Effective Medium Percolation Theory Research Articles

Conductive thin-film composite hydrogels: Trapping anionic polyelectrolyte in polyaziridine host matrix

Acid-catalyzed polymerization of sufficiently concentrated aqueous solutions of a trifunctional aziridine monomer affords hydrogels. Dynamic mechanical analysis has been used to demonstrate that composite hydrogels, obtained when the polymerization is effected in the presence of poly(sodium styrenesulfonate), have a composition dependent modulus. A region rich in the polyelectrolyte has a modulus which exceeds that of the {open_quotes}host{close_quotes} homogeneous polyaziridine hydrogel. This is consistent with ionic bonds between protonated sites on the polyaziridine matrix and sulfonate groups on the included polyelectrolyte augmenting the structural stability of the hydrogel. Thin films were prepared from coatings of the incipient hydrogel solutions. When the coatings are dried to a water content of 20%, water-insoluble thin films are obtained provided a critical weight fraction of the monomer is exceeded. Conductive thin films can be obtained, provided a critical weight fraction of polyelectrolyte is exceeded. FTIR analysis of the coatings in the attenuated total reflectance mode shows that conductivity increases as tight ion pairing decreases between the polyelectrolyte and its counter ions in the matrix. The S-shaped dependence of the normalized conductivity on the composition of the thin films is independent of the state of hydration of the film. Effective medium percolation theory, (EMPT), generally fitsmore » the S-shaped compositional dependence of the conductivity but overestimates the rate of growth of the conductivity beyond the critical point. 20 refs., 7 figs.« less

An evaluation of the ionic conductivity in AgI-doped glasses: The graded-percolation model

Various percolation theories, Effective Medium Percolation Theory (EMPT), Site Percolation Theory (SPT) and Bond Percolation Theory (BPT), have been applied to the ionic conductivity of a series of AgI-doped glasses in order to reexamine the proposed “AgI-microdomain” model for these glasses. In contrast to previous reports the possibility that percolation effects do control the conductivity in these glasses, it is found here that SPT predicts a conductivity catastrophe at x ≈ 0.3 at the percolation threshold and the EMPT model predicts too sharp a threshold as well. Both of these effects are not observed in any of the AgI-doped glass studied to date. Variation from the percolation theories and experimental data, however, has been used to support two new features of the ionic conduction in these glasses. At low AgI contents, sharp increases in conductivity are proposed to arise from a “co-connectivity” of the Ag+ cations and at higher AgI contents failure of the conductivity to reach the value of α-AgI is associated with the distortion of the I-polyhedra away from those in α-AgI.

A percolation model for the conductivity of mixed phase, mixed ion aluminas

Effective Medium Percolation Theory can be used to predict the measured conductivity in two phase systems. It is shown that this theory can be applied to mixed phase, mixed alkali ion β aluminas if adequate account is taken of such factors as grain misorientation and ion distribution. The information obtained about the mixed alkali effect is in good agreement with existing experimental data.

On the compositional dependence of the optical gap in amorphous semiconducting alloys

It is found that the optical gap E AB for amorphous A-B alloys can be determined by the energy gap E A for element A and E AB for the element B in the equation E AB ( Y) = YE A + (1− Y) E B where Y is the volume fraction of element A. Calculations based on a random bond network agree with experiments for SiGe, SbSe, and AsTe films (class A). Calculations based on a chemically ordered bond network which tends to form microscopic molecular species gree with experimental results for the AsSe, AsS, GeTe and Sb 2Se 3As 2Se 3 systems (class B). In contrast to the above systems, agreement with experiment is not obtained for the TeSe, As 2Te 3As 2Se 3 and GeTe 2GeSe 2 systems which contain atoms of both Te and Se (class C). The classification into three types (classes A, B and C) is consistent with the calculation based on effective medium percolation theory which interprets the compositional dependence of the conductivity of chalcogenide glasses.

Percolation-controlled conduction in chalcogenide glass semiconductors

The applicability of effective-medium percolation theory (EMPT) to the composition dependence of the electrical conductivity is discussed for binary and multicomponent chalcogenide glasses. Calculations assuming a mixture of atoms, which are applied to explain the experiment for As-Te films by Ast, do not agree with experiments on all the systems considered. By assuming a chemical which forms microscopic molecular species, the conductivity over the measured compositional range can be well described with EMPT in the As-Se, As-S, and ${\mathrm{As}}_{2}$${\mathrm{Se}}_{3}$-${\mathrm{Sb}}_{2}$${\mathrm{Se}}_{3}$ systems, except for Te-Se, ${\mathrm{As}}_{2}$${\mathrm{Se}}_{3}$-${\mathrm{As}}_{2}$${\mathrm{Te}}_{3}$, and ${\mathrm{As}}_{2}$${\mathrm{S}}_{2.63}$-Te which contain the isomorphous Te, Se, and S atoms. Chalcogenide glasses can be classified roughly into three groups: a random mixture of atoms type, a strong chemical ordering type, and an isomorphous-atom type. It is suggested that EMPT has broad application in structural studies of chalcogenide glasses.

Evidence for Percolation-Controlled Conductivity in AmorphousAsxTe1−xFilms

The compositional dependence of the dc conductivity of ${\mathrm{As}}_{x}{\mathrm{Te}}_{1\ensuremath{-}x}$ films with $0.3<x<0.78$ was measured. The resistivity over the entire compositional range investigated could be described with an effective-medium percolation theory. No adjustable parameters enter into this first analytical description of the compositional variation of a transport property in an amorphous multicomponent semiconductor.