Column, capillary equation

Giddings [2] estimated that, for a well-packed column, (y) takes a value of about 0.6. Equation (11) accurately describes longitudinal dispersion in GC capillary columns and equation (12) accurately describes longitudinal dispersion in GC and LC packed columns. Experimental support for these equations will be given in a later chapter. 

Chiral isocyanides such as 198 have also been used for the synthesis of chiral 4,5-disubstituted oxazoles such as 199, which are potentially useful in fluorescence-detected circular dichroism for on-column capillary electrophoresis (Equation 12) <1996JOC8750>. 

The smaller the HETP is, the better the column. The older 6 mm diameter packed columns would have values from 1 to 3 mm/plate, whereas values of 0.25 mm/plate are common for capillary columns. One equation to determine the number of theoretical plates and the HETP is the van Deemter equation shown below ... 

Since open tubular or capillary columns do not have any packing, their rate equation does not have an /4-term. This conclusion was pointed out by Golay [4], who also proposed a new term to deal with the diffusion process in the gas phase of open tubular columns. His equation had two C-terms, one for mass transfer in the stationary phase, Cs (similar to van... 

At first we tried to explain the phenomenon on the base of the existence of the difference between the saturated vapor pressures above two menisci in dead-end capillary [12]. It results in the evaporation of a liquid from the meniscus of smaller curvature ( classical capillary imbibition) and the condensation of its vapor upon the meniscus of larger curvature originally existed due to capillary condensation. We worked out the mathematical description of both gas-vapor diffusion and evaporation-condensation processes in cone s channel. Solving the system of differential equations for evaporation-condensation processes, we ve derived the formula for the dependence of top s (or inner) liquid column growth on time. But the calculated curves for the kinetics of inner column s length are 1-2 orders of magnitude smaller than the experimental ones [12]. 

As in the case of capillary rise, Sugden [27] has made use of Bashforth s and Adams tables to calculate correction factors for this method. Because the figure is again one of revolution, the equation h = a lb + z is exact, where b is the value of / i = R2 at the origin and z is the distance of OC. The equation simply states that AP, expressed as height of a column of liquid, equals the sum of the hydrostatic head and the pressure... 

Another approach to improving resolution is to use thin films of stationary phase. Capillary columns used in gas chromatography and the bonded phases commonly used in HPLC provide a significant decrease in plate height due to the reduction of the Hs term in equation 12.27. 

To minimize the multiple path and mass transfer contributions to plate height (equations 12.23 and 12.26), the packing material should be of as small a diameter as is practical and loaded with a thin film of stationary phase (equation 12.25). Compared with capillary columns, which are discussed in the next section, packed columns can handle larger amounts of sample. Samples of 0.1-10 )J,L are routinely analyzed with a packed column. Column efficiencies are typically several hundred to 2000 plates/m, providing columns with 3000-10,000 theoretical plates. Assuming Wiax/Wiin is approximately 50, a packed column with 10,000 theoretical plates has a peak capacity (equation 12.18) of... 

In both of these pieces of apparatus, isothermal operation and optimum membrane area are obtained. Good temperature control is essential not only to provide a value for T in the equations, but also because the capillary attached to a larger reservoir behaves like a thermometer, with the column height varying with temperature fluctuations. The contact area must be maximized to speed up an otherwise slow equilibration process. Various practical strategies for presetting the osmometer to an approximate n value have been developed, and these also accelerate the equilibration process. 

Column Operation To assure intimate contact between the counterflowing interstitial streams, the volume fraction of liquid in the foam should be kept below about 10 percent—and the lower the better. Also, rather uniform bubble sizes are desirable. The foam bubbles will thus pack together as blunted polyhedra rather than as spheres, and the suction in the capillaries (Plateau borders) so formed vidll promote good liqiiid distribution and contact. To allow for this desirable deviation from sphericity, S = 6.3/d in the equations for enriching, stripping, and combined column operation [Lemhch, Chem. E/ig., 75(27), 95 (1968) 76(6), 5 (1969)]. Diameter d still refers to the sphere. 

The D Arcy equation is the accepted equation for the flow of fluid through a packed bed and its derivation will be found in most physics textbooks. If a capillary column... 

Equation (11) accurately describes longitudinal diffusion in a capillary column where there is no impediment to the flow from particles of packing. In a packed column, however, the mobile phase swirls around the particles. This tends to increase the effective diffusivity of the solute. Van Deemter introduced a constant (y) to account... 

In summary, equation (13) accurately describes longitudinal dispersion in the stationary phase of capillary columns, but it will only be significant compared with other dispersion mechanisms in LC capillary columns, should they ever become generally practical and available. Dispersion due to longitudinal diffusion in the stationary phase in packed columns is not significant due to the discontinuous nature of the stationary phase and, compared to other dispersion processes, can be ignored in practice. 

It is a common procedure to assume certain conditions for the chromatographic system and operating conditions and, as a result, simplify equations (20) and (21). However, in many cases the assumptions can easily be over-optimistic, to say the least. It is necessary, therefore, to carefully consider the conditions that may allow such simplifying procedures and take steps to ensure that such conditions are carefully met when such expressions are used in practice. Now, the relative magnitudes of the resistance to mass transfer terms will vary with the type of columns (packed or capillary), the type of chromatography (GC or LC) and the type of particle, i.e., porous or microporous (diatomaceous support or silica gel). 

Equations (2) and (4) allow the permissible extra-column dispersion to be calculated for a range of capillary and packed columns. To allow comparison, data was included for a GC column, in addition to LC columns. The results are shown in Table 1. 

G. Lippmann introduced the capillary electrometer to measure the surface tension of mercury (Fig. 4.10). A slightly conical capillary filled with mercury under pressure from a mercury column (or from a pressurized gas) is immersed in a vessel containing the test solution. The weight of the mercury column of height h is compensated by the surface tension according to the Laplace equation... 

Using these equations, the KI values for four known pheromone components are estimated to be 1807.7 for Me2,Me5-17 H, 1790.6 for Me5,Me9-17 H, 1788.6 for Me5,Mell-17 H, and 1783.5 for Me7, Mell-17 H. These positional isomers separately elute from a capillary GC column in a coincidental order with these KI values [105,106],indicating the usefulness of IEX(opt) for the pheromone research. 

The second approach considers the ability of the fluid to penetrate the powder bed and involves the measurement of the extent and rate of penetration into a column of powder, better known as the Washburn Test. By considering the powder to consist of capillaries of radius R, as illustrated in Fig. 19, the equilibrium height of rise, he, is determined by equating capillary and head pressures, or... 

The methyl-[14C]-dimethyltin chloride was used to compare the performance of packed and megabore capillary columns in a gas chromatographic analysis for separating mixtures of a carbon-14 labelled trimethyllead chloride, tetramethyltin, dimethyltin dichloride and methyltin trichloride. The megabore column was able to separate all four methyltin compounds quickly, i.e., before the tetramethyltin decomposed into trimethyltin chloride and dimethyltin dichloride (equation 47), a reaction which did occur on the packed columns. Thus, the megabore column enabled the determination of the precise distribution of the various methyltin compounds in an environmental sample. The packed columns, on the other hand, could not separate dimethyltin dichloride and the methyltin trichloride and allowed significant decomposition of the tetramethyltin during the 15 minutes the analysis required. 

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