membrane occurs by convective pore flow. A Robeson plot was created by taking the selectivity of an ultrafiltration membrane as the reciprocal of the protein sieving coefficient (the ratio of protein concentration in the permeate to that in the fluid adjacent to the membrane surface) and the permeability as the solvent hydraulic permeability. A plot of literature data for bovine serum albumin separation shows the existence of an upper bound. The location of the upper bound was predicted assuming the... 

In the early 1990s Robeson (1993) found an upper limit to the performance of polymer membranes in the commercially important separation of oxygen and nitrogen from air. On a log-log plot of selectivity versus oxygen permeability (a Robeson plot), the upper bound plots as a straight line (see Problem 17.D17 for more details). Although theoretical reasons for this limit have not been found, very few new membranes have been developed that are able to perform better than Robeson s limit. Membrane research has focused on ways to do better than Robeson s upper limit. 

D17. On a Robeson plot (a log-log plot of selectivity versus oxygen permeability in Barrers) the upper bound for separation of oxygen from nitrogen plots as a straight line. Approximate values of the end points are for Pq2 = 0.0001 Barrers, 002. 2 = 42 and for Pq2 = 10,000 Barrers, ao2-N2 ... 

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.

Robeson s well-known tradeoff curve shows the strong inverse relationship between gas permeation flux (permeability) and selectivity [66], Robeson s plot also shows a line Unking the most permeable polymers at a particular selectivity. This Une is called the upper bound. Comparison of gas permeability (permeability of O2 and permeability of CO2) and the separation performances for different gas pairs (O2/N2 and CO2/CH4) of PAs have been shown in terms of Robeson plots. Permselectivity values of O2/N2 gas pair versus O2 permeabiUty values and permselectivity values of CO2/CH4 gas pair versus... 

It was the realization that there were performance limits in polymeric membranes in gas separation which prompted research on carbon membrane In 1991 Robeson set upper bounds in the selectivity-permeability plots of several gas-pairs by compiling experimental data for a large nttmber of polymeric materials. Although the boundary lines have been shifted to the desirable direction after nearly 20 years research efforts, the achievement has not yet been traly spectacular. Attention of membrane research commimity was then focussed on inorganic materials, snch as silica, zeolite and carbon, which exhibited molecitlar sieving properties. Remarkable improvements have been made in terms of the selectivity-permeability plot but the exploitation of these materials for the practical apphcation remains imder-achieved primarily due to their poor processibility. 

First MMMs were studied in the 1980s and are more and more investigated in recent years. MMMs receive attention as a possibility to enhance the properties of pure polymer membranes. Separation properties with MMMs can be above the Robeson upper bond (Figure AX which is a plot of permeability versus selectivity for most industrial relevant gas mixtures. Porous inorganic fillers can counteract the trade-off between selectivity and permeability, which is typical for pure polymer membranes. 

The performances (selectivity/permeability) of the membrane were considered to be part of the optimisation parameters of the study and were left free to vary following the Robeson plot (permeability-selectivity upper boundary) formula of the best available materials at the time, i.e. carbon membranes ... 

Another study focused in that case on ethylene/ethane separation came to the conclusion. It was shown that the coupling of a carbon-based membrane in parallel with the distillation column could lead to a little bit more than 100000 US dollars annual savings in operating costs. As in the previous study, the membrane performances were considered as a floating optimisation parameter following the Robeson plot upper limit equation. The authors chose to correlate the selectivity with the permeability after the following equation ... 

The nature of the polar substituent was significant impacts on the permeability of CO2, N2 and CH4. OEG functionalities, when included in polylLs, produced membranes that were several times more permeable than those with C CN functional groups. OEG-functionalized polylLs exhibited CO2 permeabilities on par with polylLs with n-all l group , but with improved CO2/N2 selectivities that exceeded the "upp>er bound" of the "Robeson Plot". CO2/CH4 separation was also enhanced in each of these second-generation polylLs. 

Figure 8.24 Oxygen/nitrogen selectivity as a function of oxygen permeability. This plot by Robeson [11] shows the wide range of combination of selectivity and permeability achieved by current materials. Reprinted from J. Membr. Sci. 62, L.M. Robeson, Correlation of Separation Factor Versus Permeability for Polymeric Membranes, p. 165. Copyright 1991, with permission from Elsevier...

Robeson [4] showed that there exists a trade-off relationship between selectivity and permeability for dense polymer membranes. This plot was later updated by Singh and Koros [9] (see Figure 4.1). Molecular transport of light gases in such membranes typically occurs by a solution diffusion mechanism (as discussed in Section 4.2.1). For a polymer membrane to be commercially considered for the removal of CO2 from H2, CH4, or air, both the CO2 permeability and selectivity must be competitively high. Since the gases in the mixture with CO2 often are smaller (H2) or about the same size as CO2, they may diffuse more rapidly through the polymers, and it follows that the diffusion selectivity will be <1. The only way... 

Fig. 7.2 Robeson s plot of polymer membrane oxygeninitro-gen selectivity as a function of oxygen permeability.

Figure 2.4 Double logarithmic plots of selectivity against permeability for the gas pairs (a) O2/N2, (b) CO2/CH4 and (c) CO2/N2, showing the 1991 Robeson upper bound (solid line), [23] the 2008 Robeson upper bound (dashed line), [24] literature data [16] for various polymers measured since 1991 ( j, and measurements for PlM-1 in state 1 (x), state 2 (O) and state 3 (%)...

In summary, blending of Pebax 1657 with PEG300 resulted in membranes of higher CO2 permeability and selectivity due to enhanced CO2 diffusivity. However, a phase separation that occurred at high PEG300 contents led to a stagnancy of performance. The performance of Pebax membranes are compared with those obtained for the Pebax blend membranes on a CO2/N2 Robeson s plot [5,44] (Figure 13.9). 

Figure 5.10 Double logarithmic plots of selectivity versus permeability for (top) OJ N2 and (bottom) CO2/CH4, showing (solid line) Robeson s 1991 upper bound and (dashed line) the 2008 upper bound, as well as data for (A) pol (trimethylsilyl prop me) (PTMSP), (A) indan-based polyacetylene 2e, (x) Teflon AF2400, (+) addition-type poly(trimethylsilyl norbornene), ( ) PIM-1, ( ) PIM-1 after methanol treatment, (O) 6FDA-DMN pol dmide, (O) PIM-PI-8 and ( ) PIM-PI-8 after methanol treatment. Reproduced from Ref. 15 with permission from The Royal Society of Chemistry.

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... 

Robeson s plot literature data for Oj/Nj selectivity versus Oj permeability related to polymeric and carbon membranes. (AP represents polymer precursors of PM carbon membranes. PM stands for polymeric membrane.The number that follows indicates the temperature (in °C) reached at the end of the heating)."... 

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