- Email: [email protected]
Solid Chromatography
205
RETENTION I N LIQUID/SOLID CHROMATOGRAPHY
ERVIN
SZ.
KOV~TS
L a b o r a t o i r e de Chimie-technique de 1 ' E c o l e P o l y t e c h n i q u e FCderale de Lausanne,
1015 Lausanne ( S w i t z e r l a n d ) .
SWARY R e t e n t i o n d a t a i n l i q u i d / s o l i d chromatography a r e recorded on t h e b a s i s o f e q u a t i o n s which were developed f o r l i q u i d / l i q u i d and g a s / l i q u i d chromatography. It i s shown t h a t these e q u a t i o n s a r e inadapted.
It i s a l s o shown t h a t r e t e n t i o n
i n l i q u i d / s o l i d chromatography can be g i v e n i n terms o f Gibbs' d e s c r i p t i o n o f t h e a d s o r p t i o n process. As i n systems w i t h r e v e r s i b l e a d s o r p t i o n e q u i l i b r i u m , t h e i n t r o d u c t i o n o f a c o n v e n t i o n i s necessary.
In the l i g h t o f t h i s retention
equation, t h e e n e r g e t i c s o f t h e a d s o r p t i o n process i s discussed as w e l l as d i f f e r e n t methods o f t h e d e t e r m i n a t i o n o f t h e hold-up volume.
INTRODUCTION
De V a u l t was t h e f i r s t t o g i v e an e x a c t s o l u t i o n o f r e t e n t i o n i n chromatography, c o n s i d e r e d t o proceed t h r o u g h i n f i n i t e s i m a l e q u i l i b r i u m steps ( r e f . 1). I n t h e mathematical s o l u t i o n , matrix.
r e t e n t i o n volumes appear as e i g e n v a l u e s o f a
The r e s u l t s were a p p l i e d b y Helfferich and K l e i n f o r t h e d i s c u s s i o n o f
chromatography ( r e f .
2).
R e c e n t l y i t was shown t h a t t h e model o f de V a u l t be-
comes g e n e r a l l y a p p l i c a b l e b y i n t r o d u c i n g a new s i m p l e thermodymanic f u n c t i o n the i s o c r a t i c capacity,
?iK ( r e f . 3 ) . This new f u n c t i o n i s t h e m a t e r i a l con-
t e n t o f an open system ( t h e column) i n e q u i l i b r i u m w i t h an i n f i n i t e r e s e r v o i r o f a f l u i d m i x t u r e ( s e e F i g . 1). The s p e c i f i c s o l u t i o n f o r a n a l y t i c a l chromatography under i s o t h e r m a l and i s o c r a t i c c o n d i t i o n s i s g i v e n b y eqn. 1
where vR,i
i s t h e r e t e n t i o n volume o f an i n f i n i t e s i m a l sample o f i (component
206
-
I n f i n i t e reservoir with a f l u i d m i x t u r e o f the composition: s;" = x ou,AYXp,B(=l-XA) 0 A
x
= xu
where x
, ~ * X u , ~ y X p , ~ ~
su
+
0
/
I s o c r a t i c c a p a c i t y o f t h e open system (column)
K" K
A
n
K
= no
no K,B
-
n
K,A'
- 'K,A'
where n
K ,SU
K,B'
n
K,SU
+O
F i g . 1 The i s o c r a t i c c a p a c i t y o f t h e column, ;n i n equilibrium with a binary m i x t u r e o f A and B o f t h e composition, x i and t h e i s o c r a t i c c a p a c i t y n, i n t h e presence o f a t h i r d component, su ( s o l u t e ) o f i n f i n i t e s i m a l c o n c e n t r a t i o n , xsu. o f the eluent, e l u e n t , nK,j
A,B
... o r
solute,
su),
v;
i s t h e mean molar volume o f t h e
i s t h e column c a p a c i t y o f component,
i, and p*
i s the composition
o f t h e m o b i l e phase. The i d e a l i z e d chromatographic column i s c o n s i d e r e d t o have a u n i f o r m c r o s s s e c t i o n a t any d i s t a n c e from t h e i n l e t , f i l l e d w i t h a quasi continuum o f a porous powder. E q u i l i b r i u m i s i n s t a n t a n e o u s i n any c r o s s s e c t i o n o f t h e column and t h e r e i s no a x i a l d i f f u s i o n . Therefore, t h e p e r t u r b a t i o n o f t h e e l u e n t b y an i n f i n i t e s i m a l s i g n a l a t t h e column i n l e t w i l l appear a t t h e column o u t l e t r e t a i n e d , b u t n o t deformed.
RETENTION I N M S / L I Q U I D AND LIQUID/LIQUID CHROMATOGRAPHY I n o r d e r t o demonstrate t h e use o f eqn. 1 i t w i l l now b e a p p l i e d t o g a s / l i q u i d chromatography w i t h a m o b i l e phase composed o f a m i x t u r e o f two i d e a l gases,
S and I. Component S i s s o l u b l e i n t h e s t a t i o n a r y l i q u i d , whereas compo-
nent I i s i n s o l u b l e . V,
= w,/d,
The volume o f t h e s t a t i o n a r y phase can be c a l c u l a t e d as
b y supposing t h a t t h e s t a t i o n a r y l i q u i d f i l m on t h e i n e r t sup-
p o r t has t h e same d e n s i t y , given by
d,,
as t h e b u l k .
The column c a p a c i t i e s are t h e n
207
where c i s t h e c o n c e n t r a t i o n ,
[mol
1-11, t h e s u b s c r i p t s p and
5
refer t o the
m o b i l e and s t a t i o n a r y phases r e s p e c t i v e l y and t h e o t h e r symbols a r e as b e f o r e . Having t h e necessary e x p r e s s i o n s a t hand (eqns. 2 and 4) a p p l i c a t i o n o f eqn. 1 g i v e s t h e same e x p r e s s i o n f o r t h e r e t e n t i o n volume f o r t h e p e r t u r b a t i o n o f t h e e l u e n t c o m p o s i t i o n b y i n j e c t i o n s o f v e r y small amounts of S o r I. I n j e c t i o n o f e i t h e r o f t h e gases provokes a concentration peak pressed w i t h x,s
where V,
. Its
r e t e n t i o n volume,
ex-
as t h e independent v a r i a b l e , i s g i v e n i n eqn. 5
i's t h e hold-up volune (dead volume) o f t h e column. T h i s same r e s u l t
was found by Valentin and Guiochon ( r e f . 4).
I n t h e s p e c i a l case where t h e r e i s
o n l y an i n s o l u b l e c a r r i e r and t h e s o l u b l e gas i s i n j e c t e d as s o l u t e ( S
+
su),
eqn. 5 s i m p l i f i e s t o
where
KSu
i s the partition coefficient o f the solute at
infinite dilution
Eqn.6 i s t h e c l a s s i a l r e l a t i o n s h i p o f Martin and Synge f o r r e t e n t i o n volume i n
1 i q u i d / l i q u i d chromatography ( r e f . 5)
, calculated
today as " C r a i g ' s c o u n t e r c u r r e n t b a t t e r y " machine" ( r e f . 6).
w i t h t h e a i d o f a model known
or the "droplet
counter c u r r e n t
I n t h e i r model t h e chromatographic column was compared w i t h
a h y p o t h e t i c a l b a t t e r y o f s e p a r a t i n g c e l l s g i v i n g t h e same chromatogram as t h e chromatographic column i n q u e s t i o n . The number o f t h e c e l l s o f t h e h y p o t h e t i c a l b a t t e r y was a measure o f t h e peak w i d t h and t h e r e b y t h e e f f i c i e n c y o f t h e c h r o matographic column. T h i s d e s c r i p t i o n i n i t i a l l y c r e a t e d some c o n f u s i o n about t h e meaning o f a c e l l , which was c a l l e d a p l a t e , s u g g e s t i n g t h e same r o l e p l a y e d b y a p a r t i t i o n i n g c e l l as t h a t b y a s e p a r a t i n g p l a t e i n d i s t i l l a t i o n . Furthermore, s i g n a l d e f o r m a t i o n i n t h i s model i s due t o t h e f i n i t e volume o f t h e s e p a r a t i n g c e l l s and n o t t o d i f f u s i o n and t o k i n e t i c s o f e q u i l i b r i u m a t t a i n m e n t . Nevertheless, t h e c e l l model gave t h e r i g h t answer f o r t h e r e l a t i o n s h i p of t h e r e t e n t i o n volume w i t h t h e p a r t i t i o n c o e f f i c i e n t i n l i q u i d / l i q u i d and gas/ l i q u i d chromatography ( r e f . 7 ) . It was t h e r e f o r e proposed t o use t h e net-reten-
t i o n volune.
f o r the characterization o f retention.
The hold-up volume,
Vp,
c o u l d be de-
t e r m i n e d as t h e r e t e n t i o n volume o f a n o n - r e t a i n e d substance, a substance i n s o -
208
l u b l e i n t h e s t a t i o n a r y phase. A r e t e n t i o n volume s m a l l e r t h a n t h e hold-up v o lume was n o t p o s s i b l e .
In gas chromatography t h e n e t - r e t e n t i o n volume i s r e l a -
t e d t o Henry's coefficient b y
where
nu and wu a r e t h e number o f moles and t h e mass o f t h e s t a t i o n a r y li-
q u i d i n t h e column r e s p e c t i v e l y , constant,
Tc i s t h e column temperature,
hsu i s Henry's c o e f f i c i e n t
R i s t h e gas
and gsu i s H e n r y ' s m o l a l c o e f f i c i e n t
o f the solute a t i n f i n i t e d i l u t i o n i n t h e actual solvent.
Eqn. 9 i s d e r i v e d
from eqn. 8. It g i v e s t h e r e l a t i o n s h i p o f t h e r e t e n t i o n volume w i t h t h e
diffe-
rence o f t h e standard chemical potential of the substance between t h e i d e a l d i l u t e s o l u t i o n and t h e gas s t a t e as e i t h e r h ~ p i u( r e l a t e d t o hsu) o r 9 A p i u ( r e l a t e d t o g s u ) . The gas phase i s c o n s i d e r e d t o be a m i x t u r e o f t h e i d e a l c a r r i e r and t h e substance vapor as i d e a l gas. RTclnVN,su = RTcln(n uRTc ) - h ~ p Z u= RTcln(wuRTc/lOOO)
- 9~pru
This simple r e l a t i o n s h i p between t h e l o g a r i t h m o f t h e n e t r e t e n t i o n volume and t h e standard chemical p o t e n t i a l d i f f e r e n c e has been v e r y u s e f u l f o r e s t a b l i shing l i n e a r f r e e energy r e l a t i o n s h i p s f o r t h e p r e d i c t i o n o f chromatographic data. It a l s o helped t h e u n d e r s t a n d i n g o f i n t e r a c t i o n f o r c e s . S i m i l a r r e l a t i o n s h i p s can be d e r i v e d , mutatis mutandis, f o r l i q u i d / l i q u i d chromatography.
RETENTION IN LIQUID/SOLID CHROMATOGRAPHY The success o f l i q u i d / l i q u i d chromatography had a s e r i o u s impact on t h e development o f chromatographic techniques. This impact was even a m p l i f i e d by t h e d i s c o v e r y o f g a s / l i q u i d chromatography b y Martin and James ( r e f .
7).
It gave
t h e impetus and l e a d i n g ideas f o r t h e achievement o f h i g h e r performance i n l i q u i d / s o l i d chromatography. The 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 column t e c h n o l o g y o f g a s / l i q u i d chromatography suggested t h e seducing i d e a t o a l s o a p p l y t h e succ e s s f u l r e s u l t s o f t h e model o f Martin and Synge t o l i q u i d / s o l i d chromatography b y f o r m a l analogy, and t o a p p l y eqns. 7, 8 and 9 w i t h o u t a d a p t a t i o n t o t h e desc r i p t i o n o f r e t e n t i o n . Therefore, s e v e r a l papers d i s c u s s t h e meaning o f t h e vo-
lune o f the stationary phase and t h e r e l a t e d problem o f t h e hold-up volune. Before d i s c u s s i n g these essays,
l e t us f i r s t a p p l y eqn. 1 f o r t h e r e t e n t i o n
volume i n l i q u i d / s o l i d chromatography. The molar i s o c r a t i c c a p a c i t y o f a column f i l l e d w i t h an adsorbent i s g i v e n by
209
and =
nK,tOt
where
S
Vp/CX/V$&
+
rtot/cx
i s t h e s u r f a c e area o f t h e adsorbent, T i i s t h e s u r f a c e c o n c e n t r a t i o n
of t h e i t h component and a l l o t h e r symbols a r e as b e f o r e . I n a system where adsorption i s r e v e r s i b l e , surface concentration i s not a defined q u a n t i t y without introducing
an a d d i t i o n a l e q u a t i o n d e f i n i n g
concerning t h e
adsorption
equilibrium.
By
a convention (Convention X =CX) using the
particular
convention
Nothing t h a t t h e sum o f t h e s u r f a c e c o n c e n t r a t i o n s [pmol w 2 ] i s equal t o zero (is Adsorbed i n terms o f number o f moles, n: nNA);
a d s o r p t i o n i s d e s c r i b e d i n terms o f reduced surface concentrations, ri/,,NA PAC-symbol:
n$n)
/S).
Using eqns. 10 and 11, a p p l i c a t i o n o f eqn.
(IU-
1 gives f o r
t h e r e t e n t i o n volume:
if t h e nNA-convention i s a p p l i e d . It i s seen t h a t t h e h o l d - u p volume, Vp/nNA i s defined
i n connection w i t h the given convention.
similar
A
d e r i v e d i f a d s o r p t i o n i s expressed i n an unusual u n i t , Y [ p l m-'1
equation
, is
and u s i n g an
unusual convention, vNA (Nothing i s Adsorbed i n terms o f volume, v ) . This g i v e s
where, g, i s f o r t h e volume f r a c t i o n . For chromatography w i t h a binary eluent
composed o f A and B eqn. 14 g i v e s
eqn. 15 f o r t h e r e t e n t i o n volume o f a c o n c e n t r a t i o n p e r t u r b a t i o n ( i n j e c t i o n o f a small amount o f A o r 6 ) t o g i v e a c o n c e n t r a t i o n peak, cc,
Thus,
t h i s r e t e n t i o n volume i s r e l a t e d t o t h e d e r i v a t i v e o f t h e a d s o r p t i o n
i s o t h e r m o f component A o f t h e e l u e n t , ' Y A / ~ N A . ( T h i s r e l a t i o n s h i p i s an approx i m a t i o n , i t i s s t r i c t l y v a l i d o n l y f o r p e r f e c t l i q u i d m i x t u r e s ) . The r e t e n t i o n volume o f a l a b e l l e d component o f t h e e l u e n t , A* o r B*,
i s directly related to
210 t h e a d s o r p t i o n isotherm:
F i n a l l y , t h e r e t e n t i o n volume o f a s o l u t e i s g i v e n b y
These r e l a t i o n s h i p s a l s o d e f i n e t h e a c t u a l h o l d - u p volume b y g i v i n g t h e e x p e r i mental method o f i t s d e t e r m i n a t i o n . Considering t h a t
YA/,NA
+
Y ! B / ~ N A = 0,
the
sum o f eqn. 16 g i v e s a f t e r rearrangement:
Eqn.
18 was f i r s t d e r i v e d by Knox on t h e b a s i s o f a d i f f e r e n t argumentation
( r e f . 8).
( S i m i l a r r e l a t i o n s h i p s a r e r e a d i l y d e r i v e d from eqn.
t h e method o f c a l c u l a t i o n o f V,,/nNA
13 g i v i n g a l s o
(ref. 3)).
As a t e s t o f these r e l a t i o n s h i p s l e t us examine e x p e r i m e n t a l s p e c i f i c r e t e n t i o n volumes o f l a b e l l e d ( d e u t e r a t e d ) a c e t o n i t r i l e ,
l a b e l l e d water ( H D O ) ,
and
t h a t o f t h e c o n c e n t r a t i o n peak, p l o t t e d i n F i g . 2 as a f u n c t i o n o f e l u e n t comp o s i t i o n , w i t h tetradecyldimethylsiloxy m o d i f i e d s i l i c a as adsorbent ( r e f . 9 ) . R e t e n t i o n volumes were c o r r e c t e d w i t h t h e hold-up volume from eqn. 18 t o g i v e n e t - r e t e n t i o n volumes.
The surface specific retention volune was t h e n
calcu-
l a t e d as
P o i n t s on t h e reduced excess a d s o r p t i o n isotherm,
Y A / ~ N A, c o u l d be c a l c u l a t e d
w i t h t h e a i d o f t h e r e l a t i o n s h i p s summarized i n eqns. 19 from t h e s p e c i f i c r e -
- Y!A/~NA) p l o t t e d i n Fig. 3 as a f u n c t i o n o f e l u e n t c o m p o s i t i o n . The i s o t h e r m i s o f t h e S-type. S i m i l a r
t e n t i o n volumes o f A* and B* ( n o t e t h a t Y B / ~ N A=
isotherms were observed by Schay and Nagy a t n o n - p o l a r measurements ( r e f .
interfaces i n static
10). The r e g r e s s i o n f u n c t i o n o f t h e a d s o r p t i o n isotherm,
shown i n F i g . 3 p e r m i t s us i n t u r n t o p r e d i c t t h e s p e c i f i c r e t e n t i o n volumes o f A* and B* and t h a t o f t h e c o n c e n t r a t i o n peak. The t r a c e o f t h e s e f u n c t i o n s i s shown i n F i g . 2. The agreement i s e x c e l l e n t .
211
F i g . 2. Surface s p e c i f i c r e t e n t i o n volume o f d e u t e r a t e d a c e t o n i t r i l e and HDO, and that o f t h e c o n c e n t r a t i o n peak in a c e t o n i t r i l e / H 2 0 as a f u n c t i o n o f t h e c o m p o s i t i o n o f t h e e l u e n t ( r e f . 9 ) . The volume f r a c t i o n , 0, was c a l c u l a t e d w i t h partial molar volumes. Temperature: 2 P C ; s t a t i o n a r y phase: L i c h r o s o r b - S I 1 0 0 covered with tetradecyldimethylsiloxy substituents. Curves c a l c u l a t e d w i t h eqns. 15 and 1 7 f r o m t h e a d s o r p t i o n i s o t h e r m shown i n F i g . 3.
0 Y
.o
-.2
'H20 H,O/vNA
F i g . 3. A sor t i o n isotherms, \y ~~0 V~~ , from ace ,n i r i l e / H 2 0 m i x t u r e s a( t h e s u r f ace of t e t r adecyl d i m e t h y l s i 1o x y covered s i l i c o n d i o x i d e . F u l l symbols and c u r v e f o r Tc = 20.0 O C ; open symbols and dashed l i n e f o r Tc = 4O.O0C. Points c a l c u l a t e d w i t h eqn. 19 ( r e f . 9).
-.4
-.6 0
A f i r s t c o n c l u s i o n from t h i s d i s c u s s i o n i s t h a t t h e hold-up volume i n l i q u i d / s o l i d chromatography has t o b e c o n s i d e r e d as a correctilrg volune f o r t h e c a l c u l a t i o n o f t h e n e t - r e t e n t i o n volume f o l l o w i n g eqn. 7, and as such i t cannot be i d e n t i f i e d with any physical volune inside the colunn. It was s t a t e d t h a t t h e hold-up volume, c a l c u l a t e d w i t h t h e vNA c o n v e n t i o n does correspond t o
212
t h e volume o f t h e m o b i l e phase i n t h e column. S t r i c t l y speaking,
t h i s i s not
t r u e . F i r s t l y , experiments o f Ash and Findenegg show t h a t t h e d e n s i t y o f a p u r e l i q u i d near an i n t e r f a c e i s d i f f e r e n t from t h a t i n t h e b u l k ( r e f . 11). Obviousl y , t h e l i q u i d has a d i f f e r e n t s t r u c t u r e i n t h e neighbourhood o f a s o l i d as
i l l u s t r a t e d i n F i g . 4.
Secondly,
i n a b i n a r y m i x t u r e t h e p a r t i a l molar volume
1i q u i d
solid
a
b
Fig. 4. I l l u s t r a t i o n o f t h e m o l e c u l a r o r d e r i n p u r e l i q u i d s near a l i q u i d / s o l i d i n t e r f a c e : a: t h e s t r u c t u r e o f t h e l i q u i d near t h e i n t e r f a c e i s t h e same as i n t h e b u l k ; b: t h e l i q u i d i s ordered near t h e i n t e r f a c e , t h e r e f o r e i t has a h i g h e r d e n s i t y ( c f . r e f . 11).
o f an adsorbed component i s c e r t a i n l y d i f f e r e n t from t h a t i n t h e b u l k , because t h e p a r t i a l molar volume i s a f u n c t i o n o f c o m p o s i t i o n and t h e c o m p o s i t i o n near t h e i n t e r f a c e i s d i f f e r e n t from t h a t i n t h e b u l k . These a r e m i n o r e f f e c t s i n b i n a r y systems used as e l u e n t s i n l i q u i d / s o l i d chromatography w i t h a non-polar solid,
and a l t h o u g h w a t e r -
ideality,
organic modifier mixtures deviate s e r i o u s l y from
t h i s volume can be equated w i t h a v e r y good a p p r o x i m a t i o n t o t h e
t o t a l volume o f t h e m o b i l e phase i n t h e column.
V,,/NA
,
I n experiments t h e volume,
i s almost independent o f t h e n a t u r e o f t h e m o b i l e phase ( r e f . 9).
o t h e r words,
In
b y t h e c o n v e n t i o n vNA t h e Gibbs d i v i d i n g p l a n e i s s i t u a t e d v e r y
near t o t h e r e a l , p h y s i c a l d i v i d i n g p l a n e between t h e s o l i d and t h e l i q u i d . A second c o n c l u s i o n i s t h a t a stationary phase cannot be i d e n t i f i e d
. Nume-
r o u s a t t e m p t s have been made t o c r e a t e an i m a g i n a r y s t a t i o n a r y phase b y propos i n g monolayer o r b i l a y e r a d s o r p t i o n models (see F i g . 5 ) .
In r e a l systems t h e
s i t u a t i o n i s more c o m p l i c a t e d as shown by Somorjai i n t h e s t u d y o f " f r o z e n " ads o r p t i o n e q u i l i b r i a i n l i q u i d metal m i x t u r e s ( r e f .
12). Even i f , i n c e r t a i n
systems, a monolayer o r b i l a y e r a d s o r p t i o n may be a v e r y good a p p r o x i m a t i o n f o r
I
0
1
1, -
a
1
213
-
0
1
FA
....
.... .... .... .... .... .... ....
....... ................... ................... ................... .................. ................... ................... ................... 9
solid
a
C
F i g . 5. C o n c e n t r a t i o n p r o f i l e s near a l i q u i d / s o l i d i n t e r f a c e : a: monomolecular a d s o r p t i o n ; b: b i m o l e c u l a r a d s o r p t i o n ; c : a more complex s i t u a t i o n ( c f . r e f . 12). the real situation,
t h e whole adsorbed m a t e r i a l
brium w i t h t h e b u l k : t h e where
one of
i s always i n dynamic e q u i l i -
surface phase i s not autonomous. ( A c t u a l l y , t h e case
t h e components
is really
immobilized
a t t h e surface
i s not
i n t e r e s t i n g from t h e v i e w p o i n t o f t h e chromatographic process. T h i s case has t o be considered as chromatography a t t h i s newly formed l i q u i d / s o l i d i n t e r f a c e ) . A t h i r d c o n c l u s i o n i s t h a t t h e net r e t e n t i o n volune o f a solute can be negat i v e r e g a r d l e s s o f which c o n v e n t i o n i s used f o r t h e d e t e r m i n a t i o n o f t h e h o l d up volume. The s o l u t e can have a n e g a t i v e reduced a d s o r p t i o n i f i t i s l e s s adsorbed then e i t h e r o f t h e components o f t h e e l u e n t s ( c f . eqn. 17). The l a s t c o n c l u s i o n concerns t h e e n e r g e t i c s o f t h e r e t e n t i o n .
In l i q u i d /
s o l i d chromatography t h e r e t e n t i o n volume o f a s o l u t e i s d i r e c t l y r e l a t e d t o t h e specific Helmholtz f r e e energy o f t h e i n t e r f a c e ( r e f . 1ink
13). The necessary
s g i v e n b y Gibbs' a d s o r p t i o n e q u a t i o n ( c o n s t a n t t e m p e r a t u r e ) :
dy = where y i s t h e s p e c i f i c f r e e energy o f t h e i n t e r f a c e ( i n t e r f a c i a l t e n s i o n ) , psu
i s t h e chemical p o t e n t i a l o f t h e s o l u t e and rs,/ANA
(IUPAC
t h e r e l a t i v e excess surface concentration o f t h e s o l u t e ,
symbol:
n$,A)/s)
r e l a t i v e t o A,
A is Not Adsorbed a t t h e i n t e r f a c e (ANA). The t h e c o n v e n t i o n t h a t component c o r r e s p o n d i n g hold-up volume i s g i v e n b y
is with
214
as,
b y convention,
component
A i s not
adsorbed.
The c o r r e s p o n d i n g s u r f a c e
s p e c i f i c r e t e n t i o n volume i s g i v e n b y ( c f . eqn. 13):
Combination o f eqns.
20 and 22 gives,
after
t h e necessary t r a n s f o r m a t i o n s
( r e f . 13):
F o l l o w i n g eqn. 23 t h e r e t e n t i o n volume o f a s o l u t e i s d i r e c t l y r e l a t e d t o t h e
decrease o f the specific f r e e energy o f the i n t e r f a c e
,
a d s o r p t i o n and not t o the chemical potential o f the solute
y,
caused b y s o l u t e
. Therefore,
eqn. 23
i s o f l i t t l e use i n t h e understanding and p r e d i c t i o n o f chromatographic d a t a .
CONCLUSIONS L e t us r e t u r n now t o t h e d i s c u s s i o n o f t h e current description o f renten-
t i o n i n 1 i q u i d / s o l i d chromatography. The most p o p u l a r method o f p r e s e n t a t i o n o f such d a t a i s t o c a l c u l a t e t h e k'-value o f a s o l u t e d e f i n e d b y
Furthermore, i t i s b e l i e v e d t h a t eqn. 23 i s a p p l i c a b l e RTcln k,;
=
C
-
~g~~ t
25 1
where t h e c o n s t a n t , C, i s a r b i t r a r y because (as i t i s s t a t e d ) t h e volume o f t h e s t a t i o n a r y phase i s n o t d e f i n e d .
On t h e b a s i s o f t h e f o r e g o i n g d i s c u s s i o n , eqn. 24 i s meaningless ( o r h s a t r i v i a l meaning) and eqn. 25 i s wrong. Even b y a d m i t t i n g , f o r t h e sake o f d i s cussion, t h a t t h e k ' - v a l u e i n s i m i l a r columns,
i s p r a c t i c a l f o r t h e comparison o f d a t a determined
i t i s seen t h a t t h i s c h a r a c t e r i s t i c v a l u e measures t h e
r e t e n t i o n i n t h e u n i t s o f t h e hold-up volume. F i r s t l y , t h e hold-up volume i s small,
i t can be determined w i t h a p r e c i s i o n o f o n l y f 3%. Secondly,
current
215 apinions h i g h l y d i f f e r
as t o t h e method o f
i t s determination
meaning. L e t us s h o r t l y r e v i e w t h e p r o p o s a l s ( r e f s .
and about
its
14 and 1 5 ) .
I n j e c t one o f t h e marked components (A*) o f t h e e l u e n t and accept V,
= VR,A*
( r e f . 1 6 ) . This h o l d - u p volume i s e q u i v a l e n t t o t h a t d e r i v e d w i t h t h e A i s n o t adsorbed c o n v e n t i o n (ANA; see eqn. 21) I n j e c t b o t h marked components and c a l c u l a t e V,
w i t h eqn. 8
(see discussion
t h e r e ) ( r e f . 8). I n j e c t b o t h marked components and always accept t h e s m a l l e r o f t h e r e t e n t i o n volumes, VR,A* lieved that
VR,B*
or
,
as t h e h o l d - u p volume.
r e t e n t i o n volumes
smaller
than
V,
I n t h i s p r o p o s a l i t i s beare n o t possible
(as
in
l i q u i d / l i q u i d and g a s / l i q u i d chromatography) ( r e f . 17). The column i s f i l l e d w i t h two p u r e l i q u i d s s u c c e s s i v e l y and weighed ( r e f . 1 8 ) . The h o l d - u p volume i s c a l c u l a t e d as
where Aw i s t h e weight d i f f e r e n c e o f t h e column f i l l e d w i t h t h e two l i q u i d s (Aw = wc,1-wc,2) d2). (Ad = d l
-
and Ad i s t h e d i f f e r e n c e ' o f t h e d e n s i t y o f t h e two l i q u i d s T h i s experiment i s e s s e n t i a l l y t h e same as t h a t o f Ash and
Findenegg ( r e f . 11) b u t i t i s supposed t h a t t h e r e a r e no d e n s i t y changes i n the
liquids
near
the
interface.
If
hold-up volume i s about t h e same as V,N,/ A
this
is
approximately
true,
this
(see eqn. 1 8 ) .
The l o g a r i t h m of t h e r e t e n t i o n volumes o f a homologous s e r i e s a r e " l i n e a r i zed" as t h e f u n c t i o n o f
z, t h e carbon number, t o g i v e
Vp
(ref.19).
This
procedure i s d e r i v e d by f o r m a l analogy w i t h gas chromatography. Note t h a t i n l i q u i d / s o l i d chromatography n e t r e t e n t i o n can be n e g a t i v e
and t h a t
the
l o g a r i t h m o f a n e g a t i v e number has no sense. I n j e c t a "chosen s o l u t e " , y, b e l i e v e d t o be n o n - r e t a i n e d and accept V R , ~ as hold-up volume ( r e f . 20). From t h e v i e w p o i n t o f Gibbs' d e s c r i p t i o n o f adsorption,
t h i s proposal
i n t r o d u c e s t h e c o n v e n t i o n yNA,
i.e.
y
i s not
adsorbed a t any e l u e n t c o m p o s i t i o n . Hold-up volumes determined f o l l o w i n g these p r o p o s a l s d i f f e r b y a t l e a s t as much as f 20%. Consequently,
r e t e n t i o n d a t a g i v e n i n u n i t s o f t h e hold-up volumes
w i l l v a r y a t l e a s t b y t h e same o r d e r o f magnitude. As a c o n c l u s i o n , t h e h o l d - u p volume i s n o t a s u i t a b l e u n i t f o r r e c o r d i n g r e t e n t i o n d a t a even i f i t s method o f d e t e r m i n a t i o n c o u l d be agreed upon.
If hold-up
volume i s used as a correction i n s t e a d o f a u n i t
i n order t o
c a l c u l a t e n e t - r e t e n t i o n volumes, t h e e r r o r o f t h e c o r r e c t i o n appears as a s m a l l r e l a t i v e e r r o r i n t h e d e t e r m i n a t i o n o f h i g h e r r e t e n t i o n volumes.
In t h e l i g h t
216
o f t h i s proposal,
t h e a b s o l u t e v a l u e o f t h e hold-up volume i s of
l e s s impor-
tance. From t h e n e t - r e t e n t i o n volumes s u r f a c e s p e c i f i c r e t e n t i o n volumes can be c a l c u l a t e d . With c a r e f u l work a p r e c i s i o n o f f 2% i s easy t o a t t a i n i f a r e l i a b l e method i s a v a i l a b l e f o r t h e d e t e r m i n a t i o n o f t h e s u r f a c e area o f t h e adsorbent i n t h e column.
Recent r e s u l t s suggest,
t h a t t h e s u r f a c e area o f
the
c h e m i c a l l y bonded l a y e r i s n e a r l y t h e same as t h a t o f t h e u n d e r l y i n g s i l i c o n d i o x i d e ( r e f s . 21 and 22). (See analogy i n t h e p r o p o s a l o f M a r t i n f o r t h e e s t i m a t i o n o f t h e s u r f a c e area o f a duplex f i l m on an i n e r t s u p p o r t ( r e f . 23)). In conclusion,
i t i s proposed t o r e c o r d r e t e n t i o n i n l i q u i d / s o l i d chromato-
graphy as s u r f a c e s p e c i f i c r e t e n t i o n volume. A c t u a l l y , t h e analogous v a l u e , t h e weight s p e c i f i c r e t e n t i o n volume,
played an i m p o r t a n t r o l e i n t h e development
o f t h e o r e t i c a l aspects o f r e t e n t i o n i n gas chromatography.
vs In the calculation,
=
3S
[kl
rn-23
s u r f a c e area can be t a k e n as t h e s u r f a c e
area o f
the
s i l i c o n d i o x i d e i n t h e column. It i s recommended t o use V P / , ~ ~ f o r t h e hold-up volume determined e i t h e r b y t h e weighing method o r b y t h e measurement g i v e n i n eqn. 18.
ACKNOWLEDGEMENTS T h i s paper r e p o r t s on t h e p r o j e c t supported b y t h e Fonds National Suisse de l a Recherche E i e n t i f i q u e Eng 1 is h
.
. We
thank Mrs. L i s a B e l v i t o f o r c o r r e c t i o n o f t h e
REFERENCES
1 D. de Vault, J. h e r . Chem. SOC., 62 (1940) 1583. 2 F. H e l f f e r i c h and G. K l e i n , i n J.C. Giddings and R.A. 3 4 5
6 7 8 9
10
Keller (Editors), "Mu1 ticomponment Chromatography - Theory o f I n t e r f e r e n c e " , Marcel Dekker , New York, 1970. F. Riedo and E.sz. Kovdts, J. Chromatogr., 239 (1982) 1. P. V a l e n t i n and G. Guiochon, J. Chromatogr. Sci., 14 (1976) 56 and 132; see a l s o J.F.K. Huber and R.G. G e r r i t s e , J. Chromatogr., 58 (1971) 137. A.J.P. M a r t i n and R.L.M. Synge, Biochem. J., 35 (1941) 1358. See e.g. K. Hostettman, i n J.C., Giddings, E. Grushka, J. Cazes and Ph.R. Brown ( E d i t o r s ) , "Advances i n Chromatography", Marcel Dekker Vol 21 (1982). A.T. James and A.J.P. M a r t i n , Biochem. J., 50 (1952) 679. J.H. Knox and E.sz. Kovdts, d i s c u s s i o n c o n t r i b u t i o n , Faraday Symposium No. 15, B r i g h t o n , 1980, Royal S o c i e t y of Chemistry, London, 1980, p. 171. N.L. Ha, J. Ungvarai and E.sz. Kovdts, Anal. Chem.,54 (1982) 2410. See e.g. G. Schay and L. Gy. Nagy, " A d s o r p t i o n a t L i q u i d / S o l i d and L i q u i d / Gas I n t e r f a c e s " ( i n Hungarian), i n " A k6mia djabb eredm6nyei"; 6. Csdkvdry ( E d i t o r ) , A d a d h i a i Kiadb, Budapest, 1974, Vol. 18 p.7.
217 11. S.G. Ash and G.H. Findenegg, Spec. D i s c u s s i o n Faraday SOC., 1 (1970) 105; see a l s o L . L o r i n g and G.H. Findenegg, (1. C o l l o i d I n t e r f a c e S c i . , 84 (1981) 355. 12. G.A. Somorjai, " Chemistry i n Two Dimensions: Surfaces", C o r n e l l Univ. Press It h a c a and London. 1981 , p. 100-1 75. 13. F. Riedo and E.sz. Kovats, J . Chromatogr., 186 (1979) 47. 14. See e.9. G.E. Berendsen, P.J. Shoemakers, L. de Galan, G. Vigh, Z. Varga-Puhony and J. Inczedy, J . L i q u i d Chromatogr., 3 (1980) 1669. 15. A.M. K r s t u l o v i c , H. C o l i n and G. Guiochon, Anal. Chem., 54 (1987) 2482. 16. R.M. McCormick and B.L. Karqer, $1. Chromatogr., 199 (1980) 259; see a l s o f r o m t h e same a u t h o r s , Anal. Chem., 57 (1980) 2249. 17. W.R. Velander, J.-F. E r a r d and Cs. Horvath, J . Chromatoqr., 282 (1983) 211. 18. Cs. H o r v a t h and H.-J. L i n , J . Chromatoqr., 118 (1975) 401; see a l s o E.H. S l a a t s , J . C . Kraak, W.J.T. Brugman and H. Poppe, 2 . Chromatogr., 149 (1978) 255. 19. See e.g. J.K. Haken, M.S. Wainwriqht and R.J. Smith, J . Chromatogr., 133 (1977) 1 . 20. See e.g. M.J.M. W e l l s and C . R . C l a r k , A n a l . Chem., 53 (1981) 1341; B.L. Karger, J.R. Gant, A . H a r t k o o f and P.H. Weiner, J. Chromatogr., 128 (1976) 65. 21. J . Gobet and E.sz. Kovats, A d s o r p t i o n S c i . Technol., 1 (1984) 111. 22. J . Gobet and E.sz. Kovats, A d s o r p t i o n S c i . Technol., i n p r e s s . 23. R.L. M a r t i n , Anal. Chem., 35 (1963) 116.
RETENTION I N LIQUID/SOLID CHROMATOGRAPHY
ERVIN
SZ.
KOV~TS
L a b o r a t o i r e de Chimie-technique de 1 ' E c o l e P o l y t e c h n i q u e FCderale de Lausanne,
1015 Lausanne ( S w i t z e r l a n d ) .
SWARY R e t e n t i o n d a t a i n l i q u i d / s o l i d chromatography a r e recorded on t h e b a s i s o f e q u a t i o n s which were developed f o r l i q u i d / l i q u i d and g a s / l i q u i d chromatography. It i s shown t h a t these e q u a t i o n s a r e inadapted.
It i s a l s o shown t h a t r e t e n t i o n
i n l i q u i d / s o l i d chromatography can be g i v e n i n terms o f Gibbs' d e s c r i p t i o n o f t h e a d s o r p t i o n process. As i n systems w i t h r e v e r s i b l e a d s o r p t i o n e q u i l i b r i u m , t h e i n t r o d u c t i o n o f a c o n v e n t i o n i s necessary.
In the l i g h t o f t h i s retention
equation, t h e e n e r g e t i c s o f t h e a d s o r p t i o n process i s discussed as w e l l as d i f f e r e n t methods o f t h e d e t e r m i n a t i o n o f t h e hold-up volume.
INTRODUCTION
De V a u l t was t h e f i r s t t o g i v e an e x a c t s o l u t i o n o f r e t e n t i o n i n chromatography, c o n s i d e r e d t o proceed t h r o u g h i n f i n i t e s i m a l e q u i l i b r i u m steps ( r e f . 1). I n t h e mathematical s o l u t i o n , matrix.
r e t e n t i o n volumes appear as e i g e n v a l u e s o f a
The r e s u l t s were a p p l i e d b y Helfferich and K l e i n f o r t h e d i s c u s s i o n o f
chromatography ( r e f .
2).
R e c e n t l y i t was shown t h a t t h e model o f de V a u l t be-
comes g e n e r a l l y a p p l i c a b l e b y i n t r o d u c i n g a new s i m p l e thermodymanic f u n c t i o n the i s o c r a t i c capacity,
?iK ( r e f . 3 ) . This new f u n c t i o n i s t h e m a t e r i a l con-
t e n t o f an open system ( t h e column) i n e q u i l i b r i u m w i t h an i n f i n i t e r e s e r v o i r o f a f l u i d m i x t u r e ( s e e F i g . 1). The s p e c i f i c s o l u t i o n f o r a n a l y t i c a l chromatography under i s o t h e r m a l and i s o c r a t i c c o n d i t i o n s i s g i v e n b y eqn. 1
where vR,i
i s t h e r e t e n t i o n volume o f an i n f i n i t e s i m a l sample o f i (component
206
-
I n f i n i t e reservoir with a f l u i d m i x t u r e o f the composition: s;" = x ou,AYXp,B(=l-XA) 0 A
x
= xu
where x
, ~ * X u , ~ y X p , ~ ~
su
+
0
/
I s o c r a t i c c a p a c i t y o f t h e open system (column)
K" K
A
n
K
= no
no K,B
-
n
K,A'
- 'K,A'
where n
K ,SU
K,B'
n
K,SU
+O
F i g . 1 The i s o c r a t i c c a p a c i t y o f t h e column, ;n i n equilibrium with a binary m i x t u r e o f A and B o f t h e composition, x i and t h e i s o c r a t i c c a p a c i t y n, i n t h e presence o f a t h i r d component, su ( s o l u t e ) o f i n f i n i t e s i m a l c o n c e n t r a t i o n , xsu. o f the eluent, e l u e n t , nK,j
A,B
... o r
solute,
su),
v;
i s t h e mean molar volume o f t h e
i s t h e column c a p a c i t y o f component,
i, and p*
i s the composition
o f t h e m o b i l e phase. The i d e a l i z e d chromatographic column i s c o n s i d e r e d t o have a u n i f o r m c r o s s s e c t i o n a t any d i s t a n c e from t h e i n l e t , f i l l e d w i t h a quasi continuum o f a porous powder. E q u i l i b r i u m i s i n s t a n t a n e o u s i n any c r o s s s e c t i o n o f t h e column and t h e r e i s no a x i a l d i f f u s i o n . Therefore, t h e p e r t u r b a t i o n o f t h e e l u e n t b y an i n f i n i t e s i m a l s i g n a l a t t h e column i n l e t w i l l appear a t t h e column o u t l e t r e t a i n e d , b u t n o t deformed.
RETENTION I N M S / L I Q U I D AND LIQUID/LIQUID CHROMATOGRAPHY I n o r d e r t o demonstrate t h e use o f eqn. 1 i t w i l l now b e a p p l i e d t o g a s / l i q u i d chromatography w i t h a m o b i l e phase composed o f a m i x t u r e o f two i d e a l gases,
S and I. Component S i s s o l u b l e i n t h e s t a t i o n a r y l i q u i d , whereas compo-
nent I i s i n s o l u b l e . V,
= w,/d,
The volume o f t h e s t a t i o n a r y phase can be c a l c u l a t e d as
b y supposing t h a t t h e s t a t i o n a r y l i q u i d f i l m on t h e i n e r t sup-
p o r t has t h e same d e n s i t y , given by
d,,
as t h e b u l k .
The column c a p a c i t i e s are t h e n
207
where c i s t h e c o n c e n t r a t i o n ,
[mol
1-11, t h e s u b s c r i p t s p and
5
refer t o the
m o b i l e and s t a t i o n a r y phases r e s p e c t i v e l y and t h e o t h e r symbols a r e as b e f o r e . Having t h e necessary e x p r e s s i o n s a t hand (eqns. 2 and 4) a p p l i c a t i o n o f eqn. 1 g i v e s t h e same e x p r e s s i o n f o r t h e r e t e n t i o n volume f o r t h e p e r t u r b a t i o n o f t h e e l u e n t c o m p o s i t i o n b y i n j e c t i o n s o f v e r y small amounts of S o r I. I n j e c t i o n o f e i t h e r o f t h e gases provokes a concentration peak pressed w i t h x,s
where V,
. Its
r e t e n t i o n volume,
ex-
as t h e independent v a r i a b l e , i s g i v e n i n eqn. 5
i's t h e hold-up volune (dead volume) o f t h e column. T h i s same r e s u l t
was found by Valentin and Guiochon ( r e f . 4).
I n t h e s p e c i a l case where t h e r e i s
o n l y an i n s o l u b l e c a r r i e r and t h e s o l u b l e gas i s i n j e c t e d as s o l u t e ( S
+
su),
eqn. 5 s i m p l i f i e s t o
where
KSu
i s the partition coefficient o f the solute at
infinite dilution
Eqn.6 i s t h e c l a s s i a l r e l a t i o n s h i p o f Martin and Synge f o r r e t e n t i o n volume i n
1 i q u i d / l i q u i d chromatography ( r e f . 5)
, calculated
today as " C r a i g ' s c o u n t e r c u r r e n t b a t t e r y " machine" ( r e f . 6).
w i t h t h e a i d o f a model known
or the "droplet
counter c u r r e n t
I n t h e i r model t h e chromatographic column was compared w i t h
a h y p o t h e t i c a l b a t t e r y o f s e p a r a t i n g c e l l s g i v i n g t h e same chromatogram as t h e chromatographic column i n q u e s t i o n . The number o f t h e c e l l s o f t h e h y p o t h e t i c a l b a t t e r y was a measure o f t h e peak w i d t h and t h e r e b y t h e e f f i c i e n c y o f t h e c h r o matographic column. T h i s d e s c r i p t i o n i n i t i a l l y c r e a t e d some c o n f u s i o n about t h e meaning o f a c e l l , which was c a l l e d a p l a t e , s u g g e s t i n g t h e same r o l e p l a y e d b y a p a r t i t i o n i n g c e l l as t h a t b y a s e p a r a t i n g p l a t e i n d i s t i l l a t i o n . Furthermore, s i g n a l d e f o r m a t i o n i n t h i s model i s due t o t h e f i n i t e volume o f t h e s e p a r a t i n g c e l l s and n o t t o d i f f u s i o n and t o k i n e t i c s o f e q u i l i b r i u m a t t a i n m e n t . Nevertheless, t h e c e l l model gave t h e r i g h t answer f o r t h e r e l a t i o n s h i p of t h e r e t e n t i o n volume w i t h t h e p a r t i t i o n c o e f f i c i e n t i n l i q u i d / l i q u i d and gas/ l i q u i d chromatography ( r e f . 7 ) . It was t h e r e f o r e proposed t o use t h e net-reten-
t i o n volune.
f o r the characterization o f retention.
The hold-up volume,
Vp,
c o u l d be de-
t e r m i n e d as t h e r e t e n t i o n volume o f a n o n - r e t a i n e d substance, a substance i n s o -
208
l u b l e i n t h e s t a t i o n a r y phase. A r e t e n t i o n volume s m a l l e r t h a n t h e hold-up v o lume was n o t p o s s i b l e .
In gas chromatography t h e n e t - r e t e n t i o n volume i s r e l a -
t e d t o Henry's coefficient b y
where
nu and wu a r e t h e number o f moles and t h e mass o f t h e s t a t i o n a r y li-
q u i d i n t h e column r e s p e c t i v e l y , constant,
Tc i s t h e column temperature,
hsu i s Henry's c o e f f i c i e n t
R i s t h e gas
and gsu i s H e n r y ' s m o l a l c o e f f i c i e n t
o f the solute a t i n f i n i t e d i l u t i o n i n t h e actual solvent.
Eqn. 9 i s d e r i v e d
from eqn. 8. It g i v e s t h e r e l a t i o n s h i p o f t h e r e t e n t i o n volume w i t h t h e
diffe-
rence o f t h e standard chemical potential of the substance between t h e i d e a l d i l u t e s o l u t i o n and t h e gas s t a t e as e i t h e r h ~ p i u( r e l a t e d t o hsu) o r 9 A p i u ( r e l a t e d t o g s u ) . The gas phase i s c o n s i d e r e d t o be a m i x t u r e o f t h e i d e a l c a r r i e r and t h e substance vapor as i d e a l gas. RTclnVN,su = RTcln(n uRTc ) - h ~ p Z u= RTcln(wuRTc/lOOO)
- 9~pru
This simple r e l a t i o n s h i p between t h e l o g a r i t h m o f t h e n e t r e t e n t i o n volume and t h e standard chemical p o t e n t i a l d i f f e r e n c e has been v e r y u s e f u l f o r e s t a b l i shing l i n e a r f r e e energy r e l a t i o n s h i p s f o r t h e p r e d i c t i o n o f chromatographic data. It a l s o helped t h e u n d e r s t a n d i n g o f i n t e r a c t i o n f o r c e s . S i m i l a r r e l a t i o n s h i p s can be d e r i v e d , mutatis mutandis, f o r l i q u i d / l i q u i d chromatography.
RETENTION IN LIQUID/SOLID CHROMATOGRAPHY The success o f l i q u i d / l i q u i d chromatography had a s e r i o u s impact on t h e development o f chromatographic techniques. This impact was even a m p l i f i e d by t h e d i s c o v e r y o f g a s / l i q u i d chromatography b y Martin and James ( r e f .
7).
It gave
t h e impetus and l e a d i n g ideas f o r t h e achievement o f h i g h e r performance i n l i q u i d / s o l i d chromatography. The 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 column t e c h n o l o g y o f g a s / l i q u i d chromatography suggested t h e seducing i d e a t o a l s o a p p l y t h e succ e s s f u l r e s u l t s o f t h e model o f Martin and Synge t o l i q u i d / s o l i d chromatography b y f o r m a l analogy, and t o a p p l y eqns. 7, 8 and 9 w i t h o u t a d a p t a t i o n t o t h e desc r i p t i o n o f r e t e n t i o n . Therefore, s e v e r a l papers d i s c u s s t h e meaning o f t h e vo-
lune o f the stationary phase and t h e r e l a t e d problem o f t h e hold-up volune. Before d i s c u s s i n g these essays,
l e t us f i r s t a p p l y eqn. 1 f o r t h e r e t e n t i o n
volume i n l i q u i d / s o l i d chromatography. The molar i s o c r a t i c c a p a c i t y o f a column f i l l e d w i t h an adsorbent i s g i v e n by
209
and =
nK,tOt
where
S
Vp/CX/V$&
+
rtot/cx
i s t h e s u r f a c e area o f t h e adsorbent, T i i s t h e s u r f a c e c o n c e n t r a t i o n
of t h e i t h component and a l l o t h e r symbols a r e as b e f o r e . I n a system where adsorption i s r e v e r s i b l e , surface concentration i s not a defined q u a n t i t y without introducing
an a d d i t i o n a l e q u a t i o n d e f i n i n g
concerning t h e
adsorption
equilibrium.
By
a convention (Convention X =CX) using the
particular
convention
Nothing t h a t t h e sum o f t h e s u r f a c e c o n c e n t r a t i o n s [pmol w 2 ] i s equal t o zero (is Adsorbed i n terms o f number o f moles, n: nNA);
a d s o r p t i o n i s d e s c r i b e d i n terms o f reduced surface concentrations, ri/,,NA PAC-symbol:
n$n)
/S).
Using eqns. 10 and 11, a p p l i c a t i o n o f eqn.
(IU-
1 gives f o r
t h e r e t e n t i o n volume:
if t h e nNA-convention i s a p p l i e d . It i s seen t h a t t h e h o l d - u p volume, Vp/nNA i s defined
i n connection w i t h the given convention.
similar
A
d e r i v e d i f a d s o r p t i o n i s expressed i n an unusual u n i t , Y [ p l m-'1
equation
, is
and u s i n g an
unusual convention, vNA (Nothing i s Adsorbed i n terms o f volume, v ) . This g i v e s
where, g, i s f o r t h e volume f r a c t i o n . For chromatography w i t h a binary eluent
composed o f A and B eqn. 14 g i v e s
eqn. 15 f o r t h e r e t e n t i o n volume o f a c o n c e n t r a t i o n p e r t u r b a t i o n ( i n j e c t i o n o f a small amount o f A o r 6 ) t o g i v e a c o n c e n t r a t i o n peak, cc,
Thus,
t h i s r e t e n t i o n volume i s r e l a t e d t o t h e d e r i v a t i v e o f t h e a d s o r p t i o n
i s o t h e r m o f component A o f t h e e l u e n t , ' Y A / ~ N A . ( T h i s r e l a t i o n s h i p i s an approx i m a t i o n , i t i s s t r i c t l y v a l i d o n l y f o r p e r f e c t l i q u i d m i x t u r e s ) . The r e t e n t i o n volume o f a l a b e l l e d component o f t h e e l u e n t , A* o r B*,
i s directly related to
210 t h e a d s o r p t i o n isotherm:
F i n a l l y , t h e r e t e n t i o n volume o f a s o l u t e i s g i v e n b y
These r e l a t i o n s h i p s a l s o d e f i n e t h e a c t u a l h o l d - u p volume b y g i v i n g t h e e x p e r i mental method o f i t s d e t e r m i n a t i o n . Considering t h a t
YA/,NA
+
Y ! B / ~ N A = 0,
the
sum o f eqn. 16 g i v e s a f t e r rearrangement:
Eqn.
18 was f i r s t d e r i v e d by Knox on t h e b a s i s o f a d i f f e r e n t argumentation
( r e f . 8).
( S i m i l a r r e l a t i o n s h i p s a r e r e a d i l y d e r i v e d from eqn.
t h e method o f c a l c u l a t i o n o f V,,/nNA
13 g i v i n g a l s o
(ref. 3)).
As a t e s t o f these r e l a t i o n s h i p s l e t us examine e x p e r i m e n t a l s p e c i f i c r e t e n t i o n volumes o f l a b e l l e d ( d e u t e r a t e d ) a c e t o n i t r i l e ,
l a b e l l e d water ( H D O ) ,
and
t h a t o f t h e c o n c e n t r a t i o n peak, p l o t t e d i n F i g . 2 as a f u n c t i o n o f e l u e n t comp o s i t i o n , w i t h tetradecyldimethylsiloxy m o d i f i e d s i l i c a as adsorbent ( r e f . 9 ) . R e t e n t i o n volumes were c o r r e c t e d w i t h t h e hold-up volume from eqn. 18 t o g i v e n e t - r e t e n t i o n volumes.
The surface specific retention volune was t h e n
calcu-
l a t e d as
P o i n t s on t h e reduced excess a d s o r p t i o n isotherm,
Y A / ~ N A, c o u l d be c a l c u l a t e d
w i t h t h e a i d o f t h e r e l a t i o n s h i p s summarized i n eqns. 19 from t h e s p e c i f i c r e -
- Y!A/~NA) p l o t t e d i n Fig. 3 as a f u n c t i o n o f e l u e n t c o m p o s i t i o n . The i s o t h e r m i s o f t h e S-type. S i m i l a r
t e n t i o n volumes o f A* and B* ( n o t e t h a t Y B / ~ N A=
isotherms were observed by Schay and Nagy a t n o n - p o l a r measurements ( r e f .
interfaces i n static
10). The r e g r e s s i o n f u n c t i o n o f t h e a d s o r p t i o n isotherm,
shown i n F i g . 3 p e r m i t s us i n t u r n t o p r e d i c t t h e s p e c i f i c r e t e n t i o n volumes o f A* and B* and t h a t o f t h e c o n c e n t r a t i o n peak. The t r a c e o f t h e s e f u n c t i o n s i s shown i n F i g . 2. The agreement i s e x c e l l e n t .
211
F i g . 2. Surface s p e c i f i c r e t e n t i o n volume o f d e u t e r a t e d a c e t o n i t r i l e and HDO, and that o f t h e c o n c e n t r a t i o n peak in a c e t o n i t r i l e / H 2 0 as a f u n c t i o n o f t h e c o m p o s i t i o n o f t h e e l u e n t ( r e f . 9 ) . The volume f r a c t i o n , 0, was c a l c u l a t e d w i t h partial molar volumes. Temperature: 2 P C ; s t a t i o n a r y phase: L i c h r o s o r b - S I 1 0 0 covered with tetradecyldimethylsiloxy substituents. Curves c a l c u l a t e d w i t h eqns. 15 and 1 7 f r o m t h e a d s o r p t i o n i s o t h e r m shown i n F i g . 3.
0 Y
.o
-.2
'H20 H,O/vNA
F i g . 3. A sor t i o n isotherms, \y ~~0 V~~ , from ace ,n i r i l e / H 2 0 m i x t u r e s a( t h e s u r f ace of t e t r adecyl d i m e t h y l s i 1o x y covered s i l i c o n d i o x i d e . F u l l symbols and c u r v e f o r Tc = 20.0 O C ; open symbols and dashed l i n e f o r Tc = 4O.O0C. Points c a l c u l a t e d w i t h eqn. 19 ( r e f . 9).
-.4
-.6 0
A f i r s t c o n c l u s i o n from t h i s d i s c u s s i o n i s t h a t t h e hold-up volume i n l i q u i d / s o l i d chromatography has t o b e c o n s i d e r e d as a correctilrg volune f o r t h e c a l c u l a t i o n o f t h e n e t - r e t e n t i o n volume f o l l o w i n g eqn. 7, and as such i t cannot be i d e n t i f i e d with any physical volune inside the colunn. It was s t a t e d t h a t t h e hold-up volume, c a l c u l a t e d w i t h t h e vNA c o n v e n t i o n does correspond t o
212
t h e volume o f t h e m o b i l e phase i n t h e column. S t r i c t l y speaking,
t h i s i s not
t r u e . F i r s t l y , experiments o f Ash and Findenegg show t h a t t h e d e n s i t y o f a p u r e l i q u i d near an i n t e r f a c e i s d i f f e r e n t from t h a t i n t h e b u l k ( r e f . 11). Obviousl y , t h e l i q u i d has a d i f f e r e n t s t r u c t u r e i n t h e neighbourhood o f a s o l i d as
i l l u s t r a t e d i n F i g . 4.
Secondly,
i n a b i n a r y m i x t u r e t h e p a r t i a l molar volume
1i q u i d
solid
a
b
Fig. 4. I l l u s t r a t i o n o f t h e m o l e c u l a r o r d e r i n p u r e l i q u i d s near a l i q u i d / s o l i d i n t e r f a c e : a: t h e s t r u c t u r e o f t h e l i q u i d near t h e i n t e r f a c e i s t h e same as i n t h e b u l k ; b: t h e l i q u i d i s ordered near t h e i n t e r f a c e , t h e r e f o r e i t has a h i g h e r d e n s i t y ( c f . r e f . 11).
o f an adsorbed component i s c e r t a i n l y d i f f e r e n t from t h a t i n t h e b u l k , because t h e p a r t i a l molar volume i s a f u n c t i o n o f c o m p o s i t i o n and t h e c o m p o s i t i o n near t h e i n t e r f a c e i s d i f f e r e n t from t h a t i n t h e b u l k . These a r e m i n o r e f f e c t s i n b i n a r y systems used as e l u e n t s i n l i q u i d / s o l i d chromatography w i t h a non-polar solid,
and a l t h o u g h w a t e r -
ideality,
organic modifier mixtures deviate s e r i o u s l y from
t h i s volume can be equated w i t h a v e r y good a p p r o x i m a t i o n t o t h e
t o t a l volume o f t h e m o b i l e phase i n t h e column.
V,,/NA
,
I n experiments t h e volume,
i s almost independent o f t h e n a t u r e o f t h e m o b i l e phase ( r e f . 9).
o t h e r words,
In
b y t h e c o n v e n t i o n vNA t h e Gibbs d i v i d i n g p l a n e i s s i t u a t e d v e r y
near t o t h e r e a l , p h y s i c a l d i v i d i n g p l a n e between t h e s o l i d and t h e l i q u i d . A second c o n c l u s i o n i s t h a t a stationary phase cannot be i d e n t i f i e d
. Nume-
r o u s a t t e m p t s have been made t o c r e a t e an i m a g i n a r y s t a t i o n a r y phase b y propos i n g monolayer o r b i l a y e r a d s o r p t i o n models (see F i g . 5 ) .
In r e a l systems t h e
s i t u a t i o n i s more c o m p l i c a t e d as shown by Somorjai i n t h e s t u d y o f " f r o z e n " ads o r p t i o n e q u i l i b r i a i n l i q u i d metal m i x t u r e s ( r e f .
12). Even i f , i n c e r t a i n
systems, a monolayer o r b i l a y e r a d s o r p t i o n may be a v e r y good a p p r o x i m a t i o n f o r
I
0
1
1, -
a
1
213
-
0
1
FA
....
.... .... .... .... .... .... ....
....... ................... ................... ................... .................. ................... ................... ................... 9
solid
a
C
F i g . 5. C o n c e n t r a t i o n p r o f i l e s near a l i q u i d / s o l i d i n t e r f a c e : a: monomolecular a d s o r p t i o n ; b: b i m o l e c u l a r a d s o r p t i o n ; c : a more complex s i t u a t i o n ( c f . r e f . 12). the real situation,
t h e whole adsorbed m a t e r i a l
brium w i t h t h e b u l k : t h e where
one of
i s always i n dynamic e q u i l i -
surface phase i s not autonomous. ( A c t u a l l y , t h e case
t h e components
is really
immobilized
a t t h e surface
i s not
i n t e r e s t i n g from t h e v i e w p o i n t o f t h e chromatographic process. T h i s case has t o be considered as chromatography a t t h i s newly formed l i q u i d / s o l i d i n t e r f a c e ) . A t h i r d c o n c l u s i o n i s t h a t t h e net r e t e n t i o n volune o f a solute can be negat i v e r e g a r d l e s s o f which c o n v e n t i o n i s used f o r t h e d e t e r m i n a t i o n o f t h e h o l d up volume. The s o l u t e can have a n e g a t i v e reduced a d s o r p t i o n i f i t i s l e s s adsorbed then e i t h e r o f t h e components o f t h e e l u e n t s ( c f . eqn. 17). The l a s t c o n c l u s i o n concerns t h e e n e r g e t i c s o f t h e r e t e n t i o n .
In l i q u i d /
s o l i d chromatography t h e r e t e n t i o n volume o f a s o l u t e i s d i r e c t l y r e l a t e d t o t h e specific Helmholtz f r e e energy o f t h e i n t e r f a c e ( r e f . 1ink
13). The necessary
s g i v e n b y Gibbs' a d s o r p t i o n e q u a t i o n ( c o n s t a n t t e m p e r a t u r e ) :
dy = where y i s t h e s p e c i f i c f r e e energy o f t h e i n t e r f a c e ( i n t e r f a c i a l t e n s i o n ) , psu
i s t h e chemical p o t e n t i a l o f t h e s o l u t e and rs,/ANA
(IUPAC
t h e r e l a t i v e excess surface concentration o f t h e s o l u t e ,
symbol:
n$,A)/s)
r e l a t i v e t o A,
A is Not Adsorbed a t t h e i n t e r f a c e (ANA). The t h e c o n v e n t i o n t h a t component c o r r e s p o n d i n g hold-up volume i s g i v e n b y
is with
214
as,
b y convention,
component
A i s not
adsorbed.
The c o r r e s p o n d i n g s u r f a c e
s p e c i f i c r e t e n t i o n volume i s g i v e n b y ( c f . eqn. 13):
Combination o f eqns.
20 and 22 gives,
after
t h e necessary t r a n s f o r m a t i o n s
( r e f . 13):
F o l l o w i n g eqn. 23 t h e r e t e n t i o n volume o f a s o l u t e i s d i r e c t l y r e l a t e d t o t h e
decrease o f the specific f r e e energy o f the i n t e r f a c e
,
a d s o r p t i o n and not t o the chemical potential o f the solute
y,
caused b y s o l u t e
. Therefore,
eqn. 23
i s o f l i t t l e use i n t h e understanding and p r e d i c t i o n o f chromatographic d a t a .
CONCLUSIONS L e t us r e t u r n now t o t h e d i s c u s s i o n o f t h e current description o f renten-
t i o n i n 1 i q u i d / s o l i d chromatography. The most p o p u l a r method o f p r e s e n t a t i o n o f such d a t a i s t o c a l c u l a t e t h e k'-value o f a s o l u t e d e f i n e d b y
Furthermore, i t i s b e l i e v e d t h a t eqn. 23 i s a p p l i c a b l e RTcln k,;
=
C
-
~g~~ t
25 1
where t h e c o n s t a n t , C, i s a r b i t r a r y because (as i t i s s t a t e d ) t h e volume o f t h e s t a t i o n a r y phase i s n o t d e f i n e d .
On t h e b a s i s o f t h e f o r e g o i n g d i s c u s s i o n , eqn. 24 i s meaningless ( o r h s a t r i v i a l meaning) and eqn. 25 i s wrong. Even b y a d m i t t i n g , f o r t h e sake o f d i s cussion, t h a t t h e k ' - v a l u e i n s i m i l a r columns,
i s p r a c t i c a l f o r t h e comparison o f d a t a determined
i t i s seen t h a t t h i s c h a r a c t e r i s t i c v a l u e measures t h e
r e t e n t i o n i n t h e u n i t s o f t h e hold-up volume. F i r s t l y , t h e hold-up volume i s small,
i t can be determined w i t h a p r e c i s i o n o f o n l y f 3%. Secondly,
current
215 apinions h i g h l y d i f f e r
as t o t h e method o f
i t s determination
meaning. L e t us s h o r t l y r e v i e w t h e p r o p o s a l s ( r e f s .
and about
its
14 and 1 5 ) .
I n j e c t one o f t h e marked components (A*) o f t h e e l u e n t and accept V,
= VR,A*
( r e f . 1 6 ) . This h o l d - u p volume i s e q u i v a l e n t t o t h a t d e r i v e d w i t h t h e A i s n o t adsorbed c o n v e n t i o n (ANA; see eqn. 21) I n j e c t b o t h marked components and c a l c u l a t e V,
w i t h eqn. 8
(see discussion
t h e r e ) ( r e f . 8). I n j e c t b o t h marked components and always accept t h e s m a l l e r o f t h e r e t e n t i o n volumes, VR,A* lieved that
VR,B*
or
,
as t h e h o l d - u p volume.
r e t e n t i o n volumes
smaller
than
V,
I n t h i s p r o p o s a l i t i s beare n o t possible
(as
in
l i q u i d / l i q u i d and g a s / l i q u i d chromatography) ( r e f . 17). The column i s f i l l e d w i t h two p u r e l i q u i d s s u c c e s s i v e l y and weighed ( r e f . 1 8 ) . The h o l d - u p volume i s c a l c u l a t e d as
where Aw i s t h e weight d i f f e r e n c e o f t h e column f i l l e d w i t h t h e two l i q u i d s (Aw = wc,1-wc,2) d2). (Ad = d l
-
and Ad i s t h e d i f f e r e n c e ' o f t h e d e n s i t y o f t h e two l i q u i d s T h i s experiment i s e s s e n t i a l l y t h e same as t h a t o f Ash and
Findenegg ( r e f . 11) b u t i t i s supposed t h a t t h e r e a r e no d e n s i t y changes i n the
liquids
near
the
interface.
If
hold-up volume i s about t h e same as V,N,/ A
this
is
approximately
true,
this
(see eqn. 1 8 ) .
The l o g a r i t h m of t h e r e t e n t i o n volumes o f a homologous s e r i e s a r e " l i n e a r i zed" as t h e f u n c t i o n o f
z, t h e carbon number, t o g i v e
Vp
(ref.19).
This
procedure i s d e r i v e d by f o r m a l analogy w i t h gas chromatography. Note t h a t i n l i q u i d / s o l i d chromatography n e t r e t e n t i o n can be n e g a t i v e
and t h a t
the
l o g a r i t h m o f a n e g a t i v e number has no sense. I n j e c t a "chosen s o l u t e " , y, b e l i e v e d t o be n o n - r e t a i n e d and accept V R , ~ as hold-up volume ( r e f . 20). From t h e v i e w p o i n t o f Gibbs' d e s c r i p t i o n o f adsorption,
t h i s proposal
i n t r o d u c e s t h e c o n v e n t i o n yNA,
i.e.
y
i s not
adsorbed a t any e l u e n t c o m p o s i t i o n . Hold-up volumes determined f o l l o w i n g these p r o p o s a l s d i f f e r b y a t l e a s t as much as f 20%. Consequently,
r e t e n t i o n d a t a g i v e n i n u n i t s o f t h e hold-up volumes
w i l l v a r y a t l e a s t b y t h e same o r d e r o f magnitude. As a c o n c l u s i o n , t h e h o l d - u p volume i s n o t a s u i t a b l e u n i t f o r r e c o r d i n g r e t e n t i o n d a t a even i f i t s method o f d e t e r m i n a t i o n c o u l d be agreed upon.
If hold-up
volume i s used as a correction i n s t e a d o f a u n i t
i n order t o
c a l c u l a t e n e t - r e t e n t i o n volumes, t h e e r r o r o f t h e c o r r e c t i o n appears as a s m a l l r e l a t i v e e r r o r i n t h e d e t e r m i n a t i o n o f h i g h e r r e t e n t i o n volumes.
In t h e l i g h t
216
o f t h i s proposal,
t h e a b s o l u t e v a l u e o f t h e hold-up volume i s of
l e s s impor-
tance. From t h e n e t - r e t e n t i o n volumes s u r f a c e s p e c i f i c r e t e n t i o n volumes can be c a l c u l a t e d . With c a r e f u l work a p r e c i s i o n o f f 2% i s easy t o a t t a i n i f a r e l i a b l e method i s a v a i l a b l e f o r t h e d e t e r m i n a t i o n o f t h e s u r f a c e area o f t h e adsorbent i n t h e column.
Recent r e s u l t s suggest,
t h a t t h e s u r f a c e area o f
the
c h e m i c a l l y bonded l a y e r i s n e a r l y t h e same as t h a t o f t h e u n d e r l y i n g s i l i c o n d i o x i d e ( r e f s . 21 and 22). (See analogy i n t h e p r o p o s a l o f M a r t i n f o r t h e e s t i m a t i o n o f t h e s u r f a c e area o f a duplex f i l m on an i n e r t s u p p o r t ( r e f . 23)). In conclusion,
i t i s proposed t o r e c o r d r e t e n t i o n i n l i q u i d / s o l i d chromato-
graphy as s u r f a c e s p e c i f i c r e t e n t i o n volume. A c t u a l l y , t h e analogous v a l u e , t h e weight s p e c i f i c r e t e n t i o n volume,
played an i m p o r t a n t r o l e i n t h e development
o f t h e o r e t i c a l aspects o f r e t e n t i o n i n gas chromatography.
vs In the calculation,
=
3S
[kl
rn-23
s u r f a c e area can be t a k e n as t h e s u r f a c e
area o f
the
s i l i c o n d i o x i d e i n t h e column. It i s recommended t o use V P / , ~ ~ f o r t h e hold-up volume determined e i t h e r b y t h e weighing method o r b y t h e measurement g i v e n i n eqn. 18.
ACKNOWLEDGEMENTS T h i s paper r e p o r t s on t h e p r o j e c t supported b y t h e Fonds National Suisse de l a Recherche E i e n t i f i q u e Eng 1 is h
.
. We
thank Mrs. L i s a B e l v i t o f o r c o r r e c t i o n o f t h e
REFERENCES
1 D. de Vault, J. h e r . Chem. SOC., 62 (1940) 1583. 2 F. H e l f f e r i c h and G. K l e i n , i n J.C. Giddings and R.A. 3 4 5
6 7 8 9
10
Keller (Editors), "Mu1 ticomponment Chromatography - Theory o f I n t e r f e r e n c e " , Marcel Dekker , New York, 1970. F. Riedo and E.sz. Kovdts, J. Chromatogr., 239 (1982) 1. P. V a l e n t i n and G. Guiochon, J. Chromatogr. Sci., 14 (1976) 56 and 132; see a l s o J.F.K. Huber and R.G. G e r r i t s e , J. Chromatogr., 58 (1971) 137. A.J.P. M a r t i n and R.L.M. Synge, Biochem. J., 35 (1941) 1358. See e.g. K. Hostettman, i n J.C., Giddings, E. Grushka, J. Cazes and Ph.R. Brown ( E d i t o r s ) , "Advances i n Chromatography", Marcel Dekker Vol 21 (1982). A.T. James and A.J.P. M a r t i n , Biochem. J., 50 (1952) 679. J.H. Knox and E.sz. Kovdts, d i s c u s s i o n c o n t r i b u t i o n , Faraday Symposium No. 15, B r i g h t o n , 1980, Royal S o c i e t y of Chemistry, London, 1980, p. 171. N.L. Ha, J. Ungvarai and E.sz. Kovdts, Anal. Chem.,54 (1982) 2410. See e.g. G. Schay and L. Gy. Nagy, " A d s o r p t i o n a t L i q u i d / S o l i d and L i q u i d / Gas I n t e r f a c e s " ( i n Hungarian), i n " A k6mia djabb eredm6nyei"; 6. Csdkvdry ( E d i t o r ) , A d a d h i a i Kiadb, Budapest, 1974, Vol. 18 p.7.
217 11. S.G. Ash and G.H. Findenegg, Spec. D i s c u s s i o n Faraday SOC., 1 (1970) 105; see a l s o L . L o r i n g and G.H. Findenegg, (1. C o l l o i d I n t e r f a c e S c i . , 84 (1981) 355. 12. G.A. Somorjai, " Chemistry i n Two Dimensions: Surfaces", C o r n e l l Univ. Press It h a c a and London. 1981 , p. 100-1 75. 13. F. Riedo and E.sz. Kovats, J . Chromatogr., 186 (1979) 47. 14. See e.9. G.E. Berendsen, P.J. Shoemakers, L. de Galan, G. Vigh, Z. Varga-Puhony and J. Inczedy, J . L i q u i d Chromatogr., 3 (1980) 1669. 15. A.M. K r s t u l o v i c , H. C o l i n and G. Guiochon, Anal. Chem., 54 (1987) 2482. 16. R.M. McCormick and B.L. Karqer, $1. Chromatogr., 199 (1980) 259; see a l s o f r o m t h e same a u t h o r s , Anal. Chem., 57 (1980) 2249. 17. W.R. Velander, J.-F. E r a r d and Cs. Horvath, J . Chromatoqr., 282 (1983) 211. 18. Cs. H o r v a t h and H.-J. L i n , J . Chromatoqr., 118 (1975) 401; see a l s o E.H. S l a a t s , J . C . Kraak, W.J.T. Brugman and H. Poppe, 2 . Chromatogr., 149 (1978) 255. 19. See e.g. J.K. Haken, M.S. Wainwriqht and R.J. Smith, J . Chromatogr., 133 (1977) 1 . 20. See e.g. M.J.M. W e l l s and C . R . C l a r k , A n a l . Chem., 53 (1981) 1341; B.L. Karger, J.R. Gant, A . H a r t k o o f and P.H. Weiner, J. Chromatogr., 128 (1976) 65. 21. J . Gobet and E.sz. Kovats, A d s o r p t i o n S c i . Technol., 1 (1984) 111. 22. J . Gobet and E.sz. Kovats, A d s o r p t i o n S c i . Technol., i n p r e s s . 23. R.L. M a r t i n , Anal. Chem., 35 (1963) 116.