Elution dispersion

Isolation procedures for many biochemicals are based on chromatography. Practically any substance can be selected from a crude mixture and eluted at relatively high purity from a chromatographic column with the right combination of adsorbent, conditions, and eluant. For bench scale or for a small pilot plant, such chromatography has rendered alternate procedures such as electrophoresis nearly obsolete. Unfortunately, as size increases, dispersion in the column ruins resolution. To produce small amounts or up to tens of kilograms per year, chromatography is an excellent choice. When the scale-up problem is solved, these procedures should displace some of the conventional steps in the chemical process industries. 

In a chromatographic separation, the individual components of a mixture are moved apart in the column due to their different affinities for the stationary phase and, as their dispersion is contained by appropriate system design, the individual solutes can be eluted discretely and resolution is achieved. Chromatography theory has been developed over the last half century, but the two critical theories, the Plate Theory and the Rate Theory, were both well established by 1960. There have been many contributors to chromatography theory over the intervening years but, with the... 

Recalling that a separation is achieved by moving the solute bands apart in the column and, at the same time, constraining their dispersion so that they are eluted discretely, it follows that the resolution of a pair of solutes is not successfully accomplished by merely selective retention. In addition, the column must be carefully designed to minimize solute band dispersion. Selective retention will be determined by the interactive nature of the two phases, but band dispersion is determined by the physical properties of the column and the manner in which it is constructed. It is, therefore, necessary to identify those properties that influence peak width and how they are related to other properties of the chromatographic system. This aspect of chromatography theory will be discussed in detail in Part 2 of this book. At this time, the theoretical development will be limited to obtaining a measure of the peak width, so that eventually the width can then be related both theoretically and experimentally to the pertinent column parameters. 

Consequently, the composite elution curve for the total sample originally dispersed over the first three plates will be given by,... 

It follows that the elution curve for a sample, initially dispersed over (r) plates, will be... 

Having established that a finite volume of sample causes peak dispersion and that it is highly desirable to limit that dispersion to a level that does not impair the performance of the column, the maximum sample volume that can be tolerated can be evaluated by employing the principle of the summation of variances. Let a volume (Vi) be injected onto a column. This sample volume (Vi) will be dispersed on the front of the column in the form of a rectangular distribution. The eluted peak will have an overall variance that consists of that produced by the column and other parts of the mobile phase conduit system plus that due to the dispersion from the finite sample volume. For convenience, the dispersion contributed by parts of the mobile phase system, other than the column (except for that from the finite sample volume), will be considered negligible. In most well-designed chromatographic systems, this will be true, particularly for well-packed GC and LC columns. However, for open tubular columns in GC, and possibly microbore columns in LC, where peak volumes can be extremely small, this may not necessarily be true, and other extra-column dispersion sources may need to be taken into account. It is now possible to apply the principle of the summation of variances to the effect of sample volume. 

To reiterate the definition of chromatographic resolution a separation is achieved in a chromatographic system by moving the peaks apart and by constraining the peak dispersion so that the individual peaks can be eluted discretely. Thus, even if the column succeeds in meeting this criterion, the separation can still be destroyed if the peaks are dispersed in parts of the apparatus other than the column. It follows that extra-column dispersion must be controlled and minimized to ensure that the full performance of the column is realized. 

A satisfactory chromatographic analysis demands, a priori, on an adequate separation of the constituents of the sample that will permit the accurate quantitative evaluation of each component of interest. To achieve this, an appropriate phase system must be chosen so that the individual components of the mixture will be moved apart from one another in the column. In addition, their dispersion must be constrained sufficiently to allow all the solutes of interest to be eluted discretely. At this stage it is necessary to introduce the concept of the Reduced Chromatogram. 

As has been previously discussed, the limitation of (oe) to (0.32oc), allows the variance of the peak eluted from the column to be increased by a maximum of 10% by any extra-column dispersion and, consequently, the width of the peak by a maximum of 5%. 

Consider the separation depicted in Figure 1. It is assumed that the pair of solutes represent the elution of the solute of interest and its nearest neighbor. Now, when the sample volume becomes extreme, the dispersion that results from column overload, to the first approximation, becomes equivalent to the sample volume itself as the sample volume now contributes to the elution of the solutes. Thus, from Figure 1, the peak separation in milliliters of mobile phase will be equivalent to the volume of sample plus half the sum of the base widths of the respective peaks. 

HETP of a TLC plate is taken as the ratio of the distance traveled by the spot to the plate efficiency. The same three processes cause spot dispersion in TLC as do cause band dispersion in GC and LC. Namely, they are multipath dispersion, longitudinal diffusion and resistance to mass transfer between the two phases. Due to the aforementioned solvent frontal analysis, however, neither the capacity ratio, the solute diffusivity or the solvent velocity are constant throughout the elution of the solute along the plate and thus the conventional dispersion equations used in GC and LC have no pertinence to the thin layer plate. 

The simplest mode of IGC is the infinite dilution mode , effected when the adsorbing species is present at very low concentration in a non-adsorbing carrier gas. Under such conditions, the adsorption may be assumed to be sub-monolayer, and if one assumes in addition that the surface is energetically homogeneous with respect to the adsorption (often an acceptable assumption for dispersion-force-only adsorbates), the isotherm will be linear (Henry s Law), i.e. the amount adsorbed will be linearly dependent on the partial saturation of the gas. The proportionality factor is the adsorption equilibrium constant, which is the ratio of the volume of gas adsorbed per unit area of solid to its relative saturation in the carrier. The quantity measured experimentally is the relative retention volume, Vn, for a gas sample injected into the column. It is the volume of carrier gas required to completely elute the sample, relative to the amount required to elute a non-adsorbing probe, i.e. 

Fig. 17. A schematic of the alkane line obtained by inverse gas chromatography (IGC) measurements. The relative retention volume of carrier gas required to elute a series of alkane probe gases is plotted against the molar area of the probe times the. square root of its surface tension. The slope of the plot is yielding the dispersion component of the surface energy of...

Calibrate the system. Use narrowly dispersed molecular weight standards of the polymer of interest to construct a calibration curve of log molecular weight versus elution volume (Eig. 3.2). If a more sophisticated software system is available, a broad molecular weight standard may be used to calibrate the system. 

Errors in the molecular weight data from HPSEC are usually due to improperly prepared samples, column dispersity, or flow rate variations. The sample to be analyzed should be completely dissolved in the mobile phase and filtered prior to injection onto the column. A plugged column inlet frit will invalidate results. In addition, do not load the column with excess sample. Column overloading affects the accuracy of data by broadening peaks, reducing resolution, and increasing elution volume. For best results, the concentration of the injected sample should be as low as possible while still providing adequate... 

The elution of compounds on GC columns is a complex process related to the volatility of the compound, which results from its boiling point, and the chemical interactions between the compound and the stationary phase. These interactions are typically those which arise from polar-polar interactions, dispersion forces, dipole-dipole interactions, and so forth. Collectively, they are described by the term the chemical potential, Ap.°, which derives from the potential for the compound to... 

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