Geometrical thickness

The next three layers in the numerical model are associated with the electrolyte/electrode assembly, as shown in the right half of Figure 7. The FLUENT SOFC module treats the electrolyte as a 2-D planar element. Therefore the electrolyte in the model has geometrical thickness of zero. On either side of the electrolyte are the electrodes which are created with 3-D elements. Therefore, the electrolyte/electrode assembly in the model is only as thick as the two electrodes. Around the outer periphery of the electrolyte/electrode assembly, we have include an insulator with the properties of YSZ. The insulator prevents an electrical short circuit between the top and bottom edge rails. No ionic transport occurs through this insulator. 

The correct interpretation of the frequency shift from QCM experiments in liquids is a challenge. Practitioners often just apply the Sauerbrey equation (Eq. 28) to their data and term the resulting areal mass density Sauerbrey mass and the corresponding thickness Sauerbrey thickness . Even though the Sauerbrey thickness can certainly serve to compare different experiments, it must not be naively identified with the geometric thickness. Here is a fist of considerations ... 

The QCM always measures an areal mass density, never a geometric thickness (cf. the remarks below Eq. 71). The conversion from areal mass density to thickness usually requires the physical density as an independent input. A density of 1 g cm is often assumed in soft matter experiments. Given the other uncertainties (see below), this is in many cases a fair approximation. 

Fig. 9 The acoustic contrast easily saturates. The figure shows a sketch of the contrast function (integrands in Eqs. 78 and 79) as a function of the polymer volume fraction of an adsorbed polymer film. It is assumed that both the shear modulus Gf and the dielectric constant Sf are roughly proportional to the polymer concentration. However, Gf increases much more strongly than gf. If, for instance, a swollen polymer film contains 50% water, this will not appreciably decrease the apparent acoustic thickness because the modulus of the film is still much larger than the modulus of water and (Gf - Gijq)/Gf remains about unity. This is different in optics because the contrast is roughly proportional to the concentration. As a consequence, the apparent optical film thickness is proportional to the product of concentration and thickness, which is the adsorbed amoimt. In acoustics, the apparent thickness is close to the geometric thickness. Trapped water appears as part of the film in acoustics...

Method B is a liquid immersion method, the capacitance of the cell (air-filled) being measured with and without the specimen between the electrodes. These measurements are repeated with the cell filled with a liquid of ktiow n permittivity. The permittivity and dissipation factor of the specimen can be calculated from the four values of capacitance and dissipation factor without knowledge of the thicknes.s of the specimen. It is also possible to calculate the actual thickness of the material between the electrodes. Comparison of this with the geometrical thickness enables an estimate to be made of the depth of surface profile of the material. An example of a suitable cell is shown in Fig. 6. 

The nature of radiative heat transfer within an aerogel, i.e., whether it is diffusive or nondiffusive, depends on the optical thickness of the specific type of aerogel, or to be more exact the optical thickness t of an aerogel layer with the geometrical thickness if [18] ... 

Fig. 13. Provided the geometrical thickness is known, the corresponding dispersion curve can be computed from the interference spectrum measured (from Zeiss Information).

There is no easy way to measure the geometrical thickness of a film during deposition since the thickness depends on the density for a given mass deposited. Generally, thickness is determined from the mass that is deposited, assuming a density so that the mass gauge is calibrated to provide thickness. 

Geometrical thickness - measured in millimeters, microinches, nanometers, angstroms, or microns. Does not take into account the composition, density, morphology, microstructure, etc. The location of the surface and interface must be determined and the surface morphology of the substrate is a factor. 

Property thickness - measures some property such as X-ray absorption, XRF, beta (electron) backscatter, or ion backscattering and can become a geometrical thickness by knowing property-thickness relationships, which are usually determined by calibration. Thickness measurement may be sensitive to density, composition, crystallographic orientation, porosity, etc. 

Thickness, optical (optical) The geometric thickness multiplied by the index of refraction. 

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