Dispersed barrier models

Smaller p implies stronger cooperativity and a broader spectral dispersion. Non-cooperative relaxation (P=l) yields exponential relaxation, which is only seen for polymers in high-frequency, low temperature relaxations or in their terminal relaxation at very high temperature. Exponential decay, or a Lorentzian frequency response, is often associated with an Arrhenius temperature dependence. In fact, a barrier model for relaxation leads directly to both an Arrhenius temperature dependence and exponential decay [17,18]. 

Examples of reversible breakdown of structure have been reported for procaine penicillin dispersions (7), for model systems of calcium carbonate in polybutene ( ), and for numerous other systems. During shear the particles are forced into contact with each other with sufficient kinetic energy to overcome any natural barrier against their displacement of a lyosphere around each individual particle. A dispersion which is inherently stable can thus be forced by shear into a condition of instability. 

Orientation Once the particles are dispersed in the polymer, they must be oriented so that the flat surface of the clay is parallel to the surface of the packaging material to maximize the barrier effect. Several models have been developed in order to describe the mass transfer within the nanocomposites. Most models assume that the platelets have a regular and uniform shape (rectangular, sanidic, or circular) and form a regular array in space. They are either parallel to each other or have a distribution of orientations, with the... 

The equation derived by Troelstra and Kruyt is only valid for coagulating dispersions of colloids smaller than a certain maximum diameter given by the Rayleigh condition, d 0.10 A0. Equation 4 applies in cases where particles are transported solely by Brownian motion. Furthermore, the kinetic model (Equations 2 and 3) has been derived under the assumption that the collision efficiency factor does not change with time. In the case of some partially destabilized dispersions one observes a decrease in the collision efficiency factor with time which presumably results from the increase of a certain energy barrier as the size of the agglomerates becomes larger. 

In the context of chemical reactions that are subject to dispersive kinetics as a result of structural disorder, the above model suggests that a widening of the intermediate region between the Arrhenius law and low-temperature plateau should occur. The distribution of barrier heights should also lead to nonexponential kinetic curves (see Section 6.5). 

Meroney, R. N. and D. E. Neff, 1984. Numerical Modelling of Water Spray Barriers for Dispersing Dense Gases. Journal of Boundary-Layer Meteorology, 31 (March) 233-247. 

Pfister (1977) measured hole mobilities of TPA doped PC. Figure 51 shows the temperature dependencies for different concentrations. The field was 7.0 x 105 v/cm. The concentration is expressed as the weight ratio X of TPA to PC. The mobilities were thermally activated with activation energies that increase with decreasing TPA concentration. The concentration dependence was described by the lattice gas model with a wavefunetion decay constant of 1.3 A. Figure 52 shows the field dependencies at different temperatures for X - 0.40. The solid lines were derived from the Scher-Montroll theoiy (1975) using the listed parameters. Pfister concluded that the theoiy provides a self-consistent interpretation of all experimental observations if field-induced barrier lowering and temperature-dependent dispersion are formally introduced into the expression for the transit time. 

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