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

110\n\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, \\( c_{column}^{2} \\) can be exactly known from the Taylor, Aris, and Golay equation (see Sec. II.E.4.e), so that by subtraction \\( \\sigma_{peak}^{2} - \\sigma_{column}^{2} = \\sigma_{extracolumn}^{2} \\) 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 \\( n_{h} = (L / d_{column}) \\), hence, \\( \\sigma_{column}^{2} = L^{2} / n_{h} \\). If this is inserted into the foregoing equation, it is seen that then a plot of \\( \\sigma_{peak}^{2} \\) will be linear, with a slope determining by \\( n_{h} \\) and an intercept value on the vertical \\( \\sigma^{2}_{extra} \\) axis representing \\( \\sigma^{2}_{extracolumn} \\). 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 extracoulmn contribution is minimized, to maximize the efficiency of the final separation. However, by virtue of the foreign statistical rule for which variances \\( \\sigma^{2} \\) rather than peak widths (or standard deviations \\( \\sigma \\)) 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 on \\( \\sigma \\)) is less than several (say 2) percent, we have that \\( \\sigma_{column} \\geq 0.962^{2} \\) which leaves for the extracolumn contribution: \\( \\sigma_{extracolumn}^{2} \\leq 0.04 \\sigma_{peak}^{2} \\). Hence, a criterion to be proposed so that extracolumn dispersion does not contribute significantly (about 2%) to the overall peak width is approximately:\n\n\\( \\sigma_{extracolumn} / \\sigma_{peak} \\leq 0.2 \\)\n\nor in words and applied to injection, for example: the inlet bandwidth should not exceed about one-fifth of the total outlet zone width, which ensures that\n\n1 \\( \\leq \\sigma_{peak} / \\sigma_{column} \\leq 1.02 \\)\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 plate 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 this dead volume is the time constant \\( \\tau_{v} = 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 \\( \\sigma^{2} \\) is simply \\( \\tau^{2} \\), 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/\\tau) \\) and such that after time \\( t \\) 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 4\\( \\sigma \\) = \\( \\tau \\) and so \\( \\sigma^{2} = \\tau^{2} / 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 \\( \\sigma^{2} \\) can be calculated to be \\( \\tau^{2} / 12 [15,38]. \\)\n\nAlthough the elution profile of a solute leaving a sample valve 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