Characterization diameters

A beautiful and elegant example of the intricacies of surface science is the formation of transparent, thermodynamically stable microemulsions. Discovered about 50 years ago by Winsor [76] and characterized by Schulman [77, 78], microemulsions display a variety of useful and interesting properties that have generated much interest in the past decade. Early formulations, still under study today, involve the use of a long-chain alcohol as a cosurfactant to stabilize oil droplets 10-50 nm in diameter. Although transparent to the naked eye, microemulsions are readily characterized by a variety of scattering, microscopic, and spectroscopic techniques, described below. 

The first fullerene to be characterized was the I. [ ] fullerene, which was originally identified by its four-band IR absorjDtion spectmm [2]. The proposed cagelike stmcture of [60] fullerene, with a diameter of 7.1 A, was... 

Figure C2.17.4. Transmission electron micrograph of a field of Zr02 (tetragonal) nanocrystals. Lower-resolution electron microscopy is useful for characterizing tire size distribution of a collection of nanocrystals. This image is an example of a typical particle field used for sizing puriDoses. Here, tire nanocrystalline zirconia has an average diameter of 3.6 nm witli a polydispersity of only 5% 1801.

We designate the length of the ellipsoid along the axis of rotation as 2a and the equatorial diameter as 2b to define the axial ratio a/b which characterizes the ellipticity of the particle. By this definition, a/b > 1 corresponds to prolate ellipsoids, and a/b < 1 to oblate ellipsoids. 

A surprisiagly large number of important iadustrial-scale separations can be accompHshed with the relatively small number of zeoHtes that are commercially available. The discovery, characterization, and commercial availabiHty of new zeoHtes and molecular sieves are likely to multiply the number of potential solutions to separation problems. A wider variety of pore diameters, pore geometries, and hydrophobicity ia new zeoHtes and molecular sieves as weU as more precise control of composition and crystallinity ia existing zeoHtes will help to broaden the appHcations for adsorptive separations and likely lead to improvements ia separations that are currently ia commercial practice. 

Cell si has been characterized by measurements of the cell diameter in one or more of the three mutually perpendicular directions (143) and as a measurement of average cell volume (144,145). Mechanical, optical, and thermal properties of a foam are all dependent upon the cell size. 

The time constants characterizing heat transfer in convection or radiation dominated rotary kilns are readily developed using less general heat-transfer models than that presented herein. These time constants define simple scaling laws which can be used to estimate the effects of fill fraction, kiln diameter, moisture, and rotation rate on the temperatures of the soHds. Criteria can also be estabHshed for estimating the relative importance of radiation and convection. In the following analysis, the kiln wall temperature, and the kiln gas temperature, T, are considered constant. Separate analyses are conducted for dry and wet conditions. 

Microfilaments and Microtubules. There are two important classes of fibers found in the cytoplasm of many plant and animal ceUs that are characterized by nematic-like organization. These are the microfilaments and microtubules which play a central role in the determination of ceU shape, either as the dynamic element in the contractile mechanism or as the basic cytoskeleton. Microfilaments are proteinaceous bundles having diameters of 6—10 nm that are chemically similar to actin and myosin muscle ceUs. Microtubules also are formed from globular elements, but consist of hoUow tubes that are about 30 nm in diameter, uniform, and highly rigid. Both of these assemblages are found beneath the ceU membrane in a linear organization that is similar to the nematic Hquid crystal stmcture. 

Fig. 3. Microporous membranes are characterized by tortuosity, T, porosity, S, and their average pore diameter, d. (a) Cross-sections of porous membranes containing cylindrical pores, (b) Surface views of porous membranes of equal S, but differing pore size.

Dimensionless Numbers. With impeller diameter D as length scale and mixer speed N as time scale, common dimensionless numbers encountered in mixing depend on several controlling phenomena (Table 2). These quantities are useful in characterizing hydrodynamics in mixing tanks and when scaling up mixing systems. 

The channels in zeoHtes are only a few molecular diameters in size, and overlapping potential fields from opposite walls result in a flat adsorption isotherm, which is characterized by a long horizontal section as the relative pressure approaches unity (Fig. 6). The adsorption isotherms do not exhibit hysteresis as do those in many other microporous adsorbents. Adsorption and desorption are reversible, and the contour of the desorption isotherm foUows that of adsorption. 

Characterization. When siHca gel is used as an adsorbent, the pore stmcture determines the gel adsorption capacity. Pores are characterized by specific surface area, specific pore volume (total volume of pores per gram of solid), average pore diameter, pore size distribution, and the degree to which entrance to larger pores is restricted by smaller pores. These parameters are derived from measuring vapor adsorption isotherms, mercury intmsion, low angle x-ray scattering, electron microscopy, gas permeabiHty, ion or molecule exclusion, or the volume of imbibed Hquid (1). 

Important physical properties of catalysts include the particle size and shape, surface area, pore volume, pore size distribution, and strength to resist cmshing and abrasion. Measurements of catalyst physical properties (43) are routine and often automated. Pores with diameters <2.0 nm are called micropores those with diameters between 2.0 and 5.0 nm are called mesopores and those with diameters >5.0 nm are called macropores. Pore volumes and pore size distributions are measured by mercury penetration and by N2 adsorption. Mercury is forced into the pores under pressure entry into a pore is opposed by surface tension. For example, a pressure of about 71 MPa (700 atm) is required to fill a pore with a diameter of 10 nm. The amount of uptake as a function of pressure determines the pore size distribution of the larger pores (44). In complementary experiments, the sizes of the smallest pores (those 1 to 20 nm in diameter) are deterrnined by measurements characterizing desorption of N2 from the catalyst. The basis for the measurement is the capillary condensation that occurs in small pores at pressures less than the vapor pressure of the adsorbed nitrogen. The smaller the diameter of the pore, the greater the lowering of the vapor pressure of the Hquid in it. 

The behavior of colloidal suspensions is controlled by iaterparticle forces, the range of which rarely extends more than a particle diameter (see Colloids). Consequentiy suspensions tend to behave like viscous Hquids except at very high particle concentrations when the particles are forced iato close proximity. Because many coating solutions consist of complex mixtures of polymer and coUoidal material, a thorough characterization of the bulk rheology requires a number of different measurements. 

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