The Minimum Analysis Time

The minimum analysis time is given by equation (31) in chapter 12 and takes the following form. 

The impact of the value of (k 2) is obviously linear, but controls the overall analysis time. It emphasizes the importance of carefully selecting the phase system not only to make the value of (a) as large as possible but also to keep (k 2) to a minimum. 

The minimum column length increases as the value of (a) is reduced and, at the 

Marcel Dekker 270 Madison Avenue, New York, New York 1 

The minimum analysis time is that achieved by employing the column of optimum length, packed with particles of optimum diameter and operated at the optimum velocity. Thus, the minimum analysis time, (t(min)), Is given by. 

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

It is interesting to note from equation (21) that the analysis time does not depend on the magnitude of the diffusivity of the solute in the mobile phase but only on the viscosity of the mobile phase. It does, however, increase 

Graph of Log. Minimum Analysis Time against Separation Ratio 

It is seen from f igure (3) that there is a very wide range of analysis times extending from just over ten days, which was required to analyze a mixture 

---

The HETP equation is not simply a mathematical concept of little practical use, but a tool by which the function of the column can be understood, the best operating conditions deduced and, if required, the optimum column to give the minimum analysis time calculated. Assuming that appropriate values of (u) and (Dm) and (Ds)... 

It should be noted that at a flow rate of 2 ml/min., the mobile phase velocity will be well above that of the optimum and so the maximum efficiency will not be realized. Generally, when there are more theoretical plates available than required, the flow rate is increased until the separation required is just realized. This procedure trades efficiency for time and allows the separation to be achieved in the minimum time given the column and phase system that has been chosen. It must be emphasized that the minimum analysis time can... 

Figure 11 shows the variation of the minimum analysis time with the maximum pressure available for different values of the date number. The... 

Employing the conditions defined in the three data bases and the appropriate equations derived from the Plate and Rate Theories the physical properties of the column and column packing can be determined and the correct operating conditions identified. The precise column length and particle diameter that will achieve the necessary resolution and provide the analysis in the minimum time can be calculated. It should again be emphasized that, the specifications will be such, that for the specific separation carried out, on the phase system selected and the equipment available, the minimum analysis time will be absolute No other column is possible that will allow the analysis to be carried out in less time. 

Equation (13) gives the minimum analysis time that can be obtained from an open tubular column, when separating a mixture of defined difficulty, under given chromatographic conditions. It is seen that, in a similar manner to the packed column, the analysis time is inversely proportional to the fourth power of the function (a-1) and inversely proportional to the inlet pressure. The contribution of the function of (k1), to the analysis time is not clear and can be best seen by calculation. It is also seen (perhaps a little surprisingly) that the analysis time is completely independent of the diffusivity of the solute in the mobile phase but is directly proportional to the viscosity of the mobile phase. 

Using equation (13) the minimum analysis time was calculated for the separation of a series of mixtures having (a) values ranging from 1.01 to 1,12 and for inlet pressures of 1,10,100,1000 ps.i. respectively. The results are shown as graphs relating analysis time (1) to separation ratio (a) in figure 3. 

The program can be modified slightly, to calculate the minimum analysis time required to isolate 5 gram of material, at a given inlet pressure, from a series of mixtures of differing separation difficulty. The results obtained are shown as curves relating separation time to separation ratio in figure 5. 

Figure 6 shows the effect of the three limits imposed on the column design, the need to maintain an aspect ratio greater than unity, restricts the column length to a minimum of 5 cm and confines the analysis time to between one minute and one hour, without the restriction, the column with the minimum analysis time would be operated at the maximum pressure available. However, as a result of the limitation on column length, the optimum pressure must be reduced to allow the optimum particle diameter to be ircreased. This, in turn, allows the column length to be increased to... 

The cuvette rotor receives the reagent preparations of the samples, rotates the cuvettes for light measurements and places them under the washing station. The rotor is furnished with 45 semi-micro cuvettes —the odd number allows for simultaneous filling, measurement and aspiration. Only every second cuvette is filled. Every 8 s, each cuvette returns to its initial position after two turns. The minimum analysis time is therefore 6 min or a multiple of this. 

Take 50 mg of the standard mixture and dilute with 20 ml of acetonitrile and make up to final volume of 25 ml with 2 mM KH2PO4. Find the optimum solvent composition for the separation of these components, i.e. that which requires the minimum analysis time but gives the necessary resolution of peaks (<10% overlap). Isocratic elution should be used with solvent mixtures of varying composition starting with 70% A, 30% B decreasing A down to about 25%. The response factors of the barbiturates should be calculated relative to barbitone. The order of elution of the components is... 

It must be emphasized that the minimum analysis time will be achieved only at those values of (T) and (X ) for which the expression for (t) is a minimum and which will need to be ascertained with the use of a computer. 

In many chiral separations, it is often a struggle to adequately resolve the enantiomers and achieve adequate separation ratios. In such cases, the above procedure may be essential to achieve the minimum analysis time. In addition, the time would be much extended, the column longer, and the efficiency that was needed, would be much greater. The same type of approach can be used for reversed phase systems employing water which, if in a binary mixture, will associate with the other solvent and produce a ternary mixture. Unfortunately, the procedure becomes extremely involved and its discussion is more appropriate to a text on chromatography theory and, consequently, is outside the scope of this book. 

---