Model cylindrical

The model cylindrical Li-ion battery (AA-size) was manufactured using SL-20 graphite as anode active material. The general appearance of the cells is shown by Figure 2 for more detailed description of the cells see the experimental part of the paper. 

TITANIA WITHOUT BINDERS pore model cylindrical shaped... 

TITANIA WITH PVA AND HPC (Mw = 10E5) pore model cylindrical shaped... 

Based on the above general principles, quite a number of models have been developed to estimate pore size distributions.29,30,31-32,33 They are based on different pore models (cylindrical, ink bottle, packed sphere,. ..). Even the so-called modelless calculation methods do need a pore model in the end to convert the results into an actual pore size distribution. Very often, the exact pore shape is not known, or the pores are very irregular, which makes the choice of the model rather arbitrary. The model of Barett, Joyner and Halenda34 (BJH model) is based on calculation methods for cylindrical pores. The method uses the desorption branch of the isotherm. The desorbed amount of gas is due either to the evaporation of the liquid core, or to the desorption of a multilayer. Both phenomena are related to the relative pressure, by means of the Kelvin and the Halsey equation. The exact computer algorithms35 are not discussed here. The calculations are rather tedious, but straightforward. 

Ross 3 Model Cylindrical catalyst pellets, 0.48 cm diameter and length 5.1 cm 192.6 cm... 

W. A. Steele and M. J. Bojan, Simulation Studies of Sorption in Model Cylindrical Pores, Adv. Coll. Interface Sci. 76-77 (1998) 153-178. 

A similar simulation technique was used in Ref. [19] to obtain a model cylindrical pore in porous silica. Again a bulk silica atomic structure was simulated and the surface of a pore was created by removing silicon and oxygen atoms from the interior of a cylinder inscribed around a fixed axes. The simulation technique was essentially the same as in Refs. [17, 18], the only difference being that in the former case a silica surface was created by boring a pore from bulk silica while in the latter case it was created by cutting out a sphere from the bulk. 

Since the early work of Wheeler (10), there has been a continuous effort to extract Information on adsorbent pore size distribution from gas sorption isotherms. The most crucial step is a selection of a proper pore shape model. Cylindrical (11) and parallel plate (12) pore models have been used most often. 

Thus far the two-fluid model has been derived in Cartesian coordinates. However, for working problems it is often more natural to use curvilinear coordinates like cylindrical and spherical coordinates. In reactor modeling cylindrical coordinates are of particular interest because many reactors have the shape of a tube. 

Gonzales-Tovar E, Lozada-Cassou M, Henderson D. Hypernetted chain approximation for the distribution of ions around a cylindrical electrode. II. Numerical solution for a model cylindrical polyelectrolyte. J. Chem. Phys. 1985 83 361. 

For the measurement of pore sizes on the membrane, the geometry of the tip is also important. The pore sizes or funnel shape of pore entrances determined by AFM depend on the convolution between tip shape and pore shape as illustrated in Fig. 5.5. In this figure, AFM traces for two different membrane models (cylindrical and funnel-shaped with two different pore sizes) and an idealized round-shaped tip. Only in model A can surface diameter be measured accurately from the tip traces. 

The adsorption/desorption isotherms show a mariced decrease in nitrogen adsorption due to grafted carbon deposits. As Cq increases the specific surface area, 5bet. mesopore surface, S,, pore volumes, Vp and V eso. and pore radii, (Table 4.7) decrease nearly linearly. Initial Si-60 and CSG are mesoporous materials (Figure 4.18 and Table 4.7). The deviations (Aw) of the pore model (cylindrical pores in silica gel and voids between spherical carbon or silica nanoparticles with the SCR procedure) are relatively small (4%-13%). 

Figure 3.12. The model cylindrical disks of microcrystallites of porous carbon (adapted from Segarra and Glandt, 1994). (b) Comparison of experimental and simulated adsorption isotherms for model carbons of different platelets sizes (a in nm) (A) methane at 301.4 K and (B) ethane at 300.0 K (Segarra and Glandt, 1994).

Mercury porosimetry (MP) is an extremely useful technique to characterize pore structure of materials (Giesche, 2006). This method measures an average diameter of open pores and its distribution, total volume of pores, specific surface, density, etc. Limitation of this method is that high pressures can distort the actual pore structure. Besides it does not give the actual size of pores or capillaries, but equivalent diameter of model cylindrical pores. Closed pores are inaccessible to mercury and cannot be studied. 

Elaboration of a Physical Model by Eddy Current and Application in the Characterization of Long Defects in Hollow Cylindrical Products. 

Figure C2.3.17. Model of half-cylindrical aggregates (hemimicelles) on a crystalline hydrophobic substrate, such as for tetradecyltrimethylammonium bromide on M0S2 [91], Adapted from figure 2 of [89],...

The capped sticks model can be seen as a variation of the wire frame model, where the structure is represented by thicker cylindrical bonds (figure 2-123b). The atoms are shi unk to the diameter of the cylinder and ai e used only for smoothing or closing the ends of the tubes. With its thicker bonds, the capped sticks model conveys an improved 3D impression of a molecule when compared with the wire frame model. 

In an axisymmetric flow regime all of the field variables remain constant in the circumferential direction around an axis of symmetry. Therefore the governing flow equations in axisymmetric systems can be analytically integrated with respect to this direction to reduce the model to a two-dimensional form. In order to illustrate this procedure we consider the three-dimensional continuity equation for an incompressible fluid written in a cylindrical (r, 9, 2) coordinate system as... 

The variant of the cylindrical model which has played a prominent part in the development of the subject is the ink-bottle , composed of a cylindrical pore closed one end and with a narrow neck at the other (Fig. 3.12(a)). The course of events is different according as the core radius r of the body is greater or less than twice the core radius r of the neck. Nucleation to give a hemispherical meniscus, can occur at the base B at the relative pressure p/p°)i = exp( —2K/r ) but a meniscus originating in the neck is necessarily cylindrical so that its formation would need the pressure (P/P°)n = exp(-K/r ). If now r /r, < 2, (p/p ), is lower than p/p°)n, so that condensation will commence at the base B and will All the whole pore, neck as well as body, at the relative pressure exp( —2K/r ). Evaporation from the full pore will commence from the hemispherical meniscus in the neck at the relative pressure p/p°) = cxp(-2K/r ) and will continue till the core of the body is also empty, since the pressure is already lower than the equilibrium value (p/p°)i) for evaporation from the body. Thus the adsorption branch of the loop leads to values of the core radius of the body, and the desorption branch to values of the core radius of the neck. 

Since they all necessitate a knowledge of the value of r, and of both r and either directly or indirectly, all as a function of p p°, these data are given in tabular form for reference (Table 3.2). If required, intermediate values of t may be obtained to sufficient accuracy by graphical interpolation, and the corresponding values of r can be calculated with the Kelvin formula. The values of r refer to the most commonly used model, the cylindrical pore, so that r " = r + t. The values of t are derived from the standard nitrogen isotherm for hydroxylated silica and though the values do differ... 

A procedure involving only the wall area and based on the cylindrical pore model was put forward by Pierce in 1953. Though simple in principle, it entails numerous arithmetical steps the nature of which will be gathered from Table 3.3 this table is an extract from a fuller work sheet based on the Pierce method as slightly recast by Orr and DallaValle, and applied to the desorption branch of the isotherm of a particular porous silica. 

In order to allow for the thinning of the multilayer, it is necessary to assume a pore model so as to be able to apply a correction to Uj, etc., in turn for re-insertion into Equation (3.52). Unfortunately, with the cylindrical model the correction becomes increasingly complicated as desorption proceeds, since the wall area of each group of cores changes progressively as the multilayer thins down. With the slit model, on the other hand, <5/l for a... 

To convert the core area into the pore area ( = specific surface, if the external area is negligible) necessitates the use of a conversion factor R which is a function not only of the pore model but also of both r and t (cf. p. 148). Thus, successive increments of the area under the curve have to be corrected, each with its appropriate value of R. For the commonly used cylindrical model,... 

Perhaps the best known explanation of reproducible hysteresis in mercury porosimetry is based on the ink bottle model already discussed in connection with capillary condensation (p. 128). The pressure required to force mercury with a pore having a narrow (cylindrical) neck of radius r, will be... 

These calculations lend theoretical support to the view arrived at earlier on phenomenological grounds, that adsorption in pores of molecular dimensions is sufficiently different from that in coarser pores to justify their assignment to a separate category as micropores. The calculations further indicate that the upper limit of size at which a pore begins to function as a micropore depends on the diameter a of the adsorbate molecule for slit-like pores this limit will lie at a width around I-So, but for pores which approximate to the cylindrical model it lies at a pore diameter around 2 5(t. The exact value of the limit will of course depend on the actual shape of the pore, and may well be raised by cooperative effects. 

To develop a more quantitative relationship between particle size and T j, suppose we consider the melting behavior of the cylindrical crystal sketched in Fig. 4.4. Of particular interest in this model is the role played by surface effects. The illustration is used to define a model and should not be taken too literally, especially with respect to the following points ... 

Use the model for the size exclusion of a spherical solute molecule in a cylindrical capillary to calculate for a selection of R/a values which... 

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