Standard deviation of the retention time

An example of one method to control the robustness and reproducibility of a method is to set retention time windows for the target compounds. Absolute retention times are used for compound identification. Retention time windows can be established to compensate for minor shifts in absolute retention times as a result of sample loadings and normal chromatographic variability. The width of the retention time window should be carefully established to minimize the occurrence of both false positive and false-negative results. This can be accomplished by multiple injections of standard solutions over the course of a time period (days or weeks) and then calculating the mean and standard deviation of the retention time. 

Equation (3) merely sums the two peaks to produce a single envelope. Providing retention times can be measured precisely, the data can be used to determine the composition of a mixture of two substances that, although having finite retention differences, are eluted as a single peak. This can be achieved, providing the standard deviation of the measured retention time is small compared with the difference in retention times of the two solutes. Now, there is a direct relationship between retention volume measured in plate volumes and the equivalent times, which is depicted in Figure 6. 

The theoretical treatment given above assumes that the presence of a relatively low concentration of solute in the mobile phase does not influence the retentive characteristics of the stationary phase. That is, the presence of a small concentration of solute does not influence either the nature or the magnitude of the solute/phase interactions that determine the extent of retention. The concentration of solute in the eluted peak does not fall to zero until the sample volume is in excess of 100 plate volumes and, at this sample volume, the peak width has become about five times the standard deviation of the normally loaded peak. 

An automated procedure to measure peak widths for peak capacity measurements has been proposed.35 Since peak width varies through the separation, the peak capacity as conventionally measured depends on the sampling procedure. The integral of reciprocal base peak width vs. retention time provides a peak capacity independent of retention time, but requires an accurate calculation of peak width. Peak overlap complicates automation of calculation. Use of the second derivative in the magnitude-concavity method gives an accurate value of the standard deviation of the peak, from which the base peak width can be calculated. 

Initially the substance at Rt 19.95 was identified as 2-nonen-l-ol based on mass spectrum library search. The comparison with a commercial 2-nonen-l-ol standard indeed revealed a high degree of similarity between the mass spectra, but a distinct deviation regarding the retention time suggesting a similar molecule with a chain length greater than 2-nonen-l-ol. The substance Rt 20.95 was tentatively identified as 6,10-dimethyl-5,9-undecadien-2-one which corresponds with the authentic standard regarding mass spectra and retention time. 

As readily observed in most chromatograms, peaks tend to be Gaussian in shape and broaden with time, where W, becomes larger with longer This is caused by band-broadening effects inside the column, and is fundamental to all chromatographic processes.The term, plate number (N), is a quantitative measure of the efficiency of the column, and is related to the ratio of the retention time and the standard deviation of... 

The effect of the detector time constant on the apparent efficiency depends only on the time width of the bands. It has been shown by Sch-mauch 41) and by Me William and Bolton 42) that the profile recorded with a detector having a time constant r is wider than the actual profile by a factor (1 -f r/ert), where is the time standard deviation of the profile, provided this factor is less than about 1.2. Moreover, the peak heigh becomes smaller although the peak area remains unchanged. 1 he (list mu ment (retention time) of a peak increases by r and the retention time of the... 

The features of an ideal chromatogram are the same as those obtained from a normal distribution of random errors (Gaussian distribution equation (1.2), cf. 21.3). In keeping with the classical notations, fi would correspond to the retention time of the eluting peak, a to the standard deviation of the peak (a2 represents the variance) and y represents the signal, as a function of time, from the detector located at the end of the column (see Fig. 1.3). 

Without backpressure regulation for each channel, it is necessary to minimize the flow rate fluctuation over time. The relative standard deviation (RSD%) in retention time variation among the eight channels over 1 month for compounds A and B was less than 2% and for C and D it was less than 1%. The RSD% for all channels over a 1-month period for compounds A to D was 3.2, 2.4,1.6, and 1.5%, respectively. Therefore, this system is well suited for combinatorial library analysis. The UV chromatograms from channel 5 from different days are shown as an example in Fig. 2A. The retention times of the four compounds (compounds A to D) from all eight channels during a 1-month period are shown in Fig. 2B. 

Routine GC analysis for environmental samples involve running one of the calibration check standards before sample analysis to determine if the area or height response is constant (i.e., within 15% standard deviation of the response factor or calibration factor, and to check if there is a shift in the retention times of the analytes peaks. The latter can occur to a significant degree due to any variation in conditions, such as temperature or the flow rate of the carrier gas. Therefore, an internal standard should be used if possible in order to determine the retention time shift or to compensate for any change in the peak response. If an analyte is detected in the sample, its presence must be ascertained and then confirmed as follows ... 

Efficiency, N, is defined in terms of the retention time (tR) of the solute, measured at the peak apex, and the standard deviation, cr, of the solute population in the peak measured as the peak width ... 

Six 50-mg blank hair samples were extracted by SFE and the noise was integrated for the ion used for quantification (m/z = 355 for codeine, 369 for ethylmorphine, 383 for 6-MAM, and 397 for morphine) in a retention time window of tj + 0.5 min. The LOD and LOQ were determined (n = 6) using lUPAC methods. For each substance the standard deviation of the blank value (Sg) was determined. The mean area converted from the noise was calculated as concentration equivalent based on a calibration graph. The LOD is defined as 3Sg and the LOQ as lOSg. 

The process of band broadening (Figure 2.1) is measured by the column efficiency or the number of theoretical plates N, equation (2.24)), which is equal to the square of the ratio of the retention time to the standard deviation of the peak. In theory, the value of N for packed columns has only a small dependency on k and may be considered to be a constant for a particular column. Column efficiency in open-tubular systems decreases markedly with increased retention. For this reason open-tubular liquid chromatography systems must be operated at relatively low kf values (see section 2.5.S.2). 

Haarhoff and Van der Linde [14] have studied the same problem, the determination of the band profile in the case of a moderately overloaded column, a case in which the thermodynamic effect of a nonlinear isotherm perturbs only mildly the band profile. They have used the same approach as Houghton, down to Eq. 10.17. However, since the component concentration is significantly different from 0 only around the band maximum, during a period of time which is only a few times the standard deviation of the Gaussian profile obtained imder linear conditions, they have suggested that the effect of the apparent dispersion term on the band profile can be calculated at the limit retention time, They replaced in Eq. 10.20 by... 

In Equation 12, h(t) Is the amplitude expressed as a function of time t. The constant Aj Is the peak height at t i, the retention time of the 1th component peak, and o. Is the standard deviation of the 1th peak. The constants B and m are, respectively, the baseline offset and the total number of component peaks. The baseline offset may be time dependent. 

A statistical analysis of the peak counts obtained from the simulated chromatograms was made as follows. We changed the random number sequence, by means of the seed change previously described, to generate random changes In component retention times and amplitudes while holding constant component number, zone width, and peak capacity. This procedure. In essence, mimicked the Injection of different samples with the same component number and zone width onto a column. A mean peak count and standard deviation at each of the different peak capacities were calculated. The means and standard deviations of the peak counts were fit by a least squares analysis to Equation 11 with a proper transformation of the standard deviations from an exponential to a linear function (5). From the value of the least squares slope and Intercept, an estimated component number was calculated. 

AUFS. The retention of the sample should be adjusted to minimize extracolumn influences on the measurement. If we would like less than a 5% influence of extracolumn band spreading on the plate-count measurement, the standard deviation of the peak should be about 5 times lar r than the standard deviation of the extracolumn band spreading (see Section 3.2.2). 

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