Volume fraction of voids

The density of the polymer clearly shows the formation of a foamed polymer. The density values for selected foams together with the polyimide homopolymers are shown in Table 11. The density values for the ODPA/FDA and PM-DA/FDA polyimides were both 1.28 g/cm and 3FDA/PMDA is 1.34, while most of the propylene oxide-based copolymers showed substantially lower values. The densities of the foamed copolymers derived from these copolymers ranged from 1.09 to 1.27 g/cm, which is 85-99 % of that of the polyimide homopolymers. This is consistent with 1-15 % of the film being occupied by voids. From these data (i.e., the comparison of Tables 10 and 11), it appears that the volume fraction of voids or the porosity is substantially less than the volume fraction of propylene oxide in the copolymer (i.e., 70 % or less). Thus the efficiency of foam formation is poor. Conversely, the propylene oxide-based copolymers with PMDA/ODA as the imide component did not show the expected density drop, and the values were essentially identical to that of the homopolymer. In PM-DA/ODA-based systems, molecular ordering and orientation were found to be critical in determining the stability of the foam structure. Where the character-... 

Sample Entry Initial Labile Block Density, Composition, vol.% g/cm Volume Fraction of Voids (Porosity) %... 

Foam formation was possible only in the amorphous high Tg polyimides however, the volume fraction of voids does not correspond to the volume fraction of propylene oxide in the initial copolymer. A decrease in the volume fraction of voids incorporated into the matrix in comparison to the initial volume fraction of the propylene oxide in the copolymer can be understood by consid-... 

The quantity 100A is equal to 100(pj/pv). where pj is loading density and pv voidless density. The quantity (1-A) is the volume fraction of voids in the charge... 

Another two-phase composite is chemically or physically blown foam, composed of polymer and voids only (i.e. conventional foamed or cellular polymer). Its compositions lie along the polymer-void border of Fig. 7, and it, too, is limited by the maximum volume fraction of voids allowed, while still maintaining the definition of a foam. The limits mentioned define the allowed compositions for syntactic foams and determine the area within the diagram where they are located. One limiting case is point B which represents the composition of microspheres (0.74), polymer (0.11), and voids (0.15). The microspheres, in this case, are arranged in a hexagonal close packing 85). 

A composite sample of carbon fiber and epoxy weighs 2 g. When the sample is submerged in water (density = 1 g/cm ), its weight is 0.633 g. The weight of the fibers is 0.966 g after the epoxy is degraded with concentrated nitric acid. Calculate (a) the volume fraction of fibers, (b) the density of the composite, and (c) the volume fraction of voids. 

The same result for the volume fraction of voids will be obtained by applying Eq. (15.12), which allows the determination of (j) from the weight fraction and densities of the matrix and fibers and the density of the composite. 

Initial dispeised-phase holdup in feed to a decanter Volume fraction of voids... 

Figure 12. Predicted elastic-plastic, stress-strain curves for the epoxy annulus. The volume fraction of voids is 20%.

Sample entry Initial labile block Density composition, vol% (gcnr3 Volume fraction of voids (porosity ) %... 

Although nanofoam formation was observed in the amorphous high T polyimides containing PPO blocks, the volume fraction of voids does not directly correspond to the volume fraction of propylene oxide in the initial copolymer. A decrease in the volume fraction of voids present in the matrix in comparison to the initial volume fraction of the propylene oxide in the copolymer can be rationalized by considering the distribution of sizes in the propylene oxide phase. Since the copolymer blocks are not monodisperse, a distribution of propylene oxide microdomain sizes is expected. The pressure exerted on a pore will vary as y/r, where y is the surface tension and r is the pore radius. Consequently, the higher pressure on the smaller pores will tend to cause them to collapse. In addition, there will always be a small amount of propylene oxide co-mixed within the imide phase, which will also be removed upon decomposition. However, this... 

Wood is a hygroscopic, porous, anisotropic and non-homogeneous material. After log sawing, the lumber contains liquid water in fiber cavities (capillary water) and bound water inside the fiber wall (hygroscopic water). Porosity refers to volume fraction of void space. This void space can be actual space filled with air or space filled with both water and air. Capillary-porous materials are sometimes defined as those having pore diameter less than... 

P Volume fraction of voids in a packed bed Dimensionless Dimensionless... 

Residual saturation = volume fraction of void space occupied by displaced fluid when displaced fluid stops moving... 

The relationship between the magnetic flux loss and the volume fraction of voids in injection/compression-molding bonded magnets after treatment under the same conditions is represented in fig. 37 (Mino and Hirosawa 1999). It is clear that the magnetic flux losses proportionally decrease with increasing volume fraction of voids. 

Dll. A washing operation is processing 10,000 kg/h of wet solids. The liquid is essentially water with a density of 1000.0 kg/m, the dry solids have a density of 1500.0 kg/m, and the porosity (also known as the volume fraction of void space) is measured as = 0.40. What is the flow rate of the underflow liquid in kg/h ... 

The presence of voids increases markedly the pressure sensitivity of the material. Gurson (1977a, b) modified the von Mises criterion to be used for porous solid that contains well-distributed small voids. He applied a continuum treatment to a cavitated ductile material containing a volume fraction of voids and obtained the following yield criterion ... 

Porosity (or volume fraction of voids, Vf) is defined as the percentage of the foam volume that is occupied by the gaseous phase. It can be calculated from refractive index measurements [83] or from the density of the foam (pf) and the solid precursor (Ps) using Eq. (9.3) ... 

Introducing the dimensionless volume fraction of voids also called the voids fraction ... 

Mechanical mixing or stirring is another way of introducing voids into a material. It is easy to achieve, but very difficult to control, the type, size, distribution, and volume fraction of voids. The procedure involves vigorously stirring the polymer melt, thus entraining air. 

Elastic modulus and flexural strength were plotted with the least squared lines as functions of volume fraction of voids in Figure 3.15 and Figure 3.16, respectively. Both properties are seen to be well correlated with volume fraction of voids as correlation coefficients were found to be -0.94 and -0.89 for elastic modulus and flexural strength, respectively. As expected, reduction in prop>erties occurs as the volume fraction increases. 

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