Diffusion filler concentration

Diffusion and permeability are inversely related to the density, degree of crystallinity, orientation, filler concentration, and cross-link density of a polymeric film. Generally, the presence of smaller molecules, such as plasticizers, increases the rate of diffusion in polymers since they are more mobile and can create holes or vacancies within the polymer. The rate of diffusion or permeability is fairly independent of polymer chain length just as long as the polymer has a moderately high chain length. 

As the filler concentration increases so does the initial slope of Wt = f(j/x), see Fig. 12. According to Eq. (5) this may be due either to an increase of the diffusion coefficient or to the increased effective thickness of the specimen due to the addition of the filler that does not absorb water. Initially, there are small increments of the relative content of absorbed water, but the absolute quantity (referred to the binder) is almost independent of the filler concentration however in the next stages the absolute quantity of absorbed water becomes proportional to the microsphere concentration. Thus there are different absorption mechanisms effective in the course of time. 

The reduced value of the scaling exponent, observed in Fig. 29 and Fig. 30a for filler concentrations above the percolation threshold, can be related to anomalous diffusion of charge carriers on fractal carbon black clusters. It appears above a characteristic frequency (O when the charge carriers move on parts of the fractal clusters during one period of time. Accordingly, the characteristic frequency for the cross-over of the conductivity from the plateau to the power law regime scales with the correlation length E, of the filler network. 

At higher filler concentrations, above the gel point (

filler particles come sufficiently close to each other. Under this condition a diffusion... 

Another example given by Stephen et al. [66] evaluated the transport properties of solvents in membranes fabricated using ZnO-filled NR, carboxylated styrene-butadiene rubber (SBR), and a 70/30 blend using the two polymers. In the unblended samples containing filler, the diffusion coefficient was dramatically decreased with the increase of filler content. However, the blends exhibited high diffusion coefficients for high filler concentrations. 

The effect of the filler particle size on the permeability of a PDMS film has also been addressed [41]. By increasing the particle size, the permeability of silicone to gases such as Oj, Nj and CO increases, presumably due to enhanced gas solubility that counteracts the decrease on diffusivity. As it was expected, the higher the filler concentration used, the more pronounced the effect is. 

Several properties of the filler are important to the compounder (279). Properties that are frequentiy reported by fumed sihca manufacturers include the acidity of the filler, nitrogen adsorption, oil absorption, and particle size distribution (280,281). The adsorption techniques provide a measure of the surface area of the filler, whereas oil absorption is an indication of the stmcture of the filler (282). Measurement of the sdanol concentration is critical, and some techniques that are commonly used in the industry to estimate this parameter are the methyl red absorption and methanol wettabihty (273,274,277) tests. Other techniques include various spectroscopies, such as diffuse reflectance infrared spectroscopy (drift), inverse gas chromatography (igc), photoacoustic ir, nmr, Raman, and surface forces apparatus (277,283—290). 

A mathematical model was proposed for evaluating the diffusion of a material which can react with the filler (e.g., acid). The proposed method permits the study of process kinetics for different concentrations of penetrant and filler. ... 

SBR filled with intercalated montmorillonite had substantially lower toluene uptake compared with the same rubber filled with carbon black (see Figure 15.42). Figure 5.28 shows that the diffusion coefficient of kerosene, which defines penetration rate, decreases when the concentration of carbon black in SBR vulcanizates is increased. Figure 15.33 compares the uptake rate of benzene by unfilled rubber and by silica and carbon black filled rubber. Both fillers reduce the solvent uptake but carbon black is more effective. 

This equation stresses the importance that diffusion of the crystallizing species has on the crystallization rate, concentration of nuclei, the molecular arrangement, and the required degree of supercooling. Figure 10.2 shows that the rate of crystallization is increased in the presence of silica. This is an effect of nucleation. The filler surface also lowers the free enthalpy barrier which promotes the formation of nuclei. 

The physical properties of some fillers play a role in their function as stabilizers. A1(OH)3 undergoes endothermic decomposition which lowers temperature of material. Loss of water from MgiOH), may increase stability in some cases. In others, it may cause degradation. This is discussed below. The platelet structure of some fillers (e.g., talc or mica) contributes to an increased thermal stability because the degradation rate is increased as oxygen concentration increases. The structure formed by the platelets reduces the diffusion rate of oxygen. 

Quemada (1978a, 1978b) examined the rheology and modelling of concentrated dispersions and described simple viscosity models that incorporate the effects of shear rate and concentration of filler and separate effects of Brownian motion (or aggregation at low shear) and particle orientation and deformation (at high shear). The ratio of structure-build-up and -breakdown rates is an important parameter that is influenced by the ratio of the shear rate to the particle diffusion. A simple form of viscosity relation is given here ... 

Frolov, Shabanova, and co-workers (37-39) studied the transition of a sol into a gel and the aggregate stability of colloidal silica. Their aim was to develop a technology for the production of highly-concentrated silica sols and to use them as binders, catalyst supports, polymer fillers, adsorbents, and so forth. Kinetic studies were made of polycondensation and gel formation in aqueous solutions of silicic acids. At the stage of particle growth, poly condensation proceeds in the diffusion-kinetic region. With changes in pH, temperature, concentration, and the nature of electrolytes,... 

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