Optimizing Counting Conditions

Equation (5.40) imphes that the uncertainty of the estimate of the background must depend upon the number of background channels used. Since tbe more channels that are used the better the background estimate, it would appear that the mote channels the better. 

However, as one nses mote channels there are decreasing returns and one must not overlook the possibility of neighbouring peaks causing a wide background region to be nonlinear. What is the optimum number of channels to use This depends upon the circumstances. 

If the peak is well defined and has a large area, then there may be little to be gained by using more than three or four channels. In such cases, the background uncertainty will have a much smaller effect on the uncertainty of the net peak area estimate. Note that the number of channels used for background estimate does not have any statistically significant effect on the net area, only on the uncertainty with which it is measured. 

Taking into account peak area measurement uncertainty, and the need for a reasonable number of channels within a peak (to facilitate peak searches and fitting), it would seem that spectrum sizes of 4096 and 8192 channels would be optimum. With current detectors and spectrum analysis software, there seems little point in seeking larger spectrum sizes. 

In many laboratories, samples will not be submitted one by one for individual attention but in batches aU to be counted within as little time as possible. Efficient use of counting equipment in terms of the time devoted to counting each sample can pay dividends when time and equipment are limited. 

---

For MS work, the electron impact (El) mode with automatic gain control (AGC) was used. The electron multiplier voltage for MS/MS was 1450 V, AGC target was 10,000 counts, and filament emission current was 60 pA with the axial modulation amplitude at 4.0 V. The ion trap was held at 200°C and the transfer line at 250°C. The manifold temperature was set at 60°C and the mass spectral scan time across 50-450 m/z was 1.0 s (using 3 microscans). Nonresonant, collision-induced dissociation (CID) was used for MS/MS. The associated parameters for this method were optimized for each individual compound (Table 7.3). The method was divided into ten acquisition time segments so that different ion preparation files could be used to optimize the conditions for the TMS derivatives of the chemically distinct internal standard, phenolic acids, and DIMBOA. Standard samples of both p-coumaric and ferulic acids consisted of trans and cis isomers so that four segments were required to characterize these two acids. The first time segment was a 9 min solvent delay used to protect the electron multiplier from the solvent peak. 

To optimize the conditions for the maximum binding capacity assay, different concentrations of receptors (0.83-6.63 mg/mL) were incubated with a fixed amount of purified labelled molecule (up to 50 000 counts/min per tube). Also, for the 3.3 mg/mL receptor concentration, different amounts of the DOTATATE purified by reversed phase HPLC (2000-70 000 counts/min per tube) were used, and experiments for inhibition studies were initiated. 

Column effects. In order to establish optimal operating conditions, it is useful to consider the effects of system parameters on the resolution characteristics of an HDC system. HDC has been described as a chromatographic method with very low capacity but very high efiBciency. For example, the calibration curves show that the spectrum of sizes from less than 100 nm to greater than 300 nm is encompassed in less than about 5% of the column void volume. On the other hand, the theoretical plate count corresponding to the marker peak is typically in the range of several thousand per foot. Comparisons in terms of the specific resolution factor, enable a more precise analysis, since both the separation factor and peak dispersion are included in its definition. A simple form for the specific resolution between two particle populations of diameter Dpi and Dp2 is [11]. 

FIGURE 4. Maximal leaf conductance as related to CO assimilation under optimal climnatic conditions and ambient CO2/ and CO2 assimilation as related to leaf nitrogen content and leaf position. The leaf nodes are counted with the youngest developing leaf being node number 1. 

In multielement analysis, choosing the optimal irradiation, cooling, and counting conditions for each element is obviously not feasible, so a compromise must be found. The balance between working up a reasonable number of samples and the desired quality of the analytical results will dictate the mode of the irradiation-counting scheme. A typical scheme has been described for atmospheric aerosols (Fig. 3) [35]. For the shortlived radionuclides, irradiation of a 2- to 25-mg sample for a few minutes, together with a flux monitor, is employed. Typically, 10-15 elements are determined from this irradiation. Longer irra-... 

We now analyze the chemical species prevalent in water at these extreme conditions by defining instantaneous species based on the O-H bond distance. If that distance is less than a cut-off value rc, we count the atom pair as being bonded. Determining all bonds in the system gives the chemical species at each point in time. Species with lifetimes less than an O-H bond vibrational period (10 fs) are transient and do not represent bound molecules. The optimal cut-off rc between bonded and nonbonded species is given by the location of the maximum in the free energy surface.83... 

Clearly, it is advisable to substitute Rs (a quantity which depends on the plate count) or S (independent of N) for a. In judging a chromatogram on the basis of thcminimum value for Rs (Rs nun) or S (Smin), it becomes very easy to estimate the number of plates that is required to realize the separation with sufficient but not excessive resolution. For instance, if the final result of a selectivity optimization process is a chromatogram with an Rs min value of 0.5 on a column with 2,500 theoretical plates, then a column with 10,000 plates will yield an Rs mjn value of 1 under identical conditions. 

A different method became available with modern meson factories, where the characteristic X-radiation from exotic atoms can be studied under optimized conditions and with reasonable count rates. Such experiments require the use of high-intensity external beam lines together with a particle concentrator like the cyclotron trap and a high-resolution low-energy crystal spectrometer. 

These conditions are the central point of the factorial plan and are counted four times for the purposes of optimization. 

These conditions are used to generate results on the cost relationships. These results are obtained by solving the partial differential equations for different amounts loaded, column length and plate count to obtain chromatograms. The yield is calculated from each chromatogram. A surface of yield versus the amount loaded and the number of plates, table or surface is prepared. Then the flow rate, column length and amount loaded are optimized to the objective function 174]. No solvent recycling is assumed. 

---