Radius, column, minimum

Thus, for significant values of (k") (unity or greater) the optimum mobile phase velocity is controlled primarily by the ratio of the solute diffusivity to the column radius and, secondly, by the thermodynamic properties of the distribution system. However, the minimum value of (H) (and, thus, the maximum column efficiency) is determined primarily by the column radius, secondly by the thermodynamic properties of the distribution system and is independent of solute diffusivity. It follows that for all types of columns, increasing the temperature increases the diffusivity of the solute in both phases and, thus, increases the optimum flow rate and reduces the analysis time. Temperature, however, will only affect (Hmin) insomuch as it affects the magnitude of (k"). 

Another critical instrument specification is the total extra-column dispersion. The subject of extra-column dispersion has already been discussed in chapter 9. It has been shown that the extra-column dispersion determines the minimum column radius and, thus, both the solvent consumption per analysis and the mass sensitivity of the overall chromatographic system. The overall extra-column variance, therefore, must be known and quantitatively specified. 

Where Q, is the minimum detectable amount, R the detector noise level and s the detector sensitivity [135,146,151,152]. For a concentration sensitive detector the minimum detectable concentration is the product of Q, and the volumetric gas flow rate through the detector. The minimum detectable amount or concentration is proportional to the retention time, and therefore, directly proportional to the column radius for large values of n. it follows, then, that very small quantities can be detected on narrow-bore columns. 

Equation (13) shows that the minimum value of (H) is solely dependant on the column radius (r) and the thermodynamic properties of the solute/phase system. As opposed to the optimum velocity, the minimum value of (H) is not dependent on the solute diffusivtty. 

The total extra column dispersion that takes place in a liquid chromatographic system places a limit on the minimum column radius that can be employed for a given separation. The effect of extra column dispersion on the minimum column radius was examined by Reese and Scott (13) who derived an equation that allows the minimum column radius to be calculated for any particular separation. 

Equation (19) shows that the minimum radius will increase as the square root of the extra column dispersion and as the square root of (a-1) but, increase inversely with the square root of the particle diameter. (However,it will be shown later that, that if the column is packed with particles of optimum diameter for the particular separation then the column radius will become linearly related to the function (a-1)). 

Nevertheless, for unoptimized columns, and for simple separations, the minimum column radius will be relatively large and for difficult separations the minimum column radius will be relatively small, it will be seen later, that It is highly desirable to operate with a column of minimum diameter as this will provide the maximum mass sensitivity from the... 

Equation (24) allows the minimum column radius to be calculated from its length, the particle diameter of its packing and the extra column dispersion of the chromatographic system. Unfortunately, the extra column dispersion is rarely known and very few manufacturers even provide data on the overall dispersion of the detector. When values are given for the detector dispersion, it is often for the sensing cell alone and does not include internal connecting tubes and, as a consequence, can be very misleading. 

Narrow-bore columns of between 1.0 and 2.5 mm ID are available for use in specially designed liquid chromatographs having an extremely low extracolumn dispersion. For a concentration-sensitive detector such as the absorbance detector, the signal is proportional to the instantaneous concentration of the analytes in the flow cell. Peaks elute from narrow-bore columns in much smaller volumes compared to those from standard-bore columns. Consequently, because of the higher analyte concentrations in the flow cell, the use of narrow-bore columns enhances detector sensitivity. The minimum detectable mass is directly proportional to the square of the column radius (107) therefore, in theory, a 2.1-mm-ID column will provide a mass sensitivity about five times greater than that of a 4.6-mm-ID column of the same length. 

Equation (19) allows the minimum column radius to be calculated for a column of given length and efficiency. Consequently, as the volume flow of mobile phase through a column is directly... 

Another important detector specification is the total detector system dispersion. It is made up of the dispersion in the connecting tube and that in the sensing cell. The dispersion inherent in the detector controls the minimum column radius that can be used and consequently, the solvent consumption. Detector dispersion also indirectly controls the mass sensitivity. Connecting tubes can take various forms straight, coiled or serpentine. Serpentine connecting tubes are recommended, as they provide the... 

The optimum mobile phase velocity will also be determined in the above calculations together with the minimum radius to achieve minimum solvent consumption and maximum mass sensitivity. The column specifications and operating conditions are summarized in Table 4. 

The maximum degree of bending on a field cold bend may be determined by either method in Table PL-3.7.5(a)(2). The first column expresses the maximum deflection in an arc length equal to the nominal outside diameter, and the second column expresses the minimum radius as a function of the nominal outside diameter. 

Note that Vg is proportional to the square of the inner radius of the column. It is important to have a rough idea of the void volume of the column since it often dictates the operating flow-rate range, sampleloading capacity, and mass sensitivity (the minimum detectable amount) of the assay. For instance, a typical analytical column (150mm x 4.6mm i.d.) has a Vg of about 1.5 mL and is operated at 1.0mL/min. In contrast, by reducing the inner diameter to 2.0 mm, a typical LC/MS column (150mm X 2.0mm i.d.) has a Vg of about 0.3mL and is operated at... 

For capillary columns, it is possible to use the equation below derived from Golay (cf. 2.5.2) to relate the minimum theoretical H value to the retention factor, where r represents the radius of the column. The coefficient of efficiency of the column is... 

Plate height is reduced in an open tubular column because band spreading by multiple flow paths (Figure 23-19) cannot occur. In the van Deemter curve for the packed column in Figure 23-15. the A term accounts for half of the plate height at the most efficient flow rate (minimum H) near 30 mL/min. If A were deleted, the number of plates on the column would be doubled. To obtain high performance from an open tubular column, the radius of the column must be small and the stationary phase must be as thin as possible to ensure rapid exchange of solute between mobile and stationary phases. 

Theoretical performance in gas chromatography. As the inside radius of an open tubular gas chromatography column is decreased, the maximum possible column efficiency increases and sample capacity decreases. For a thin stationary phase that equilibrates rapidly with analyte, the minimum theoretical plate height is given by... 

The importance of the extra column dispersion now becomes apparent, as equation (26) shows that the minimum detectable mass Increases linearly with the extra column dispersion. It Is also becomes obvious that it is of little use designing a detector for increased sensitivity (Xp) if this is achieved (as is often the case) at the expense of increased extra column dispersion (oe). Conversely, if the chromatographic system is designed to have very low extra column dispersion, a proportional reduction in the minimum detectable mass will be achieved even if the actual detector concentration sensitivity remains the same. It follows, that in the design of an optimized column for a particular analysis, the extra column dispersion will determine both the radius of the column and the mass sensitivity that will be available. 

The sealing capacity of a rock under hydrostatic conditions is determined by the minimum hydrocarbon-water displacement pressure of the rock, which depends on the radius of the largest connected pore throats in the rock and the oil-water and gas-water interfacial tensions, and in addition on the densities of groundwater and hydrocarbons accumulating in the adjacent reservoir rock. The maximum height of an oil or gas column that can accumulate below a seal is given by Equation 4.17 (Section 4.1.3)... 

Expression 1.33 leads to the minimum value for the HETP for a column of radius r, if the retention factor of the particular compound under examination is known. 

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