Surface area from size distributions

Stokes law is another concept around which several instruments are designed to give particle size or size distributions. Stokes law is used to determine the settling velocity of particles in a fluid medium as a function of their size. Equation (1.10) below is a useful form of Stokes law 

Optical devices, based upon particle attenuation of a light beam or measurement of scattering angles, also give equivalent spherical diameters. 

Permeametric methods, discussed in a later chapter, are often used to determine average particle size. The method is based upon the impedance offered to the fluid flow by a packed bed of powder. Again, equivalent spherical diameter is the calculated size. 

Sieving is another technique, which sizes particles according to their smallest dimension but gives no information on particle shape. 

Electron microscopy can be used to estimate particle shape, at least in two dimensions. A further limitation is that only relatively few particles can be viewed. 

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Effectiveness of selective adsorption of phenanthrene in Triton X-100 solution depends on surface area, pore size distribution, and surface chemical properties of adsorbents. Since the micellar structure is not rigid, the monomer enters the pores and is adsorbed on the internal surfaces. The size of a monomer of Triton X-100 (27 A) is larger than phenanthrene (11.8 A) [4]. Therefore, only phenanthrene enters micropores with width between 11.8 A and 27 A. Table 1 shows that the area only for phenanthrene adsorption is the highest for 20 40 mesh. From XPS results, the carbon content on the surfaces was increased with decreasing particle size. Thus, 20 40 mesh activated carbon is more beneficial for selective adsorption of phenanthrene compared to Triton X-100. 

From the above results, one can conclude that different NiO/MgO solid-solution catalysts can have very different catalytic performances. For example, Fujimoto et aV s Nio.03Mgo.97O solid-solution catalyst exhibited relatively low activities. To reach about 82% conversion of CH4 in the presence of this Nio.03Mgo.97O catalyst, the space velocity had to be reduced to 18,670 mL (g catalyst)-1 h-1 at 1123 K (Fig. 15) (238). In contrast, Ruckenstein and Hu s NiO/MgO catalysts have very high activities (>91% conversion of CH4 and >95% selectivities of CO and H2 at the space velocity of 60,000 mL (g catalyst)-1 h-1 at 1063 K) (Fig. 14) (239). Hu and Ruckenstein (239,257,259) noted that the properties of the MgO, such as its surface area, pore size distribution, and crystal structure, have important effects on the NiO/MgO solid-solution catalysts. They found that the MgO supplied by Aldrich, which has... 

Because of their biocompatibility, chemical stability, high thermal and electrical conductivity, sorption ability, tuneable surfaces area, pore-size distribution and straightforward functionalization chemistry, porous carbons have found application in diverse topical areas such as sensors, fuel cells, hydrogen storage, and sorption.39 11 One particular property that distinguishes porous carbon from porous silica materials is the electrical conductivity of the former that has no counterpart in siliceous-based scaffoldings. This feature opens the route for certain applications... 

The resulting CBPs are usually identified by the length of the alkyl chain. For example, when the number of carbon atoms in the alkyl chain (nj is equal to 18, by far the most popular chain length [318], we speak of an octadecylsilica (ODS) or of an RP-18 phase. The second most popular chain length [318] is the octylsilica or RP-8 (nc= 8). Apart from the characteristics of the starting material (specific surface area, pore size distribution) and the reagent used, the alkyl chain length is the only variable to be considered. 

The simple theoretical description of the adsorption from solutions on solids can be useful for characterizing sorption properties of inorganic sorbents. Such properties as the energetical and structural heterogeneities, surface phase capacity, specific surface area, pore size distribution curves and others are very important with regard to wide application of inorganic adsorbents on laboratory and industrial scales. 

The term texture refers to the general pore structure of particles and includes surface area, pore size distribution, and shape. Total surface area, g is possibly the most important particle parameter specified without regard to the type of surface. No attempt is made to distinguish one component from another. 

Large-pore mesoporous materials with enhanced textural characteristics (surface area, pore size distribution and pore volume) were obtained from a pH-adjusted synthesis with a surfactant mixture of hexadecyl- and dodecyltrimethylammonium salts in combination with mesitylene-swelling. This material was grafted with phenyl-alkoxysilanes and subsequently sulphonated. Nitrogen adsorption and multinuclear MAS NMR were performed to monitor the different synthesis steps. 

Porosity properties, e.g. specific surface areas, pore size distribution and pore volume were calculated from low-temperature nitrogen adsorption-desorption isotherms measured by means of a Sorptomat ASAP 2405 VI.01 with a special program for the preparation of the isotherms (Micrometries Co., USA) and a Porosimeter 4000 (Carlo Erba Instruments). 

The fibers were characterized with respect to their density, specific surface area, pore size distribution, microstructure (SEM), and tensile strength (using a special device to ensure fracture of the filaments and not fracture at the spanning clamps fixing the filaments). One example of supercritically dried filaments is shown in Figure 9.11. The filaments are white, soft and ductile with a diameter of 250 pm and in this respect their optical appearance is not different from the monoliths. It would be interesting to use the method of Cai et al. [28] described above in order to investigate whether transparent filaments can be produced. 

An activated carbon in contact with a metal salt solution is a two-phase system consisting of a solid phase, which is the activated carbon surface, and a liquid phase which is the salt solution. The solution contains varying amounts of different metal ion species and their complexes so that the interface between the two phases will behave as an electrical double layer and determine the adsorption processes taking place in the system. The adsorptive removal capacity of an activated carbon for metal cations from the aqueous solutions generally depends on the physicochemical characteristics of the carbon surface, which include the surface area, pore-size distribution, electrokinetic properties, and the chemical structure of the carbon surface, as well as on the nature of the metal ions in the solution. 

It is apparent from the perusal of the literature that the investigations concerning the adsorptive removal of different pesticides from water have generally been directed toward determining the efficiencies of powdered and granulated activated carbons for their removal. None of the studies have discussed the effect of such parameters as the surface area, pore-size distribution, or the chemistry of the carbon surface on the adsorption and its mechanism. Only in one paper Prakash indicated that the adsorption of diquat and paraquat depended on the surface area of the carbon. Thus, there is need to study the influence of these parameters on the adsorption of pesticides. 

The nitrogen adsorption/desorption isotherms allow the specific surface area, pore size distribution as well as the micro/meso ratio to be estimated. The total surface area is quite similar for the investigated samples and it ranges from 329 to 403 m /g being the most developed for the Nt+3M+F composite as shown in Fig. 9.6. The nitrogen adsorption isotherms showed that the carbon materials are typically mesoporous (apart from the material M+F, that is, without nanotubes), and the amount of micropores is very moderate. The micropore volume values for all the samples are comparable var3dng from 0.152 to 0.174 cm /g. The porosity characteristics of all the composites are illustrated in Table 9.1. 

Cumulative surface area from pore size distribution... 

In writing the present book our aim has been to give a critical exposition of the use of adsorption data for the evaluation of the surface area and the pore size distribution of finely divided and porous solids. The major part of the book is devoted to the Brunauer-Emmett-Teller (BET) method for the determination of specific surface, and the use of the Kelvin equation for the calculation of pore size distribution but due attention has also been given to other well known methods for the estimation of surface area from adsorption measurements, viz. those based on adsorption from solution, on heat of immersion, on chemisorption, and on the application of the Gibbs adsorption equation to gaseous adsorption. 

It would be difficult to over-estimate the extent to which the BET method has contributed to the development of those branches of physical chemistry such as heterogeneous catalysis, adsorption or particle size estimation, which involve finely divided or porous solids in all of these fields the BET surface area is a household phrase. But it is perhaps the very breadth of its scope which has led to a somewhat uncritical application of the method as a kind of infallible yardstick, and to a lack of appreciation of the nature of its basic assumptions or of the circumstances under which it may, or may not, be expected to yield a reliable result. This is particularly true of those solids which contain very fine pores and give rise to Langmuir-type isotherms, for the BET procedure may then give quite erroneous values for the surface area. If the pores are rather larger—tens to hundreds of Angstroms in width—the pore size distribution may be calculated from the adsorption isotherm of a vapour with the aid of the Kelvin equation, and within recent years a number of detailed procedures for carrying out the calculation have been put forward but all too often the limitations on the validity of the results, and the difficulty of interpretation in terms of the actual solid, tend to be insufficiently stressed or even entirely overlooked. And in the time-honoured method for the estimation of surface area from measurements of adsorption from solution, the complications introduced by... 

Surface Area Determination The surface-to-volume ratio is an important powder property since it governs the rate at which a powder interacts with its surroundings. Surface area may be determined from size-distribution data or measured directly by flow through a powder bed or the adsorption of gas molecules on the powder surface. Other methods such as gas diffusion, dye adsorption from solution, and heats of adsorption have also been used. It is emphasized that a powder does not have a unique surface, unless the surface is considered to be absolutely smooth, and the magnitude of the measured surface depends upon the level of scrutiny (e.g., the smaller the gas molecules used for gas adsorption measurement the larger the measured surface). 

The study of fine particles in pharmaceutical applications involves a number of different techniques. Micromeritic investigations involve surface areas, particle sizes and their distributions, the nature of solid surfaces, and particle shapes [4]. Scientists working in this field realize that a number of techniques are necessary to fully investigate a system and that an interdisciplinary approach is essential. This ability to correlate data from different techniques allows a more thorough understanding of the system, process, or problem being investigated. 

Several factors influence TGA data. Sample size and shape affect the rate and efficiency of decomposition. Powdered versus solid bulk samples will have different decomposition profiles due to the differing surface areas from which exiting decomposition products can leave the sample and be registered as mass losses. Similarly, the packing of the sample in the pan must be even and reproducible from run to run. Loosely distributed particles will heat more evenly and evolve volatilized products more evenly than mounded or densely packed samples. This can be especially important when looking at determinations of residual solvents, moisture or diffusion controlled losses such as plasticizer in the samples. 

The number (or size) of bubbles observed in a frontal unit surface area from a cut layer of the frozen foam differs from the bubble number in the volume for two reasons. The first one is related to the fact that small bubbles (because of their small sizes) very often do not fall into the cut surface [8,41 ]. That is why the number of bubbles in the cut surface Ns is smaller than the number of bubbles Nf in a layer from the foam volume with height equal to two average bubble radius. The relation between bubble distribution functions by the radius R in the foam volume and in the frontal layer is given by de Vries [8]... 

Porosity within a particle is a manifestation of the shape of a particle. Fractal particles will have internal porosity as a result of their shapes. Fractal particles with low fractal dimensions (i.e., <2.0) will have a broad pore size distribution, where the largest pore approaches the size of the aggregate. Fractal particles with large fractal dimensions (i.e., >2.0) will have narrower pore size distributions with most of the porosity occurring at a size much smaller than that of the aggregate. Calcination of metal salt particles or metal hydroxides to produce oxides is another common method to produce internal porosity. In the gas evolution that takes place in transformation to the oxide, pores are opened up in the particle structure. The opening of pores in a hydrous alumina powder can increase its surface area from 0.5 m /gm (its external area) to 450 mVgm (its internal pore area). 

For the pure alumina sample the chosen model for computing cumulative surface area. SedB, cumulative volume Fedn and surface area and volume distribution as a function of pore size is a cylinder closed at one end. This choice is motivated by the type IV shape of the isotherm and by the E type hysteresis. In the case of the cylinder model closed at one end, the relevant branch of the isotherm is the adsorption. The calculation is carried out from the saturation pressure down to the pressure corresponding to the hysteresis loop s closing. The cumulative specific surface area, SadB, is close to both 5bet and St values for the pure mesoporous material, X(0) (Table 1). 

Wilson and co-workers have measured platinum catalyst ripening in PEFC cathodes of ultra-low platinum loading which operated continuously for 25(X)h at a cell voltage of 0.5 V, on pressurized hydrogen and air [46]. Results obtained for the cathode catalyst show that slow catalyst ripening takes place in these PEFC cathodes. The typical degree of ripening for Pt/C catalysts can be summarized as a decrease of platinum surface area from an initial value of 100 m /g to 70 m /g after 1000 h and to 40 m /g after 2500 h. The results of particle size distribution analyses for as-supplied... 

A) Pressure-controlled mercury porosimetry procedure. It consists of recording the injected mercury volume in the sample each time the pressure increases in order to obtain a quasi steady-state of the mercury level as P,+i-Pi >dP>0 where Pj+i, Pi are two successive experimental capillary pressure in the curve of pressure P versus volume V and dP is the pressure threshold being strictly positive. According to this protocol it is possible to calculate several petrophysical parameters of porous medium such as total porosity, distribution of pore-throat size, specific surface area and its distribution. Several authors estimate the permeability from mercury injection capillary pressure data. Thompson applied percolation theory to calculate permeability from mercury-injection data. 

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