Distribution retention-time

Figure 9.2 shows a two-compartment Markov model with parameters /iio, hi2, and h21 and the semi-Markov model with exponentially distributed retention times with parameters q, n2, and uj. The conversion relationships are... 

Erlang distributed retention times describing the elimination from the... 

A correlation between retention times and boiling points is established by calibration with a known mixture of hydrocarbons, usually normal paraffins, whose boiling points are known (see Figure 2.2). From this information, the distribution of boiling points of the sample mixture is obtained. 

It is important to realize that many important processes, such as retention times in a given chromatographic column, are not just a simple aspect of a molecule. These are actually statistical averages of all possible interactions of that molecule and another. These sorts of processes can only be modeled on a molecular level by obtaining many results and then using a statistical distribution of those results. In some cases, group additivities or QSPR methods may be substituted. 

Thus far all the separations we have considered involve a mobile phase and a stationary phase. Separation of a complex mixture of analytes occurs because each analyte has a different ability to partition between the two phases. An analyte whose distribution ratio favors the stationary phase is retained on the column for a longer time, thereby eluting with a longer retention time. Although the methods described in the preceding sections involve different types of stationary and mobile phases, all are forms of chromatography. 

Dropsize Distribution Monodisperse (nearly uniform droplet size) fogs can be grown by providing a long retention time for growth. However, industrial fogs usually show a broad distribution, as in Fig. 14-91. Note also that for this set of data, the sizes are several orders of magnitude smaller than those shown earlier for entrainment and atomizers. 

A plot of In n versus L is a straight line whose intercept is In and whose slope is —l/Gt. (For plots on base-10 log paper, the appropriate slope correc tion must be made.) Thus, from a given product sample of known shiny density and retention time it is possible to obtain the nucleation rate and growth rate for the conditions tested if the sample satisfies the assumptions of the derivation and yields a straight hne. A number of derived relations which describe the nucleation rate, size distribution, and average properties are summarized in Table 18-5. 

An eluted solute was originally identified from its corrected retention volume which was calculated from its corrected retention time. It follows that the accuracy of the measurement depended on the measurement and constancy of the mobile phase flow rate. To eliminate the errors involved in flow rate measurement, particularly for mobile phases that were compressible, the capacity ratio of a solute (k ) was introduced. The capacity ratio of a solute is defined as the ratio of its distribution coefficient to the phase ratio (a) of the column, where... 

It follows that measurements must be made with a precision of about 0.2 second if quantitative results are to be of any value. It is seen from figure 4 that the experimental points lie very close to the line and a fairly accurate measurement of the distribution of the two isotopes can be obtained from retention time measurements. This method has very limited areas of application and is given here, more to demonstrate the effect of unresolved impurities on retention time, than to suggest it as an alternative to adequate chromatographic resolution. In some cases, however, particularly in the analysis of isotopes, it may be the only practical way to obtain a quantitative evaluation of the mixture by a liquid chromatographic method. 

Since in continuous degradation processes it is expected to reach a molecular weight distribution of the products, which is optimal for their further use, the investigation was devoted to test the effect of a key parameter such as the enzyme to substrate ratio (E/S). For a fixed mean retention time in the UF-membrane reactor, the following behaviour can be... 

In analysis of homopolymers the critical interpretation problems are calibration of retention time for molecular weight and allowance for the imperfect re >lution of the GPC. In copolymer analysis these interpretation problems remain but are ven added dimensions by the simultaneous presence of molecular weight distribution, copolymer composition distribution and monomer sequence length distribution. Since, the GPC usu y separates on the basis of "molecular size" in solution and not on the basB of any one of these particular properties, this means that at any retention time there can be distributions of all three. The usual GPC chromatogram then represents a r onse to the concentration of some avera of e h of these properties at each retention time. 

For complex mixtures, the k values should be distributed in the range of 0.5 to 20,3 corresponding to retention times of about 3 to 45 minutes on a column with a void time of 2 minutes. If the components of a sample are neutral, i.e., nonionizable, the correct proportion of water and organic solvent gives the optimum k value by which symmetrical, well -resolved peaks are obtained. Figure 1 is a chromatogram of the separation of a neutral... 

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