Poppe plots

There have been very few method development processes proposed for 2DLC. One study (Schoenmakers et al., 2006) is titled A protocol for designing comprehensive two-dimensional liquid chromatography separation systems. This study advocates that one initially chooses the first-dimension maximum acceptable analysis time, the first-dimension maximum workable pressure drop, and the smallest first-dimension column diameter. The first two variables are then used to construct a Poppe plot (Poppe, 1997)—pronounced Pop-puh (Eksteen, 2007). 

The Poppe plot is a log-log plot of H/uq = t(JN versus the number of plates with different particle sizes and with lines drawn at constant void time, t(). H is the plate height, Vis the number of plates, and u() is the fluid velocity (assumed equal to the void velocity). The quantity H/u() is called the plate time, which is the time for a theoretical plate to develop and is indicative of the speed of the separation, with units of seconds. In the Poppe plot, a number of parameters including the maximum allowable pressure drop, particle diameter, viscosity, flow resistance, and diffusion coefficient are held constant. 

FIGURE 6.1 A Poppe plot for the required plate number in conventional HPLC. The parameters are taken from Poppe s original paper (Poppe, 1997). The parameters are maximum pressure AP = 4x 107 Pa, viscosity / = 0.001 Pa/s, flow resistance factor

diffusion coefficient D= lx 1CT9 m2/s, and reduced plate height parameters using Knox s plate height model are A — 1, B— 1.5, C = 0.05. 

Given the construction of the Poppe plot, the number of plates, the column length, the peak capacity, and the particle diameter are determined in the Schoenmakers et al. (2006) scheme all for the first-dimension column. These are then used to determine the second-dimension parameters that include the particle diameter, the number of plates, column length, and peak capacity. Other variables are utilized and optimized from this scheme. 

Fig. 13. Equilibrium fractionation plot showing possible combinations of water S 0 values and temperatures which are compatible with the intergranular and vein-fill dolomites. Curves plotted using the equation from Land (1983). Estimated 0%o smow for Carboniferous sea water from Popp et at. (1986) low-latitude meteoric water from Anderson Arthur (1983). Burial temperatures calculated from subsidence history (Fig. 3), 20"C surface temperature and 30"C km geothermal gradient.

Figure 2. Chemostat experimental results representing controls on the isotopic fractionation by marine algae, (a) Plot of isotopic fractionation (Cp) as a function of growth rate (p) divided by the concentration of dissolved CO2 for selected marine organisms, (b) Plot of the slopes of the relationships represented in (2a) as a function of the ratio of cellular carbon to cell surface area. Dashed lines represent relationships estimated from other studies, (c) Plot of the slopes from (2a) as a function of observed cell volume to smface area ratios, (d) Plot of isotopic fractionation (Cp) as a function of the product of the growth rate divided by CO2 concentrations and the volmne-to-smface area ratios for the eukaryotic species in (2a). [Used by permission of the editor of Geochimica et Cosmochimica Acta, from Popp et al., (1998), Figirre 2]...

The minimum on the H-u plot (Eq. 5) corresponds to the best separation efficiency, but separations are often performed at a higher-than-optimum flow rate to decrease the run time. The speed vs. efficiency characteristics of various HPLC columns can be optimized using kinetic plots proposed by Poppe. There, the minimum column holdup time, fo, necessary to produce the desired number of theoretical plates, N, can be determined from the diagonal line at the point on the plots of H/u, characterizing the speed of separation vs. N in logarithmic coordinates. The plots are charted for different column types assuming a maximum allowed instrumental pressure, = 40... 

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