effect due to slight evalioration of the sample on warming i n d e the spectrograph. ACCURACY AND PRECISION
Tables I11 and IV gire typical comparisons for single u-ray and chemical determinations of iron and chromium in iron-chromium alloys and chromium ore. The accuracy of the determination of iron, chromium, and manganese in other materials is indicated by the lack of scatter of solution sample points on the various figures. Table T’ shows the precision of m e a s u r ~ n i ~ noft the ratio of the control
element to the elements being determined for a steel sample. Fresh aliquots of the sample were taken for each reading. Complete details of solution saniple preparation and the calibration systems may be obtained from the mthors upon request. ACKNOWLEDGMENT
The authors are grateful to members of the Technology Ainalytical Laboratory, without whose careful chemical analyses of the many samples used for standardization and comparison this work would not have been 110ssihle.
LITERATURE CITED
Adler, I.. Aselrod, J. >I.,Spectrochir?i. Acta 7, 91 (1955). ( 2 ) Andermann, George, Kemp. J . ASAL. CHEX 30, 1306 (1958). (3) Campbell, L., Thatcher, R., U. 8. Bur. Mines, Rept. Invest. 5497 (1959). (4) Houk, W. W.,Silverman, L., AXAL. CHEK 31, 1069 (1959). (5) Jones, R. W., Ashley, R. W., Ibid., 31, A629 (1959). (6) Mitchell, B. J., Ihzd., 32, 1652 (1960). ( 7 ) Palen, T’ern W.,Atom Industry 9, 8 (1960). (8) Sherman, J., Spectrochzm. A c t a 7, 283 (1955). RECEIVEDfor review June 7 , 1962. $ccepted September 6 , 1963. International Spectroscopy Colloquium, College Park, >Id., June 1962.
(1)
Determination of Molecular Weight of Polyethylenes with an Oscillating Ebulliometer J. E. BARNEY, Ill and W. A. PAVELICH Research and Development Department, Spencer Chemical Co ., Merriam, Kan.
b Number-average molecular weights of polyethylenes and polyethylene fractions up to 20,000 have been determined with an improved oscillating ebulliometer. The major refinements in the apparatus include the use of highly sensitive thermistors in a sensitive Wheatstone bridge circuit and better control of temperature to minimize thermal gradients. Sensitivity of the method i s =k0.00002” C.; it is limited b y long-term temperature drift and short-term nonuniform heat dissipation b y the thermistors. The upper limit o f number-average molecular weight that can be measured i s set b y superheating of the polymer solution. Studies on seven pure compounds of molecular weights from 150 to 900 indicate that the ebullioscopic constant varies with molecular weight. N o reason is proposed for this phenomenon.
T
o D E V E L O P polyethJ-lenes with improved physical properties, such as higher film strength. better film clarity, and improved stress-crack resistance, it is necessary to understand holv these properties are affected by changes in polymer composition. Among the ways b y which the composition of polyethylene may be studied is the nieasurement of its number-arerage molecular weight, AV,l. This quantity is especially useful in conjunction with the weightPresent address, llidwest Research Institute, Kansas City 10, 310.
-vu,
the d&gn to permit greater temperaaverage molecular weight, for obture stability, and b y using highly sentaining a measure of the breadth of the sitive thermistors in a sensitive Wheatmolecular weight distribution of both stone bridge circuit to give greater low and high density polyethylenes, and sensitivity. This apparatus was then in characterizing fractions, used to determine the ,Vn’s of some Methods for determining the -Vnof polymers have been fully described ( 7 ) . whole polyethylenes and fractions. After this study was completed, Ezrin Those applied to polyethylene include ebulliometry (2, 8, 13, 14, 16, 18) cryand Claver ( 8 ) described the application of this ebulliometric method to the deteroscopy ( I ) , and osmometry (19). The mination of -V,,’s for poly(viny1 chloride) first two are generally useful up to and poly(styrenema1eic anhydride) beX n ’ s of about 30,000 while the latter is usually applied to polymers of IT,, low 10,000, and for an anionic polystygreater than 20,000. It 1%-as the purpose rene of 25.000. of this investigation to develop a reliable method that mould be generally EXPERIMENTAL applicable to whole polyethylenes and The general plan of the complete < 30,000. fractions of ebulliometer is shown in Figure 1. I n After examination of technique> useful mechanical design, it differs from for measuring colligative properties of Schon and Schultz’s apparatus: The solutions of polymers in this _tl, range, oil bath is self-contained (the oil does ebulliometry was selected for further not have to circulate externally t o the bath), only a small amount (about 10%) study. Cryoscopy was rejected priof the heat input is controlled through marily because polyethylene tends t o a relay to minimize thermal gradients oxidize under the experimental conin the oil bath, and a small fan is ditions required. The primary limimounted in the air bath to minimize tation of ebulliometry was the necessity thermal gradients in the air both. Kithof using complicated, fragile, glass out these modifications, temperature ebulliometers. such as the ekgant, instability was not good enough to permit genious device described b y Blackmore measurements of M,’s above 5000. (6). Horvvever, the oscillating ebulliomOperating conditions for the ebulliometer are: shaking rate, 180 to 260 eter of Schon and Schulz (17) for the cycles per minute; volume of solvent, 5 determination of the .Vnof polystyrenes ml.; float temperature, 0.2” C. above and polymethacrylates, in R hich boiling boiling point; bridge current, 0.50 ma.; is maintained without ebullition, for RC constant, 2 seconds. Too low a shakwhich no Cottrell pump is required and ing rate permits excessive superheating, which is simple to fabricate, offered while too high a rate decreases the promise. signal-to-noise ratio. The smaller the Consequently, a n ebulliometer was volume of solvent, the greater the constructed that makes use of this novel signal-to-noise ratio as long as the principle. It was improved b y refining thermistor well is co1-ered a t all times.
-v,&
VOL. 34, NO. 12, NOVEMBER 1962
1625
Figure 1. eter
Detailed view of ebulliom-
A. Fan, tube cooling type, Barber-Colman Model DYAB 61 67-1 B . Thermometer, precision type, 100' to 200' C. range C. Shaking device: brass holder for ebulliometers and aluminum connecting rod, coupled to 3-inch shaft fltted with sleeve bearings and 1-pound tly-wheel, driven b y Stanco Type CA-2 variable speed stirrer D. Ebulliometers (Figure 2), with 10/30 joints, fltted with stoppers containing capillary openings E. Circulating pump, American Instrument Co. Model 4-603 P, fltted with 90' elbow on, outlet side to deflect oil stream downward F. Thermoregulator, Precision Micro-set G. Aluminum foil H. Fiberglas, 1-inch batting 1. Glass [or, cylindrical, 16-inch diameter by 12-inch heiaht 1. Silicone ail, Low Corning Type 550, or G.E. SF-81 (501 .. -, K. Stainless steel 4-liter beaker 1. Continuous heater, immersion type, copper sheath, 500 watts M. Intermittent heater, immersion type, copper sheath, 200 watts N. Flexible hose, auto heater type, 2-inch diameter - . I -
permitted use of higher bridge currents. A block diagram of the electrical circuit, plus details of the bridge circuit and the filter circuit, is shown in Figure 3. Use of thermistors as sensors in ebulliometers has been treated thoroughly by Blackmore (2-6) and by Kilson, Bini, and Hofstader (20). The circuit used in this apparatus follows closely that described by Neuniayer ( 1 4 ) . Extensive studies were carried out to determine the optimum operating current for the bridge circuit. The optimum thermistor current could not be calculated by conventional methods because the dissipation constant for the thermistor, potted in the alloy, was not known. Maximum signal-to-noise ratio was obtained when 0.50 ma. was indicated on the milliammeter in the bridge supply circuit. This current jyas achieved by using the rheostat on the Sorensen power supply as a coarse control and the 10,000-ohm Micropot as a fine control. The bridge circuit was normally balanced by setting Helipots R1 and RI* to nearly the same value and adjusting Rz. If the Keithley 150A amplifier is used, its "Zero Suppress" controls may also be used for this purpose. RIA usually equaled R1 Rz, as the thermistors were matched within 1% by the manufacturer at the temperature used. Circuit values for the filter circuit were also selected to produce the maximum signal-to-noise ratio. Because both Keithley amplifiers have outputs of 0 to 10 volts, the large time constant (2 seconds) could be employed very effectively. The Sargent SR recorder was fitted with a 1:lo0 input voltage divider and the 0- to 100-mv. variable range attachment supplied by the manufacturer. The latter was adjusted to provide 100 mv. full scale when a calibrated, 10-volt signal was
+
Figure 2. eter
Detailed view of ebulliom-
A. Glass tubing, 7-mm. i.d. 8. Fabricated from 2 5 4 . round bottom nark
C. Approximate liquid level D. Smallwell E. Wedges of wood splints F. Thermistors VECO Type TX 143, R = 100,000 ohms at 25' C., Victory Engineering Co., Union, N. J. G. Alloy of 2 0 parts Bi, 40 parts Pb, 40 parts Sn, m.p. 145' C., to fill well
fed across the input of the filter circuit. Variable ranges could then be obtained on the recorder with the stepping switch on the Keithley amplifier. This arrangement made full use of the excellent stability and low noise level of the amplifiers to permit a high level of flexibility. Use of the filter circuit increased the signal-to-noise ratio bv about 50%. The sensitivity of the ebulliometer a t the boiling Doint of toluene was estimated b y measuring the bridge unbalance in ohms that mould produce an output signal of 0.005 mv., the smallest difference that could be measured. I
TEERMISTOR 1506 OR 151 AMPLIFIER
Because the system is open to the atmosphere, the optimum float temperature is dependent on the atmospheric pressure. One may change this temperature as the pressure changes, or operate a t a temperature which is optimum for the highest barometric pressure t o be encountered. Most of the results reported here were obtained at 110.4' C., although during periods of high atmospheric pressure, the ebulliometer was operated a t 110.8 C. A detail of the mounting of the thermistors is shown in Figure 2. Dimensions do not appear t o be critical. hlercury may be used in place of a lowmelting alloy, but lower signal-to-noise ratios are obtained a t higher shaking rates because the thermistor tip is not held rigidly. Wood splints (replaced as they dried out) prevent wobbling of the upper section of the thermistor. Teflon splints have also been used. Use of the bismuth-tin-lead alloy as a heat transfer medium instead of silicone oil increased the signal-to-noise ratio because the larger dissipation constant
1626
ANALYTICAL CHEMISTRY
SR RECORDER
SEE DETAIL 2
SEE DETAIL I
'
RIP
AMPLIFIER
1-
Figure 3.
RECORDER
DETAIL 2
Block diagram of electrical circuit
Nobatron, Sorenson Model Q6-2 Capacitors 1 mf. M. Milliammeter, 1 ma. full scale Helipots 1 0-turn 5000 ohms R1. RIA. RP. Helipat 40-turn 100 ohms Ra. Micropot 1 0-turn 10,000 ohms %. Resistor, 1 megohm S. Switch, SPST T,I Tz. Thermistors, VECO TX 143, 100,000 ohms at 25' C. matched within 1 % a t 1 10' c.
B.
C.
This resistance was then converted to degrees Centigrade by use of the resistance-temperature curves supplied for the thermistors by the manufacturer. h recorder trace illustrating the sensitivity of the ebulliometer is shown in Figure 4. This trace was obtained while measuring the ebullioscopic constant; it represents a typical noise level. Under the conditions of operation set forth above, the sensitivity was 10.000020” C. Sensitivity was limited both b y long-term temperature drift and by short-term noises apparently produced by nonuniform heat dissipation from the thermistors. It compares favorably with 10.00003° C. reported by Blackmore (6) and 10.00002 by Lehrle and Majury (12) for thermistors; and with ~ 0 . 0 0 0 0 3 ” C. by Glover and Stanley (10, 11), and =k0.00015° C. b y Smith (18), for multijunction thermocouples. Our apparatus is similar to that described by Ezrin and (:laver (8),except for the method of heating; use of a steel inner container rather than glass; use of the external flexible hose and reciprocating shaker, after the manner of Schon and Schultz, rather than a vibrator; operation a t atmospheric pressure rather than a t constant pressure; and use of a n improved thermistor bridge circuit and high-gain amplifier. Use of a pressure-regulating device would h a r e permitted operation at a single float temperature. but i t was felt to be a n unnecessary complication. I n our thermistor bridge circuit the matched thermistors are placed in separate arms which do not contain any other resistance, hence, as shown by Blackmore (67, when the thermistors are matched so that their constants are equal, the output is independent of pressure, even when the bridge is slightly off balance. This latter conclusion was borne out by determining the ebullioscopic constant with zone-refined dotriacontane during periods when the atmospheric pressure varied as much as 30 mm. I n no instance did the ebullioscopic constant vary more than 1%. Furthermore, the ebullioscopic constant did not vary more than 1% over periods of 6 months, even when the thermistors were changed. Thus calibration needed to be carried out only rarely. PROCEDURE
T o calibrate the ebulliometer or determine a M n ,from 5 to 10 pellets of the sample are prepared with a l / 8-inch diameter pellet press or cut off the specimen with a clean razor blade. The ebulliometer is rinsed with 10 to 15 ml. of redistilled, reagent-grade toluene added with a 5-ml. hypodermic syringe fitted with a 6-inch S o . 17 stainless steel needle. The toluene is wmoved by suction using a long capillary tube. With the same syringe, 5.00 ml. of redistilled, reagent-grade toluene is added to both ebulliometers, and they are permitted to attain thermal equilibrium. The bridge circuit, amplifier, and recorder are adjusted t o provide the correct range arid zero reading.
Figure 4. Recorder trace sensitivity of ebulliometer
showing
The sample is then added incrementally to the sample ebulliometer, each succeeding pellet being added after temperature equilibrium has been attained. Equilibration will require only a minute or two during calibrations, but i t may require as long as 45 min. for polymers that are not readily soluble in toluene-Le., high density polyethylenes, or low density polyethylenes with low methyl branching. After a run has been completed, the polyethylene solution is removed by suction, and 10 to 15 ml. of toluene is added immediately to rinse the ebulliometer. It is convenient to add the toluene to the sample ebulliometer a t the end of a working day if possible, so that thermal equilibrium may be established overnight. The toluene in the reference ebulliometer need be changed only occasionally, as it is not lost a t any appreciable rate. Several methods are used to calculate the ebullioscopic constant, j, or the number-average molecular weight M,. If the graph of AE, in millivolts, vs. weight, w,in milligrams, fits a straight line, the slope of the regression line through the data points is calculated by standard methods, and j or M , is evaluated from the equation
small added weights of polyethylene. I n this event, the slope S is plotted as a function of w (18), and the slope a t w = 0 is evaluated graphically. A precise approach, although it depends on t h e judgment of the analyst, involves construction of a smooth curve through the data points, using values of AE and w read off this smooth curve to construct a graph of slope us. weight of added polymer, and evaluation of the slope a t w = 0 b y extrapolation. This technique permits observation of the deviations described below; i e h a s been used to obtain most, of the X n ’ s presented in this paper. RESULTS AND DISCUSSION
This apparatus was used t o obtain the
Li7n’s of seven whole polyethylenes and five fractions, and to study the variation of the ebullioscopic constant, j , with molecular weight, as reported b y Glover and Hill (9). The latter study was made possible b y the excellent precision obtained with the apparatus. Number - Average Molecular Weights. T o test t h e precision of t h e
method a n d t o determine t h e upper limit of Xn’s that could be measured, the iVn’sof seven whole polyethylenes and five fractions were determined. The whole polyethylenes represented a range of low density polyethylenes plus one experimental high density polyethylene. The fractions were obtained by a modified coacervation technique flj) which yielded fractions of reasonably narrow molecular weight distributions. Results are shown in Table I. All these W,’s were calculated usin, zonerefined dotriacontane for calibration. Precision of the duplicate analysis was considered satisfactory. Accuracy of
where
m
=
a
S
= =
Ain
= mol. wt. of polymer
A
=
mol. wt. of solvent grams of solvent slope of regression line =
AE/w
21.26, for 5.0 ml. of toluene
If the data points fit a straight line except for the initial points, for reasons discussed below, a straight line is drawn through them, and the slope S , is evaluated graphically. B, is calculated from Equation 1. If_ the data points fit a smooth curve, M n may be calculated b y fitting the points to a quadratic regression curve of the form (7)
where cr =
instrument constant
/3 = first coefficient in the Margules
series for activity coefficients (7) Often however, the data points show deviations from a smooth curve at
Table 1. Number-Average Molecular Weights of Some Whole Polyethylenes and Polyethylene Fractions
an
Sample Spencer experimental 5,400 polyethylene A 18,400, 17,500 Tenite lOOlF Spencer experimental 12,700 polyethylene B 10,100 Bakelite DYNH-3 Spencer experimental high-density poly3,800, 1,100 ethylene C 12,100, 13,500 “Poly-Eth”a 1008 5 “Poly-Eth” 1008 5 , 3 920 fraction 1 “Poly-Eth” 1008 5 , 9,200 fraction 2 “Poly-Eth” 1008 5, 19,100 fraction 3 Spencer experimental 10,800, 9,400 polyethylene D Spencer polyethylene D. fraction 1 4,400 Spencer polyethylene D, 9,100 fraction 2 a Trademark of Spencer Chemical Co.
VOL. 34, NO. 12, NOVEMBER 1962
e
1627
-53'0
W, MG.
Figure 5. Theoretical and experimental boiling-point-elevation curves A. Experimental 8. Theoretical
the results map be estimated by comparing the L ? n obtained for D Y S H - 3 with the value of 9000 reported ( I S ) . Based on this one sample. the accuracy appears to be comparable to the precision. Appearance of Boiling-Point Elevation Curves. Tn o experimental phenomena affect both t h e precision (and accuracy) of the method and t h e upper limit of Apn'sthat can be measured. If Equation 2 were obeyed for experimental boiling point elevation curves, a curve similar to B in Figure 5 would be obtained. The amount of currature would depend on the relative values of the termq
With this apparatus. the curves that are olltained have the general shape of curve A in Figure 5 . The deriations at low signals usually disappear above a concentration of 2 mg. per nil.; they have been observed previously in Cottrell-
pump ebullionieters by Smith (16). He has attributed this behavior to the adsorption of polyethylene a t the surface of the boiling solution. His analysis was based on the formation of foam which would yield a liquid of concentration higher than the original bulk concentration. The shaking mechanism, with a glass inner container and a lighted peephole, did not reveal the formation of any foam when from 5 to 10 ml. of solvent was in the ebulliometer. Ezrin and Claver ( 8 ) reported the presence of foam in this type of ebulliometer when 10 ml. of solvent was used, although they did not specify the type of polymer or solvent. Most probably the formation of foam in their ebulliometer was intensified by the type of shaking they employed. If the polymer tends to concentrate in the surface layer at low concentrations, even without foaming, its fugacity n-ould increase, and the observed boiling point elevation would be greater than calculated from the bulk concentration. Attempts to eliminate the phenomenon by pretreating the ebulliometer with polymer solution, as recommended by Glover and Stanley (IO),were not successful. The deviations a t large signals appear to be caused by superheating of the polymer solution due to an increase in viscosity. Onset of superheating is governed by the float temperature, shaking rate, the molecular weight of the polymer, and its molecular weight distribution. The float temperature is normally set as close to the boiling point as possible to minimize these deviations. Shaking rate is set as fast as possible consistent with optimum signalto-noise ratios. When high molecular weight components are present, con>iderable superheating is observed. I n Figure 6 are shown boiling point elevation curves for a fraction of relatively narrow molecular weight distribution (curve B ) and for a whole polymer, DYXH-3 (curve -4)of broad molecular w i g h t distribution. Both polymers
Table II. Apparent Variation of Ebullioscopic Constant with Molecular Weight Compounds Diphenyl Bnthracene Benzil Tetrachlorotetrahydronaphthalene Glyceryl tribenzoate Dotriacontane Tristearin Tristearin
Level of purity Eastman. Red Label Fisher, Zone-Refined Fisher, Zone-Refined Eastman, Red Label
wt. 154 2 1;s 2 210 2 270 0
1 1 1 1
Eastman, Red Label
404 4
150. 1.50
1.50
Fisher, Zone-Refined
450 9
1 465
Eastman, Red Label Eastman, Red Label, Recryst. from toluene
891 4 s91 4
148, 147 1 455, 1 455 1 30, 1 29
~~
1628
Mol
ANALYTICAL CHEMISTRY
j (mv.-I) 5 3 5 , 1 595, 1 550 50, 1 56 535, I 505
1 56 1 53
49, 1.475
1 48
1 3 5 5 , 1 395
*lv.
1 52
1 205 1 375
W,MG
Figure 6 . Boiling point elevation for two polyethylenes of similar curves M,,'s A DYNH-3, M,, = 10,000 B "Poly-Eth" 1008.5, fraction 2,
&,, =
9200
.un,
have nearly the same but the latter shows superheating at lower concentrations because of the presence of high molecular Iveight components. The combination of these two effects limits the utility of the method to -Vzl,'sof 20,000 or less. although the signal-tonoise ratio should permit the measurement of R,,'s as high as 50,000 to 100,000. Superheating was probably not observed by Schon and Schulz because the polymers examined had relatively narrow molecular weight distributions and hence produced litble superheat'ing for belov 20,000. Examination of Figure 6 rereals that curvature is more ~ironouncedfor the n-hole polymer of broad molecular weight distribution than for tlie fraction of relatively narron- tliat,rihution. This difference n-as noted consistently throughout these ctudies. The more narrow the niol~cular weight distribution, the less the curvature. It appears t,o be related to tlie coefficient p in Equation 2 . The lattrr should more accurately he n-ritten a. -?$,,Is
for polydisperae -!-stem- n lierein p increases as the molecular weight increases. Hence a greater contribution from the quadratic term viould be expected as the niolecular weight increases. Variation in Ebullioscopic Constant with Molecular Weight. -4 critical study of the variation in j with molecular Tveight a. reported b y Glover and Hill (9) was carried out in toluene on pure compounds representing a variety of mdecular types. One compound was analyzed a t two different levels of purity. Results are shown in Table 11. Clearly, j decreases with increasing molecular weight, regardle- of molecular type,
and the difference between the j ' s for diphenyl and for recrystallized tristearin is significant a t the 95y0 confidence level. Thus, one of two conclusions must be drawn: the ebullioscopic constant in toluene varies n-ith molecular weight, or the purity of the compounds decreases with increasing molecular weight and the ebullioscopic constant is a true constant. The latter conclusion u-ould fit the observed deviations in j if the compounds were contaminated with impurities of lower molecular weight. However, as the compounds used were all of high purity, it is most probable that j does vary with molecular weight, a t least in toluene. No reasons are proposed for the deviation.
more widespread usage for the determination of molecular weights of compounds of lower molecular weight. I n these applications, the amplifier on the recorder could be used, thus reducing the expense. Several approaches to increasing the usable upper molecularweight limit are being studied, such as new schemes for agitating the solution t o minimize superheating and use of thermistors of higher sensitivity.
CONCLUSIONS
(1) iishley, C. E., Reitenour, J. S.,Hammer, C. F., J . A m . Chem. Soc. 79, 5086
Although this method suffers two limitations. one of them common t o other ebullioscopic methods, that limit its usefulness for polyethylenes to X,'s of 20,000 or less, i t offers the advantage of simplicity of construction and ease of operation. Because of the speed and accuracy of the method. it should find
ACKNOWLEDGMENT
The assistance of N. Scarritt, Jr., in designing and assembling the ebulliometer is gratefully acknowledged. LITERATURE CITED
(1957).
W.R., Can. J . Chem. 37, 1508 (1959). (3) Blackmore, W.R., Can. J . Phys. 37, 1365 (1959). (4) Ibid., p. 1517. (5) Ibid., 38, 565 (1960). (6) Blackmore, W. R., Rrv. Sci. Instr. 31, 317 (1960). ( 2 ) Blackmore,
(7) Bonner, R. V., Iliinbat, M., Stross, F. H., "Sumber-Average Molecular Weights," Interscience, 4ew Tork, 1958. (8) Ezrin, If.,Claver, G. C., Abstracts, 141st Meeting, .4CS, Washington, D. C., March 1962. (9) Glover, C. -4..Hill, C. P., ANAL. CHEV.25, 1379 (1953). (10) Glover, C. -4., St,anley: R . K., Ibid., 33, 447 (1961). (11) Ibid., p. 477. (12) Lehrale, R . S.. hlajury, T. G., J . Polymer Sei. 29, 919 (1958). (13) Morawetz, H . . J . Polymer Sci. 6, 117 (1951). (14) Xeumayer, J. J., .4nul. Chim. Acta 20, 519 (1960j. (15) Nicholas, L.,.Ilokromol. Chem. 24, 173 (1957). (16) Ray, S . H., Trans. Faraday SOC.48, 809 (1952). (17) Schon, I
