Size Exclusion Chromatography - American Chemical Society

9 Evaluation of Füzes Statistical Methods For Testing Identity of Size Exclusion Chromatography Molecular

Downloaded by UNIV OF CALIFORNIA SANTA BARBARA on March 2, 2018 | https://pubs.acs.org Publication Date: March 30, 1984 | doi: 10.1021/bk-1984-0245.ch009

Weight Distributions of Polymers SADAO

MORI

Department o f Industrial Chemistry, Faculty of Engineering, M i e University, Tsu, M i e 514, Japan

The sequential U test proposed by L . Füzes could differentiate two polymers whose molecular weight averages are identical within the experimental errors. Parallel measurements of SEC chromatograms of the two polymers were performed in series and the distinguised points (DPs), which are defined as the elution volumes at 10, 30, 50, 70, and 90 % of the each integral chromatogram, were calculated. By the statistical treatments of the DP values, identity of molecular weight distributions (MWDs) of the two polymers was established with more than four pairs of parallel measurements, and the disagreement of MWDs with two to four pairs of runs. However, this statistical treatment could not detect small differences in shapes of the both chromatograms.

Polymer samples of same s p e c i e s can be confirmed i n t h e i r i d e n t i t y by the agreement w i t h the r e s p e c t i v e values of both the molecular weight average and the molecular weight d i s t r i b u t i o n (MWD). These values are to be measured by s i z e e x c l u s i o n chromatography (SEC). In the determination of SEC, we o f t e n experience the c o n f l i c t s that polymer samples having the i d e n t i c a l molecular weight aver ages, w i t h i n the experimental errors,show d i f f e r e n t SEC chromato grams or v i c e v e r s a . I t i s very important to know i f the observed d i f f e r e n c e s between MWDs or between the molecular weight averages are due to r e a l d e v i a t i o n s or to experimental e r r o r s . The i d e n t i t y of molecular weight averages can be t e s t e d by the t - t e s t by determining these values repeatedly and by knowing the standard d e v i a t i o n . However, another s t a t i s t i c a l treatment must be r e q u i r e d i n the case of MWDs i n order to judge the d i f f e r e n c e to be due to the experimental v a r i a t i o n s or the r e a l MWD. Recently, L. Fuzes reported the method of " d i s t i n g u i s h e d p o i n t s (DPs) f o r comparing the SEC chromatograms of two or more polymer samples ( 1 ) . The s e q u e n t i a l U and t t e s t s were suggested i n order 11

0097-6156/84/0245-0135506.00/ 0 © 1984 American Chemical Society

Provder; Size Exclusion Chromatography ACS Symposium Series; American Chemical Society: Washington, DC, 1984.

SIZE EXCLUSION


136

CHROMATOGRAPHY

to i n d i c a t e the s i g n i f i c a n t d e v i a t i o n or the agreement of the DP values of SEC chromatograms of two polymer samples. In t h i s r e p o r t , the v a l i d i t y of t h i s s t a t i s t i c a l method was t e s t e d by using s e v e r a l p o l y s t y r e n e mixtures of known broad and narrow MWDs. Whether the d i f f e r e n c e i n the two MWDs of p o l y s t y r e n e s having the s i m i l a r molecular weight can be regarded as s i g n i f i c a n t or not was t e s t e d u s i n g s e v e r a l p a i r s of t e s t samples, one i s p o l y s t y r e n e NBS 706 and the other the mixture of p o l y s t y r e n e NBS 706 and another p o l y s t y r e n e having d i f f e r e n t molecular weights than NBS 706. Calculation B a s i c parameters

f o r the comparison of two polymers, A and B, are 2a

1 In (

z

h

- -h» ο 1

«

0.5a )

(1)

n

and 2σ = -h * °

h 1

2

1 - β In ( ) 0.5α

δ

(2)

where α i s the e r r o r of type I , β the e r r o r of type I I , 6 the l e a s t d i f f e r e n c e of the e l u t i o n volume i n t h i s case one wants to d e t e c t , a the standard d e v i a t i o n of the DP values which are the e l u t i o n volumes a t 10, 30, 50, 70, and 90 % of the i n t e g r a l curves of the chromatograms i n the order of i n c r e a s i n g e l u t i o n volume. The term Δ Τ ^ i s d e f i n e d as Δ τ

ΐί =

T A i j

T

-

( 3 ) B i j

where T ., and T„.. are the DP values of each chromatogram, the Aij Bij index i d e f i n e s the number of p a r a l l e l measurements ( 1 , 2, , n ) , and the index j i d e n t i f i e s the per cent of the i n t e g r a l curve of each chromatogram (10, 30, 50, 70, and 90 % ) . A f t e r every p a r a l l e l run of polymers A and B, compute Δ Τ ^ f o r each i and j A

and summarize the ΔΤ,^ values f o r i i n the case of each j η Σ ΔΤ.. i-1

(4)

± 3

and p l o t t h i s value at each n. The broken l i n e s on F i g u r e 2 are d e f i n e d as Τ (= h + Sn) , T (= h + Sn) , Τ ' (= - Sn) , and χ

Τ

1

(= h

1

±

q

Q

χ

- Sn) i n the order from the top to the bottom, where

ο ο S = δ/2 and η i s the number of p a r a l l e l measurements.


9.

MORI

Fuzes Statistical

137

Methods

Experimental SEC measurements were performed on a Jasco TRIROTAR h i g h - p e r f o r mance l i q u i d chromatograph w i t h a Model SE-11 d i f f e r e n t i a l r e f r a c tometer. Two Shodex A80M high-performance SEC columns (50 cm χ 8 mm i.d.) packed w i t h a mixture of p o l y s t y r e n e g e l s o f nominal e x c l u s i o n l i m i t s o f ΙΟ , ΙΟ , 1 0 , and about 10 molecular weights as p o l y s t y r e n e were used and thermostated a t 25 °C i n an a i r oven, Model TU-100. The data were evaluated a u t o m a t i c a l l y by u s i n g a Sord micro-computor Model 220 t o which the out-put of the d e t e c t o r was connected v i a an A/D c o n v e r t e r . Tetrahydrofuran was used as the mobile phase. The f l o w r a t e of the pump d i a l was adjusted t o 1.0 mL/min and sample concentra t i o n was 0.2 % (w/v). A 0.25-mL loop was used t o i n j e c t these sample s o l u t i o n s . Sample polymers were standard p o l y s t y r e n e NBS 706 (M « 2.71 χ ΙΟ , M « 1.30 χ 1 0 measured a t our l a b o r a t o r y ) , w η


5

5

6

7

8

5

commercial p o l y s t y r e n e ESBRITE (M^ = 2.26 χ 1 0 , M - 1.08 χ 1 0 ) and two narrow MWD p o l y s t y r e n e s , PS 411000 and PS 200000 (molecu l a r weights a r e 411,000 and 200,000, r e s p e c t i v e l y ) . 5

5

r

R e s u l t s and D i s c u s s i o n F i r s t , we estimated the parameters α t o be 0.01 and β t o be 0.05. For the e s t i m a t i o n o f the standard d e v i a t i o n o f the DP v a l u e s , twenty chromatograms of NBS 706 p o l y s t y r e n e were measured and e l u t i o n volumes a t the d i s t i n g u i s h e d per cent p o i n t s o f the i n t e g r a l curve of each chromatogram were c a l c u l a t e d . Then, the value σ was obtained to be 0.042 mL. The value 6 was estimated to be 0.1 mL, which corresponds to 0.3 % of the e l u t i o n volume a t the center of the c a l i b r a t i o n curve of t h i s SEC system and 5 % d i f f e r e n c e of molecular weight. The s e q u e n t i a l U t e s t was performed by u s i n g s e v e r a l p a i r s o f polymer samples. F i r s t example i s shown i n F i g u r e 1. The sample mixture i s a combination of NBS 706 (98.5 %) and PS 200000 (1.5 % ) . Two normalized chromatograms, NBS 706 (A) and the mixture (Β), a r e n e a r l y the same and molecular weight averages (the mean from three determinations) c a l c u l a t e d are almost i d e n t i c a l . The r e s u l t s o f the s e q u e n t i a l U t e s t i s shown i n F i g u r e 2. A f t e r the f o u r t h p a i r of runs, a l l the values of ΣΔΤ^. were found to be l o c a t e d i n the area A = B, and i t could be s t a t e d w i t h a r i s k of 5 % t h a t the two polymer samples had the same MWDs. Normalized chromatogram of a s i m i l a r mixture of NBS 706 (97 %) and PS 200000 (3 %) i s shown w i t h that of NBS 706 i n F i g u r e 3 and the s e q u e n t i a l U t e s t i s shown i n F i g u r e 4. I n t h i s example, the v a l u e of Σ Δ Τ ^ a t j = 10 % exceeded the c r i t i c a l value a f t e r the f i f t h p a i r o f p a r a l l e l measurements. I t could be s t a t e d w i t h a r i s k of 5 % that the MWD of the mixture was not the same to that of NBS 706 though they had the almost i d e n t i c a l molecular weight averages. Since the


CHROMATOGRAPHY


SIZE E X C L U S I O N

F i g u r e 2. S e q u e n t i a l U t e s t f o r (A) NBS 706 and (B) the mixture of NBS 706 (98.5 %) and PS 200000 (1.5 % ) .



9. MORI Fuzes Statistical Methods


139


140 SIZE EXCLUSION CHROMATOGRAPHY


Fuzes Statistical


MORI

20

22

14

Methods

24 26 28 30 elution volume ( ( )

32

34

m

F i g u r e 7. Normalized SEC chromatograms of NBS 706 ( and the mixture of NBS 706 (95 %) and ESBRITE (5 %) (

ι

20

i

ι

22

1

i

24 elution

i

ι

ι

26 volume

ι

ι

ι

28 30 ( ml )

ι

ι

) ).

ι,

ι

32

34

F i g u r e 8. Normalized SEC chromatograms o f NBS 706 ( and the mixture o f NBS 706 (90 %) and ESBRITE (10 %) (


) ).


142

SIZE E X C L U S I O N C H R O M A T O G R A P H Y

d i s t i n g u i s h e d p o i n t a t j « 10 % was l o c a t e d i n the area A > B, i t means that the MWD o f the mixture was s h i f t e d t o the higher molecular weights a t the high molecular weight p a r t . However, t h i s t e s t method could not detect the abnormality o f the shape o f the chromatogram at around center. Figure 5 i s the case o f a mixture NBS 706 (98.5 %) and PS 411000 (1.5 % ) . The value o f M o f the mixture is about 8 % higher than that o f NBS 706, bu? both values o f M are n e a r l y the same. B o t h normalized chromatograms have s i m i l a r shapes as i n the case o f Figure 1. However, the s e q u e n t i a l U t e s t (Figure 6) revealed a f t e r the t h i r d p a i r o f p a r a l l e l measurements that the MWD o f the mixture i s d i f f e r e n t from that o f NBS 706. F i g u r e s 7 and 8 show the normalized chromatograms o f NBS 706 and o f the mixture o f NBS 706 and ESBRITE. Molecular weight averages of each p a i r o f runs can be regarded as i d e n t i c a l w i t h i n the experimental e r r o r s . The chromatograms i n Figure 7 were judged to be i d e n t i c a l by the s e q u e n t i a l U t e s t o f four p a i r s o f p a r a l l e l measurements. Only two p a i r s o f runs were necessary f o r the d e c i s i o n o f disagreement i n the case o f Figure 8. In c o n c l u s i o n , the s e q u e n t i a l U t e s t i s u s e f u l f o r the judge ment o f i d e n t i t y between MWDs o f a p a i r o f polymer samples whose molecular weight averages are i d e n t i c a l w i t h i n the experimental e r r o r s . I d e n t i t y o f MWDs o f the two polymer samples was estab l i s h e d w i t h more than four p a i r s o f p a r a l l e l measurements, and the disagreement o f MWDs w i t h two t o four p a i r s of p a r a l l e l measure ments. Though t h i s s t a t i s t i c a l treatment i s u s e f u l f o r the i d e n t i f i c a t i o n o r d i f f e r e n t i a t i o n o f the MWDs o f the p a i r o f polymers, i t can not detect s m a l l d i f f e r e n c e s i n shapes o f the both chromatograms.

Literature Cited 1. Füzes, L. J. Appl. Polym. Sci. 1979, 24, 405-416. RECEIVED

September 27, 1983


Size Exclusion Chromatography - American Chemical Society

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