Critical sample mass

The exponentially decrease of the total variance with increasing sample mass is shown in Fig. 2.7. It can be seen that the uncertainty of sampling, s2samp, decreases and becomes statistically insignificant when the sample amount m exceeds the critical sample mass. Instead of mcnt the proportional critical sample volume vcrit may also be considered, represented, e.g. by a critical microprobe diameter dcnt. Results of homogeneity investigations of alloys, ores, and lamellar eutectics by EPMA (Electron Microprobe Analysis), which correspond to the curve of Fig. 2.7, have been presented by Danzer and Kuchler [1977]. 

Fig. 2.7. Dependence of the total variance on the sample amount characterized by mass merit is the critical sample mass. The statement of homogeneity or inhomogeneity is always related to a given analyte A... 

In this volume the term slow decomposition is reserved for non-self-sustaining decompositions, such as may take place over periods of many minutes, or even days, weeks, or years. The interest in the long-term stability of azides under a variety of more exacting ambient conditions has increased to an extent not anticipated 20 years ago, when, for example the lifetime of an azide in a space vehicle was a subject not likely to be broached. On the other hand, while the transition from slow decomposition to an explosive regime is definable in terms of a temperature for a given ignition delay and a critical sample mass (see Chapter 6, Volume 2), the interest in slow decomposition as an indicator of sensitivity to thermal, mechanical, and electrical stimuli has tended to diminish quantitative relationships have not been forthcoming. 

Correct determination of the sample mass is critical. Usually drying conditions are specified by the producer. The user has to be aware that there is an amazing variety of recommended drying conditions presented in the various certificates. Since the optimum conditions are very dependent on matrix and composition, it is of utmost... 

Fig. 26 Critical molar mass of melt-crystallised linear polyethylene as a function of crystallisation temperature. Filled circles data for a broad molar mass sample with Mn=8500 g mor1, Mw=153,000 g mor1 of Mehta and Wunderlich [149], Open circles data for a sample with Mn=12,900 g mor1, Mw=108,000 g mol-1 from Gedde et al. [152]. From [91] with permission from Kluwer, Doordrecht, Netherlands...

A critical aspect, however, is the so-called matrix effect in biological samples. Mass spectrometric detection can be adversely affected by ion suppression (or enhancement) caused by other unknown components within the sample matrix. These matrix effects can lead to quantitatively false results. J Krause has described... 

It has been tried to put the result of Kennedy et al (//) in a la-Mw graph (Fig. 7). Two samples families are distinguished quenched samples and slowly crystallized samples. In both families, the ductile-brittle transition occurs at lac = 6 nm. The corresponding critical molar mass defined in scheme A is higher for slowly crystallized samples (M c 100 kg.mof ) than for quenched ones (M c 60 kg.mof ). This result can be considered as a proof that scheme B is more pertinent than scheme A. 

The approximate relationship between the constitution heterogeneity (CH) and the statistical variance, discussed in the next section, can be used to determine the optimal sample mass when sampling to determine the relative amount of trace constituents in the lot. Two series of samples of large and small sample masses are collected and analyzed. The statistical coefficients of variation are calculated. These, together with the values of the sample mass, can be used to determine the minimum sample mass needed to obtain the desired sampling precision of the estimated critical content of the trace constituent. For details, see Chapter 20 of Pitard (1993). 

Figure k. 13 9" ion profiles using flame sampling mass spectrometer technique in C2H2/O2 flame (2.1 kPa, 50 cm s" unburned velocity). Critical threshold, 2.5. 

As a general rule of thumb for small molecules, a broadening of a peak doe to mass overload is observed at a load of 0.1-1 mg of sample per milliliter of packed bed. However, if the separation is not critical, the mass load can be up to a factor of 10 higher. Also, if we want to separate a major compound from impurities, and if all impurities elute behind the parent peak, a significantly larger load can be appli. ... 

Visually inspect the nitrocellulose targets for quality and sort into two categories high quality for critical samples, i.e., high-molecular-mass or small quantities lower quality for other samples (Fig. 1). 

The difference between the applied molar mass range and critical molar mass range (symbols US and CR in Table 1-3) reflects separation difficulties. For example, it has often been reported that the polymer was partially, or fully, retained within the column. Several authors also indicate a lack of solubility in the eluent or a molar mass independent retention observed only over a limited range of molar masses. In several published works, it is also stated that separation range at critical conditions is limited to lOOkD. However, as shown data in Table 5, polymer samples with much higher molar mass are eluted under critical and limiting conditions. 

---