Column Length L

Column length (L) determines column efficiency (N), analysis speed, and pressure drop (see Chapter 2)  

Plate number (N) = L/H (Since plate height H is a constant at a given 

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The average linear velocity u of the mobile phase in terms of the column length L and the average linear velocity of eluent (which is measured by the transit time of a nonretained solute) is... 

Now, the velocity of a solute band along the column (Z) is obtained by dividing the column length (L) by the retention time, (tr)j consequently. 

Thus, for a packed column length (L), radius (r), with a mobile phase volume equivalent to 60% of the column volume,... 

Thus, the minimum column length (L) will be given by... 

The next equation of importance is the relationship between the column length (L) and the height of the theoretical plate (H),... 

Now, the column length (L) can be defined as the product of the minimum plate height and the number of theoretical plates required to complete the separation as specified by the Purnell equation. 

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. 

The column performance (efficiency) is measured either in terms of the plate height (H), the efficiency of the column per unit length, or the plate number (N), i.e. the nnmber of plates for the column. This number depends upon the column length (L), whereas the plate height does not. The mathematical relationships between the nnmber of plates, the retention time of the analyte and the width of the response is shown in the following equations ... 

A van Deemter plot for a given particle size dp and diffusion coefficient Du shows the relation of the theoretical peak height H to the linear velocity u that can be expressed as column length L... 

Column length (L) Retention times longer peaks are separated further Peaks broaden with length, but N higher... 

Based on the following information, we can relate ux to retention time tR, the time, a component, is retained in the column, and column length L The retention time tR is the time required for band X to travel the length of column and is generally given as seconds or minutes the distance is the column length L (in centimeters), and the velocity is that of band X, ux (cm/sec). 

Equation 4 Estimation of pressure drop, Ap (10 bar), with linear velocity (flow/cross section), u (cm/s) column length, L (cm) viscosity, rj (cP) characteristic constant (600 for spherical particle), kp, and particle size, dp (cm). 

Substituting for (Uopt) from equation (9) and the column length (l) from equation (13) then analysis time is seen to be given by,... 

The column length, (l), is also defined by the Poiseuille equation that describes the flow of a fluid through an open tube in terms of the tube radius, the pressure applied across the tube (column), the viscosity of the fluid and the linear velocity of the fluid, The Poiseuille equation is given as follows,... 

These successive equilibria are the basis for the static model for which the column length L is partitioned into N theoretical plates numbered from 1 to N, all with the same height. For each of these plates, the concentration of analyte in the mobile phase is in equilibrium with the main concentration of analyte in the stationary phase. The height equivalent to a theoretical plate (HETP or II) is thus given by equation (1.5) ... 

The table below contains values of the retention factor k for four refinery gases, studied at three different temperatures upon the same capillary column (length L = 30cm, internal diameter = 250 pm), whose stationary phase is of type SE-30. The chromatograph is supplied with a cryogenic accessory. 

As to the number of steps, we can determine these in terms of the total column length, L, and the equivalent length of the step Therefore,... 

As is apparent from Eq. (8.86), resolution improves with increasing column length l and decreasing h as well as with both increasing 8 and k2. Resolution suffers both at similar retention times [8 —> 1, (8 - l)/8 — 0] and at capacity factors close to the void volume (kj —> 0). 

Geometric variables area moment of inertia I and column length L... 

Band broadening arises from three principal mechanisms, one of which depends on the mean velocity of the carrier and two of which are independent of . The latter two represent nonidealities in instrument and sample. The total variance of an eluting peak is the sum of variances contributed by each bandbroadening mechanism. Expressed as plate height H, which is the total variance divided by column length L (12), the zone broadening is described by... 

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