Jay Janzen

On the critical conductive filler loading in antistatic composites

Conductive particulate inclusions in a continuous insulating matrix typically impart a precipitous drop in electric resistivity commencing at a threshold volume fraction φcrit which depends on filler particle form and spatial distribution. An illuminating formulation relating threshold composition to the morphology of particles having density ρ is φcrit=1/(1+4ρν), where ν is the readily measurable specific void space in a random dense−packed bed of the (powder) filler. Use of this simple expression permits the first satisfactory semiquantitative rationalization not only of most data obtained recently for model systems comprised of polymer−embedded metal spheres, but also of known behavior of rubbers containing carbon blacks having varied complicated sintered−aggregate (aspherical) morphologies.

The refractive index of colloidal carbon

Abstract A critical evaluation of published data on complex refractive index leads to the conclusion that for absorbing paracrystalline colloidal carbons (carbon blacks) no accurate determination of this significant fundamental material property has been made. It is readily demonstrated that the usual scheme of matching the generalized Fresnel equations to two (or more) catoptrically measured data points leads to results which, although reproducible, are purely formal artifacts because the particulate nature of the material precludes preparation of optically smooth and homogeneous test pieces, without which the Fresnel equations do not hold. An alternative approach is to derive the index from measurements of dilute suspension optical properties by way of the Mie equations, but this is rendered difficult by the effects of polydispersity and particle nonsphericity. Nevertheless, progress has proved possible through extinction measurements made on a specially made carbon black comprised of very small (and consequently also relatively paucidisperse) particles. At visible wavelengths (350–1000 nm) a result near m0 = 2.0 − 1.0i has been obtained for this material. It is foreseen that additional refinement of this estimate will be feasible by use of the same technique on further improved (e.g., sizefractionated) samples, but for the present this result appears to be a needed improvement over others published before.

Extinction of light by highly nonspherical strongly absorbing colloidal particles: spectrophotometric determination of volume distributions for carbon blacks

Despite serious nonsphericity of the particulate entities involved, observed extinction spectra for dilute carbon black sols are fitted precisely by Mie theory for ensembles of spheres which it is shown must be quite nearly volume-equivalent to the actual colloidal carbon units. Hence volume distribution statistics are obtainable for carbon blacks by inversion of spectrophotometric data on suspensions.

Specific Surface Area Measurements on Carbon Black

Abstract Various methods for estimating specific areas of carbon blacks are compared. These include the electron microscope count, methods based on adsorption of nitrogen, iodine and surfactants, and optical reflectance tests.

Short derivation of the influence of particle size ratio on the conductivity threshold in binary aggregates

A model developed by R.P. Kusy for predicting the composition at which the sudden onset of conductivity occurs in polymer/metal powder compacts is shown to yield quantitative results practically equivalent to those given by a previously published solution to the same problem. Significant differences nevertheless exist in the two theoretical developments leading to the concurring results; both approaches are appraised with reference to these differences.

Stereological functions for estimating surface areas and volumes of random flocs

Abstract An algorithm has been developed for converting perimeter and area data on silhouettes of random flocs into estimates of their higher-dimensional analogs, surface areas, and volumes. In essence the algorithm comes from inversion of statistical relationships revealed by Monte Carlo simulation of random floc formation. A silhouettes reciprocal isoperimetric quotient (a dimensionless shape factor) is the key variable in convenient formulas for effecting the stereological conversions. The resulting expressions enable the user of modern image analysis instrumentation to derive, automatically, from rudimentary measurements made in two dimensions, desired estimates of basic 3-D morphological descriptors of irregular particulate materials having floc-like structures. Specific surface areas and packing characteristics of carbon blacks are discussed to illustrate applications to practical problems in colloid science.