H/u-curve

In the emulsion phase/packet model, it is perceived that the resistance to heat transfer lies in a relatively thick emulsion layer adjacent to the heating surface. This approach employs an analogy between a fluidized bed and a liquid medium, which considers the emulsion phase/packets to be the continuous phase. Differences in the various emulsion phase models primarily depend on the way the packet is defined. The presence of the maxima in the h-U curve is attributed to the simultaneous effect of an increase in the frequency of packet replacement and an increase in the fraction of time for which the heat transfer surface is covered by bubbles/voids. This unsteady-state model reaches its limit when the particle thermal time constant is smaller than the particle contact time determined by the replacement rate for small particles. In this case, the heat transfer process can be approximated by a steady-state process. Mickley and Fairbanks (1955) treated the packet as a continuum phase and first recognized the significant role of particle heat transfer since the volumetric heat capacity of the particle is 1,000-fold that of the gas at atmospheric conditions. The transient heat conduction equations are solved for a packet of emulsion swept up to the wall by bubble-induced circulation. The model of Mickley and Fairbanks (1955) is introduced in the following discussion. 

Figure 10 The effect of pore size on the H-u curves of fluorene in reversed-phase CEC. Columns packed with 10- xm reversed-phase particles with a nominal pore size of , 50 nm . 100 nm A, 400 nm.

No such details can be given for the H(u) curve as its position is a function of particle diameter and diffusion coefficient alone. 

The more common H/u curve (the classical van Deemter relationship, upper right) is derived from the h/v curve by taking into account the particle diameter and the diffusion coefficient H = hcl and u = vD ld. The curve shown here is valid for a particle diameter of 5 pm and a diffusion coefficient of 1 x 10 m s typical for reversed-phase separations. For packings of smaller particles the curve is lower. For normal-phase separations its minimum is more to the right because the diffusion coefficients are higher (see Section 8.8). The ranges of both axes correspond to the ones of the hiv curve. 

The theoretical plate height, H, can be expressed as a function of mobile phase flow velocity, u (Fig. 2.7). The H/u curve is also called the van Deemter curve. The optimum flow rate Wopt depends on the properties of the analyte. 

Fig. 2.7 Van Deemter curve (H/u curve). 1=eddy diffusion and flow distribution connponent of band broadening 2 = longitudinal diffusion component—flow-rates at which this diffusion is not a factor of any significance should be used in liquid chromatography 3 = mass-transfer component— the slope of the line is greater for 50 am than it is for 5)am particles 4 = the resultant van Deemter H/ucurve. ...

In his book (see Further Reading), Jennings presents a compilation oi H — u curves for a range of capillary columns that vary from short (5 m) and very narrow bore (0.05 mm), to long (60 m) and wide bore (0.53 mm ID) columns, as an aid to understanding optimization of the operational conditions. 

MPa, as is usual in conventional LC, and at the optimum flow velocity, u, corresponding to the minimum height equivalent to theoretical plate, H, on the van Deemter H-u curve (Eq. 5). An example of the kinetic plots for... 

The selection of a capillary column depends on the complexity of the sample to be analyzed. The column length, the internal diameter, the stationary phase, and its fdm thickness determine the separation power (resolution), the sample capacity. the speed of analysis, and the detectability or sensitivity. Theoretical considerations [12], [13] indicate that for capillary columns with thin films (< 1 pm), the Wniin value is roughly equal to the column diameter. This is illustrated in Figure 4. which shows experimental H-u curves for columns varying in internal diameter. H was calculated for dodecane at I00°C with hydrogen as carrier gas. measured experimentally is indeed very close to deduced theoretically. By knowing this, the maximum plate number that a capillary column can provide may be calculated without performing any analysis ... 

Increasing analysis speed for complex profiles without impairing resolution can only be realized by reduction of the internal diameter and the length of the capillary column. A lOmxO.l mm i.d. column offers the same resolution as a 25 m X 0.25 mm i.d. column. Because the column is 2.5 limes shorter, the analysis time is reduced drastically. Moreover, since the optimum carrier gas velocity is higher and the H-u curves are flatter for narrow bore columns, higher average carrier gas velocities can be used without loss of resolution. Presently, capillary columns with internal diameters in the order of 100 pm are in the picture for routine operation because state-of-the art cap-... 

It is also useful to plot H against 1 /m (Figure 2.21). In both presentations (Figures 2.20, 2.21) the intercept of the linear portion of the H plot will equal Tkd. Thus, if the particle size dp is known, can be calculated and a measure of packing regularity obtained. From the slope of the linear part of the H-u curve one also can estimate the film thickness rff, if A and k are known (resistance to mass transfer in liquid-phase term). 

---