Single point measurement

Fig. 23. Viscosity vs shear rate curves for two fluids showing the fallacy of a single point measurement. Fluid Vl would appear to be more viscous than fluid B if measured only at point X, of the same viscosity if measured at point V, and less viscous if measured only at point Z.

ITie BET method is the most widely used procedure for determining the surface area of porous materials. In this chapter, BET results were obtained from single point measurements using a Micromeritics Flowsorb II 2300 surface area analyzer. A mixture of nitrogen in helium (30 70 mole percentage) was used. Although this simple method is not quantitative for the microporous materials studied in section 5, it still allows qualitative comparisons to be made. 

To describe single-point measurements of a random process, we use the first-order probability density function p/(/). Then p/(/) df is the probability that a measurement will return a result between / and / -I- df. We can characterize a random process by its moments. The nth moment is the ensemble average of /", denoted (/"). For example, the mean is given by the first moment of the probability density function. 

The viscosity level in the range of the Newtonian viscosity r 0 of the flow curve can be determined on the basis of molecular models. For this, just a single point measurement in the zero-shear viscosity range is necessary, when applying the Mark-Houwink relationship. This zero-shear viscosity, q0, depends on the concentration and molar mass of the dissolved polymer for a given solvent, pressure, temperature, molar mass distribution Mw/Mn, i.e. 

Another important question that had to be answered was if the results in the ARCO pilot unit were repeatable when North Sea atmospheric residue is used as feed. The repeatability is well demonstrated in ARCO pilot units with vacuum gas oils, but this had to be confirmed for atmospheric residue feedstocks. To be able to achieve repeatability in the ARCO unit, independent of the feed used, the catalyst circulation has to be calibrated for each single catalyst the first time it is used in the pilot unit. If the same catalyst is used more than once, it is not necessary to calibrate the catalyst circulation again according to ARCO [7]. We have experienced the same, but nevertheless the calibration of the catalyst circulation is always checked by a single point measurement if a catalyst is used more than once. 

There are several advantages to a tunable filter system. First, it is unnecessary to have a multichannel detector (for single-point measurements), since only one wavelength is being selected at a time. The size of the detector is also much more flexible, since spectral resolution of the system is not a function of the detector and input aperture as it is in a classical monochromotor, but rather limited only by the functional characteristics of the filter. Second, since focusing and dispersive elements are minimized the spectrometer could be made very small. Third, the entire spectrum does not need to be obtained the random access nature of the filter allows only the spectral features required for a measurement to be made. This can be a significant advantage for routine measurements. 

The melt flow indexer. The melt flow indexer is often used in industry to characterize a polymer melt and as a simple and quick means of quality control. It takes a single point measurement using standard testing conditions specific to each polymer class on a ram type extruder or extrusion plastometer as shown in Fig. 2.45. 

Sometimes, from such a single-point measurement of the solution viscosity, an arbitrary measure has been defined, which for a given polymer supplies a useful measure for comparing levels of the molar mass. An example is the so-called k-value for PVC k values of 55, 60, 65 and 70 denote grades of increasing M. (see Qu. 2.40 and 2.41). 

All chemisorption experiments were single point measurements at 8.10 Pa. By measuring the adsorption isotherms from 10 -10 Pa for a few catalysts, it was checked that a relative comparison of the thus obtained chemisorption values was as justifiable as any other method based on other measuring points, or on extrapolation of measuring points to zero pressure, as advocated by Benson and Boudart (24). No corrections were made for chemisorption on the bare supports as such, because this was found negligible. 

Ionic liquids are however more just than a bulk medium and the dielectric constant may be not the best parameter to define ILs polarity. They are constituted by positive and negative ions which can exert various effects. Recently, the microscopic properties of ILs, i.e. the ability of these media to interact with specific dissolved species (reagents, transition states, intermediates and products), have been measured and several polarity scales, previously developed for common molecular solvents, have been extended to ILs. At variance with molecular solvents, ILs are characterized by complex interaction forces between anion and cation and these interactions are competitive with the ability of both anion and cation to interact with dissolved species thus, multiparameters solvatochromic correlations, better than single point measurements, resulted useful to understand the solvent polarity. ... 

For single point measurements, individual cells were selected from the visually acquired sample image, as seen on the screen. For each cell position on the sample substrate, the aperture was selected to straddle the cell, and typically was 30 gm x 30 gm. The cell position and apertures were stored for each cell, and the data acquisition of aU stored positions proceeded automatically. The microscope and optical bench were continuously purged with purified, dry air. In addihon, the sample area in the focal plane of the microscope was enclosed in a purged sample chamber. 

Parallel Plate. Plashchina et al. (73) studied the creep of HM pectin gels placed between two corrugated parallel plates. Creep compliance curves were obtained for 0.5 to 2.5% pectin at temperatures from 25 to 55 C. Reversible and irreversible strain components were separated. Pectin macromolecules were characterized as being very stiff and only a slight decrease in entropy was required to form a pectin gel (7 ). Mitchell and Blanshard (50) used an automated parallel plate vlscoelastometer to study the creep compliance on low methoxyl pectins. The value of these experiments was that a continuous response was obtained from the gel rather than a single point measurement. 

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