Plate height additive

There is some disagreement on the correct equation for describing the relationship between plate height and mobile-phase velocity. In addition to the van Deemter equation (equation 12.28), another equation is that proposed by Hawkes... 

The important parameters to consider are the selectivity (dKJdlogR), the ratio of pore volume, Vp, over void volume, Vq, the plate height, H, and the column length, L. The distribution coefficient, Kq, has a slight effect on resolution (with an optimum at Kp 0.3-0.5). In addition to this, extra column effects, such as sample volume, may also contribute to the resolution. 

Thanks to the additivity of variance, the total plate height can be divided up into contributions due to independent factors. In FFF, this can be represented as... 

The additional plate height contribution due to Joule heating is given by Equation (6.7) [352]. 

As stated previously, additional information on the sample is obtainable from band broadening (plate height) measurements. If plate height is measured as a function of flow velocity at a fixed retention level, a linear relationship is obtained, as predicted by Equation 7. The slope of the line yields the diffusivity D of the sample, and the intercept provides the polydispersity a. . The D value translates into a value for the average particle diameter d via the Stokes-Einstein relationship... 

We see, then, two distinct kinds of plate height terms for the mobile phase a term HD proportional to flow velocity v, valid when diffusion terminates a molecule s velocity bias, and a velocity-independent term Hfy valid when flow terminates the bias. The question yet unanswered is how HD and Hf combine in contributing to the overall experimental plate height. Plate heights are usually additive because variances (for independent processes) are additive it is tempting to apply the additive rule here. However, additivity does not apply to HD and Hf. We see this in simple physical terms by looking at two extremes of flowrate. 

Additivity also decreases plate height, Eq. 11.21, which, with Eq. 11.32, assumes the form... 

The coupling equations shown above are applicable to one kind of velocity bias, such as that between adjacent channels. However, the theory is more or less the same for the other kinds of velocity biases listed previously, but the constants (a>fi9 a>A, (oa) are different, yielding different a> and A in the foregoing coupling expressions. Each kind of velocity bias generates its own independent random walk, leading to an additive plate height term H,. The overall mobile phase term is therefore the sum... 

In addition to the enhanced diffusivity effect, another issue needs to be taken into account when considering stationary-phase mass transfer in CEC with porous particles. The velocity difference between the pore and interstitial space may be small in CEC. Under such conditions the rate of mass transfer between the interstitial and pore space cannot be very important for the total separation efficiency, as the driving mechanism for peak broadening, i.e., the difference in mobile-phase velocity within and outside the particles, is absent. This effect on the plate height contribution II, s has been termed the equilibrium effect [35], How to account for this effect in the plate height equation is still open to debate. Using a modified mass balance equation and Laplace transformation, we first arrived at the following expression for Hc,s, which accounts for both the effective diffusivity and the equilibrium effect [18] ... 

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