Polymer Molecular Weight Methods

11 Gel Permeation Chromatography Calibration

Downloaded by UNIV OF MICHIGAN ANN ARBOR on February 18, 2015 | http://pubs.acs.org Publication Date: June 1, 1973 | doi: 10.1021/ba-1973-0125.ch011

II. Preparative GPC Fractionation and Characterization of Poly(methyl methacrylate) for Calibration in 2, 2, 2-Trifluoroethanol

THEODORE PROVDER Glidden-Durkee Division of SCM Corp., Strongsville, Ohio 44136 JAMES C. WOODBREY and JAMES H. CLARK Monsanto Co., St. Louis, Mo. 63166 ESMOND E. DROTT Monsanto Co., Texas City, Tex. 77590

Because of the insolubility of polystyrene standards in 2,2,2trifluoroethanol (TFE), poly(methyl methacrylate) (PMMA) is suggested as the standard for gel permeation chromatography (GPC) in TFE. PMMA standards used here were whole polymers made by free-radical polymerization and fractions from them. The primary molecular weight calibration curve is compared with the indirect molecular weight calibration curve generated with polystyrene standards in tetrahydrofuran (1). Differences among molecular weight averages and intrinsic viscosities calculated from the direct PMMA molecular weight calibration curve and corresponding experimental values are attributed to experimental errors and to an apparent molecular weight dependence of the specific refractive index increment in TFE. An error in an earlier paper (1) is corrected, and methods for obtaining secondary molecular weight calibration curves from hydrodynamic volume—calibration curves are reviewed. *Tphe solvent 2,2,2-trifluoroethanol ( T F E ) is excellent for gel permeation -*· chromatography ( G P C ) characterization of polyamides and polyacrylates and has many more desirable properties than m-cresol, the solvent commonly used. The advantages of using T F E rather than 117 In Polymer Molecular Weight Methods; Ezrin, M.; Advances in Chemistry; American Chemical Society: Washington, DC, 1973.

118

P O L Y M E R M O L E C U L A R WEIGHT METHODS

m-cresol for polyamide characterization have been cataloged elsewhere ( J ) . The one main disadvantage of using T F E as a G P C solvent is the insolubility of the readily available characterized polystyrene standards. This insolubility prevents the generation of a hydrodynamic volume ( H D V ) calibration curve and the subsequent generation of secondary molecular weight calibration curves i n T F E ( I , 2 ) .


Theory Methods for Generating Molecular Weight Calibration Curves from Hydrodynamic Volume Calibration Curves. Hydrodynamic volume cali

bration curves can be constructed simply by plotting the product of_the intrinsic viscosity [η] and the weight-average molecular weight (M ) for a narrow molecular weight distribution polymer standard against the peak retention volume ( P R V ) of the standard for a given column set i n a specific solvent at a given temperature. Once an H D V curve is obtained, secondary molecular weight calibration curves for polymers of interest could be obtained, provided the Mark-Houwink parameters e and K are known (denoted by subscript x) from the relation where Z is the effecw

x

x

s

Z

M

x

=

[ ]ΑΤ

=

Η

KM**

(1)

1

(2)

= (Z./K y«* +» x

x

tive H D V obtained from the polymer standards and M is the molecular weight for the polymer of interest. If the Mark-Houwink parameters are known or can be established for a polymer standard that is soluble i n T F E as well as for the polymer of interest, the molecular weight calibration curve for the polymer of interest, x

logioM

x

= f (v), x

(3)

can be expressed i n terms of the molecular weight calibration curve for the polymer standard i n T F E , logioM, = f (v) 8

(4)

Two polymer species eluting at the same retention volume have the same hydrodynamic volume. In terms of the polymer standard and the polymer of interest in T F E , this equality of hydrodynamic volume can be expressed as

(hW. =

(MM).

In Polymer Molecular Weight Methods; Ezrin, M.; Advances in Chemistry; American Chemical Society: Washington, DC, 1973.

(5)

11.

119

GPC Calibration

PROVDER ET AL.

Substitution of Equations 1,3, and 4 into Equation 5 leads to an expression first derived by C o l l and Prusinowski (3) hg M


10

x

= (^ρ7 ) χ

lo o(K /K ) gl

s

+

x

(fjjr^)

(> 6

If the Mark-Houwink parameters are unknown and there is insuffi cient data available for their direct generation, molecular weight calibra tion curves can be generated by (a) an empirical technique based upon the determination of the intrinsic viscosity of each polymer fraction ob tained by the G P C syphon counter or ( b ) using at least two out of three experimental observables, number- and weight-average molecular weights M , M , and [η] to fit mathematically for effective values of e and K. Meyerhoff (4) and Goedhart and Opschoor (5) have measured the viscosity of each eluting G P C fraction by coupling an automatic capillary tube viscometer with the G P C syphon. The low polymer concentration in each fraction necessitated an extremely accurate efflux time measure ment to ±0.01 second since the flow time of each fraction containing polymer has flow times, t greater than that of pure solvent, t , by at most 2.00 seconds. The specific viscosity of the i polymer fraction is cal culated from the flow times of the pure solvent and the polymer fraction. n

w

iy

0

t h

s p

flspi

=

1

—

f}ri

=

1

—

(7)

(ti/to)

The concentration Q of the polymer fraction is given by

d = (Ai/A) (w/Av)

(8)

where w is the total amount of injected polymer i n grams, Av is the vol ume of the syphon i n deciliters, A is the total peak area, and Ai is the area corresponding to the i polymer fraction. Since the concentration of each fraction is i n the concentration range approaching infinite dilu tion (Ci $^ 0.02 wt-vol % ), the intrinsic viscosity of each polymer fraction i can be taken as ^ p / C * . A more accurate value of the intrinsic viscosity i can be obtained from the following equation: t h

r ι

_

[r,]i

~\

/Vsp/Ci

-

In

ψ/Ci

ôlc

ο,ΑΡΡ o - T F E

Α

_ _

Z

_L_

_ L _ V

M

THF

V

H

COUNTS A )

P S - H D V C U R V E

r

is

t,r\

V

M

T F E M L

H

C O U N T S F.)

CALIBRATION IN

M

V

L

(THF)

APPARENT

T H F

CURVE

PMMA F©25 C THi -

(TFE)

H D V

CALIBRATION

IN T F E

E

V

MH

V

COUNTS C.)

RETENTION

TFE

* M

VOLUME

CALIBRATION

" M

L

E.)

T R U E

VTHF

V

M

L

(THF)

Β.) P M M A - M W C A L I B R A T I O N C U R V E IN T H F

H D V

CURVE

CURVE

r

COUNTS

V

H

COUNTS

(TFE)

\/

T F E

M

V

L

(TFE)

CALIBRATION IN T F E

PMMA T F E © 50* C

MH COUNTS

TFE

' M

L

(TFE)

D.) P M M A - M W C A L I B R A T I O N C U R V E IN T F E

Figure 2. Illustrative method for generating PMMA molecular weight and HDV calibration curves in TFE using a polysty rene-HDV calibration curve in tetrahydrofuran


124

POLYMER MOLECULAR WEIGHT METHODS

parent H D V calibration curve i n T F E . I n this step the retention volume axis is transformed from UTHF to D T F E . However the H D V axis still corre sponds to ZÇ| and therefore is denoted as Z J | , the apparent H D V i n T F E . This step is illustrated by the pictographs A to C to F i n Figure 2. ( b ) Using the Mark-Houwink parameters of P M M A i n tetrahydrofuran and i n T F E , convert the apparent H D V calibration curve. This step is illustrated by the pictographs F to Ε i n Figure 2. A

F

A n equation can be derived relating Ζ%ψ$

(I>TFE) to ZÇIp (I>THF).

Α


As was pointed out i n step C , the retention volume calibration curve relating t>r F to I>T E was constructed by relating U ^ F E to I>THF at points of H

F

equal weight percent polymer on the integral distribution of retention volume curves i n tetrahydrofuran and i n T F E . A t these points the mo lecular weight of the polymer species i n tetrahydrofuran is the same as the molecular weight of the polymer species i n T F E . M?^

= Μ™*

A

(15)

ΙΑ

Use of Equation 2 leads to the expressions

(

7 P M M A \

/

/ 7 P M M A \

M

PMMA

1

/

\

ι

\

( £ ρ _ Λ {^tij

=

(17)

Noting that ^TFE

^THF

=

A

^THP

=

(18) and combining Equations 16, 17, and 18 with Equation 15 leads to the expression l

o

„ , „ 7 P M M A

_

(

1

\, „

f(g) FE' T

( ! T F E ^ \ log Z?| 10

\2 IIF T

J H F +

'1

, (19)

F

/

Using the Mark-Houwink parameters for P M M A i n tetrahydrofuran and in T F E leads to the following expressions relating Z?^| (I>TFE) to ZÇ| IA

F

( l?THF ) .

logioZÇïï£ = 0.0480 + 1.0428 l o g i Z ? | ; M < 31,000

(20)

logioZ^

(21)

A

A

0

v

F

= 0.02610 + 1.0554 logioZ5S ; M > 31,000 P

v

Route 1 was used i n Réf. 1 to construct a H D V calibration curve shown as the curve designated b y + in Figure 10, Réf. I . Route 2 was used


11.

PROVDER E T A L . Table I.

Comparison of H D V Values in T F E

Retention Volume, counts


32 36 40

125

GPC Calibration

1.06 Χ ΙΟ 1.07 Χ ΙΟ 0.804 Χ ΙΟ

6 5 4

ZTFE(CÎWT.)

ZTFE(true)

2.28 Χ ΙΟ 2.03 Χ ΙΟ 1.25 Χ ΙΟ

1.94 Χ ΙΟ 2.20 Χ ΙΟ 1.25 Χ ΙΟ

6 5 4

6 5 4

as far as step 3, A to C to F , to construct an apparent H D V calibration curve denoted by the solid line in Figure 10, Réf. J . The difference be tween the apparent H D V calibration curve and the true H D V calibration curve i n that figure was believed to be on the order of experimental errors, and the correction shown by Equations 20 and 21 was not made. Reevaluation of the experimental data indicates that the values of the H D V obtained from route 1, Z r (true), are in very good agreement with the corresponding values of the H D V obtained from route 2, ZTFE (corr.), by using Equations 20 and 21 on the apparent H D V , Z T (app). This is shown in Table I. If the correction denoted by Equations 20 and 21 is not made, the apparent H D V calibration curve can still be used to gen erate secondary molecular weight calibration curves by the previously discussed method of Provder and co-workers ( I , 2) if the difference be tween the two H D V curves is small as is shown in Figure 10, Réf. I , and if the two H D V curves are reasonably parallel to each other over the retention volume range of interest. These small differences w i l l be reflected along with instrument spreading effects and experimental errors i n the effective values of e and Κ obtained by the mathematical fitting procedures. F E

F E

Materials

and Methods

Samples. Fourteen P M M A whole polymers were prepared by routine free-radical bulk and solution polymerization methods to cover a wide molecular weight range. Reagent grade methyl methacrylate was poly merized without removing inhibitor, according to the specifications de scribed i n Table II. The 14 polymer samples were recovered from the reaction mixture by standard techniques (10). The recovered samples were combined in amounts specified under "blend" in Table II and were ground to form a physically homogeneous polymer blend for preparative G P C fractionation. The molecular weight characterization data of the whole polymers and blend are shown i n Table III. Solvents. Reagent grade T H F ( n = 0.888, bp = 64-66°C) con taining 0.025 wt-vol % di-ter£-butyl-p-cresol which served as an antioxi dant was used for the preparative G P C fractionation. The solvent T F E (n = 1.2907, d — 1.3823, bp = 76 °C, ionization constant K = 4.3 X 10" ) was obtained from Halocarbon Products Corp., Hackensack, N . J., and was used for both analytical G P C and viscometry. The recovery and D

D

2 0

25

2 5

a

13


126

P O L Y M E R M O L E C U L A R WEIGHT METHODS


Table II.

Synthesis Conditions for Experimental P M M A Samples

Sample

BPO", mole/liter X W

122-1 122-2 122-3 122-4 122-5 122-6 122-7 122-8 123-9 123-10 123-12

1,8 1.8 1.8 1.8 1.8 1.8 0.72 0.72 0.72 0.72 0.72

Sample

AIBN mole/liter X 1Œ

3

Reaction Time at 75°C, hours

OM", mole/'liter X W

0.13 0.33 0.66 6.6

70.7 14.7 14.7 14.7 70.7 70.7 70.7 14.7 14.7 14.7 14.7

Solvent Concn.

Reaction Time at 60°C, hours

0.13 0.33 0.66 3.3 6.6

—

d

140-1 140-2 140-3

4.6 3.0 3.0

e

19.4 9.7 4.8

4. 4. 4.

Conv.

%

Blend", grams

89 86 80 69 89 53 91 95 99 87 44

8.02 8.00 8.01 5.02 8.01 5.00 5.06 5.02 5.02 8.00 3.00

Conv.

%

Blend", grams

45 53 40

7.68 8.00 5.12

° Benzoyl peroxide. Octyl mercaptan. Components of blend for preparative G P C fractionation. Azobisisobutyronitrile. Molar ratio, benzene: methyl methacrylate. b

c

d

9

purification of the GPC-eluted, polymer-contaminated T F E has been described previously ( I ) . Reagent grade benzene ( n = 1.4979, bp = 80.9°C) also was used for viscometry. Gel Permeation Chromatography. A Water Associates model 200 gel permeation chromatograph fitted with five Styragel columns having nominal porosity designations ΙΟ , ΙΟ ,10 ,1.5 χ 10 , and 1.5 Χ 10 A was used for the analysis of molecular weight distribution in T F E at a tem perature of 50.0 ± 0.5 °C and a flow rate of 1.00 ± 0.05 m l / m i n . Further details concerning instrumental and operational parameters, sample prepa ration and injection, and data acquisition and reduction have been re ported elsewhere ( J ) . A Waters Associates Anaprep G P C fitted with one 4 ft X 2.4 inches od Styragel column having a nominal porosity of 10 A was used for the preparative fractionation of the P M M A blend in tetrahydrofuran at a temperature of 25 °C and at a flow rate of 30 m l / m i n . The degasser and differential refractometer were operated at 35° and 25 °C, respectively. Samples having concentrations of 0.25 wt-vol % were respectively, auto matically injected from a 100 m l loop over a 5-minute period. Ten 125 m l fractions were automatically collected for each sample injection. U p o n D

7

7

6

2 5

5

4

4



11.

127

GPC Calibration

PROVDER E T A L .

evaporation of the tetrahydrofuran, eight fractions containing significant amounts of polymers were obtained and denoted as C , D , E , F , G , H , I, and J . Fractions Ε through J were purified to remove the antioxidant and peroxides of tetrahydrofuran by twice dissolving the fractions i n acetone, reprecipitating with methanol, and then drying under vacuum. Fractions C and D first were extracted with methanol, and then the swollen polymer was extracted with cyclohexane and dried under vacuum. The baseline-adjusted retention volume curves of these fractions i n T F E are shown i n Figure 3. A l l fractions are reasonably bell-shaped except E . As a result of some inadvertent mixing, fraction Ε had a high molecular weight tail. This fraction was not used i n the construction of the primary molecular weight calibration curve. However, it was used i n establishing intrinsic viscosity relationships. Membrane Osmometry and Viscometry.

Number-average molecular

weights of P M M A were determined with a Mechrolab model 501 high speed membrane osmometer i n toluene at 60 °C except for samples 122-4 and 122-6 which were determined at 40°C. Viscometry measurements were made in benzene at 30 °C and in T F E at 50 °C with uncalibrated Cannon-Ubbelohde dilution viscometers which gave solvent times greater than 100 seconds. The viscometers used had centistoke ranges denoted by viscometer sizes of 50 and 75 for benzene and T F E , respectively. Stock solutions were made up on gram solute/100 gram solution basis and converted to gram/deciliter via the solvent density at the temperature of measurement. The solvent densities used were d™^ = 0.8686 (11a) and d™;% = 1.3429 obtained from pycnometric measurements (12). The density-temperature relationship for T F E obtained from regression analysis of the experimental pycnometric data is ne

TFE

d

=

x

4

229 - 0.0016*,

20°C < t < 55°C

(22)

The solvent and solution efflux times were determined by means of the Hewlett-Packard Autoviscometer system. The intrinsic viscosity was 60 50

024

Figure 3,

G

28

F

32 36 COUNTS (TFE)

Ε

40

44

Baseline-adjusted chromâtο grams of PMMA frac tions C, D, E, F, G, Η, I, and J


128

P O L Y M E R M O L E C U L A R W E I G H T METHODS

determined from an equivalent form of the Schulz-Blaschke equation (13) derived by Heller (14) and Ibrahim (15). The intrinsic viscosity was the reciprocal of the intercept obtained from a linear least-squares fit of ( C , C/^sp) where ^ is the specific viscosity and C (gram/deciliter) is the concentration and the abscissa of the parameter set. In most cases the experimental error i n [η] was less than 0.5%. Further details con cerning instrumental and operational parameters of the Autoviscometer system and membrane osmometer as well as sample preparation tech niques and data reduction have been reported elsewhere ( 1 ). Downloaded by UNIV OF MICHIGAN ANN ARBOR on February 18, 2015 | http://pubs.acs.org Publication Date: June 1, 1973 | doi: 10.1021/ba-1973-0125.ch011

sp

Results and Discussion Evaluation and Preparative G P C Fractionation of P M M A . T h e base

line-adjusted retention volume curves of the preparative G P C fractions are shown i n Figure 3. The characterization data are shown i n Table III. Table III.

Sample 122-1 122-2 122-3 122-4 122-5 122-6 122-7 122-8 123-9 123-10 123-12 140-2 140-3 Blend C D Ε F G H I J

Methyl methacrylate

Molecular Weight Characterization D a t a for P M M A Whole Polymers and Fractions

GPC Peak, counts 29.25 30.13 29.75 32.25 38.00 40.08 33.13 34.00 33.38 35.13 40.00 40.60 39.00 41.88 40.15 38.13 35.30 33.30 31.40 30.00 29.30 46.60

M

n

1

0

χ

M

v

- 3 «

547 479 415 234 50 33.4 140 194 234 121 48.5 17.5 32.3 19.5 15.3 30.8 68.9 130 227 513 671

—

1

e

0

X

- 3 6

1680 1250 1460 585 106 45.3 565 448 454 270 55.6 32.7 74.6 358 16 36.4 196 281 513 918 1490 1370

M /M v

M

n

3.08 2.61 3.52 2.50 2.12 1.36 4.04 2.31 2.37 2.14 1.15 1.86 2.32 18.3 1.05 1.18 2.85 2.15 2.26 1.78 2.24

2.798 2.213 2.464 1.255 0.355 0.189 1.224 0.981 1.041 0.707 0.217 0.147 0.273 0.871 0.104 0.160 0.559 0.729 1.139 1.757 2.510 2.349

TFE

4.829 4.262 4.376 2.522 0.567 0.358 2.193 1.717 1.745 1.196 0.336 0.217 0.440 1.673 0.152 0.225 0.908 1.179 1.985 3.032 4.328 4.187

Specific Area

34.7 33.6 34.4 32.7 32.3 32.7 31.5 33.4 34.5 27.2 31.6 18.8 27.9 31.4 33.7 34.2 31.6 30.7 33.9

0.1001

° Measurements made in toluene at 60°C except for samples 122-4 and 122-6 which werejnade at 40°C in toluene. M values obtained from [ n ] l n C data. M value has been diffusion corrected. 6

e

v

n


11.

GPC Calibration

PROVDER E T A L .

129

The M / M values of Table III and the G P C traces of Figure 3 indicate that a reasonable fractionation was achieved with a single 10 A porosity preparative G P C column. Narrower molecular weight distribution frac tions could have been achieved if another preparative column was used in series (e.g., 10 A porosity column) with the 10 A column. Because of the high molecular weight and high viscosity of the P M M A polymers, we found that 0.25 wt-vol % was an upper limit to the sample concen tration that could be injected in the preparative G P C without producing severe column overloading. Again, narrower molecular weight distribu tion fractions with less tailing could have been achieved by lowering the injected sample concentration with a concomitant reduction in sample through-put. It is recommended that tetrahydrofuran not be used as a preparative G P C solvent because the annoying presence of the antioxidant and peroxides i n tetrahydrofuran makes recovery of the polymer fractions unnecessarily difficult. A good room temperature preparative G P C solvent substitute for tetrahydrofuran is methylene chloride which does not absorb water as does tetrahydrofuran. v

n

4


6

4

0.1

0.2

0.5

M

Figure 4. C ?] TFS f 7

Intrinsic

or

1.0 5

T

?;

C

2.0

5.0

(dl/g)

Rehtionship between [T?]!^ and P M M A whole polymers and fractions 0

Viscosity-Molecular Weight Relationship for

PMMA

in

T F E . The intrinsic viscosities of the P M M A preparative G P C fractions and whole polymers in T F E at 50 °C and in benzene at 30 °C are shown in Table III and plotted in Figure 4. A least-squares analysis of the data plotted in Figure 4 yields the relation


130

P O L Y M E R

lQgiofo]5££ = 0.2321 +

M O L E C U L A R

W E I G H T

M E T H O D S

1.070 l o g i o h ] 8 £ , 0.152 < [ η ] ^ < 4.765 C

5

(23)


where the standard errors i n the slope and intercept are ±0.010 and db 0.0013, respectively. The Mark-Houwink intrinsic viscosity-molecular weight relationship for P M M A in benzene at 30°C can be obtained from the data of Cohn-Ginsberg, Fox, and Mason (16). Their data consist of 14 well characterized narrow molecular weight distribution polymer frac tions. A least-squares analysis of their data yields the relations fo]*£

c

[ri]l°H

C

= 6.83 X 10- M ,°- , M > 31,000

(24)

= 166 X 10- M °- , M

(25)

5

5

U

W

739

431

w

31,000

(26)

[η]{Ρ;|

= 181 X Î O - W /

Polymer Molecular Weight Methods

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