Relative volume fractions

Figure 2. MSssbauer Spectrum and Corresponding Computer Simulation for Sample 2 Under Water-Gas Shift Reaction Conditions at 613 K. A) situ MSssbauer spectrum of sample 2 at 613 K B) Computer-simulated spectrum C) Distribution of particle radii D) Relative volume fractions as a function of radius (A). For the computer simulation, the following pareimeters were used 0-1.25, mean radius = 65A, k-8 x 10 ergs/cm3. The Klebsch-Gordon coefficients used were 3 3 1.

Therefore, at room temperature Fluoro-PSB-II a thermoplastic elastomer with a soft polymer phase (fluorinated block) and a hard phase (PS-block), similar to the parental polystyrene-6-polybutadiene block copolymer. Depending on the relative volume fraction of both components and the continuity of the phases, the resulting bulk material is rubbery or a high-impact solid. 

Since it is assumed that mixing sets in at once, the initial concentration in the mixed lake is the weighted average of CE(tst) and CH(/St). From Table 21.1 the relative volume fractions are VE/V = 1/3, VH/V = 2/3, thus ... 

FIGURE 2.6. Block copolymer morphologies obtainable via phase separation. The exact structure will depend on the relative volume fractions of the two blocks, as well as /N (where / is the interaction parameter and N the length of the polymer). 

Xab - interaction parameter of the constituent polymers 0j - relative volume fraction of polymer component i Thus, one arrives at... 

It was also possible to analyze data from the DPPC/OA monolayers using the optical matrix method. A one-layer model represents an oversimplification of the complex structure of this monolayer, and the quality of the fits to experimental data is generally poorer than for the DPPC monolayer. Despite these problems it has been possible to estimate the relative volume fraction of DPPC, OA, and water in these mixed monolayers. It is apparent at all surface coverages that the volume fraction of DPPC is approximately twice that of OA, as expected, and that the volume fraction of water in the monolayer increased steadily as the monolayer was expanded to 70 A /molecule. 

The majority of polymers are immiscible and, in bulk, they phase separate to form domains of varying sizes and shapes, depending on their relative volume fraction. This happens because of the very low entropy of mixing in the case of large polymeric molecules. Therefore, unless there is a large favorable enthalpic contribution, most polymers do not form molecularly miscible systems. The same is true for block copolymers, in which the length of each block exceeds a certain critical value. As mentioned earlier, block copolymers are systems wherein two (or more) different types of homopolymers are linked to each other at the chain end(s) diblock copolymers, represented as (A) -(B) , are systems in which two homopolymers are linked to each other at one end, while triblock copolymers, represented as (A)m-(B) -(C)p, are systems in which one central homopolymer block is linked at either end with two other homopolymers. The values m, n and p, represent the... 

Rod—coil copolymers are a type of amphiphile that can self-assemble into a variety of ordered nanostructures in a selective solvent.36-37-71 In solvents that selectively dissolve only coil blocks, rod—coil copolymers can form well-defined nanostructures with rod domain consisting of the insoluble block. This results in an increase of the relative volume fraction of the coil segments relative to the rod segments, which gives rise to various supramolecular structures. Particularly, poly(alkylene oxide) as the coil block of rod—coil molecule has additional advantages due to complexation capability with alkali metal cation, which can provide an application potential for solid polyelectrolytes and induce various supramolecular structures.72-75... 

Lehr and Mewes [67] included a model for a var3dng local bubble size in their 3D dynamic two-fluid calculations of bubble column flows performed by use of a commercial CFD code. A transport equation for the interfacial area density in bubbly flow was adopted from Millies and Mewes [82]. In deriving the simplified population balance equation it was assumed that a dynamic equilibrium between coalescence and breakage was reached, so that the relative volume fraction of large and small bubbles remain constant. The population balance was then integrated analytically in an approximate manner. 

Figure 13.13. Comparison of the behavior predicted from Equation 13.35 with the data tabulated by de Kruif et al [43] for the viscosity of dispersions of sterically stabilized hard silica spheres in cyclohexane. There are no adjustable parameters in Equation 13.35. Relative viscosity denotes r (dispersion)/r (cyclohexane). Relative volume fraction denotes 0/0. Couette and parallel refer to measurements with a Couette rheometer and a parallel plate rheometer, respectively. Zero and infinite refer to the limits y —>0 and y- < >, respectively.

If the ratio of the volume fraction of bitumen-rich component to that of air in the aggregates is denoted by G, then this value will be constant throughout the froth formation process. The only variable along the path from a dilute dispersion of aggregates to a froth is the relative volume fraction middlings. If G is greater than 2.67, the resultant froth is regarded as stable and has the component volume fractions ... 

For bimodal sterically stabilized silica suspensions in cyclohexane, Figure 18 shows the variation of the Einstein and Huggins constants with the relative volume fraction of the larger particles in the total solids,... 

Figure 19 shows the steady shear relative viscosity variation with the relative volume fraction of the large particles, eL, for various large to small particle size ratios, dh/ds, and different total solid volume fraction, 0, for bimodal concentrated dispersions of submicron resin particles at a shear stress level of 0.0155 Pa. The experimental data are taken from Hoffman (129). We can observe that the relative viscosity exhibits a minimum near eL = 0.8. The minimum viscosity behavior is more-pronounced at large particle diameter ratios, djds. The bimodal system viscosity can be several order of magnitudes lower than the corresponding monodispersed systems when the larger particles composed of about... 

The concentrated solution regime characterized by values of the chain segment density or monomer concentration p such that p 1, i.e., the solvent is present as the minor component in terms of relative volume fraction. 

Maximum entropy approach for 0-solvents. The volume fraction of polymer in the region between two parallel plates separated by a distance h was determined in a like fashion by introducing a second surface, parallel to the first, and rejecting all conformations that cross it. The relative volume fractions of polymer so calculated are shown in Fig. 17.7 for poly(oxyethylene) of molecular weight 4 000 (272 bonds). 

The residual stress field around a misfitting fiber can now be estimated. These stresses can have important consequences in terms of the fracture behavior of fiber composites. If these stresses are high, failure may initiate near the fiber. For the case in which the fiber is in tension ( f>a ), the interface or the fiber may fail as O , and a are tensile in the fiber. For the case in which the fiber is in compression ( flongitudinal stresses in the matrix are tensile and this can lead to matrix cracking. In order to account for changes in the residual stresses with the volume fraction of fibers, several different approaches have been taken. For example, Budiansky et al. (1986) have derived exact solutions for a composite cylinder. The approach is the same as that already outlined, except that the outer cylinder is assumed not to be infinite. Instead, the outer radius (r ) is determined by the relative volume fractions, using In fiber composites, there is usually a variability in fiber spacing... 

The simplest case of a block copolymer is a diblock consisting of two covalently bonded polymers with chemically distinct repeat units A and B. If A and B are incompatible, below the order-disorder transition at Todt microphase separation is obtained into, for example, a spherical, cylindrical, or lamellar phase. The phase behavior depends on the relative volume fraction of A and B and on the magnitude of the product xabN, where xab is the Flory-Huggins interaction parameter between the two polymers, and N the total degree of polymerization [7]. We can write... 

Fig. 4 Detailed nomenclature for the characterization of layered silicate nanocomposite structures. The arrangement of the layered silicates in the polymer matrix is classified on the basis of the relative change in rf-spacing and correlation d and Sd) the relative volume fraction of layers and stacks of layers and the dependence of single-layer separation on the layered silicate volume fraction, 0 [42]...

Figure 9.9 shows the theoretical scattering from a system containing a low number density of spherical scattering features of radius R. The size and relative volume fraction of the scattering features can be determined... 

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