Volumetric weight

Structure (Fig. 13) with hollows inside. These tests thus exhibit an extremely low volumetric weight. Already a small amount of radiolarians can markedly change the behavior of the sediment its volumetric weight decreases and its porosity increases with the radiolarian content. 

In order to establish and evaluate quantitatively the relation between the morphology and the properties of foamed polymers the basic macrostructural parameters must be determined. These parameters include relative number of open and closed cells, volumetric weight or apparent density cell size, shape, wall thickness, cell distribution according to size and shape in a given volume and specific surface area of the foamed plastic material. 

The relation between volumetric weight and the proportion in the polymer of opencell or closed-cell GSE has not yet been studied. It is only known that for any polymer composition the relative percentage of open GSE increases as the volumetric weight of the foamed plastic decreases. This is due to cell growth involving a decrease of the thickness of cell and struts. It adversely affects the aggregation stability and may ultimately cause fracture of the cell walls. 

Fig. 2. Relationship between the volume ratio of open gas structural elements 3, and the volumetric weight y and volume ratio of gas Sg for rigid polyurethane foam (Grade PPU-3)...

We should now consider the factor 6 in the numerator of the pre-exponential in Eq. (14) which has the physical meaning of either a form factor, packing factor or coordination number of the closest spherical (cubic) sphere packing. The points of Fig. 3 are somewhat scattered probably because of the equal proportions of open cells (9J in samples of different volume weights. Eq. (14) has a maximum when 9(,/9p = 1 (Fig. 3), i.e. when the volume ratio of polymer in a sample is equal to that in a plastic foam with closest spherical packing the gas phase volume is then 74% which, for polyurethane foam, corresponds to a volumetric weight of 315 kg/m. ... 

In general, the volumetric weight is determined by the true densities of the polymer phase and the gas phase. It is related with the gas-filling of the foam as follows... 

In practive, the volumetric weight of plastic toams is calculated as the ratio of sample weight Q to its geometrical volume ... 

The relation between the volumetric weight and the mean cell diameter is described by a hyperbolic function. This function has been analytically derived by Romanenkov et al. from the following geometrical model. 

Since the volume V = b, the volumetric weight of the foamed plastic is ... 

If we assume that 8 = const, Eq. (20) will present a good approximation of the relation between the volumetric weight and the mean cell diameter within small volumetric weight ranges. A plot of relation (20) at constant wall thickness 8 = 1 micron for a PSB polystyrene foam yields the curve shown in Fig. 5. The deviation from the experimental result was in this case 22-28 %. 

Fig. S. Relationship between the volumetric weight of polystyrene foam, y, and mean diameter d of macrocells (1) and (2) curves plotted according Eq. (20) for grades PSB and PSB-S respectively...

Within a sufficiently broad range of volumetric weights the wall thickness is not constant but a linear function of the volumetric weight ... 

The use of other geometrical models for the analytical treatment of the relation Y = f(5, d) does not markedly affect the form of Eqs. (20) and (22) but only alters the value of the factor in the numerator of Eq. (22) For the spherical model discussed above, this factor is tc = 3.14. For other models it may vary from 3.0 to 3.3. In contrast to the spherical model, other models involve greater discrepancies between the experimental and theoretical results. For example, when using a cubic model for PSB plastic foam having a volumetric weight of 90 + 0.5 kg/m, the discrepancy is 18% as compared with 9% in a spherical model. 

Fig. 6a and b. Volumetric weight distribution of (a) polyurethane foam and (b) polystyrene (1) intermediate (core) layer (2) surface layer... 

The mold material has a marked effect on the density distribution pattern in a foam block. It has been shown for the grade FRP-1 of phenolic foam in panels with aluminum or asbestos cement claddings that, due to the different thermoconductivity coefficients of the claddings, the thickness of the compacted layer may be 1.5 to 2.0 cm for aluminium and 0.5 to 1.0 for asbestos cement. For phenolic foams the variation of the volumetric weight across the depth of the intermediate layer of a three-layer panel may be described by the following equation (Fig. 7) ... 

Yi the volumetric weight increment near the interface of the cladding intermediate layer Ay a compaction gradient characterizing the rate of volumetric weight variation across the direction of compaction and I the intermediate layer depth (expansion space). 

Fig. 7. Volumetric weight distribution over the depth h of resol phenolic foam inside the sandwich panel ...

Very interestingly, Harding ound that the compressive strengths of polyurethane and polystyrene foams in one case and of polyurethane and phenolic foams in another case display the same dependence on the height-to-width ratio over a range from 1/2 to 2/1, despite the fact that the volumetric weights of these materials are... 

The volumetric weight and the ratio between the number of open and closed cells are the fundamental morphological parameters of foamed plastics. Nevertheless, it has been reported that even for the same volumetric weight and number of open (or closed) cells the strength and thermophysical parameters may be widely different in plastic foams made of the same polymer grade. The differences in cell shapes and sizes are responsible for this fact. 

A structure in which the same volumetric weight can be achieved with different cell sizes is attainable by the following relation. It is known that for monodisperse spherical cells of a plastic foam the general relation between mean wall thickness 8 and mean cell diameter D is given by Aleksandrov s formula... 

If Yp = 1000 kg/m , than the wall thickness in a foam of volumetric weight y = 1000 kg/m at D = 0.2 nun will be 8 microns. A plot of 8 versus D yields a straight line (Fig. 17). From this relation it follows that for a given polymer the same wall thickness or the same cell size may be obtained at different gas phase contents. Thus, the volumetric weight of a plastic foam may be controlled not only... 

Fig. 17. Relationship between average cell wall thickness 5 and mean diameter of spherical cells D of foamed polymers at different ratios of the volumetric weight of foams y and density of unfoamed polymer Yp (1) 0,05 (2) 0,10 (3) 0,15 (4) 0,20 (5) 0,25...

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