# liquid chromatography column - Scott R.P.W.

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Gradient Elution

The design procedure described above will, in theory, be applicable only to samples that are separated by isocratic development. Under gradient elution conditions the (k') values of each solute are continually changing, together with the viscosity of the mobile phase and the diffusivity of each solute in the mobile phase. As a consequence the equations derived from the plate and rate theories will only be approximate at best and in most cases give very misleading values particularly for column efficiency. As the efficiency required to separate the critical pair is crucial to column design, the optimum column for use in gradient elution development is almost impossible to calculate.

However, gradient elution is often employed, as an alternative to isocratic development, to avoid the design and construction of the optimum column which is seen as a procedure which can be tedious and time consuming. Samples that contain solutes that cover a wide polarity range, when separated with a solvent mixture that elutes the last component in a

reasonable time, often fails to provide adequate resolution for those solutes eluted early in the chromatogram. For the occasional sample, gradient elution provides the best and immediate solution to this problem. However, for quality control, where there is a high daily throughput of samples, isocratic development, employed in conjunction with an optimized column, is likely to be more economic. In many applications, the optimized column, operated isocratically, will provide a shorter analysis time than that obtained by gradient elution used with an ad hoc column Furthermore, isocratic development eliminates the time required after gradient elution to bring the column back to equilibrium with the initial solvent mixture before commencing the next analysis. Excluding samples of biological origin, isocratic development is the preferred methoa for routine LC analysis as, with an optimized column, it is usually faster, utilizes less solvent and requires less expensive apparatus.

Samples of biological origin fall in a class of their own. Many biological samples can only be separated by gradient elution particularly the macromolecules, polypeptides, proteins etc. However, due to the nature of the samples, the gradient is often very small indeed as a slight change in mobile phase composition can make a dramatic change in elution rate of many macromolecules. Consequently, the solvent viscosity and solute diffusivity does not change significantly during the program and, for the purposes of column design, the chromatogram can be treated a though the separation was developed isocratically and separation ratios, capacity ratios and efficiencies calculated in the normal way

References

(1) J. H. Purnell, Nature,No.4704,Dec, 9,(1959)2009,

(2)J.J.Van Deemter,F.J.Zuiderweg and AKlinkengerg, Chem?ng.Sci,b( 1956)24

(3XJ C. Giddings, DynamicsofChromatography Marcel Dekker,

New York,( 1965) 56,

(4) J. A. Riddick and W. B. Bunger, Organic Solvents, John Wiley and Sens,

New York,Sydney and Toronto (1970),

(5) J H Arnold, J Ampr fhprn Soc, 52(1930)3937

Chapter 13

LC COLUMN DESI6N-THE DESIGN PROCESS Open Tubular Columns

In a similar manner to the design process for packed columns, the physical characteristics and the performance specifications can oe calculated theoretically for the open tubular columns Again, the procedure involves the use of a number of equations that have been previously derived and/or discussed (1). However, it will be seen that as a result of the geometric simplicity of the open tubular column, there are no packing factors and no multipath term and so the equations that result are far less complex and easier to manipulate and to understand.

The basic starting equation is again that of Purnell (2) which allows the number of theoretical plates required to separate the critical pair of solutes to be calculated.

n =

4(l+k.) _ A

êä(à-1)

- 16-

<K>2 •2 ; êä (a-1)

(1)

where (a) is the separation ratio of the critical pair, and (êä) is the capacity ratio of the first eluted peak of the critical pair

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

1 = nH ...................................................... (2)

where m) is the column efficiency as defined in equation (1)

216

Now, it has been previously shown from the Golay equation (3), that the value of -H) is given by.

H = - + Cu ............(3)

u

where, (u) is the linear velocity of the mobile phase and (B) and (C) are constants

Now, Â = 2Din ..... ..............(4)

where (Dm), is the Diffusivity of the solute in the mobile phase

and

(l + 6k + l lk'2]r Ñ =--^— +

k-V

24(l + k')2D

6(l+k'fK2Ds

(5)

where (K) is the distribution coefficient of the solute between the two phases,

(Ds) is the diffusivity of the solute in the stationary phase, and (r) is the radius of the tube.

Restating the second expression in equation (5), which is for the resistance to mass transfer in the stationary phase,

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