Dependence of Spreading Factor on the Retention Volume of Size

Chapter 16 Dependence of Spreading Factor on the Retention Volume of Size Exclusion Chromatography

Downloaded by UNIV OF CALIFORNIA SANTA BARBARA on March 8, 2018 | https://pubs.acs.org Publication Date: October 2, 1987 | doi: 10.1021/bk-1987-0352.ch016

Rong-Shi Cheng, Zhi-Liu Wang, and Yang Zhao Department of Chemistry, Nanjing University, Nanjing, People's Republic of China The variance of the instrumental spreading function, i . e . the spreading factor of monodispersed polymer in a SEC column was determined experimentally with narrow MWD polystyrene standard samples by the method of simultaneous calibration. The dependence of the spreading factor on the retention volume deduced from a simple theoretical approach may be expressed by a formula with four physically meaningful and experimentally determinable parameters. The formula f i t s the experimental data guite well and the conditions for the appearance of a maximum spreading factor are explicable. In the previous paper (1) a method for simultaneous c a l i bration of molecular weight separation and instrumental spreading of SEC with characterized polymer standards was proposed. A thorough knowledge about how the spreading factor varies with the retention volume is of decided importance when applying broadening corrections for MWD determination. It is also useful for studying the pore surface structure of the SEC packings (2) and for deciding whether a resolvable peak of the chromatogram corresponds to a monodisperse species or not. In the present a r t i c l e a theoretical formula relating the spreading factor to the retention volume with four physically meaningful and experimentally determinable parameters is given and tested with experimental results. THEORY

The variance of the spreading function, i . e . the spreading factor of monodisperse polymer in a SEC column may be written as 0097-6156/87/0352-0281$06.00/0 © 1987 American Chemical Society

Provder; Detection and Data Analysis in Size Exclusion Chromatography ACS Symposium Series; American Chemical Society: Washington, DC, 1987.

282

DETECTION AND DATA ANALYSIS IN SIZE EXCLUSION CHROMATOGRAPHY

«-S =

+


i

s

t

(1

i e

The f i r s t t e r m * combined c o n t r i b u t i o n o f t h e l o n g i t u d i n a l d i s p e r s i o n and extracolumn e f f e c t t o t h e s p r e a d i n g f a c t o r a n d may b e r e g a r d e d a s a c o n s t a n t nearly independent o n t h e molecular weight o f polymer. The second term oS?w„ i s t h e c o n t r i b u t i o n o f t h e S E C p r o c e s s . SEC According t o t h e rate theory (3,4), 0* i s p r o p o r t i ona1 to t h e d i s t r i b u t i o n c o e f f i c i e n t Κ ana i n v e r s e l y p r o p o r t i o n a l t o t h e d i f f u s i o n c o e f f i c i e n t D o f t h e polymer in t h e pore

°Lc *= «SEC ° 1

The

( 2 )

d i s t r i b u t i o n c o e f f i c i e n t Κ.,„^ i s d e f i n e d a s bEC K (V V V (3>

SEC = R - 0 > ' !

and t h e d i f f u s i o n c o e f f i c i e n t i s e m p i r i c a l l y the molecular weight o f t h e polymer as D

oc Μ ~

related t o

ε

(4)

I n E g . 3 a n d 4, a n d V\ a r e t h e i n t e r s t i t i a l v o l u m e a n d t o t a l pore volume o f t h e packings i n t h e column r e s p e c t i v e l y and ε i s a constant n e a r l y egual t o one. The molecular weight i s r e l a t e d t o t h e r e t e n t i o n volume bya l i n e a r c a l i b r a t i o n f u n c t i o n M(V^) : In M = A Substituting

M

-B

°SEC = " W ' V which

(5)

K

= ( c / V. 1

b — substituting

Eg. 2

EXP[£(A

B

)

constant.

E X P (

ε

( 6 )

Putting

A ) M

(7)

£ Β

(8)

Eg. 6 i n t o

E g . 1, we g e t

°0 *k R - V P(" R> =

we h a v e ]

M- MV

c i s a proportionality a

and

V

Eg. 3, 4 and 5 i n t o C

in

M

+A(V

EX

BV

9

which r e l a t e s the spreading f a c t o r t o the retention volume V w i t h f o u r p h y s i c a l l y meaningful parameters a a n a b . T h e f o r m e r t w o p a r a m e t e r s / (16) T h e a v e r a g e s p r e a d i n g f a c t o r < or^> o f n a r r o w MWD poly s t y r e n e s t a n d a r d s may b e r e g a r d e d a s t h e s p r e a d i n g factor O^Q o f a m o n o d i s p e r s e p o l y m e r f o r w h i c h V = V. A l l the r e s u l t s thus obtained are l i s t e d i n Taole I I . The v a r i a t i o n o f t h e s p r e a d i n g f a c t o r w i t h r e t e n t i o n v o l u m e i s s h o w n i n F i g . 1. The e x i s t e n c e o f a maximum


283

DETECTION A N D DATA ANALYSIS IN SIZE EXCLUSION CHROMATOGRAPHY

284


Table

I . T h e M o l e c u l a r W e i g h t a n d SEC D a t a of P o l y s t y r e n e Standards

Polymer

*1ΰ w

TSK-2 TSK-10 TSK-20 TSK-40 TSK-80 TSK-128 NPS-2 NPS-3 NPS-4 NPS-5 NPS-6 NPS-7

1 .73 9.89 18.4 42.7 79. 1 130 0.563 1 .20 2.78 5.00 12.0 15.4

/ w η 1 .02 .02 1 .07 1 .05 I .01 1 .05 1 .05 1 .04 1 .03 1 .02 1 .06 1 .07

1

V

37. 80 32. 96 31 .44 28..49 26..50 25..50 42..05 39..52 36..89 35..05 32..40 31 .63 .

ςτ£ Τ 0..67 0..80 1 .51 . 1 .43 . 0..70 0..95 0,.91 0 .86 0..80 0 .77 1 .28 1 .39

Table I I . The C o e f f i c i e n t s o f t h e E f f e c t i v e r e l a t i o n s and t h e S p r e a d i n g F a c t o r s o f P o l y s t y r e n e Standards

Polymer

A *

Β *

ξ

TSK-2 TSK-10 TSK-20 TSK-40 TSK-80 TSK-128 NPS-2 NPS-3 NPS-4 NPS-5 NPS-6 NPS-7

16.24 16.68 18.73 18. 17 16.60 19.81 19.15 21 .00 19.27 21 .91 20.50 19.38

0., 172 0., 157 0., 21 1 0.. 184 0.,114 0. 226 0..253 0..299 υ..247 0..316 0..270 û..233

0. 500 0..462 0..623 0..535 0..329 0..663 0 .746 . 0,.873 0..723 0,.928 0,.794 0..685

V V = i " a - b V

R

(17)

the l o g a r i t h m i c term s h o u l d d e c r e a s e s l i n e a r l y w i t h . S u c h a p l o t i s shown i n F i g . 2 i n w h i c h t h e v a l u e o f and V a r e e s t i m a t e d f r o m t h e chromatograms o f t o t a l l y e x c l u d e d s a m p l e s a s 0.37 a n d 25.3 r e s p e c t i v e l y . From t h e i n t e r c e p t a n d s l o p e o f t h e l i n e i n F i g . 2, t h e p a r a m e t e r a a n d b a r e e v a l u a t e d a n d e q u a l t o 1190 a n d 0.309 r e s p e c V tively. The c a l c u l a t e d c u r v e o f ° "O^R ^ with these evalua t e d p a r a m e t e r s i s drawn i n F i g . 1 t o o . T h e c o i n c i d e n c e with the experimental data i s q u i t e well. Q



C H E N G ET A L .

1

.6

1

.2

Spreading Factor Dependence on Retention Volume of SEC

o.8h-

0.4h-

0

Figure

. Ol

1.

Dependence o f t h e s p r e a d i n g the r e t e n t i o n

volume.

2 F i g u r e 2.

P l o t o f l n { CT

f a c t o r on t h e

2. - ° * _ , ) / ( j

versus


V

D

285

286

DETECTION AND DATA ANALYSIS IN SIZE EXCLUSION CHROMATOGRAPHY

I t s h o u l d be n o t i c e d t h a t t h e v a l u e o f p a r a m e t e r b ( 0 . 3 0 9 ) i s s l i g h t l y s m a l l e r than the s l o p e o f the c a l i bration function Β ( 0 . 3 4 2 ) a s e x p e c t e d by t h e t h e o r y . From t h e r e l a t i o n s h i p between b and Β„ ( E g . 8 ) , we g e t Λ


jyj

S - 0 . 9 0 f o r t h e p r e s e n t c a s e . The c a l c u l a t e d t h e o r e t i c a l O ^ ( V ^ ) curves a r e very sensitive t o the value of the p a r a m e t e r £ as shown i n F i g . 1 . I t i n d i c a t e s t h a t t h e d i f f u s i o n b e h a v i o r o f m a c r o m o l e c u l e s i n t h e p o r e o f SEC P a c k i n g s c a n be s t u d i e d i n a q u a n t i t a t i v e way by s y s t e m a t i c investigation of instrumental spreading e f f e c t .

Literature Cited 1. Rong-shi Cheng and Shu-qin Bo, ACS Symposium Series 245, "SEC, Methodology and Characterization of Polymers and Related Materials", 1984; p. 125. 2. Rong-shi Cheng and Shu-qin Bo, Gaofenzi Tongxun (Polymer Communication, China), 1986 ( 5 ) ; 3 6 5 . 3. M. Kubin, J. Chromatogr., 1975; 108, 1. 4. W. W. Yau, J. J. Kirkland and D. D. Bly, "Modern Size Exclusion Liquid Chromatography", 1979; p. 8 2 . 5. R. Groh and I. Halasz, Anal. Chem., 1981; 53, 1325. RECEIVED May 15, 1987


Dependence of Spreading Factor on the Retention Volume of Size

Recommend Documents