Kemer-Nielsen model

The following input parameters were used for the Kemer-Nielsen model vm = 0.5 for mbbery matrix Vmax 0-b for random packing of spheres modulus of the rabbery epoxy network matrix Gm(=Ge) = 2.2 x 10 Pa modulus of incompletely condensed siloxane-silica domains was taken from literature data (12) on xerogels... 

Figure 10. Relative modulus of the O-I hybrid as a function of the effective volume fraction of the hard phase, Veff. Curves - theoretical models, Gsi = 4 x 10 Pa, Ge = 2.2 X 10 Pa, 1 Kemer-Nielsen model (eq. 1) Vmax = 0.6, vm = 0.5, 2 Davies model (eq. 4) Veff = vsi + VEg. Experimental results A ET-1,0 ET-2, E1-T2, DGEBA-D2000.

The considerable increase of elastic modulus with low amoimt of ultrafine amorphous silica Si02 (< 0.1 pm) shows the nanoparticles to be well dispersed. It cannot be explained by classical models (Kemer, Nielsen) we have to take into account that a part of the polymer matrix is occluded in the aggregates. It can also be explained by adsorption of the polymer on the surface of the silica. Silica-PP adhesion is high, and so the molecular mobility is reduced this effect is all the more important as the surface area is high (> 150 m /g). This effect has been observed on elastomeric materials, where polymer adsorption on silica control the modulus [23]. 

The analysis of DMA results shows that theoretical models of a composite with a hard filler dispersed in a soft matrix do not account for the observed increase in the modulus. The experimental moduli in Fig. 9 are much higher compared with the theory of the Kemer-Nielsen (11) model (curve 1) (eq.l). 

There are no adjustable parameters. Such models include the Kemer equation [68], Halpin-Tsai equation [69] and Chow equation [70]. The second group of equations, on the other hand, incorporate adjustable parameters to account for interactions between particles as well as between the matrix and the particles. Factors such as critical solid volume fraction, degree of agglomeration and powder-matrix adhesion are taken into account. Equations and models under this group would include the Nielsen generalized equation [71] and the modified Kemer equation [72,73]. 

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