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Pure Appl . Chem., Vol. 61, No. 11, pp. 2037-2040, 1989.Printed in Great Britain.@ 1989 IUPAC

Physico ch em cal aspects of I qu d chrom atography

Yu.V.Kazakevitch*, O.G.Larionov, Yu.A.Eltekov

I n s t l t u t e of P h y s i c a l C h e m i s t r y of t h e Academy of Sciencesof t h e USSR, Le n i ns k i p rosp . , 31, MOSCOW, SSR

ABSTRACT

Connection Between liqu id chromatography rete nti on param eters and t h eadsorpt ion equi l ibr ium constant i s disc usse d. The methods of deaQ volumedeterminations are considered and also the dependence of retention volumeson the eluent composition and surface chemistry o adsorben t a re descr ibed .

T H E O RYT he c r i t e r i o n of e q u i l i b r i u m i n t h e a d s o r p t i o n t h e r m o d y n a m i c s i s t h e

d G ) ( 1 )

or t h e e q u a l i t y o f c h em i ca l p o t e n t i a l s of t h e s o l u t i o n c o m po n e nt s i n v o lu m ea n d a d s o r p t i o n s o l u t i o n s

e q u a l i t y o f t h e G i b b s e n e r g y c h a ng e t o z e r o

m i l m is ( 2 )

m i m i o R T l n ( x i y i ) ( 3 )

C h em i ca l p o t e n t i a l s o f s o l u t i o n c om p o n en t s m ay be w r i t t e n i n fo rm :

F r o m e q u a t i o n (2) i t f o l l o w s t h a t :

A f t e r d i v i d i n g s u c h a n e q u a t i o n f o r c om po ne nt 1 b y a S i m i l a r e q u a t i o n f o rcomponent 2 r e o b t a i n :

E q u a t i o n 5 ) i s v a l i d f o r t h e c a s e of m ol ec ul e s i z e e q u a l i t y o f s o l u t i o ncomponents . T h i s e q u a t i o n d e s c r i b e s a n a d s o r p t i o n i s o t h e r m of s o l u t i o n s .From eqn. (5) w e c an d e r i v e e n e q u a t i o n f o r x is i .e . a n i s o t h e r m o t h ew hole c o n t e n t a n d a l s o G l b b s e x c e s s a d s o r p t i o n i s o t h e r m a s t h e d i f f e r e n c ex is -x iLr

T h i s i s s o c a ll e d e xc e ss a d s o r p t i o n i s o t h e r m , w h i c h v a l u e m ay b e b o t hg r e a t e r or l e s s t h a n z e r o . I t i s e s s e n t i a l t h a t i f t h e c om p ou nd su n d e r i n v e s t i g a t i o n i n t e r a c t w i t h t h e s u r f a c e wea ker t h a n t h e s ol ve n t, t h e nt h e i r e x c e s s a d s o r p t i o n i s n e g a t i v e .

T h e a d s o r p t i o n p he no m en a i n c h r o m a t o g r a p h y o c c u r u n d e r d y na mi cc o n d i t i o n s . M . S . Ts w e t t was t h e f i r s t w h o d i s c o v e r t h e c o n n e c t i o n o fadsorpt ion phenomena w i t h t h e speed of t h e component moving through column.

m -

G -K -Y -r -y -c -x -

N O TAT I O N

c h e m l c a l p o t e n t i a l s of s o l u t i o ncomponents (dG/dxi) ;

G i b b s f r e e e n e rg y ;a d s o r p t i o n e q u i l i b r i u m c o n s t a n t ;a c t i v i t y c o e f f ic l en t ;G i b b s e x c e s s a d s o r p t i o n ;dead volume o f c h r o m a t o g r a p h i ccolumn;c o n c e n t r a t i o n ( m o l e / l )

mole f r a c t i o n of s o l u t l o ncomponent ;

S - a d s o r be n t s u r f a c e a r e a ;V a - v ol um e of a d s o r p t i o n l a y e r ;w - e l u e n t f l o w r a t e ;Vr - r e t e n t l o n v o l u m e ;k’ - c a p a c i t y f a c t o r ;

s u b s c r i p t i - 1 - t h s o l u t i o n c o m p o n e n t ;

s u p e r s c r i p t s 1 a n d s - r e l a te d t ov olum e a n d s u r f a c e s o l u t i o n ;

2037

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2038 Yu. V. KAZAKEVITCH, 0. G. LARIONOV AND Yu . A. ELTEKOV

Ha the ma t i ca l de s c r i p t i on of t h a t was sugges ted b y Whilson l] nd DeVault [2]

The a bo ve equa t i on is f u n d a m e n t a l f o r t h e m a t er i al b a la nc e i n t h ea d s o r b e n t l a y e r w i t h t h i c k n e s s d x w h e r e w i s t h e f l o w r a t e of e l u e n t , Voan d S a r e t h e i n t e r n a l p or e volume a n d t h e s u r f a c e of t h e a d s or b e n t p e ru n i t le ng th of column, dI'/dc is t h e d e r i v a t i v e of a d s o r p t i o n i s o t h er m , uc i st h e l i n e a r v e lo c it y of t h e c o n c e n t r a t i o n zone.

P r i n c i p a l l y i n t h i s e q u a t io n we ca n us e t h e d e r i v a t i v e b o t h a s t h ee xc es s a d s o r p t i o n i s o t h e r m a n d a s t h e i s o t h e r m of t h e whole c o n t e n t. O nlyt h e v a l u e s o f V, w i l l d i f f e r . T h i s p a r a m e t e r h a s t h e same m ea nin g a s t h es ys te m v olum e i n t h e s t a t i c a d s o r p t i o n i n v e s t i g a t io n s .

T he p r i n c i p a l d i f f e r e n c e o f t h e s e t w o a p p r o a c h e s ( on t h e b a s i s ofexc es s ad so rp t i on , and on t h e ba s i s o f whole con t en t ) is t h a t i n t h e f i r s tcase we have t o t a ke i n to accoun t t h e volume of a d so rb e d l a y e r i n t h e s y st emvolume, b u t i n t h e second ca se we must d iv ide t h e sy st em in two p a r t s - t h eb u l k s o l u t i o n a n d t h e s u r f a c e a d s o r p t i o n s o l u t i o n . O bv io us ly. t h e volum e oft h e l a t e r w i l l d ep en d on t h e p r o p e r t i e s of t h e mo le cu le s u n d e ri n v e s t l g a t i o n .

Equat ion 7 ) g i v e s t h e d e pe n de n ce of c h r o m a t o g ra p h i c p e ak s h a p e on t h es h a p e of t h e a d s o r p t i o n i s o t h e r m , a n d a l s o t h e d ep en de nc e of t h e r e t e n t i o nof t h e pea k maxima on t h e conc en t r a t i on of t h e so lu t i on i n maxima.

The retent lon volume of compounds i s connected w i t h uc a s follows:L

v r w 8 )

combin ing equa t ions 7 ) a n d 8 ) we get: V r Vo S(--Ic 9 )

U Cr

d C

T h i s e q u a t i o n c o n n ec t s t h e r e t e n t l o n volum e w i t h t h e a d s o r p t i o n i s o t he r m .we have t o P o i nt e d o u t t h a t t h e a bo ve e q u a t i o n s w ere d e r i v e d o r

q u a s i e q u i l i b r i u m c o n d i t i o n s , 1.e. w hen i n t h e colum n t h e a d s o r p t i o ne q u i l i b r i um is per formed i n ev er y moment o f time.

C O N N E C T I O N O F T H E E Q U I L I B R I U M C O N S TA N T W I T H R E T E N T I O N

Let us c o n s i d er t h e S i m pl es t f o r m of a n a d s o r p t i o n i s o t h e r m ( e q u a t i o n(6). w r i t e i t s d e r i v a t i v e a n d i n t r o d u ce i t i n t o e q n . 9 )

d?? 1 - X)2 - Kx2

dx [ i - K - 1)Xl2_ _ = K - 1) _ _ _ _ _ _ _ _ _ _ _ _ _

obviously i f x = 0 t h e n d r / d x K - 1hence V r = Vo Va K - 1)

o rk V r - Vo ) / Vo Va/Vo(K - 1)

Th e re f o r e= k'Vo/Va 1 1 lC'VoW/S i

t h e l i m i t of poss ib le nega t ive va lues of k w i l l be

V p Vo - Va k -Vo/Va K = 0 1 4 )

T h e a d s o r p t i o n e q u i l i b r i u m c o n s t a n t may b e w r i t t e n a s t h e c o n s t a n t ofsu r f ace e x cha nge r eac t i o n or i n t h e f orm

G )

X i l X 2 S R T R T

xpx21 mots - m o i l - mO2S m 0 2 11 15 1exp(

_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ - - - _ - - - - - ) =exp(

____

L et u s c o n s i d e r now 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 of t h e mem bers ofhomologous s e r i e s . Sup pose t h e i r p l a na r o r i e n t a t i on is on t h e s u r f a c e . T he nt h e d i f f e r ence of ad so r p t i on e ne rg y of ne ighbo r members w i l l be e q u al t o t h ea ds o r p t i o n ene rgy o f o ne CH2-group i n t h e absence of so lva t i on , a s soc i a t i ona n d i n t ra m o l e c u la r i n t e r a c t i o n e f f e c ts . I n t h i s c a s e t h e a d d i t i v i t y o fadso r p t i on e ne rgy o ccu r s

In K Eo n i E i ( 1 6 )

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Ph ysico chemical aspects of l iqu id chromatography 2039

combining eqn. 's (13) a n d (16): In K ln(Vo/Va k 1) a n b ( 1 7 )

N o w c o n s i d e r c a p a c i t y f a c t o r , k : In K = ln(Vo/Vak' 1) a n b ( 1 8 )

f o r t h e lowest members of t h e homologious s e r i e s , k ' v a lue s a r e low an d d i g i tone und e r t h e In - func t i o n p l aye s a va luab l e r o l e . For t h e h i g h e r m em bers o ft h e homologous se r i e s we can appro xima te ly wr i te :

Y O Y O

Va VaIn(---k' 1) In In k 1 9 )

or In k a ' nb ( 2 0 )u n e q u a t io n s a r e v e r y o f t e n m en ti on ed i n p u b l i s h e d a r t i c l e s .

Th e h i gh e r members o f t h e h om ologous s e r i e s ha ve more con fo rma t iona ld e g r e e s o f f r e e d o m a n d f o r m i n n e r m o l e c u l a r c o n ne c ti o ns , a s f o r e xa mp leo x y e t h y l a t e d p h e n o l s , b u t i t occu r s only f o r n 6 . T he d e vi a ti o ns f o r t h elower homologous s e r i e s members a r e now exp lain ed b y i n s u f f i c i e n t a c c u r a c yi n V o d e t e r m i n a t i o n , b ec a us e a t l o w r e t e n t i o n v a l u es t h e i n f l u e n c e of V,d e t e r m i n a t i o n e r r o r i n c r e a s e s .

The problem of dea d volume de te rm in at io n is n o t a s e a sy a s o ne c a nt h i n k . For exa mple , for t h e s ys te m a c e t o n i t r i l e - w a t e r - S e p a r o n - C 1 8p ra c t i c a l l y a l l t h e known m e thods gave t h e dead volume va lue f o r one co lumn(100x3 mm) n o t l es s t h a n 1.03 m l , bu t compounds l i ke 4 ,6 -d ioxypy r imid ine oru r i c a c i d h a d n o t i c a b l y l e s s r e t e n t i o n v olu me s, a n d c o n se qu e nt ly t h e i rvalues of k were less t h a n zero. However, it d oe s n o t c o r r e s p o nd t o t h eo p in io n t h a t l nk ' i s t h e e n e r g e t ic p a r a m e t e r o f a chromatographic Sys tem.T h i s op in i on i s base d on t h e well known equa t i on o f f e r ed b y S c k o t t a n dKucera [3]

k = Vo/Va K i ( 2 1 )

where K i i s t h e c o e f f i c i e n t o f d i s t r i b u t i o n of s u b s t a n c e s b et we en t h e volum ea n d t h e a d s o r p t io n p ha s es . I n c as e of s u c h a p p r o a c h i t i s imposs ib l e t oc om pa re d i f f e r e n t c h r o m a to g r a p h ic s y s te m s a n d r e t e n t i o n o f d i f f e r e n tc om pounds i n one sy s t e m, a s i n t h i s ca se t h e adso rp t i on volume i s s p e c i f i cf o r each compound.

I f we con s id er eq ua t io n 9), we see t h a t V r = V, only i f d r / d c = 0i.e. t h e i n t e r a c t i o n of a d s o r b a t e m olecu le s w i t h t h e s u r f a ce i s t h e sam e a st h a t of e lu en t molecules.

d e t e r m i n a t i o n .Let u s d i s c u ss f u r t h e r t h e m e th od s wh ic h a r e u se d f o r t h e d e a d Volume

1. Re ten t i on o f unadsorbing component .2. R e t en t i on of eluent component .

I f t h e e l u e n t c o n s i st s of two components, i t i s c l ea r t h a t t h e a d s o rp t io n ofone component b y a n o t h e r o c cu rs , a nd t h e r e t e n t i o n of one component Obeyse q u a t i o n (7) a nd depends on t h e e lu en t compos i ti on .

T h i s m eth od m u st g i v e a c c u r a t e r e s u l t s b u t i t i s r a t h e r c o m p l i c a t e de x p e r i m e n t a l l y.

T h i s method i s b a se d u po n t h e p r o p o r t i o n of l i n e a r i t y of 1nK' on n , b u t a swe hav e alre ad y shown, i t i s n o t a b s o l u t e l y t r u e .

To d e t e r m i n e V, exa c t l y we can u se equa t i on 9 ) , f o r t h e c o n d i t i o n sdr / dc 0 ,we ge t Vo = V I t can be done i f t h e e x ce ss a d s o r p t i o n i s o t h e r mof t h e s u b s t a n c e i s known. But i f i t i s not known, it i s p o s s i b l e t o m e a s u r eit w i t h t h e h e l p of t h e d i s t u r b a n c e m eth od . T h e r a t e of m ot io n of d i s t u r b a n c epeak i s d e t e rmin ed b y e q u a t i o n (7). A f t e r m e a s u r i g s u c h d i s t u r b a n c e s f o rd i f f e r e n t e q u i l i b r iu m c o n c e n t r a t i o n s f o r a l l c o n c e n t r a t i o n ra n g e we o b t a i n ac u r v e . A f t e r i n t e g r a t i n g e q u a ti o n 9) f r o m 0 t o 1 we get:

3. Weighing method.

4. T h e l i n e a r i s a t i o n of homologous series.

1 1 dl?d x E [[V V --I dx 2 2 )

vr J @ d x0

? la ki ng i n t o a c c ou nt t h a t I 0 a t x = 0 a n d 1, we get V, Vo, 1.e. f o r

t h e o b t a i n ed d ep en de nc e t h e a v e r a g e i n t e g r a t e d v a l u e i s t h e v a l u eo

t h esystem dead volume.

r e t e n t i o n of s u b s t a n c e s , T h e r e a r e many d e s c ri p t io n s of t h e r e t e n t i o ndependences on eluent cornposi t ion

L e t u s c o n s i d e r now t h e i n f l u e n c e of t h e e l u e n t c o m po s it io n on t h e

K a bx cxl,In k E a* b'x c'x?,In k a w b w lnx.

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F r e q u e n t l y m e nt io ne d i n d i f f e r e n t a r t i c l e s d e p en d en c es of 1nK' on 1nCcan be s i m p l y exp l a ined f o r medium r ang e of e l u e n t c o n c e n t r a t i o n s . A s i t w a sshown, t h e compos i t ion o f t h e a c e to n i t r i l e - w a t e r s ys te m a d s o r p t i o n l a y e r i nt h e r a n g e o f c o n c e n t r a t i o n s f r o m 2 0 t o 80 i s cons t a n t . Le t one of t h ecomponents A C H ) be adso r p t i o na l l y a c t i ve . and t h e second one be a so lven t ,th e n we can der iv e :

( 2 6 )a s nB1 X nBS

1nK = lnKi + n In [Bs] n ln[B1l ( 2 8 )

ka Vo/Va K iIn k A - n lnc

th u s , we hav e ob t a i n ed l i ne a r dependence. I t i s c l e a r t h a t o u t of t h e ch os enr a n g e t h i s co r r e spond ence i s n o t t r u e .

From t h e e q u a l i t y o f t h e sys t em components chemica l po t en t i a l s weo b t a i n :

I n t h e e l u t i v e c h r o m a t og r a p h y n eg l i g i b l y sm al l q u a n t i t i e s o fs u b s t a n c e s a r e us u a l ly i n t r o d u c e d , h e nc e

th en we can w r i te XI x2 1 3 3 )

o r 3 4 )

a two -component e l ue nt can be cons id ered a s a two-component adsorp t ionsys tem a t f i r s t a p p r o a c h

K i x1( 3 5 )s = _-_---------

1 K I - 1) X1

[l 9 1 - 1) X1123 6 )f K l - 1) _____----------

K lhence

T h e l a s t e q u a t l o n s ho ws t h e c o n n ec t lo n of t h e e l u e n t c o m po si ti on w i t ht h e a d s o rp t i o n e q u l l i b r l u m c o n s t a n t of t h e s u b s t a n c e u n d e r i n v e s t l g a t l o n . Too b t a i n t h e d e pe n de n ce o f k on x i t i s n e ce s sa r y t o i n t r o d u c e e q u a t i o n 17).A s you can s ee , t h e fo rm of t h i s e q u a t i o n i s v e r y n e a r t o t h a t of eq n. 24) .

In conclusion we hav e t o m e n t i o n t h a t i f a n a d s o r p t i o n e q u i l i b r i u mc o n s t a n t K ) i s u se d i n s t e a d of t h e c a p a c i t y f a c t o r (k ), t h e d i r e c tconnection of t h e s ys tem w i t h t he rmodynamic pa r ame te r s t h rou gh t h e equa t i on sf o r che mi ca l po t en t i a l s and Haxwe l l e qua t i ons i s ob t a ined .

C O N C L U S I O N

I n c o nc lus ion we can s ay t h a t t h e main r e su l t of t h i s a r t i c l e i s t h e

connection of t h e c h r om a t o g r a ph i c p a r a m e t e r s ( l i k e k , Vr a n d Vo) w i t h t h ethermodynamic param eters of t h e same ads orp t ion sys tem. We Suggest t h emethods fo r dead volume de te rmina t ion on t h e bas i s o f thermodynamic t h e o ry(eqn. 2 2 ) a n d f r o m t h e e qn . 18 i t c an b e se en t h a t e a r l i e r s ug g es te d m e th od sa r e u n u s a b l e .

REFERENCES

1. W.R.Whilson, J. Amer. Chem. S O C . 63, 6 4 5 1943).2. D.DeVault J. Amer. Chem. a 2, 1583 1940).3. R.P.W.Scott. P.K uce ra, J.Ch rom ato g., 112 425 1975).