Dispersion Bruggeman equation

Conductivity. Of the numerous equations proposed (12) to describe the conductivity of dispersions (x), one is cited here for illustration. The Bruggeman equation gives... 

Remarkably, the thermal conductivities of the composites filled with BP40 and BP80 are much higher than the prediction of Bruggeman equation. This demonstrates that the brush-like AlN particles enhance the thermal conductivity of the polymer matrix significantly. The intrinsic reason can be explored by Agari model [16], which considers the effect of dispersion state by introducing factors Cj and Cj ... 

The evolution of a gas during an electrolytic reaction produces a dispersion of bubbles in the electrolyte. Since the bubbles have virtually zero electrical conductivity the current flow path becomes restricted and ohmic voltage losses become greater than those for the electrolyte. The usual way to deal with bubbles is to assign to the electrolyte an effective conductivity which is typically correlated as a function of gas voidage There are a number of correlations of this type one of the most reliable is the so-called Bruggeman equation ... 

The Maxwell equation as written in Eq. (8.32) has been used by many researchers to describe the behavior of MMMs. It was however later suggested that the Maxwell equation is applicable for the low loading level of dispersed phase since it was assumed that the streamline around the dispersed articles were not affected. Instead the Bruggeman model was recommended in which the effect of the particles added to the dilute suspension is considered. The Bruggeman equation is given by... 

A system with clearly defined disperse (A) and continuous (B) component phases is afforded by copolymers of styrene (A) grafted onto a polydimethyl siloxane matrix (B)101 Lack of appreciable interaction between the components was indicated by gas solubility and Tg measurements. The permeability coefficient of propane and other paraffins over a composition range vA = 0 — 0.55 followed the trend described by Eqs. (30)—(33) (with PA = 0, in view of the fact that the polystyrene phase is practically impermeable). Of particular relevance to the present discussion is the close agreement with the Bruggeman, and definite deviation from the Bottcher, equations at higher vA (cf. Fig. 11). Corresponding block copolymer membranes with vA = 0.34 also fitted into this pattern, except in one case where the structure was found to be lamellar and P was considerably lower. 

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