Other surface area methods

Because of its simplicity and straightforward applicability, the BET theory is almost universally employed for surface area measurements. However, other methods and theoretical models have been developed which are briefly outlined in this chapter. No attempt is made to completely derive and discuss these alternate methods but rather to present their essential features and to indicate how they may be used to calculate surface areas. 

---

Transmission and scanning electron microscopy are employed for a direct study of microclusters while the distribution of sizes (or average diameter) is provided by sedimentation and other techniques. The average particle diameter is obtained by the Brunauer-Emmett-Teller (BET) surface-area method and by X-ray line broadening. 

BS 598-112. 2004. Sampling and examination of bituminous mixtures for roads and other paved area Method for the use of road surface hardness probe. London British Standards Institution. 

The specific surface area of a solid is one of the first things that must be determined if any detailed physical chemical interpretation of its behavior as an adsorbent is to be possible. Such a determination can be made through adsorption studies themselves, and this aspect is taken up in the next chapter there are a number of other methods, however, that are summarized in the following material. Space does not permit a full discussion, and, in particular, the methods that really amount to a particle or pore size determination, such as optical and electron microscopy, x-ray or neutron diffraction, and permeability studies are largely omitted. 

A number of methods have been described in earlier sections whereby the surface free energy or total energy could be estimated. Generally, it was necessary to assume that the surface area was known by some other means conversely, if some estimate of the specific thermodynamic quantity is available, the application may be reversed to give a surface area determination. This is true if the heat of solution of a powder (Section VII-5B), its heat of immersion (Section X-3A), or its solubility increase (Section X-2) are known. 

The general type of approach, that is, the comparison of an experimental heat of immersion with the expected value per square centimeter, has been discussed and implemented by numerous authors [21,22]. It is possible, for example, to estimate sv - sl from adsorption data or from the so-called isosteric heat of adsorption (see Section XVII-12B). In many cases where approximate relative areas only are desired, as with coals or other natural products, the heat of immersion method has much to recommend it. In the case of microporous adsorbents surface areas from heats of immersion can be larger than those from adsorption studies [23], but the former are the more correct [24]. 

The existence of this situation (for nonporous solids) explains why the ratio test discussed above and exemplified by the data in Table XVII-3 works so well. Essentially, any isotherm fitting data in the multilayer region must contain a parameter that will be found to be proportional to surface area. In fact, this observation explains the success of Ae point B method (as in Fig. XVII-7) and other single-point methods, since for any P/P value in the characteristic isotherm region, the measured n is related to the surface area of the solid by a proportionality constant that is independent of the nature of the solid. 

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. 

Catalyst performance depends on composition, the method of preparation, support, and calcination conditions. Other key properties include, in addition to chemical performance requkements, surface area, porosity, density, pore size distribution, hardness, strength, and resistance to mechanical attrition. 

Analysis. Excellent reviews of phosphate analysis are available (28). SoHds characterization methods such as x-ray powder diffraction (xrd) and thermal gravimetric analysis (tga) are used for the identification of individual crystalline phosphates, either alone or in mixtures. These techniques, along with elemental analysis and phosphate species deterrnination, are used to identify unknown phosphates and their mixtures. Particle size analysis, surface area, microscopy, and other standard soHds characterizations are useful in relating soHds properties to performance. SoHd-state nmr is used with increasing frequency. 

The large majority of activated alumina products are derived from activation of aluminum hydroxide, rehydrated alumina, or pseudoboehmite gel. Other commerical methods to produce specialty activated aluminas are roasting of aluminum chloride [7446-70-0], AIQ calcination of precursors such as ammonium alum [7784-25-0], AlH2NOgS2. Processing is tailored to optimize one or more of the product properties such as surface area, purity, pore size distribution, particle size, shape, or strength. 

Surface Area and Permeability or Porosity. Gas or solute adsorption is typicaUy used to evaluate surface area (74,75), and mercury porosimetry is used, ia coajuactioa with at least oae other particle-size analysis, eg, electron microscopy, to assess permeabUity (76). Experimental techniques and theoretical models have been developed to elucidate the nature and quantity of pores (74,77). These iaclude the kinetic approach to gas adsorptioa of Bmaauer, Emmett, and TeUer (78), known as the BET method and which is based on Langmuir s adsorption model (79), the potential theory of Polanyi (25,80) for gas adsorption, the experimental aspects of solute adsorption (25,81), and the principles of mercury porosimetry, based on the Young-Duprn expression (24,25). 

Copper Hydroxide. Copper(II) hydroxide [20427-59-2] Cu(OH)2, produced by reaction of a copper salt solution and sodium hydroxide, is a blue, gelatinous, voluminous precipitate of limited stabiUty. The thermodynamically unstable copper hydroxide can be kiaetically stabilized by a suitable production method. Usually ammonia or phosphates ate iacorporated iato the hydroxide to produce a color-stable product. The ammonia processed copper hydroxide (16—19) is almost stoichiometric and copper content as high as 64% is not uncommon. The phosphate produced material (20,21) is lower ia copper (57—59%) and has a finer particle size and higher surface area than the ammonia processed hydroxide. Other methods of production generally rely on the formation of an iasoluble copper precursor prior to the formation of the hydroxide (22—26). 

Values for hydrocarbons other than alkynes and alkadienes can be predicted by the method of Suzuki et al. The best model includes the descriptors T, P, the parachor, the molecular surface area (which can be approximated by the van der Waals area), and the zero-order connectivity index. Excluding alkynes and alkadienes, a studv for 58 alkanes, aromatics, and cycloalkanes showed an average deviation from experimental values of about 30 K. 

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). 

---