Unretained peak time

It is accepted as a rule of thumb that optimum programming rate performance is taken as 10°Cmin per unretained peak time (e.g., if /m = 0.6 min, then Topt-10/0.6 = 16°C min-i). 

Here kf is the retention factor from eqnation 4.5 expressed as a function of the temperature program, and tu,t expresses the effect of changing temperature on the unretained peak time. This type of calculation is conveniently carried out on a personal computer using either a commercially available elution prediction program or a spreadsheet, and we will discuss it in more detail in the next section on computerized optimization. 

The peaks retention times are a function of their individual retention factors and the unretained peak time, (m ... 

Therefore, in addition to knowing the retention factors from Equation 4.5, we will need to predict the unretained peak time at the desired temperatures. Fortunately, if not simply, the unretained peak time is a function of the column dimensions, pressure drop, carrier-gas type, and column temperature it can be calculated for simulation according to Equation 4.2. 

The unretained peak time can be related to the pressure drop, column dimensions, and carrier-gas viscosity by combining the—hopefully—familiar relationship between column length, unretained peak time, and average carrier-gas linear velocity tM = Liu with liquation 4.10 to yield... 

Interestingly, this equation predicts that at constant temperature and pressure drop, the unretained peak time will not change if the ratio of the colunm length to the diameter remains constant. A 30-m x 200-p.m-i.d. colunm should have the same unretained peak time as a 15-m, x 100-p,m-i.d. colunm at the same temperature and pressure drop, for example. 

To use Equation 4.13, we will need to relate the retention factor A to the distribution coefficient. Chromatographers can measure retention factors directly from the chromatogram if the unretained peak time is known. The distribution coefficient K in Equation 4.13, however, is not directly evident, but it can be computed from the measured retention factor, if the column film thickness d and inner diameter are known. These two column measurements determine the phase ratio P, which is the ratio of the gas to stationary-phase volumes in the column ... 

When the column is ready to be used, the chromatogram of a suitable test mixture should be obtained. The plate number and retention times of the test solutes should be noted, and the peaks should have a satisfactory shape (minimal tailing). For measurement of the plate number, the recorder should be used at a high chart speed. Fig. 5.1b(i) and (ii) show test chromatograms for a C-18 column prepared by the above method, and Fig. 5.1c and 5.Id show the data that you should report with the chromatogram. The retention for an unretained peak is taken as the small baseline disturbance just before the first peak. 

Possible difficulties in obtaining accurate retention data for physicochemical measurements should be recognized, however. The evaluation of to, the elution time of an "unretained peak (274) is often connected with systematic error and the measurement of the retention time of asymmetrical peaks may not be accurate. Moreover, no satisfactory methods are available for the precise evaluation of the phase ratio in the column. Consequently, the measurement of the equflibrium constant proper is beset with difficulties as discussed in Section VII.B. 

Fig. 1 Diagram depicting the retention volume, corrected retention volume, dead point, dead volume, and dead time of a chromatogram. Fq total volume passed through the column between the point of injection and the peak maximum of a completely unretained peak F total volume of mobile phase in the column F (a) retention volume of solute A F (a) corrected retention volume of solute A F extra column volume of mobile phase volume of mobile phase, per theoretical plate vy. volume of stationary phase per theoretical plate distribution coefficient of the solute between the two phases n number of theoretical plates in the column Q column flow rate measured at the exit.

An unretained ideal peak with k = 0 and a very small injection volume is likely to have a peak width of 0.032 min at the base. An indirect injection of a much larger volume requires that the loop contents be swept onto the column over an extended time. If the total flow rate is 70 mL/min and the initial concentration is 5% modifier (modifier flow = 3.5 mL/min), a 2-mL loop is swept in 0.285 min. An unretained peak would have a peak width >0.285 min. Injecting into the modifier line thus artificially broadens a peak compared to the ideal with a small injection volume. 

From the raw retention values, retention factors can be calculated, which are dimensionless numbers correcting for variations in instrumental instabilities such as variation in flowrate. The retention factor is defined as the ratio of the net retention time (tT - tu) and the retention time of an unretained peak (tu), where tr is the retention time of the solute. This is standard practice in liquid chromatography [Christian O Reilly 1986]. Moreover, taking the logarithms of these retention factors ideally linearizes the data, e.g., with respect to fractions of organic modifier in the mobile phase composition [Schoenmakers 1986],... 

The number of theoretical plates, N, is not the best measure of the column efficiency since in measuring tr the retention time (tm) of an unretained peak has... 

Column dead time, time for unretained peak to pass through column... 

The underlying purpose in utilizing HPLC, namely to increase the speed of separation, also causes the main difficulty in detector design. A separation efficiency of 10,000 plates with an unretained retention time of 100 sec will generate peaks with a width of 1 sec (standard deviation o -) and the detection systems should have a response time that is less than this in order to avoid distortion of the chromatogram. 

The classical definition of the chromatographic linear velocity u is based on the breakthrough time of an unretained peak, (q ... 

For thorough theoretical work, the type of velocity on which the reduced velocity is based should be spedfied. In the following, we will follow the common practice to associate the reduced velocity with the mobile-phase velocity on the basis of the breakthrough time of an unretained peak. 

The value of 0.4 in the denominator of the coupling term is derived from Reference 12, using the reduced velocity based on the migration time of an unretained peak here. The remaining coefficients were chosen from typical curve-fit results. 

The retention factor k is measured as the retention time of an analyte minus the retention time of an unretained peak divided by the retention time of the unretained peak. It is a convenient way to normalize retention for comparison of difierent colunms or the same column at difieient flow rates ... 

However, there is more to it. An unietained peak spends all its time in the mobile phase. Any analyte migrating through the colunm will qiend the same amount of time in the mobile phase as an unretained peak (provided neither is mrduded from all or part of the pores). The difference between the total time that an analyte spends in the column and the time that it spends in the mobile phase has to be spent in the stationary phase. Therefore, the retention factor is the ratio of the time tg that an analyte spends in the stationary phase to the... 

We will now look at graphs of resolution versus analysis time for various hoioes of particle size and column length. As a measure for resolution, we aply use the square root of the plate count, as shown in the resolution luation. Equation 3.1. As analysis time, we use 10 times the breakthrough of an unretained peak, as shown in Equation (32). We use the van ater equation to calculate the HETP, from which we determine the plate Dt From the Kozeny-Carman equation [Eq. (3.3)] we calculate the lire drop across the column. We set an upper pressure limit of 20 MPa 3000psi). The curves will stop when this pressure limit is reached. 

A peak with a retention time of 1 min at an efficiency of 10,(XX) plates has a ff of 0.6 s. This would be the case for an unretained peak eluting from a S>/tm 3.9-mm x ISO-mm column at a flow rate of l.S mL/min. If the detector time constant is 1 s, a significant distortion of the peak results, with the total peak width increasing by a factor of nearly 2. Therefore, for normal operating conditions the detector time constant should be significantly less than 1 s, best around 0.1 s. For fast chromatography, special attention should be paid to the detector time constant. 

Theoretical plates calculation uses retention from the time of injection (/ = 0). This means that even a peak eluting almost with the solvent or unretained peak will have quite good efficiency. But this is not really usable efficiency in terms of the ability to resolve peaks. It is often more realistic to represent efficiency in terms of effective plates, where /r is used in the respective formulas in eqn [6]. Thus, a peak eluting near the unretained peak has a low number of effective plates. 

---