Upper-bound limit polymer

Despite all the advantages, polymeric membranes eannot overcome the polymer upper-bound limit between permeability and selectivity. On the other hand, some inorganie membranes sueh as zeolite and carbon molecular sieve membranes oIFct mueh higher permeability and selectivity than polymeric membranes but are expensive and difficult for large-scale manufacture. Therefore, it is highly desirable to provide an alternate eost-effeclive membrane in a position above the trade-off curves between permeability and seleelivity. 

Most of the research work has been focused on polymer membrane materials involving a solution-diffusion mechanism. The performances of such materials generally fall within the trade-off relationship between permeability and selectivity suggested by Robeson [5], with an upper bound limit for the membrane performances. 

In recent years, fluorinated PAs have been explored for gas separation, for PV, and as PEMs in fuel cell application. The high mechanical strength and the film-forming ability of fluorinated PAs have endowed this class of polymers to be used in membrane-based application. In general, a combination of >C(CF3>2 or -CF3 groups and sterically hindered moieties in the same polymer structure has showed improved results in terms of permeability and permselectivity. It is noteworthy to observe that fluorinated PAs containing groups like tert-butyl, adamantyl, te(phenyl)fluorene, and to(phenylphenyl)fluorene showed excellent separation performance for O2/N2 gas pairs and touched or even exceeded the upper bound limit drawn by... 

It has been observed that membranes of carbon molecular sieves can exceed the upper bound of conventional polymeric membranes. The carbon molecular sieve membranes are produced by carbonization of aromatic polymers (e.g., polyimides), yielding pore dimensions in the range of O2 and N2 molecular dimensions. Polyimide/poly(vinyl pyrrolidone) blends subjected to carbonization conditions also yielded carbon molecular sieve membranes that exceeded the upper bound limit for conventional polymeric membranes [195, 196]. Specific values were O2 permeability of 560-810 barrers with a O2/N2 separation factors of 10-7 well above the upper bound. 

Most of the more recent research has focused on developing membrane materials with a better balance of selectivity and productivity (permeability) as that seems the most likely route for expanding the use of this technology. There appear to be natural upper bounds [9,10] on this tradeoff that limit the extent of improvement that can be realized by manipulating the molecular structure of the polymer used for the selective layer of high-flux membranes, at least in many cases. This has led to interest in nonpolymeric and so-called mixed-matrix materials for membrane formation [8] however, at this time, polymers remain the materials of choice for gas-separation... 

The frequency with which two reactive species encounter one another in solution represents an upper bound on the bimolecular reaction rate. When this encounter frequency is rate limiting, the reaction is said to be diffusion controlled. Diffusion controlled reactions play an important role in a number of areas of chemistry, including nucleation, polymer and colloid growth, ionic and free radical reactions, DNA recognition and binding, and enzyme catalysis. 

The temperature limits for each polymerization process are set by the melting point of polyethylene. In the solution process there is no upper bound, other than that imposed by the MW of the polymer. That is, as temperature is increased the polymer MW decreases until the product eventually becomes wax. There is, however, a lower bound on temperature. At temperatures below approximately 120 °C, the polymer solution becomes too viscous to be handled easily. 

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. 

If one of the polymers is dispersed in the other, see Section 4.3, there are two limiting cases (81). Consider two polymers, 1 and 2, in a phase separated blend. The upper bound case is expressed by a parallel model ... 

In polymer theories, one proceeds even one step further and introduces the infinite Brownian chain , which is associated with the passage to the limit R ) oo. By this procedure, the upper bound for the self-similarity is also removed, and we have now an object which is self-similar on all length scales. This is exactly the situation of physical systems at critical points. Hence, the infinite Brownian chain represents a perfect critical object and the consequence are far-reaching. Application of all the effective theoretical tools developed for the study of critical phenomena now becomes possible also for polymer systems. In particular, scaling laws may be derived which tell us how certain structure properties scale with the degree of polymerization. As mentioned above, scaling laws always have the mathematical form of a power law, and we have already met one example in Eq. (2.35)... 

Despite rapid advances in polymeric gas separation membrane performance in the 1980 s, recent efforts have yielded only small improvements. Six years ago, the upper bound tradeoff limit between O2 permeability and O2/N2 selectivity was constructed (i), and it still defines the effective performance bounds for conventional soluble polymers. Consequently, an alternate approach to gas separation membrane construction is suggested to exceed current technology performance. Molecular sieves, such as zeolites and carbon molecular sieves (CMS), offer attractive transport properties but are difficult and expensive to process. A hybrid process exploiting the processability of polymers and the superior gas transport properties of molecular sieves may potentially provide enhanced gas separation properties. 

These are the limiting cases for permeability of a polymer, which comprise the continuous or dispersed phases and the parallel model represents the upper bound and the series model represents the lower bound. Another model typically employed, where spheres of one polymer are dispersed in a matrix of the other, is the Maxwell s equation ... 

A supported SAPO-34 membrane has been developed using the seeding technology which can separate a COj/CH mixture with a selectivity of 115 and a reasonable CO permeance of 4x1 0 mol m s Pa at the feed pressure of 70 bar [3]. Also a supported DD3R zeolite membrane can separate CO from CH with a selectivity of over 4000 at 225 K and 1 bar of the equimolar feed [4,5], The Robeson upper bound showing the limit of polymer membrane performance is from 1991. From Van den Bergh J, Zhu W, Kapteijn F, Moulijn JA, Yajima K, Nakayama K, etal. Separation ofCO and CH by a DDR membrane. Res Chem Intermediates 2008 34 467-74, with permission. 

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