2348
R. CHIANG
Temperature Coefficient of the Unperturbed Dimension of Linear Polyethylene from Intrinsic Viscosity Measurements in e Solvents
by R. Chiang Contribution No. 963 from the Chemstrand Research Center, Inc., Durham, North Carolina (Received February 7, 1966)
Intrinsic viscosity measurements have been made on polyethylene fractions in various 8 solvents, biphenyl, diphenylmethane, diphenyl ether, octanol-1, decanol-1, and dodecanol-1 at 127.5, 142.2, 161.4, 180.1, 153.3, and 137.3", respectively. The linear relationship between [?]e and M"z for polyethylene in diphenyl ether previously observed appears to be valid in all the 8 solvents investigated, the proportionality constant K ([.?le = KM"' with [ q ] ein dl g-') being equal to 3.23, 3.15, 2.95, 2.86, 3.02, and 3.07 X at the respective 8 temperatures. The temperature coefficient, d In (r2)o/dT X lo3 of the unperturbed dimension calculated from the intrinsic viscosities in biphenyl and diphenylmethane is - 1.16 f 0.5, in agreement with the results obtained by Nakajima, et al.; the same quantity calculated from the intrinsic viscosities in the higher alcohols is - 1.19 f 0.2 deg-l. One of the most striking features of the results reported here is the small difference between the alcohols on the one hand and the aromatic hydrocarbons on the other. The close similarity seems to indicate rather clearly that specific solvent effects for this nonpolar polymer must be quite small. The temperature coefficient values obtained here are essentially identical with those obtained by stress-temperature measurements (- 1.16 f 0.10) and by intrinsic viscosity measurements in athermal solvents (-1.2 f 0.2). We are led to conclude that the results obtained with the three independent methods are consistent.
Introduction
measuring the intrinsic viscosities directly in different
The determination of the unperturbed dimension of polyethylene and its temperature coefficient has been a subject of interest in recent Comparison of experimental results with theoretical calculations yields valuable information on the conformation and internal rotation of the polymer chain.h6 As is known, the temperature coefficient has been successfully determined by the stress-temperature coefficient of a cross-linked network' and by the temperature coefficient of the intrinsic viscosity [q] of the polymer in athermal solvents.8 Recently, close agreement between the values of the unperturbed dimension obtained by intrinsic viscosity measurements in athermal solvents (with appropriate corrections for the excluded volume effect) and by direct measurements in a e solvent (diphenyl ether at 161.4") has been achieved.9 One may be inclined to think that the temperature coefficient can be determined by
0 solvents a t the respective 8 temperatures by making
The Journal of Physical Chemistry
use of eq 1 _ d In_ (r2)o _ _ - d 1x1 l ~ l e
dT
-
"3
___ dT
(1)
where (r2)ois the unperturbed mean-square end-to-end distance. However, careful examination reveals that (1) See, for example, M. V. Volkenstein, "Configurational Statistics of Polymer Chains" (English transl), Interscience Publishers, Inc., New York, N. Y., 1963. (2) P. J. Flory, C. A. J. Hoeve, and A. Ciferri, J . Polymer Sci., 34, 337 (1959). (3) P. J. Flory, Proc. Natl. Acad. Sci. U.S., 51, 1060 (1964). (4) C. A. J. Hoeve, J . Chem. Phys., 3 5 , 1266 (1961). (5) K. Kagai and T. Ishikawa, ibid., 37, 496 (1962). (6) P. J. Flory and R. L. Jernigen, ibid., 42, 3509 (1965). (7) A. Ciferri, C. A. J. Hoeve, and P. J. Flory, J. Am. Chem. SOC., 83, 1015 (1961). (8) P. J. Flory, A. Ciferri, and R. Chiang, ibid., 83, 1023 (1961). (9) R. Chiang, J . Phya. Chem., 69, 1645 (1965).
DETERMINATION OF TEMPERATURE COEFFICIENT OF POLYETHYLENE
this direct procedure is not as simple as it may seem to be. In the first place, the temperature coefficient of [?]eto be determined is very small, usually much smaller than that of [q] itself near the 9 point; an error of 1-2” in the 8 point, which is not unlikely, will introduce an appreciable error in the final value of d In (r2)o/dT. Even more bothersome is the fact that the solvent used plays an important role in determining the unperturbed dimension of the polymer chain (the so-called specific solvent The specific solvent effect, though small, may easily be sufficient to invalidate the calculation. Thus Schulz and Baumannls obtained the temperature coefficient for polystyrene in various solvents with no definite correlation, and Abe and Fujita,14 studying the effect of mixed solvents, reached the conclusion that the temperature coefficient can be positive, negative, or zero, depending on the values of the energy parameter K ~ . Orofino and Ciferri’5 were the first to obtain the temperature coefficient for polystyrene in agreement with the stress-temperature value by limiting their intrinsic viscosity measurements in 1-chloro derivatives of hydrocarbons with similar chemical structures. In the case of polyethylene, Nakajima, Hamada, and Hay ashi16 have determined the intrinsic viscosities in three different solvents, biphenyl, diphenylmethane, and diphenyl ether, and found that the temperature coefficient calculated from these three [v ] e values is in excellent agreement with the values obtained by stresstemperature measurements and by intrinsic viscosity measuremcnts in athermal solvents. However, no reference was made to measurements in other solvents, nor to the possible influence of the specific solvent effect on the calculated value of the temperature coefficient of the unperturbed dimension. Thus any specific solvent effects would not have been revealed in their investigation. In the present study, we are primarily concerned with this effect and therefore determined the intrinsic viscosities of polyethylene in different series of 8 solvents for the purpose of (1) obtaining more data to check our previous intrinsic viscosity [q]e obtained in diphenyl ether;g (2) determining the specific solvent effect, if any; and (3) confirming, in a definitive manner, the value of the temperature coefficient obtained by other method^.^^^ Polyethylene, the simplest member in the polymer family, is of particular interest because its unperturbed dimension has been treated most extensively. It is also the most nonpolar polymer whose dimension should be least affected by the solvent. The 8 solvents used here belonged to three different homologous series, each with great similarities in chemical structure, and hence in physical properties such as dipole moments,
2349
cohesive energy densities, etc., which might affect the dimension of the polymer. The 8 solvents included (1) aromatic hydrocarbons (biphenyl and diphenylmethane), (2) diphenyl ether, and (3) higher alcohols (octanol-1, decanol-1, and dodecanol-1). The Flory 8 points for the respective solvents are taken from the paper by Nakajima, et al.1’ The values in biphenyl and dodecanol-1 reported by these authors are in agreement with the corresponding values obtained by Stacy and ArnetP and the value in diphenyl ether is in agreement with that reported by Chiang.g All of the above 8 points were obtained by the liquidliquid phase separation technique first developed by Shultz and F10ry.l~ Scholte and KoningsveldlZ0on the basis of the light scattering results, confirmed Nakajima’s result of 127” as a correct 8 temperature for polyethylene in biphenyl.
Experimental Section Polymer Samples. The samples used here were fractions separated from Marlex 50 and most of them were used in our previous studies.9 Characteristics of the fractions are given in Table I. Solvents. All of the solvents were obtained from the Eastman Kodak Co. and used without further purification. Since polyethylene is sensitive to oxidation a t elevated temperatures, it is imperative to protect the polymer during measurements by the addition of a stabilizer and rigorous exclusion of air. In the experiments reported here phenyl-fl-naphthylamine used as a stabilizer was introduced a t room temperature at a concentration of 0.2% into the solvent. In order to decompose any peroxides originally present, the solvent was first saturated with nitrogen, then heated to a (10) K. J. Ivin, H. A. Ende, and G. Meyerhoff, Polyner, 3, 129 (1962). (11) V. Crescenzi and P. J. Flory, J. Am. Chem. SOC.,86, 141 (1964). (12) T.A. Orofino and J. W. Mickey, Jr., J. Chem. Phys., 38, 2512 (1963). (13) G. V. Schule and H. Baumann, Makromol. Chem., 60, 120 (1963). (14)M.Abe and H. Fujita, J. Phys. Chem., 69, 3263 (1965). (15)T.A. Orofino and A. Ciferri, ibid., 68, 3136 (1964). (16)A. Nakajima, F. Hamada, and S. Hayashi, paper presented at the joint U. S.-Japan Symposium on Polymer Physics, Kyoto, Japan, Oct 1965. (17)A. Nakajima, H. Fujiware, and F. Hamada, “Phase Relation-
ships and Thermodynamic Interactions in Linear PolyethyleneDiluent Systems,” J . Polymer Sci., in press. The author is indebted to Prof. Nakajima and his co-workers for allowing him to use their results. (18) C.J. Stacy and R. L. Arnett, J. Phys. C h a . , 69, 3109 (1965). (19) A. R. Shulte and P. J. Flory, J . Am. Chem. SOC.,74, 4760 (1952); P. J. Flory, “Principles of Polymer Chemistry,” Cornel1 University, Ithaca, N. Y.,1953. (20) Results cited by A. Opschoor, Makromol. Chem., 85, 249 (1965).
Volume 70, Number 7 July 1966
R. CHIANG
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Table I : Polymer Fractions
Fraction no.
VII-1 VII-2 VIII-4 VI114 VIII-I3 YIII-7 TIII-8
IX X
[71 in deoalin at 1 3 5 O , dl g-1
QWx 10-8
0.530 0.618 0.936 1,055 1,445 1.885 2.13 3.80 9.85
(15.4)' 21.9 35.6 (41.2) 74.4 (94.7) 126 299 1035
Numbers in the parentheses are calculated from the equaii?,O.'O. tion, [ q ]136deI.a1in = 6.2 X
temperature a few degrees above the temperature required for the viscosity measurement. Bubbling of nitrogen was not interrupted until the solvent had cooled down to room temperature. Under no conditions was the polymer or the solvent allowed to come in contact with air at evelated temperatures. Specific volumes used to calculate the concentrations in grams per deciliter were measured pycnometrically. Viscometry. Viscosities were measured a t the respective 9 temperature with a modified CannonUbbelohde dilution viscometer, the construction of which has been described previously.s A coarse sintered glass filter was fitted in the viscometer to remove any extraneous insoluble material before the solution was allowed to come into the capillary. Viscometers with appropriate capillary sizes were used; flow times, measured to the nearest 0.1 sec, were 169.10, 151.02, 131.72, 110.58, 181.48, and 161.30 sec for biphenyl, diphenylmethane, diphenyl ether, octanol1, decanol-1, and dodecanol-1 at the corresponding 9 temperatures. Solutions were prepared by introducing measured quantities of the polymer and the solvent into the viscometer. Concentrations of the solutions were so adjusted that the specific viscosities ranged from 0.08 to 0.40. To exclude traces of air, the viscometer was operated wider a slight positive pressure of nitrogen. The procedure of degassing, dilution, and measurement has been described previously.s Special attention was given to the preparation of uniform solutions, rigorous exclusion of air, and proper alignment of the viscometer. In the absence of air, polyethylene is very stable. One sample, for example, heated in dodecanol a t 200" for 1 hr, 190" for 2 hr, and maintained at 150" overnight, showed no sign of change in viscosity. Failure The Journal of Physical Chemistry
to exclude oxygen often yielded abnormally high viscosity. Possibly, the polymer radical combines with another radical (or molecule), forming a polymer with molecular weight higher than the original polymer. Loss of solvent by evaporation presents a problem a t elevated temperatures since octanol, bp 194", has an appreciable vapor pressure a t 180" and biphenyl tends to sublime somewhat. However, the specific viscosity obtained on each solution by successive dilution and by the use of a fresh solution at the corresponding concentration did not exceed 1% and the solution upon standing overnight did not show change in flow time. Thus under the experimental conditions the amount of solvent lost was negligible.
Results and Discussion Since the temperature coefficient of the intrinsic viscosity of polyethylene is very small, in the neighborhood of - 1.8 X deg-l, intrinsic viscosities must be determined with a high degree of accuracy. To optimize the conditions of measurements, the temperature range over which the measurements are carried out should be as wide as possible and the temperature coefficient of the intrinsic viscosity near the 8 point should be small. Using samples of high [ q ] helps somewhat, but the advantage is offset by the weighing error of the small size of the sample and by the difficulties of dissolving the high molecular weight material. Among all the solvents studied, higher alcohols seem to best meet the above requirements. It is important to note that the temperature coefficient of the intrinsic viscosity near the 8 point is relatively small; for example, the temperature coefficient, d In [q]/dT, is approximately 0.0021 deg-l in dodecanol as compared to 0.0070 deg-l in diphenyl ether. Thus, an error of 2' in e point results in an error of 0.4% in [71e when measured in alcohols, as compared to 1.40/, in diphenyl ether. Everything else being equal, this three- to fourfold reduction in d In [q]/dT of the polymer near the 9 point in alcohols will make the error in d In (r2)o/dT tolerable even if we have an experimental error of 2" in locating the true 9 point. Intrinsic Viscosities in Dodecanol-1 at Its 9 TemperaTable 11: Viscosity Data on Polyethylene Fractions in Dodecanol-1 a t 137.3' k in eq 2
0.621 0.945 1.060 3.13
0.70 0.69 0.78 0.63-0.70
DETERMINATION OF TEMPERATURE COEFFICIENT OF POLYETHYLENE
t
+ Dodeconol-I 0
cf 137.3*C6
Diphtnyl d h t r
01
l61.4'C.
Figure 1. Logarithmic plot of [ q ] eagainst M for polyethylene in various 8 solvents. The lines are drawn with a theoretical slope of l/2, illustrating the linear relationship between [?]eand W 2 .
ture. To illustrate the consistency of the results, the intrinsic viscosities obtained on different polyethylene fractions in dodecanol-1 at 137.3' are shown in Table 11. The concentration dependence can be described by the equation %P
- = 1111 C
+
k[r112*6C
The exponent 2.5 of [17] in the second term of eq 2 was adjusted arbitrarily in order to retain the constancy of the value of IC over a wide range of molecular weights. The [rl]e-M"' Relathship. Intrinsic viscosities of various samples determined in diphenyl ether, dodecanol-l, and biphenyl are plotted against the molecular weight (calculated from the intrinsic viscosity measured in decalin a t 135") on a logarithmic scale (Figure 1). The lines are drawn with a theoretical slope of The linearity between [?le and M"' reported previouslyg appears to be valid for all the solvents investigated, the proportionality constant K ( [qIe = KM"' dl g-I) being equal to 3.23, 3.15, 2.95, 2.86, 3.02, and 3.07 X in biphenyl, diphenylmethane, diphenyl ether, octanol-1, decanol-1, and dodecanol-1 a t their respective 8 temperatures. The Temperature Coejicient d En [qIe/dT. I n the determination of the effect of temperature on [77Ie, only one fraction, VIII-7, was used to avoid uncertainties due to sample variations. Results thus obtained are given in Table 111. When [?]evalues are plotted against 0, two lines can
2351
be drawn, one passing through the points for biphenyl and diphenylmethane (line 1) and the other for the higher alcohols (line 2). The two nearly parallel lines obtained are separated by a "gap" of 0.03 to 0.04 in intrinsic viscosity units which exceeds the limit of the experimental error. This seems to suggest that the specific solvent effects commonly observed on polar polymers can also be detected even in the case of polyethylene. It further indicates that the specific solvent effects are minimized by grouping the intrinsic viscosities according to the chemical structures of the solvents. The temperature coefficients d In
