Foamed cell size distribution

To calculate the foam cell size distribution function we consider, following Mihira an isolated cell foam structure model (Fig. 24). Let r be a true cell radius, and s the radius of sectional circles on the cut surface X, f and s their mean values, of and of their mean square deviations, and f(r) and f(s) their distribution functions. We will denote by x the depth of a cell dissected by the plane X (Fig. 24) and calculate the probability P(r,x) of cells having a radius in the range from r to (r + dr) and a depth from x to (x + dx). The probability P(r) for the cells dissected by the plane X to have a radius r is ... 

Foam cell size and shape, foam cell size distribution (if aerosol-type product)... 

While the quahty of the foam was not discussed, changes in surfactant type and concentration were the primary determinants of cell size, distribution, and type and doubtless affected the cell effectiveness and retention of cells in the foams. 

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. 

Microcellular foaming, bimodal cell size distributions, and high open-celled contents of molecular composites of HT-polymers were reported by Sun et al. [33], investigating blends of a rod-like polymer polybenzimidazole with an aminated PSU and poly(phenyl sulfone) by using carbon dioxide as a blowing agent. The complex foaming behavior was related to phase separation within the otherwise... 

By foaming an immiscible blend system of a poly(ethylene glycol)PEG/ polystyrene (PEG/PS), Taki et al. detected a similar foaming behavior as well as a bimodal cell size distribution [78], While smaller cells formed in the more... 

A strong similarity is found for the present blends with a PPE/PS ratio of 50/50, as reflected by a similar bimodal cell size distribution for all SAN contents. Small differences can be related to the distinct foaming kinetics of the PPE/PS blend phase. Compared to the PPE/PS 75/25 blend phase, the higher content of PS in the PPE/PS 50/50 phase leads to a cell nucleation and growth kinetics close to the SAN phase. Nevertheless, the PPE/PS phase still appears to restrict the cell growth and expansion in the SAN phase to some extent, and smaller cells are found within the cell walls. Independent of the SAN content, cell growth within the dispersed SAN phase proceeds under the constraints of the continuous, higher Tg PPE/PS phase. 

The cellular structure of the quaternary blend systems after foaming at 180°C for 10 s is highlighted in Fig. 33. An excellent homogeneity down to the microscale can be detected for all foamed blend compositions. As already discussed in the previous section, simultaneous foaming of the PPE/PS and the SAN phase in the noncompatibilized blend leads to a bimodal cell size distribution. Besides larger cells induced by the highly expanded SAN phase, smaller cells are formed in the PPE/PS phase (Fig. 33a). 

In order to overcome this drawback, the concept of selective blending was exploited. Selective blending of PPE with low-viscous PS allowed one to control the microstructure, to refine the phase size, and to adjust the foaming characteristics of the individual phases of PPE/SAN blends. Appropriate blend compositions allowed simultaneous nucleation and cooperative expansion of both phases, generally leading to bimodal cell size distributions in the micron range. Due to cell nucleation and growth in both blend phases, the density could be further reduced when compared to PPE/SAN blends. Moreover, the presence of coalesced foam structure and particularly macroscopic defects could be avoided, and the matrix of the foamed structure was formed by the heat resistant PPE/PS phase. 

Foam cell size and size distribution are important variables when studying foams. Other surfactant properties crucial to the success of an enhanced oil recovery process include critical... 

This survey deals with the fundamental morphological parameters of foamed polymers including size, shape and number of cells, closeness of cells, cellular structure anisotropy, cell size distribution, surface area etc. The methods of measurement and calculation of these parameters are discussed. Attempts are made to evaluate the effect and the contribution of each of these parameters to the main physical properties of foamed polymers namely apparent density, strength and thermoconductivity. The cellular structure of foamed polymers is considered as a particular case of porous statistical systems. Future trends and tasks in the study of the morphology and cellular structure-properties relations are discussed. 

However, a real foam structure is composed of cells having differing shapes, sizes and volumes. In studying the properties of foamed polymers as well as in developing and elaborating preparative processes, it is necessary to find out cell size, shape and volume distribution. The methods for calculating the respective distribution functions will be discussed in Sect. 9.2, 9.3 here, we only note that the cell size distribution function is a most comprehensive and valuable characteristic of plastic foam structures. 

The foam cell diameter depends on the number of faces (Fig. 16) and, on the average, is proportional to their volume cubed. The cell size distribution in a cut-off section is never symmetrical, and the maximum value of this distribution will be a diameter larger than the mean cell diameter. It must be noted that the above distribution law depends on the assumed range of cell sizes which manifests itself in the numerical value of the factor k in Eq. (37). 

Fig. 19. Cell size distribution of rigid polyurethane foam (grade PPU-3) samples having the volumetric weight (I) 40 and (2) 500 kg/m according to mercury penetration data...

Reid developed analytical tools for studing the cell size distribution from dissected sphere size data measured on a section surface. The first to introduce a general theory of cell size distribution in a solid body was Ceilings who calculated the macrostructural parameters of a number of real metal systems, On the basis of Ceilings method, Mihira et al. developed the principles of the statistical analysis of plastic foam morphology. 

In investigations of the structure and properties of disperse materials, particularly plastic foams, it is necessary to find out the distribution pattern of one phase in the material. It is simpler to consider the distribution of the gas phase in a solid body, i.e. the gas-filled cell distribution within a foam bulk] In their turn, the cells, as shown above, may be characterized by several parameters (size, shape, volume and surface area). The cell size distribution pattern is the most comprehensive characteristic of the dispersity of the gas structural elements of plastics. Furthermore, the cell size can, be determined by one of the methods which will be discussed below, and the foam dispersity is expressed in terms of the nominal cell diameter distribution function. 

Statistically, the cell size distribution has been studied for many types of foamed plastics. In most cases, the plots of such functions have a sharp asymmetrical maximum (steep towards smaller cells and smoother towards larger cells, see (Fig. 19). 

Eyres, G. The Effect of Foam Air-Cell Size Distribution on the Stability of Marshmallow, NZIFST Annual Meeting, Dunedin, New Zealand, 2001. 

In PU foams, the cells have neither regular shapes, nor a uniform size. The foam microstructure can be specified in terms of the cell size distribution, and the cell shape anisotropy. PU slabstock foams rise while being supported on a moving belt, so the cells have a greater height than diameter. 

As shown by Equations (1-5), the insulation properties of an open cell foam depend on a complicated interplay of different parameters such as the PU thermal conductivity, foam density, cell size and cell size distribution, cell morphology and anisotropy, which have to be optimised during the foam preparation to obtain the best trade-off among the three thermal conductivity contributions, and... 

Lesser [88] studied the continuous extrusion of a range of high-melt-viscosity polymers using a single screw extruder with a temperature-controlled die. Control of the foam morphology (cell density and cell size distribution) of polytetra-fluoroethylene (PTFE), fluorinated ethylene propylene cofxtlymer (FEP), and... 

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