Pore area volume

Vanadium (wt %) Loss of Surface Loss of Pore Area (%) Volume (%)... 

An excellent reference that discusses the methods for determination of pore area, volume, and size distributions is Gregg and Sing [29], where they show how to utilize nitrogen adsorption data for these purposes. 

Each of the procedures described in Section 3.6 for the calculation of pore size distribution involves a value of the pore area y4f for each successive group of pores. In the Roberts procedure 6A, can be immediately obtained from the corresponding pore volume and pore radius as (for... 

The rate of reaction is given by the volume of the shell 4jrr dr [m <-at] multiplied by the pore area per volume of catalyst S [m surfcat/iti cat] multiplied by the rate constant k [m /(m surfcat (itiol) " s)] multiplied by the concentration of the reactant C (r). Thus the rate of reaction in the shell is... 

In this exercise we shall estimate the influence of transport limitations when testing an ammonia catalyst such as that described in Exercise 5.1 by estimating the effectiveness factor e. We are aware that the radius of the catalyst particles is essential so the fused and reduced catalyst is crushed into small particles. A fraction with a narrow distribution of = 0.2 mm is used for the experiment. We shall assume that the particles are ideally spherical. The effective diffusion constant is not easily accessible but we assume that it is approximately a factor of 100 lower than the free diffusion, which is in the proximity of 0.4 cm s . A test is then made with a stoichiometric mixture of N2/H2 at 4 bar under the assumption that the process is far from equilibrium and first order in nitrogen. The reaction is planned to run at 600 K, and from fundamental studies on a single crystal the TOP is roughly 0.05 per iron atom in the surface. From Exercise 5.1 we utilize that 1 g of reduced catalyst has a volume of 0.2 cm g , that the pore volume constitutes 0.1 cm g and that the total surface area, which we will assume is the pore area, is 29 m g , and that of this is the 18 m g- is the pure iron Fe(lOO) surface. Note that there is some dispute as to which are the active sites on iron (a dispute that we disregard here). 

We have recently tested the Tx model described above by obtaining T, measurements in powder samples with known S/V. Samples used were constructed from fumed silica (CAB-O-SIL M-5 and TS-500, Cabot Corp.), and were either hydrophilic (M-5) or treated by the manufacturer to be hydrophobic (TS-500). Powder of each type was pressed into a polycarbonate cylinder, with a degree of compression controlling the pore space volume of each sample. These materials have a very high specific surface area (200 m2 g 1 for M-5, 212 m2 g-1 for TS-500), which is not expected to change significantly even at the maximum compaction pressure used. 

Since mercury has a contact angle with most solids of about 140°, it follows that its cosine is negative (i.e., it takes applied pressure to introduce mercury into a pore). In a mercury porosimeter, a solids sample is evacuated in a cell, mercury is then intruded, and the volume, V, is noted (it actually reads out), and the pressure, P, is then increased stepwise. In this fashion it is possible to deduce the pore volume of a particular radius [corresponding to P by Eq. (21)]. A pore size distribution will give the total internal pore area as well, which can be of importance in dissolution. 

The pore diameter on the abscissa is calculated by employing a particular pore model, usually to the intrusion branch. As a matter of convenience, a cylindrical pore model is traditionally applied. On the ordinate, steep changes in the cumulative diagram are reflected as peak maxima in the incremental curve. From several possible representations (incremental, differential, log differential), the log differential plot seems to be the most revealing, since the areas under the peaks are proportional to the pore volume [79]. Data that can easily derived from mercury intrusion are the pore size distribution, median or average pore size, pore volume, pore area, bulk and skeletal density, and porosity. 

Trade name or code Chemical composition Specific surface area (m /g) Mean pore Pore diameter volume Particle (A) (ml/g) shape ... 

The pore size of the membrane could also be controlled independently of the porosity by altering the size of the salt particles (Fig. 5a). Membranes with high surface area/volume ratios were produced and the ratio was dependent on both salt weight fraction and particle size (Fig. 5b). In addition, the crystallinity of PLLA membranes can be tailored to that desired for each application. These characteristics are all desirable properties of a scaffold for organ regeneration. The major disadvantage of this technique is that it can only be used to produce thin wafers or membranes (up to 2 mm in thickness). A three-dimensional scaffold cannot be directly constructed. This problem may be circumvented however, by membrane lamination. 

Brunauer s modelless method uses pore volume and pore area not as functions of the Kelvin radius but rather as functions of hydraulic radii that he defines as ... 

The total area under the volume and area distribution curves is proportional to the total pore volume and pore area, respectively. By taking the ratio of the graphical area in any interval to the total graph area A, the pore volume or surface area in any interval can be calculated... 

The mean primary particle sizes of pigment blacks he in the range 10-100 nm specific surface areas are between 20 and 1000 m2/g. The specific surface area, determined by N2 adsorption and evaluation by the BET method [4.29], is often cited as a measure of the fineness of a black. Blacks with specific surface areas >150 m2/g are generally porous. The BET total specific surface area is larger than the geometric surface area measured in the electron microscope, the difference being due to the pore area resp. the pore volume. 

The three parameters specific surface area (m2/g), pore size distribution (fv(rp) and fA(rp)-distributions based on pore volume and pore area respectively) and particle size are sufficient to fully characterize the physical properties of the silica matrix. 

Figures 2.4 and 2.5 present the pore size distributions of the three silicas under study, based on the pore volume (fv(rp)) and on the pore area (fA(rp)) respectively. It is obvious from these figures that the pore size distributions of Kieselgel 40 and 60 are centered reasonably well around the average (Wheeler) pore diameter.

Taking the ratio of the two equations gives the variation of pore volume to the variation of pore area. 

Bartholomew and Sorensen [23] also measured loss of nickel surface area, BET surface area, and pore radius/volume after sintering of 15% Ni/alumina and 13.5% Ni/silica in H2 at 923, 973, and 1023 K. Their results for Ni/alumina were generally consistent with those of Bartholomew et al. [27] that is, percentage losses in nickel surface area of 5-13% at 923 and 973 K were comparable with observed losses in BET surface area and pore volume (e.g., 14% at 973 1C), while a 25% observed decrease in nickel area at 1023 K was twice as large as the... 

Below the adsorption isotherm data, the detailed pore size distribution data are listed in seven columns. These include the pore radii corresponding to the 64 data points, the volume of liquid nitrogen desorbed at each step, the mean pore radii corresponding to each of the desorbed decrements, the pore volume per unit change in radius (AV/Ar), the cumulative pore volumes at each pore radius, the calculated surface area in each of the pore radius steps, and the cumulative pore areas in pores larger than each of the listed radii. The print-out sheet is completed with the two sections discussed in connection with Figure 2. 

Fluorination of this catalyst altered the pore structure in the following way. The sample pore volume increased from 0.78 to 1.42 cc. per gram, and the median pore radius increased to 154 A. However, the BET surface area of the sample remained close to 228 sq. meters per gram. The total calculated pore area changed only from 226 to 216 sq. meters per gram. The surface area had probably de-... 

Surface area Porosity (pore size, volume, and distribution) BET method (Brunauer, Emmett, and Teller method) Physical gas sorption Chemical gas sorption Helium picnometry Mercury intrusion porometry (MIP)... 

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