Chapter 9 Retention Processes in Supercritical Fluid Chromatography
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Clement R. Yonker and Richard D. Smith Chemical Sciences Department, Pacific Northwest Laboratory, Richland, WA 99352 The understanding of retention processes in supercritical fluid chromatography is important for the continued growth and development of the analytical technique. Chromatographic retention has been studied using a simple thermodynamic model involving solute retention as a function of pressure and through assessment of the effect of density on the enthalpy of solute transfer between the supercritical mobile phase and bonded stationary phase. The solvatochromic behavior of solute probes in pure and binary supercritical fluids can be used to determine their polarity/polarizability as a function of density and related solvent effects on solute retention in supercritical fluid chromatography. S u p e r c r i t i c a l f l u i d chromatography (SFC) i s a r a p i d l y e x p a n d i n g a n a l y t i c a l t e c h n i q u e f o r t h e s e p a r a t i o n o f a wide range o f compound c l a s s e s , some o f which a r e n o t e a s i l y amenable t o gas chromatography o r l i q u i d chromatography. I t c a n be a r g u e d t h a t t h e c o n t i n u a t i o n o f t h i s r a p i d growth and e x p a n s i o n i n t o o t h e r a n a l y t i c a l a p p l i c a t i o n s would b e n e f i t from an improved fundamental u n d e r s t a n d i n g o f s o l u t e r e t e n t i o n i n SFC u s i n g b o t h pure and b i n a r y s u p e r c r i t i c a l f l u i d s as m o b i l e phase s o l v e n t s . The b a s i c p h y s i c o c h e m i c a l s t u d i e s t o be d i s c u s s e d i n t h i s chapter e f f e c t not only chromatographic r e t e n t i o n , but a l s o s u p e r c r i t i c a l f l u i d e x t r a c t i o n p r o c e s s e s and c h e m i c a l r e a c t i o n mechanisms i n s u p e r c r i t i c a l f l u i d s . ( l n l ) The d i s t r i b u t i o n c o e f f i c i e n t f o r t h e c h r o m a t o g r a p h i c r e t e n t i o n process i s s i m i l a r t o the bulk d i s t r i b u t i o n c o e f f i c i e n t studied i n supercritical f l u i d extraction. Reaction rates i n s u p e r c r i t i c a l f l u i d s o l v e n t s as a f u n c t i o n o f p r e s s u r e a r e d e t e r m i n e d by t h e change i n p a r t i a l m o l a r volume (Δν^) between the p r o d u c t s and r e a c t a n t s . The same parameter (Avp a f f e c t s s o l u t e r e t e n t i o n i n SFC, as w i l l be shown i n t h e Theory s e c t i o n . T h e r e f o r e , t h e s t u d y and u n d e r s t a n d i n g o f s o l u t e r e t e n t i o n i n SFC i s r e l e v a n t t o a l l t e c h n o l o g i c a l applications of supercritical fluids. Three major a r e a s o f i n v e s t i g a t i o n i n o u r l a b o r a t o r y u s i n g s u p e r c r i t i c a l f l u i d s w i l l be d i s c u s s e d . These e n t a i l : 1) s o l u t e r e t e n t i o n m o d e l i n g u s i n g a s i m p l e thermodynamic d e s c r i p t i o n o f r e t e n t i o n as a f u n c t i o n o f p r e s s u r e a t c o n s t a n t t e m p e r a t u r e i n SFC;
0097-6156/88/0366-0161 $06.00/0 © 1988 American Chemical Society
In Supercritical Fluid Extraction and Chromatography; Charpentier, B., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1988.
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162
SUPERCRITICAL
FLUID EXTRACTION
AND
CHROMATOGRAPHY
2) the i n v e s t i g a t i o n o f the thermodynamics o f s o l u t e r e t e n t i o n by s t u d y i n g t h e b e h a v i o r of the e n t h a l p y o f s o l u t e t r a n s f e r between the f l u i d m o b i l e phase and the bonded s t a t i o n a r y phase, f o r b o t h pure and b i n a r y s u p e r c r i t i c a l f l u i d s , and 3) the s t u d y of the s o l v a t o c h r o m i c b e h a v i o r o f pure and b i n a r y s u p e r c r i t i c a l f l u i d s at d i f f e r e n t p r e s s u r e s and t e m p e r a t u r e s . The l a t t e r method a l l o w s one t o s t u d y the s o l v a t i o n process ( s o l u t e - s o l v e n t i n t e r a c t i o n s ) i n the f l u i d m o b i l e phase as a f u n c t i o n o f d e n s i t y independent o f the p r e s e n c e of t h e bonded s t a t i o n a r y phase. The c o m b i n a t i o n o f t h e s e fundamental s t u d i e s p r o v i d e s a b a s i s f o r an i n t e g r a t e d approach t o u n d e r s t a n d i n g r e t e n t i o n p r o c e s s e s i n SFC. I n h e r e n t i n t h i s approach i s a concommitant i n c r e a s e i n the understanding of s u p e r c r i t i c a l f l u i d s f o r a p p l i c a t i o n s i n e x t r a c t i o n and c h e m i c a l r e a c t i o n phenomena. In t h i s c h a p t e r the r e s u l t s o f our i n i t i a l s t u d i e s on s o l u t e r e t e n t i o n i n SFC w i l l be p r e s e n t e d and discussed.
Theory Thermodynamics of R e t e n t i o n i n SFC. Solute f u n c t i o n o f p r e s s u r e i s g i v e n as, (6,7) (3lnk'/3P)T = l / R T t v ^ P '
0 0
r e t e n t i o n i n SFC
as
a
0 0
- v^P' ] - Κ
(l)
where k' i s t h e d i m e n s i o n l e s s r e t e n t i o n f a c t o r o f the s o l u t e , R i s t h e gas c o n s t a n t , Τ i s temperature, v ^ P ' and v ^ P ' a r e the s o l u t e p a r t i a l m o l a r volumes i n the m o b i l e and s t a t i o n a r y phases at i n f i n i t e d i l u t i o n r e s p e c t i v e l y , and K, the i s o t h e r m a l c o m p r e s s i b i l i t y of the f l u i d s o l u t i o n , i s d e f i n e d as 1/V (3v/3P). T h i s term r e l a t e s the change i n molar volume o f t h e c o m p r e s s i b l e f l u i d (V) as a f u n c t i o n of p r e s s u r e t o s o l u t e r e t e n t i o n i n SFC. Under the e x p e r i m e n t a l c o n d i t i o n s d i s c u s s e d i n t h i s c h a p t e r (and almost u n i v e r s a l l y r e l e v a n t t o SFC), the mole f r a c t i o n o f the s e l e c t e d s o l u t e , n a p h t h a l e n e , i n the f l u i d phase i s v e r y low ( X ^ p « 1 0 " 2 ) (£) , t h e r e f o r e , v ^ P ~ ν-^p, . 0 0
0 0
00
The p a r t i a l molar volume o f infinite dilution is a sensitive interactions. The p a r t i a l molar d i l u t i o n can be e x p r e s s e d as two relationship. Vl
mp,oo
=
K
2
V
2
[Op/a
n i
)
the s o l u t e i n probe o f the volume of the terms t h r o u g h
T /
the m o b i l e phase at solvent-solute s o l u t e at i n f i n i t e a t r i p l e product
( 2 )
v n 3 f
2
where K i s the i s o t h e r m a l c o m p r e s s i b i l i t y of the pure s o l v e n t and i s the m o l a r volume of the pure s o l v e n t . (^.,lu) S u b s t i t u t i o n of e q u a t i o n 2 i n t o e q u a t i o n 1 y i e l d s a r e l a t i o n s h i p f o r the s l o p e o f s o l u t e r e t e n t i o n i n SFC.
V
2
f
(3lnk /3P)T
s
= l / R T { K V O P / a n ) v , n 2 -vi P'°°] - Κ 2
2
1
T f
(3)
From e q u a t i o n 3, u s i n g an a p p r o p r i a t e e q u a t i o n of s t a t e (EOS) t h a t d e s c r i b e s the P,V,T e q u i l i b r i a f o r the s o l u t e and the f l u i d , s o l u t e r e t e n t i o n i n SFC can be p r e d i c t e d f o r systems f a l l i n g w i t h i n the scope o f our assumptions.
In Supercritical Fluid Extraction and Chromatography; Charpentier, B., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1988.
2
9.
YONKER AND SMITH
Retention
Processes
in SFC
163
The d e n s i t y dependence o f r e t e n t i o n a t c o n s t a n t t e m p e r a t u r e i s d e f i n e d as,
(3lnk'/3p)
T
= (3lnk'/3P)
T
(3P/3p)
4
T
where p i s d e n s i t y (g/cm ) . The f i r s t term on t h e r i g h t hand s i d e (RHS) o f e q u a t i o n 4 has a l r e a d y been e v a l u a t e d i n t h e p r e v i o u s equation. The second term on t h e RHS o f e q u a t i o n 4 i s t h e s l o p e o f p r e s s u r e v e r s u s d e n s i t y a t c o n s t a n t t e m p e r a t u r e f o r t h e f l u i d and can be r e a d i l y o b t a i n e d from an EOS. The Peng-Robinson, two-parameter, c u b i c EOS was u s e d t o e v a l u a t e t h e p a r t i a l molar volume o f t h e s o l u t e i n t h e m o b i l e phase ( e q u a t i o n 2 ) , t h e i s o t h e r m a l c o m p r e s s i b i l i t y o f the f l u i d s o l u t i o n and s o l v e n t , and (3Ρ/3ρ)τ i n E q u a t i o n 4. F o r systems composed o f a pure f l u i d s o l v e n t and an o r g a n i c s o l u t e , s t a n d a r d m i x i n g r u l e s were u s e d f o r t h e c a l c u l a t i o n o f t h e m i x t u r e p a r a m e t e r s (10.11) . T h e r e f o r e , a l l t h e terms i n e q u a t i o n 3 and 4 c a n be e v a l u a t e d as a f u n c t i o n o f p r e s s u r e and d e n s i t y a t c o n s t a n t t e m p e r a t u r e , e x c e p t f o r t h e p a r t i a l m o l a r volume o f t h e s o l u t e i n t h e s t a t i o n a r y phase a t i n f i n i t e d i l u t i o n vi P'°°. The p a r t i a l molar volume o f t h e s o l u t e i n t h e s t a t i o n a r y phase c a n be estimated, allowing solute retention i n the s u p e r c r i t i c a l region t o be c a l c u l a t e d as a f u n c t i o n o f p r e s s u r e . Assuming c o n d i t i o n s o f i n f i n i t e d i l u t i o n d u r i n g r e t e n t i o n i n SFC, t h e s o l u t e d i s t r i b u t i o n c o e f f i c i e n t c a n be r e l a t e d t o t h e f r e e e n e r g y o f t r a n s f e r by,
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3
s
AG = -RT I n K
(5)
D
where AG i s t h e change i n G i b b s f r e e e n e r g y o f s o l u t e t r a n s f e r from t h e m o b i l e phase t o t h e s t a t i o n a r y phase (12.) r and K i s t h e s o l u t e distribution coefficient. The thermodynamic r e l a t i o n s h i p between t h e s o l u t e d i s t r i b u t i o n c o e f f i c i e n t and temperature i s , D
In K
= -ΔΗ/RT + AS/R
D
(6)
where ΔΗ i s t h e change i n e t h a l p y o f s o l u t e t r a n s f e r and As i s t h e change i n e n t r o p y o f s o l u t e t r a n s f e r . The s o l u t e d i s t r i b u t i o n c o e f f i c i e n t c a n be r e l a t e d t o t h e s o l u t e r e t e n t i o n f a c t o r by, K
D
= C /C s
m
= k'
