Kemer model

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]. 

Sjoerdsma S.D., Bleijenberg A.C.A.M., and Heikens D., The Poisson ratio of polymer blend, effects of adhesion and correlation with the Kemer packed grain model. Polymer, 22, 619, 1981. 

Figure 26.11 shows the stress-strain behavior of ES30 filled with various levels of ATH. It can be seen that the yield stress increases with increasing level of ATH while the ultimate elongation is in excess of several hundred percent even for materials with more than 50wt% ATH. The modulus of composite materials can be modeled by the generalized Kemer equation ... 

In presence of nodules, ultimate properties in tension for non-notched samples remain unchanged. The only visible effect is a decrease in young modulus, E, and yield stress due to the rubber content. In example, young modulus of blends, E, obeys Kemer model [1IJ ... 

FIGURE 2.6 Viscosity of the composition at a temperature of 180°C (a) and 170 C (b) (theoretical calculations on model of Kemer-Takayanagi A experimental data). 

Kerner [104] made the first sophisticated analysis of thermoelastic properties of composite media using a model which had been considered earlier by van der Poel for calculation of the mechanical properties of composite materials. Here the dispersed phase has been assumed for spherical particles. Kemer s model accounts for both the shear and isotactic stresses developed in the component phases and gives for the composite ... 

Other proposed models for particulate composites are variants of Kemer s model or have specific temperature ranges or volume fractions of reinforcements over which they can be used. 

Runyon M, Johnson-Kemer B, Ismagilov R (2004) Minimal functional model of Hemostasis in a biomimetic microiluidic systerrr. Angew Chem Int Ed 43 1531-1536... 

The moduli of PPO/glass bead composites are reported by Trachte and DiBenedetto (23) to follow the Kemer equation and by Wambach al (24), to follow the equation of Van der Poel. These may therefore be more appropriate choices in modeling the composite behavior of the PpCIS/PPO blends but considering the low moduli ratio of the PpCIS/PPO blends, EppQ] 3/EppQ = 1.3, the difference between values of moduli predicted by use of either of these equations or use of the simpler Eq. 3 would be slight. 

Here GJo jpogj ion represents complex shear modulus of the blend without interfacial effects while GJ p is the interface contribution, which comprises the extra elasticity originating in drop deformability. The former contribution was computed from the Kemer model [equivalent to Eq. (2.23) with v 2 = 0], while the second was calculated from the Palierne model. The computed dependencies for PP with ethylene-vinyl acetate (EVAc) copolymer and Si02, hydrophilic or hydro-phobic, well represented the frequency dependencies of G, G", and rf. Also, the addition of 3wt% silica reduced EVAc droplet size from 2.2 to about 0.5 m. The hydrophilic silica migrated to EVAc, while hydrophobic silica migrated to the PP phase. 

Flesch, J., Kemer, D., Riemenschneider, H., and Reimert, R. 2008. Experiments and modeling on the deacidification of agglomerates of nanoparticles in a fluidized bed. Powder Technol. 183 467-479. 

Kemer KP, Imielinska C, RoUand J, Tang H. Augmented reality for teaching endotracheal intubation MR imaging to create anatomically correct models. Proc Annu AMIA Symp 2003 2003 888-9. 

Elanthikkal et al. investigated the effect of CNCs (from banana waste fibers) (0-10% w/w) on the morphological, thermal, and mechanical properties of poly(ethylene-co-vinyl acetate) (PEVA)/cellulose composites. The produced composites showed superior thermal and mechanical properties as compared to that of the EVA copolymer alone. In this study, three different theoretical models (Halpin-Tsai model, the Kemer model and the Nicolais-Narkis model) have been employed to compare the results with observation of tensile data from mechanical tests. Here, experimental results showed better agreement with the prediction given by the use of the Halpin-Tsai model, assuming that there is perfect wetting of filler by the polymer matrix [217]. 

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). 

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.

Another mode of natural nanocomposites reinforcement degree description is micromechanical models application, developed for pol5mier composites mechanical behavior description [1, 37-39]. So, Takayanagi and Kemer models are often used for the description of reinforcement degree on composition for the indicated materials [38, 39]. The authors of Ref. [40] used the mentioned models for theoretical treatment of natural nanocomposites reinforcement degree temperature dependence on the example of PC. 

Hence, the stated above results have shown the modified Kemer equation application correctness for natural nanocomposites elastic response description. Really this fact by itself confirms the possibility of amorphous glassy polymers treatment as nanocomposites. Microcomposite models usage gives the clear notion about factors, influencing polymers stiffness. 

The interlayer model represents an extension of van der Pool s theory derived from works by Frohlich and Sack devoted to viscosity of suspension by a shell-model. Van der Poel obtained expressions for G and K (bulk modulus). In his model, the filler sphere of a radius, a, is supposed to be sturounded by the sphere of the matrix material with radius 1. The sphere in sphere obtained in this way is sturotmded by the great sphere of radius, R, consisting of material with macroscopic properties of heterogeneous composition. The residts of calculations according to the equations proposed by van der Poel are very close to those obtained using the Kemer equation. Detailed description of this approach can be found elsewhere. ... 

The interlayer model was developed by Maurer et al. The model of the particulate-filled system is taken in which a representative volume element is assumed which contains a single particle with the interlayer surrounded by a shell of matrix material, which is itself surrounded by material with composite properties (almost the same as Kemer s model). The radii of the shell are chosen in accordance with the volume fraction of the fQler, interlayer, and matrix. Depending on the external field applied to the representative volmne element, the physical properties can be calculated on the basis of different boundary conditions. The equations for displacements and stresses in the system are derived for filler, interlayer, matrix, and composite, assuming the specific elastic constants for every phase. This theory enables one to calculate the elastic modulus of composite, depending on the properties of the matrix, interlayer, and filler. In... 

Thermal property evaluation took place with respect to thermal expansion, diffusivity, specific heat, and ultimately thermal conductivity. Instantaneous CTE data at 20°C is presented in Figure III. The thermal expansion of these materials is an important consideration to take account of, as many applications require matching CTE s to help reduce thermal mismatch stresses during cycling. Results are plotted with a rule of mixture model as well as the Turner and Kemer models for CTE. These are shown in Equations 5, 6, and 7 respectively. These predictions were also based on the SiCrSi system, with the property inputs provided in Table II. 

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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