Polymer Molecular Weight Methods - ACS Publications - American

16 Average Degree of Polymerization of Cellulose by GPC without Viscosity

Downloaded by UNIV OF MONTANA on January 25, 2016 | http://pubs.acs.org Publication Date: June 1, 1973 | doi: 10.1021/ba-1973-0125.ch016

Measurements J. I. WADSWORTH, L. SEGAL, and J. D. TIMPA Southern Regional Research Laboratory, Southern Marketing and Nutrition Research Division, Agricultural Research Service, U. S. Department of Agriculture, New Orleans, La. 70179

In an earlier procedure applying universal calibration, viscosities of the four most concentrated fractions eluting about the peak were measured, and the intrinsic viscosities were plotted against count. The intrinsic viscosities of all the fractions were obtained by extrapolation of the plot for use in the calculations to obtain degree of polymerization (DP). In the present method the DP of each fraction is obtained from the relationship MW = (coil size/K) derived from Benoit's concept and the Mark-Houwink equation. Results from the new procedure are in excellent agreement with those obtained independently on cotton by others. Anomalies in results obtained previously on some samples disappear while marked improvement is noted for others. The determination is speeded up greatly by computer processing of data, and experimental error is reduced. 1/1+а

*Tphe use of gel permeation chromatography ( G P C ) i n studies of cellulose and cellulose derivatives has expanded greatly within the past few years. In common with similar studies of other polymers the matter of calibration of the G P C instrument and of conversion of G P C data into average molecular weight or average degree of polymerization ( D P ) of the polymer is of considerable importance. The application of universal calibration in an investigation of the chain-length distributions i n various celluloses by G P C has already been described i n an earlier publication ( I ) . In the procedure average D P values are obtained i n a manner unlike that normally used in G P C . There 178 In Polymer Molecular Weight Methods; Ezrin, Myer; Advances in Chemistry; American Chemical Society: Washington, DC, 1973.


16.

WADS WORTH E T A L .

Polymerization of Cellulose

179

is a totally different mathematical procedure, and measurements are made of the intrinsic viscosities of the four most concentrated fractions eluting around the peak. The intrinsic viscosities of these fractions are plotted against half-count, from which the intrinsic viscosities of all of the other, more dilute fractions are obtained by a least-square linear extrapolation of a log count vs. log viscosity plot. The DP values of the fractions, necessary in the calculations of average DP, are obtained by first dividing coil size ( Benoit's parameter, [η] M where [η] is intrinsic viscosity and M is molecular weight) by intrinsic viscosity and then dividing the resulting molecular weight by the proper unit monomer weight of the nitrated anhydroglucose unit. C o i l size is taken from the polystyrene calibration curve, coil size vs. count, at each half-count i n the chromatogram. Meas urements of areas under the curve on the chromatogram are made for obtaining the concentrations of the eluted fractions, also needed i n the calculations. Goedhart and Opschoor (2) developed a procedure that is basically similar. The conversion of G P C data to molecular weight, however, is accomplished by another mathematical approach which is unrelated to the preceding while intrinsic viscosities of the eluted fractions are meas ured by an automatic capillary-tube viscometer coupled to the discharge leg of the syphon of the G P C instrument. These authors comment that measurement of the viscosity of very dilute polymer solutions requires high accuracy and careful control in order to avoid anomalous results. This measurement when done manually is a tedious and time-consuming operation requiring a fair degree of skill. The present paper describes a procedure by which the average DP values can be obtained by G P C without making measurements of intrinsic viscosity, thereby drastically reducing the time necessary for G P C char acterization of samples as well as increasing the accuracy and reproduci bility of average DP values as compared with those obtained by other experimental methods. Experimental The G P C instrumentation and G P C procedures used here are the same as described earlier ( J ) but with slight alterations. The Kroeger H A K - 1 pads furnished with the pressure filter were replaced by Millipore 5-μ Mitex membranes to reduce changes i n solution concentrations arising from adsorption of the solute on the fibrous material of the pad. W h e n retention of eluted fractions was desired, two shallow aluminum pans filled with tetrahydrofuran ( T H F ) were placed in the syphon box, and then the door was closed and latched. The saturation of the enclosed air space by T H F vapor minimized evaporation of the solution during drop formation, drop fall, and retention of fraction i n the syphon. The possi bility of diluting the sample solution when charging the sample loop was

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

180

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

METHODS


eliminated by first removing the T H F held in the loop and then drying the loop by passing air through it. Several celluloses are included i n this study. One is a purified, par tially hydrolyzed cotton made available through the courtesy of K . A . Kuiken, The Buckeye Cellulose Corp. The D P data furnished with this cotton are to be found i n Table I; the low values are the consequences of acid hydrolysis to which the cotton was subjected prior to characteriza tion. This cotton was nitrated for G P C and handled i n the manner already described ( I ) . The data obtained i n the previous study ( I ) of celluloses I, II, III, and I V are used as w e l l as the data from a study of crosslinked cottons (3). Table I. Degrees of Polymerization of Cellulose Samples Obtained by Conventional Methods and by the N e w G P C Procedure

DP

Method Conventional methods Gel permeation chromatography

DP

W

1570 1560

725 680

a

n

DP /DP

6

w

n

2.17 2.30

° B y viscometry in Cadoxen. B y osmometry of the nitrate in butyl acetate. b

Calculations of the average D P values were carried out by means of the same scheme given earlier ( I ) . Because the scheme is markedly different from the usual one for handling G P C data, it is repeated here in Table II for convenient reference. The required weight data of column 2 are obtained directly from the area measurement about the half-count i n the chromatogram as described i n the preceding paper ( 1 ). The D P (column 3), however, is calculated differently. The intrinsic viscosities necessary for calculating molecular weights of the fractions are not meas ured. These molecular weights are obtained by means of the relationship ι

which is derived from the concept of Benoit et al. (4) and the MarkHouwink equation, [η] = K M . F o r cellulose trinitrate i n T H F , Κ = 8.3 X 10" and a = 0.76 for D P > 1000; for D P ^ 1000, Κ = 0.075 X 10" and a = 1.14 (5). To obtain M for a given elution volume, the value of the coil size corresponding to that elution volume is obtained from the universal calibration curve. Then M is calculated from the above equation using the appropriate values for coil size, K, and a. D P then follows as already mentioned. A l l of the calculations were done by computer. The program, which is general and can be applied to polymers other than cellulose nitrate, is available on request. A

4

4

Results and

Discussion

The earlier procedure for converting G P C data to average D P values was an advance over that of the original based on extended molecular


16.

WADSWORTH E T A L . Table II.

181


Calculation of Weight- and Number-Average Degrees of Polymerization from Fractionation D a t a


a &

Fraction

Weight (W) in Polymer, grams

DP

W/DP

W X DP

1 2 3 4 5 6

10 20 25 25 10 10

500 1,000 2,000 2,500 3,000 4,000

0.0200 0.0200 0.0125 0.0100 0.0033 0.0025

5,000 20,000 50,000 62,500 30,000 40,000

0.0683

207,500

Total Data in columns 1, 2, and 3 are strictly arbitrary.

α

DP

b

w

= Σ(Ψ X DP)/YW = 207,500/100 = 2,075; DP

n

100/0.0683 = 1,464; DP /DP w

=

n

= ΣΨ/Σ(Ψ/ϋΡ)

=

1.42.

chain length in that it was founded on more acceptable principles and incorporated automation of data acquisition as well as data processing by computer. The results obtained were more i n the range of those from conventional methods. Inherent in the method as developed, however, is the measurement of the viscosities of very dilute polymer solutions—i.e., the eluted fractions. The possibility of eliminating this measurement appeared when consideration was given to Benoit's coil-size parameter [η] M for universal calibration and to the Mark-Houwink equation [η] = KM relating intrinsic viscosity of a polymer solution to the molecular weight of the dissolved polymer. It can easily be shown that the relation ship expressed in Equation 1, where Κ and a are the Mark-Houwink constants for the particular system, is derived from the above equations (6). The molecular weight M of the fraction is obtained from the cali bration curve by means of this equation. In another approach towards eliminating the viscosity measurements, the parameter Κ Μ , related to the above, has been reported (7). It is claimed that this could be substituted for the coil-size parameter [ 7 7 ] M . A more complex function relating M to elution volume where no viscosity measurements are made has been proposed by C o l l and co-workers (8). This function, derived from the Mark-Houwink equation and the equa tion of Ptitsyn and Eizner (9), lacks the simplicity of that described above. Application of the present procedure to the characterized cotton supplied by The Buckeye Cellulose Corp. gives the results shown i n the lower part of Table I. The agreement among the data is particularly good, even though the value for DP is somewhat lower than that determined by osmometry (this raises slightly the polymolecularity ratio DP /DP ). This behavior of DP and the ratio has been noted previously ( 1 ) and is still in accord with reports of others (10). The polymolecularity ratios for the cellulose I, II, III, and I V samples reported i n the preceding paper a

1 + α

n

w

n


n

182

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

Nitrated Sample

Cellulose Cellulose Cellulose Cellulose

Comparison of Results Weight-Average D P

ViscosityAverage D P Using Cadoxen*

Present Procedure

Prior Procedure"

4990 3760 3780 2330

4140 3380 3370 2490

5190 4520 4795 3390

I II III IV


° Data of Segal, Timpa, and Wadsworth (1).

( I ) are unusually large. Recalculation of the data by the new procedure gives the results tabulated i n Table III. The ratios are now more of the order usually obtained for material of this sort. Also, the values for DP are shifted; those for DP are lowered to the range of the Cadoxen viscosity-DP's, while those for DP are raised. In the preceding publication (I ), five replications for the cellulose II sample were tabulated in Figure 3 to show that variations in DP were noted when the related DP data were i n good agreement. The polymolecularity ratios for the DP values fluctuate widely as a consequence of this. These results are compared in Table I V with those now obtained from the same data. The improvement in the values is quite marked as the statistical analysis of the data indicates. In recent work with cotton crosslinked with formaldehyde (3), it was noted that (a) DP remained constant with treatment time when decreasing values were anticipated from concurrent viscosity measure ments, and (b) DP became quite low, whereby very high values ap peared for the polymolecularity ratios. These values are compared i n Table V with those resulting from application of the new procedure. Now DP decreases with treatment time as expected, while DP and polymo lecularity ratio assume more consistent values. The inclusion in this table of the viscosity-average D P data presents an interesting picture. The agreement between DP by the present procedure and DP for the initial cotton is quite good; it is satisfactory for the next two samples. However, with increasing time of treatment DP and DP decrease greatly, indicat ing that much chain cleavage has taken place. The smaller decrease i n DP is marked. W

n

n

W

W

n

W

n

W

V

V

n

W

The lesser change here i n DP illustrates the power of G P C i n studies of changes i n molecular weight brought about by various means. Factors are brought out that are not detected by other techniques. The reasons for the lesser change i n DP i n the above data become apparent when the chromatograms for these samples (3) are re-examined. Thus, as the combined formaldehyde i n the sample increases, the chromatogram be gins to rise at lower count than does that of the initial cotton, and reaches W

W


16.


WADSWORTH E T A L .

183

Obtained According to Procedure Used Number-Average D P Present Procedure

Present Procedure

1580 1040 1140 490

1.90 2.07 2.02 2.48


quant

41 42 43 44 45

A A A A A

Mean Std. dev. Coeff. of var., % a

n

Prior Procedure"

3.35 4.67 4.21 7.07

Statistical Comparison of Results Obtained by the Present and Prior Procedures with Nitrated Cellulose II

Weight-Average D P

£β

w

Prior Procedure"

2180 1640 1680 1000 Table IV.

Ratio D P / D P

Ν umber-Aver age D P

Present Prior Procedure Procedure"

Ratio

DP /DP w

Present Prior Present Prior Procedure Procedure" Procedure Procedure"

3500 3460 3480 3190 3250

4525 4655 4470 4520 4430

1840 1614 1850 1440 1430

1370 980 1390 770 710

1.90 2.15 1.88 2.22 2.27

3.30 4.76 3.21 5.84 6.24

3380

4520

1630

1040

2.08

4.67

140

85

210

323

0.18

1.40

4.2

1.9

n

12.6

30.9

8.7

30.0

Data of Segal, Timpa, and Wadsworth {1).

appreciable levels by the time the latter chromatogram does start up. This is evidence of nonhydrolyzed formaldehyde linkages that effectively increase molecular chain length, producing a small amount of polymer of higher molecular weight than initially present. Small amounts of such material w i l l influence DP as this parameter is weight sensitive. The presence of such material is not even hinted at i n the viscosity measure ments, which may explain the occasional lack of agreement between viscosity and G P C data that has been observed. The marked improvement in results presently obtained lies in the elimination of sources of error now recognized as being present i n the prior procedure. A major source of error was the extrapolation from the log-log plot of half-count vs. intrinsic viscosity for the four eluates which lay about the peak of the chromatogram. It is this extrapolation that supplied the necessary intrinsic viscosities of the remaining more W


184

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


Formaldehyde Content of Sample, %

Results Obtained According to Procedure Used

Minutes of ViscosityTreatment Average D P

Initial cotton 0.08 0.09 0.18 0.32 0.63 0.72 0.83 0.98

0 1 3 8 20 60 105 180 360

3430 3010 2970 2620 2460 1970 1930 1600 1360

Weight-Aver age D P a

Present Procedure

Prior Procedure "

3500 3310 3120 3060 3060 3200 2840 2780 2485

4120 3900 4130 4120 4200 4170 4130 3790 3590

1

° In ethyl acetate, G = 1,200 sec , constants for conversion to DP according ta Marx-Figini and Schulz (11). Data of Segal and Timpa (3). -1

b

dilute fractions (Figure 3, Réf. J ) . As the four points making up the plot seemed to fall about a straight line, a linear least-squares regression was applied and extrapolated. Closer study and more refined analysis of these data have disclosed that this is not a simple linear relationship. Because this is so, the values of the intrinsic viscosities of the more dilute fractions become more i n error as extrapolation is made further and further from the central four points. As a consequence, the values of DP obtained through the calibration curve deviate from the true values. Experimental error entered the data, of course, through the manual measurement of the viscosities of the four very dilute fractions. Another error in the viscosities was introduced by contamination of each fraction by some of the fraction preceding it. Not all of the liquid i n the measuring syphon could be removed as the syphon emptied; thus a small portion of the fraction was retained and added to the incoming fraction. Further more, the previous procedure required exact weights in each fraction, whereas now only relative weights are necessary. The relationship de veloped here can be extended to polymers other than cellulose. To do this, the values of Κ and a have to be determined for the particular polymer, dissolved in the desired G P C solvent which was used to establish the calibration curve. Although only DP and DP are mentioned i n the tables of data presented here, the computer program includes instructions for obtaining DP and DP . The latter have been helpful i n indicating the extent of crosslinking produced or retained i n treated cotton samples under study in connection with other work underway. W

Z

n

Z+1


16.

WADSWORTH E T A L .

185


with Formaldehyde-Crosslinked Cotton A f t e r Nitration Ν umber-Aver age D P


Present Procedure

1590 1380 1215 1100 1040 850 840 710 635

Ratio D P / D P w

n

Prior Procedure '

Present Procedure

Prior Procedure*

800 710 520 405 440 380 370 280 290

2.21 2.41 2.58 2.78 2.96 3.79 3.39 3.91 3.92

5.15 5.49 7.94 10.17 9.55 10.97 11.16 13.54 12.38

1

Conclusions A relationship has been developed by means of which more valid values are obtained by G P C for the average degrees of polymerization for cellulose. This can be extended to other polymers. W i t h automation of data acquisition and computer processing of data, a differential mo lecular weight distribution and complete information on D P of the sample are available i n very short order with a low degree of error. T h e ready availability of narrow, well characterized polystyrene fractions for calibra tion makes this procedure highly attractive i n view of the lack of similar standards of cellulose.

Literature Cited 1. Segal, L., Timpa, J. D., Wadsworth, J. I.,J.Polym. Sci.A-1(1970) 8, 3577. 2. Goedhart, D., Opschoor, Α., J. Polym. Sci. A-2 (1970) 8, 1227. 3. Segal, L., Timpa, J. D., Proc. 10th CottonUtil.Res. Conf., New Orleans, La., Apr. 29-May 1, 1970, ARS No. 72-83. 4. Benoit, H., Grubisic, Ζ., Rempp, P., Decker, D., Ziliox, J.G.,J.Chim. Phys. (1966) 63, 1507; Grubisic, Z., Rempp, P., Benoit, H., J. Polym. Sci. Β (1967) 5, 753; Grubisic, Z., Reibel, L., Spach,G.,C. R. Acad. Sci., Paris, Ser. C (1967) 246, 1690. 5. Timpa, J. D., Segal, L., J. Polym. Sci., Pt. A-1 (1971) 9, 2099. 6. Weiss, A. R., Cohn-Ginsberg, E., J. Polym. Sci., Β (1969) 7, 379. 7. Chang, M., Abstracts, 161st National Meeting of the American Chemical Society, Los Angeles, Calif., Mar. 28-Apr. 2, 1971. 8. Coll, H., Prusinowski, L. R., J. Polym. Sci. Β (1967) 5, 1153; Coll, H., Gilding, D., J. Polym. Sci. A-2 (1970) 8, 89.


186

POLYMER MOLECULAR WEIGHT METHODS


9. Ptitsyn, O. B., Eizner, Y. E., Soviet J. Technol. Phys. (Engl. Trans.) (1960) 4, 1020. 10. Alliet, D. F., in "International Symposium on Polymer Characterization" (Appl. Polymer Symp. 8), K. A. Boni and F. A. Sliemers, Eds., Interscience, New York, p. 39; Boni, Κ. Α., Sliemers, F. Α., in "International Symposium on Polymer Characterization," p. 65; Crouzet, P., Fine, F., Mangin, P., J. Appl. Polym. Sci. (1969) 13, 205. 11. Marx-Figini, M., Schulz, G. V., Makromol. Chem. (1962) 54, 102. RECEIVED January 17, 1972. Mention of a commercial product does not imply endorsement by the U. S. Department of Agriculture over similar products not mentioned.


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