1 Determination of Number-Average Molecular Weights by Ebulliometry Downloaded via 148.251.232.83 on December 28, 2018 at 11:08:15 (UTC). See https://pubs.acs.org/sharingguidelines for options on how to legitimately share published articles. CLYDE A. GLOVER Research Laboratories, Tennessee Eastman Co., Division of Eastman Kodak Co., Kingsport, Tenn. 37662 This paper describes an ebulliometric system for routine and special determinations of molecular weights. The system uses a simple ebulliometer, an immersion heater, and a Cottrell-type pump. Temperature sensing is by differential thermopile. Precision varies from about 1 to 6%, and values compare well with those from other laboratories and those from other methods. Values as high as 170,000 have been successfully measured. Some problems encountered in using the ebulliometric method are: selection and effect of reference temperature, limitations of the vapor lift pump and a possible substitute for it, measurement of equilibrium concentrations within the operating ebulliometer, and the experimentally determined ebulliometric constant and some factors which influence its value. "Ebulliometry, one of the classical methods for determining molecular weights, has undergone great improvement in recent years. The requirements of a successful ebulliometric system are thermal stability, temperature and concentration equilibrium, and temperature sensing. These requirements have been met by a number of investigators in various ways. The systems of each are reported to have met the need for which they were designed; in spite of this, however, the method does not now appear to be used widely either for routine determinations or in special problems. Here we present the case for what appears to be a neglected technique which is felt to have great potential. We describe a system which has been in use for several years for both routine and special molecular weight measurements, discuss some of the results obtained, and finally consider some of the problems and unanswered questions which have been encountered. 1
2 POLYMER MOLECULAR WEIGHT METHODS The Ebulliometric System The system consists of a simple ebulliometer, a temperature sensing element, and an electrical recording device. The ebulliometer is essentially the same as that described by Glover and Stanley (I ) and is shown in Figure 1. It consists of a platinum immersion heater, a vapor lift pump of the Cottrell type, and a recycle arrangement patterned after that described earlier by Ray (2). There are other successful designs, such as those of Ray (2), Lehrle (3), and others, which differ in detail from the one shown, and there are different types, such as the shaking apparatus of Schultz (4) which was improved by Ezrin (5). Temperature sensing is an important part of ebulliometry. In the work being described, thermopiles are used. They are very stable in operation and change little, if any, with age. One advantage is the leveling effect of the multiple temperature sensing points of the thermopile on rapid temperature fluctuations caused by uneven boiling or pumping. Thermistors have been used, with equal success, for temperature sensing by many workers. Also, devices such as the quartz crystal thermometer might be adapted to this application. Finally, the signal from the thermopile is amplified in this system by a Leeds and Northrup stabilized microvolt amplifier No. 9835A and is recorded on a strip chart recorder. Thermal stability is obtained with a vapor jacket. This jacket normally contains the solvent to be used in the determination and is covered with aluminum foil which serves as a light shield as well as a thermal barrier. The jacket is connected directly to the ebulliometer to prevent pressure differences, and
1. GLOVER Ebulliometry 3 the system is vented to ambient pressure through a surge tank. With a thermopile having 80 measuring junctions in the ebulliometer, temperature differences of 2 X 10" C can be detected with satisfactory accuracy. 5o Operation of the system has been simplified to permit routine determinations by a laboratory technician with no active supervision. The procedure differs from those published by Dimbat and Stross (6) and others chiefly in that the ebulliometer is neither washed nor dried between determinations. However, after fresh solvent is added, the output of the thermopile ("zero line") for the solvent is recorded. Further, a decreasing heat input program is followed to eliminate the effects of foaming and superheating. Normally three or four weighed portions of the sample are added successively, and the elevation in boiling temperature is recorded for each portion. The molecular weight is obtained from these data by the limiting slopes calculation, or by any of the established calculation procedures (6, 7), with the aid of an IBM 1130 computer programmed to give the molecular weight and an "error" indication for each data point. About 8000 determinations involving a range of solvents and solutes have been made with the system as described. The most recent and perhaps most interesting development in this respect is the use of hexafluoro-2-propanol (HFIP) as an ebulliometric solvent for the study of polyesters and polyamides. HFIP has an ebulliometric constant (K6) of 3.0, compared with a value of 3.3 for toluene, and behaves satisfactorily as an ebulliometric solvent. Precision of these measurements varies with molecular weight level, solvent, and to some extent, solute. With a series of polyglycols, as shown in Table I, the standard deviation was about 1% at a molecular weight level of about 4100. For polyethylene, as shown in Table II, precision does vary with molecular weight and is obviously influenced by other factors, such as homogeneity and purity of the sample. Table I. Precision in Molecular Weight Determination: Poly glycol in Toluene Determination Molecular Weight 1 4189 2 4138 3 4112 4 4112 5 4164 Mean 4143 Standard Deviation 36 or 0.85% Table III shows some surprising results obtained from the NBS ( National Bureau of Standards) polystyrene sample 705. This material has a very narrow molecular weight distribution; since it is a specially prepared
4 POLYMER MOLECULAR WEIGHT METHODS Table II. Precision in Molecular Weight Determination: Polyethylene in Toluene α Av. Mol. Wt. 18,170 η 7 Standard Dev. 756 or 4.2% Av. Mol. Wt. 24,620 η 5 Standard Dev. 1886 or 5.6% Av. Mol. Wt. 34,280 Standard Dev. 942 or 2.7% α Data from Anal Chem. (1961) 31, 449. Table III. Precision in Molecular Weight Determination: Polystyrene in Toluene NBS Reference Material 705 Mol.Wt. Found 171,900 168,400 169,700 Av. 170,000 Standard Dev. 1756 or 1.03% reference material, it probably is more homogeneous than most samples and thus gives more precise data. Assessment of accuracy presents a problem since few authentic reference materials exist in the molecular weight range of interest. However, our results have been compared with those obtained by other laboratories and those obtained by other methods. One comparison is shown in Table IV. The accuracy of the method is also shown by the data obtained from the previously mentioned NBS sample. These data are shown in Table V. Effect of Experimental Variables In spite of the apparently successful performance of the ebulliometric system in routine use, a number of variables exist in connection with the operation of the system as it has been described. Many of these variables, as many as possible, are overcome by standardization in routine operation. However, they must be recognized if the ebulliometric method is to be understood and applied to special problems. First, the use of the condensing solvent vapors as a reference temperature can lead to considerable uncertainty, particularly with nonpolymeric solutes, because changes in the reference temperature, which
1. GLOVER Ebulliometry 5 result from the presence of impurities in the solvent or the solute or from solute volatility, may go undetected. Such changes have actually been measured with special thermopile circuits and are real and significant. If a boiling liquid reference (twin ebulliometer) is used, the problem is less acute. An example is shown in Table VI; the results were obtained when both types of reference temperatures were used to determine the molecular weight of biphenyl (bp, 256 C) in toluene (bp, 110 C). These results may explain some of the confusion found in the literature concerning the required difference between the boiling temperatures of a solute and a solvent necessary for valid use of the ebulliometric method. Table IV. Accuracy in Molecular Weight Determination: Polyethylene in Toluene* Ebulliometry r r Vapor Lab Lab Lab Pressure Sample A B C Cryoscopy Osmometry 1 11,500 11,500 11,500 10,700 10,900 2 18,400 19,200 19,100 18,800 α * 'Advances in Analytical Chemistry and Instrumentation," Vol. 5, Table XII, Chapter 1, p. 63, Wiley, New York 1966. Table V. Accuracy in Molecular Weight Determination: Polystyrene in Toluene NBS Reference Material 705 Mol. Wt. (Elbulliometry) 170,000 Mol. Wt. (Osmometry NBS) 170,900 Table VI. Molecular Weight of Biphenyl in Toluene Reference Type Mol. Wt. Found Theory Condensing Vapor 512 154 Boiling Liquid 171 154 The Cottrell-type pump presents an additional variable. With it the rate and the heat input to the boiling solution cannot be varied independently. For this reason, the possibility of superheating cannot be rigorously eliminated. To overcome superheating, a no-dead-space mechanical pump ( Figure 2 ) was designed, constructed, and installed in an experimental ebulliometer as shown in Figure 3. The unique feature of this pump is the loose fit of the piston which permits continuous flow of liquid through the piston chamber during operation. The problems of superheating and equilibration are currently being reexamined with this apparatus in a twin configuration.
6 POLYMER MOLECULAR WEIGHT METHODS PLATINUM WIRE 4-MM.-O.D. TUBE 6-MM. ROD 8-MM.-O.D. TUBE 6-MM.-O.D. TUBE Figure 2. Mechanical pump for ebulliometer SAMPLING CAPILLARIES PLATINUM WIRE SAMPLING CUP SOLVENT LEVEL PUMP Figure 3. Experimental ebulliometer A further need is to know the actual solute concentration at the temperature sensing point in the ebulliometer at operating equilibrium. Amounts of solvent and solute added to the ebulliometer can be accurately measured and controlled; however, their distribution within the apparatus at equilibrium is difficult to establish. As shown in Figure 3, provisions have been made for removing samples during operation. The problem of solvent-solute distribution and the accompanying problem of analysis are being studied, but so far the studies have been less than completely successful. The last variable to be discussed is that of the experimentally determined value for the ebulliometric constant, Kb. Equation 1 indicates
1. GLOVER Ebulliometry 7 that theoretically ΔΓ6 varies with solute molecular weight to make Kb constant. π _ Solute mol wt (grams) X ATb ( C) X solvent wt (grams),. 6 ~ 1000 X solute wt (grams) ^ ' In the work described here, this has not been found to be true. Considerable effort has been expended to eliminate this apparent inconsistency or to explain it as instrumentally induced. To date neither has been successful, and the observations remain unexplained. It appears from this work that the experimentally determined value of Kb is influenced by both the chemical nature and the molecular weight of the solute. (C6H5)2 (C6 Hs )2Si Si(C6 H5 )2 (C6 H5 )2Sr ^Si(C6 H5 )2 (C6H5)2Si.Si(C6H5)2 (C6H5)2Si Si(C6Hs)2 (C6H5)2 (C6H5)2 MOL WT.911 I (C6H5)2Si Si(C6H5)2 MOL WT. 1094 II (C6H5)2Si Si(C6H5)2 Figure 4. MOL. WT. 729 III Organosilicon compounds This is demonstrated by a problem in which an effort was being made to establish the structure of an unidentified organosilicon compound prepared by Dr. Gilman of Iowa State University. Other data and the history of the compound indicated that the structure was either I or II as shown in Figure 4. The boiling point elevation of the unknown compound was obtained in toluene with the apparatus shown in Figure 1. A Kb which had been established with tristearin (molecular weight 891) was used to calculate the molecular weight of the unknown, and an inconclusive value of 973 was obtained. A new Kb was then established with an authentic compound of structure III, Figure 4. The new Kb was used to recalculate the molecular weight of the unknown, and a value of 921 was obtained. The structure was later confirmed by x-ray diffraction as I, Figure 4. This paper has attempted to show that the ebulliometric method can be used successfully for the routine determination of molecular
8 POLYMER MOLECULAR WEIGHT METHODS weights and in special problems. It still presents some worthy challenges and some opportunities of a theoretical nature. Literature Cited 1. Glover, C. Α., Stanley, R. R., Anal Chem. (1961) 33, 477. 2. Ray, Ν. H., Trans. Faraday Soc. (1952) 48, 809. 3. Lehrle, R. S., Majury, T. G., J. Polym. Sci. (1958) 29, 219. 4. Schön, K. G., Schultz, G. V., Z. Physik. Chem. (Frankfurt am Main) (1954) 2, 197. 5. Ezrin, M., Eastern Analytical Symposium, Symposium on Molecular Weight Measurements, New York, 1962. 6. Dimbat, M., Stross, F. H., Anal Chem. (1957) 29, 1517. 7. Lehrle, R. S., "Progress in High Polymers," Robb, J. C., Peaker, F. W., Eds., pp. 57-61, 1961, Academic Press, New York. RECEIVED January 17, 1972.