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

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= 1.1

12 44oE k'(a-1)

(1+k1)

4(1 +k’) k’(a-l)

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selected and thus, (k‘) is normally not considered a variable Nevertheless, it is of interest to determine if the value of the capacity ratio of the first

Figure 8

Graph of Log. Analysis Time against Capacity Ratio

è

w

CO

Ô

I

i-

to

»

Ý)

e

ñ

<

î

e

? Sep .Ratio 1.01 ¦ Sep .Ratio 1.06 ¦ Sep Ratio 1.12

Capacity Ratio

peak of the eluted pair does have a profound effect on the performance of the optimized column. As the critical parameter in the efficient operation the chromatographic system is the analysis time which should be made a minimum, the effect of (k') on the analysis time will be determined. Employing equation (21), that allows the minimum analysis time to be calculated, the values of tmin were calculated for (k‘) values ranging from 0.1 to 5, for separation ratio values of 1.01, 1.05 and 1.10 and for an operating pressure of 4000 p.s.i.. The results obtained are shown as graphs relating minimum analysis time to capacity ratio values in figure (8).

It is seen from figure (8) there is no true optimum value for (k) that will produce a minimum analysis time, but the shortest times will occur when the critical pair are close to the last eluted solutes of the mixture. This situation will be rarely possible in practice. However, it is also seen from the curves in figure (8), that if the phase system is adjusted such that the value for (k‘) is 2.5 or greater, then the (k‘) value will not greatly ef fect the analysis time This is because the curves are very flat subsequent to a (k-)

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value of 2.5. In general when selecting the phase system, the operator should make it a first priority to obtain a minimum value for (a). Furtner adjustment of the phase system to make the (k') of the first eluted peak of the critical pair 2.5 or greater should be carried out only if the minimum value of (a) is not compromised

It now possible to summarize the design equations for a packed column which are given as follows.

PACKED COLUMN DESIGN EQUATIONS

The Optimum Particle Diameter

_ 8(I+K)

W) -

ôÐ

2X

3Y (1+ ê-)2

0.5

(l+6k'+1 Ik'2)

4

+ Y

0.5

The Optimum Column Length

lopt - 2

0.5' 0.5 '

4(l+k')^3 2X + (l+6k‘+1Ik'2] nDm 2\ 9 3Y (1+ê'Ã

(k'(a-l)j Y 3(l+k')2 ôÐ (l+6k'+l ik'2) + Y

* '

0.5

The Minimum Analysis Time

×Ï1Ï

= (|*K2)

’8(1+10 V

k'(Q-l)j

Ë

ôÐ

2X

y(i + 6k' +1 Ik'2 3(1+ ê'I2

,0.5

207

The Optimum Column Radius

ropt

0.3l2k'(a-l)VoE

^ñë()+ê‘)2

2ß+

(l+6k'+l Ik'2))05

3(l+k')'

0.5

ôÐ

21

3y(l+k'

ë2

ë 0.5

(i+6k’+i ik'2)

V ',

+Y

025

The Optimum Flow-Rate

Qopt ~

Î 0486ôÐê,3(à-|)3îÅ

ï(1+ê'

•È

/ Î \ 0.5’

l+áê'+Ïê'2

2/U ‘ f Y 0

3(1+ k) L

Minimum Solvent Consumption

\2A

ê'(à- l)

Peak Capacity

log

1-

k‘9(Hk')

0.5

Maximum Sample Volume

(1+k’)k'(a-l)

2k'(a -l)j

2+k‘+ka

log

2 + Çê'-ê'ñË

VSamp _ 3.42 oe

The design equations can be used in a simple computer program to report the basic data and print the column and analytical specifications for any particular analysis carried out on a specified liquid chromatograph. The program is written In the Microsoft Quick Basic language that can be used on

205

any Macintosh computer or with some slight modification on other types of computers The program is written in a very simple form so that those unfamiliar with computer programming can still enter the program and use it and furthermore.it is interrogative, in that the required basic data is asked for, and then entered by the operator

Certain values can be assumed. For example, for a well packed column the packing factors (X) ans (y) can be taken as those recommended by Biddings,

(3) namely, 0.5 and 0.6 respectively. The value assumed internally in the program for the D'Arcy constant is 35 as previous'y discussed. Values for the viscosity of the mobile phase can be obtained from "Organic Solvents " by Riddick and Bunger (4) and values for solute diffusivity can either be estimated from the data given in the appendix or calculated from the Arnold equation (5). The program for packed column design is given as follows.

Computer Program for the Design of Packed Columns

LPRINT

LPRINT" PACKED COLUMN DESIGN FOR LC"

LPRINT

LPRINT

LPRINT"PERFORMANCE CRITERIA"

LPRINT

LPRINT"! / A defined resolution must be obtained "

LPRINT“2/ The analysis must be completed in the minimum time "

LPRINT"3/ The analysis must be completed with the minimum solvent" LPRINT

PRINT"Enter Separation Ratio of the Crical Pair":INPUT A

PRlNT"Enter Capacity Ratio of the First Peak of the Pair".INPUT K1

PRiNT"Enter Capacity Ratio of the Last Eluted Peak" INPUT K2

PRlNT"Enter Diffusivity of Solute in Mobile Phase'MNPUT D1

PRINT"Enter Viscosity of Mobile Phase (Poises)":INPUT M

PRINT" Enter Column Inlet Pressure (p.s.i.Ã:INPUT P

PRINT" Multipath Packing Factor'':INPUT LI

PRINT" Longitudinal Diffusion Packing Factor":INPUT G

PRINT" Column Mobile Phase Fraction":INPUT E

PRINT" Extra Column Dispersion‘':INPUT S

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