Dead volume

Fig. 6 shows both the actual cycle (shown in dashed lines) and the idealised cycle, which consists of two isosteres and two isobars. Heat flows in J/kg adsorbent q) are shown as shaded arrows. For most purposes, analysis of the ideal cycle gives an adequate estimate of the COP and cooling or heating per kg of adsorbent. An accurate calculation of the path of the actual cycle needs information on the dead volume of the whole system and of the heat transfer characteristics of the condenser and evaporator. General trends are more apparent from an analysis of the idealised cycle. 

The dead point is the position of the peak maximum of an unretained solute. It is not the initial part of the dead volume peak as this represents a retarded portion of the peak that is caused by dispersion processes. The importance of employing the peak maximum for such measurements as dead volume and retention volume will be discussed in later chapters of the book that deal with peak dispersion. 

The dead volume (Vq) is the volume of mobile phase passed through the column between the injection point and the dead point. 

In practice, the retention volume of an unretained peak eluted at the dead volume (Vo), will be made up of the volume of mobile phase in the column (Vm) and extracolumn volumes, from sample valves, connecting tubes, unions, etc. (Ve)-... 

Again it is seen that only when second order effects need to be considered does the relationship become more complicated. The dead volume is made up of many components, and they need not be identified and understood, particularly if the thermodynamic properties of a distribution system are to be examined. As a consequence, the subject of the column dead volume and its measurement in chromatography systems will need to be extensively investigated. Initially, however, the retention volume equation will be examined in more detail. 

It is clear that the separation ratio is simply the ratio of the distribution coefficients of the two solutes, which only depend on the operating temperature and the nature of the two phases. More importantly, they are independent of the mobile phase flow rate and the phase ratio of the column. This means, for example, that the same separation ratios will be obtained for two solutes chromatographed on either a packed column or a capillary column, providing the temperature is the same and the same phase system is employed. This does, however, assume that there are no exclusion effects from the support or stationary phase. If the support or stationary phase is porous, as, for example, silica gel or silica gel based materials, and a pair of solutes differ in size, then the stationary phase available to one solute may not be available to the other. In which case, unless both stationary phases have exactly the same pore distribution, if separated on another column, the separation ratios may not be the same, even if the same phase system and temperature are employed. This will become more evident when the measurement of dead volume is discussed and the importance of pore distribution is considered. 

As already mentioned, there are two so called "dead volumes" that are important in both theoretical studies and practical chromatographic measurements, namely, the kinetic dead volume and the thermodynamic dead volume. The kinetic dead volume is used to calculate linear mobUe phase velocities and capacity ratios in studies of peak variance. The thermodynamic dead volume is relevant in the collection of retention data and, in particular, data for constructing vant Hoff curves. 

In equation (37), for an incompressible mobile phase, the kinetic dead volume is (Vi(m)) which is the volume of moving phase only. Consequently, at a flow rate of... 

It is seen that the expression for the thermodynamic dead volume is more complex than the kinetic dead volume and depends, to a significant extent, on the si2e of the... 

Equation (38) shows that the measurement of (k ) incorporates the same errors as those met in trying to measure the thermodynamic dead volume. However, providing the solute is well retained, i.e.,... 

The silica dispersion showed the smallest retention volume. It should be noted, however, that the authors reported that the silica dispersion required sonicating for 5 hours before the silica was sufficiently dispersed to be used as "pseudo-solute". The retention volume of the silica dispersion gave the value of the kinetic dead volume, /.e., the volume of the moving portion of the mobile phase. It is clear that the difference between the retention volume of sodium nitroprusside and that of the silica dispersion is very small, and so the sodium nitroprusside can be used to measure the kinetic dead volume of a packed column. From such data, the mean kinetic linear velocity and the kinetic capacity ratio can be calculated for use with the Van Deemter equation [12] or the Golay equation [13]. 

The thermodynamic dead volume would be that of a small molecule that could enter the pores but not be retained by differential interactive forces. The maximum retention volume was recorded for methanol and water which, for concentrations of methanol above 10%v/v, would be equivalent to the thermodynamic dead volume for small molecules viz, about 2.8 ml). It is interesting to note that there is no significant difference between the retention volume of water and that of methanol over the complete range of solvent compositions examined, which confirms the validity of this... 

It is seen that there is a good correlation between experimental and calculated values. The scatter that does exist may be due to the dead volume of the column not being precisely independent of the solvent composition. The dead volume will depend, to a small extent, on the relative proportion of the different solvents adsorbed on the stationary phase surface, which will differ as the solvent composition changes. A constant value for the dead volume was assumed in the computer program that derived the equation. 

The idea of the effective plate number was introduced and employed by Purnell [4], Desty [5] and others in the late 1950s. Its conception was evoked as a direct result of the introduction of the capillary column or open tubular column. Even in 1960, the open tubular column could be constructed to produce efficiencies of up to a million theoretical plates [6]. However, it became immediately apparent that these high efficiencies were only obtained for solutes eluted at very low (k ) values and, consequently, very close to the column dead volume. More importantly, on the basis of the performance realized from packed columns, the high efficiencies did not... 

Equation (33) shows that the maximum capacity ratio of the last eluted solute is inversely proportional to the detector sensitivity or minimum detectable concentration. Consequently, it is the detector sensitivity that determines the maximum peak capacity attainable from the column. Using equation (33), the peak capacity was calculated for three different detector sensitivities for a column having an efficiency of 10,000 theoretical plates, a dead volume of 6.7 ml and a sample concentration of l%v/v. The results are shown in Table 1, and it is seen that the limiting peak capacity is fairly large. 

Unions can also be a serious source of dispersion, depending on their design. Today, low dead volume unions are generally available which exhibit reduced dispersion... 

It is seen that a linear curve is not obtained with the use of (k ) values derived from the fully permeating dead volume and, thus, (k ) can not be used in the kinetic studies of columns. In contrast, the linear curve shown when using (k"), obtained from the use of the dynamic dead volume, confirms that (k e) values based on the excluded... 

In order to relate the value of (H) to the solute diffusivity and, consequently, to the molecular weight according to equation (11), certain preliminary calculations are necessary. It has already been demonstrated in the previous chapter (page 303) that the dynamic dead volume and capacity ratio must be used in dispersion studies but, for equation (11) to be utilized, the value of the multipath term (2Xdp) must also be... 

The reduced chromatogram contains four peaks the first will be the dead volume peak (which, as has been shown previously, must be the fully excluded peak determined from the retention volume of a salt or solute of large molecular weight). 

It should be noted that Purnell s equation utilizes the thermodynamic capacity ratio calculated using the thermodynamic dead volume. 

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