Dispersion experimental determination

Now consider some examples of the influence of sedimentation process upon PT sensitivity. Let us consider the application of fine-dispersed magnesia oxide powder as the developer. Using the methods described in [4] we experimentally determined the next characteristics of the developer s layer IT s 0,5, Re s 0,25 pm. We used dye sensitive penetrant Pion , which has been worked out in the Institute of Applied Physics of National Academy of Sciences of Belarus. Its surface tension ct = 2,5 10 N m V It can be shown that minimum width of an indication of magnesia powder zone, imbibed by Pion , which can be registered, is about W s 50 pm. Assume that n = 1. 

Contemporary development of chromatography theory has tended to concentrate on dispersion in electro-chromatography and the treatment of column overload in preparative columns. Under overload conditions, the adsorption isotherm of the solute with respect to the stationary phase can be grossly nonlinear. One of the prime contributors in this research has been Guiochon and his co-workers, [27-30]. The form of the isotherm must be experimentally determined and, from the equilibrium data, and by the use of appropriate computer programs, it has been shown possible to calculate the theoretical profile of an overloaded peak. 

Recalling that a separation is achieved by moving the solute bands apart in the column and, at the same time, constraining their dispersion so that they are eluted discretely, it follows that the resolution of a pair of solutes is not successfully accomplished by merely selective retention. In addition, the column must be carefully designed to minimize solute band dispersion. Selective retention will be determined by the interactive nature of the two phases, but band dispersion is determined by the physical properties of the column and the manner in which it is constructed. It is, therefore, necessary to identify those properties that influence peak width and how they are related to other properties of the chromatographic system. This aspect of chromatography theory will be discussed in detail in Part 2 of this book. At this time, the theoretical development will be limited to obtaining a measure of the peak width, so that eventually the width can then be related both theoretically and experimentally to the pertinent column parameters. 

Unfortunately, any equation that does provide a good fit to a series of experimentally determined data sets, and meets the requirement that all constants were positive and real, would still not uniquely identify the correct expression for peak dispersion. After a satisfactory fit of the experimental data to a particular equation is obtained, the constants, (A), (B), (C) etc. must then be replaced by the explicit expressions derived from the respective theory. These expressions will contain constants that define certain physical properties of the solute, solvent and stationary phase. Consequently, if the pertinent physical properties of solute, solvent and stationary phase are varied in a systematic manner to change the magnitude of the constants (A), (B), (C) etc., the changes as predicted by the equation under examination must then be compared with those obtained experimentally. The equation that satisfies both requirements can then be considered to be the true equation that describes band dispersion in a packed column. 

Unfortunately, some of the data that are required to calculate the specifications and operating conditions of the optimum column involve instrument specifications which are often not available from the instrument manufacturer. In particular, the total dispersion of the detector and its internal connecting tubes is rarely given. In a similar manner, a value for the dispersion that takes place in a sample valve is rarely provided by the manufactures. The valve, as discussed in a previous chapter, can make a significant contribution to the extra-column dispersion of the chromatographic system, which, as has also been shown, will determine the magnitude of the column radius. Sadly, it is often left to the analyst to experimentally determine these data. 

Energy-dispersive X-ray analyses were carried out by using the ratio technique (equation 1) to relate compositions to the intensities of the CoKa and WL characteristic X-ray peaks. The value of the kw Co factor was experimentally determined using single-phase eCo samples. A series of EDX analyses was performed from the edge to the interior of the foil and the results plotted in the form of the relationship ... 

The value of 3 and its dispersion for a molecule, or polymer chain, can be experimentally determined by DC induced second harmonic generation (DCSHG) measurements of liquid solutions -1 2). The experimental arrangement requiring an applied DC field E° to remove the natural center of inversion symmetry of the solution is described in Figure 4. The second harmonic polarization of the solution is expressed as... 

The interesting information is the correlation between first shell coordination numbers from EXAFS and H/M values from chemisorption, shown in Fig. 6.18. The correlation is as expected high dispersions correspond to low coordination numbers. Of course, what we really need is a relationship between particle size and H/M values. The right hand panel of Fig. 6.18 translates the experimentally determined H/M values of the catalysts into the diameter of particles with a half-spherical shape. Similar calibrations can be made for spherical particles or for particles of any other... 

This limit, which might be referred to as the ultimate tinctorial strength , reflects the maximum degree of dispersion which can be achieved in a particular vehicle system under a certain set of conditions. However, experimental results may deviate more or less from the theoretical concepts and an ideal dispersion is not normally realized not all agglomerates are broken down entirely. This, however, is of no consequence, because even the experimentally determined ultimate tinctorial strength is by no means considered a standard for industrial application technical operations are not always allowed to go to completion, and the dispersion process is often discontinued, mainly for economical reasons. 

Lipophilicity is a molecular property experimentally determined as the logarithm of the partition coefficient (log P) of a solute between two non-miscible solvent phases, typically n-octanol and water. An experimental log P is valid for only a single chemical species, while a mixture of chemical species is defined by a distribution, log D. Because log P is a ratio of two concentrations at saturation, it is essentially the net result of all intermolecular forces between a solute and the two phases into which it partitions (1) and is generally pH-dependent. According to Testa et al. (1) lipophilicity can be represented (Fig. 1) as the difference between the hydrophobicity, which accounts for hydrophobic interactions, and dispersion forces and polarity, which account for hydrogen bonds, orientation, and induction forces ... 

In practice the value of (w) will vary between about 2 and 5 ( i.e sample concentrations will lie between 2%w/v and 5%w/v) before mass overload becomes a significant factor In band dispersion. A numerical value for (g>) of 5 will be taken In subsequent calculations. The correct value of ( ), for the particular solute concerned, can be experimentally determined on an analytical column carrying the same phase system If so required. 

Experimental Determination of Dispersion Coefficient from a Pulse Input... 

Fig. 2.16. Experimental determination of dispersion coefficient-ideal-pulse injection. Expected symmetrical distribution of concentration measurements. Small DJuL value...

Fig. 2.17. Experimental determination of dispersion coefficient. (a) Treatment of data by linear interpolation (b) Treatment of mixing-cup data...

Fig. 2.20. Dimensionless axial-dispersion coefficients for fluids flowing in circular pipes. In the turbulent region, graph shows upper and lower limits of a band of experimentally determined values. In the laminar region the lines are based on the theoretical equation 2.37...

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