Pores density

The temperature, pore width and average pore densities were the same as those used by Snook and van Megen In their Monte Carlo simulations, which were performed for a constant chemical potential (12.). Periodic boundary conditions were used In the y and z directions. The periodic length was chosen to be twice r. Newton s equations of motion were solved using the predictor-corrector method developed by Beeman (14). The local fluid density was computed form... 

Equilibrium Systems. Magda et al (12.) have carried out an equilibrium molecular dynamics (MD) simulation on a 6-12 Lennard-Jones fluid In a silt pore described by Equation 41 with 6 = 1 with fluid particle Interactions given by Equation 42. They used the Monte Carlo results of Snook and van Me gen to set the mean pore density so that the chemical potential was the same In all the simulations. The parameters and conditions set In this work were = 27T , = a, r = 3.5a, kT/e = 1.2, and... 

Chemical and electrochemical techniques have been applied for the dimensionally controlled fabrication of a wide variety of materials, such as metals, semiconductors, and conductive polymers, within glass, oxide, and polymer matrices (e.g., [135-137]). Topologically complex structures like zeolites have been used also as 3D matrices [138, 139]. Quantum dots/wires of metals and semiconductors can be grown electrochemically in matrices bound on an electrode surface or being modified electrodes themselves. In these processes, the chemical stability of the template in the working environment, its electronic properties, the uniformity and minimal diameter of the pores, and the pore density are critical factors. Typical templates used in electrochemical synthesis are as follows ... 

Hence, Tct is seen to increase with pore density and pore radius. However, a problem appears at a porous substrate when thin films are to be deposited during metallization to form interconnections, thin-film capacitors, etc.335 Sputtered material falls deep into the pores, which affects the planarity of the deposited layer and the electrical resistivity of the oxide layer underneath.335 To cope with this effect, the porous oxide should be padded by inorganic (A1203 and Si02) or organic (polyimide, negative photoresist) layers. 

An alumina matrix may be prepared with high pore density (more than 60 %) and pore diameters ranging from 5 to 250 nm. Ruiz-Hitzky et al. [214] immobilized GOD in nanoporous alumina membranes with regular hexagonal arrays of highly ordered cylindrical pores aligned perpendicularly to the membrane surface. GOD was anchored in the membrane by the highly hydrophilic chitosan biopolymer. Full activity was maintained for at least 50 hours. 

Examples of Pore Diameter, Interpore Spacing and Pore Density of the PS Formed under Different Conditions (a More Extensive List is Given in Ref.1) ... 

Anisotropicity increase with increasing i, V Both , W increases with V Pore density reduces with V Dendritic PS formation possible... 

Figure 11. SEM photograph showing smaller pore diameter and larger pore density near the surface than in the bulk in 5% HF at 6 V.24...

The observation of pores in the anodic oxide with a density in the order of 1011 cnT2 [Agl] supports the so-called fluctuating pore model [Lel3]. This model assumes that randomly distributed pores in the oxides work as charge collecting centers, which lead to oscillations synchronized by the applied external electric field. It should be noted that the observed pore density corresponds well with the roughness at the oxide-electrolyte interface observed after the stress-induced transition of an anodic oxide, as shown in Fig. 5.5. 

An electric field in the semiconductor may also produce passivation, as depicted in Fig. 6.1c. In semiconductors the concentration of free charge carriers is smaller by orders of magnitude than in metals. This permits the existence of extended space charges. The concept of pore formation due to an SCR as a passivating layer is supported by the fact that n-type, as well as p-type, silicon electrodes are under depletion in the pore formation regime [Ro3]. In addition a correlation between SCR width and pore density in the macroporous and the mesoporous regime is observed, as shown in Fig. 6.10 [Thl, Th2, Zh3, Le8]. 

Porosity, Pore Density and Specific Surface Area... 

In contrast to porosity, the pore density and the specific surface area are quantities directly related to the actual size of pores and pore walls. The pore density NP is defined as the number of pores per unit area and it usually refers to a plane normal to the pore axis. For (100) oriented substrates this plane is parallel to the electrode surface, but for other orientations or strongly branched pores, there is no preferred plane orientation and NP refers to an average of the pore density of different planes. For arrays of straight pores the pore density can be directly calculated from the array geometry. For cylindrical pores of diameter d orthogonal to the electrode surface, for example, the average pore density NP is given by ... 

If the pore density is plotted versus the doping density of the silicon electrode, it can be seen that the micropore density is independent of doping, while the macropore and mesopore densities increase linearly with doping density, as shown in Fig. 6.10. This is a consequence of the QC formation mechanism being independent of doping, while the SCR-related mechanisms are not, as discussed in Section 6.2. 

Fig. 6.10 Pore density versus silicon electrode doping density for PS layers of different size regimes. The broken line shows the pore density of a triangular pore pattern with a pore pitch equal to twice the SCR width for 3 V applied bias. Note that only macropores on n-type substrates may show a pore spac-...

Because the SCR width depends not only on doping density but also on bias, the average pore density is expected to decrease with the square root of bias. This, however, is not observed. An increase in bias often leads to the formation of breakdown-type mesopores at the macropore walls. Because these spiking pores show diameters on the order of a few tens of nanometers they are hard to identify even in an SEM. Spiking pores can be identified if they are enlarged by subsequent chemical etching, as shown in Fig. 8.10. Details of their branched morphology become visible by formation of an oxide replica and after etchback of the sub-... 

The realization of a desired pore pattern requires a certain doping density of the n-type Si electrode. A good rule of thumb for the selection of an appropriate substrate is to multiply the desired pore density given (in pnT2) by 1016 and take this number as doping density (in cm-3). This dependency is shown in Fig. 6.10. A square pattern of 10 pm pitch, for example, produces a pore density of 0.01 pores pm-2, which can best be etched using a n-type substrate doping density of 1014 cm-3. 

Hamalainen KM, Kontturi K, Auriola S, Murtomaki L, Urtti A. Estimation of pore size and pore density of biomembranes from permeability measurements of polyethylene glycols using an effusion-like approach. J Control Release 49 97-104 (1997). 

Nanoelectrode ensembles were prepared by electroless deposition of Au within the pores of polycarbonate membrane filters (Poretics). Filters with pore diameters of 10 and 30 nm were used [25]. The pore densities and average center-to-center distances between pores for these membranes are shown in Table 1. Multiplying the pore density (pores cm ) by the cross-... 

The pores in a commercially available polycarbonate filtration membrane (Poretics) were used as templates to form the nanotubules (pore diameter = 50 nm pore density = 6 X 10 pores cm thickness = 6 pm). As before, the electrolessly plated Au deposits both on the pore walls and the membrane faces [71]. The gold surface layers on the membrane faces allow us to make electrical contact to the Au nanotubules within the pores. The thickness of the gold layers deposited on the pore walls can be controlled... 

It is thought that the increased hardness (Tab. 6.11) is due in part as a result of the reduced pore density and the increase in dislocation density caused by work hardening. It is well known that raising the temperature of a metal work hardens that metal and it is thought that the implosion of cavitation bubbles dose to the electrode raises the microscopic temperature. In addition collapse will produce surface impacts by solvent also generating work hardening. 

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