Foam cell, ideal

Polyolefin foams are easier to model than polyurethane (PU) foams, since the polymer mechanical properties does not change with foam density. An increase in water content decreases the density of PU foams, but increases the hard block content of the PU, hence increasing its Young s modulus. However, the microstructure of semi-crystalline PE and PP in foams is not spherulitic, as in bulk mouldings. Rodriguez-Perez and co-workers (20) showed that the cell faces in PE foams contain oriented crystals. Consequently, their properties are anisotropic. Mechanical data for PE or PP injection mouldings should not be used for modelling foam properties. Ideally the mechanical properties of the PE/PP in the cell faces should be measured. However, as such data is not available, it is possible to use data for blown PE film, since this is also biaxially stretched, and the texture of the crystalline orientation is known to be similar to that in foam faces. 

Support for this postulation came from work done on the shape of the ideal foam cell [32-40]. Ross and co-worker [34,35] proposed three minimal geometric structures, i.e. those which will subdivide space with minimum parti-tional area. These were the pentagonal dodecahedron, the minimal tet-rakaidecahedron, originally suggested by Thomson (Lord Kelvin), and the P-tetrakaidecahedron (Fig. 4). 

The pentagonal dodecahedron, however, is not entirely space-filling, i.e. a close-packed array of such figures has a number of interstitial voids. On the other hand, Kelvin s tetrakaidecahedron and the P-tetrakaidecahedron are. The latter requires 4% more surface area, so a system of such figures would spontaneously rearrange to the more stable array of Kelvin cells. Thus, it would seem that Kelvin s tetrakaidecahedron is the ideal candidate nevertheless, this is not observed in real systems Pentagonal faces are shown on foam cells. These... 

In foams the gas-filled areas are separated by thin films of dispersion medium. A characteristic idealized example of foam cells (Fig. VIII-2) is the... 

As pointed out by Reinelt and Kraynik (54), however, the idealized vertex does not adequately represent an equilibrium structure. Similar reservations apply to the work of Budiansky and Kimmel (95), who considered the behavior of an isolated foam cell in the form of a rectangular pentagonal dodecahedron and obtained a shear modulus between the two above values. 

The main driver for fluoroplastic foams has been the insulation for data transmission cables. An example is coaxial cables that have relatively thick insulation. Its low dielectric constant and dissipation factor are desirable electrical properties. Air has the ideal dielectric constant (1.0). The ideal dissipation factor for data-cable insulation is zero. Perfluoropolymers have low dielectric constant and dissipation factor values (Table 11.2, see Ch. 6 for additional data). Foaming perfluorinated fluoropolymers further reduces the dielectric constants toward 1.0 and moves the dissipation factors closer to zero because the resin is replaced with air-filled cells in the insulation. The decrease in the dielectric constant is proportional for example, FEP insulation with 60% void content had a dielectric constant of More uniform foam cell size and smaller cells yield foams with the best electrical properties. 

The big question is whether the seemingly ideal properties of a reticulated foam will be maintained when we start to change the chemistry (for cell adhesion, extraction, etc.). Changes in the polyol or isocyanate will inevitably affect its physical properties. A balance of chemical activity would have to be established. In many cases, this balance will degrade the desirable properties. An answer is the recent development of a composite of a chemistry designed according to desirable chemical features grafted to a reticulated scaffold. " Such a composite was developed and patented and it will be cited as an example for several applications. 

We discussed reticulated foams earlier in this book. They appear to have many desirable properties of ideal scaffolds. Depending on the feedstock, the manufacturers can produce a wide variety of pore sizes. Foams made specifically for reticulation have very narrow pore size distributions. If we compare the reported cell size distribution with that of Zeltringer, we can illustrate the precision of the reticulated foam process in the context of scaffolds for cell growth. Caution is advised in reviewing the Figure 7.6 plot. It is qualitative and assumes a normal distribution for both systems. It estimates the Zeltringer data based on the published standard deviation. 

The question of the ( -potential value at the electrolyte solution/air interface in the absence of a surfactant in the solution is very important. It can be considered a priori that it is not possible to obtain a foam film without a surfactant. In the consideration of the kinetics of thinning of microscopic horizontal foam films (Section 3.2) a necessary condition, according to Reynolds relation, is the adsorption of a surfactant at both film surfaces. A unique experiment has been performed [186] in which an equilibrium microscopic horizontal foam film (r = 100 pm) was obtained under very special conditions. A quartz measuring cell was employed. The solutions were prepared in quartz vessels which were purified from surface impurities by a specially developed technique. The strong effect of the surfactant on the rate of thinning and the initial film thickness permitted to control the solution purity with respect to surfactant traces. Hence, an equilibrium thick film with initial thickness of about 120 nm was produced (in the ideal case such a film should be obtained right away). Due to the small film size it was possible to produce thick (100 - 80 nm) equilibrium films without a surfactant. In many cases it ruptured when both surfaces of the biconcave drop contacted. Only very precise procedure led to formation of an equilibrium film. 

Fig. 5.1 Cell edge bending of an idealized open-celled foam (Ashby and Gibson 1997)...

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