Polymer Characterization - ACS Publications - American Chemical

4 Characterization of Synthetic Charge-Containing Polymers by Gel Electrophoresis Downloaded by UNIV OF IOWA on November 12, 2014 | http://pubs.acs.org Publication Date: May 5, 1990 | doi: 10.1021/ba-1990-0227.ch004

David L . Smisek and David A. Hoagland* Department of Polymer Science and Engineering and Department of Chemical Engineering, University of Massachusetts, Amherst, MA 01003

The effectiveness of gel electrophoresis as a tool for determining the molecular weight distributions of long-chain synthetic polyelectrolytes was evaluated extensively, primarily from results obtained with poly(styrene sulfonate) (PSS). We established that narrow distribution samples, when available, can be employed to construct chain length-mobility calibration curves. From these curves the full molecular weight distribution of an unknown can be calculated once its mobility distribution is measured. With PSS, this procedure was verified for 7 X 10 < M < 15 X 106, a much broader molecular weight (M) range than has been achieved with size exclusion chromatography (SEC). The resolution of these fractionations is also significantly higher than normally observed in aqueous SEC. The quality and simplicity of gel electrophoresis, as documented here, provide strong motivation for wider application of the method in polymer science. 3

- E L E C T R O P H O R E S I S PLAYS A K E Y R O L E in biopolymer research whenever complex protein or polynucleotide mixtures are to be analyzed (J). The first attempt to extend this traditional biopolymer technique to the realm of synthetic polymer science was by Chen and Morawetz (2), who described high-resolution electrophoretic separations of synthetic polymers in chem*Corresponding author. 0065-2393/90/0227-0051$06.00/0 © 1990 American Chemical Society

In Polymer Characterization; Craver, C., et al.; Advances in Chemistry; American Chemical Society: Washington, DC, 1990.

52

POLYMER CHARACTERIZATION

ically c r o s s - l i n k e d p o l y a c r y l a m i d e gels. T h e s e researchers l i m i t e d t h e i r exp e r i m e n t a l efforts to poly(styrene sulfonate) (PSS) a n d poly(acrylic acid) samples w i t h m o l e c u l a r weights b e t w e e n 2 X 1 0 a n d 1 X 1 0 . 4

5

W e are p r i n c i p a l l y i n t e r e s t e d i n materials w i t h m o l e c u l a r weights above this range; o u r objective is a characterization tool for the aqueous p o l y m e r s u s e d i n processes s u c h as w a t e r treatment a n d o i l recovery. I n these a p p l i cations, h i g h m o l e c u l a r w e i g h t is essential, a n d m o l e c u l a r w e i g h t averages above 1 X 1 0 are c o m m o n . W e are therefore c o n d u c t i n g e l e c t r o p h o r e t i c studies p r i m a r i l y i n agarose gels, m e d i a appropriate to the separation of the largest maeromolecules; agarose gels have a m u c h " l o o s e r " p o r e structure than p o l y a c r y l a m i d e gels a n d c o n s e q u e n t l y p e r m i t e n t r y of larger p e n e t r a n t species. Variants o f the t e c h n i q u e s discussed h e r e , s u c h as those i m p o s i n g p u l s e d e l e c t r i c fields, have b e e n e m p l o y e d to isolate e n t i r e c h r o m o s o m e s of i m m e n s e size (3). S u c h m e t h o d s , as yet p o o r l y u n d e r s t o o d , m a y p r o v e c r u c i a l to the p r o p o s e d effort to m a p the h u m a n genome.

Downloaded by UNIV OF IOWA on November 12, 2014 | http://pubs.acs.org Publication Date: May 5, 1990 | doi: 10.1021/ba-1990-0227.ch004

6

A l t h o u g h size exclusion c h r o m a t o g r a p h y ( S E C ) is a valuable m e t h o d for a n a l y z i n g l o w - a n d m e d i u m - m o l e c u l a r - w e i g h t p o l yelectrolytes, fractions o f h i g h e r m o l e c u l a r w e i g h t ( M > 1.0 X 10 ) have generally resisted this a p p r o a c h to m o l e c u l a r w e i g h t d e t e r m i n a t i o n (4, 5). T h i s failure can b e a t t r i b u t e d to p o l y e l e c t r o l y t e expansion i n the i o n i c solvent m e d i u m , to long-range electrostatic interactions w i t h the chromatographic support, a n d to i r r e v e r s i b l e p o l y m e r adsorption o n c o l u m n surfaces. A l l three effects can b e t r o u b l e s o m e e v e n w h e n m o l e c u l a r weights are r e l a t i v e l y small. A d s o r p t i o n p h e n o m e n a are p a r t i c u l a r l y difficult to e l i m i n a t e i n aqueous p o l y m e r systems, a n d surface-active agents are often a necessary a d d i t i o n to the m o b i l e phase. 6

A l t e r n a t i v e analytical schemes to S E C have sometimes b e e n e m p l o y e d to c i r c u m v e n t these difficulties, b u t the few successful options (band s e d i m e n t a t i o n , field-flow fractionation, a n d h y d r o d y n a m i c chromatography) are generally too c o m p l e x for r o u t i n e use; t h e y are c e r t a i n l y m o r e difficult to operate than c o n v e n t i o n a l g e l electrophoresis. G i v e n these conditions, c o m m e r c i a l w a t e r - s o l u b l e p o l y m e r samples are c o m m o n l y sold u n d e r the vague labels o f " l o w " , " m e d i u m " , or " h i g h " m o l e c u l a r w e i g h t . T h e a p p l i c a t i o n o f g e l electrophoresis to these samples w o u l d p r o v i d e the same advantages c i t e d for b i o p o l y m e r characterization: r e d u c e d e q u i p m e n t cost ( ~ $ 2 5 0 p e r device), m o r e r a p i d sample t u r n o v e r (up to 25 samples a n a l y z e d i n a single r u n o f several hours), a n d h i g h e r r e s o l u t i o n . Poly(styrene sulfonate) (PSS) was selected as a m o d e l c o m p o u n d i n this study because o f its w e l l - u n d e r s t o o d a n d w e l l - d o c u m e n t e d b e h a v i o r i n d i l u t e i o n i c solutions (6, 7). A l s o , n a r r o w d i s t r i b u t i o n samples are c o m m e r c i a l l y available or r e a d i l y s y n t h e s i z e d . A l t h o u g h g e l electrophoresis is e x p e c t e d to have b r o a d a p p l i c a b i l i t y for other h i g h l y c h a r g e d p o l y m e r s , quantitative m o l e c u l a r w e i g h t i n f o r m a t i o n can b e o b t a i n e d rigorously o n l y w h e n m o l e c ular size standards are available. P o l y m e r s other t h a n P S S w i l l b e discussed


4.

SMISEK & H O A G L A N D

Synthetic Charge-Containing Polymers

53


o n l y briefly. H y d r o l y z e d p o l y a c r y l a m i d e s w i l l b e specifically discussed b e cause, i n contrast to P S S , they possess a relatively l o w , easily adjusted charge d e n s i t y along t h e p o l y m e r b a c k b o n e . I n this case the separation of p o l y m e r fractions is a f u n c t i o n of b o t h m o l e c u l a r w e i g h t a n d charge density; w h e t h e r u n a m b i g u o u s m o l e c u l a r w e i g h t data can be d e d u c e d f r o m s u c h separations is not yet c e r t a i n . E s t a b l i s h i n g a r e l i a b l e p r o c e d u r e for d e t e c t i n g p o l y m e r i n an aqueous gel constitutes a significant i n t e r m e d i a t e step i n a p p l y i n g electrophoresis to a n e w p o l y e l e c t r o l y t e species. H i g h contrast of p o l y m e r bands against the g e l regions not p e r m e a t e d b y p o l y m e r is r e q u i r e d ; at the same t i m e , the p o l y m e r concentration i n the bands m u s t be b e l o w the c o i l overlap c o n c e n tration. F o r h i g h - m o l e c u l a r - w e i g h t p o l y m e r s , these c o n f l i c t i n g r e q u i r e m e n t s are not easily satisfied. A n effort to d e v e l o p a s i m p l e y e t sensitive d e t e c t i o n p r o c e d u r e for c a r b o x y l - c o n t a i n i n g p o l y m e r s i n agarose gels is c u r r e n t l y u n derway.

Experimental Details Our electrophoresis technique is nearly identical to methods originally developed to isolate medium- to high-molecular-weight DNA fragments (8). Separation of samples loaded in a gel occurs as a steady electric field is applied over a time from 2 to 10 h. The gels are prepared by dissolving agarose powder at high temperature (95 °C) in an appropriate aqueous buffer. As the agarose solution is cooled to room temperature, it forms a mechanically stable gel possessing properties determined mainly by the agarose concentration. The gel is cast as a horizontal slab, with sample wells formed by the indentations of the teeth of a Plexiglas comb. The slab, typically measuring 15 cm on each horizontal edge, is about 1 cm thick. The different polymer fractions separate across the plane of the slab over distances on the order of several centimeters. During the electrophoresis experiment, the weak agarose gel is supported on a tray bridging the two buffer reservoirs of a submarine cell (BioRad). Submersed platinum electrodes impose a voltage drop of 0.1 to 2 V/cm when connections have been made to a constant-voltage power supply (Ephortec 500 V). At the start of a run, polyelectrolyte solutions are pipetted into the sample wells, and the upper surface of the gel is left uncovered; after 15 min at constant voltage (a period designed to allow the polymer chains to migrate away from sample wells and into the gel matrix), the gel is submerged under a thin layer of buffer by carefully pouring additional solution into the buffer reservoirs. Throughout the remainder of the run, buffer solution is gently recirculated over the top of the gel by a peristaltic pump to ensure uniform electric field strength and solvent composition. Whenever desired, the field strength in the gel is measured with a hand-held voltmeter attached to platinum electrodes inserted in the gel at fixed separation; the magnitude of the measured field has always matched closely with the one that is applied. When experiments with sulfonated polymer species are terminated, the transparent gel is transferred to a bath containing an aqueous dye solution (0.01% methylene blue, pH 4 acetate buffer). The dye attaches to the polymer, presumably by electrostatic interaction, over a period of 15 min. During this period the dye diffuses throughout the entire gel slab. Residual dye is then removed by placing the gel in a bath of distilled water. Complete destaining of agarose may take 12 to 15 h, although


54


polyelectrolyte bands become visible after a few minutes. At this point, qualitative features of the molecular weight distribution are evident from even a cursory inspection of the stained gel. Quantitative analysis of the completely destained gels is accomplished with a densitometer (Isco model 1312) adjusted to measure absorbance at 580 nm. PSS samples with a narrow molecular-weight distribution, derived from anionically polymerized polystyrene (PS) of polydispersity less than 1.25, constitute the largest class of materials so far examined. The PSS materials are either purchased from Pressure Chemical (for lower molecular weights) or prepared in our own laboratory from the PS molecular weight standards available from a variety of vendors (for M > 1.2 X 10 ). The preparation and characterization of the linear PSS materials, as well as the electrophoresis apparatus, are described in detail in a separate publication (9). PSS "star" molecules are prepared from star polystyrenes (Polysciences) by the same methods employed to prepare linear PSS. In all cases the polyelectrolyte solutions that are pipetted into sample wells at the start of the experiment are dilute ( 1 X 10 ); this effect is not yet u n d e r s t o o d . T h e u p p e r i o n i c strength that can b e a c h i e v e d is l i m i t e d b y the c u r r e n t capacity o f the p o w e r s u p p l y . F o r the standard conditions o f this study, the u p p e r i o n i c strength l i m i t is about 0.3 M . A m o r e c o m p l e t e discussion of i o n i c strength effects, p a r t i c u l a r l y at l o w i o n i c strength, has b e e n p u b l i s h e d e l s e w h e r e (9). 2

4


6

T h e " c o u n t e r i o n c o n d e n s a t i o n " theory of M a n n i n g (J 5) p r e d i c t s that the effective l i n e a r charge density of a h i g h l y c h a r g e d p o l y m e r is i n d e p e n d e n t of the actual d e n s i t y of covalently attached i o n i c groups. F o r electrophoresis, this effective l i n e a r charge d e n s i t y is associated w i t h the asymptotic l o n g range solution o f the P o i s s o n - B o l t z m a n n e q u a t i o n a r o u n d a h i g h l y c h a r g e d c y l i n d e r (7). T h i s result has significant i m p l i c a t i o n s for the present w o r k : w i t h any h i g h l y c h a r g e d p o l y m e r species the d i s t r i b u t i o n of charge w i t h i n a sample s h o u l d not affect its e l e c t r o p h o r e t i c behavior. T h e separation is thus d e p e n d e n t o n l y o n the d i s t r i b u t i o n o f m o l e c u l a r w e i g h t . C h a r g e effects s h o u l d b e significant, h o w e v e r , for p o l y m e r s c o n t a i n i n g w e a k l y i o n i z a b l e groups because the l i n e a r charge d e n s i t y is c o r r e s p o n d i n g l y l o w e r (assuming, i n this case, that the charge d e n s i t y is b e l o w the onset o f condensation). A t n e u t r a l p H , for e x a m p l e , the separation of a c a r b o x y l - c o n t a i n i n g p o l y m e r is l i k e l y to b e h i g h l y sensitive to the actual d e n s i t y pf carboxyl groups. A t the sulfonation levels of the P S S samples (>70%), effects of sulfonation l e v e l o n m o b i l i t y are not e x p e c t e d a n d have not b e e n o b s e r v e d . I n particular, a specially p r e p a r e d 7 0 % sulfonated sample (the degree o f p o l y m e r i z a t i o n was 1550) has the m o b i l i t y p r e d i c t e d b y the c a l i b r a t i o n c u r v e for a 1 0 0 % sulfonated sample w i t h the same degree of p o l y m e r i z a t i o n . T h i s agreement is to w i t h i n the e x p e r i m e n t a l e r r o r i n the m o b i l i t y m e a s u r e m e n t ( ± 1 % ) . H y d r o l y z e d p o l y a c r y l a m i d e s constitute a class of p o l y m e r s for w h i c h the density of i o n i c groups along the p o l y m e r b a c k b o n e is m o r e r e a d i l y v a r i e d . T a b l e I lists the c a r b o x y l substitutions a n d m o b i l i t i e s of the t h r e e h y d r o l y z e d p o l y a c r y l a m i d e s s t u d i e d . I n contrast to the h i g h l y sulfonated P S S samples, the m o b i l i t y displays a clear d e p e n d e n c e o n the p o l y m e r s charge d e n s i t y . A c c o r d i n g to M a n n i n g s theory, these l o w charge densities do not l e a d to condensation, a p r e d i c t i o n consistent w i t h the m o b i l i t y results. I n fact, the m o b i l i t y r o u g h l y follows the l e v e l of h y d r o l y s i s , as e x p e c t e d from t h e o r y at


60


Table I. Mobility as a Function of the Degree of Carboxyl Substitution in Hydrolyzed Polyacrylamides Sample

Carboxyl Substitution (%)

Mobility (cm /V h)

9.5 20 35

0.12 0.46 0.55

SF210 SF212 SF214

11

2

At fluorescence maximum.


fl

such l o w charge densities. Q u a n t i t a t i v e comparisons to theoretical models are to b e a v o i d e d because the polydispersities of these samples are so large. Efforts to m o r e accurately verify the range of charge densities over w h i c h c o u n t e r i o n condensation compensates for charge variations are c u r r e n t l y being conducted. T h e a p p l i c a t i o n of gel electrophoresis to materials of b r o a 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 c a n b e i l l u s t r a t e d b y p r e s e n t i n g data o n two heterogeneous P S S samples. F i g u r e 4 displays the d i s t r i b u t i o n of c h a i n l e n g t h for a l i n e a r P S S as d e t e r m i n e d b y b o t h S E C a n d b y g e l electrophoresis. T h e S E C analysis is actually of the P S parent c o m p o u n d (Polysciences catalog no. 18544) i n tetrahydrofuran ( P o l y m e r Laboratories P L g e l c o l u m n s i n the p o r e size series 1 0 , 1 0 , a n d 1 0 A; flow rate = 1.0 m L / m i n ) . C h a i n - l e n g t h d i s t r i b u t i o n s of the sulfonated a n d unsulfonated forms can b e d i r e c t l y c o m p a r e d because the sulfonation reaction does not degrade o r cross-link P S chains. T h e d i s t r i b u t i o n s p l o t t e d i n F i g u r e 4 show excellent agreement. O n l y m i n o r discrepancies arise, m a i n l y f r o m noise i n the detector signals a n d from uncertainties i n selection of base-line levels. T h e P S parent sample d i d possess a significant fraction o f m o n o m e r a n d short o l i g o m e r i c m a t e r i a l ; these c o m p o n e n t s are excised f r o m the P S c h a i n d i s t r i b u t i o n d i s p l a y e d i n the figure. A n y s u c h fractions w o u l d have b e e n r e m o v e d b y the dialysis steps e m p l o y e d i n p r e p a r i n g P S S samples for electrophoresis. 5

4

3

F i g u r e 5 shows the m o b i l i t y d i s t r i b u t i o n of a sulfonated star p o l y m e r that n o m i n a l l y possesses six arms (Polysciences catalog n u m b e r 18145) of w e l l - c o n t r o l l e d a r m m o l e c u l a r w e i g h t ( M ^ — 116,700; unsulfonated form). A series of discrete fractions is o b s e r v e d , each c o r r e s p o n d i n g to a star topology w i t h a different n u m b e r of arms. S u c h a d i s t r i b u t i o n i n the n u m b e r of arms w i t h i n a single sample is expected i f synthesis of the star topology is b y the " n o d u l e " m e t h o d (16). T h e S E C of the P S parent i n tetrahydrofuran (two W a t e r s U l t r a S t y r a g e l (cross-linked s t y r e n e - d i v i n y l b e n z e n e ) l i n e a r c o l u m n s i n series, flow rate = 1.0 m L / m i n ) displays a single b r o a d peak ( F i g u r e 6), g i v i n g no h i n t o f the actual c o m p l e x d i s t r i b u t i o n of m o l e c u l a r fractions. T h e h i g h r e s o l u t i o n o f the g e l electrophoresis characterization is obvious, e x t e n d i n g over m o r e t h a n an o r d e r of m a g n i t u d e i n m o l e c u l a r w e i g h t . T h e fractionation d i s p l a y e d i n F i g u r e 5 is superior to any p r e v i o u s l y o b t a i n e d for a synthetic p o l y m e r at h i g h m o l e c u l a r w e i g h t ; fractions w i t h m o l e c u l a r w e i g h t above 1 X 1 0 differing b y an i n c r e m e n t of o n l y one a r m 6


4.

S M I S E K 6C H O A G L A N D

61


Electrophoresis


SEC

2

3

4

5

L o g (N) Figure 4. Comparison of the molecular weight distributions obtained by SEC and by agarose gel electrophoresis; N is the degree of polymerization. The SEC analysis is of the PS parent (nominal molecular weight 50,000), and the electrophoresis analysis is of the sulfonated product. By SEC: N = 1100; NJN = 2.5. By electrophoresis: N = 1600, NJN = 2.6. w

n

w

n

0.03n

c

Position, c m Figure 5. Densitometry scan of a PSS star nominally possessing six arms. The optical density is measured as a function of position from the sample well. (Conditions: 0.6% agarose; 1.3 V/cm; 7.3 h; I = 0.03 M.)


62


0.03 T


c o

Elution V o l u m e , m L Figure 6. SEC chromatogram of the parent PS star for the PSS sample of Figure 5. Note the lack of detail as compared to the previous figure. are r e s o l v e d . M o l e c u l a r m e c h a n i s m s that c o u l d e x p l a i n h o w these star p o l y m e r chains are b e i n g separated i n the g e l w i l l b e p u b l i s h e d e l s e w h e r e .

Discussion T h e d e v e l o p m e n t o f g e l electrophoresis as a c e n t r a l m e t h o d of b i o p o l y m e r research has b e e n largely o v e r l o o k e d b y traditional p o l y m e r science, a n d one can foresee m a n y n e w applications i n synthetic p o l y m e r systems. I n the m o d e d e s c r i b e d h e r e the m e t h o d s h o u l d b e r e g a r d e d as a relative t e c h n i q u e , one that p r o v i d e s o n l y qualitative results i n the absence of m o l e c u l a r w e i g h t standards. Q u a l i t a t i v e i n f o r m a t i o n , h o w e v e r , may be sufficient i n m a n y cases. F o r e x a m p l e , w e have s t u d i e d p o l y m e r degradation i n elongational flows b y c o m p a r i n g the m o b i l i t y d i s t r i b u t i o n before a n d after flow; c h a i n cleavage can b e r e a d i l y d e t e c t e d b y electrophoresis. E s s e n t i a l l y , any h i g h l y sulfonated w a t e r - s o l u b l e p o l y m e r can b e s t u d i e d b y the techniques w e have d e s c r i b e d . O u r efforts to generalize these t e c h niques to o t h e r c h a r g e d p o l y m e r species (those c o n t a i n i n g c a r b o x y l groups, for example) have not yet b e e n e n t i r e l y successful, m a i n l y because of d e tection p r o b l e m s . S t a i n i n g appears to b e the best t e c h n i q u e for v i s u a l i z i n g p o l y e l e c t r o l y t e bands, a n d w e are w o r k i n g to d e v e l o p a d y e t r e a t m e n t that w i l l u n i v e r s a l l y stain any negatively c h a r g e d p o l y m e r w h i l e l e a v i n g the agarose m a t r i x u n c o l o r e d . T h e p r i n c i p l e b e h i n d this approach is the electrostatic attraction o f cationic dye m o l e c u l e s for oppositely c h a r g e d p o l y e l e c t r o l y t e chains. T h i s attraction is weak for chains that contain w e a k l y i o n i z a b l e groups, so the p H a n d i o n i c strength conditions m u s t be p r o p e r l y adjusted to p r o d u c e


4.

SMISEK

6r

HOAGLAND


63

a strong b i n d i n g . T h e d y e process that has b e e n successful for P S S has not b e e n effective w h e n a p p l i e d to such species as poly(acrylic acid). F l u o r e s c e n t tagging constitutes a successful alternative i n some situations, b u t caution m u s t always b e exercised w h e n i n t e r p r e t i n g the b e h a v i o r of p o l y m e r chains c o n t a i n i n g covalently attached labels. O p t i m a l conditions for the highest q u a l i t y separations have not b e e n c o m p l e t e l y d e t e r m i n e d yet. T h e n u m b e r of e x p e r i m e n t a l variables is s u b stantial, a n d w e have f o l l o w e d the p r e c e d e n t of D N A separations i n selecting most p a r a m e t e r values. T h e u l t i m a t e r e s o l u t i o n o f the t e c h n i q u e has t h e r e fore not b e e n a c h i e v e d . F o r e x a m p l e , w e have not fully e x p l o r e d effects Downloaded by UNIV OF IOWA on November 12, 2014 | http://pubs.acs.org Publication Date: May 5, 1990 | doi: 10.1021/ba-1990-0227.ch004

associated w i t h m o d i f y i n g electric f i e l d strength, l e n g t h e n i n g the g e l , or v a r y i n g t e m p e r a t u r e . F u t u r e w o r k w i l l address these issues. W e b e l i e v e that the r e s o l u t i o n can b e i m p r o v e d e n o u g h to explore p r o b l e m s as sensitive as the c h a i n - l e n g t h d i s t r i b u t i o n s from i d e a l a n i o n i c p o l y m e r i z a t i o n . I n this case polydispersities b e l o w 1.005 m u s t b e accurately m e a s u r e d .

Summary T h e major advantages of p o l y e l e c t r o l y t e analysis b y gel electrophoresis are h i g h r e s o l u t i o n a n d easy adjustment of the m o l e c u l a r w e i g h t range. T h e m e t h o d appears to possess an u p p e r chain-size l i m i t that is w e l l above the m o l e c u l a r w e i g h t o f any synthetic p o l y m e r of c o m m e r c i a l significance; the operational ease at h i g h m o l e c u l a r w e i g h t stands i n contrast to the w e l l k n o w n b a r r i e r s e n c o u n t e r e d w h e n a t t e m p t i n g to operate aqueous S E C at m o l e c u l a r w e i g h t above 1 X 1 0 . T h e r e s o l u t i o n remains h i g h t h r o u g h o u t the e n t i r e m o l e c u l a r w e i g h t range i f the g e l concentration a n d i o n i c strength are adjusted p r o p e r l y . A t this stage, the major difficulty i n a p p l y i n g e l e c trophoresis to u n k n o w n polyelectrolytes is the d e v e l o p m e n t of a sensitive a n d u n i v e r s a l d e t e c t i o n scheme for locating p o l y m e r bands i n the gel. O v e r a l l , g e l electrophoresis has the p o t e n t i a l to lift the most i l l - c h a r a c t e r i z e d class o f synthetic p o l y m e r s , polyelectrolytes of h i g h m o l e c u l a r w e i g h t , to a position for w h i c h characterizations o f e q u a l or greater q u a l i t y to those a c h i e v e d w i t h o t h e r synthetic p o l y m e r s are possible. 6

Acknowledgments W e gratefully a c k n o w l e d g e the N a t i o n a l Science F o u n d a t i o n M a t e r i a l s R e search L a b o r a t o r y at the U n i v e r s i t y of Massachusetts for financial s u p p o r t ; a c k n o w l e d g e m e n t is also m a d e to the D o n o r s o f T h e P e t r o l e u m R e s e a r c h F u n d , a d m i n i s t e r e d b y the A m e r i c a n C h e m i c a l Society, for partial support of this research.

References 1. Jorgenson, J. W. Anal. Chem. 1986, 58, 743A. 2. Chen, J.-L.; Morawetz, H. Macromolecules 1982, 15, 1185.


64


3. Schwartz, D. C.; Cantor, C. R. Cell 1984, 37, 67. 4. Giddings, J. C. In Advances in Chromatography; Giddings, J. C.; Grushka, E.; Cazes, J . ; Brown, P. R., Eds.; Marcel Dekker: Washington, D C , 1982; Vol. 20, pp 217-254. 5. Muller, G . ; Yonnet, C. Makromol. Chem. Rapid Commun. 1984, 5, 197. 6. Davis, R. M . ; Russel, W. B. Macromolecules 1987, 20, 518. 7. Davis, R. M . ; Russel, W. B. J. Polym. Sci. Polym. Phys. Ed. 1986, 24, 511. 8. Hervet, H . ; Bean, C. P. Biopolymers 1987, 26, 727. 9. Smisek, D. L . ; Hoagland, D. A. Macromolecules 1989, 22, 2270. 10. Holzwarth, G. L. Carbohydr. Res. 1978, 66, 173. 11. Rodbard, D . Chrambach, A. Proc. Natl. Acad. Sci. U.S.A. 1970, 65, 970. 12. Lumpkin, O. J . ; Dejardin, P.; Zimm, B. H . Biopolymers 1985, 24, 1573. 13. Adolf, D. Macromolecules 1987, 20, 116. 14. Andrews, A. T. Electrophoresis: Theory, Techniques, and Biochemical and Clinical Applications; Oxford University Press: New York, 1986. 15. Manning, G. S. J. Chem. Phys. 1969, 51, 924. 16. Mays, J. W.; Hadjichristidis, N . ; Fetters, L. J. Polymer 1988, 29, 680.


;

RECEIVED

1989.

for review February 14, 1989.

ACCEPTED

revised manuscript July 31,


Polymer Characterization - ACS Publications - American Chemical

Recommend Documents