Bandbroadening

Although the above listing of contributions to the colunn plate height is not coq>rehensive, it encompasses the major bandbroadening factors and the overall plate height can be expressed as their sun, equation (1.30). 

Another reason for using small electrode dimensions, is to prevent bandbroadening. An expression for the detector performance was derived by Sternberg ... 

Hence the reaction coil volumes were kept as small as possible to reduce bandbroadening, i.e. 17 pL and 33 pL, for coil I and coil II, respectively. 

Band broadening arises from three principal mechanisms, one of which depends on the mean velocity of the carrier and two of which are independent of . The latter two represent nonidealities in instrument and sample. The total variance of an eluting peak is the sum of variances contributed by each bandbroadening mechanism. Expressed as plate height H, which is the total variance divided by column length L (12), the zone broadening is described by... 

Do not dissolve the solute in an organic solvent. This will lead to bandbroadening and possibly peak splitting. Try dissolving the solute in BGE for scouting runs if it is insoluble in water. 

Parameter t in equation (2-13) is the standard deviation and expressed in the same units as retention time. Since we considered symmetrical bandbroadening of a Gaussian shape, we can use Gaussian function to relate its standard deviation to more easily measurable quantities. The most commonly used points are the so-called peak width at the baseline, which is actually the distance between the points of intersections of the tangents to the peaks inflection points with the baseline (shown in Figure 2-1). This distance is equal to four standard deviations, and the final equation for efficiency will be... 

D. Gowanlock, R. Bailey, and F. F. Cantwell, Intra-particle sorption rate and liquid chromatographic bandbroadening in porous polymer packings I. Methodology and validation of the model, /. Chromatogr. A 726 (1996), 1-23. 

Fig. 1 Electrophoretic bandbroadening effects of benzoates as sample. Destacking trace a (1-mM sample in 1-mM buffer), stacking trace b (0.01-mM sample in 25-mM buffer), and trace c (1-mM sample in 25-mM buffer) and peak triangulation trace d (1-mM sample in 25-mM chloride buffer).

With the proper technique [5], such plots are linear and the y intercept is equivalent to Hp. Alternatively, Hp can be obtained by subtracting the nonequilibrium bandbroadening contribution to plate height (Hj ) from the experimentally measured value. Methods for calculating... 

Since for a given column and a set of operating conditions N is approximately constant and (1 + k) is roughly equal to k in most cases where k is much greater than 1, peak volume is proportional to k and VM. This relationship is important because of the increasing use of smaller-diameter columns (column i.d. <3 mm) with smaller VM, since the smaller peak volumes from these columns are highly affected by the deleterious effect of dispersion by the instrument (extra-column bandbroadening). This effect will be discussed section 4.10 of Chapter 4. 

The degree of bandbroadening is statistical in nature in that a great many random events occur, some pushing the pollen grains (or analyte molecules) back toward the center of concentration and some away from the center of concentration. It can be shown that this statistical distribution, represented by the variance, a, is equal to the product of the square of average step length, I, and the number of steps taken, n, or... 

However, the diffusion coefficient is not merely a proportionality constant joining bandbroadening and time, but is much more fundamental. This perhaps... 

In the expanded form of Equation (11.11) many important elements relating temporally based formation of spatially apparent bandbroadening are evident including temperature (T), analyte size or molecular weight R), mobile phase viscosity (rj), time (t), and spatial distribution (a). 

Plate height is very important both practically and theoretically representing the most universal measure of bandbroadening. A peak moving down a column at a uniform velocity of Vp, will transverse, in time t, a distance of X, or... 

Bandbroadening is a very complex process but can be dissected into four essential components ... 

At two conceptual extremes, we might envision that there are only two flow paths an analyte might take as it passes down the column, a slow path and fast path, and that at times the analyte may jump from one to another. There are also two conceptual extremes in traveling between the flow streams (1) diffusion of the analyte molecule between flow streams and (2) a mobile phase flow-mediated transfer between flow streams. The former will be slow in comparison to the latter because diffusion mediated processes are much slower. In the case of eddy diffusion, flow-mediated transfer will overwhelmingly dominate the bandbroadening process. 

The van Deemter Curve and Equation The total plate height for a separation is equal to the sum of all its component plate heights. One such sum is known as the van Deemter Equation, originally pubhshed in 1956 by van Deemter and colleagues. In terms of the bandbroadening expression presented herein it takes the form where the first term represents bandbroadening contributions from eddy diffusion, the second term represents contributions from longitudinal diffusion, and the third term represents contributions from resistance to mass transfer. 

Figure 11.6 The van Deemter Equation plotted as a curve. The full expression is the sum of the three individual components. Eddy diffusion, the A term, a constant, does not change as the mobile linear flow rate changes. Bandbroadening from longitudinal diffusion steadily decreases the shorter the analyte remains on the column, in other words, the faster the flow rate is. Contributions from resistance to mass transfer of the analyte into and out of the stationary phase increase linearly with the mobile phase flow rate. The separation will be most efficient at the flow rate that minimizes plate height, in this case about 0.1 cm/s.

Contributions from longitudinal diffusion are greatest as the flow rate approaches zero at which point, of course, any separation would cease and the band would merely spread out gradually. Eddy diffusion (A) has no flow-related component but does contribute an absolute limit on the how small the overall plate height can be. Finally, the mass transfer term (C w) contributes increasing amounts of bandbroadening as the mobile phase flowrate increases. 

Both mathematically and obviously graphically, it is possible to determine an optimal flow rate that minimizes bandbroadening. Mathematically this is easily obtained from taking the first derivative of the van Deemter Equation with respect to flow rate and setting it equal to zero or... 

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