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

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LET X1 =2*L 1 *((3*6*( 1+K1)‘2)/(l+6*Kl-4 1*K1 ‘2))'.5+6

LET D2=R*( 1 +K.1 )*((M*D1 *X 1 /(35*P))*.5)/(K’ *(A- ’))

LET B=2*G*DI:A1 =2*L I*D2:C=(( 1 +6*K 1 ¦ 1 1 *K 1 '2)*D2~2)/(24*D1 *( 1+K1Ã2) LET H=AI+2*(B*Cy.5:U=(B/Cr.5:N=(4*( 1+K1 )/(Kl*(A-1 )))“2:L=N*H LET T=( I +K2)*L/U:R=(S/( 1,0053*E*H*( I+KI )*(N‘.5)))‘.5 LET 0= 188495i*E*U*R~2

209

LET Y=Q*T/60000!:V=3.12*S

LET JI =(2*K 1 *( A-1 ))/(2Æ 11 *A):J2=(2+ 3*K i -Ê i *A)/(2+K 1+K i *A)

LET J3=l -((K2*( 1+K1))/((1 +K2)*KI*(A-1 )K5)*(J I):

LET N1 =LOG(J3)/LOG(J2)

LPRINT “INSTRUMENT CONSTRAINTS"

LPRINT

LPRINT“Maximum Column Inlet Pressure ",P "p.s.i"

LPRINT“Extra Column Dispersion ",S “ul"

LPRINT“Multipath Packing Factor ",L I

LPRINTTongitudinal Diffusion Packing Factor ",G

LPRINTTolumnMobile Phase Fraction ",E

LPRINT

LPRINT "ELECTIVE VARIABLES"

LPRINT

LPRINT"5eparation Ratio of the Critical Pair “,A

LPRINT "Capacity Ratio of the First Peak of the Pair ",K1 LPRINT "Capacity Ratio of the Last Eluted Peak ",K2 LPRINT"Diffusivity of Solute in Mobile Phase ",DI“sq.cm per sec"

LPRINT "Viscosity of Mobile Phase (Poises) ",M "Poises

LPRINT

LPRINT "COLUMN SPECIFICATIONS"

LPRINT

LPRINT "OptimumColumn Radius LPRINT USING "****“; R,

LPRINT”cm"

LPRINT "OptimumColumn Length LPRINT USING "***** **;L,

LPRINT"cm"

LPRINT "Optimum Particle Diameter LPRINT USING -*****"; 20000 *D2,

LPRINT"um"

LPRINT

LPRINT "ANALYTICAL SPECIFICATIONS"

LPRINT

LPRINT "Minimum Analysis Time LPRINT USING "****** **,T,

LPRINT''sec"

LPRINT "Column Efficiency ",N

LKfMINI UplllllUIII Ã IUW ,

LPRINT USING “****"; Q,

LPRINT"um/min"

LPRINT "Maximum Sample Volume LPRINT USING ** ***"; V*IOOO,

210

LPRlNT"u!

LPRINT USING “****"¦' Y,

LPRINT“ml“

LPRINT “Peak Capacity LPRINT USING N1

If the program is run on a Macintosh computer, then it will start processing immediately. However, it will obviously not complete the program until the last entry is made (the value of the extra column dispersion). The data is entered sequentially on request from statements given on the computer screen. On completion, the results are sent to the printer and an example of a computer print out is given below

The Computer Report

PERFORMANCE CRITERIA

I/ A defined resolution must be obtained

2/ The analysis must be completed in the minimum time

3/ The analysis must be completed with the minimum solvent

"INSTRUMENT CONSTRAINT

Maximum Column Inlet Pressure Extra Column Dispersion Multipath Packing Factor Longitudinal Diffusion Packing Factor Column Mobile Phase Fraction

6000 p.s.i. 0.0025 ul

.5

.6

.65

"ELECTIVE VARIABLES''

"Separation Ratio of the Critical Pair "Capacity Ratio of the First Peak of the Pair

l.OI

2.5

5

"Capacity Ratio of the Last Eluted Peak "Diffusivity of Solute in Mobile Phase "Viscosity of Mobile Phase

0.000035 sq.cm per sec 0.023 Poises

COLUMN SPECIFICATIONS

Optimum Column Radius Optimum Column Length Optimum Particle Diameter

0.0197 cm 1577 cm 46.2um

211

ANALYTICAL SPECIFICATIONS

Minimum Analysis Time 306089 sec

Column Efficiency 313600

Optimum Flow-Rate I.47 ul/min

Maximum Sample Volume 8.59 ul

Solvent Consumption per Analysis 7.50 ml

Peak Capacity 251

Table 2 Design Data on a Series of Optimized Columns

Separation Ratio Particle Diameter (micron) Column Length (cm) Analysis Time Peak Capacity

1.006 38 5 7300 27.3 days 419

1.008 288 3079 8.6 days 314

1.010 23.1 1576 3.5 days 251

1.012 19.3 913 41 hrs 210

1.014 16.5 574 22 hrs 180

1.016 14.4 385 13 hrs 157

1.018 12.8 270 8.1 hrs 140

1.020 1 1.6 197 5.3 hrs 126

1.02 10.5 148 3.6 hrs 1 15

1.026 8.9 112 111.6 min 97

1.030 7.7 58.4 58.4 min 84

1.035 6.6 36.8 34.0 min 72

1.040 5.8 24.6 19 9 min 63

1.050 4.6 12.6 8.2 min 51

1.060 3.9 7.3 3.9 min 42

1.070 3.3 4.6 128 sec 36

1.080 2.9 3.1 74.7 sec 32

1.100 2.3 1.6 30.6 sec 26

1.120 1.9 0.9 14.8 sec 21

Note

k'=2.5, k’2=5, Diffusivity of solute =3.5XI0~5, viscosity=0.023 Poises X=0.5, Y=0.6,0=0.65 and extra column dispersion is taken as 0.0025 ö1

il ib üååï that uy the appropriate use of liquid chromatography column theory it is possible to design the optimum packed column for any specific separation. In the next chapter a similar procedure will be adopted to develop a regime for designing the optimum open tubular column. The

conditions used to obtain the data given in table 2 is fairly typical for most LC analyses of relatively small molecular weight substances. It is seen, that there is a limited range over which the operation of LC columns would be practical. A nine meter column, packed with 20 micron particles, would separate a critical pair with a separation ratio of only 1.012, but it would take 41 hours to complete an analysis. It is possible that there might be a sample of sufficient importance to spend this amount of time on the analysis, but it is more likely that the analyst would seek an alternative method. At the other extreme particles having diameters less than 3 micron, although available, are difficult to pack. Assuming that the practical peak capacity is about half the theoretical peak capacity, a column 3.1 cm long packed with particles 2.9 micron in diameter would separate a mixture containing about 16 components in just over 30 seconds This particular column is commercially available in close-to-optimized form (known colloquially as the 'three by three') and would probably be the most suitable for the rapid analysis of simple mixtures. The two other common, commercially available, particle sizes, 5 and 10 micron, should be packed into columns 12.6 and 148 centimeters long respectively for optimum performance. Such columns would provide a 'column family' for general use which would encompass the vast majority of LC applications that face the analyst today. It should be emphasized, however, that for a repetitive analysis that is repeated many times every day, as in a quality control laboratory, the construction of the fully optimized column that is specific for the particular analysis would always be economically worthwhile.

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