Thermodynamics dead volume

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. 

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

The kinetic dead volume is represented in equation (13) by (Vj(m)), and is solely that volume of mobile phase In the column that is moving. The thermodynamic dead volume is given, in equation (13), by,... 

The thermodynamic dead volume includes those static fractions of the mobile phase that have the same composition as the moving phase, and thus do not contribute to solute retention by differential interaction in a similar manner to those with the stationary phase. It is seen that, in contrast to the kinetic dead volume, which by definition can contain no static mobile phase, and as a consequence is independent of the solute chromatographed, the thermodynamic dead volume will vary from solute to solute depending on the size of the solute molecule (i.e. is dependent on both ( i )and (n). Moreover, the amount of the stationary phase accessible to the solute will also vary with the size of the molecule (i.e. is dependent on (%)). It follows, that for a given stationary phase, it is not possible to compare the retentive properties of one solute with those of another in thermodynamic terms, unless ( ), (n) and (fc) are known accurately for each solute. This is particularly important if the two solutes differ significantly in molecular volume. The experimental determination of ( ), (n) and( ) would be extremely difficult, if not impossible In practice, as it would be necessary to carry out a separate series of exclusion measurements for each solute which, at best, would be lengthy and tedious. 

For the assessment of the extent of change of the phase ratio of a HPLC column system with temperature or another experimental condition, several different experimental approaches can be employed. Classical volumetric or gravimetric methods have proved to be unsuitable for the measurement of the values of the stationary phase volume Vs or mobile phase volume Vm, and thus the phase ratio ( = Vs/Vm). The tracer pulse method266,267 with isotopically labeled solutes as probes represents a convenient experimental procedure to determine Vs and V0, where V0 is the thermodynamic dead volume of the column packed with a defined chromatographic sorbent. The value of Vm can be the calculated in the usual manner from the expression Vm = Eo — Vs. In addition, the true value of Vm can be independently measured using an analyte that is not adsorbed to the sorbent and resides exclusively in the mobile phase. As a further independent measure, the extent of change of 4> with T can be assessed with weakly interacting neutral or... 

J. H. Knox, R. KaUszan, Theory of solvent distnrbance peaks and experimental determination of thermodynamic dead-volume in colnmn liqnid chromatography, J. Chromatogr. A, 349 (1985), 211-234. 

There are two types of dead volume (i.e., the dynamic dead volume and the thermodynamic dead volume [2]). The dynamic dead volume is the volume of... 

Equation [3.18] assumes that the extra-column volume Vg is negligible. However, there are two definitions of void volume, and thus also of the capacity ratio of a solute. The two void volumes are called the thermodynamic and the dynamic void volumes and they are not equal (Scott, www.chromatography-online.org) the two void volumes and capacity ratios are used for different purposes. Equations [3.16-3.18] incorporate the thermodynamic dead volume and all further discussion in this chapter assumes this definition. 

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 size of the solute molecule. In common with the kinetic dead volume, it includes the volume of moving phase Vi(m), but it also includes that volume of the interstitial volume that is size dependent (W), as well as the volume of pores available to the solute which is... 

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