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liquid chromatography column - Scott R.P.W.

Scott R.P.W. liquid chromatography column - John Wiley & Sons, 2001. - 144 p.
Download (direct link): liquidchromatographycolumntheory2001.djvu
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PR
th ~ 31875-0.2P ................................................ (,4)
One further property of the preparative column is often required and that is its unpacked weight (W(coi)). This is simply given by,
Wcol - n((r0pt + th )2 Topt^ ) I opt
where (d) is the density of the column material and the other symbols have the meaning previously ascribed to them.
Taking the density of stainless steel to be 7.8g/ml and simplifying,
Wcol = 7.8 (2roPtth + th2) lopt .............................. 15)
250
The equation for the optimization of a preparative LC column can be summarized as follows.
PREPARATIVE COLUMN DESIGN EQUATIONS
Optimum Particle Diameter
dpfopt) -
8(1+ k)
k'(o -1)
21
3v(ukf
0.5
(l+6k' + 1 Ik'2)
+ Y
0.5
Optimum Column Length
4(1+~. (, + 6k+I ,k'2)
bpt - 2 -
k'(a-1)
2 +
,.\2
' ( 9 ^ 0.5 1
nDm 21 3y(i + k) + Y
/ (l+6k'+l ik'2) v' 4
05
The Minimum Analysis Time
\(8U+\<))
tmin - (1+)[^(
;(a- 1),
The Optimum Column Radius

^ n
21 +

v(l + 6k + 1 IK2)
05
3(1 + ' Y
r=
K(-0
x0.5
45.5 M
col
(1+')
2X+
(l+6k'+{ Ik'2)''
05
3(1 + k)
, \2
nDm

a
2X
^+
.9 V
05
(l+6k+1 Ik'5
+Y
0.5
oi
The Maximum Sample Volume
Vi = 10OM/to
The Optimum Flow-Rate
i3
Qopt
k'M)
4(1 + k*)
91M<pP
r|w( I + k')
2X +
(| + '+'2[
3(l + k')
05
The Solvent Consumption
V$ol =
The Column Wall Thickness
5824fl(l + k, cok'(a-1)
th =
PDn
2(SE + )
+ C
The Weight of the Column
Wcoi = 7.8 (2roptth + th2) lopt
THE USE OF THE DESIGN EQUATIONS
The design equations can be incorporated into a simple program to calculate the dimensions and properties of a preparative LC column, together with the optimum operating conditions that would allow the isolation of a specific mass of a solute from a given mixture in the minimum time. In a similar nidnner to the previous programs, this program has also been written in Microsoft Quick Basic that is appropriate for a Macintosh computer. The program can be easily modified to be suitable for other types of computers that, perhaps, use a different basic language. The program is not

sophisticated and not designed to be 'user friendly1 and thus, it is recommended that it be only used by someone with some knowledge of computer programming. The program can be entered as typed below, the interrogative procedure will be carried using the computer screen and when the run is complete the results will be printed as an output from the associated printer.
COMPUTER PROGRAM FOR PREPARATIVE COLUMN DESIGN
2 LPRINT
3 LPRINT
4 LPRINT
5 LPRINT PREPARATIVE COLUMN DESIGN FOR LC"
6 LPRINT
7 LPRINT
8 LPRINT"PERFORMANCE CRITERIA"
9 LPRINT
10 LPRINT" 1! A defined resolution must be obtained
11 LPRINT2/ The analysis must be completed in the minimum time "
12 LPRINT"3/ The analysts must be completed with the minimum solvent"
13 LPRINT
14 PRINTEnter Separation Ratio of Critical Pair( 1.05 or greater)":INPUT A
15 PRlNTTnter Capacity Ratio of the First Peak of the Pair'MNPUT I
16 PRINT'Enter Capacity Ratio of the Last Eluted Peak":INPUT K2
17 PRINT'Enter Diffusivity of Solute in Mobile Phase'':INPUT D1
18 PRINT''Enter Viscosity of Mobile Phase (Poises)":INPUT M
22 PRINT" Enter Minimum Column Inlet Pressure (p.s.i.)":INPUT PI
23 PRINT" Enter Maximum Column Inlet Pressure (p.s.i.):INPUT P2
24 PRINT" Enter Column Pressure Increment (p.s.i.)":INPUT P3
25 PRINT" Multipath Packing Factor:!NPUT LI
30 PRINT" Longitudinal Diffusion Packing Factor":INPUT G
31 PRINT" Column Mobile Phase Fraction":lNPUT E
32 PRINT" Column Load (gram):INPUT Ml
33 PRINT" Sample Concentration %w/v:INPUT F
37 T9= 1000000000*:D9=0:L9=0:R9=0
38 FOR P=P1 TO P2 STEP P3
39 PRINT A,P,T9
50 LET XI =2*L 1 *((3*G*( 1+K1 )2)/( 1 +6*K 1 II *K I *2))'.5+G 60 LET D2=8*( I+K1 )*((M*DI *X1 /(35*P))*.5)/(K1 *(A-1))
70LETB=2*G*DI
75 LET Al =2*L i*D2:C=(( 1+6*K1 + I I*K1"2)*D2'2)/(24*D1*( 1+KI 2)
80 LET H=Al + 2*(B*Cr.5:U=(B/C)".5:N=(4*( 1+K1 )/(1*(-1 )))2:L=N*H
90 LET =( I +K2)*L/U R=((28.93*M I *(N'5))/(L*E*F*( I+KI ))Y 5 V=! OWi I /F
100 IF D2< 0005 THEN 180
110 IF D2> .01 THEN 180
120 IF L<5 THEN 180
130 IF L> 150 THEN 180
140 IF L/R< 1 THEN 180
150 IF T<60 THEN 180
160 IF T>3600 THEN 180
165 IF T>T9 THEN 180
170 LET D9=D2:L9=L:T9=T:R9=R:P9=P.V9=V
171 LET TH=P9*R9/(31875-.2*P9): Q= 188.5*E*R"2*U
172 LET W= 49*TH*( R9+TH/2 )*L9: Y=0*T9/60 180 NEXT P
260 LPRINT "INSTRUMENT CONSTRAINTS
270 LPRINT 280 LPRINT
290 LPRINT" Inlet Pressure ",P9"p s i"
300 LPRiNTMaxirriurn Column Load ".'"
310 LPRINT 'Multipath Packing Factor ,L1
320 LPRINTLongitudinal Diffusion Packing Factor "fi
330 LPRINT"Column Mobile Phase Fraction ",E
340 LPRINT
350 LPRINT "ELECTIVE VARIABLES"
360 LPRINT
370 LPRiNT"Separation Ratio of the Critical Pair \A
380 LPRINT "Capacity Ratio of the First Peak of the Pair ",KI
390 LPRINT "Capacity Ratio of the Last Eluted Peak ",K2
395 LPRINT"Sample Concentration %w/v .F
400 LPRINT"Diffusivity of Solute in Mobile Phase ",Dl"sq.cm per
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