Kinetic 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. 

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... 

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 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. 

Alternatively, sodium nitro prusside gives a value, close to that of dispersed silica, and, in practice, could be used to determine the total excluded volume or the kinetic dead volume without incurring serious error. Values for the kinetic dead volume measured in this way could be... 

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... 

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... 

Microfabricated fluidic devices (microchips) are potentially useful for multidimensional separations because high-efficiency separations can be achieved and small sample volumes can be manipulated with minimal dead volumes between interconnecting channels. Electro-kinetically driven separation techniques demonstrated on microchips include... 

The straight line confirms that the excluded dead volume must not only be used for measuring mobile phase velocities but in kinetic studies of LC columns and LC column design it must also be employed for the measurement of capacity factors. 

Experiments in which catalyst wafers are used may suffer from reactant mass transfer problems, which limit the validity of the data or complicate their analysis. To determine the reaction kinetics and activation energies, mass transfer effects have to be understood (Burcham and Wachs, 1999). These difficulties can be avoided if a conventional fixed-bed reactor is mimicked closely and the catalyst is used in powder form and the reactant gases flow through the bed. It is also important to prevent homogeneous gas-phase reactions by reducing the dead volume. 

The cell designs described above are in general not ideal for providing simultaneous measurements of spectra and kinetics of the catalytic reaction, because each cell has a large dead volume, and the catalyst is a pressed wafer, which may not be fully accessible to the reactants because of mass transfer limitations. 

Figure 6 illustrates the progressive overloading of an anti-HSA polyclonal antibody column after repeated injections of 2 /zg of HSA. At first injections, impurities elute from the column at the dead volume, while HSA is totally adsorbed. The gradual emergence of the nonretained HSA elution peak is due to two different effects, the saturation of the support and the slow adsorption kinetic process. The unretained fraction is calculated from peak area measurements, subtracting the area of the impurity response peak. 

For an inert substance (elution at tj only the physics plays a role i.e. diffusion coefficient, viscosity, linear velocity (mm/s), dead volume of the device, particle size, quality of packing, column length. At an actual separation also the chemistry naturally is important, because the kinetics of the adsorption <=> desorption, for example, depends on the surface of the stationary phase and the temperature. 

There is flow through the reactor and one aims to determine the total volume of the reactor in order to achieve a desired final conversion. Usually one knows the reaction intrinsic kinetics, but additional data such as feed flow and mean residence time are necessary. The residence time of the molecules is not uniform and there is dead volume with preferential paths. In this reactor, let us consider the steady state, disregarding the accumulation term. 

There are two types of dead volume (i.e., the dynamic dead volume and the thermodynamic dead volume. The dynamic dead volume is the volume of the moving phase in the column and is used in kinetic studies to calculate mobile-phase velocities. 

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