optimization of temperature-programmed gas chromatographic

8/10/2019 Optimization of Temperature-programmed Gas Chromatographic

1/9

E L S E V I E R

Journal of Chromatography A , 756 (1996) 175-183

JOURN L OF

CHROM TOGR PHY

O ptim ization of temp erature programm ed gas chrom atographic

separations

II. O ff l ine Sim plex optim ization and colum n select ion

H e n r i S n i j d e r s , H a n s - G e r d J a n s s e n , C a r e l C r a m e r s

Laboratota ~f bzs trumental Ana lys is , D epa rtmen t ~[ Chemical Engineer ing, Eindhoven Univers ity o f Technology, P .O. Box 513, 5600

MB Eindhoven, Nether lands

Received 3 May 1996: revised 9 July 1996; accepted 15 July 1996

A b s t r a c t

I n th i s w o r k a m e t h o d i s d e s c r i b e d w h i c h a l l o w s o f f - l i n e o p t i m i z a t i o n o f t e m p e r a t u r e - p r o g r a m m e d G C s e p a r a ti o n s . T h e

m e t h o d i s b a s e d o n a n e w n u m e r i c a l m e t h o d t h a t a l lo w s t h e o f f - l i n e p re d i c t i o n o f r e te n t i o n t i m e s a n d p e a k w i d t h s o f a

m i x t u r e c o n t a i n i n g c o m p o n e n t s w i t h k n o w n i d e n t it i e s in c a p i ll a r y G C . I n t h e p r e s e n t w o r k w e a p p l y t h i s m e t h o d f o r o f f - l i n e

o p t i m i z a t i o n o f s i n g l e - a n d m u l t i - r a m p t e m p e r a t u r e - p r o g r a m m e d G C s e p a r at i o n s. F i rs t , it w il l b e s h o w n h o w t h e n u m e r i c a l

m e t h o d s a r e i n c o r p o r a t e d i n a S i m p l e x o p t i m i z a t i o n m e t h o d . N e x t , i t i s d e s c r i b e d h o w t h e m e t h o d c a n b e u s e d t o d e t e r m i n e

t h e o p t i m a l t e m p e r a t u r e p r o g r a m f o r t h e s e p a r a ti o n o f a m i x t u r e c o n t a i n i n g c o m p o n e n t s o f d i f f e r e n t f u n c ti o n a l it i e s . F i n a l ly ,

i t i s s h o w n t h a t t h e o p t i m i z a t i o n s t r a t e g y f o l l o w e d h e r e a l l o w s s e l e c t i o n o f t h e c a p i l l a r y c o l u m n m o s t s u i t e d f o r t h e

s e p a r a t io n p r o b l e m u n d e r s t u d y f r o m a g i v e n s e t o f c ap i l l a ry c o l u m n s c o n t a i n i n g t h e s a m e s t a ti o n a r y p h a s e a n d v a r y i n g i n n e r

d i a m e t e r s a n d f i lm t h i c k n e ss e s . T h e p r o c e s s c a n b e p e r f o r m e d w i t h o u t a n y e x p e r i m e n t a l e f f o rt . T h e r e s u l t s i n d i c a te t h a t f u l ly

o f f - l i n e s i m u l a t i o n a n d o p t i m i z a t i o n o f s i n g l e - a n d m u l t i - r a m p t e m p e r a t u r e - p r o g r a m m e d G C s e p a r a t i o n s a s w e l l a s c o l u m n

se l ec t i on i s poss ib l e .

K e v w o r d s

Simplex optimization; Temperature-programming; Optimization; Column selection; Capillary columns; Chemo-

metrics

1 I n t r o d u c t i o n

In a prev ious a r t ic le [1] we desc r ibed a numer ica l

me th o d to p r e d i c t ( t r u ly o f f - l i n e ) l i n e a r t e mp e r a tu r e -

p r o g r a mme d r e t e n t i o n t ime s a n d p e a k w id th s f o r

mix tu r e s c o n t a in in g c o mp o n e n t s w i th k n o w n id e n -

t i t i e s i n c a p i l l a r y G C . T h e p r o c e d u r e i s b a se d o n

Corresponding author.

e x t r a c t i n g t h e r mo d y n a mic v a lu e s ( e n t r o p y a n d e n -

th a lp y t e r ms ) f r o m p u b l i sh e d K o v f i ts re t e n t i o n i n -

d i c e s . A n u me r i c a l me th o d w a s d e v e lo p e d , t h a t u se s

th e se t h e r mo d y n a mic v a lu e s t o c a l c u l a t e l i n e a r ( s i n -

g l e o r m u l t i - r a m p ) t e m p e r a t u r e - p r o g r a m m e d r e t e n -

t i o n t ime s a n d p e a k w id th s o n a n y c a p i l l a r y G C

c o lu mn c o n ta in in g t h e s a me s t a t i o n a r y p h a se b u t

wi th a d i f fe ren t phase ra t io and/or length . In shor t ,

t h e n u m e r i c a l a p p r o a c h mo d e l s t h e so lu t e s c h r o -

ma to g r a p h ic p r o c e s s i n to v e r y sma l l s e g me n t s o f

e q u a l t ime . F o r e v e r y t ime in t e r v a l t h e v a r io u s

0021-9673/96/ 15.00 19 96 Elsevier Science B.V. All rights reserved

P l l S 0 0 2 1 - 9 6 7 3 ( 9 6 ) 0 0 6 2 6 - 7


2/9

1 7 6

H. Snijders et al, / J. Chromatogr. A 756 1996) 1 75- 183

c h r o ma to g r a p h i c p a r a me te r s a r e c a l c u l a t e d , b a s e d o n

a m o d e l d e v e l o p e d f r o m s o u n d c h r o m a t o g r a p h i c

theory . Re ten t ion t imes a re ca lcu la ted f rom loca l

r e t e n t i o n f a c to r s a n d t h e p r e s s u r e a n d t e mp e r a tu r e

cor rec ted loca l ve loc i ty in eve ry t ime in te rva l . Ana l -

o g o u s ly , p e a k w id th s a r e c a l c u l a t e d f r o m lo c a l p l a t e

h e ig h t s ( d e r i v e d f r o m th e w e l l - k n o w n G o la y e q u a -

t i o n ) i n e v e r y s e g me n t . D u r in g t h e c a l c u l a t i o n s

p h y s i c a l mo d e l s a n d a p p r o x ima t io n s a r e u s e d t o

obta in v iscos i ty and d i f fus ion da ta .

A p a r t f r o m th e t h e r mo d y n a mic q u a n t i t i e s a n d t h e

s o lu t e s mo le c u l a r f o r mu la , t h e o n ly a d d i t i o n a l i n p u t

p a r a me te r s n e e d e d f o r t h e p r e d i c t i o n s a r e t h e c o l -

u mn c h a r a c t e r i s t i c s ( d ime n s io n s a n d c o a t i n g e f -

f ic iency) , the ca r r ie r gas type and seve ra l in -

s t r u me n ta l p a r a me te r s s u c h a s t h e t e mp e r a tu r e p r o -

g r a m a n d t h e c o lu mn d e a d t ime o r i n l e t p r e s s u r e .

I n t h e t e m p e r a t u r e - p r o g r a m m e d m o d e a w i d e t e m -

p e r a tu r e r a n g e i s a l l o w e d a n d i s o th e r ma l p l a t e a u s

c a n b e i n c lu d e d i n t h e p r o g r a m. A n a t t r a c t i v e

f e a tu r e o f th e a p p r o a c h i s t h a t, o n c e t h e t h e r mo -

d y n a mic v a lu e s o f t h e s o lu t e s o f i n t e r e s t a r e

k n o w n , t h e y c a n b e s t o r e d i n a d a t a b a s e a n d f u tu r e

p r e d i c t i o n s c a n b e p e r f o r me d w i th o u t t h e n e e d t o

p e r f o r m n e w e x p e r ime n ta l i n p u t r u n s .

I n t h e p r e s e n t w o r k w e a p p ly t h i s n e w n u me r i c a l

me th o d t o o f f - l i n e o p t imiz a t i o n o f t e mp e r a tu r e - p r o -

g r a mme d G C s e p a r a t i o n s , w h e r e w e d e f in e t h e t e r m

o p t imiz a t i o n a s a c h i e v in g b a s e l i n e r e s o lu t i o n i n t h e

s h o r t e s t p o s s ib l e a n a ly s i s t ime . T h e u l t ima t e g o a l o f

t h e w o r k i s t o d e v e lo p a n o p t imiz a t i o n s t r a t e g y t h a t

does not r equi re any exper imenta l input run . In o the r

w o r d s , a me th o d t h a t e n a b l e s t r u ly o f f - l i n e o p t imi -

za t ion . F i r s t , i t wi l l be shown how the numer ica l

me th o d s f o r r e t e n t i o n t ime a n d p e a k w id th p r e d i c t i o n

p r e v io u s ly d e v e lo p e d a r e i n c o r p o r a t e d i n a S imp le x

o p t imiz a t i o n me th o d . N e x t , i t i s d e s c r i b e d h o w th e

me th o d c a n b e u s e d t o d e t e r min e o f f - l i n e t h e o p t ima l

( e i t h e r s i n g l e - o r mu l t i - r a mp ) t e mp e r a tu r e p r o g r a m

f o r t h e s e p a r a t i o n o f a mix tu r e c o n t a in in g c o m-

ponents of d i f f e ren t func t iona l i t ie s . F ina l ly , i t i s

s h o w n th a t t h e o p t imiz a t i o n s t r a t e g y f o l l o w e d h e r e

a l l o w s s e l e c t i o n o f t h e c a p i l l a r y c o lu mn mo s t s u i t e d

f o r t h e s e p a r a t i o n p r o b l e m u n d e r s t u d y , f r o m a g iv e n

s e t o f c a p i l l a r y c o lu mn s c o n t a in in g t h e s a me s t a t i o n -

a r y p h a s e b u t w i th v a r y in g p h a s e r a t i o s a n d /o r

lengths .

2. T h e o r y

2 .1 . C h r o m a t o g r a p h i c r e s p o n s e f u n c t i o n

S u c c e s s f u l a p p l i c a t i o n o f a n o p t imiz a t i o n p r o c e s s

i s p r e c e d e d b y c a r e f u l s e l e c t i o n o f t h e q u a n t i t y

( r e s p o n s e f a c to r ) t o b e o p t imiz e d . F o r c h r o ma to -

g r a p h i c s e p a r a t i o n s t h e ma in p r o b l e m l i e s i n p r o p e r

c o n v e r s io n o f t h e r e te n t i o n t ime s a n d p e a k w id th s o f

a l l r e l e v a n t c h r o ma to g r a p h i c p e a k s i n to a s i n g l e

n u mb e r w h ic h a c c u r a t e ly r e f l e c t s t h e o p t imiz a t i o n

c r i t e r i u m. S e v e r a l a u th o r s h a v e r e c o g n i z e d a n d d i s -

c u s s e d th i s p r o b l e m [ 2 - 4 ] a n d m a n y c h r o m a t o g r a p h -

i c r e s p o n s e f u n c t i o n s ( C R F ) h a v e b e e n s u g g e s t e d . I n

th i s w o r k w e a d o p t e d t h e C R F u s e d b y D o s e [ 5 ] . F o r

a g iv e n c h r o ma to g r a m th e C R F v a lu e c a n b e c a l c u -

l a t e d f r o m:

C R F + ~ e

e~ ~.r

(1)

t R c r i t i~i

w h e r e

tR

i s the r e ten t ion t ime of the la s t - e lu t ing

peak , tR ,~r~, i s a u se r - se lec ted t im e-cos t w e ight ing or

c o m p r o m i s e f a c t o r a n d

R~.cr~

i s a use r - se lec ted

reso lu t ion ta rge t va lue . R ~ j i s t he r e s o lu t i o n b e tw e e n

pea k i and j which i s de f ined a s:

AtR .~ i

R ~ ~ -

2 ( ~ + ) ( 2 )

w h e r e

A t R ~ j

i s the r e ten t ion t ime d i f f e rence (ex-

pressed pos i t ive ) be tween pe ak i and j . ~ and ~ a re

th e s t a n d a r d d e v i a t i o n s o f p e a k i a n d p e a k j , r e s p e c -

t ive ly .

F r o m E q . ( 1 ) i t c a n b e s e e n t h a t b o th a n a ly s i s time

a n d r e s o lu t i o n a r e i n c o r p o r a t e d i n t h e C R F . Mo r e -

over , a l l poss ib le peak- to-peak in te rac t ions a re in -

c lu d e d . T h e o c c u r r e n c e o f o v e r l a p p in g p e a k s i s

s t r o n g ly d i s c o u r a g e d . A d d i t i o n a l ly , i t e mp h a s i z e s t h e

l e a s t re s o lv e d p e a k p a i r s w i th o u t t o t a l l y i g n o r in g t h e

o th e r p e a k p a i r s. F u r th e r m e r i t s o f t h e C R F u s e d h e r e

a r e e x t e n s iv e ly d i s c u s s e d b y D o s e [ 5 ] .

2.2.

O p t i m i z a t i o n a l g o r i t h m

T h e o p t imiz a t i o n p r o c e d u r e u s e d i n t h i s w o r k i s

t h e Mo d i f i e d S imp le x Me th o d ( MS M) a s d e s c r i b e d


3/9

H . S n i jd e r s et a l . / J . C h r o m a t o g r . A 7 . 56 1 9 9 6 ) 1 7 5 - 1 8 3 1 7 7

b y N e ld e r a n d Me a d [ 6 ] . S u c c e s s f u l a p p l i c a t i o n o f

t h e S i m p l e x m e t h o d f o r t h e o p t i m i z a t i o n o f G C

s e p a r a t i o n p r o b l e m s w a s d e m o n s t r a t e d b y s e v e r a l

au thors , e .g . [5 ,7] . In th is sec t ion i t wi l l be shown

h o w th e n u me r i c a l me th o d s p r e v io u s ly d e r i v e d f o r

t h e c a l c u l a t i o n o f r e t e n t i o n t ime s a n d p e a k w id th s i n

t e m p e r a t u r e - p r o g r a m m e d G C s e p a ra t io n s [1 ] a re

in c o r p o r a t e d i n a n MS M f o r t h e p u r p o s e o f o f f - l i n e

o p t i m i z a t i o n o f t e m p e r a t u r e - p r o g r a m m e d G C s e p a -

r a t i o n s . Mo r e o v e r , i t w i l l b e s h o w n h o w th e s t r a t e g y

f o l l o w e d h e r e a l l o w s s e l e c t i o n o f t h e c a p i l l a r y

c o lu mn mo s t s u i t e d f o r a g iv e n s e p a r a t i o n p r o b l e m

f r o m a s e t o f a v a i l a b l e c o lu mn s . T h e d i s c u s s io n o f

t h e v a r i o u s imp o r t a n t a s p e c t s o f t h e o p t imiz a t i o n

p r o c e s s i s g u id e d b y t h e o v e r a l l o p t imiz a t i o n a lg o -

r i thm, presented in F ig . 1 .

P r io r t o s t a r t i n g t h e o p t imiz a t i o n , i t mu s t b e

d e c id e d w h ic h p a r a me te r s a r e t o b e o p t imiz e d .

N o r ma l ly o n ly t h o s e f a c to r s a r e i n c lu d e d w h ic h

e x h ib i t th e l a r g e s t imp a c t o n t h e C R F th e q u a n t it y

to b e o p t imiz e d ) . F o r t h e ma jo r i t y o f G C s e p a r a t i o n s

th e t e mp e r a tu r e - p r o g r a mmin g r a t e i s t h e d e c i s i v e

p a r a me te r i n o r d e r t o a t t a i n t h e u l t ima t e s e p a r a t i o n

g o a l . A p a r t f r o m th e p r o g r a mmin g r a t e , a l s o o th e r

imp o r t a n t p a r a me te r s s u c h a s e . g . t h e i n i t i a l o v e n

t e mp e r a tu r e , c a n b e i n c lu d e d i n t h e o p t imiz a t i o n .

W i th t h e p r e s e n t a l g o r i t h m th e n u mb e r o f d ime n s io n s

to b e o p t imiz e d c a n b e f u l l y u s e r - s e l e c t e d . T h i s

me a n s t h a t t h e o p t imiz a t i o n c a n b e p e r f o r me d f o r

s i n g l e - a n d / o r m u l t i - r a m p t e m p e r a t u r e - p r o g r a m m e d

s e p a r a t i o n s e i t h e r w i th o r w i th o u t t h e i n c o r p o r a t i o n

of i so the rma l p la teaus . In f ac t , a l l va r iab les which

d e s c r ib e a G C t e mp e r a tu r e p r o g r a m c a n b e i n c lu d e d

a s o p t imiz a t i o n p a r a me te r s . P a r a me te r s w h ic h a r e n o t

inc luded in the opt imiza t ion a re he ld cons tan t .

As a l r eady ment ioned in the in t roduc t ion , the

p r ima r y g o a l o f t h e w o r k p r e s e n t e d h e r e i s t o a t t a i n

t r u ly o f f - l i n e o p t imiz a t i o n s . D u r in g t h e o p t imiz a t i o n

ca lcu la t ions the mean l inea r ve loc i ty a t the in i t ia l

o v e n t e mp e r a tu r e w a s k e p t c o n s t a n t . H e n c e , t h e

n u me r i c a l me th o d s a p p l i e d h e r e r e q u i r e a r e p r e s e n t a -

t i v e v a lu e f o r t h e me a n l i n e a r v e lo c i t y . T h i s v a lu e

w a s e s t i m a t e d f o r a g i v e n c o m b i n a t i o n o f c o l u m n

in n e r d i a me te r a n d c a r r i e r g a s t y p e u s in g T a b l e 1 .

T h i s t a b l e i s c o mp i l e d b y u s in g t h e c o mp u te r p r o -

g r a m d e s c r i b e d i n [ 8 ] . W i th t h e v a lu e f r o m th e t a b l e

a n d g iv e n t h e in i ti a l o v e n t e mp e r a tu r e d e t e r min e d

n o

y e s

I n p u t d a t a

1 ) C o l u m n l i s t

- c o l u m n ( s ) d i m e n s i o n s

- s t a ti o n a r y p h a s e t y p e

- c a r r i e r g a s

- c o a t i n g e f f i c i e n c y

2 ) C o m p o n e n t l i s t

- e n t h a l p y / e n t r o p y - t e r m

- m o l e c u l a r f o r m u l a

R e a d c o l u m n d a t a

Rea d m ea n l i n ea r v e lo c it y

( T a b l e I )

S e l ec t s i m p l ex

- p a r a m e t e r s

- b o u n d a r i e s

- r e a d s e t f i x e d v a l u e s

rea t e s i m p l ex

R e a d c o m p o n e n t d a t a

a l cu l a t e t a ~

I a l o u l a t e I

~ O p t i m u m

, ~

M o r e c o l u m n s

[ S e l e c t b e s t c o l u m n [

end

n o

F i g . 1 . O v e r a l l a l g o r i t h m o f t h e o p t i m i z a t i o n p r o c e d u r e .

b y t h e v e r t e x d a t a ) , t h e c o r r e s p o n d in g c o lu mn d e a d

t ime a n d r e q u i r e d i n l e t p r e s s u r e c a n b e c a l c u l a t e d

u s in g t h e a p p r o a c h d e s c r i b e d i n p a r t I o f t h i s w o r k

[ 1] . T h i s me a n s t h a t d u r in g t h e e x e c u t i o n o f th e

o p t imiz a t i o n n o e x p e r ime n ta l d a t a h a v e t o b e a c -


4/9

1 7 8 H. Snijders et al. / J. Chromatogr. A 756 1996) 175-18 3

T a b l e 1

E s t i m a t e d m e a n l i n e a r v e l o c i t i e s [8 ] a s a f u n c t io n o f c o l u m n

d i a m e t e r a n d c a r r i e r g a s t y p e

C o l u m n i n n e r d i a m e t e r ( ~ m ) M e a n l i n e a r v e l o c i t y ( c m s )

C a r r i e r g a s t y p e

H 2 H e N 2

1 5 0 3 2 0 5 5 - 4 5 4 0 - 3 3 1 7 1 2

3 2 1 - 5 5 0 4 5 - 2 8 3 3 - 2 5 1 2 - 7

T h e v a l u e s f o r t h e m e a n l i n e a r v e l o c i t ie s a re r e t r i e v e d f r o m t h e

t a b l e b y l i n e a r i n t e r p o l a t io n b e t w e e n t h e i n d i c a t e d c o l u m n d i a m e -

t e r s .

quired, which satisfies our goal of truly off-line

optimization.

An other important aspect to be addressed are the

constraints which have to be put on the variables to

be optimized. Often, those boundaries are dictated by

the chromatographic equipment used. As an exam-

ple, contemporary gas chromatographs have limited

maximum programming rates. Moreover, the maxi-

mum and minimum allowable operating temperatures

of the separation column are limited. Also parameter

values that would lead to highly undesirable results

such as too low a programming rate or too low an

initial oven temperature can be excluded from the

factor space. By taking those limitations into ac-

count, the factor space can thus be adapted to

practical and/or experimental considerations. The

simplex is held within the boundaries by assigning

unfavourable (very high) CRF values to vertices

which fall outside the factor space.

The location of the initial simplex should be

carefully chosen. The classical problem associated

with Simplex optimizations is that the final optimum

may not be the global optimum but a local optimum

with a less desirable response (in this case a less

desirable CRF value). For GC optimizations conver-

gence to a local optimum can easily occur when e.g.

peak orders change under temperature-programmed

conditions. To locate the optimum which yields the

shortest possible analysis time (while maintaining

baseline resolution), the initial simplex is selected

near the upper or lower boundaries of the factor

space. In case of a three-factor optimization this

could mean that the initial simplex is located close to

the maximum allowable programming rate and initial

temperature and close to the minimum allowable

time for an isothermal plateau.

Once the initial simplex is determined, the optimi-

zation procedure proceeds as follows. Given the

conditions specified by the factors of each vertex of

the initial simplex, the retention times and peak

widths for each component are calculated by using

the numerical procedures. For this purpose the

entropy and enthalpy term and the molecular formula

for each component must be known. The calculated

peak data are than used to calculate the CRF for each

vertex. The optimization continues by rejecting the

vertex with the least desirable response followed by

determination of the next simplex, guided by the

Modified Simplex algorithm (note that a high CRF

value indicates a low response ). The process is

ended when the step size of each factor to be

optimized is less than a preselected maximum allow-

able difference. This value is usually given by the

accuracy of the instrumentation for each individual

factor.

The process described above is restarted when the

optimal chromatogram should be predicted for

another column, with a different phase ratio and/or

length, until all column data are processed. Finally,

comparison of the results yields the column ex-

hibiting the lowest analysis time (indicated by the

retention time of the last-eluting component) for the

given separation problem. Here it should be realized

that in practical situations the final selection of the

column most suited for the separation problem under

study can also be guided by additional practical

considerations such as e.g. the oven cooling down

time.

3 Experimental

3 1 Instrumentation

GC was performed on an HP 5890 gas chromato-

graph equipped with a split-splitless injector and a

flame ionization detection (FID) system (Hewlett-

Packard, Wilmington, DE, USA). The columns used

in this study are indicated in Table 2. Columns A, B

and D are coated with 100% methyl silicone, HP-1

(Hewlett-Packard). Column C is coated with 100%

methyl silicone, CP-Sil 5 CB (Chrompack, Middel-


5/9

H. Snijders et al. / J. Chromatogr. A 756 1996) 1 75-183 179

T a b l e 2

D i m e n s i o n s o f t h e c o l u m n s u s e d i n t h is s t u d y

S y m b o l L (m ) d (~ xm ) d ~ (~ m ) / 3

A 2 5 3 2 0 0 .5 2 1 53

B 2 5 3 2 0 0 .1 7 4 7 0

C 2 5 2 5 0 0 .2 5 2 5 0

D 2 5 2 0 0 0 .3 3 2 6 4

L - c o l u m n l e n gt h ; d e = c o l u m n d i am e t e r; d , = s t at io n a r y p h a s e

f i l m t h i ck n ess ; / 3 co l u m n p h ase ra t i o . A l l co l u m n s a re co a t ed

w i t h 1 0 0 m e t h y l s i l i co n e .

b u r g , T h e N e th e r l a n d s ) . I n j e c t i o n s w e r e p e r f o r me d i n

the sp l i t mode ( sp l i t r a t io 1 :100) to min imize in-

j e c t i o n b a n d b r o a d e n in g . T h e i n s t r u me n t w a s o p e r -

a t e d i n t h e c o n s t a n t p r e s s u r e mo d e . I n e x p e r ime n ta l

v e r i f i c a t i o n s o f p r e d i c t e d o p t ima l c h r o ma to g r a ms ,

t h e o p t ima l c o lu mn d e a d t ime , r e p o r t e d a f t e r t h e

o p t imiz a t i o n , w a s s e t o n t h e i n s t r u me n t b y a d ju s t i n g

th e c a r r i e r g a s ( h e l i u m) p r e s s u r e t o t h e c o r r e s p o n d in g

va lue v ia me thane in jec t ions . Both in jec tor and

d e t e c to r t e mp e r a tu r e w e r e h e ld c o n s t a n t a t 3 0 0 C

d u r in g t h e e x p e r ime n ta l w o r k . T h e d e t e c to r ma k e - u p

g a s f l o w - r a t e ( n i t r o g e n ) w a s ma in t a in e d a t 3 0 ml

r a in t . A n O m e g a d a t a s y s t e m ( P e r k in - E lme r , N o r -

w a lk , C T , U S A ) w a s u s e d f o r d a t a a c q u i s i t i o n a n d

p r o c e s s in g .

3 . 2 . C a l c u l a t i o n s

D u r in g t h e s imu la t i o n s n o c o r r e c t i o n f o r t h e

c o lu mn c o a t i n g e f f i c i e n c y w a s a p p l i e d . F o r t h e

c a l c u l a t i o n s i t w a s a s s u me d t h a t t h e c o lu mn o u t l e t

pressure equa ls 100 kPa (abs . ) . The s tepwidth At was

1 0 0 0 ms [ 1 ] . T h e ma x imu m a l l o w a b le d i f f e r e n c e f o r

the f ac tor s i s I C for tem pera tu res and 0 .1 C ra in 1

f o r t e mp e r a tu r e p r o g r a mmin g r a t e s . F o r C R F c a l c u -

la t ions ,

R~ ~ri~

and tR,cr it are s e t to 1.5 and 20 ra in

r e s p e c t i v e ly . A l l c o mp u ta t i o n s w e r e c a r r i e d o u t o n a

4 8 6 - D X 2 / 6 6 M H z p e r s o n a l c o m p u t e r . S o f t w a r e w a s

wr i t ten in Turbo Pasca l 6 .0 (Bor land , USA) . A

c o mp le t e o p t imiz a t i o n f o r o n e c o lu mn t a k e s a b o u t 1 5

ra in . Da ta en t ry i s a r ranged through f i led input .

3 . 3 . T e s t m i x t u r e

T o d e t e r min e t h e a p p l i c a b i l i t y o f th e o p t imiz a t i o n

a p p r o a c h p r e s e n t e d a b o v e , a t e s t mix tu r e w a s c o r n -

p i l e d , c o n t a in in g s i x t e e n c o mp o n e n t s o f d i f f e r e n t

f u n c t i o n a l i t y , p - C h lo r o to lu e n e ,

s e c . - b u t y l b e n z e n e

d ip h e n y l e t h e r , a n th r a c e n e , p y r e n e a n d h e x a d e c e n e

w e r e p u r c h a s e d f r o m J a n s s e n C h imic a ( G e e l , B e l -

g iu m) . Me th y l e s t e r s o f my r i s t i c a c id , p a lmi t i c a c id

a n d o l e i c a c id w e r e o b t a in e d f r o m P o ly s c i e n c e

C o r p o r a t i o n ( I L , U S A ) . n - U n d e c a n e , n - u n d e c e n e , n -

t r i d e c a n e a n d n - t e t r a d e c a n e w e r e p u r c h a s e d f r o m

Me r c k ( D a r ms t a d t , G e r ma n y ) . 1 - C h lo r o t e t r a d e c a n e

w a s o b t a i n ed f r o m H u m p h r e y W i l k in s o n ( C T , U S A )

a n d n a p h th a l e n e a n d q u in o l i n e f r o m A ld r i c h ( B o r -

nem, Be lg ium) . The pur i ty of a l l ana ly te s was a t

leas t 98 . The so lven t used to prepa re the mixture

w a s a n a ly t i c a l g r a d e n - h e x a n e ( Me r c k ) .

T h e e n t r o p y a n d e n th a lp y t e r ms o f t h e t e st c o m-

ponents were obta ined f rom Ref . [1] . For te s t

c o mp o n e n t s f o r w h ic h n o d a t a w e r e a v a i l a b l e t h e

e n t r o p y a n d e n th a lp y t e r ms w e r e e x p e r ime n ta l l y

es tab l i shed .

4 R e s u l t s a n d d i s c u s s i o n

T o d e mo n s t r a t e t h e a p p l i c a b i l i t y o f t h e n o v e l

o p t imiz a t i o n a p p r o a c h , o p t imiz a t i o n s o f t h e t e s t

mix tu r e w e r e p e r f o r me d f o r a l l c o lu mn s . I d e a l l y , t h e

o p t imu m lo c a t e d b y t h e S imp le x p r o c e d u r e s h o u ld b e

th e g lo b a l o p t imu m. T o c h e c k w h e th e r t h e p r e d i c t e d

o p t imu m e q u a l s t h e g lo b a l o p t imu m, d e t a i l e d k n o w l -

e d g e o f th e r e s p o n s e s u r f a c e s h o u ld b e a v a i l a b l e . F o r

a tw o - f a c to r o p t imiz a t i o n t h e r e s p o n s e s u r f a c e c a n b e

graphica l ly r epresented by e .g . a contour p lo t . In F ig .

2 . the ca lcu la ted re sponse sur faces for the sepa ra t ion

o f t h e t e s t mix tu r e o n a l l c o lu mn s a r e p r e s e n t e d . T h e

tw o f a c to r s p lo t t e d a r e th e i n i t ia l c o lu m n t e m p e r a tu r e

a n d t h e o v e n p r o g r a m m i n g r a t e . T h e C R F v a l u e s

w e r e c a l c u l a t e d o f f - l i n e b y u s in g t h e n u me r i c a l

me th o d s . I n t h e c o n to u r p lo t s t h e i s o - r e s p o n s e ( i s o -

C R F ) p o in t s a r e c o n n e c t e d b y l i n e s . F r o m th e f i g u r e

i t can be seen tha t in a l l p lo ts seve ra l loca l op t ima

c a n b e o b s e r v e d . T h i s o c c u r s e . g . w h e n p e a k o r d e r s

c h a n g e d u r i n g t e m p e r a t u r e p r o g r a m m i n g . C l o s e l y

lo c a t e d o p t ima a r e o b s e r v e d w h e n t h e g a in i n

a n a ly s i s t ime b y s t a r t i n g t h e t e mp e r a tu r e p r o g r a m a t

a h ighe r in i t ia l tempera ture i s pa r t ia l ly of f se t by a

d e c r e a s e i n t h e p r o g r a mmin g r a t e . T h i s l e a d s t o o n ly

min o r d i f f e r e n c e s i n t h e c h r o ma to g r a p h i c s e p a r a t i o n


6/9

1 8 0

H. Snijders et al. / J. Chromatogr. A 756 1996) 17 5-1 83

C o l u m n C o l u m n B

25

o

' i 1 5

lO

5

2 5

o

50 7 '5 150 125 150 5 50 75 100

Ini t i a l empera ture C)

15 150


C o l u m n C C o l u m n D

25

'~. 20

i 15

1o

5 5 0 1 5 0

7~5 100 125


,=

J

5 o 7 5 t 6 0 l ~ 5

In i t i a l empera ture C)

t~o

Fig. 2. Iso-response plots of the separation of the test mixture on all four the columns.Parameters included n the optimizationare the initial

oven temperature and the programming rate. The optima found by the corresponding Simplex optimizationare indicated by the cross. The

temperature programs located by the optimizationare for column A: 100C ~ 13.0C rain ~ --- 300C; column B: 108C ~ 10.3C min

---+ 300C; column C: 97C ~ 20.4C min ~ -4 300C; column D: 108C -- 13.7C min ~ --~ 300C.

and/ or analysis time. The corresponding CRF values

are nearly equal.

In parallel, the corresponding two-factor Simplex

optimization was performed for the test components

for all columns. The parameters plotted in the

contour plots were now optimized by using the novel

optimization approach. No initial hold time was

used. The final optima, located by the optimization,

are indicated in the contour plots of Fig. 2 as well.

From the figure it can be seen that the opti ma located

in all cases equal the global optima.

To verify the resemblance between predicted and

experimental optimal chromatograms, the test mix-

ture was analyzed under the conditions determined

by the values of the optimum for each column. The

results of these measu rement s are presented in Fig. 3.

The figure clearly shows that for all columns the

experimental and predicted chromatograms are very

similar. In the chromatograms several critical peak

pairs can be distinguished. The experimental data

corresponding to the optimization on column C and

D reveal partial peak overlap for the second critical

peak pair. Due to the smaller inner diameter of these

columns, compared to columns A and B, injection

band broadening becomes more critical and is proba-

bly responsible for the partial peak overlap observed.


7/9

H. Snijders et al. / J. Chromatogr. A 756 1996) 175- 183

1 8 1

, 1

0

C o l u m n C o l u m n

B

I L I L J l 11

,~ t 2 (5 o.oo 230 5.bo 7.~o

Time (rain) Time (min)

I 1 1

10 .00

9 ( 2 ( 5 0 . 0 0 2 . 5 0

Time (min)

12150

5 . 0 0 7 . 5 0 1 0 . 0 0 1 2 . 5 0

Time (min)

C o l u m n

C

C o l u m n

D

L I

6 8 1 0 0 . 0 0 2 . 5 0

Time (rain)

2 4

Time (rain)

1 I 1

5.bo 7.~o lOlOO 12150

Time (rain)

8 1 o o o o 2 ~ o 5 b o

7.50 io lo o 12 .5o

Time (rain)

Fig. 3. Comparison of predicted (upp er trace) and experimental (lower trace) chromatograms for single-ramp temperature-programmed

optimizations of the separation of the test mixture for all four the columns. Conditions see Fig. 2.

T h e c h r o m a t o g r a p h i c d a t a f u r th e r i n d i c a t e th a t t h e

c o l u m n m o s t s u i te d f o r s i n g l e - r a m p a n a l y s i s o f th e

m i x t u r e w o u l d b e c o l u m n B . T h i s c o l u m n y i e l d s t h e

s h o r t e s t a n a l y s i s t i m e w h i l e a l l c r i t i c a l p e a k p a i r s a r e

b a s e l i n e s e p a r a t e d .

O p t i m i z a t i o n o f t h e s e p a r a t io n o f t h e t e s t m i x t u r e

w a s a l s o p e r f o r m e d f o r a t w o - s t e p m u l t i - r a m p t e m -

p e r a t u re p r o g r a m . P a r a m e t e r s o p t i m i z e d n o w a r e t h e

i n it ia l a nd m i d - p o i n t c o l u m n t e m p e r a t u r e a n d t h e

c o r r e s p o n d i n g t w o p r o g r a m m i n g r a te s . I n t o t al f o u r

p a r a m e t e r s a r e o p t i m i z e d s i m u l t a n e o u s l y . A g a i n , t h e

p r e d i c t e d a n d e x p e r i m e n t a l c h r o m a t o g r a m s a r e p r e -

s e n t e d i n F i g . 4 . F r o m t h e f i g u r e i t c a n b e c o n c l u d e d

t h a t f o r a l l f o u r c o l u m n s t h e e x p e r i m e n t a l a n d

p r e d i c t e d c h r o m a t o g r a m s a r e v e ry s i m i l a r . T h e e x -

p e r i m e n t a l d a t a c o r r e s p o n d i n g t o t h e o p t i m i z a t i o n s


8/9

1 8 2

H . S n i d e r s e t a l . I J . C h r o m a t o g r . A 7 5 6 1 9 9 6 ) 1 7 5 ; - 1 8 3

C o l u m n A C o l u m n B

J l l i I I l l

0 . 0 0 2 . 5 0 5 .0 0 7 .5 0 1 0 . 0 0 1 2 , 5 0 0 . 0 0

T i m e m i n )

0 . 0 0 2 . 3 0 5 . 0 0 7 . 5 0 1 0 : 0 0 1 2 : 5 0

T i m e r a i n )

C o l u m n C

1 i i t J l I

0 00

1 . 5 0 3 . 0 0 4 . 5 0 6 . 0 0 7 . 5 0

T i m e m i n )

1 . 5 0 3 . 0 0 4 . 5 0 6 . 0 0 7 . 5 0

T i m e r a i n )

C o l u m n D

I l l J i t l J l _

4 6 8

T i m e (rain)

1 0 0 . 0 0

t l l l J

2 . 5 0 5 . 0 0 7 . 5 0 1 0 .0 0

T i m e m i n )

1 2 . 5 0

8 i 0

T i m e m i n )

0 . 0 0 2 . 5 0 5 . 0 0 7 . 5 0

T i m e r a i n )

]

lo . oo 12 .5o

F i g . 4 . Co m p a r i s o n o f p r e d i c te d (u p p e r t r a c e ) a n d e x p e r i m e n ta l ( l o we r t r a c e ) c h r o m a to g r a m s fo r m u l t i - r a m p te m p e r a tu r e -p r o g r a m m e d

o p t i m i z a t i o n s o f th e s e p a r a t i o n o f th e t e s t m i x tu r e fo r a l l fo u r th e c o l u m n s . T h e t e m p e r a tu r e p r o g r a m s l o c a te d b y th e o p t i m i z a t i o n a r e fo r

c o l u m n A: 1 0 5 C - -- ) 1 3 . 8C r a i n ~ - - -) 2 4 2 C ~ 2 3 . 6 C m i n ~ - -~ 3 0 0 C; c o l u m n B : 9 1 C ~ 2 4 . 8 C m i n ~ - -~ 2 4 5 C ~ 2 1 . 4 C r a i n ~ - -~

3 0 0 C; c o l u m n C: 9 9 C ~ 1 9 .3 C r a in ~ - - ) 2 4 3 C ~ 1 9 .9 C m i n ~ ~ 3 0 0 C: c o l u m n D: 1 0 5 C - -~ [3 . 8 C m i n ~ - - -) 2 6 6 C - - -) 1 5 .0 C

m i n ~ - -~ 3 0 0 C.

o n c o l u m n A , C a n d D a g a i n r e v e a l p a r t ia l p e a k

o v e r l a p f o r t h e s e c o n d c r i t i ca l p e a k p a i r. A g a i n ,

a d d i t i o n a l p e a k b r o a d e n i n g d u e t o i n j e c t i o n i s t h e

m o s t p r o b a b l e c a u s e f o r t h e s e o b s e r v a t i o n s . T h e d a t a

f u r t h e r in d i c a t e t h a t f o r s e p a r a t i o n o f t h e t e s t m i x t u r e

c o l u m n B s h o u l d b e u s e d u n d e r t h e m u l t i - r a m p

t e m p e r a t u r e - p r o g r a m m e d c o n d i t i o n s i n d i c a t e d in F i g .

4 .

I t s h o u l d b e n o t e d t h a t , i n p r i n c i p a l , m o r e v a r i -

a b l e s c o u l d b e a d d e d t o th e o p t i m i z a t i o n f o r f u r th e r


9/9

optimization of temperature-programmed gas chromatographic

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