Takayanagi model parameters

The Takayanagi model parameters are related with filler concentration and interphase thickness by the following simple relationships ... 

Table II. Takayanagi Model Parameters of Volume Fraction of PG-PST Blends...

Wavelength Takayanagi model parameter Optimal wavelength of spinodal decomposition Chemical potential... 

Lipatov et al. [116,124-127] who simulated the polymeric composite behavior with a view to estimate the effect of the interphase characteristics on composite properties preferred to break the problem up into two parts. First they considered a polymer-polymer composition. The viscoelastic properties of different polymers are different. One of the polymers was represented by a cube with side a, the second polymer (the binder) coated the cube as a homogeneous film of thickness d. The concentration of d-thick layers is proportional to the specific surface area of cubes with side a, that is, the thickness d remains constant while the length of the side may vary. The calculation is based on the Takayanagi model [128]. From geometric considerations the parameters of the Takayanagi model are related with the cube side and film thickness by the formulas ... 

Analysis of Stress—Optical Data. The slight, if indeed real, improvement of the isotropic model over the Takayanagi model would be of little consequence were it not for a more pronounced difference between the two models in their ability to describe the stress-optical data. When the parameters obtained from the dynamic data (Table IV) are substituted into Equations 8 and 9, Equation 8 produces results which are uniformly too low. Equation 9 also underestimates the magnitude of Ka but only by an average 7% (Figure 14). For most blends the discrepancy is less than 5%, and all calculated values show the characteristic elevation of the birefringence attributed to the multiphase structure. 

Gg in different ways. By fixing the weighting ratio according to Eq. 7, we also avoid the need to retain it as a fitting parameter. By contrast, the Takayanagi model (28) demands the unique assignment of this parameter to each microstructure, but such numerical values may have little relevance to the macroscopic bulk sample. 

Even for block copolymers, in which the phase separation can be distinguished in electron micrographs, there are problems in matching parameters such as Poisson s ratios of the two components nevertheless the simple Takayanagi models, particularly when extended by a treatment to account for the finite length of the reinforcing component, can describe numerous features of static and d3mamic elastic behaviour. 

In accordance with the data, the real G and imaginary G parts of the shear modulus in the Takayanagi model may be expressed using parameters Xi and Oi and mechanical characteristics of components G and G ... 

The Takayanagi model allows calculation of the value of the complex modulus . In [184] the methods of calculating E and E were proposed. For this purpose, using the parameters of the Takayanagi model, the following set of equations was derived ... 

Takayanagi s model is a phenomenological model obtained by combination of serial and parallel models. The composite modulus ( c(T)) is determined by (17.4) with X, an adjustment parameter. 

Figure 17.7 shows that Takayanagi s equation seems to be an excellent model to predict the modulus evolution, on the range 0-30 wt.% of filler. The parameter (2) has been determined by adjustment at 4.5. Reuss and Voigt s models are not well adapted to estimate correctly the composite moduli. This is because the matrix and the fillers mechanical characteristics are too different. But, we can show that the composite moduli are comprised between both boundaries, fcCR) and c(V). 

---