Polymer Characterization - American Chemical Society

1 Polymer Separation by Thermal FieldFlow Fractionation

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High-Speed Power Programming J. Calvin Giddings, Vijay Kumar, P. Stephen Williams, and Marcus N . Myers Field-Flow Fractionation Research Center, Department of Chemistry, University of Utah, Salt Lake City, U T 84112

In this chapter we describe the mechanism of thermal field-flow frac tionation (thermal FFF), explain its uses and advantages for polymer analysis, and report its first implementation in the form of a high -speed power-programmed system. Thermal FFF is characterized by high resolving power and remarkable adaptability such that a single system can be readily tuned to work effectively for almost any mo lecular weight, polymer type, and solvent. Because shear degradation and surface interaction effects are minimal, the method is applicable to ultra-high-molecular-weight polymers. The method exhibits selec tivity with respect to both molecular weight and polymer composition. By combining a thin (76-μm) thermal FFF channel with power-pro grammed operation, in which the temperature drop is decreased according to a specified powerfunction during the run, we can resolve six polymer standards with molecular weights from 9 x 10 to 5.5 X 10 in approximately 8-20 min. The effects of changes in various operating parameters on these programmed separations are reported. 3

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F I E L D - F L O W F R A C T I O N A T I O N (FFF) is a suite o f separation t e c h n i q u e s car r i e d o u t i n t h i n flow channels. T h e s e t e c h n i q u e s are especially applicable to t h e separation a n d characterization o f m a c r o m o l e c u l a r a n d particulate species (1-4). D i f f e r e n t s u b t e c h n i q u e s o f F F F have specific characteristics that m a k e t h e m advantageous for particular categories o f macromaterials. 0065-2393/90/0227-0003$06.00/0 © 1990 American Chemical Society

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

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POLYMER CHARACTERIZATION


A l t h o u g h w e first r e p o r t e d p o l y m e r separation b y the subteehnique o f t h e r m a l F F F 20 years ago, the m e c h a n i s m was not w e l l u n d e r s t o o d a n d the separation not efficient. T h e r m a l F F F has c o n t i n u o u s l y i m p r o v e d i n the i n t e r v e n i n g years a n d , as a p r i m e tool for p o l y m e r characterization, it has f o u n d a p a r t i c u l a r n i c h e i n the separation of synthetic p o l y m e r i c materials (5, 6). I n this chapter, the nature of t h e r m a l F F F a n d its a p p l i c a t i o n to p o l y m e r s w i l l be s u r v e y e d b r i e f l y . W e w i l l t h e n illustrate t h e r m a l F F F a p p l i c a b i l i t y to p o l y m e r s b y r e p o r t i n g a n e w h i g h - s p e e d p r o g r a m m i n g t e c h n i q u e a n d associated i n s t r u m e n t a t i o n capable of fractionating p o l y m e r i c c o m p o n e n t s from 1 0 to 5 X 1 0 m o l e c u l a r w e i g h t i n a single r u n whose t y p i c a l d u r a t i o n is 1 0 - 2 0 m i n . 4

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I n t h e r m a l F F F , a t h i n r i b b o n l i k e c h a n n e l is c l a m p e d b e t w e e n two heatc o n d u c t i v e (copper) bars ( F i g u r e 1). B y h e a t i n g the top bar a n d c o o l i n g the b o t t o m b a r , a t e m p e r a t u r e d r o p r a n g i n g t y p i c a l l y f r o m 20 to 80 ° C , a n d i n exceptional cases from 5 to 150 ° C , is established across the c h a n n e l . Because the c h a n n e l is t h i n , t y p i c a l l y 7 5 - 1 2 5 jxm t h i c k i n c u r r e n t w o r k , t e m p e r a t u r e gradients o n the o r d e r o f 1 0 ° C / c m are established across the c h a n n e l . S u c h t e m p e r a t u r e gradients a c t i n g t h r o u g h the p h e n o m e n o n of t h e r m a l diffusion are capable of c r e a t i n g strong d r i v i n g forces o n p o l y m e r i c components (4). P o l y m e r s are u s u a l l y d r i v e n to the c o l d w a l l o f the c h a n n e l b y the t h e r m a l diffusive process (7), as s h o w n i n F i g u r e 2. 4

W h e n the flow of solvent is i n i t i a t e d i n the c h a n n e l , the p o l y m e r i c materials of an i n j e c t e d sample are swept d o w n s t r e a m . H o w e v e r , the v e l o c i t y of d o w n s t r e a m d i s p l a c e m e n t of the p o l y m e r molecules depends u p o n w h e r e the p o l y m e r is located i n the c h a n n e l cross section because o f the differential (parabolic) nature of the c h a n n e l flow. I n p a r t i c u l a r , components d r i v e n closest to the c o l d w a l l w i l l be c a r r i e d d o w n s t r e a m o n l y slowly because the flow v e l o c i t y approaches zero at a l l solid walls a n d surfaces. C o n s e q u e n t l y , w i t h the onset of flow, a fractionation process is i n i t i a t e d i n w h i c h the p o l y m e r c o m p o n e n t s d r i v e n closest to the c o l d w a l l are r e t a r d e d i n t h e i r passage t h r o u g h the c h a n n e l m o r e t h a n the p o l y m e r i c species w i t h a greater average distance away from the c o l d w a l l . Because 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 are d r i v e n closer to the c o l d w a l l t h a n are those of l o w m o l e c u l a r w e i g h t , the l o w - m o l e c u l a r - w e i g h t species e m e r g e first, followed b y fractions of successively h i g h e r m o l e c u l a r w e i g h t . T h u s the e l u t i o n o r d e r established i n t h e r m a l F F F is opposite to that f o u n d i n size exclusion c h r o m a t o g r a p h y (SEC) (5). T h e r m a l F F F was first a p p l i e d to p o l y m e r s i n o u r laboratory early i n the latter h a l f of the 1960s, a t i m e a p p r o x i m a t e l y c o i n c i d e n t w i t h the b e ginnings o f S E C i n the f o r m o f gel p e r m e a t i o n chromatography (8). H o w e v e r , S E C was d e v e l o p e d m o r e r a p i d l y into practical laboratory i n s t r u m e n t a t i o n than was t h e r m a l F F F , w h i c h was largely i g n o r e d except for o n g o i n g w o r k i n o u r laboratory.


Thermal Field-Flow Fractionation


GIDDINGS ET AL.



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Figure 2. Flow and polymer separation in thermal FFF system. A c o m b i n a t i o n o f three factors has substantially i n c r e a s e d the interest of p o l y m e r scientists i n t h e r m a l F F F i n recent years. O n e factor is the continuous i m p r o v e m e n t i n F F F i n s t r u m e n t a t i o n a n d m e t h o d o l o g y a n d the c o n s e q u e n t i n t r o d u c t i o n o f a t h e r m a l F F F i n s t r u m e n t into the c o m m e r c i a l market. T h e s e c o n d factor is the i n c r e a s i n g n e e d for n e w t e c h n i q u e s i n p o l y m e r analysis to c o v e r an e v e r - e x p a n d i n g v a r i e t y o f n e w p o l y m e r i c m a terials. T h e t h i r d factor is the h e i g h t e n e d d e m a n d for i m p r o v e d characterization. I n this context t h e r m a l F F F appears to b e p a r t i c u l a r l y advantageous i n the analysis o f v e r y - 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 , species subject to shear degradation, c o p o l y m e r s , p o l y m e r s that t e n d to interact w i t h surfaces, p o l y m e r s n e e d i n g corrosive solvents, h i g h - t e m p e r a t u r e p o l y m e r solutions, a n d n a r r o w p o l y m e r samples r e q u i r i n g an accurate d e t e r m i n a t i o n of p o l y dispersity. A t the same t i m e , t h e r m a l F F F is n o w a w o r k h o r s e t e c h n i q u e flexibly applicable to r o u t i n e p o l y m e r analysis p r o b l e m s . A l t h o u g h the m e c h a n i s m o f t h e r m a l F F F bears v e r y little r e s e m b l a n c e to that o f S E C , the two methods can i n some cases b e u s e d for the same applications: the d e t e r m i n a t i o n o f 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 s for various i n d u s t r i a l p o l y m e r s . H o w e v e r , the u n i q u e m e c h a n i s m of t h e r m a l F F F i m parts some e q u a l l y u n i q u e characteristics a n d advantages. T h e s e are s u m m a r i z e d as follows.


1.

GIDDINGS ET AL.


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F i r s t , as already n o t e d , the e l u t i o n o r d e r i n t h e r m a l F F F is opposite to that o b s e r v e d for S E C : i n t h e r m a l F F F the l o w - m o l e c u l a r - w e i g h t c o m p o nents e m e r g e first a n d the h i g h - m o l e c u l a r - w e i g h t species last. D e s p i t e this difference, the r e s o l u t i o n a n d s p e e d of separation of the two methods appear to b e c o m p a r a b l e as m e a s u r e d w i t h present i n s t r u m e n t a t i o n (5). A n o t h e r u n i q u e feature o f t h e r m a l F F F is its flexibility. A major e l e m e n t of this flexibility arises f r o m the fact that the t e m p e r a t u r e d r o p A T across the c h a n n e l can b e v a r i e d r a p i d l y a n d p r e c i s e l y to any d e s i r e d l e v e l . Because the t e m p e r a t u r e d r o p controls r e t e n t i o n , t h e r m a l F F F is a single system that can b e q u i c k l y t u n e d (by means o f AT) to accommodate almost any p o l y m e r analysis p r o b l e m . F o r example, the t e m p e r a t u r e d r o p can b e raised (to o v e r 100 °C) to accommodate l o w - m o l e c u l a r - w e i g h t p o l y m e r s (9), it can be l o w e r e d (to u n d e r 10 °C) to accommodate u l t r a - 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 (10), a n d i t can b e c h a n g e d c o n t i n u o u s l y (programmed) to h a n d l e a p o l y m e r sample h a v i n g a w i d e m o l e c u l a r - w e i g h t range (JI). T h u s a n e n o r mous v a r i e t y of p o l y m e r s can b e h a n d l e d i n a single system w i t h o u t special requirements. I n t h e r m a l F F F , greater flexibility arises t h r o u g h the c o n t r o l of flow v e l o c i t y than i n S E C . R e s o l u t i o n is m o r e h i g h l y flow sensitive i n t h e r m a l F F F t h a n i n S E C , a n d t h e r m a l F F F gives a b e t t e r - d e f i n e d tradeoff b e t w e e n p o l y m e r r e s o l u t i o n a n d analysis speed (5). T h e o p e n u n o b s t r u c t e d c h a n n e l o f a t h e r m a l F F F system is v e r y different from the p a c k e d c o l u m n s u s e d i n S E C . T h e absence o f extensional shear i n the F F F c h a n n e l reduces shear degradation or s h e a r - i n d u c e d structural changes (10). T h e u n i f o r m c h a n n e l structure also yields a far m o r e p r e d i c t a b l e flow than a p a c k e d b e d . C o n s e q u e n t l y , the theoretical p r e d i c t a b i l i t y of r e t e n t i o n , b a n d b r o a d e n i n g , a n d r e s o l u t i o n is m u c h better a d v a n c e d i n t h e r m a l F F F t h a n i n S E C (12). T h i s p r e d i c t a b i l i t y is a substantial advantage i n the d e t e r m i n a t i o n o f o p t i m u m separation conditions. I n a d d i t i o n , it has several special advantages, such as m a k i n g it possible to exactly compensate for b a n d b r o a d e n i n g b y u s i n g d e c o n v o l u t i o n techniques (13) a n d to measure the ext r e m e l y l o w p o l y d i s p e r s i t y values o f n a r r o w p o l y m e r standards i n a straightforward fashion (14). F i n a l l y , t h e r m a l F F F r e t e n t i o n is sensitive to the c h e m i c a l c o m p o s i t i o n of a p o l y m e r as w e l l as to its m o l e c u l a r w e i g h t . T h u s t h e r m a l F F F has the p o t e n t i a l to b e u s e d i n the c o m p o s i t i o n a l analysis of c o p o l y m e r s a n d b l e n d s (15). I n e a r l i e r w o r k , t h e r m a l F F F was a p p l i e d almost exclusively to p o l y styrene standards, b u t it has i n m o r e recent times b e e n e x t e n d e d to p o l y m e r s s u c h as p o l y ( m e t h y l methacrylate), p o l y i s o p r e n e , p o l y - ( a - m e t h y l ) s t y r e n e , p o l y t e t r a h y d r o f u r a n , p o l y e t h y l e n e , polycarbonate, p o l y u r e t h a n e , a n d a v a r i e t y of other p o l y m e r s that suggest that the m e t h o d is almost u n i v e r s a l for p o l y m e r s soluble i n organic l i q u i d s . I n a d d i t i o n , t h e r m a l F F F has b e e n f o u n d applicable to p o l y m e r s d o w n to ~ 1 0 0 0 m o l e c u l a r w e i g h t at one ext r e m e (9) a n d u p to > 6 0 X 1 0 m o l e c u l a r w e i g h t at the other extreme (10). 6

A n o t h e r field-flow fractionation m e t h o d has b e e n p r o v e n a p p l i c a b l e to In Polymer Characterization; Craver, C., et al.; Advances in Chemistry; American Chemical Society: Washington, DC, 1990.

8


p o l y m e r s ; that m e t h o d is flow F F F . T h e flow subteehnique o f F F F has b e e n u s e d p r i m a r i l y w i t h aqueous systems i n c l u d i n g water-soluble p o l y m e r s (16), m a n y o f w h i c h cannot b e a n a l y z e d b y t h e r m a l F F F . H o w e v e r , flow F F F can also b e a p p l i e d to l i p o p h i l i c p o l y m e r s i n organic solvents, p r o v i d i n g the right m e m b r a n e is chosen (17).

Power-Programmed Thermal FFF


A s n o t e d e a r l i e r , the a b i l i t y to c o n t r o l the t e m p e r a t u r e d r o p A T i n t h e r m a l F F F introduces great

flexibility

i n t o t h e r m a l F F F operation a n d makes it

possible to t u n e the system to accommodate almost any m o l e c u l a r - w e i g h t range o f p o l y m e r . W h e n the m o l e c u l a r w e i g h t extends o v e r a range greater than about 2 5 - to 50-fold, this

flexibility

is best e x p l o i t e d b y u s i n g p r o -

g r a m m e d o p e r a t i o n . I n this t e c h n i q u e , first a p p l i e d to t h e r m a l F F F i n 1976 (II), the field s t r e n g t h A T begins at a h i g h value a n d t h e n drops c o n t i n u o u s l y d u r i n g the r u n . T h e h i g h A T o p t i m a l l y separates the l o w - m o l e c u l a r - w e i g h t c o m p o n e n t s ; the h i g h - m o l e c u l a r - w e i g h t c o m p o n e n t s are separated as A T drops to l o w e r values. I n the first e x p e r i m e n t a l realization o f p r o g r a m m e d t h e r m a l F F F , A T was h e l d constant at 70 °C for a p e r i o d of t i m e (the p r e d e c a y time), after w h i c h A T was forced to decrease parabolically as a f u n c t i o n of t i m e (II). A linear p r o g r a m was also u s e d . T h e s e e x p e r i m e n t s s h o w e d that p o l y m e r s r a n g i n g i n m o l e c u l a r w e i g h t f r o m 4000 u p to 7.1 X

1 0 c o u l d be separated 6

i n a single r u n . A n example o f the o r i g i n a l p r o g r a m m e d separation is s h o w n i n F i g u r e 3. A l t h o u g h this early p r o g r a m m i n g w o r k e x h i b i t e d excellent r e s o l v i n g

1 hr

6 hours

Figure 3. Slow but effective separation of polystyrene standards of indicated molecular weights by parabolic programming as reported in initial 1976 paper on programmed thermal FFF. (Reproduced from reference 11. Copyright 1976 American Chemical Society.)


1.

9


GIDDINGS ET AL.

p o w e r a n d broad-range m o l e c u l a r - w e i g h t a p p l i c a b i l i t y , it was flawed i n one major respect: the r u n t i m e of the e x p e r i m e n t was o v e r 6 h . Since that t i m e e x t r e m e l y fast p o l y m e r fractionation has b e e n a c h i e v e d b y t h e r m a l F F F . O n e study s h o w e d that several p o l y m e r standards c o u l d be r e s o l v e d i n o n l y a few m i n u t e s (18). A n example f r o m that study is s h o w n i n F i g u r e 4. D e s p i t e the success of the latter e x p e r i m e n t s , the conditions n e e d e d for h i g h - s p e e d p o l y m e r separation have not since b e e n u s e d i n c o n j u n c t i o n w i t h p r o g r a m m e d t h e r m a l F F F . T h e p u r p o s e of this w o r k is to illustrate the successful Downloaded by NORTHEASTERN UNIV LIB on February 18, 2015 | http://pubs.acs.org Publication Date: May 5, 1990 | doi: 10.1021/ba-1990-0227.ch001

marriage of p r o g r a m m i n g m e t h o d o l o g y a n d h i g h - s p e e d i n s t r u m e n t a t i o n .

I 0

I 1

2

1

1 3

TIME

(min)

1 4

I 5

Figure 4. Fast separation of polystyrene standards by thermal FFF in 51-jxmthick channel. Numbers are molecular weights; k indicates thousand. (Reproduced with permission from reference 18. Copyright 1978.) A s s h o w n i n the h i g h - s p e e d study j u s t n o t e d , the k e y r e q u i r e m e n t n e e d e d to r e d u c e separation t i m e is a t h e r m a l F F F c h a n n e l of r e d u c e d thickness. W h e r e a s the slow p r o g r a m m i n g r u n of F i g u r e 3 was a c h i e v e d i n a c h a n n e l h a v i n g a thickness w of 254 jxm, the separation i n F i g u r e 4 was r e a l i z e d w i t h a c h a n n e l thickness of 51 (xm. Because the t i m e of the r u n (other things b e i n g constant) is approximately p r o p o r t i o n a l to the c h a n n e l thickness squared (18), there is a b u i l t - i n 25-fold difference i n the i n t r i n s i c o p e r a t i n g speeds of the two systems. H o w e v e r , p r o g r a m m i n g runs for p o l y d i s p e r s e samples generally r e q u i r e a longer t i m e than do o p t i m i z e d isocratic runs a c h i e v i n g separation o v e r a n a r r o w m o l e c u l a r - w e i g h t range. T h u s the t i m e r e q u i r e d for the r u n i n F i g u r e 3 was nearly 2 orders of m a g n i t u d e greater than that r e q u i r e d to reach separation i n F i g u r e 4. A l t h o u g h w e have not f o u n d it practical to carry out p r o g r a m m e d operation i n a 51-|xm-


10


thick c h a n n e l , w e have b e e n able to achieve effective p r o g r a m m e d o p e r a t i o n i n a 76-p.m-thick c h a n n e l . T h e e n h a n c e m e n t o f s p e e d relative to that o f the 254-jxm c h a n n e l s h o u l d b e g o v e r n e d b y the factor ( 2 5 4 / 7 6 )

2

=

11.2, or


a p p r o x i m a t e l y 1 o r d e r of m a g n i t u d e . I n the e a r l i e r p r o g r a m m i n g study, the m a t h e m a t i c a l f o r m of the p r o g r a m ( A T versus time) was parabolic i n one case a n d l i n e a r i n another (J J). A n y c o n t i n u o u s l y decreasing f u n c t i o n can b e u s e d . H o w e v e r , different m a t h e matical p r o g r a m m i n g functions display different e l u t i o n spectra (molecular w e i g h t versus time) a n d different r e s o l u t i o n levels i n different parts of the resultant fractogram (19). I n recent years special p r o g r a m functions have b e e n d e v e l o p e d to c o n t r o l these e l u t i o n characteristics. K i r k l a n d et a l . (20), for e x a m p l e , have d e v e l o p e d a t i m e - d e l a y e d e x p o n e n t i a l p r o g r a m m i n g f u n c t i o n such that plots of the l o g a r i t h m of m o l e c u l a r w e i g h t versus r e t e n t i o n t i m e are a p p r o x i m a t e l y linear. I n o u r laboratory w e have d e v e l o p e d p r o g r a m m i n g a c c o r d i n g to a p o w e r f u n c t i o n (power p r o g r a m m i n g ) for the p u r pose o f a c h i e v i n g u n i f o r m r e s o l u t i o n or fractionating p o w e r o v e r the f u l l m o l e c u l a r - w e i g h t range o f the e x p e r i m e n t (21). I n p o w e r p r o g r a m m i n g the field strength S is c h a n g e d w i t h t i m e t a c c o r d i n g to the f u n c t i o n (21)

w h e r e S is the i n i t i a l f i e l d s t r e n g t h , £ is an arbitrary t i m e constant, t is the predecay t i m e b e t w e e n the start of the r u n a n d the b e g i n n i n g of decay, a n d p is the decay p o w e r . T h e s e parameters are subject to the constraints t > t > t a n d p > 0. 0

x

x

a

a

F o r F F F , the r e t e n t i o n ratio R is g i v e n b y the e q u a t i o n

R = 6X

coth ( - M

-

2X

(2)

p r o v i d i n g the a s s u m p t i o n of a parabolic f l u i d velocity profile is v a l i d . F o r t h e r m a l F F F , the r e t e n t i o n p a r a m e t e r X is g i v e n to a good a p p r o x i m a t i o n b y (22)

D w(dT/dx)

v

T

7

w h e r e D is the n o r m a l mass diffusion coefficient, D is the t h e r m a l diffusion coefficient, w is the c h a n n e l thickness, a n d dT/dx is the local t e m p e r a t u r e gradient. T h e t e m p e r a t u r e gradient dT/dx differs o n l y slightly f r o m the o v e r a l l t e m p e r a t u r e gradient A T / u ? e v e n at h i g h A T (23). T


1.

11


GIDDINGS ET AL.

A t h i g h r e t e n t i o n levels, w h e r e the p o l y m e r b a n d is c o m p r e s s e d closely to the a c c u m u l a t i o n w a l l , D a n d D

T

i n e q 3 m a y be assumed to c o r r e s p o n d

closely to t h e i r values at the t e m p e r a t u r e T of the a c c u m u l a t i o n (cold) w a l l . c

H e n c e w e o b t a i n the s i m p l e approximate equation

D AT T

in which D and D Downloaded by NORTHEASTERN UNIV LIB on February 18, 2015 | http://pubs.acs.org Publication Date: May 5, 1990 | doi: 10.1021/ba-1990-0227.ch001

T

values are those c o r r e s p o n d i n g to t e m p e r a t u r e T . c

Coef-

ficient D was s h o w n (24) to b e essentially i n d e p e n d e n t of p o l y m e r m o l e c u l a r T

w e i g h t for any p a r t i c u l a r p o l y m e r - s o l v e n t system, a n d the m o l e c u l a r - w e i g h t d e p e n d e n c e of X therefore parallels that of D . A t h i g h r e t e n t i o n (corresponding to R «

1), e q 2 reduces to the f o r m

H = 6X =

(5)

again w i t h D a n d D taken at T . I n practice, a p l o t of - I n R vs. In M , w h e r e M is the p o l y m e r m o l e c u l a r w e i g h t , is f o u n d to be a straight l i n e , the slope of w h i c h is d e f i n e d as the selectivity, generally taking a v a l u e b e t w e e n 0.5 a n d 0.65. Because D is i n d e p e n d e n t of M , e q 5 makes i t apparent that this d e p e n d e n c e reflects p r i n c i p a l l y the d e p e n d e n c e of D o n M . It follows that T

c

T

w h e r e is a constant for a p a r t i c u l a r s o l u t e - s o l v e n t system at some

fixed

c o l d w a l l t e m p e r a t u r e a n d n i n this e q u a t i o n is an exponent that b e c o m e s the l i m i t i n g v a l u e of selectivity for small X. F o r significantly r e t a i n e d components

e l u t e d u n d e r conditions of a

p o w e r - p r o g r a m m e d field strength, the mass-based fractionating p o w e r F

M

is g i v e n b y (21)

M

"48u;L

P + l

J

w h e r e t is the system v o i d t i m e a n d X is the value of X at the i n i t i a l f i e l d strength. T h e mass-based fractionating p o w e r is s i m p l y d e f i n e d as the reso l u t i o n for t w o closely e l u t i n g components d i v i d e d b y t h e i r relative differ0

0


12


ence i n m o l e c u l a r w e i g h t (19), that is,

8M/M

M

4a, 8 M

v

;

w h e r e R is the r e s o l u t i o n 8 f / 4 a „ i n w h i c h bt is the difference i n the two s

r

r

r e t e n t i o n times a n d a

f

is the m e a n standard d e v i a t i o n i n r e t e n t i o n t i m e .

Q u a n t i t y 8 M is the difference i n the two m o l e c u l a r weights a n d M is the Downloaded by NORTHEASTERN UNIV LIB on February 18, 2015 | http://pubs.acs.org Publication Date: May 5, 1990 | doi: 10.1021/ba-1990-0227.ch001

m e a n m o l e c u l a r w e i g h t . F o r the special case of f n F

m

[6(4p

L

+ l)

[an

~ 48«,

= -pti,

a

J

e q 7 reduces to

*

J

P + l 2(p + 1)

(9)

F r o m the d i r e c t p r o p o r t i o n a l i t y b e t w e e n X a n d D expressed b y e q 4, it is apparent that (10) A fractionating p o w e r i n d e p e n d e n t of D , a n d therefore i n d e p e n d e n t of M , is g i v e n for significantly r e t a i n e d components w h e n the p o w e r o f D i n e q 10 is r e d u c e d to zero, that is, w h e n p = 2. I n this case

F

M

= |^(2D AT *y* r

(11)

0

w h e r e a substitution u s i n g e q 4 was made i n e q 9 for X, A T is the i n i t i a l t e m p e r a t u r e d r o p across the c h a n n e l , a n d it is assumed that t = -2t A fractionating p o w e r i n d e p e n d e n t of m o l e c u l a r w e i g h t is desirable w h e n w i d e l y p o l y disperse samples are to be characterized. 0

a

v

T h e f o l l o w i n g expression was also d e r i v e d (21) for e l u t i o n t i m e of s i g nificantly r e t a i n e d components I

P

W h e n p = 2 and t

a

= -2t

x

+i

(12)

e q 12 reduces to Mi

-

2*!


(13)

1.


GIDDINGS E T AL.

13

T h e approach j u s t d e s c r i b e d presupposes a parabolic fluid velocity p r o file. I n t h e r m a l F F F t h e assumption o f such a profile is n o t strictly correct. A d e v i a t i o n f r o m t h e parabolic f o r m occurs because o f t h e t e m p e r a t u r e d e p e n d e n c e of the solvent viscosity. C l o s e to the c o l d w a l l w h e r e the viscosity is greatest, t h e v e l o c i t y is l o w e r e d relative to that o f the parabolic profile, w h i l e t o w a r d t h e hot w a l l the v e l o c i t y is r e l a t i v e l y greater (22, 25-27). T h i s d e v i a t i o n , w h i c h has a n influence o n b o t h b a n d s p r e a d i n g a n d r e t e n t i o n ratio, is a function o f A T ; thus for p r o g r a m m e d t h e r m a l F F F t h e d e v i a t i o n Downloaded by NORTHEASTERN UNIV LIB on February 18, 2015 | http://pubs.acs.org Publication Date: May 5, 1990 | doi: 10.1021/ba-1990-0227.ch001

w i l l b e t i m e d e p e n d e n t . T h e r e f o r e , constant fractionating p o w e r s h o u l d b e o b t a i n e d for a p o w e r p close to, b u t not e q u a l to, 2. N e v e r t h e l e s s , b y setting p e q u a l to 2 w e l i k e l y have established conditions close to those n e e d e d for the o p t i m u m fractionation o f p o l y d i s p e r s e samples. I n o r d e r to achieve u n i f o r m fractionating p o w e r , the three constants (t , x

t , a n d p) i n e q 1 d e s c r i b i n g t h e f i e l d p r o g r a m m u s t b e fixed at specified a

levels. F o r t h e r m a l F F F , p = 2 a n d £ a n d t are r e l a t e d b y £ = a

x

a

-2t

v

W h e n t h e latter c o n d i t i o n holds, t h e f i e l d s t r e n g t h — i n this case t h e t e m perature d r o p A T — f o r t h e r m a l F F F is g i v e n b y

(14)

F o r t h e general p o w e r - p r o g r a m m e d decay d e s c r i b e d b y e q 1, t h e t i m e r e q u i r e d for A T to decay to h a l f o f the i n i t i a l v a l u e A T is g i v e n b y 0

t

%

= 2 "(t v

l

-

w h i c h reduces to ty = 2 . 2 4 3 ^ for p = 2 a n d t 2

(15)

O + *, a a

=

-2t

v

Experimental Details The channel system employed in these studies is similar to that used in the model T100 thermal F F F system from FFFractionation, Inc. (Salt Lake City, UT). It consists of two highly polished chrome-plated bars of electrolytic grade copper clamped together over a thin (76-|xm) polyester (Mylar) spacer. The channel form was cut into the spacer. The resulting channel has dimensions of 76-jxm thickness, 2.0-cm breadth, and 46.3-cm tip-to-tip length. The measured void volume V° was 0.685 mL. Four cartridge heaters of 1500 W each were used to heat the upper bar. The cold bar had slots milled in it to provide efficient water circulation throughout the bar for cooling. The cold wall temperature was maintained at 32 ± 1 °C during programming by adjusting the flow of water. The temperature of the hot wall was controlled by programmed computer-activated solid-state relays. An 80-s time lag



14


was used to account for the time required for the conduction of heat from the heating cartridges to the hot wall. Small holes were drilled at two places on each bar to within 0.76 mm of the polished surfaces for the measurement of temperature by copper-constantan thermocouples with digital thermometers (Omega, Stamford, CT). The maximum variation in the temperature drop AT along the length of the channel relative to the setting was 2 °C. The variation became less as AT decreased. Two holes, one in the hot wall and one in the cold wall, were drilled from the smooth surfaces to the sides of the bars to form the inlet and the outlet of the channel, respectively. The channel spacer was positioned in such a way that the two apices at the tapered ends aligned with the inlet and outlet holes. All connections were made with stainless steel tubing of 0.01 in. (0.0254 cm) internal diameter. The volume of the tubing used was 0.055 mL, 8% of the channel void volume of 0.685 mL. Sample injections of 10 \LL were made with a Valco (Houston, TX) valve. There was no stop-flow for relaxation following injection. A helium gas pressurized pump was used to generate the flow of carrier, which in all these experiments was ethylbenzene. The polystyrene samples were detected with a refractive index monitor (model 401, Waters Associates, Amherst, MA). The samples in ethylbenzene solution had typical concentrations of approximately 2 mg/mL. The samples of high molecular weight, of the order of millions, had concentrations of 3 to 4 mg/mL. The samples used in the study are polystyrene standards as described in Table I. Sample retention times were measured from the chart paper of an Omniscribe chart recorder (Houston Instruments, Austin, TX).

Table I. Polystyrene Standards Used in This Study Supplier 9,000 Supelco, Inc. 35,000 Supelco, Inc. 90,000 Supelco, Inc. 200,700 Supelco, Inc. 575,000 Supelco, Inc. 1,970,000 American Polymer Standard Corp. 5,480,000 Polyscience, Inc. a

h

Cat. No.

Polydispersity

4-5703 4-5705 4-5707 4-5708 4-5710 PS 2000k

Polymer Characterization - American Chemical Society

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