Wall thickness, pore

Porosity relates to the ratio of the pore diameter d and the pore wall thickness w, but it contains no information about the absolute dimensions of the porous... 

According to the macropore formation mechanisms, as discussed in Section 9.1, the pore wall thickness of PS films formed on p-type substrates is always less than twice the SCR width. The conductivity of such a macroporous silicon film is therefore sensitive to the width of the surface depletion layer, which itself depends on the type and density of the surface charges present. For n-type substrates the pore spacing may become much more than twice the SCR width. In the latter case and for macro PS films that have been heavily doped after electrochemical formation, the effect of the surface depletion layer becomes negligible and the conductivity is determined by the geometry of the sample only. The conductivity parallel to the pores is then the bulk conductivity of the substrate times 1 -p, where p is the porosity. 

Fig. 9.5 Values of pore wall thickness from Fig. 9.4 a-d as a function of doping density (error bars), together with the SCR width for a potential (Vbl + V-2kT/e) of 0.1 V (line). After [Le21].

For a square pattern and square pores the pore wall thickness w is given by ... 

Maceral behaviour and interaction on carbonization Mesophase development during carbonization Relation of coke strength (stability) to coke texture, pore size distribution, pore wall thickness... 

TPA7 CTA+ Treatment Abet (m2,f0 Vbjh (cm3,g) Dbjh (A) Peak pore diameter (A) do (A) Pore wall thickness (A)... 

Table 1 lists the BET surface areas and other physical properties of the calcined and hydrothermally treated samples. It can be seen that these samples possess very high surface area in the range of 800-1000 m2/g. Pore wall thickness of the calcined samples was found to be about 19 A and no increase in wall thickness was noticed by adding additional TPA ions However, the wall thickness was found to increase slightly after hydrothermal treatment due to pore wall restructuring during such treatment [12,13],... 

Mesopore size distribution analysis showed a very narrow distribution with a peak pore diameter of about 27 A for the calcined samples. It can be seen that the pore wall thickness of the calcined samples was in the 18-19 A and did not change much by adding additional cations. The increased hydrothermal stability observed was, therefore, not due to any increase in pore wall thickness. For the water-treated samples, the adsorption isotherms and pore size distribution curves showed that after hydrothermal treatment the pore size distribution was... 

The BET specific surface area, mesopore volumes, and pore wall thickness of the calcined and water-treated samples are given in Table 3. BET surface area of the samples prepared with Cm surfactants were found to be less affected by hydrothermal treatment. When the samples synthesized without TPA+ subjected to hydrothermal treatment the sharp inflection in the isotherm became very broad indicating wide distribution of pores. In contrast, the mesopore distribution of the samples prepared with TPA was found to be less affected by hydrothermal treatment. For the samples prepared without TPA, the mesopore volume was found to decrease sharply and the pore diameter was broadened over a large range indicating loss of the mesopore structure. Addition of TPA was found to minimize the structural collapse and thereby helps to preserve the mesoporosity. 

From the 20 values, the inter-pore distance for the SFE and the calcined samples are calculated to be 47.2 and 43.2 A respectively. The pore wall thickness can then be calculated from the difference between their inter-pore distance and their pore diameter and they are 19.2 and 18.2 A respectively. The thicker pore wall of the SFE sample implies that SFE produces sample of higher thermal stability [3] than that prepared by calcination. Hence, all these results establish SFE as a feasible technique used for surfactant removal. 

Structural parameters of the MCM-41 materials calculated by means of the NLDFT method are listed in Table 1. We note very good agreement between the results obtained from the desorption and adsorption branches of the isotherms, especially for samples 1 - 3. It is worth noting that the pore wall thickness (1.2-1,8 nm) of wide-pore MCM-41 materials is larger than that usually obtained for conventional MCM-41, and tends to increase with the pore diameter. 

Dpdft is the mean pore diameter calculated from the NLDFT pore size distribution ctpdft is the standard deviation calculated from the NLDFT pore size distribution dwaii = ao - DPDFT- the pore wall thickness assuming cylindrical pores... 

In Table 1, the pore wall thickness (W) was estimated by subtracting the average pore diameter (APD) value from ao = 2 dio / V3, the unit cell dimension. At the synthesis conditions used, the thickness of the condensed aluminosilicate phase that constitutes the pore wall varied between 1.3 nm and 1.9 nm and the pore diameter is in 2.5 to 3.5 nm range (7, 8). SEM images have shown that these MCM-41 samples contain what seems to be minor amounts of unreacted gel particles (11). 

Gravimetric Capacitance (Q, BET- and DFT-Specific Surface Area, Normalized Capacitance (Q, Field Screening Length (8SC) and Pore Wall Thickness (8W) for Different ACs... 

RESULTS. MICROPORE VOLUME EVOLUTION ON FUNCTION OF MICROPORE WIDTH AND PORE WALL THICKNESS... 

The synthesis of the CMK-n carbons is controlled to various pore shapes, connectivity, diameters (typically, 1-10 nm in diameter) and pore wall thickness. These carbons exhibit high specific surface areas (typically, the BET specific surface areas up to 2000 mV )> uniform pore diameters, large adsorption capacities, and high thermal, acid-base and mechanical stabilities. The CMK-type carbons are also suitable for the formation of well-defined nanocomposite with organic polymers, so that the nanopore walls can be modified with various functional groups. These carbons show new possibilities for various applications in adsorption, catalysis and electrochemistry. 

Lee J. S., Joo S. H. and Ryoo R., Synthesis of mesoporous silicas of controlled pore wall thickness and their replication to ordered nanoporous carbons with various pore diameters. J. Am. Chem. Soc. 124 (2001) pp. 11S6-1157. 

Fig. 1 shows the porous silicon structures formed on different silicon wafers. Porous silicon on p-type wafer is characteri d by a sponge-like structure with pore wall thickness of 2-4 nm and 5-6 rnn for wafers with resistivity of 12 and 0.03 Q cm, respectively (Fig. la,b). Porous silicon on n-type silicon (0.01 Q cm) shows a branch-like structure (Fig. lc,d). In this case mother pores branch out and form the daughter pores. The pore wall thickness is 7-10 nm for porous silicon anodized with the light exposition (Fig. Ic) and 15-20 nm for porous silicon anodized without the light exposition (Fig. Id). 

Figure 2. Flash diameter vs pore wall thickness for difFerent porosity in porous silicon impregnated with NaClOi. Porous silicon thickness was 30 pm.

Fast oxidation process in a way of combustion and, in some cases, of explosion in porous silicon films has been observed at pore wall thickness less than 10 nm. The increasing of porous specific area results in an enhancement of combustion and explosion intensity. The explosion process has been observed at the specific area more than 200 m /cm. Thus combustion and explosion processes in the porous silicon layers can be attributed to nanoscale phenomena. 

By combining the DFT analysis of the sorption isotherm with X-ray diffraction data on the pore spacing, the pore wall thicknesses of a set of MCM-class adsorbents were determined. These thicknesses were found to be consistent across the set of adsorbents, which lends further strong evidence to the validity of the DFT adsorption model. The Kelvin and modified Kelvin equations, by contrast, overestimate the condensation pressures of nitrogen in cylindrical oxide pores [21]. 

Figure 4 Comparison of PSDs obtainedfor MCM-41 type adsorbents from nitrogen and argon porosimetry using DFT (left). The pore wall thickness of five different MCM adsorbents, found by combining results from XRD and sorption DFT measurements, is consistent in four of the five samples (right) [20].

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