Compressibility Fluids are employed as mobile phases in chromatography and all fluids are to some extent compressible. The compressibility of liquids, however, is very small and, thus, has little impact on liquid chromatography performance. Gases, however, have high compressibility, as described by Boyle’s law, which states that at a given temperature, the product of the pressure and volume of a gas is constant. Thus, as there is a significant pressure drop across a GC column, although the mass of gas passing a give point is constant along the column length, the volume of gas passing through the column continually increases from the start of the column to the end. This has important ramifications when attempting to measure the specific retention volume of a solute for thermodynamic analysis. It is clear that, as the volume flow will continually increase as the solute passes along the column, then a pressure correction must be applied. The true retention volume of a solute can be calculated as 1.5 times the product of the retention time and exit flow rate, times (the inlet-outlet pressure ratio squared minus 1) over (the inlet-outlet pressure ratio cubed minus 1).

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Author: RPW Scott Book:Dispersion in Chromatography Columns
Section:Dispersion   Summary

functions contained in it, are well substantiated by experiment. The Knox equation is obtained from an empirical fit to experimental data and the individual functions of other pertinent variables contained in the equation are not all substantiated by experiment. The Golay equation accurately described dispersion in capillary or open tubular columns but in GC the compressibility of the mobile phase must also be taken into account (Golay in his original derivation did not accommodate gas compressibility). It would appear from the data available at this time, that the Van Deemter equation (for packed columns) or the Golay equation (for capillary or open tubular columns) would be the most appropriate to use in column design and in the interpretation of column properties

Dispersion   Summary

Author: RPW Scott Book:Principles and Practice of Chromatography
Section:Principles   Peak-Dispersion   Multi-Path-Effect

Peak Dispersion in a Chromatographic Column The first comprehensive approach to dispersion in chromatographic columns was taken by Van Deemter (8) who developed the dispersion equation for a packed GC column. Van Deemter's development did not take into account the compressibility of the mobile phase which was dealt with later by Katz, Ogan and Scott (9). A simple form of this theory will be given that does not accommodate the compressibility of the mobile phase but a more detailed and comprehensive treatment is given in Dispersion in Chromatography Columns and Extra Column Dispersion. Van Deemter et al. assumed that there were four band spreading processes responsible for peak dispersion, namely, multi-path dispersion, longitudinal

Principles   Peak-Dispersion   Multi-Path-Effect

Author: RPW Scott Book:Dispersion in Chromatography Columns
Section:Dispersion   Compressibility-Effects-GC

Effect of Mobile Phase Compressibility On the HETP Equation for a Packed GC Column  As the pressure falls along the column length, the velocity changes and, as the solute diffusivity depends on the pressure, the diffusivity of the solute will also change. The multi-path term, which contains no velocity or gas pressure dependent parameters, will be unaffected and the expression that describes it the same. The other terms in the  HETP equation, however, all contain parameters that are affected by gas

Dispersion   Compressibility-Effects-GC

Author: RPW Scott Book:Extra Column Dispersion
Section:EC-Dispersion   GC-Capillary-Columns

GC Capillary Columns The maximum permissible extra column dispersion for a GC capillary column must be corrected for the compressibility of the mobile phase and the alternative geometry of the tube, Thus, for a GC capillary tube,  equation (3) becomes   and equation (4) becomes In a similar manner, the maximum sample volume that can be placed on a GC capillary column, assuming half the permissible extra column dispersion is allotted to sample volume, follows directly from equation (6) which becomes

EC-Dispersion   GC-Capillary-Columns

Author: RPW Scott Book:Dispersion in Chromatography Columns
Section:Dispersion   Compressibility-Effects-GC

;  or              Thus,                                                   (27) Thus, the complete HETP equation for a packed GC column, that takes into account the compressibility of the carrier gas, will be          (28

Dispersion   Compressibility-Effects-GC

Author: RPW Scott Book:Dispersion in Chromatography Columns
Section:Dispersion   Compressibility-Effects-GC

It is seen that using the average velocity data, the extracted value for the multi-path term is negative, which is physically impossible (for a capillary column should be zero or very close to zero). In contrast, the values obtained from data involving the exit velocity give small positive, but realistic values for the multi-path term. In all aspects of column evaluation and column design in GC, the compressibility of the mobile phase must be taken into account or serious errors will be incurred.                     Figure 10. De-Convolution of the HETP Curve Obtained Using the Average Mobile Phase Velocity

Dispersion   Compressibility-Effects-GC