Chromatography Handbook Of Hplc - Katz Eksteen Schocnmakers Miller wiley Sons -120

110\nTijssen\n\ntractive, is to use, in place of the short connection, a relatively long open tubular column with known length and internal diameter. Here, σ²column = r²iσ²peak is exactly known from the Taylor, Arris, and Golay equation (see Sec. II.E.4.e), so that by subtraction σ²peak − σ²column = σ²extracolumn becomes known.\n\nThe first method using linear extrapolation is based on the fact that the column contribution to the peak variance can be expressed in terms of retention times and the true column efficiency in terms of the number of theoretical plates. By definition nh = (tr / t0)2; hence, σ²column = r²i / nh. If this is inserted into the foregoing equation, it is seen that then a plot of σ²peak against τi will be linear, with a slope determined by nh and an intercept value on the vertical σ² column axis representing σ²extracolumn. This method is relatively straightforward and yields good results if the solutes used have sufficiently large retention (say k > 5).\n\nObviously, it is our purpose to carry out chromatography such that the extracolumn contribution is minimized, to maximize the efficiency of the final separation. However, by virtue of the regressing statistical rule for which variances σ² rather than peak widths (or standard deviations σ) are summed, there is some actual room for allowing extracolumn dispersion. For example, if we require that the influence of extracolumn dispersion on the peak widths (so σ) is less than several (say 2) percent, we have that σ²column = 0.96σ²peak and so σ²column ≈ 0.96σ²peak which leaves for the extracolumn contribution: σ²extracolumn ≤ 0.04σ²peak implying that σ²extracolumn ≤ 0.2σ²peak. Hence, a criterion to be proposed so that extracolumn dispersion does not contribute significantly (about 2%) to the overall peak widths is approximately:\n\nσextracolumn / σpeak ≤ 0.2\n\nor in words and applied to injection, for example: the inlet bandwidth should not exceed about one-fifth of the final outlet zone width, which ensures that\n\n1 ≤ σpeak / σcolumn (63a)\n\nAs a result of this estimation, extracolumn dispersion can be allowed to have an appreciable contribution of about 20% of the total dispersion, without influencing the final peak width significantly. Equation (63a) allows the calculation of the minimum pixel height or plate number required to fulfill the criterion.\n\nInjectors and detectors in the chromatographic setup represent dead volumes (V), which are swept with the flow velocity F produced by the solvent-propelling system, often a pump. The characteristic time spent by the mobile phase and the solute molecules in that dead volume is the time constant τv = V/F, the time needed to flush the volume once. An estimate of the variance of this process can be obtained, provided we know something about the extent of internal mixing within the volume.\n\n(a) Injection. For example, if the volume V is ideally mixed [15,38], the variance σ² is simply r², and the concentration profile leaving the dead volume and serving as the inlet profile for the column on injection, for example, is an exponentially decaying (tailing) profile, proportional to exp[−t/τ] and such that after time τ concentration has been lowered by the factor 1/e, as compared with the maximum concentration. As another example, handheld syringe injections are observed to yield almost symmetrical gaussian-like injection profiles (with base width 4σ, ≈ τ, and so σ² = τ2/16). Another interesting example is that of the plug, or block injection profile, which can be envisaged to occur in modern sample loop injector valves, where ideally a discrete plug of sample solution is displaced by a fresh mobile phase and is pushed as an undisturbed plug onto the top of the column. For such an ideal plug profile, the variance σ² can be calculated to be τ²/12 [15,38].\n\nAlthough the outlet profile of a solute leaving a sample volume is largely controlled by the geometry of the sample volume (sudden changes in diameters or cross sections are large contributors), contemporary sample injectors are so carefully designed that there is no danger of any other contribution (in unions and such) than the injected volume itself. Hence, in a