Gradient theoretical plates

The peak capacity is not pertinent as the separation was developed by a solvent program. The expected efficiency of the column when operated at the optimum velocity would be about 5,500 theoretical plates. This is not a particularly high efficiency and so the separation depended heavily on the phases selected and the gradient employed. The separation was achieved by a complex mixture of ionic and dispersive interactions between the solutes and the stationary phase and ionic, polar and dispersive forces between the solutes and the mobile phase. The initial solvent was a 1% acetic acid and 1 mM tetrabutyl ammonium phosphate buffered to a pH of 2.8. Initially the tetrabutyl ammonium salt would be adsorbed strongly on the reverse phase and thus acted as an adsorbed ion exchanger. During the program, acetonitrile was added to the solvent and initially this increased the dispersive interactions between the solute and the mobile phase. 

Figure 1.17 Separation of large ring polycyclic aroaatic hydrocarbons extracted from carbon black on a 1.8 x 0.2 n I.D. fused silica capillary column packed with 3 micrometer spherical octadecylsllanized silica gel eluted with a stepwise solvent gradient at a flow rate of 1.1 mlcroliters/min with an inlet pressure of about 360 atmospheres. Under isocratic conditions this column yielded ca. 225,000 theoretical plates. (Reproduced with permission from ref. 238. Copyright Friedr. Vieweg t Sohn).

Golay equation 21, 611 gradient (LC) 490 height equivalent to a theoretical plate 11 longitudinal diffusion 16 mass transfer resistance 17 nonlinear chromatography SOS plate model 14 rate theory IS reduced parameters 78, 361, 611... 

A typical HPLC separation using a 15-cm column of 15,000 theoretical plates produces peak capacity (Giddings, 1991) of about 80-100 under isocratic conditions and up to 150 under gradient conditions in 1 h(Eq. 7.3, n peak capacity, A number of theoretical plates of a column, and fR and t retention time of the last and the first peak of the chromatogram, respectively). An increase in the number of separated peaks per unit time can be achieved by increased separation speed made possible by monolithic silica columns (Deng et al., 2002 Volmer et al., 2002). This has also been shown for peptides and proteins (Minakuchi et al., 1998 Leinweber et al., 2003). 

N is the average number of theoretical plates determined under isocratic conditions in mobile phases within the gradient concentration range is the hold-up volume of the column... 

N is the average column isocratic theoretical plate number is the retention factor at the point of elution controlling the bandwidths in gradient elution— Equation 5.5... 

However, if the samples had a wider MWD, the overlapping of the zones of differing functionality would be much stronger. This overlapping is not connected with the efficiency of the separation system (in our case the column had 4000 theoretical plates). In such a situation it would be more convenient to use a gradient, but in working with OBD problems of detection arise. 

Pf is the instantaneous concentration of the strong eluting component in the mobile phase at the outlet of the column at the time the band maximum elutes from the column, Ri. R2 are the retention volumes of sample compounds with adjacent peaks, N is the number of theoretical plates determined under isocratic conditions and T, is the hold-up volume of the column. It should be noted that the correct plate number value cannot be determined directly from a gradient-elution chromatogram using Eq. (1.7) or Eq. (1.8), which assume a constant value of the retention factor A and hence can be applied for isocratic elution only. 

The authors of Refs. [15,16] erroneously evaluated the expanding term 4.32 by differentiating Eq. 4.23. They also used this equation to find the optimal gas flow rate (which gives the smallest height of the theoretical plate) for the columns with a constant temperature gradient and came to ... 

Assumption 1 The column is assumed to be radially homogeneous. Experiments show that it is possible to pack wide columns (up to at least 80 cm in diameter) and achieve packed beds that are nearly as homogeneous as those in analytical columns 1/4 inch in diameter. This homogeneity is witnessed by the values of the reduced height equivalent to a theoretical plate achieved, sometimes less than 3 [10]. Such a result is possible only if the input profile is radially homogeneous. Accordingly, appropriate flow distributors should be used [11,12]. This also requires that the column be operated isothermally or adiabatically. For the influence of a radial gradient of the column temperature, see [13]. 

The above-mentioned equation for n in fact is only valid for isocratic separations and if the peaks are symmetric the peak capacity is larger with gradient separations. Tailing decreases the peak capacity of a column. In real separations the theoretical plate number is not constant over the full k range. However, it is even more important to realize that a hypothetical parameter is discussed here. It is necessary to deal with peaks that are statistically distributed over the accessible time range. The theory of probabilities allows us to proceed from ideal to near-real separations. Unfortunately, the results are discouraging. 

The number of theoretical plates must be determined only under isocratic conditions Solvent gradients will compress the peaks. 

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