Effective Media

Bonig L, Liu S and Metiu FI 1996 An effective medium theory study of Au islands on the Au(IOO) surface reconstruction, adatom diffusion, and island formation Surf. Sot 365 87... 

For the case of nonzero temperatures the vacuum averages in Eq.(7) should be replaced by thermal averages over phonon populations. Using (7) and (5) we obtain that the scattering of an exciton in the effective medium by the perturbation fi — v z)) is described by the following self-consistent condition... 

Use of an excess of the halogenating agent results in halogenation at the 3-position of the oxindole[3,4]. The halogenation and hydrolysis can be carried out as two separate steps. One optimized procedure of this type used NCS as the halogenating agent and it was found that 70% phosphoric acid in 2-mcthoxycthanol was the most effective medium for hydrolysis[2]. If the halogenation is carried out in pyridine, the intermediate is trapped as an... 

A reverse-wipe appHcation is seen ia the clothes dryer fabric softener sheet whereia the spunbonded fabric is coated with a complex combination of compounds that are released iato the environment of a hot clothes dryer to soften and perfume the clothes, as weU as provide an antistatic quaHty. The spunbonded sheet, which must be made of polyester or nylon for temperature resistance, provides a simple and cost-effective medium to store the chemical compounds prior to release ia the dryer. 

Filtration. The filtration process depends on the physical retardation of microorganisms from a fluid by a filter membrane or similarly effective medium. The effectiveness of this process is also influenced by the bioburden (6). HoUow-fiber membranes (qv) are most often employed. The resultant... 

Electrochemical polymeriza tion of heterocycles is useful in the preparation of conducting composite materials. One technique employed involves the electro-polymerization of pyrrole into a swollen polymer previously deposited on the electrode surface (148—153). This method allows variation of the physical properties of the material by control of the amount of conducting polymer incorporated into the matrix film. If the matrix polymer is an ionomer such as Nation (154—158) it contributes the dopant ion for the oxidized conducting polymer and acts as an effective medium for ion transport during electrochemical switching of the material. 

D. E. Aspnes. Thin Solid Films. 89, 249, 1982. A detailed review of effective medium theory and its use in studies of optical properties of solids. 

We examined the role of vector percolation in the fracture of model nets at constant strain and subjected to random bond scission, as shown in Fig. 11 [1,2]. In this experiment, a metal net of modulus Eo containing No = 10" bonds was stressed and held at constant strain (ca. 2%) on a tensile tester. A computer randomly selected a bond, which was manually cut, and the relaxation of the net modulus was measured. The initial relaxation process as a function of the number of bonds cut N, could be well described by the effective medium theory (EMT) via... 

Fig. 5. Schematic representation of the measured CNT films. The effective medium is the result of tubes dispersed in an insulating host (glassy graphite).

Fig. 6. MG model the metal with dielectric function (e ,((0)) particles are surrounded by an insulator ( ((0)) (left). The jnixture results in an effective medium e,.jy(right).

Fig. 7. Model calculations for the reflectivity (a) and the optical conductivity (b) for a simple (bulk) Drude metal and an effective medium of small metallic spherical particles in a dielectric host within the MG approach. The (bulk) Drude and the metallic particles are defined by the same parameters set the plasma frequency = 2 eV, the scattering rate hr = 0.2 eV. A filling factor/ = 0.5 and a dielectric host-medium represented by a Lorentz harmonic oscillator with mode strength fttOy, 1 = 10 eV, damping ftF] = I eV and resonance frequency h(H = 15 eV were considered for the calculations.

Fig. 11. The Bruggeman model (BM) lakes into account the modification of the effective medium by the adjunction of metal in the medium. The net effect is a broadening of the resonance peak. The parameters of the metallic spheres in these calculations are fuHp = I eV and fiV = 0.1 eV. The insulating host is defined by ftcOp i = 1 eV and ftf = 1 eV and fidiy = 20 eV. Note that the normal Drude curve is superimposed with the Bruggeman curve with/= 1.

We have defined the solvent effect (medium effect) on a reaction by 8mAC = 8G - hGl =... 

The idea of adding smaller and smaller particles to fill in the interstices left by the larger particles can be continued. The viscosity of a multimodal suspension may be predicted from unimodal data based on the premise that the viscosity of the mixture of smaller fractions is the medium viscosity for the next largest fraction. This is an effective medium theory and basically assumes that the smaller particles act as a medium toward the larger particles. This was assuming at least an order of magnitude difference in size between successive fractions [26]. Thus, the viscosity of the ith component is ... 

As a matter of fact there is an infinite number of possible choices for the effective medium. But if one deals with an alloy problem, it is well-known that the best single-site effective medium is given by the CPA. In fact, it fulfills all the criteria mentioned above. That is, the Green s function for the CPA effective medium decays, apart from an oscillating factor, exponentially as, where I is the mean free... 

Here R, R LIZ, and the effective medium Green s function for the LIZ gnni is calculated only once for the entire system... 

The model has been treated analytically employing the effective medium approach [58] and by Monte Carlo simulation. It makes the following predictions A dilute ensemble of non-interacting charge carriers, initially generated at random within the DOS, lends to relax toward the tail slates and ultimately equilibrates at... 

In a concentrated solution, characterized by an effective medium viscosity r e "Hs, the hydrodynamic field decays much faster due to the shielding effect of the encountered polymer segments ... 

In view of eqs. (6.51) and (6.52) one can now appreciate the advantages of the effective medium double layer approach used to derive Equation... 

Cukier [87], using an effective medium-type approach, analyzed the diffusion of Brownian spheres in two semidilute polymer solutions The first was composed of long... 

For heterogeneous media composed of solvent and fibers, it was proposed to treat the fiber array as an effective medium, where the hydrodynamic drag is characterized by only one parameter, i.e., Darcy s permeability. This hydrodynamic parameter can be experimentally determined or estimated based upon the structural details of the network [297]. Using Brinkman s equation [49] to compute the drag on a sphere, and combining it with Einstein s equation relating the diffusion and friction coefficients, the following expression was obtained ... 

Johnson, EM Berk, DA Jain, RK Deen, WM, Hindered Diffusion in Agarose Gels Test of Effective Medium Model, Biophysical Journal 70,1017, 1996. 

In order to be useful in practice, the effective transport coefficients have to be determined for a porous medium of given morphology. For this purpose, a broad class of methods is available (for an overview, see [191]). A very straightforward approach is to assume a periodic structure of the porous medium and to compute numerically the flow, concentration or temperature field in a unit cell [117]. Two very general and powerful methods are the effective-medium approximation (EMA) and the position-space renormalization group method. 

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