Size Exclusion Chromatography - American Chemical Society

12 High-Performance High-Speed Gel Permeation Chromatography

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A Systems Approach

RONALDL.MILLER and JACK D. KERBER The Perkin-Elmer Corporation, Main Avenue, Norwalk, CT 06856 The tremendous advances in size-exclusion column technology in the last decade have resulted in an order of magnitude reduction in analysis times in gel-permeation chromatography (GPC) since the technique was first introduced in the 1960's. The availability of highly efficient (up to 50,000 plates/meter) columns containing a broad pore-size distribution has enabled many separations to be performed using a single column, with no loss of resolution. The more recent development of 5-µm polystyrene-divinylbenzene gel packings has resulted in capabilities for oligomer separations which were unheard of just a few years ago. As GPC separations are performed in less time, with fewer columns, the performance of other components of the chromatographic system becomes critical. A well-designed system for high-resolution, high speed GPC should embody precise control of flow rate and column temperature, minimal peak-broadening effects from both extra-column sources and the columns themselves, and sophisticated data acquisition and processing. The separation of oligomers is an application which clearly demonstrates the advantages of a systems approach to high-resolution, high-speed GPC. Since the i n t r o d u c t i o n o f gel-permeation chromatography (GPC) i n the I960 s, there have been tremendous advances i n polymer g e l s i z e - e x c l u s i o n column technology. P o l y s t y r e n e - d i v i n y l benzene copolymer g e l s , and the techniques by which they are packed i n t o columns, have improved t o the p o i n t where commercial columns e x h i b i t up t o 50,000 plates/meter. These 10-ym g e l s are s u f f i c i e n t l y rugged t o permit flow r a t e s o f up t o 3.0 ml/minute 1

0097 6156/ 84/0245-0189506.00/0 © 1984 American Chemical Society

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

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w i t h low v i s c o s i t y GPC s o l v e n t s such as tetrahydrofuran (THF), w i t h l i t t l e o r no impact on e f f i c i e n c y or column l i f e t i m e . The more recent development of 5-ym g e l s has r e s u l t e d i n columns w i t h e f f i c i e n c i e s of up t o 80,000 p l a t e s / m e t e r , usable at flow r a t e s of up t o 2.0 ml/minute w i t h low v i s c o s i t y s o l v e n t s . The l a s t decade has seen an order-of-magnitude i n c r e a s e i n e f f i c i e n c y of GPC columns, which means a t h r e e - f o l d r e s o l u t i o n i n c r e a s e f o r the same number and l e n g t h of columns, or a l t e r n a t i v e l y , the a b i l i t y t o generate e q u i v a l e n t r e s o l u t i o n i n a f r a c t i o n of the t o t a l column l e n g t h . Separations of low-molecular-weight m a t e r i a l s may be performed i n minutes u s i n g the 5-pm g e l s , r a t h e r than hours, w i t h a s e p a r a t i o n power unheard of j u s t a few years ago. Of course, r e s o l u t i o n i s not the only c r i t e r i o n f o r determining the optimum column s e t f o r a given s e p a r a t i o n : the column s e t must cover the molecular-weight range of the sample as w e l l . A second development which minimized the number of GPC columns needed f o r many s e p a r a t i o n s was the development of columns packed w i t h a mixture of d i f f e r e n t p o r e - s i z e d g e l s . Operating ranges of these columns span f o u r t o f i v e orders of magnitude i n molecular-weight u n i t s . The r e s u l t i s t h a t most GPC s e p a r a t i o n s can be adequately performed w i t h e i t h e r a s i n g l e "mixed-bed" column, o r a column s e t c o n s i s t i n g of a mixed-bed column p l u s a second column geared t o the molecular-weight range of the sample of i n t e r e s t . The net r e s u l t i s t h a t GPC separations which r e q u i r e d s e v e r a l hours t o perform i n the I 9 6 0 s can now be performed i n 15 t o 20 minutes i n most cases, and i n 6 t o 10 minutes i n some cases, w i t h b e t t e r r e s o l u t i o n than c o u l d be p r e v i o u s l y achieved. H i g h - r e s o l u t i o n , high-speed GPC has thus acquired a whole new meaning. The b e n e f i t s of t h i s advanced column technology cannot be f u l l y r e a l i z e d without corresponding e v o l u t i o n of other c a p a b i l i t i e s o f the chromatographic system, however. Because the time s c a l e of the s e p a r a t i o n i s d r a s t i c a l l y shortened, f a c t o r s such as constancy and r e p r o d u c i b i l i t y of temperature and mobile phase f l o w r a t e become much more important. As the c o n t r i b u t i o n to peak broadening i s lessened, extra-column c o n t r i b u t i o n s become more s i g n i f i c a n t . More data must be taken, and taken f a s t e r ; manual c a l c u l a t i o n of molecular-weight averages has a l r e a d y become o b s o l e t e . The i n c r e a s i n g a v a i l a b i l i t y of and dependence on the l a b o r a t o r y microcomputer f o r GPC c a l c u l a t i o n s has spurred development of powerful software t o o l s u s i n g computer graphics t o p r o v i d e a v i s u a l dimension t o GPC data r e d u c t i o n . A systems approach t o h i g h - r e s o l u t i o n , high-speed GPC takes a l l of these f a c t o r s i n t o c o n s i d e r a t i o n . S e v e r a l aspects are worthy of d e t a i l e d d i s c u s s i o n . 1


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Modern GPC Columns The heart of a GPC s e p a r a t i o n system i s , of course, the columns. As has been p r e v i o u s l y s t a t e d , column e f f i c i e n c i e s have g r e a t l y improved over the l a s t decade. The high e f f i c i e n c y of today's GPC column provides a b e t t e r s e p a r a t i o n i n l e s s time. Nowhere i s t h i s more apparent than i n a p p l i c a t i o n s which r e q u i r e the s e p a r a t i o n of oligomers. Low-molecular-weight condensation polymers o f t e n f a l l i n t o t h i s c l a s s . The a n a l y s t can, v i a j u d i c i o u s column s e l e c t i o n , g a i n very high r e s o l u t i o n i n a reasonably s h o r t time frame. The s e p a r a t i o n of F i g u r e 1 was obtained u s i n g only two 30-cm columns packed w i t h 10-μπι g e l s , e l u t e d w i t h t e t r a h y d r o f u r a n (THF) a t 1.0 ml/minute. This degree of s e p a r a t i o n , u s i n g only 60 cm of column l e n g t h , was not p o s s i b l e a few years ago, when column e f f i c i e n c i e s of 5,000 t o 7,000 p l a t e s represented the s t a t e of the a r t ; more columns or r e c y c l e would have been r e q u i r e d . F i g u r e 2 i l l u s t r a t e s a s e p a r a t i o n c a r r i e d out u s i n g a s i n g l e 5-ym g e l column, e l u t e d w i t h THF a t a flow r a t e of 1.5 ml/minute. E x c e l l e n t r e s o l u t i o n i s obtained w i t h a s i n g l e column; the l a s t two compounds to e l u t e d i f f e r by only 28 molecular-weight u n i t s . The r e s o l u t i o n shown i n Figure 2 r e q u i r e s a column e f f i c i e n c y of over 20,000 p l a t e s , generated between 4.5 and 6 minutes, or about 80 plates/second. E f f i c i e n c i e s of 24,000 p l a t e s a t permeation and 23,000 p l a t e s at t o t a l e x c l u s i o n were measured at flow r a t e s of 1.0 ml/minute f o r t h i s column. Separation speed i s q u i t e good a l s o , but does not represent the l i m i t which can be a t t a i n e d .

Bandwidth. Column e f f i c i e n c y may a l s o be expressed i n terms of a bandwidth. The bandwidth i s d e f i n e d as the volume of mobile phase c o n t a i n i n g 95% of an e l u t e d compound, o r , e q u i v a l e n t l y , f o u r standard d e v i a t i o n s of a s t a t i s t i c a l d i s t r i b u t i o n of the same shape as the chromatographic peak: Bandwidth = 4 σ

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Equation 1 shows t h a t bandwidth i s merely a means of expressing column e f f i c i e n c y , N, as a f u n c t i o n of e l u t i o n volume, V . Assuming an e x c l u s i o n volume of 5 ml per column a l l o w s c o n s t r u c t i o n of Table I from Equation 1. Table I l i s t s the bandwidth i n m i c r o l i t e r s as a f u n c t i o n of column p l a t e number and the number of columns i n s e r i e s . The data assume t h a t the p l a t e number may be generated at t o t a l e x c l u s i o n , as w e l l as a t t o t a l permeation; a c t u a l measurements made u s i n g the s m a l l e r pore s i z e column s u b s t a n t i a t e t h i s . R



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F i g u r e 1. Separation o f epoxy c r e s o l Novolac oligomers. Columns: Perkin-Elmer/PL g e l 10-μm 100 A and 10-μιη 1000 A.

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F i g u r e 2. GPC s e p a r a t i o n o f p h t h a l a t e e s t e r s . Perkin-Elmer/PL g e l 5-μπι 100 A.

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Table I . Bandwidths (μΐ) of GPC columns at t o t a l e x c l u s i o n P l a t e s per Column 12,000 16,000 20,000 24,000

1 183 158 141 129

Number of Columns 2 3 258 316 224 274 200 245 183 224

4 365 316 283 258

Polymer g e l GPC columns packed w i t h 10-ym g e l s can e x h i b i t e f f i c i e n c i e s of 12,000 t o 16,000 p l a t e s depending on the pore s i z e . S i n g l e columns of t h i s type produce bandwidths from 160 t o 180 μΓ. As columns are coupled i n s e r i e s , bandwidth i n c r e a s e s as the square r o o t of the number of columns, as may be seen from Equation 1. P l a t e number doubles, but so does the e x c l u s i o n volume. The 5-ym g e l columns t y p i c a l l y achieve 20,000 t o 24,000 p l a t e s , and are represented by the bottom two rows of the t a b l e . The i m p l i c a t i o n s of the bandwidth values i n Table I w i l l be discussed below. Separation Speed. Figure 3 shows chromatograms of p o l y s t y r e n e standards e l u t e d w i t h THF from a GPC column packed w i t h a mixture of d i f f e r e n t p o r o s i t y p a r t i c l e s , the s o - c a l l e d "mixed-bed" column. A s i n g l e column of t h i s type covers a s u f f i c i e n t l y broad molecular-weight range so t h a t i t alone may be used f o r many analyses. Furthermore, s i n c e the r e s i s t a n c e t o flow f o r a s i n g l e column i s low, higher mobile-phase flow r a t e s may be used without generating an excessive pressure drop across the column. F i g u r e 3 shows the s e p a r a t i o n of standards at flow r a t e s of 1.0 and 3.0 ml/minute. The column generated 13,000 p l a t e s at the higher flow r a t e , compared w i t h 12,900 at 1.0 ml/minute. Number-average and weight-average molecular weights of a p o l y d i s p e r s e p o l y s t y r e n e sample run at flow r a t e s of 1.0, 2.0, and 3.0 ml/minute were observed t o vary by l e s s than 2% when computed a g a i n s t c a l i b r a t i o n s obtained a t the same flow r a t e . The v a r i a t i o n of the molecular-weight averages w i t h flow r a t e appears t o be w e l l w i t h i n reason, p a r t i c u l a r l y when no attempt was made t o thermostat the column during these experiments; the d i f f e r e n c e s between the molecular weights could e a s i l y be a consequence of small changes i n column temperature between c a l i b r a t i o n and running the samples. At h i g h flow r a t e s , the d i f f u s i o n r a t e s of macromolecules l i m i t the r e s o l u t i o n o b t a i n a b l e . This i s apparent from Figure 3; the r e s o l u t i o n between e a r l y e l u t i n g peaks s u f f e r s as the flow r a t e i s i n c r e a s e d . The r e s o l u t i o n near the permeation l i m i t i s not g r e a t l y a f f e c t e d , however, and the e f f e c t on c a l c u l a t e d molecular-weight averages was observed t o be small even f o r l a r g e molecules. What i s s i g n i f i c a n t i s t h a t s e p a r a t i o n speed i s l i m i t e d by the nature of the sample, and not by the column.


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F i g u r e 3. GPC s e p a r a t i o n o f p o l y s t y r e n e standards a t d i f f e r e n t f l o w r a t e s . Column: Perkin-Elmer/PL g e l 10-μπι mixed.


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Instrumental Band Broadening The data i n Table I i l l u s t r a t e s t h a t very h i g h - e f f i c i e n c y GPC columns separate compounds w i t h a minimum o f d i l u t i o n . T h i s i s j u s t another way o f e x p r e s s i n g column e f f i c i e n c y ; the g r e a t e r the p l a t e number, the lower the d i l u t i o n a t a g i v e n r e t e n t i o n volume. When the peak d i l u t i o n from the column i s s m a l l , i . e . when a small number o f h i g h l y e f f i c i e n t columns are used, the degree t o which other system components c o n t r i b u t e t o peak d i l u t i o n and broadening becomes much more s i g n i f i c a n t . DiCesare e t . a l . (_1) have d i s c u s s e d extra-column c o n t r i b u t i o n s t o bandwidth f o r very h i g h speed reversed-phase l i q u i d chromatography; most o f the same c o n s i d e r a t i o n s apply t o GPC as w e l l . In chromatographic systems, the v a r i o u s c o n t r i b u t i o n s t o peak broadening are g e n e r a l l y independent. T h i s means t h a t the v a r i a n c e o f the system i s the sum o f the v a r i a n c e s from each c o n t r i b u t i o n . Combining t h i s r e l a t i o n s h i p w i t h Equation 1 y i e l d s an e x p r e s s i o n f o r the system bandwidth: Bandwidth

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The peak broadening f o r the e n t i r e chromatographic system, .columns p l u s the instrument, may thus be estimated from the bandwidth c o n t r i b u t i o n o f each component o f the system. The e f f e c t i v e p l a t e number o f the system may then be c a l c u l a t e d from Equation 1. E f f e c t o f I n j e c t i o n Volume. Table I I shows the e f f e c t o f i n j e c t i o n volume on peak broadening and measured column e f f i c i e n c y . The bandwidths l i s t e d i n Table I I are due t o i n j e c t i o n volume alone, and were measured u s i n g an i n j e c t o r connected d i r e c t l y i n t o the f l o w c e l l o f a low-bandwidth d e t e c t o r . The p l a t e r e d u c t i o n s were then c a l c u l a t e d f o r a 24,000 p l a t e column, such as t h a t represented by the bottom l i n e o f Table I , assuming 5 and 10 ml, r e s p e c t i v e l y , f o r e x c l u s i o n and t o t a l permeation volumes. E f f i c i e n c i e s o f 23,000 p l a t e s a t e x c l u s i o n and 25,000 p l a t e s a t permeation were a c t u a l l y measured f o r the column i n d i c a t e d i n Table I I . The e f f e c t o f l a r g e i n j e c t i o n volumes i s thus t o lose 25 t o 50% o f the p o t e n t i a l column efficiency. The i n j e c t i o n volume chosen f o r a n a l y s i s must represent a compromise between the amount o f sample needed t o p r o p e r l y d e t e c t the e l u t i n g m a t e r i a l , and the amount o f extra-column d i s p e r s i o n the a n a l y s t i s w i l l i n g t o t o l e r a t e . I t i s a l s o important t h a t the same i n j e c t i o n volume be used f o r both samples and standards, and t h a t sample i n j e c t i o n be p r o p e r l y synchronized w i t h the s t a r t of data a c q u i s i t i o n .



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Table I I . E f f e c t o f i n j e c t i o n volume on bandwidth and r e a l i z e d e f f i c i e n c y o f a Perkin-Elmer/PL G e l 5- m 100 Angstrom column e l u t e d w i t h THF at 1.0 ml/min Injection Volume, y l 3.0 6.0 10.0 23.5 50.0 100.0

Injector Bandwidth, μΐ 30 31 36 47 86 160

P l a t e Reduction at E x c l u s i o n 1,132 1,204 1,595 2,592 6,863 13,696

P l a t e Reduction a t Permeation 320 341 458 770 2,397 6,659

E f f e c t o f Tubing Diameter. The c o n t r i b u t i o n o f the connecting tubing i n the system t o the bandwidth can a l s o be estimated. A t y p i c a l chromatograph might employ about 80 cm o f connecting t u b i n g between the i n j e c t o r and the d e t e c t o r . The bandwidth o f 80 cm o f .007-inch i . d . tubing has been determined t o be about 31 μΐ,(1) équivalent t o t h a t due t o a 6-μ1 i n j e c t i o n . I t may be shown t h a t the bandwidth o f the connecting t u b i n g i s p o r p o r t i o n a l t o the square r o o t o f the l e n g t h and a t l e a s t the square o f the i n s i d e diameter.(2) The bandwidth due t o 80 cm o f .015-inch i . d . tubing i s more than 140 μΐ, a c o n t r i b u t i o n n e a r l y as l a r g e as t h a t f o r a 100-μ1 i n j e c t i o n . E f f e c t o f Detector F l o w c e l l . The same c o n s i d e r a t i o n s may be a p p l i e d t o the d e t e c t o r f l o w c e l l . For example, DiCesare e t . al.(1) determined t h a t an 8-μ1 f l o w c e l l i n a " c o n v e n t i o n a l " UV d e t e c t o r might have a bandwidth o f 70 μΐ o r more. The UV d e t e c t o r employed i n F i g u r e s 2 and 3 (LC-85B, Perkin-Elmer) has a 1.4-μ1 f l o w c e l l w i t h a bandwidth below 5 μΐ. I n a GPC system employing a s i n g l e 24,000 p l a t e column, a d e t e c t o r w i t h a 70-μ1 bandwidth would degrade e f f i c i e n c y by about 24% a t e x c l u s i o n , w h i l e the e f f e c t o f the 1.4-μ1 f l o w c e l l o f the d e t e c t o r used i n t h i s work i s n e g l i g i b l e . R e f r a c t i v e index d e t e c t o r s t y p i c a l l y have higher bandwidths, ranging from 25 t o 100 μΐ o r more f o r commerical instruments. F i g u r e 4 i l l u s t r a t e s the advantages o f o p t i m i z i n g the GPC system w i t h respect t o i n s t r u m e n t a l band broadening. The lower chromatograms were obtained from a " c o n v e n t i o n a l " chromatographic system employing a 10-μ1 loop i n j e c t o r , about 80 cm o f .015-inch i . d . connecting t u b i n g , and a UV d e t e c t o r w i t h an 8-μ1 f l o w c e l l (LC-75, Perkin-Elmer). The sample i s a l i q u i d p o l y s t y r e n e r e s i n separated u s i n g f i r s t a 10-μπι g e l column (Perkin-Elmer/PL G e l 10-μ m 100 A) and then a 5-μπι g e l column (Perkin-Elmer/PL G e l 5-μπι 100 A) o f the same p o r o s i t y . The same sample was separated on an optimized system, which employed a 6-μ1 loop i n j e c t o r , 80 cm o f .007-inch i . d . t u b i n g , and a UV d e t e c t o r w i t h a 1.4-μ1 f l o w c e l l (LC-85B, P e r k i n - E l m e r ) , producing the two upper


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Figure k. Separation o f l i q u i d p o l y s t y r e n e r e s i n on d i f f e r e n t chromâtographic systems. System c o n f i g u r a t i o n and column type are d e f i n e d i n the t e x t .



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chromatograms i n F i g u r e 3. The columns used were those used f o r the lower chromatograms. A l l four separations were performed w i t h a THF mobile phase a t 1.0 ml/minute. The t o t a l extra-column bandwidths, c a l c u l a t e d from Equation 2, were 195 μΐ and 44 μΐ, r e s p e c t i v e l y , f o r the c o n v e n t i o n a l and optimized systems. Column e f f i c i e n c i e s were 16,000 p l a t e s f o r the 10-μπι g e l column and 24,000 p l a t e s f o r the 5-μπι g e l column; the column c o n t r i b u t i o n s t o bandwidth are g i v e n i n Table I . The d i f f e r e n c e i n r e s o l u t i o n o b t a i n a b l e between the two chromatographic systems i s r e a d i l y apparent from F i g u r e 4. The optimized system produces much narrower peaks, and more of them as a d d i t i o n a l oligomer are r e s o l v e d . In terms of r e q u i r e d bandwidth, the extra-column bandwidth o f the o p t i m i z e d system i s about a t h i r d of t h a t inherent i n the 5-μπι g e l column a t t o t a l e x c l u s i o n , w h i l e the c o n v e n t i o n a l system has a bandwidth g r e a t e r than t h a t of e i t h e r column. The h i g h i n s t r u m e n t a l bandwidth of the conventional system i s l a r g e l y due t o the c o n t r i b u t i o n from the connecting t u b i n g ; the bandwidth of t h i s system could have been reduced t o about 94 μΐ by s u b s t i t u t u n g .007 i . d . t u b i n g . A system bandwidth o f 94 μΐ i s s t i l l unacceptable f o r work employing a s i n g l e 5-μπι g e l column, but may be t o l e r a b l e f o r separations employing m u l t i p l e 10-μπι g e l columns. Table I I I summarizes the r e s u l t s represented by F i g u r e 4. The bandwidth v a l u e s i n the t a b l e are those c a l c u l a t e d f o r the t o t a l system: the instrument p l u s the column. The values f o r number of p l a t e s are f o r the number of p l a t e s r e a l i z e d i n the t o t a l system. I t can be seen t h a t the o p t i m i z e d system does not g r e a t l y impact column e f f i c i e n c y , the t o t a l l o s s i n p l a t e s being only about ten percent a t t o t a l e x c l u s i o n f o r a 24,000 p l a t e column. T h i s i s c o n s i s t e n t w i t h an i n s t r u m e n t a l bandwidth equal to a t h i r d of the bandwidth of the column. The c o n v e n t i o n a l system, w i t h a bandwidth equal t o o r g r e a t e r than t h a t of the column, e x h i b i t e d a severe l o s s i n r e a l i z e d e f f i c i e n c y , p a r t i c u l a r l y a t or near e x c l u s i o n . Table I I I .

E f f e c t of i n s t r u m e n t a l bandwidth on column e f f i c i e n c y

Conventional System Inherent Total Column System Effective Efficiency Bandwidth, μΐ Plates 16,000 p l a t e s at permeation 372 11,600 at permeation 256 6,300 20,000 p l a t e s a t permeation 344 13,500 a t permeation 255 6,900 24,000 p l a t e s a t permeation 324 15,200 at permeation 234 7,300

Optimized System Total System Effective Bandwidth, μΐ Plates 319 164

15,700 14,800

286 148

19,500 18,200

261 136

23,300 21,500


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The data of Table I I I represent c a l c u l a t e d bandwidths and e f f i c i e n c i e s . A c t u a l r e a l i z e d e f f i c i e n c i e s were measured f o r the four chromatograms of F i g u r e 4. For the 10-μπι g e l column, the conventional system produced an e f f e c t i v e e f f i c i e n c y of 11,000 p l a t e s , compared with an e f f e c t i v e e f f i c i e n c y of 16,000 p l a t e s f o r the optimized systems. These values are i n e x c e l l e n t agreement with the c a l c u l a t e d values shown on the top l i n e of Table I I I . S i m i l a r measurements on chromatograms obtained from the 5-μπι g e l columns y i e l d e d values of 16,000 and 20,000 p l a t e s , r e s p e c t i v e l y , f o r the conventional and optimized systems. T h i s a l s o represents good agreement with c a l c u l a t e d e f f e c t i v e e f f i c i e n c i e s a t t o t a l e x c l u s i o n f o r a 24,000 p l a t e column. The 5-μπι g e l GPC columns are seen t o produce tremendous e f f i c i e n c i e s , but these e f f i c i e n c i e s are only r e a l i z e d when the chromatographic system i s optimized with r e s p e c t t o bandwidth. T h i s a l s o holds true to a l e s s e r degree f o r a well-packed 10-μπι g e l column. E f f e c t of Detector Response Time. The speed of response of the d e t e c t o r e l e c t r o n i c s can a l s o a f f e c t r e s o l u t i o n . Response times can a l s o be expressed as bandwidths by m u l t i p l y i n g by the flow r a t e i n the appropriate u n i t s . In the previous d i s c u s s i o n , t h i s e f f e c t was ignored, as the time constant bandwidths were negligible: l e s s than 12.5 μΐ f o r e i t h e r d e t e c t o r . F i g u r e 5 shows an example of what can happen when the time constant bandwidth i s too l a r g e . The chromatographic system used f o r the separations shown i n F i g u r e 5 i s an optimized system i n c o r p o r a t i n g a r e f r a c t i v e index detector? bandwidth c o n t r i b u t i o n s from the f l o w c e l l , tubing, and i n j e c t o r combine to produce a volume bandwidth of 52 μΐ f o r t h i s system. The time constants of 5 and 0.5 seconds equate to bandwidths of 167 and 16.7 μΐ, r e s p e c t f u l l y , f o r t o t a l system bandwidths of 174 and 55 μΐ. The e f f e c t on r e s o l u t i o n i s r e a d i l y apparent? the f a s t e r response time produces a t o t a l bandwidth acceptable f o r a l l a p p l i c a t i o n s except where maximum r e s o l u t i o n f o r a s i n g l e 5-μπι g e l column i s r e q u i r e d near t o t a l e x c l u s i o n . The 5 second response time, on the other hand, i s o f l i t t l e use except when s e v e r a l of the 10-μπι g e l columns are used. I t i s i n t e r e s t i n g to p o i n t out, however, t h a t a system bandwidth of 174 μΐ was thought to be q u i t e s u i t a b l e a few years ago, when column e f f i c i e n c i e s were s i g n i f i c a n t l y lower, and more columns were used.

Data A c q u i s i t i o n and Processing The data a c q u i s i t i o n r a t e can a l s o c o n t r i b u t e t o the i n t e g r i t y of GPC data. Chromatograms t r a c e d on a recorder are i n response to an analog s i g n a l , and are continuous t r a c e s . C a l c u l a t i o n of molecular weights, however, r e q u i r e s d i g i t i z e d data. The frequency of measurement used when d i g i t i z i n g an analog s i g n a l i s



T i m e Constant 5 sec.

1

2

3

Minutes

T i m e Constant 0.5 sec.

1

2

3

Minutes

Figure 5 . The e f f e c t o f detector time constant on the GPC s e p a r a t i o n o f a l i q u i d epoxy r e s i n . Column : Perkin-Elmer/ PL g e l 5-Mm 1 0 0 Angstrom. E l u e n t : THF at 2 . 0 ml/min. I n j e c t i o n volume: 6 μ ΐ . Detector: L C - 2 5 RI d e t e c t o r (Perkin-Elmer).


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known as the i n f o r m a t i o n bandwidth, and can a l s o be converted t o volume u n i t s . Table IV shows the q u a n t i t a t i v e e f f e c t of the s i z e of the i n f o r m a t i o n bandwidth. The sample and c o n d i t i o n s are those o f F i g u r e 5, except t h a t flow r a t e was 1.5 ml/minute, and the 0.5 second d e t e c t o r response time was used throughout. Separations of the l i q u i d epoxy r e s i n were performed a t v a r i o u s data a c q u i s i t i o n r a t e s , and molecular-weight averages c a l c u l a t e d a g a i n s t c a l i b r a t i o n data obtained a t a data r a t e of 0.1 seconds/point.

Table IV.

E f f e c t of sampling r a t e on

GPC r e s u l t s

Data Rate, Molecular-Weight Averages* Time of Largest Seconds/point No. Ave. Wt. Ave. Ζ Ave Data P o i n t , Min. 435 0.1 377 400 4.93 0.2 433 398 4.94 375 430 0.5 395 372 4.95 420 1.0 387 4.97 366 408 2.0 379 5.00 360 375 5.0 5.17 328 343 * R e l a t i v e t o c a l i b r a t i o n data taken a t 0.1 seconds/point.

The data r a t e s i n Table IV correspond t o i n f o r m a t i o n bandwidths v a r y i n g from 2.5 μΐ t o 125 μΐ. The r e t e n t i o n times of the l a r g e s t peak, when taken as the time of the laVgest data p o i n t i n the d i g i t i z e d d a t a , show a d e f i n i t e t r e n d , i n c r e a s i n g as the time between measurements i n c r e a s e s . T h i s i s e n t i r e l y a consequence of the i n f o r m a t i o n bandwidth? the analog chromatograms were i d e n t i c a l . Table IV a l s o shows the e f f e c t on the c a l c u l a t e d molecular-weight averages, when c a l c u l a t i o n s were performed r e l a t i v e t o c a l i b r a t i o n data taken from a d i g i t i z e d chromatogram f o r which a very f a s t data r a t e was used. The decreasing molecular-weight averages a l s o v a r i e s as the slope of the c a l i b r a t i o n curve, and would be much g r e a t e r f o r a broader range column. Thus, data r a t e s of 0.5 seconds/point are r e q u i r e d t o suppress band-broadening c o n t r i b u t i o n s from data a c q u i s i t i o n . T h i s does not d e f i n e the l i m i t i n g requirement of the data system, however. Between 50 and 100 data p o i n t s are d e s i r e d t o a c c u r a t e l y d e f i n e a molecular-weight average f o r a s i n g l e peak, p a r t i c u l a r l y an average r e p r e s e n t i n g a higher s t a t i s t i c a l moment such as the Z-average. The chromatograms of F i g u r e 3 c o n t a i n seven peaks? 400 t o 800 data p o i n t s are optimum f o r t h i s chromatogram, when s u f f i c i e n t data p o i n t s are i n c l u d e d t o adequately d e f i n e b a s e l i n e . The chromatogram of F i g u r e 3 obtained a t a flow r a t e of 3 ml/minute thus r e q u i r e s data r a t e s of 100 t o 200 p o i n t s per minute (300 p o i n t s per minute were a c t u a l l y used).



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Needless t o say, p r o c e s s i n g t h i s data i n a time frame compatible w i t h the time needed f o r chromatography cannot be done without the a i d of a computer; t h i s i s t r u e f o r even the 20-minute separations of F i g u r e 1. Since the polymer chemist working w i t h GPC i s becoming more dependent on the computer programmer, i t i s p e r t i n e n t t o i n c l u d e software as an i n t e g r a l p a r t of the GPC data system. The sheer volume of data generated by high r e s o l u t i o n , h i g h speed GPC mandates some type o f media storage f o r raw data, together w i t h the a b i l i t y t o r e c a l l , r e p l o t , and rework any of t h i s raw data. Automation of both data a c q u i s i t i o n and data p r o c e s s i n g i s r e q u i r e d t o keep pace w i t h the speed a t which samples can be run. T h i s alone may be s u f f i c i e n t f o r the q u a l i t y c o n t r o l l a b o r a t o r y , but the research l a b o r a t o r y a l s o r e q u i r e s the a b i l i t y t o d e a l w i t h a p a r t i c u l a r chromatogram i n g r e a t e r d e t a i l i n a more l e i s u r e l y manner. The advantages o f i n t e r a c t i v e computer g r a p h i c s i n GPC come i n t o p l a y here. I f the molecular weight averages of two samples d i f f e r , the r e p l o t t i n g of chromatograms o r d i s t r i b u t i o n s on the CRT of a computer t e r m i n a l p e r m i t s a f a s t , easy comparison of j u s t how the samples d i f f e r . Given a p p r o p r i a t e software, screen graphics can be used t o not only r e d i s p l a y , but a l s o t o r e s c a l e , expand, and even s u b t r a c t chromatograms and d i s t r i b u t i o n s , t o p l o t and manipulate GPC c a l i b r a t i o n s , and t o d e f i n e b a s e l i n e and summation l i m i t s t o be used i n numerical computations. These c a p a b i l i t i e s provide a v i s u a l dimension not a v a i l a b l e from mere numbers, and enable the chemist t o s o l v e problems f a s t e r and easier. The most important c o n s i d e r a t i o n o f software, however, i s t h a t i s must p r o v i d e the c o r r e c t answers. T h i s r e q u i r e s t h a t the a p p r o p r i a t e molecular weight be a s s o c i a t e d w i t h each data p o i n t , which r e l a t e s t o the techniques and algorithms used i n c o n s t r u c t i n g the c a l i b r a t i o n curve. C a l i b r a t i o n curves are generated from chromatographic data obtained on standards o f known molecular weight; both monodisperse and p o l y d i s p e r s e standards have been used. A d i s c u s s i o n of the r e l a t i v e m e r i t s o f each technique i s beyond the scope of t h i s paper; s u f f i c e i t t o say t h a t the model used by the software should r e f l e c t the t r u e c a l i b r a t i o n as c l o s e l y as p o s s i b l e .

Temperature C o n t r o l The importance o f temperature c o n t r o l o f the GPC column cannot be o v e r s t a t e d . The use of temperatures above ambient r e s u l t s i n lower mobile-phase v i s c o s i t y , which i n t u r n reduces the back pressure generated by the column. Column l i f e i s prolonged, and i n some cases higher flow r a t e s may be employed. The r e d u c t i o n i n mobile-phase v i s c o s i t y improves both the r a t e and e f f i c i e n c y of mass t r a n s f e r p r o c e s s e s , enhancing column performance. While


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the b e n e f i t s of e l e v a t e d temperature are c e r t a i n l y d e s i r a b l e , the use of constant temperature i s c r i t i c a l . Mark-Houwink c o e f f i c i e n t s , the parameters which d e s c r i b e the r e l a t i o n s h i p between molecular weight and hydrodynamic volume (and t h e r e f o r e e l u t i o n volume) , are s i g n i f i c a n t l y t e m p e r a t u r e dependent. Polymer s o l u b i l i t y improves w i t h i n c r e a s i n g temperature; polymer molecules i n s o l u t i o n u n c o i l t o a g r e a t e r degree, and hence occupy l a r g e r volume and e l u t e e a r l i e r from the GPC column. The e f f e c t of changing temperature on GPC r e s u l t s i s i l l u s t r a t e d i n Table V f o r a p o l y s t y r e n e sample; a column was c a l i b r a t e d u s i n g monodisperse p o l y s t y r e n e standards. The standards and the sample were both run a t 25 and 30 C. The d e t r i m e n t a l e f f e c t of a change i n temperature between c a l i b r a t i o n and sample a n a l y s i s i s obvious; a f i v e - d e g r e e C change i n temperature was seen t o produce e r r o r s of 11-14% i n the weight-average molecular weight. In t h i s case the sample and the standards were i d e n t i c a l c h e m i c a l l y . I f they are not, t h e i r Mark-Houwink c o e f f i c i e n t s may show d i f f e r e n c e s i n temperature dependency, and the e r r o r s become compounded. I f the g o a l of the chemist i s t o a t t a i n r e p r o d u c i b i l i t y t o w i t h i n 1%, the column temperature must be maintained t o w i t h i n 0.5 C o r b e t t e r throughout the course of the experiments.

Table V. E f f e c t of temperature on weight average molecular weight Analysis Temperature 25 C 25 C 30 C 30 C

Calibration Temperature 25 C 30 C 25 C 30 C

Weight-Average Molecular Weight 357,000 313,000 400,000 352,000

An a i r - b a t h oven i s an e x c e l l e n t choice f o r GPC i n t h a t a s u b s t a n t i a l number of columns may be accomodated by a s i n g l e u n i t . Costs are low and temperature s t a b i l i t y and r e p r o d u c i b i l i t y q u i t e good. Some type o f heat-exchange device should be p l a c e d i n the oven t o r a i s e the temperature of the mobile phase t o the d e s i r e d p o i n t before i t reaches the column; t h i s p r a c t i c e h e l p s e l i m i n a t e temperature g r a d i e n t s along the column a x i s . I n j e c t o r s can be mounted d i r e c t l y on (or even i n ) an oven, m i n i m i z i n g the amount of heat exchange between the mobile phase and the i n j e c t o r .

Solvent D e l i v e r y E f f e c t of Flow Rate E r r o r s . The e f f e c t of flow r a t e e r r o r s on molecular-weight averages c a l c u l a t e d from GPC data has been



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d i s c u s s e d by B l y , e t a l . (_3) These workers concluded t h a t flow r a t e r e p e a t a b i l i t y of b e t t e r than 0.3%, flow r a t e d r i f t of l e s s than 1% over the time of the chromatogram, and short-term random v a r i a t i o n (noise) of b e t t e r than 4%, are a l l r e q u i r e d t o reproduce molecular-weight averages t o w i t h i n 6%. Thus, the most important c r i t e r i a f o r a GPC pumping system a r e , r e s p e c t i v e l y , r e s e t t a b i l i t y , d r i f t , and p u l s a t i o n . Absolute accuracy of flow r a t e must a l s o be considered i f comparison of r e s u l t s obtained on d i f f e r e n t instruments i s a l s o important. The exact magnitude of f l o w - r a t e induced e r r o r s i n the molecular-weight averages depends on the slope of the c a l i b r a t i o n curve: the steeper the s l o p e , the more a given flow r a t e v a r i a t i o n a f f e c t s r e p r o d u c i b i l i t y of the averages. GPC separations employing a s i n g l e 25- t o 30-cm mixed bed column probably represent the worst case. Table VI i l l u s t r a t e s the e f f e c t o f a one percent e r r o r i n the flow r a t e r e s e t t a b i l i t y f o r a column o f t h i s type. Using a g i v e n s e t of c a l i b r a t i o n data and a given s e t of raw s l i c e areas f o r a p o l y s t y r e n e sample, reference values of the v a r i o u s molecular-weight averages were computed. The mobile phase was THF a t 1.0 ml/minute flow. A flow r a t e i n c r e a s e o f one percent between the time of c a l i b r a t i o n and sample a n a l y s i s was then simulated by m u l t i p l y i n g each of the r e t e n t i o n times i n the c a l i b r a t i o n data s e t by 1.01, and repeating the molecular-weight c a l c u l a t i o n s . A decrease i n flow r a t e was simulated i n a l i k e manner. The r e s u l t s i n d i c a t e d t h a t even a s m a l l e r r o r i n flow r a t e generates very l a r g e e r r o r s i n molecular weight, p a r t i c u l a r l y f o r a column w i t h a steep c a l i b r a t i o n curve.

Table V I . E f f e c t of flow r a t e e r r o r s on molecular-weight Molecular Weight Number-Average Weight-Average Z-Average

No Change 125,000 384,900 1,621,000

1% Increase 141,700 (+13%) 452,800 (+18%) 2,628,000 (+62%)

averages

1% Decrease 110,100 (-12%) 331,000 (-14%) 1,078,000 (-27%)

While the e f f e c t s of flow r a t e d r i f t or noise a t the one percent l e v e l over the d u r a t i o n of the s e p a r a t i o n are not n e a r l y as d i s a s t r o u s as the case i l l u s t r a t e d i n Table V I , the data serve t o demonstrate the need f o r flow r a t e s t a b i l i t y and r e p e a t a b i l i t y . The absolute accuracy of flow r a t e i s of l e s s e r importance, as t h i s type of v a r i a t i o n only manifests i t s e l f when comparing raw data obtained on d i f f e r e n t instruments, a l l of which should be c a l i b r a t e d independently of each other i n any case. I t should be p o i n t e d out t h a t the GPC c a l i b r a t i o n should always be redetermined whenever any component o f the system i s changed? t h i s i s simply good l a b o r a t o r y p r a c t i c e .


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Pumps f o r GPC. The most important c o n s i d e r a t i o n s when s e l e c t i n g a s o l v e n t d e l i v e r y system are those i n v o l v i n g flow r a t e r e s e t t a b i l i t y , d r i f t , and n o i s e . R e c i p r o c a t i n g - p i s t o n pumps, e i t h e r i n s i n g l e - p i s t o n o r m u l t i p l e - p i s t o n c o n f i g u r a t i o n s , are by f a r the most commonly used s o l v e n t d e l i v e r y devices f o r GPC. I n a dual-head pump, f o r example, each pump head operates e s s e n t i a l l y 180 degrees out o f phase w i t h the o t h e r , so t h a t one pump head i s always d e l i v e r i n g s o l v e n t ; p u l s a t i o n occurs only a t the p o i n t o f "crossover" between one pump head and the other. Advanced designs o f s i n g l e - p i s t o n pumps minimize p u l s a t i o n by r e f i l l i n g the p i s t o n a t a much f a s t e r r a t e than i t d e l i v e r s s o l v e n t . I n e i t h e r case, some a d d i t i o n a l pulse-dampening c a p a b i l i t y i s g e n e r a l l y provided t o f u r t h e r reduce short term flow r a t e f l u c t u a t i o n s , o r flow r a t e "noise". Since the pumps used f o r GPC tend by and l a r g e t o be those designed f o r " c o n v e n t i o n a l " chromatography, t h e i r pulse dampeners may be optimized f o r a p p l i c a t i o n s producing higher back pressures than GPC. I n t h i s case, p l a c i n g a flow r e s t r i c t o r between the pump and i n j e c t o r may improve flow r a t e r e p r o d u c i b i l i t y . I n t h i s work, 3 t o 9 meters o f c o i l e d t u b i n g , 0.007" i . d . , was used as a flow r e s t r i c t o r . T h i s c o i l was placed i n s i d e the oven, and a l s o served t o preheat the mobile phase. A f i n a l aspect o f GPC s o l v e n t d e l i v e r y r e l a t e s t o the s o l v e n t r e s e r v o i r s themselves. The a b i l i t y t o perform i n s i t u helium degassing o f s o l v e n t s , provide i n e r t gas b l a n k e t s over s o l v e n t s , and p r o t e c t s o l v e n t s from contamination from e x t e r n a l sources are worth c o n s i d e r a t i o n from the standpoints o f convenience and s a f e t y alone. I f these f e a t u r e s are provided f o r , i t i s a s m a l l step t o a l s o provide a s m a l l p o s i t i v e p r e s s u r e , say 10 p s i o r so, t o the s o l v e n t r e s e r v o i r . T h i s p o s i t i v e pressure helps minimize the formation o f s o l v e n t vapors i n the pump chamber during the r e f i l l p a r t o f the pump s t r o k e , and improves the flow r a t e r e p r o d u c i b i l i t y o f r a p i d - r e f i l l type pumps d e l i v e r i n g high-vapor-pressure s o l v e n t s . %

System R e p r o d u c i b i l i t y . Table V I I d e s c r i b e s the r e p r o d u c i b i l i t y achievable w i t h an optimized GPC system. Twelve consecutive analyses o f the same p o l y s t y r e n e sample were analyzed t o produce these data. The pump used was a s i n g l e - p i s t o n r a p i d - r e f i l l type r e c i p r o c a t i n g pump (Series 10, Perkin-Elmer) equipped w i t h r e s e r v o i r p r e s s u r i z a t i o n and r e s t r i c t o r c o i l as d i s c u s s e d above. The mobile phase was THF a t 1.0 ml/minute, and the r e s e r v o i r pressure 11 p s i . The column temperature was c o n t r o l l e d a t 40 C by p l a c i n g the column (Perkin-Elmer PL G e l 10-μ MIXED) and the r e s t r i c t o r c o i l i n an a i r bath oven (LC-100, Perkin-Elmer) t o reduce any v a r i a b i l i t y due t o temperature. Samples were i n j e c t e d w i t h an autosampler (Model 420B, Perkin-Elmer) c o n t a i n i n g a fixed-volume loop i n j e c t i o n v a l v e . A v a r i a b l e wavelength UV d e t e c t o r (LC-75) o p e r a t i n g a t 265 nm was used as the d e t e c t o r . Molecular-weight averages were c a l c u l a t e d f o r a l l twelve



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i n j e c t i o n s u s i n g the same b a s e l i n e times, c a l i b r a t i o n curve, and summation l i m i t s . The r e s u l t s , summarized i n Table V I I , i l l u s t r a t e the p r e c i s i o n which can be r o u t i n e l y obtained when a l l sources o f v a r i a t i o n are c o n t r o l l e d . R e l a t i v e standard d e v i a t i o n s lower by about a f a c t o r o f three have been obtained u s i n g t h i s system f o r low-molecular-weight p o l y e t h o x y l a t e d phenol, separated u s i n g a column w i t h a l e s s "steep" c a l i b r a t i o n curve.

Table V I I . Summary o f r e s u l t s from twelve r e p e t a t i v e analyses o f polystyrene.

Parameter Number-Average Mol. Wt. Weight-Average Mol. Wt. Ζ-Average Mol. Wt.

Mean 140,010 381,500 1,211,000

Standard Deviation 970 2,799 13,872

R e l a t i v e Standard Deviation, % 0.69 0.73 1.15

Summary We have demonstrated the b e n e f i t s which can be obtained from h i g h - e f f i c i e n c y GPC column technology when the chromatographic system i s p r o p e r l y o p t i m i z e d . Band broadening from extra-column sources must be minimized t o r e a l i z e the f u l l e f f i c i e n c y o f modern GPC columns. Proper c o n t r o l o f both flow r a t e and column temperature i s v i t a l t o maximizing r e p r o d u c i b i l i t y i n GPC.

Literature Cited 1. DiCesare, J. L.; Dong, M. W.; Atwood, J. G. J. Chromatogr. 1981, 217, 369-85. 2. Martin, M.; Eon, C.; Guiochon, G. J. Chromatogr. 1975, 108, 229-41. 3. Bly, D. D.; Stoklosa, H. J.; Kirkland, J. J.; Yau, W. W. Anal. Chem. 1975, 47, 1810-3. RECEIVED

September 12, 1983


Size Exclusion Chromatography - American Chemical Society

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