System, peak dispersion

Peak dispersion can happen in any part of the chromatographic system, from the... 

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. 

The problem is made more difficult because these different dispersion processes are interactive and the extent to which one process affects the peak shape is modified by the presence of another. It follows if the processes that causes dispersion in mass overload are not random, but interactive, the normal procedures for mathematically analyzing peak dispersion can not be applied. These complex interacting effects can, however, be demonstrated experimentally, if not by rigorous theoretical treatment, and examples of mass overload were included in the work of Scott and Kucera [1]. The authors employed the same chromatographic system that they used to examine volume overload, but they employed two mobile phases of different polarity. In the first experiments, the mobile phase n-heptane was used and the sample volume was kept constant at 200 pi. The masses of naphthalene and anthracene were kept... 

As the individual components of a mixture are moved apart on the basis of their differing retention, then the separation can be partly controlled by the choice of the phase system. In contrast, the peak dispersion that takes place in a column results from kinetic effects and thus is largely determined by the physical properties of the column and its contents. 

At this point, it is important to stress the difference between separation and resolution. Although a pair of solutes may be separated they will only be resolved if the peaks are kept sufficiently narrow so that, having been moved apart (that is, separated), they are eluted discretely. Practically, this means that firstly there must be sufficient stationary phase in the column to move the peaks apart, and secondly, the column must be constructed so that the individual bands do not spread (disperse) to a greater extent than the phase system has separated them. It follows that the factors that determine peak dispersion must be identified and this requires an introduction to the Rate Theory. The Rate Theory will not be considered in detail as this subject has been treated extensively elsewhere (1), but the basic processes of band dispersion will be examined in order to understand... 

Where peak dispersion has not been constrained to very small volumes the external sample loop injector can be used and the external loop sample system, which employs six ports, is depicted in figure 15. In the external loop sample valve, three slots are cut in the rotor so that any adjacent pair of ports can be connected. In the loading position shown on the left, the mobile phase supply is connected by a rotor slot to port (4) and the column to port (5) thus allowing mobile phase to flow directly through the column. In this position the sample loop is connected to ports (3) and (6). Sample flows from a syringe into port (1) through the rotor slot to the sample loop at port (6). At the same... 

On the other hand, in.the case of the nonionic surfactants C-15, NP-15 and 0-15 (the nonionic surfactant/cyclohexane system), mono-dispersed silicalite nanocrystals were obtained as shown in Fig. 1(c), 1(d) and 1(e), respectively. The X-ray diffraction patterns of the samples showed peaks corresponding to pentasile-type zeolite. The average size of the silicalite nanocrystals was approximately 120 nm. These results indicated that the ionicity of the hydrophilic groups in the surfactant molecules played an important role in the formation and crystallization processes of the silicalite nanocrystals. 

FIGURE 3.6 Decreasing peak dispersion of a conventional Agilent 1100 Series HPLC instrument by stepwise optimization of components. System dispersion determined by injecting low volumes of acetone without a column. (Courtesy of Michael Woodman, Agilent Technologies, Inc.)... 

Equations (105) and (106) provide an important linkage between the three essential parameters that dictate the overall quality of the chromatographic resolution, namely, the relative retention, expressed in terms of the capacity factor k the relative selectivity a, and the extent of peak dispersion Nt or he i. Higher system performances and thus larger values of Rs, per unit time... 

Unfortunately the counting efficiency of the system was relatively poor, 0.2% for tritium and 17% for carbon. However, the advantage of this method is that due to the cell being packed with beads, it would have little flow resistance and limited peak dispersion and thus if used in conjunction with suitable low dispersion connecting tubes, it could be used with relatively high efficiency columns. As a consequence, many modem commercial radioactivity detectors are designed on the same principle, but with more efficient scintillators and more efficiently designed sensors. 

As mentioned previously, the drug may be present in one of several forms in the final product. The advantages and disadvantages of each form have been discussed in both injection molding and melt extrusion systems. Solid dispersion systems may be more stable and more easily processed than solid solution systems, but solid solution systems may be produced that are transparent and have increased bioavailability of poorly soluble compounds. Figs. 3 and 4 show the X-ray diffraction patterns for a polymer film containing lidocaine. The absence of the lidocaine peaks in the extruded samples, and the reported... 

The rate theory examines the kinetics of exchange that takes place in a chromatographic system and identifies the factors that control band dispersion. The first explicit height equivalent to a theoretical plate (HETP) equation was developed by Van Deemter et al. in 1956 [1] for a packed gas chromatography (GC) column. Van Deemter et al. considered that four spreading processes were responsible for peak dispersion, namely multi-path dispersion, longitudinal diffusion, resistance to mass transfer in the mobile phase, and resistance to mass transfer in the stationary phase. 

The dimensionless mean retention time, Hi/to is independent of the carrier gas velocity and is only a function of the thermodynamic properties of the polymer-solute system. The dimensionless variance, i2 /tc2. is a function of the thermodynamic and transport properties of the system. The first term of Equation 30 represents the contribution of the slow stationary phase diffusion to peak dispersion. The second term represents the contribution of axial molecular diffusion in the gas phase. At high carrier gas velocities, the dimensionless second moment is a linear function of velocity with the slope inversely proportional to the diffusion coefficient. 

Chapters 10 to 13 review the solutions of the equilibrium-dispersive model for a single component (Chapter 10), and multicomponent mixtures in elution (Chapter 11) and in displacement (Chapter 12) chromatography and discuss the problems of system peaks (Chapter 13). These solutions are of great practical importance because they provide realistic models of band profiles in practically all the applications of preparative chromatography. Mass transfer across the packing materials currently available (which are made of very fine particles) is fast. The contribution of mass transfer resistance to band broadening and smoothing is small compared to the effect of thermodynamics and can be properly accounted for by the use of an apparent dispersion coefficient independent of concentration (Chapter 10). 

System Peaks with the Equilibrium-Dispersive Model... 

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