Aqueous Size Exclusion Chromatography - Advances in Chemistry

18 Aqueous Size Exclusion Chromatography J. E. ROLLINGS—Worcester Polytechnic Institute, Department of Chemical Engineering, Worcester, M A 01609 A. BOSE—Battelle Columbus Laboratories, Columbus, OH 43201

Downloaded by CORNELL UNIV on June 20, 2017 | http://pubs.acs.org Publication Date: June 1, 1983 | doi: 10.1021/ba-1983-0203.ch018

J. M . C A R U T H E R S and G. T . TSAO—Purdue University, School of Chemical Engineering, West Lafayette, IN 47907 M . R. OKOS—Purdue University, Department of Agricultural Engineering, West Lafayette, IN 47907

The important aspects of aqueous size exclusion chromatography are reviewed. The molecular size of polyelectrolytes in dilute solutions depends on the molecular weight and the ionic strength of the solution. Size exclusion chromatography calibration procedures based on the dilute solution conformation statistics of polymers have been proposed previously. The applicability of these calibration procedures to aqueous size exclusion chromatography is examined critically. In aqueous size exclusion chromatography secondary separation mechanisms such as adsorption, ion exclusion, and ion inclusion can also be important. The criteria to be considered in the design of an efficient size exclusion chromatographic system are discussed.

SIZE EXCLUSION CHROMATOGRAPHY

( S E C ) is a n i m p o r t a n t t e c h n i q u e for d e t e r m i n i n g the m o l e c u l a r w e i g h t a n d the m o l e c u l a r w e i g h t d i s t r i b u t i o n o f p o l y m e r s i n d i l u t e s o l u t i o n (1, 2). O f p a r t i c u l a r i n t e r e s t i s the d e v e l o p m e n t o f a q u e o u s S E C to b e u s e d i n the c h a r a c t e r i z a t i o n o f water-soluble natural polymers a n d synthetic polyelectrolytes. M a n y p o l y m e r s o f b i o l o g i c a l i n t e r e s t , s u c h as p r o t e i n s , p o l y s a c c h a r i d e s , a n d n u c l e i c a c i d s , are w a t e r s o l u b l e (3, 4); t h u s , t h e d e v e l o p m e n t o f a q u e o u s S E C as a n a n a l y t i c a l t o o l i s o f c o n s i d e r a b l e i m p o r t a n c e f o r b o t h b i o c h e m i c a l a n d m e d i c a l research. T h i s chapter r e v i e w s the i m p o r tant aspects of aqueous S E C . 0065-2393/83/0203-0345$06.00/0 © 1983 A m e r i c a n C h e m i c a l Society

Craver; Polymer Characterization Advances in Chemistry; American Chemical Society: Washington, DC, 1983.


346

POLYMER CHARACTERIZATION

F o r p o l y m e r s s o l u b l e i n organic solvents, S E C is a c o m m o n a n a l y t i c a l t e c h n i q u e (I); h o w e v e r , S E C m e t h o d s for w a t e r - s o l u b l e p o l y m e r s h a v e n o t y e t r e a c h e d t h e s a m e l e v e l o f d e v e l o p m e n t as S E C t e c h n i q u e s for p o l y m e r s s o l u b l e i n o r g a n i c s o l v e n t s . S o m e o f t h e r e a s o n s f o r t h e l e s s a d v a n c e d state o f a q u e o u s S E C are (1) a l a c k o f r e a d i l y a v a i l a b l e , m o n o d i s p e r s e , w a t e r - s o l u b l e p o l y m e r s t a n d a r d s ; (2) d i f f i c u l t i e s i n o b t a i n i n g c h r o m a t o g r a p h i c s u p p o r t s for a q u e o u s s y s t e m s t h a t p o s s e s s t h e n e c e s s a r y s e p a r a t i o n c h a r a c t e r i s t i c s ; (3) i n h e r e n t difficulties i n the description of the dilute solution conformation s t a t i s t i c s o f p o l y e l e c t r o l y t e s ; a n d (4) t h e p r e s e n c e o f a d d i t i o n a l s e p a r a t i o n m e c h a n i s m s , s u c h as i o n i n c l u s i o n a n d i o n e x c l u s i o n , t h a t a r e usually unimportant i n organic S E C . H i g h performance c o l u m n supp o r t s t h a t a r e s u i t a b l e f o r a q u e o u s S E C , s u c h as A q u a p o r e a n d T S K G E L (5, 6) h a v e r e c e n t l y b e c o m e a v a i l a b l e , as w e l l as m o n o d i s p e r s e p o l y e l e c t r o l y t e s (7) a n d d e x t r a n s (8) w i t h r e l a t i v e l y n a r r o w m o l e c u l a r weight distributions. As a result of these two key developments, a q u e o u s S E C s h o u l d n o w b e a b l e t o r e a l i z e i t s f u l l p o t e n t i a l as a n analytical technique. I n the next section w e w i l l discuss the f u n d a m e n t a l separation mechanisms i n aqueous S E C . First w e w i l l consider separation by m o l e c u l a r s i z e , e x a m i n i n g t h e effects of m o l e c u l a r w e i g h t a n d i o n i c strength on the size of the m a c r o m o l e c u l e f o l l o w e d b y discussions of various p o l y m e r — s o l v e n t — s u p p o r t interactions that c a n occur i n a d d i t i o n to t h e s e p a r a t i o n b y m o l e c u l a r s i z e . S u b s e q u e n t l y , t e c h n i q u e s for c a l i b r a t i o n of a q u e o u s S E C u s i n g s e c o n d a r y standards w i l l b e p r e s e n t e d ; a n d f i n a l l y , the e x p e r i m e n t a l m e t h o d s r e q u i r e d to i m p l e m e n t aqueous S E C effectively w i l l be reviewed.

Separation

in Aqueous SEC

Separation by M o l e c u l a r Size. T h e principal separation m e c h a n i s m i n S E C i s d i f f e r e n t i a l m i g r a t i o n o f m o l e c u l e s b e t w e e n t h e flowing solvent a n d the solvent w i t h i n the porous matrix of an S E C colu m n p a c k i n g (1, 2 ) . S e p a r a t i o n o c c u r s b e c a u s e t h e t o t a l a c c e s s i b l e v o l u m e o f t h e c o l u m n (i.e., i n s i d e a n d o u t s i d e t h e p o r e m a t r i x ) v a r i e s w i t h the size of the p o l y m e r molecules i n solution. S m a l l e r macr o m o l e c u l e s w i l l , o n t h e a v e r a g e , see m o r e p o r e v o l u m e a n d s p e n d a longer p e r i o d of t i m e i n the relatively stationary solvent i n s i d e the porous matrix than larger macromolecules. T h e larger macr o m o l e c u l e s h a v e a s m a l l e r p o r e v o l u m e a v a i l a b l e to t h e m a n d t h u s elute from the c o l u m n earlier than the smaller macromolecules. B e c a u s e t h e p r i n c i p a l s e p a r a t i o n m e c h a n i s m is g o v e r n e d b y t h e s i z e o f the macromolecules—size b e i n g correlated w i t h molecular conformat i o n — d i l u t e s o l u t i o n c o n f o r m a t i o n statistics o f p o l y e l e c t r o l y t e s is o f paramount importance.


18.

ROLLINGS ET A L .

Aqueous

Size Exclusion

347

Chromatography

T h e p r i n c i p a l o b j e c t i v e o f S E C is t o d e t e r m i n e t h e m o l e c u l a r w e i g h t and/or molecular weight distribution of macromolecules. H o w e v e r , the separation process i n S E C d e p e n d s p r i m a r i l y o n the size of the polymer. T o interpret S E C e l u t i o n data effectively, the relationship b e t w e e n the size of the m a c r o m o l e c u l e i n solution a n d the m o l e c u l a r w e i g h t m u s t b e a v a i l a b l e . F l o r y has p r o p o s e d that the m o l e c u l a r w e i g h t M is r e l a t e d t o t h e m o l e c u l a r v o l u m e ( r ) as f o l l o w s (9) 2

[η] = Φ

0

(r ) 2

3 / 2

/ M = Φ a (r§) 0

3

3 / 2

3 / 2

/M

(1)

w h e r e [η] is t h e i n t r i n s i c v i s c o s i t y , (r ) i s t h e m e a n - s q u a r e e n d - t o - e n d d i s t a n c e , (r ,) i s t h e u n p e r t u r b e d m e a n s q u a r e e n d - t o - e n d d i s t a n c e , a i s t h e e x p a n s i o n f a c t o r , a n d Φ i s a c o n s t a n t e q u a l t o 3.6 x 1 0 d L / c m . Because the intrinsic viscosity can be measured i n d e p e n d e n t l y for a g i v e n p o l y m e r s a m p l e , E q u a t i o n 1 is the d e s i r e d r e l a t i o n ship b e t w e e n m o l e c u l a r w e i g h t a n d the size of the m a c r o m o l e c u l e i n solution. 2

2

2 1


0

3

I n t h e d e r i v a t i o n o f E q u a t i o n 1, e x c l u d e d v o l u m e effects w e r e n o t c o n s i d e r e d i n the c a l c u l a t i o n of the front factor, Φ . O t h e r treatments of the intrinsic viscosity that i n c l u d e the contributions of e x c l u d e d v o l u m e h a v e b e e n s u m m a r i z e d b y Y a m a k a w a (10). R e p r e s e n t a t i v e o f t h e s e t h e o r i e s is t h e o n e d e v e l o p e d b y P t i t s y n a n d E i z n e r (11) 0

[η] · Μ = Φ ( r ) 2

3 / 2

= Φ /(€) (r ) 0

2

3 / 2

(2)

w h e r e f(e) = 1 - 2 . 6 3 e + 2 . 8 6 e , e = (2a - l ) / 3 , w h e r e a i s t h e M a r k - H o u w i n k exponent. T h e M a r k - H o u w i n k exponent qualita tively indicates the thermodynamic interaction b e t w e e n the p o l y m e r a n d t h e s o l v e n t (12). T h e e x p o n e n t a i n c r e a s e s as t h e q u a l i t y o f t h e solvent increases, reflecting the increase i n hydrodynamic v o l u m e , a n d a as t h e p o l y m e r — s o l v e n t i n t e r a c t i o n i n c r e a s e s (12). T h e p r o p o s e d t h e o r i e s that a c c o u n t for e x c l u d e d v o l u m e i n c o m p u t i n g t h e i n t r i n s i c v i s c o s i t y front factor p r e d i c t that Φ is a m o n o t o n i c a l l y d e c r e a s i n g f u n c t i o n o f t h e e x p a n s i o n f a c t o r a. 2

T h e s i z e o f a n u n c h a r g e d , i s o l a t e d m a c r o m o l e c u l e i n s o l u t i o n as specified by the mean-square end-to-end distance d e p e n d s on the molecular weight, the interaction b e t w e e n the p o l y m e r a n d the sol vent, and intramolecular polymer—polymer interactions. T h e confor m a t i o n statistics o f n e u t r a l p o l y m e r s i n n o n p o l a r solvents are w e l l u n d e r s t o o d (12); h o w e v e r , t h i s i s n o t t h e c a s e f o r p o l y i o n s i n p o l a r s o l v e n t s (13). F o r p o l y e l e c t r o l y t e s t h e m o l e c u l a r c o n f o r m a t i o n d e p e n d s o n the amount a n d type of charged species, the i o n i c strength of the solvent, a n d the m o l e c u l a r weight. T h u s , the separation of polyelectrolytes b y S E C d e p e n d s o n the ionic strength of the solvent.

1155 16th It N. W. Washington. D. C. 200S9 Craver; Polymer Characterization Advances in Chemistry; American Chemical Society: Washington, DC, 1983.


348


F o r polyelectrolytes i n solution, electrostatic r e p u l s i o n b e t w e e n the charged moieties on the m a i n c h a i n b a c k b o n e w i l l cause an expan s i o n o f t h e m a c r o m o l e c u l e a n d i n c r e a s e t h e l o c a l c h a i n s t i f f n e s s (13). T h i s c h a i n e x p a n s i o n c a n b e c o n s i d e r e d to b e l i k e a n i n c r e a s e i n t h e excluded volume. Numerous theoretical developments have b e e n p r o p o s e d to d e s c r i b e t h e c o n f o r m a t i o n s o f p o l y i o n s i n s o l u t i o n a n d h a v e b e e n s u m m a r i z e d e l s e w h e r e (23). T h e s e t h e o r e t i c a l t r e a t m e n t s are o f t w o m a j o r t y p e s : o n e g r o u p e m p l o y s a r a n d o m - c o i l c h a i n o n w h i c h d i s c r e t e c h a r g e s are l o c a t e d , w h i l e t h e o t h e r g r o u p m o d e l s t h e m a c r o m o l e c u l e as a s p h e r e i n w h i c h t h e c h a r g e s are u n i f o r m l y d i s tributed. M o s t of the theoretical descriptions of the conformation of p o l y e l e c t r o l y t e s c a n b e cast i n t o a f o r m that relates the e x p a n s i o n f a c t o r to t h e e x c l u d e d v o l u m e . A t y p i c a l r e l a t i o n s h i p o f t h i s k i n d is t h a t o f F l o r y (14) a

5

where Z tions.

el

- a

3

= 2.60 Z

(3)

el

c o n t a i n s the effects o f i n t r a m o l e c u l a r electrostatic i n t e r a c

T o d e t e r m i n e the m o l e c u l a r w e i g h t of polyelectrolytes b y S E C , w e a g a i n n e e d to relate the m o l e c u l a r w e i g h t to the m o l e c u l a r size o f the m a c r o m o l e c u l e . Electrostatic interactions w e r e not c o n s i d e r e d ex p l i c i t l y i n t h e d e r i v a t i o n s o f E q u a t i o n s 1 a n d 2. If, h o w e v e r , t h e e x p a n sion of polyelectrolytes can be d e s c r i b e d b y the e x c l u d e d v o l u m e , a n d t h e e f f e c t o f e x c l u d e d v o l u m e o n t h e i n t r i n s i c v i s c o s i t y is t h e s a m e f o r neutral polymers a n d polyelectrolytes, the relationships b e t w e e n m o l e c u l a r w e i g h t a n d m o l e c u l a r size g i v e n i n E q u a t i o n s 1 a n d 2 s h o u l d a l s o b e v a l i d for p o l y e l e c t r o l y t e s . T h e p r o p o s a l o f P t i t s y n a n d E i z n e r (11) as g i v e n i n E q u a t i o n 2 a s s u m e s t h a t t h e f a c t o r Φ c h a n g e s w i t h expansion of the macromolecule. T h e predictions of Ptitsyn a n d E i z n e r a l o n g w i t h e x p e r i m e n t a l data for b o t h n e u t r a l p o l y m e r s a n d p o l y e l e c t r o l y t e s are s h o w n i n F i g u r e 1 (15). F o r n e u t r a l p o l y m e r s t h e v a l u e o f Φ / Φ i n i t i a l l y d e c r e a s e s as t h e m a c r o m o l e c u l e s b e g i n to e x p a n d , t h e n Φ/Φ g r a d u a l l y increases a g a i n w i t h a d d i t i o n a l c h a i n ex p a n s i o n . H o w e v e r , the c h a n g e s i n Φ/Φ are s m a l l o v e r the l i m i t e d r a n g e o f c h a i n e x p a n s i o n s a c c e s s i b l e to o r g a n i c p o l y m e r s . B e c a u s e Φ / Φ is n e a r l y c o n s t a n t for o r g a n i c p o l y m e r s , t h e r e l a t i o n s h i p b e t w e e n m o l e c u l a r w e i g h t a n d the m o l e c u l a r size g i v e n i n E q u a t i o n 1 is p r o b a b l y s u f f i c i e n t to d e s c r i b e t h e S E C o f p o l y m e r s s o l u b l e i n o r g a n i c s o l v e n t s . F o r p o l y e l e c t r o l y t e s t h e r a t i o Φ / Φ c h a n g e s s i g n i f i c a n t l y as the m a c r o m o l e c u l e s e x p a n d . E x p e r i m e n t a l data for s o d i u m p o l y styrene sulfonate ( N a P S S ) is d e s c r i b e d r e a s o n a b l y w e l l b y the P t i t s y n E i z n e r t h e o r y (11); h o w e v e r , t h e r a t i o Φ / Φ for o t h e r p o l y e l e c t r o l y t e s is n o t a l w a y s d e s c r i b e d a c c u r a t e l y b y t h e P t i t s y n — E i z n e r t h e o r y . F o r 0

0

0

0

0

0



18.

ROLLINGS E T A L .

Aqueous

Size Exclusion

Chromatography

349

Figure 1. Intrinsic viscosity constant, Φ/Φ vs. α . Theoretical predic tions of Flory (F) and Ptitsyn-Eizner (PE). Experimental data for sodium polystyrene sulfonate (NaPSS), sodium poly(3-methacrylogloxypropane-l-sulfonate) (NaPMOS), and nonionic polymer-solvent sys tems (O). (Reproduced with permission from Ref. 15. Copyright 1975, John Wiley ir Sons, Inc.) 0

η

N a P S S i t is a n t i c i p a t e d t h a t t h e S E C d a t a w o u l d b e m o r e e f f e c t i v e l y d e s c r i b e d b y E q u a t i o n 2 t h a n b y E q u a t i o n 1. I n a d d i t i o n to m o l e c u l a r s i z e , s e p a r a t i o n b y s i z e e x c l u s i o n is a l s o strongly dependent o n the molecular shape. T h e more extended the conformation of a macromolecule, the more it w i l l be e x c l u d e d from t h e p o r e s o f S E C p a c k i n g s ( F i g u r e 2) (16). F o r a g i v e n m o l e c u l a r weight, a rod shaped molecule elutes earlier than a random c o i l poly m e r of the same m o l e c u l a r w e i g h t . T h e more compact h a r d sphere elutes e v e n later t h a n a r a n d o m c o i l p o l y m e r . P o l y e l e c t r o l y t e s i n so l u t i o n s o f l o w i o n i c s t r e n g t h h a v e b e e n p r e d i c t e d to a t t a i n a n a s y m m e t r i c a l s h a p e (17,18), a n d t h e s e s h a p e e f f e c t s m u s t b e c o n s i d e r e d i n d e s c r i b i n g t h e S E C r e s p o n s e o f p o l y i o n s (19). S o l u t e - S u p p o r t I n t e r a c t i o n s . I n a d d i t i o n to the effect o f m o l e c u l a r size o n the s e p a r a t i o n m e c h a n i s m , o t h e r effects c a n i n f l u e n c e the s e p a r a t i o n p r o c e s s . M a n y o f t h e s e are i m p o r t a n t f o r p o l y e l e c t r o l y t e s , w h e r e ionic interactions b e t w e e n the polymer, solvent, a n d support can be significant. T h i s section addresses these secondary separation mechanisms and discusses their relative significance. A d s o r p t i o n o f a p o l y m e r o n t h e c h r o m a t o g r a p h i c r e s i n m a y affect t h e s e p a r a t i o n . N o n p o l a r p o l y m e r s , s u c h as p o l y s t y r e n e , c a n a d s o r b o n a p o l y s t y r e n e s u p p o r t (20, 21 ) as w e l l as o n i n o r g a n i c s u p p o r t s (20,22,


350


1

Rg (sphere) oc M Rg(coil)0CM

a

1 / 3

a*

1/2

Sphere Rg(rod)0CM

7

Coil

\

6


Rod

^

5

4 I V

o ELUTION VOLUME

Figure 2. Effect of molecular geometry on SEC calibration (Reproduced from Ref. 16. Copyright 1980, American Chemical

curves. Society.)

23). S p e c i f i c a d s o r p t i o n e f f e c t s o f t h i s t y p e d e p e n d o n t h e s o l v e n t u s e d a n d / o r t h e a d d i t i o n o f c o s o l u t e s (21 —25). I n s y s t e m s w h e r e t h e p o l y m e r a n d t h e s u p p o r t are o p p o s i t e l y c h a r g e d , the p o l y m e r e l u t e s l a t e r as t h e e l e c t r o s t a t i c a t t r a c t i o n s r e t a r d m o v e m e n t o f t h e p o l y i o n t h r o u g h t h e p o r o u s m a t r i x (26).

I n a d d i t i o n to a f f e c t i n g the average e l u t i o n

v o l u m e from the c o l u m n , sorption p h e n o m e n a m a y also cause elution

profile

to

exhibit

multiple

peaks

for

m o n o m o d a l m o l e c u l a r w e i g h t d i s t r i b u t i o n (25, 27).

polymers

the

with

I n extreme

a

cases,

t h e p o l y m e r m a y b e i r r e v e r s i b l y a d s o r b e d to t h e s u r f a c e o f t h e s u p port

(25). F o r p o l y m e r s a n d c h r o m a t o g r a p h i c supports that do not interact

electrostatically, the p e n e t r a t i o n of the p o l y m e r into the pores is r e stricted o n l y b y t h e m o l e c u l a r size. H o w e v e r , i f c h a r g e d g r o u p s are present o n the surface of the r e s i n , electrostatic r e p u l s i o n prevents the d i f f u s i o n o f p o l y e l e c t r o l y t e s o f l i k e c h a r g e i n t o t h e p o r e (28-30).

This

w o u l d d i m i n i s h the effective pore v o l u m e , a n d hence, the p o l y m e r w o u l d elute from the c o l u m n earlier than a neutral p o l y m e r of the


18.

ROLLINGS ET AL.

Aqueous

Size Exclusion

Chromatography

351

same size. T h i s p h e n o m e n o n is c a l l e d i o n e x c l u s i o n , a n d has b e e n d i s c u s s e d i n c o n n e c t i o n w i t h i o n - e x c h a n g e c h r o m a t o g r a p h y (31). I o n e x c l u s i o n is a t t r i b u t e d to the e a r l y e l u t i o n f r o m c o n t r o l p o r e glass p a c k i n g of N a P S S i n l o w ionic strength aqueous phosphate solutions ( 3 2 ) . A d d i t i o n o f s m a l l a m o u n t s o f c o s o l u t e s ( ~ 1 0 M ) to t h e e l u e n t w i l l s u p p r e s s i o n e x c l u s i o n (28).


- 2

W h e n a s o l u t i o n contains t w o or m o r e i o n i c solutes a n d one o f the i o n i c species is e x c l u d e d f r o m some r e g i o n o f the g e l or m e m b r a n e that c a n be penetrated b y the other i o n i c species, a D o n n o n e q u i l i b r i u m i s e s t a b l i s h e d (3, 2 9 , 33-35). I n the chromatography of the p o l y e l e c t r o l y t e s , the size of the p o r e o p e n i n g c a n p r o h i b i t free passage o f t h e p o l y i o n ; h o w e v e r , t h e p o r e is c o m p l e t e l y p e r m e a b l e to s i m p l e e l e c t r o l y t e s . T h u s , the l a r g e r ions e x t e r i o r to the p o r e w i l l c a u s e t h e s m a l l e r i o n s o f l i k e c h a r g e to m i g r a t e i n t o t h e p o r e to m i n i m i z e electrostatic r e p u l s i o n . T h i s p h e n o m e n o n is c a l l e d i o n i n c l u s i o n (29). U s i n g a c o n d u c t o m e t r i c d e t e c t o r c o u p l e d w i t h a r e f r a c t i v e i n d e x detector, D o m a r d et a l . o b s e r v e d a salt p e a k for p o l y e l e c t r o l y t e s i n D M F a n d D M F w i t h a d d e d electrolyte. T h e y attributed the obs e r v e d results to i o n i n c l u s i o n a n d d e t e r m i n e d that the p h e n o m e n a c o u l d be s u p p r e s s e d i f the e l u e n t c o n t a i n e d 5 x 10~ M of a d d e d e l e c t r o l y t e (36). 2

In any particular aqueous S E C system, these nonsize related separation m e c h a n i s m s m a y exist. A d s o r p t i o n a n d a s s o c i a t i o n effects are a consequence of the specific choice of polymer, solvent, a n d support e m p l o y e d . I t m a y n o t b e p o s s i b l e to s u p p r e s s t h e s e e f f e c t s ; t h e r e f o r e , o n e m u s t c r i t i c a l l y e x a m i n e t h e d a t a to a c c o u n t for a d s o r p t i o n a n d association. Ion i n c l u s i o n and i o n exclusion can i n general be e l i m i n a t e d b y a p p r o p r i a t e a d d i t i o n of s i m p l e e l e c t r o l y t e s to t h e e l u t i n g media. Calibration

Procedures

S E C c a n b e u s e d for t h e r o u t i n e c h a r a c t e r i z a t i o n o f p o l y m e r s , p r o v i d e d the relationship b e t w e e n p o l y m e r molecular w e i g h t and retention volume can be established. D i r e c t calibration can be e m p l o y e d i n the a n a l y s i s o f those p o l y m e r s for w h i c h w e l l c h a r a c t e r i z e d s t a n d a r d s are a v a i l a b l e . S u c h c a l i b r a t i o n s c h e m e s h a v e b e e n e m p l o y e d for t h e a n a l y s i s o f g l o b u l a r p r o t e i n s (37, 38) a n d l o w m o l e c u l a r w e i g h t p o l y s a c c h a r i d e s (39). U n f o r t u n a t e l y , f o r m o s t w a t e r s o l u b l e p o l y m e r s of interest, w e l l - c h a r a c t e r i z e d standards are not available. H e n c e calibration curves usually must be constructed w i t h c o m m e r c i a l l y a v a i l a b l e s t a n d a r d s t h a t are d i f f e r e n t t h a n t h e p o l y m e r of interest. T h e m o l e c u l a r w e i g h t a n d m o l e c u l a r w e i g h t d i s t r i b u t i o n can be calculated from the secondary calibration curve i f the relation-



352


s h i p b e t w e e n m o l e c u l a r w e i g h t a n d m o l e c u l a r s i z e is k n o w n f o r b o t h the polymers. V a r i o u s s e c o n d a r y c a l i b r a t i o n s c h e m e s h a v e b e e n p r o p o s e d for r e l a t i n g S E C e l u t i o n d a t a to m o l e c u l a r c h a r a c t e r i s t i c s o f t h e p o l y m e r . T h e u n i v e r s a l c a l i b r a t i o n p r o c e d u r e p r o p o s e d b y G r u b î s i c e t a l . (40) has f o u n d the w i d e s t a p p l i c a b i l i t y . T h i s t e c h n i q u e is b a s e d o n the p r e d i c t i o n s o f E q u a t i o n 1. T h e p r o d u c t M [ n ] i s p r o p o r t i o n a l to t h e h y d r o d y n a m i c v o l u m e ; t h e r e f o r e , a p l o t o f l o g M[rj] v s . t h e S E C e l u t i o n v o l u m e s h o u l d y i e l d a c o m m o n c u r v e for a g i v e n c h r o m a t o g r a p h i c c o l u m n irrespective of the c h e m i c a l structure of the p o l y m e r . T h e calibration curve can be constructed from S E C and intrinsic viscosity data of p o l y m e r standards w i t h k n o w n m o l e c u l a r w e i g h t s , t y p i c a l l y monodisperse polystyrene. Because the intrinsic viscosity can be m e a s u r e d i n d e p e n d e n t l y for a n y p o l y m e r , the m o l e c u l a r w e i g h t o f a n u n k n o w n p o l y m e r can be d e t e r m i n e d from the e l u t i o n v o l u m e a n d the S E C c a l i b r a t i o n c u r v e . T h e v a l i d i t y o f t h i s c a l i b r a t i o n m e t h o d has b e e n d e m o n s t r a t e d e x t e n s i v e l y for n e u t r a l p o l y m e r s i n n o n p o l a r s o l v e n t s (41, 42). L i t t l e w o r k has b e e n d o n e t o e x t e n d G r u b i s i c ' s t e c h n i q u e to S E C i n p o l a r s o l v e n t s . S p a t o r i c o a n d B e y e r (43) h a v e s h o w n t h a t [η]Μ c o u l d d e s c r i b e t h e e l u t i o n d a t a for N a P S S a n d d e x t r a n s i n a q u e o u s s o l u t i o n s o f 0.2 M a n d 0.8 M N a S 0 as s h o w n i n F i g u r e 3. F u r t h e r s u p p o r t for t h i s c o n c e p t has b e e n p r o v i d e d b y R o c h a s et a l . (33) for d e x t r a n s , p o l y ( s o d i u m g l u t a m a t e ) , a n d N a P S S i n 0.1 M N a N 0 . H o w e v e r , as s h o w n i n F i g u r e 4 t h i s m e t h o d p r o v e s i n v a l i d for N a P S S and dextrans i n 0 . 0 0 5 - 0 . 8 7 7 Ν N a O H solutions a n d 0 . 0 0 5 - 1 . 0 M N a C l s o l u t i o n s (19). 2

4

3

A n a l t e r n a t e c a l i b r a t i o n s c h e m e f o r S E C has b e e n p r o p o s e d b y C o l l a n d P r u s i n o w s k i (44). I t i s b a s e d o n P t i t s y n — E i z n e r ' s t h e o r e t i c a l d e v e l o p m e n t ( E q u a t i o n 2), w h i c h a c c o u n t s for e x c l u d e d v o l u m e ef fects. I n t h i s m e t h o d , l o g {M[7]]/f(e)} i s p l o t t e d a g a i n s t e l u t i o n v o l u m e . T h i s p r o c e d u r e is v a l i d for n e u t r a l p o l y m e r s i n n o n p o l a r s o l v e n t s (45 46) a n d has a l s o b e e n s h o w n to b e a p p l i c a b l e for N a P S S i n 0 . 0 9 7 - 0 . 8 7 7 Ν N a O H s o l u t i o n s ( F i g u r e 5). Several researchers have a n a l y z e d S E C data b y both the proce d u r e p r o p o s e d b y G r u b î s i c a n d t h e C o l l - P r u s i n o w s k i m e t h o d (19,45, 46). N o d i f f e r e n c e w a s f o u n d b e t w e e n t h e t w o m e t h o d s f o r n e u t r a l p o l y m e r s i n o r g a n i c s o l v e n t s . I f t h e M a r k - H o u w i n k e x p o n e n t s are s i m i l a r for t h e v a r i o u s p o l y m e r - s o l v e n t s y s t e m s e x a m i n e d b y S E C , E q u a t i o n s 1 a n d 2 are i d e n t i c a l u p to a m u l t i p l i c a t i v e c o n s t a n t a n d t h e two proposed calibration techniques w i l l be indistinguishable. M o l e c u l a r c o n f o r m a t i o n o f p o l y e l e c t r o l y t e s i n p o l a r solvents is strongly d e p e n d e n t o n t h e salt c o n c e n t r a t i o n a n d , t h u s , t h e M a r k - H o u w i n k e x p o n e n t s for p o l y e l e c t r o l y t e s e x h i b i t s i g n i f i c a n t c h a n g e s w i t h the i o n i c strength of the solvent. C o m p a r i n g the calibration curves s h o w n >


18.

ROLLINGS ET AL. 7

I0 i

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r

1

\

I0

6

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1

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1

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1

14 \


I0

5

X

Έ

10'

I0

3

I0

2

50

60

J I 1 JL 70 80 90 100 Retention volume,ml

L HO

120

Figure 3. Plot of log [η] · M vs. elution volume for NaPSS and dextrans. Key: Π, NaPSS in 0.2 M sodium sulfate; A, dextrans in 0.2 M sodium sulfate; •, NaPSS in 0.8 M sodium sulfate; and A, dextrans in 0.8 M sodium sulfate. (Reproduced with permission from Ref. 43. Copyright 1975, John Wiley ù Sons, Inc.) i n F i g u r e s 4 a n d 5, w e o b s e r v e t h a t for N a P S S a n d d e x t r a n s i n N a O H solutions of varying ionic strength the C o l l - P r u s i n o w s k i procedure describes the S E C data better than the universal calibration technique p r o p o s e d b y G r u b î s i c et a l . T h e C o l l — P r u s i n o w s k i p r o c e d u r e is u n a b l e to d e s c r i b e the S E C data o f N a P S S i n v e r y l o w i o n i c s t r e n g t h solutions of N a O H , a n d this d i f f i c u l t y is p r o b a b l y r e l a t e d to c h a n g e s i n



354


Figure 4. Plot of log [η] M vs. K for NaPSS and dextrans. NaOH concentrations of0.005 N, 0.0185 N , 0.075 N , 0.287 N , 0.501 N , 0.671 N, and 0.877 Ν are indicated by pips starting upward and moving clockwise at 45° angles, respectively (19). A V

the shape of the m a c r o m o l e c u l e i n l o w i o n i c strength solutions or s o l u t e - s u p p o r t interactions. T h e C o l l - P r u s i n o w s k i technique was n o t c o m p l e t e l y s u c c e s s f u l i n d e s c r i b i n g t h e S E C data for N a P S S a n d dextrans i n N a C l solutions, although the technique was better than t h e u n i v e r s a l c a l i b r a t i o n p r o c e d u r e (19).


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18.

Figure 5. Coll-Prusinowski calibration curve for NaPSS and dextrans. NaOH concentrations are the same as indicated in Figure 4 (19).

Experimental T h e efficiency of separation i n a S E C system d e p e n d s o n the p r o p erties of the p a c k i n g material a n d the flow rate. T h e c o l u m n efficiency is related to plate height w i t h l o w e r plate heights corresponding to a more efficient c o l u m n . T h e plate height H depends on the properties of the p a c k i n g materials as follows


356


vd

p

1 (4)

l/adp + D IC vd% M

M

w h e r e C and a are constants for a g i v e n S E C system, d is particle p a c k i n g diameter, C is a constant associated w i t h the stationary l i q u i d phase mass transfer, D is solute diffusion coefficient i n stationary l i q u i d phase, D is solute diffusion coefficient i n m o b i l e phase, a n d ν is eluent linear v e l o c i t y (I ). E q u a t i o n 4 shows that the most efficient c o l u m n operation is r e a l i z e d w h e n the eluent velocity is l o w and the p a c k i n g is c o m p o s e d of small particles. A narrow distribution of particle sizes is also r e q u i r e d for efficient c o l u m n oper ation (47). T h e operation of any real S E C system is l i m i t e d by numerous practical considerations. T h e use of small particles for the c o l u m n p a c k i n g causes a h i g h pressure drop across the c o l u m n , w h i c h the p a c k i n g material may not be able to tolerate or the p u m p may be unable to attain. E x t r e m e l y slow flow rates l e n g t h e n analysis t i m e ; hence, some loss of separation effi c i e n c y is generally sacrificed for experimental convenience. T h e d e v e l o p m e n t of aqueous S E C has b e e n l i m i t e d b y a lack of h i g h performance chromatographic supports. A s discussed p r e v i o u s l y , it is desir able that the c o l u m n have sufficient m e c h a n i c a l strength to w i t h s t a n d a large pressure drop across the c o l u m n becaμse the time r e q u i r e d to obtain a chro matogram can be decreased significantly b y h i g h pressure operation. T r a d i tional aqueous S E C p a c k i n g materials have o n l y b e e n able to separate p o l y mers over a relatively narrow m o l e c u l a r w e i g h t range, and these c o l u m n s have not possessed the necessary m e c h a n i c a l integrity (I). T h e c o m p o s i t i o n and properties of these traditional aqueous S E C p a c k i n g materials have a l ready b e e n discussed i n d e t a i l (48, 49). R e c e n t l y , h i g h performance, aqueous chromatographic supports have become available (5, 6): T S K - G E L (Biorad) and Aquapore (Chromatix). B o t h c o l u m n packings are s i l i c a based, have ex c e l l e n t m e c h a n i c a l strength, and are available i n small particle sizes. Separa t i o n efficiency is reported to be four to five times better than w i t h c o n v e n tional supports (5). T h e T S K - G E L has b e e n u s e d successfully for fractionation of proteins, polysaccharides, a n d water-soluble synthetic polymers (26, 50). H o w e v e r , polymers such as p o l y a c r y l a m i d e , s o d i u m polystyrene sulfonate, and p o l y e t h y l e n e i m i n e s h o w e d d e l a y e d responses, w h i c h w e r e p r e s u m a b l y due to selective adsorption on the support (26). These p a c k i n g materials have a l i m i t e d range of p H stability and are available o n l y i n a few pore sizes. A l t h o u g h these n e w c o l u m n s have not b e e n characterized c o m p l e t e l y , they represent a significant i m p r o v e m e n t over the traditional aqueous S E C pack i n g materials. C o l u m n selection for S E C depends on the range of m o l e c u l a r sizes to be separated, subject to the restrictions i m p o s e d by c h e m i c a l properties of the solvent. T h e traditional approach for e x t e n d i n g the fractionation range of a S E C system has b e e n to c o m b i n e several columns i n series, each of w h i c h separates a small range of m o l e c u l a r weights. W e have c o m b i n e d t w o Sepharose columns w i t h different m o l e c u l a r w e i g h t ranges of separation (47). U s i n g the composite c o l u m n , S E C data for N a P S S a n d dextrans i n various i o n i c strength N a O H solutions were obtained a n d are plotted according to the C o l l - P r u s i n o w s k i procedure i n F i g u r e 6. T h e range of m o l e c u l a r weights that can be resolved has increased considerably w i t h this composite c o l u m n . A s an a d d e d advantage, the lengths of the i n d i v i d u a l columns can be adjusted so that the calibration curve is a l i n e a r function of the e l u t i o n v o l u m e . T h e traditional procedure of c o m b i n i n g i n series many small c o l u m n s of M

p

SL


SL


M

18.

ROLLINGS ET A L .


τ

Aqueous 1

0.2

1

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Γ

0.4

0.6

0.8

1.0

Καν Figure 6. Coll-Prusinowski calibration curve for NaPSS and dextrans on Sepharose CL-6B and Sepharose CL-2B series column. NaOH con centrations are 0.185 Ν (pip directed upward) and 0.501 Ν (pip di rected downward) (52). various pore sizes into a single S E C system is not the best means for a n a l y z i n g a p o l y m e r sample w i t h a broad molecular w e i g h t d i s t r i b u t i o n (51). T h e s e composite columns often result i n longer analysis times and l o w e r separation efficiency. T h e most efficient separation w i l l result i f narrow pore size d i s t r i b u t i o n support particles are u s e d a n d their m o l e c u l a r w e i g h t separation ranges do not overlap (51). T h e effectiveness of the b i m o d a l pore-size d i s t r i b u t i o n concept has b e e n demonstrated i n the fractionation of polystyrenes o n a p a i r of porous s i l i c a microsphere columns (51). W e have e m p l o y e d aqueous S E C i n the study of polysaccharide h y d r o l y sis (52). A n a l y s i s of the hydrolysis products b y aqueous S E C is more accu rate, can be u s e d to resolve a w i d e r range of m o l e c u l a r weights, a n d is i m p l e m e n t e d more easily than traditional b u l k c h e m i c a l assays. B u l k assays are insensitive above a degree of p o l y m e r i z a t i o n of20—25, whereas aqueous S E C can easily ascertain quantitative differences b e t w e e n the hydrolysis products


358


w i t h a degree of p o l y m e r i z a t i o n of 5 x 10 . T h e analytical capabilities of aqueous S E C were an integral part of this overall investigation, a n d i n the future s h o u l d be a p p l i e d effectively to other b i o c h e m i c a l p r o b l e m s . 4


Conclusions A q u e o u s S E C i s a v a l u a b l e t o o l for t h e r o u t i n e c h a r a c t e r i z a t i o n o f biopolymers and polyelectrolytes. T h e molecular conformation of polyelectrolytes d e p e n d s on the ionic strength of the solvent. B e cause the p r i n c i p a l separation m e c h a n i s m i n S E C is differential m i gration, governed b y the size of the macromolecules, the ionic strength of the solvent can i n f l u e n c e m a r k e d l y the e l u t i o n b e h a v i o r of p o l y e l e c t r o l y t e s . T h e effect of the i o n i c strength of the solvent o n the S E C o f p o l y i o n s c a n b e t r e a t e d as e x c l u d e d v o l u m e . A S E C c a l i b r a t i o n p r o c e d u r e t h a t a c k n o w l e d g e s e x c l u d e d v o l u m e effects has b e e n p r o p o s e d (44). T h e u s e o f p o l a r s o l v e n t s o r i o n i c s o l u t i o n s i n a q u e o u s S E C r e q u i r e s t h a t s o l u t e — s u p p o r t i n t e r a c t i o n s s u c h as a d s o r p t i o n , ion exclusion, a n d i o n i n c l u s i o n be considered. I n most systems these s e c o n d a r y effects c a n b e s u p p r e s s e d b y c o n t r o l l i n g t h e i o n i c s t r e n g t h of the solvent. Advances have b e e n made i n our understanding a n d use of aqueo u s S E C . H o w e v e r , t h e r e i s s t i l l t h e n e e d for f u r t h e r i m p r o v e m e n t s , especially i n the d e v e l o p m e n t of chromatographic supports a n d the synthesis of n e w , well-characterized, water-soluble, p o l y m e r standards. D e s i r a b l e characteristics i n support materials i n c l u d e higher m e c h a n i c a l strength, c o m p a t i b i l i t y w i t h a w i d e variety of solvents, narrow pore-size distributions, a n d smaller particle sizes. T h e full potential of aqueous S E C w i l l only be r e a l i z e d through further advances i n both the theoretical understanding, a n d the experimental implementation of the technique. Acknowledgment Part of this research was sponsored u n d e r D O E G r a n t N o . D E A C 0 2 - 7 8 C S 40071. Literature Cited 1. Yau, W. W.; Kirkland, J. J.; Bly, D. D. In "Modern Size Exclusion Liquid Chromatography"; Wiley: New York, 1979; p. 1. 2. Tung, L. H.; Moore, J. C. In "Fractionation of Synthetic Polymers— Principle and Practice"; Tung, L. H., Ed.; Dekker: New York, 1977; p. 545. 3. Tanford, C. In "Physical Chemistry of Macromolecules"; Wiley: New York, 1962; p. 1. 4. Eisenberg, H. In "Biological Macromolecules and Polyelectrolytes in Solution"; Oxford Univ.: Oxford, England, 1976; p. 1.


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5. 6. 7. 8. 9. 10. 11. 12. 13.


14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29. 30. 31. 32. 33. 34. 35. 36. 37. 38. 39. 40. 41. 42. 43.

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RECEIVED for review October 14, 1981. ACCEPTED July 6, 1982.


Aqueous Size Exclusion Chromatography - Advances in Chemistry

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