Frequent use

Derived from an aldehyde or ketone and an alcohol using an acid catalyst. Ethylene glycol or 1,3-dihydroxypropane are frequently used to give 5-or 6-member cyclic products. 

The measurement techniques most frequently used are derived from Raoult s and Van t Hoff s laws applied to cryometry, ebulliometry, osmometry, etc. They are not very accurate with errors on the order of ten per cent. Consequently, the molecular weight is often replaced by correlated properties. The mean average temperature or viscosity can thus replace molecular weight in methods derived from ndM. 

The resolution of capillary columns enables the separation of all principal components of a straight-run gasoline. The most frequently used stationary phases are silicone-based, giving an order of hydrocarbon elution times close to the order of increasing boiling point. 

The luminometer index (ASTM D 1740) is a characteristic that is becoming less frequently used. It is determined using the standard lamp mentioned above, except that the lamp is equipped with thermocouples allowing measurement of temperatures corresponding to different flame heights, and a photo-electric cell to evaluate the luminosity. The jet fuel under test is compared to two pure hydrocarbons tetraline and iso-octane to which are attributed the indices 0 and 100, respectively. The values often observed in commercial products usually vary between 40 and 70 the official specification is around 45 for TRO. 

Additives that affect the cloud point are no longer in frequent use however, it has been shown that certain polymers having branched paraffins can recognize paraffins of equivalent size and keep them in solution. It is therefore possible to complex the longest paraffins selectively and to decrease the cloud point by 3 to 4°C (Damin et al., 1986). 

The most frequently used bit types are the roller cone or rock bit (F g. 3.8) and the polycrystalline diamond cutter or PDC bit. 

ERD wells are technically more difficult to drill and because of the degree of engineering required for each well the term designer well is frequently used. 

Other information that can be obtained from such map is the location of faults, the status and location of wells and the location of the fluid contacts. Figure 5.45 shows some of the most frequently used map symbols. Structural maps are used in the planning of development activities such as well trajectories/targets and the estimation of reserves. 

The other parameters used in the calculation of STOMP and GIIP have been discussed in Section 5.4 (Data Interpretation). The formation volume factors (B and Bg) were introduced in Section 5.2 (Reservoir Fluids). We can therefore proceed to the quick and easy deterministic method most frequently used to obtain a volumetric estimate. It can be done on paper or by using available software. The latter is only reliable if the software is constrained by the geological reservoir model. 

Since the drop volume method involves creation of surface, it is frequently used as a dynamic technique to study adsorption processes occurring over intervals of seconds to minutes. A commercial instrument delivers computer-controlled drops over intervals from 0.5 sec to several hours [38, 39]. Accurate determination of the surface tension is limited to drop times of a second or greater due to hydrodynamic instabilities on the liquid bridge between the detaching and residing drops [40],... 

A few of the most frequently used techniques are discussed briefly in this chapter references to those not covered are given in the table. Useful reviews are Refs. 2-5 and 6 and, for organic surfaces. Refs. 7-9 and 10. Also, many of the various measurements have found use in the study of the adsorbed state, and further examples of their use are to be found in Chapters VII, XVI, and XVII. 

There are many large molecules whose mteractions we have little hope of detemiining in detail. In these cases we turn to models based on simple mathematical representations of the interaction potential with empirically detemiined parameters. Even for smaller molecules where a detailed interaction potential has been obtained by an ab initio calculation or by a numerical inversion of experimental data, it is usefid to fit the calculated points to a functional fomi which then serves as a computationally inexpensive interpolation and extrapolation tool for use in fiirtlier work such as molecular simulation studies or predictive scattering computations. There are a very large number of such models in use, and only a small sample is considered here. The most frequently used simple spherical models are described in section Al.5.5.1 and some of the more common elaborate models are discussed in section A 1.5.5.2. section Al.5.5.3 and section Al.5.5.4. 

Flere, we shall concentrate on basic approaches which lie at the foundations of the most widely used models. Simplified collision theories for bimolecular reactions are frequently used for the interpretation of experimental gas-phase kinetic data. The general transition state theory of elementary reactions fomis the starting point of many more elaborate versions of quasi-equilibrium theories of chemical reaction kinetics [27, M, 37 and 38]. 

A sine-shape has side lobes which impair the excitation of a distinct slice. Other pulse envelopes are therefore more commonly used. Ideally, one would like a rectangular excitation profile which results from a sine-shaped pulse with an infinite number of side lobes. In practice, a finite pulse duration is required and therefore the pulse has to be truncated, which causes oscillations in the excitation profile. Another frequently used pulse envelope is a Gaussian frmction ... 

It is especially useflil for liquid samples in flat cells, which may extend through tlie entire height of the cavity. In the cylindrical cavity a TEq mode is frequently used because of its fairly high g-factor and the very strong along the sample axis. 

Other frequently used resonators are dielectric cavities and loop-gap resonators (also called split-ring resonators) [12]. A dielectric cavity contains a diamagnetic material that serves as a dielectric to raise the effective filling factor by concentratmg the B field over the volume of the sample. Hollow cylinders machmed from Ilised quartz or sapphire that host the sample along the cylindrical axis are conunonly used. 

Figure Bl.18.4. The most frequently used illumination system in bright-field mieroseopy.

One fiirther method for obtaining surface sensitivity in diffraction relies on the presence of two-dimensional superlattices on the surface. As we shall see fiirtlrer below, these correspond to periodicities that are different from those present in the bulk material. As a result, additional diffracted beams occur (often called fractional-order beams), which are uniquely created by and therefore sensitive to this kind of surface structure. XRD, in particular, makes frequent use of this property [4]. Transmission electron diffraction (TED) also has used this property, in conjunction with ultrathin samples to minimize bulk contributions [9]. 

X-ray photoelectron spectroscopy (XPS) is among the most frequently used surface chemical characterization teclmiques. Several excellent books on XPS are available [1, 2, 3, 4, 5, 6 and 7], XPS is based on the photoelectric effect an atom absorbs a photon of energy hv from an x-ray source next, a core or valence electron with bindmg energy is ejected with kinetic energy (figure Bl.25.1) ... 

TPD is frequently used to detenuine (relative) surface coverages. The area below a TPD spectrum of a certain species is proportional to the total amount that desorbs. In this way one can detennine uptake curves that correlate gas exposure to surface coverage. If tire pumping rate of the UHV system is sufiBciently high, the mass spectrometer signal for a particular desorption product is linearly proportional to the desorption rate of the adsorbate [20, 21] ... 

The reaction vessel is situated inside a metal of high themial conductivity having a cylindrical, spherical, or other shape which serves as the calorimetric medium. Silver is the most suitable material because of its high themial conductivity, but copper is most frequently used. 

If there is no approximate Hessian available, then the unit matrix is frequently used, i.e., a step is made along the gradient. This is the steepest descent method. The unit matrix is arbitrary and has no invariance properties, and thus the... 

This type of basis functions is frequently used in popular quantum chemishy packages. We shall discuss the way to evaluate different kinds of matrix elements in this basis set that are often used in quantum chemistt calculation. 

Chebyshev Approximation The well known expansion of exp(— into Chebyshev polynomials T, [23] is one of the most frequently used integration technique in numerical quantum dynamics ... 

Records in this category make multiple appearances as single lines without continuation and they ai c used to form lists (of atoms, hydrogen bonds, etc.) Tire two most frequently used records belonging to this category, namely ATOM and CON-ECT, arc presented and discussed in more detail later. 

Hence, they take account of only the structure constitution (topology). One of the first and most frequently used topological indices is the Wiener index. It has the form of Eq. (3), where D,y are all the routes from atom i to atom j. 

Other quite frequently used indices are the Randic index and the information-topological indices such as the Bonchev index (see Chapter VIll, Section 1 in the Handbook), Up to now several hundred indices have been devised. 

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