Polymer Molecular Weight Methods

17 Gel Permeation Chromatography VI. Molecular Weight Averages and Molecular Weight 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.ch017

Distribution of Cellulose Nitrate A. C. OUANO and EDWARD M. BARRALL II IBM Research Laboratory, San Jose, Calif. 95193 A. BROIDO Pacific Southwest Forest and Range Experiment Station, Forest Service, U. S. Department of Agriculture, Berkeley, Calif. 94701 A. C. JAVIER-SON Statewide Air Pollution Research Center, University of California, Riverside, Calif. 92502

Cellulose samples which have undergone various stages of thermal decomposition were characterized for changes in molecular weight and molecular weight distribution using gel permeation chromatography (GPC) and viscometry. Calculation of cellulose molecular weights (as cellulose nitrate) from the chromatogram and polystyrene calibration curves using the extended chain length-retention volume relationship (Q factor) resulted in very poor agreement between GPC and viscometric molecular weight values. Molecular weight averages determined by GPC were approximately five times greater than those obtained by viscometric technique. Application of various hydrodynamic considerations completely corrected this problem. The effects of calibration standard distribution and range are also discussed. el permeation chromatography using polystyrene standards and viscometry were employed to determine molecular weight distribution and molecular weight averages of cellulose. The cellulose samples were all nitrated to about 13.5% nitrogen to make them soluble in T H F ( G P C 187 In Polymer Molecular Weight Methods; Ezrin, M.; Advances in Chemistry; American Chemical Society: Washington, DC, 1973.

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.ch017

188

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

solvent). The agreement between the molecular weight averages deter mined by G P C and viscometry ranged from very poor ( order of magnitude difference) to good (within 1 0 % ) depending on the model used to calculate molecular weights from G P C data. The previously described laboratory automation system (computer controlled) for gel permeation chromatography developed i n this lab oratory ( I ) was particularly well suited for calculating absolute molec ular weights of cellulose nitrate from G P C data and a polystyrene cali bration using the universal calibration model. The laboratory automation consisted of two main parts: data-logging and data-reduction programs. The data-logging program converts the analog signal of the G P C differ ential refractometer detector to digital form and stores it i n a disk data storage system. The data-reduction program calls the stored G P C data and reduces it to normalized molecular weight distribution curves and molecular weight averages using polystyrene calibration and the universal calibration of extended chain length model (Q factor). The computer programs allow a minimum of interaction with the technician. The only external input the program requires is: integration limits, sample identi fication, and the Mark-Houwink constants. The reduced data output consists of a normalized molecular weight distribution ( Cal-Comp plots ) and molecular weight averages (number-, weight-, viscosity-, and Z-average molecular weights ) in digital forms. Q-Factor (Extended Chain Length—Retention

Volume

Calibration)

This method of computing molecular weight averages from G P C data assumes that molecules having equal extended chain length have equal retention volume. Hence, by computing the average molecular size from the G P C data and the polystyrene calibration curve (plot of retention volume vs. extended chain length) one can presumably calculate the aver age molecular weight by simply multiplying the computed molecular size by a Q factor (Q = molecular weight/molecular size). Segal (2) re ported a Q factor for cellulose of 58. A comparison between the weightaverage molecular weights computed from G P C (Q = 58) and viscometric data is shown i n Table I. The very poor agreement between the two sets of data is obvious, the G P C computed molecular weights being more than a magnitude larger than viscometric results. The very large disagreement is not unexpected and can be explained satisfactorily by the present generally accepted model of G P C separation. That is, molecules are separated according to hydrodynamic volume i n solution and not according to the extended chain length. Consequently, molecules with identical extended chain length but different chain stiffness i n solution w i l l not have identical retention volumes.

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

17.

OUANO E T A L .

Table I.

Molecular Weight Averages of Cellulose by Viscometric and G P C Weight Average Methods Using Extended Chain Length Model ( Q Factor)


Sample

Microcrystalline 1 2 3 4 5 6 7 8 9 Universal

189

Cellulose Nitrate

Viscometry

GPC

DP

DPw

195 110 185 210 285 310 790 850 900 965

1,650 970 1,545 1,810 2,640 2,820 12,900 16,700 21,800 31,000

Disagreement, %

745 780 735 760 810 1,530 1,535 1,870 2,320 3,120

Calibration

Grubisic et al. (3) showed that for many polymers a single calibration curve can be drawn through a plot of the product of intrinsic viscosity and molecular weight ( [η] M ) vs. retention volume. This relationship certainly supports the model of molecular separation based on hydrodynamic volume since [η] M is proportional to the hydrodynamic volume of the molecule i n solution. Hence, molecular weights of the two polymers ( calibration standard polymer and sample ) which have identical retention volume under identical G P C analytical conditions can be expressed i n terms of each other by combining the Grubisic relationship: folxMx = W M 2

(1)

2

and the Mark-Houwink relationship (2)

[η] = KM" Thus, the expression

permits the computation of the molecular weight ( M ) of a cellulose sample from the known molecular weight (Mi) of the standard poly styrene samples with identical retention volume. The Mark-Houwink constants for polystyrene (Ki and «i) i n T H F at 30°C were measured i n this laboratory to be 2.89 Χ 10" and 0.65, re spectively, while those of cellulose nitrate were reported by Jenkins (4) 2

4


190

POLYMER

MOLECULAR WEIGHT METHODS

to be 0.606 Χ 10" and 1.014, respectively. Dawkins, Maddock, and Coupe ( 5 ) suggested the use of an additional parameter for Equation 3 because of the excluded volume effect.


4

The excluded volume correction Φ 2 / Φ 1 for polystyrene and cellulose i n T H F was computed to be 0.58 from the relationship ( 5 ) , Φ = Φ ( 1 — 0

( € )

2.63c + 2.86c ), where € — (2* 2

l)/3.

Meyerhoff ( 6 ) suggested the relationship Mi

1 / 2

[7j]i

1 / 3

(5)

= M21/2M21/3

to be more appropriate for cellulose nitrate and polystyrene with equiva lent retention volume. Equation 5, when combined with Equation 2 yields

M 2 = [f-;](^) Μ,ΟΜ

(β)

which is analogous to Equation 3. Rudin and Hoegy ( 7 ) suggested fur ther correction because of the concentration effects on the universal calibration method. MeyerhofFs relationship and Rudin's correction, however, have not yet been applied i n interpreting our results. A comparison of the weight-average molecular weights of cellulose computed from both Equations 3 and 4 and from viscometric data are shown in Table II. It is apparent that the agreement between viscometric Table II. Viscometric and G P C Weight Average Molecular Weight Data Using the Hydrodynamic Volume (Universal Calibration Model)

Sample

Viscometry DP

GPC DPw

Disagree ment, %

GPC" DPw

Microcrystalline 1 2 3 4 5 6 7 8 9

195 110 185 210 285 310 790 850 900 965

240 145 220 260 350 375 1,230 1,580 1,970 2,650

23 32 19 24 23 21 56 86 119 175

135 110 165 200 265 285 935 1,200 1,500 2,100

a h

Disagree ment,'' %

Calculated using Equation 3. Calculated using Equation 4.


8 0 11 5 7 8 18 41 67 118

17.

OUANO ET AL.

Cellulose Nitrate

191

and G P C computer molecular weight is much better for either Equation 3 or 4 than for the Q factor values i n Table I. The poorer agreement for the higher molecular weight sample is interpreted as being a result of errors incurred i n extrapolating the calibration curve beyond the highest molecular weight (1.8 Χ 10 ) polystyrene calibration standard used. Figure 1 shows the effect of extrapolation of the calibration curve on the agreement between G P C and viscosity-molecular weight. It is also inter esting to note that the use of excluded volume correction, Equation 4, results in consistently lower molecular weights than the viscometric re sults while Equation 3 consistently yields higher molecular weight relative to viscometric values.


6

WEIGHT P E R C E N T C E L L U L O S E N I T R A T E WITH DP>1.11 Χ 1 0 3

Figure 1. Disagreement be tween viscometnc and GPC viscosity-average molecular weight vs. weight percent of the sample component with re tention volume less than the highest molecular weight cali bration standard As evidenced i n Table III, a closer agreement than those previously obtained i n Tables I and II is made possible by comparing the G P C viscosity-average molecular weight (using Equation 3) and molecular weight averages obtained by viscometry. The above comparison is per haps more valid than the previous comparisons (Table I and II) since for a polydisperse system the viscometric method of measurement deter mines the molecular weight average as defined by:


192

P O L Y M E R

"

M

=

M O L E C U L A R

M E T H O D S

(7)

[ - Σ Ψ Γ ]

and not the weight-average molecular weight. Since Equation 7 is i n fact the relationship used in computing the viscosity-average molecular weight from the G P C chromatogram, the comparison made i n Table III is justified. Note, however, that a similar computation using Equation 4 would yield poorer agreement since D P is less than D P and the values obtained from Equation 4 are already low. Some uncertainty is introduced in the value of the Mark-Houwink constants for cellulose i n this work because they were obtained from [ 7 7 ] - M relationship of samples which had polydispersities of between 1.5 and 2.5. Since cellulose has a rela tively low polydispersity (M /M ^ 2.0) and « — 1, the values of M and M are usually within 1 0 % . Furthermore, the literature (8) shows that the « values of fractionated and unfractionated cellulose are essen tially the same. Hence, the above uncertainty is somewhat mitigated. V


W E I G H T

W

W

N

W

w

Table III.

Viscometric and G P C Viscosity Average Molecular Weights Using the Universal Calibration Model

Sample

Viscometry

Microcrystalline 1 2 3 4 5 6 7 8 9

195 110 185 210 285 310 790 850 900 965

a

DP

GPC

DP/

200 115 185 230 310 340 1,010 1,360 1,690 2,370

Disagreement,

%

3 5 0 10 9 10 28 60 88 146

Calculated using Equation 3.

The results discussed i n the preceding paragraphs indicate clearly that the extended chain length model (Q factor) is unsatisfactory for calculating cellulose molecular weight averages from the G P C retention volume distribution and polystyrene calibration curves. However, calcu lations based on the hydrodynamic volume of cellulose i n solution give average molecular weights which agree well with results obtained by both the viscometric method and the literature values for microcrystalline cellulose (9, 10). The best agreement between G P C and viscometric data is obtained by comparing the viscosity-average molecular weight computed from G P C chromatograms using a model without the excluded volume effect.


17. OUANO ET AL. Cellulose Nitrate

193

Literature Cited


1. 2. 3. 4. 5.

Ouano, A. C., J. Polym. Sci., in print. Segal, L., J. Polym. Sci. Part C (1968) 21, 267. Grubisic, Z. etal.,J. Polym.Sci.Β (1967) 5, 753. Jenkins, R. G., Masters Thesis, The University of Waterloo. Dawkins, J. V., Maddock, J. W., Coupe, D., J. Polym. Sci. Part A-2 (1970) 8, 1803. 6. Meyerhoff, G., Makromol. Chem. (1965) 89, 282. 7. Rudin, Α., Hoegy, H., J. Polym. Sci. A-1 (1972) 10, 217. 8. Brandrup, J., Immergut, E., Eds., "Polymer Handbook," Interscience, New York, 1967. 9. Patai, S., Halpern, Y., Israel J. Chem. (1970) 8, 655. 10. Battista, Ο. Α., Smith, P. Α., Ind. Eng. Chem. (1962) 54, 20. RECEIVED January 17, 1972. Work supported in part by Grant AP00568 from Air Pollution Control Office, Environmental Protection Agency, to the Univer sity of California Statewide Air Pollution Research Center, Riverside, Calif.


Polymer Molecular Weight Methods

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