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

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î 1000 p.s i

Separation Ratio

Bearing in mind that the the sample volume is measured in microlitres, it is seen that the largest sample volume calculated was for the separation of the most difficult mixture where the separation ratio of the critical pair is

1.01 at an inlet pressure of I p.s i Even then, the sample volume is only about 1.0 microlitre. For a separation ratio of 1 04 (a moderately difficult separation) the maximum sample volume is only about 8 0 nanolitres and such a small sample volume would be difficult to inject, even with a stream splitting system. Furthermore, a charge so small, would certainly reduce the dynamic range that could be covered by the detector, particularly as the sensing volume of the detector would also have to be very small. A reduction in the sensing volume will, as a conseguence, reduce the absolute detector sensitivity It follows that by employing a charge of only a few nanoiitres, the total concentration range that could be sensed by the detector would be restricted to about two orders of magnitude or even less. It should be noted that the dynamic range of a detector lies between the maximum concentration sensed when the sample volume consisted entirely of pure solute, and the detector noise level (5)

From the curves shown in figure (5) it would appear that trie very small permissible sample volume would limit the use of the open tubular column

2^0

to the separation of fairly difficult mixtures (mixtures where a<l 04 ) and for inlet pressures less than Þ p.si wnere tne analysis times tan he extremely long

(a d) the Maximum Permissible Detector Dispersion

The expression for the maximum permissible detector dispersion, given by equation (21), also shows it's strong dependance on the product of the solute diffusivity and the viscosity of the mobile phase together with the inverse of the fourth power of (a-1) A graph relating (op) to the separation ratio of the critical pair is shown inf igure (6)

Figure 6

Log. Maximum Detector Dispersion against Separation Ratio

Separation Ratio

The results In figure (6) emphasizes the stringent demands that open tubular columns place on system design. Even when separating solute pairs having an (a) value of 101. and operating at an in'et pressure of only 1 p.s.i., the maximum value for (op) will only be about 0.16 microlitres If it is assumed that in practice (op) can not be reduced to much less than 5 nanolitres (and this would be extremely difficult) the use of open tubular

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columns would oe restricted to inlet pressures below 10 p.s.i.. Furthermore, they would then be only suitable for the separation of relatively difficult mixtures where the separation of the critical pair is less than 1 04.

Design Equations

The baste design equations for the design of open tubular columns in LC can be summarized as follows

Column Radius

ropt -

i6(i+k-)fDmnla5

k‘(a -1)

(II)

Column Length

•opt -

256(1 + k')2 |i + 6k' + k'3(a-l)3 \ 3

I Ik'2 DmT|

Ðë

(12)

Analysis Time

'-min

(l + k?)

1024 r)( 1 + k') | + 6k' + llk^

Optimum Flow-Rate Qopt = 64

k'4(a- l) (l + kf

k' (a -1)

3nD3t] m '

ÇÐë

0.5

p(l+6k' + iik'2

(13)

(14)

Maximum Sample Volume V,=

269l(l+k2j(i

1+kl

k'4 (a-1)

K6k'+1 Ik'

2

Çë

I P

0.5

..(20)

Detector Dispersion

î D=

3664 K) (we)3 f J l+6k + 1 lie Dm4

k'4(a-l 3k I P

3^

0.5

...(21)

Employing the design equations, a simple program can be written that will allow the optimum parameters to be calculated for any given set of chromatographic conditions. Such a program is given in table (2) and is written in Microsoft Quick Basic for the Macintosh Computer The program is interactive and the user is asked sequentially, by a series of input statements, the value of the pertinent variables required by the equations.

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Table 2

OPTIMISATION PROGRAM FOR OPEN TUBULAR COLUMNS

PRINT'OPEN TUBULAR COLUMN DESIGN FOR LC"

PRINT'Enter Separation Ratio of the Critical Pair" INPUT A PRINT'Enter Capacity Ratio of the First Peak of the Pair" INPUT ê I PRINT"Enter Capacity Ratio of the Last Eluted Peak" INPUT K2 PRINT'Enter Diffusivity of 5olute in Mobile Phase'':INPUT Di PRINT'Enter Viscosity of Mobile Phase (Poises)".INPUT M PRINT” Enter Column Inlet Pressure (p.s i )“¦ INPUT P PRINT"BASIC CHROMATOGRAPHIC DATA"

PRlNT'Separation Ratio of the Critical Pair",A PRINT"Capacity Ratio of the First Peak of the Pair",ÊI PRINT'Capaeity Ratio of the Last Eluted Peak"K2 PRINT"Diffusivity of Solute in Mobile Phase"D1 PRINT'Viscosity of Mobile Phase (Poises)'M PRiNT"Column Inlet Pressure (p s.i.)"P LET N=( 16*( I+K1 Ã2)/(((À-1 Ã2)*(ÊÃ2))

LET R-( 16*( I+KI))*(((DI *M)/(3 142*P*68948&))'.5)/(KI *(A- I))

LET B=2*DIC=((f6*KMl*KI'2)*R~2)/(24*DI*(I+K1 )*2).U-(B/C)‘.5

LET L=N*2*(B*C)' 5 T=( 1 ¦K2)*L/U.Q=3.142*U*R‘2

LET V=((3 1416*0 7746*L*R'2)*( 1 +K2))/N'0 5

LET S=(.22*L*3 142*( I +K2)*R'2)/(N)' 5

PRINT "DESIGN SPECIFICATIONS"

PRINT "Optimum Column Radius" R "cm"

PRINT "Optimum Column Length" L 'em"

PRINT "Minimum Analysis Time" T "sec"

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