Minimum detectable mass

If the mass load on the electrode is not uniform, a calibration is then necessary to account for the radial sensitivity of the vibrating device (Lazare, S. Granier, V., unpublished results). The maximum of sensitivity is obtained at the centre of the electrode. This allows, for instance, etching over surface areas as small as a 2 mm diameter disc, with a minimum detectable mass of one nanogram. The calibration is performed in this case by using a fluence at which the ablation rate is known, in order to determine the sensitivity factor. 

The sensitivity of the detector (Xd) (or minimum detectable concentration) is defined as that concentration of solute that will provide a signal equivalent to twice the noise level. Now the concentration of solute at the peak maximum is approximately twice the average concentration of the solute in the peak, volume. Thus, the minimum detectable mass will be that mass (m) that, when dissolved in a volume of mobile phase equivalent to the peak volume, will produce a concentration of Xp/2. 

The importance of the extra column dispersion now becomes apparent, as equation (26) shows that the minimum detectable mass increases linearly with the extra column dispersion. It is also becomes obvious that it is of little use designing a detector for increased sensitivity (Xd) if this is achieved (as is often the case) at the expense of increased extra column dispersion (oe). Conversely, if the chromatographic system is designed to have very low extra column dispersion, a proportional reduction in the minimum detectable mass will be achieved even if the... 

Narrow-bore columns of between 1.0 and 2.5 mm ID are available for use in specially designed liquid chromatographs having an extremely low extracolumn dispersion. For a concentration-sensitive detector such as the absorbance detector, the signal is proportional to the instantaneous concentration of the analytes in the flow cell. Peaks elute from narrow-bore columns in much smaller volumes compared to those from standard-bore columns. Consequently, because of the higher analyte concentrations in the flow cell, the use of narrow-bore columns enhances detector sensitivity. The minimum detectable mass is directly proportional to the square of the column radius (107) therefore, in theory, a 2.1-mm-ID column will provide a mass sensitivity about five times greater than that of a 4.6-mm-ID column of the same length. 

However, a detectivity of 10 9 g/mL for a concentration detector means that this concentration is the smallest one that can be detected at that concentration in the detector cell. Consequently if a sample of this concentration is introduced into a chromatograph and run, its concentration will be somewhat less when it reaches the detector, because we have seen that an analyte is diluted and its zone becomes wider as it passes through the column. Thus, the amount of analyte that can actually be run and detected can differ from the MDQ. This situation has produced other terms like minimum detectable concentration, MDC, which will depend on the peak width (in milliliters). Analogously, for the mass flow rate detectors, the minimum detectable mass, MDM, will depend on the peak width in time units. In both cases, the quantity to be injected depends on... 

Interpolation with these values from Table 3 indicates that the minimum mass fraction of 1,2-diethylbenzene that can be detected by density measurement is 0.014. This corresponds to a purity of 98.6 mass %. The minimum detectable mass fraction of 1,3-diethylbenzene is 0.127 for the same assumptions. Hence density measurement is not a sensitive method to determine purity when the density of the impurity is close to that of the compound under consideration. 

The concentration sensitivity of a chromatographic system (XJ is defined as that which will provide a peak with a height equivalent to twice the noise level and can be obtained directly from the system mass sensitivity. If the minimum detectable mass is dissolved in the maximum permissible sample volume [9] (that sample volume that will limit the increase in sample variance to 10% of the column variance), then this solute concentration will constitute the minimum detectable sample concentration. 

Estimation of the minimum detectable mass estimated from this chromatogram was again made to be about 10 ng of solute. To some extent, this detector provides a replacement for the transport detector as it detects all substances irrespective of their optical or electrical properties. 

Stolyhwo et al. [17] attempted to improve the sensitivity of the detector by using metal spirals wound on wire and stranded wire to increase the surface area of the carrier and thus increase the proportion of the column eluent taken into the detector. The authors claimed a minimum detectable mass of 100 ng of triolein. However, again the exact volume of mobile phase in which the mass of solute was contained was not clear from the publication. If the solute was eluted in a peak 1 ml wide at the base, the concentration at the peak maximum would be twice the average concentration /.e., 2 x g/ml, which, for a transport detector, would be a greatly improved sensitivity. If, however, the same mass was eluted as an early peak in the chromatogram with a band width of only 50 pi, then the sensitivity would be 4 x 10 g/ml, which would be no better than the previously developed transport detectors. This confusion emphasizes the importance of specifying sensitivity in terms of concentration, which allows the direct comparison of one detector with another. 

Some manufacturers have taken the minimum detectable concentration and multiplied it by the sensor volume and defined the product as the minimum detectable mass. This gives values that are very misleading. For example, a detector having a true sensitivity of 10 g/mL and a sensor volume of 10 /rL would be attributed to a mass sensitivity of 10 g. This is grossly incorrect, as it is the peak volume that controls the mass sensitivity, not the sensor volume. Conversely, if the peak volume does approach that of the sensor, then a very serious peak distortion occurs with loss of resolution thus, this way of specifying sensitivity remains meaningless. 

Reproducibility. An expected consequence of the types of reactant heterogeneity described above, would be irreproducibility of kinetic behaviour in which every specimen studied exhibited different kinetic characteristics (see, for example, [7] p. 171-2). From these differences in behaviour, kinetic analyses might, in principle, provide information on the numbers, types and reactivities of the imperfections present in each individual specimen studied. (An assumption would have to be made that irreproducibility stems only from the characteristics of the samples and not from slight variations in the experimental conditions, e.g. temperature control and/or the efficiency of removal of gaseous products.) In practice, the main techniques used for measurement of the extent of reaction, a, (e.g. thermogravimetry or evolved gas pressures, see Chapter 6) are all averaging techniques and are thus insensitive to variations in behaviour at a molecular level. For example, loss of a minimum detectable mass of 1 pg from a 10 mg sample of CaCOs corresponds to the formation of 10 mol of COj and the decomposition of 6x10 COj ions. 

In the case of the detection limit we have to distinguish between the minimum detectable concentration and the minimum detectable mass. The minimum detectable concentration of a solute in the sample solution depends only on the detector properties and on the optical properties of the solute, i.e. its absorbance, if the maximum tolerable sample volume with respect to the retention volume of this solute is injected. The minimum detectable concentration is independent if the column dimensions, plate number or capacity factor. 

In contrast to the concentration, the minimum detectable mass depends on the retention factor of the solute. The earlier a peak is eluted, the smaller is the maximum injection volume and, with the concentration of the sample solution being constant, the smaller is the absolute mass of solute injected. The same is true if the column inner diameter is reduced. 

Sensitivity of the activation analysis method for a particular element refers to the minimum mass of that element that can be reliably detected. The minimum detectable mass is determined from Eq. 15.4 by assuming the most favorable conditions for the measurement and by setting an upper limit for the acceptable error of the result. The process is similar to the determination of the minimum detectable activity discussed in Sec. 2.20. 

The ionization process is not very efficient, only 0.0018% of the solute molecules produce ions, (about two ions or electrons per lO molecules). Nevertheless, because the noise level is very small, the minimum detectable mass of n-heptane is only 2 x 10-12 g/g column flow rate of 20 ml/min, this is equivalent to a minimum detectable concentration of about 3 x 10-12 g/ml. The detector responds to mass per unit time entering the detector, not mass per unit volume, consequently, the response is almost independent of flow rate. It follows that the FID can be used very easily with capillary columns. Although the column eluent is mixed with the hydrogen prior to entering the detector, the diluting effect has no impact on the sensitivity. The FID detects virtually all carbon containing solutes, with the exception of a limited number of... 

Proton microprobes represent a natural evolution of the PIXE analysis work which seek smaller area beams for lowered minimum detectable mass levels and allows an expansion of such analyses to encompass even the spatial... 

Table 13.1 Comparison of the relative sensitivity and minimum detectable mass density of the different acoustic...

Sensors Sensitivities (cmVg) Minimum detectable mass density (ng/cm )... 

The FID can detect all organic compounds containing C and H, with the exception of formic acid and methane. It is a mass-sensitive detector. The minimum detectable mass is about 0.01-0.1 ng and the FID has a large dynamic range of 10. Other detector characteristics can be found in Table 2.4. 

It is seen from equation (20) that the minimum detectable mass, or mass sensitivity of a chromatographic system, where the column has been designed to have the optimum radius for the detector employed, is directly proportional to the extra column dispersion and the detector concentration sensitivity. It follows that detector dispersion is as important as detector sensitivity in its influence on the overall chromatographic mass sensitivity where the chromatographic system has been optimized with respect to the radius of the column. The effect of extra column dispersion and in particular, detector dispersion on the overall mass sensitivity of the chromatogaphic system is not generally appreciated or completely understood. As the total extra column dispersion is the integral of a variety of sources, the distribution and nature of the various sources of dispersion will now be considered in some detail. 

If we replace p - pi by its uncertainty in equation (1.11) then W2 is the minimum value of the mass fraction of the impurity that could be reliably detected. The uncertainty in p - pi includes the uncertainty in the measurement of p but also the uncertainty in p, the density of the pure sanqrle. The value of pi must be determined for a sanqrle whose purity is known, by some independent means, with an accuracy considerably greater than the one being tested. An example of the use of equation (1.11) and Table 2 is the determination of a small inqmrity of (Z)-2-pentene in 1-pentene. (Table 2 contains numerical solutions of equation (1.11) at various densities and uncertainties.) The selected densities of 1-pentene and (Z)-2-pentene are (640.61 + 0.47)kg m and (654.74 + 1.17)k gm respectively at 298.15 K. Assuming that the density of the sample with the inqnuity is measmed with an accuracy of 0.4 kg m, then the total uncertainty is (0.4) + (0.47) = 0.62 kg-m l Since pi/p2 = 0.978 then pi -P2I / = 22.8. Interpolation with these values from Table 2 shows that the minimum mass fraction of (Z)-2-pentene that can be detected by the density measurement is 0.042. This corresponds to a purity of 95.8 mass %. The minimum detectable mass fraction of (E)-2-pentene is 0.078 for the same assumptions. Hence density measurements is not a sensitive method for purity determination when the density of the impurity is close to that of the compound under consideration. 

---