Schroder paradox

Based on the fact that interleukin-1 (IF-1) induces migration of leukocytes to sites of injection, IF-1 was thought to have chemotactic activity. In fact, leukocyte-derived chemoattractants for phagocytic cells were present in partially purified preparations of IF-1 (Fuger et al, 1983 Sauder et al, 1984). However, when purified to homogeneity, IF-1 lost its chemotactic activity. Further studies revealed that the partially purified IF-1 preparations were contaminated with both a chemotactic factor for monocytes and a monocyte-derived neutrophil chemotactic factor, termed MDNCF (Yoshimura et al, 1987, 1989 Matsushima et al, 1988, 1989). These paradoxical observations were resolved by data showing that IF-1 was a potent inducer of these chemotactic factors. The same mononuclear cell-derived neutrophil attrac-tants were also identified by several other laboratories of (Schroder et al, 1987 Walz et al, 1987). Eater, Farsen et al (1989) reported that MDNCF was chemotactic for T lymphocytes as well as neutrophils, and, based on the presumed involvement of MDNCF in the immune response, it was renamed IF-8 (Farsen et al, 1989 Oppenheim et al, 1991). 

It is also well documented [2-7] that fuel-cell membranes and ionomers in general typically show a phenomenon known as Schroder s paradox [8]. Schroder s paradox is the difference in water uptake (and therefore other properties) due to the type of reservoir in contact with the membrane. As seen in Figure 5.1, the water content of the membrane, X or moles of water per mole of sulfonic acid sites, for a saturated-vapor reservoir is different from that for a liquid-water reservoir even though the chemical potential is identical. This is seen in practice and the size of the difference depends on the membrane state and history. This effect is an important issue since fuel cells are often operated with humidified gases resulting in situations where there is liquid water on the cathodic side of the membrane but only water vapor on the anodic side. 

Figure 5.1. Water-uptake isotherm at 25°C showing the effect of Schroder s paradox.

On the other side of the scale are the macroscopic models, which are in line with the macrohomogeneous approach taken in this chapter. There are two main schools of thought regarding membrane models, those that assume the membrane is a single phase and those that assume it is two phases. The former usually leads to a diffusion model [11, 12] and the latter to a hydraulic one [13, 14]. Both models can be made to agree with experimental data, but neither describes the full range of data nor all of the observed effects, like Schroder s paradox. 

The lower left panel corresponds to a membrane that is in contact with saturated water vapor where a complete cluster-channel network has formed. When there is liquid water at the boundary of the membrane, structural reorganization and a phase transition occur allowing for bulk-like liquid water to exist in the channels resulting in a pore-like structure, the final panel in Figure 5.2. Because the channels are now filled with liquid, the uptake of the membrane has increased without a change in the chemical potential of the water (i.e., Schroder s paradox). 

There are various improvements that can be made to the presented model, some improvements could be accomphshed. Foremost among these possible future-work directions is the inclusion of nonisothermal effects. Such effects as ohmic heating could be very important, especially with resistive membranes or under low-humidity conditions. Also, as mentioned, a consensus needs to be reached as to how to model in detail Schroder s paradox and the mode transition region experiments are currently underway to examine this effect. Further detail is also required for understanding the membrane in relation to its properties and role in the catalyst layers. This includes water transport into and out of the membrane, as well as water production and electrochemical reaction. The membrane model can also be adapted to multiple dimensions for use in full 2-D and 3-D models. Finally, the membrane model can be altered to allow for the study of membrane degradation, such as pinhole formation and related failure mechanisms due to membrane mechanical effects, as well as chemical attack due to peroxide formation and gas crossover. 

When studying the literature on water uptake, the special case of total humidification of a sample seems to cause some additional problems. Confusion exists as to whether the exposure of a sample to 100% relative humidity (RH) gives the same results as exposure to water directly. This is often termed Schroder s paradox. Nevertheless, Jeck et al. [40] showed that the history of the polymer and the activity of the solvent - here water - are important and that such a paradox does not exist The difference in the data obtained for total humidification can therefore be simply explained by different water activity. This activity is different for the wetting condition, for example, direct contact with water, and the humidifying condition, where the contact is with the water vapor. 

The transition from equilibrium under saturated vapor conditions to liquid water conditions, implies a discontinuity in the liquid pressure in the pore, which debunks Schroder s paradox as a first-order phase transition at the pore level. At the PEM level, the jump in water uptake is tied to the maximal wall charge density a that is physically possible. 

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