Dimensioning an array

If the spectra are too crowded with sidebands, 2D NMR spectroscopy can advantageously spread the overlapping CSA patterns across a second dimension. An array of these techniques is currently available (PASS, MAT, VACSY, FIREMAT, etc.), and they are described in excellent review articles. However, the analysis of powdered samples with the natural abundance of C and is not capable of providing information about the orientation of individual shielding-tensor components in the molecular frame. At present, the orientation of the principal components in the molecular frame is available from quantum chemical calculations. This topic will be discussed briefly in Section 5. 

This latest extension illustrates how a macro handles arrays. The array must be dimensioned, i.e., the computer must be told to expect a multi-valued parameter that is organized in rows and/or columns. In VBA it is easiest to dimension an array As Variant, which leaves its precise size and nature unspecified. (The only disadvantage of always using As Variant is that it is inefficient in terms of computer memory and execution speed. Fortunately, with modern computers, we only need to consider those factors in programs that involve rather large data arrays.)... 

A system of mutually impinging spherulites develop into an array of irregular polyhedra, the dimensions of which can be as large as a centimeter or so. 

In addition to an array of experimental methods, we also consider a more diverse assortment of polymeric systems than has been true in other chapters. Besides synthetic polymer solutions, we also consider aqueous protein solutions. The former polymers are well represented by the random coil model the latter are approximated by rigid ellipsoids or spheres. For random coils changes in the goodness of the solvent affects coil dimensions. For aqueous proteins the solvent-solute interaction results in various degrees of hydration, which also changes the size of the molecules. Hence the methods we discuss are all potential sources of information about these interactions between polymers and their solvent environments. 

In order to provide resolution in two-dimensions, the light sensitive material is subdivided into an array of pixels, as shown in Fig. 5. These pixels are defined by electric fields that are created within the light sensitive material. The electric fields can be generated one of two ways (1) permanently defined by implanting (doping) a very small amount of another material, or (2) programmably defined by electric fields produced by wires in the solid state electronics. 

A CCD array collects simultaneously the spectral data emanating from an array of spatial locations on the irradiated sample surface [20]. Thus, recorded is a three-dimensional data cube, with two coordinates representing the sample and one for the spectral dimension at each (x,y) point (cf. Figure 2). The spectral dimension in this case is only the intensity of a certain Raman band, used to identify the component of interest. This band should be unique for the component of interest of the sample and its intensity should be high enough in... 

The complete charge array is built by the juxtaposition of this cell in three dimensions so that to obtain a block of 3 x 3 x 3 cells, the cluster being located in the central cell. In that case the cluster is well centered in an array of475 ions. Practically and for computational purposes, the basic symmetry elements of the space group Pmmm (3 mirror planes perpendicular to 3 rotation axes of order 2 as well as the translations of the primitive orthorhombic Bravais lattice) are applied to a group of ions which corresponds to 1/8 of the unit cell. The procedure ensures that the crystalline symmetry is preserved. 

Another approach to improve the effective speed of the second-dimension separation is the use of an array of second-dimension columns, used in parallel [10,11,15,24,25,45,47,52-55,57], especially with 1.5 J,m i.d. pellicular columns [10,15,54,55,58]. This approach is more complicated due to the fact that different columns are rarely identical, and it is critical to achieve precision of retention time in consecutive second-dimension separation containing the same analyte peak. 

In order to correctly form the four-dimensional protein, the original information may be conveyed by a molecule one dimension higher than the one-dimensional DNA sequence. Perhaps this hyper-DNA would exist as a 2-D DNA sheet which could be schematically represented as an array or matrix of letters. A closed circular surface would offer more combinations or possibilities for DNA information, but this would require more accurate and sophisticated start and stop codons to specify the boundaries of the DNA used for coding a particular protein. 

For decades, there have been many popular science books and science-fiction novels on the subject of the fourth dimension. My favorite science book on the subject is Rudy Rucker s The Fourth Dimension, which covers an array of topics on space and time. My favorite science-fiction story is Robert Hein-lein s — And He Built a Crooked House, first published in 1940. It tells the tale of a California architect who constructs a four-dimensional house. He explains that a four-dimensional house would have certain advantages ... 

The increasing importance of the surface area as the linear dimensions of particles decrease is stated concisely in a quantity known as the specific surface area Asp of a substance. This quantity is determined as the ratio of the area divided by the mass of an array of particles. If the particles are uniform spheres, as we have assumed throughout this section, this ratio equals... 

The concept of specific area defined by Equation (1) is important because this is a quantity that can be measured experimentally for finely divided solids without any assumptions as to the shape or uniformity of the particles. We discuss the use of gas adsorption to measure Asp in Chapter 9. If the particles are known to be uniform spheres, this measured quantity may be interpreted in terms of Equation (2) to yield a value of Rs. If the actual system consists of nonuniform spheres, an average value of the radius may be evaluated by Equation (2). Finally, even if the particles are nonspherical, a quantity known as the radius of an equivalent sphere may be extracted from experimental values. This often proves to be a valuable way of characterizing an array of irregularly shaped particles. We have a good deal more to say about average dimensions in this chapter and about equivalent spheres in Chapter 2. 

Mathematically, the harmonic displacements of an array of coupled oscillators in any dimension may be described by the set of equations ... 

Perhaps the most important new approach to chemical measurements has been the use of sensors for oceanic chemistry. Sensors comprise a transducer and its supporting electronic instrumentation. The key feature of sensors is their ability to monitor the concentration of a particular analyte continuously, so that the dimension of time can be added to the traditional three dimensions of spatial measurements. An example of a sensor is a pH electrode, coupled with a high-impedance voltmeter and a means of standardization and temperature compensation in situ. In principle, such a sensor can monitor pH continuously for days at a time while transferring the data to a recorder or memory device. One can contemplate towing an array of sensors at various depths simultaneously, obtaining three-dimen-o tin us d ta t. i Dr v e th two- imensional data a ail-... 

Definitions. Colloids are solid particles with diameters of 1 100 nanometers, A sol is a dispersion of colloidal particles in a liquid. A gel is an interconnected rigid network of sub-micrometer dimensions. A gel can be formed from an array of discrete colloidal particles (Method I) or the 3-D network can be formed from the hydrolysis and condensation of liquid meial alkoxide precursors (Methods 2 and 3). shown in Fig. 11. The metal alkoxide precursors used in Methods 2 and 3 are usually Si(OR)4 where R is CHj. C-Hj. or C3H7. The metal ions can be Si, Ti. Sn. Al, and so on,... 

Great activity has also been evidenced in microlithographically fabricated arrays of microelectrodes, which are typically formed in one plane on an insulating substrate [7,8,13,34-45] for experiments involving either an array of electrodes held at a common potential [37,40,42,43], or an array of noninteracting electrodes held at two or more different applied potentials [42,44], or an array of interdigitated electrodes held at two different potentials [13,34,36,38,39,45-47]. Arrays have significantly better analytical detection limits than continuous electrodes of the same overall dimensions, due to enhanced mass transport fluxes that arise from an increase in the spatial dimensionality of mass transport due to the alternation of electrode zones with pas-... 

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