Impedance solid media

Attia, A. Zukalova, M. Pospisil, L. Kavan, L. 2007. Electrochemical impedance spectroscopy of mesoporous Al-stabilized Ti02 (anatase) in aprotic medium. J. Solid State Electrochem. 11 1163-1169. 

Notwithstanding the excellent analytical features inherent in molecular phosphorimetric measurements, their use has been impeded by the need for cumbersome cryogenic temperature techniques. The ability to stabilize the "triplet state" at room temperature by immobilization of the phosphor on a solid support [69,70] or in a liquid solution using an "ordered medium" [71] has opened new avenues for phosphorescence studies and analytical phosphorimetry. Room-temperature phosphorescence (RTF) has so far been used for the determination of trace amounts of many organic compounds of biochemical interest [69,72]. Retention of the phosphorescent species on a solid support housed in a flow-cell is an excellent way of "anchoring" it in order to avoid radiationless deactivation. A configuration such as that shown in Fig. 2.13.4 was used to implement a sensor based on this principle in order to determine aluminium in clinical samples (dialysis fluids and concen-... 

Both Knudsen and molecular diffusion can be described adequately for homogeneous media. However, a porous mass of solid usually contains pores of non-uniform cross-section which pursue a very tortuous path through the particle and which may intersect with many other pores. Thus the flux predicted by an equation for normal bulk diffusion (or for Knudsen diffusion) should be multiplied by a geometric factor which takes into account the tortuosity and the fact that the flow will be impeded by that fraction of the total pellet volume which is solid. It is therefore expedient to define an effective diffusivity De in such a way that the flux of material may be thought of as flowing through an equivalent homogeneous medium. We may then write ... 

When passing through a material medium the vibrations are impeded and hence become sensitive to the arrangement of matter in the medium. In many solid structures, especially crystals, a preferred direction of vibration that allows ready transit is selected by the waves. In the process a beam... 

In rocks and soils, the only appreciable diffusion of gases occurs in the voids or pores, which may be occupied by air, water or a mixture of both. Migration over any ap preciable distance is possible only if the soil pores are continuous with each other. Collisions of the gaseous molecules with liquids or solids impede their progress, so that diffusion in a porous medium is slower than in a free space. The important factors are the shape, size, tortuosity... 

The complex mechanical impedance can be obtained by measuring force, velocity, and their phase difference using probes or pickups attached to the transducer at suitable points [144], This method is very convenient with solids [52] (sometimes the most accurate), but not with liquids, although in this case it can be a convenient method of checking the performance of a transducer. The output from an accelerometer or strain-sensitive pickup gives information on resonant frequency and vibrational amplitude. However subsequent correlation with the power transmitted to the sonicated medium is not straightforward. 

In order to analyze the influence of the different loading mechanisms on the QCM response one has to model a dependence of the mechanical impedance Zl or the complex resonance frequency shift on the chemical and physical properties of the contacting mediiun. Various models for the mechanical contact between the oscillating quartz crystal and the outer medium are discussed below. The QCM is now so widely and extensively used that, in the framework of this chapter, it is not possible to review all the available literature. Hence we limited ourselves here to a review of the experimental data and theoretical ideas concerning the studies of structure and interaction at solid-hquid interface. Furthermore, we did not present here studies on... 

Electrical techniques primarily measure the electrical impedance of a mixed-phase medium. Because the dielectric constant or electrical conductivity of a solid phase differs from that of the fluid, one can measure electrical conductance or capacitance to determine phase distribution. To attain better sensitivity, conductance flowmeters are usually applied to conducting media, such as aqueous solutions or solids/water slurries, whereas capacitive flowmeters are applied to solid/gas flows and solid/nonconducting-liquid flows. Capacitance measurements are generally more reproducible because they are not affected by the ion concentration of the solution, which is difficult to control during processing. 

In some skin applications, the electrode polarization impedance may still he a source of error. With solid gel contact electrolytes, the series resistance of the contact medium may he disturbing at higher frequencies. When the stratum corneum is highly penetrated hy electrolytes (Figure 7.5), the skin impedance is so low (50 kO) that the electrode polarization impedance becomes important. 

Double-layer capacitance values of the solids were similar to those in an aqueous solution for every electrolyte. The double-layer capacitance values estimated from impedance spectra were almost independent of the polysaccharide concentration. These results clearly showed that the present solids could be used as an ionic conductive soUd as a medium for electrochemistry in the same manner as an aqueous solution. 

The diffusion coefficient of holes via the I /l3 redox couple in the solid containing 2.5 wt % carrageenan, 0.3 M KI, 0.03 MI2, and excess water was investigated by an impedance spectroscopy it was ca. 1.7 x 10 cm s , which is almost the same as that in liquid water, showing that the hole transport in the solid is not a problem in comparison with the liquid medium system. Similar results have been obtained also for a solid containing redox electrolyte and organic liquid [57]. In the present solid material, transport of small ions and molecules takes place in the same way as in a liquid, showing that the liquid contained in this solid behaves as if it were a pure liquid. 

These reactions generate electrochemical impedances due to charge transfer, gas or solid state diffusion, etc. Since these impedances appear specifically at the boundaries between dissimilar phases, the composites cannot be fully described by simple effective medium models, even if these impedances are approximated by linear resistive elements. As pointed out by several authors, in the mixture of electronic and ionic phases there are clusters connected to (i) both current collector and electrolyte, (ii) only to the electrode, and (iii) isolated clusters. Clusters of all three types are visible in Figure 4.1.14. 

We extend the analysis and consider the entire ladder network in terms of distinct R and C circuit elements. The impedance x can be represented by a resistance Ri, which defined the resistance of counterions in the pore electrolyte. Furthermore the impedance element z, which is that of the solid polymer, is replaced by a Randles equivalent circuit (see Fig. 1.84), where there is a parallel arrangement of a resistor Rj. and a capacitor Q in series with a resistor Ra- Hence we see that the pore solution is modeled in terms of a simple resistor, whereas the solid polymer is a binary composite medium. TTie latter assumption can be justified as follows. From a macroscopic viewpoint (and this has been demonstrated experimentally), the electronic resistance of the polymer is due to two contributions the first, Ra, from regions of high structural order the second, R, from regions of low structural order. Hence Ra is smaller than R. From a microscopic point of view, the polymer may exhibit two fundamentally different types of conduction. As noted in... 

Besides the DC or transient amperometric techniques described earlier, several research groups have also explored and shown that AC impedance measurements at solid-liquid interfaces with SECM (AC-SECM or IMP-SECM) could provide information on topography and conductivity of substrates. The distance dependence of the AC feedback signal can be employed for constant distance imaging of insulating substrates immersed in dilute electrolyte solutions and of live cells in a growth medium. ... 

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