INTRINSIC
VISCOSITY O F LINEARPOLYETHYLENE
IN A
3109
@-SOLVENT
T* wave length. This is compatible with the explanation of the abnormally short wave length of the fourmembered propiolactone in terms of bond angle strain advanced by Closson and Haug. lo According to their interpretation, reduction of the internal angles leads to an increase in the s-character in the u-bond of the carbonyl group, which in turn leads to the shortening of both the U- and T-bonds and thus raises the ?r*-level. This explanation is also compatible with the high energy of the n 4 T* transition observed in cyclobutanone in comparison with the other members of the series. However, this theory fails to explain the lowest n 4 T* transition energy in cyclopentanone. Also, compounds I and I11 would be expected to differ significantly, in the degree of strain, yet their n 4
T * transition energies are experimentally indistinguishable. At the same time, compound IV should be less strained than either I or I11 and does show a lower n + T* transition energy, which is in qualitative agreement with the strain theory. In spite of the preliminary and tentative nature of the correlations presented in this work, they point to the importance of considering excitation energies in the discussion of CIa chemical shifts.
Acknowledgments. The work described is part of the research supported by the National Science Foundation under Grant GP 2644. The authors wish to thank Professor Paul von R. Schleyer for kindly supplying a sample of bicyclooctanone and the Hooker Chemical Co. for a generous gift of hexachlorocyclopentadiene.
Intrinsic Viscosity of Linear Polyethylene in a @-Solvent
by Carl J. Stacy and Raymond L. Arnett Research Division, Phillips Petroleum Company, Bartlemille, Oklahoma
74004 (Received April 8, 1966)
An investigation of critical precipitation temperatures has established the @-temperature for the system, linear polyethylendodecanol-1, at 138” and has estimated @-temperatures for other solvents with the same polymer. The intrinsic viscosity-molecular weight relaX tionship for linear polyethylene in dodecanol-1 at 138” is found to be [ q ] e = 3.16 X Me1’*, where M e (= (M”’),2) is that viscosity-average molecular weight appropriate for @-conditions. The mean-square molecular radius obtained from these measurements is compared with recent theoretical estimates.
I. Introduction
II. Experimental
Unbranched polyethylene as the simplest hydrocarbon polymer is of unique importance to conformation Much attention h a been given recently to its ratio of mean-square radius to molecular weight, as unperturbed by long-range segmentsegment intera~tion,~-~ including estimates from both and However, the experimental values have not included results from intrinsic viscosities measured under @-conditions. It is the purpose of this paper to report such measurements.
Polymers. The linear polyethylenes used in this investigation are whole polymers. Those numbered (1) M. V. Volkenstein, “Configurational Statistics of Polymeric Chains,” Interscience Publishers, Inc., New York, N. Y.,1963. (2) P.J. Flory, “Principles of Polymer Chemistry,” Cornell University Press, Ithaca, N. Y., 1953. (3) M. Kurata and W. H. Stockmayer, Fortschr. HochpolymerForsch., 3 , 196 (1963). (4) C. A. J. Hoeve, J . Chem. Phys., 3 5 , 1266 (1961). (5) K.Nagai and T. Ishikawa, ibid., 37, 496 (1962).
Volume 69,Number 9 September 1966
3110
CARLJ. STACY AND RAYMOND L. ARNETT
1 through 9 in Table I have previously been characterizedS19as to molecular weight. Although they have a relatively broad molecular weight distribution, M,/M, = 11.3, the distribution function (logarithmic normal by number of molecules) is sufficiently well known to allow calculation of the appropriate viscosity-average molecular weights. Polymer 11 is a relatively narrow distribution linear polyethylene'O having the ratio M,/M, = 1.6.
SEBACATE
140
Table I : Intrinsic Viscosity of Linear Polyethylenes in
I
90b
Docecanol-1 nt 138" Polymer
[de
Yw X IO-:
2 1 3 6 7 8 9 11
0.673 0.679 0.726 0.817 0.875 0.827 1.072 1.58
82 92 101 118 122 133 165 317
Me X
10-8
44.7 50.2 55.2 64.4 66.6 72.6 90.0 282.0
@-Conditions. A problem in this investigation was finding a solvent for linear polyethylene with an experimentally accessible @temperature. Obvious criteria (boiling points, chemical stability, etc.) were used to select a list of possible solvents which included those previously suggested as @-solventsfor branched polyethylene (nitrobenzene," amyl acetate," 2-ethylhexyl adipate12). The list was narrowed by preliminary observation of the precipitation temperature of a single polymer sample from a 0.5% solution. 6Temperatures were estimated for several solvents by measuring precipitation temperatures over a concentration range for several molecular weights.I3 Shultz and F10ry14 suggest that, when whole polymers are used in these experiments, the temperature, e, is found by correlating the critical precipitation temperatures with an average molecular weight that lies between M , and Mz, We used M , measurements, which in view of a constant M z / M w ratio for the logarithmic normal dist,ribution will correctly give e at Mw-l'z = 0. Results of phase equilibria measurements on a single sample are summarized in Figure 1. The required amorphous phase separation is confirmed by the wellestablished maxima in the curves. For contrast, a few points for p-xylene are included. This solvent shows only the increasing precipitation temperature with polymer concentration characteristic of crystallization from good solvents.2116 The Journal of Physieal Chemistry
I
10 20 WTX POLYMER
I 30
Figure 1. Summary of phase equilibria data.
The @conditions found by this work are listed in Table 11. The most promising solvents for polymer work, from the standpoint of chemical stability of both solvent and polymer, are biphenyl and dodecanol-1. The viscosity measurements reported here were made using dodecanol-1 at 138". Table I1 : e-Conditions for Linear Polyethylene Solvent
Diphenylene oxide Biphenyl Dodecanol-1 ZEthylhexyl sebacate 2-Ethylhexyl adipate Nitrobenzene Dibutyl phthalate
e, "C. -118 -125 138 150 170 >200 >200
Viscometry. Polymer solutions were prepared in the same manner as for measurements of scattered (6) P.J. Flory, A. Ciferri, and R. Chiang, J. Am. Chem. Soc., 83,1023 (1961). (7) C. A. J. Hoeve and M. K. O'Brien, J. Polymer Sci., A I , 1947 (1963). (8) R. L. Arnett, M. E. Smith, and B. 0. Buell, ibid., Al, 2573 (1963). (9) C. J. Stacy and R. L. Arnett, ibid., A2, 167 (1964). (lo? Sample kindly supplied by Joseph J. Smith, Plastics Division, Union Carbide Corp. See W. L. Carrick, R. W. Kluiber, E. F. Bonner, L. H. Wartman, F. M. Rugg, and J. J. Smith, J. A m . Chem. Soc.. 82, 3883 (1960). (11) See ref. 2,p. 574. (12) L. D. Moore, Jr., J. Polymer Sci., 36, 155 (1959). (13) See ref. 2,p. 547. (14) A. R. Shultz and P. J. Flory, J. Am. Chem. SOC., 74, 4760 (1952). (15) L. Mandelkern, "Crystallization of Polymers" McGraw-Hill Book Co., Inc., New York, N. Y., 1964.
INTRINSIC vISCOSITY OF
LINEARPOLYETHYLENE IN A
light.* Solution concentration was varied by making dilutions of stock solutions in the viscometer. The viscometer is similar to others described in the literature. Provisions were made for dilution, for inert atmosphere, and for two shear rates. The viscometers were rigidly mounted in a stirred silicone oil bath regulated to ~ 0 . 0 1 "near 138". They were cleaned with a filtered solvent and flushed dry with filtered nitrogen. The hot filtered solution was added and manipulated by means of valves so as to be lifted and timed as it flowed between fiduciary marks. Flow times for the solvent were about 100 and 200 sec. for the upper and lower bulbs, respectively. The shear rate dependence of the observed viscosities was quite negligible for the polymers reported here. Relative viscosities (corrected for kinetic energy) were calculated from the measured flow times, t, by means of the expression qr =
t(so1ution) t(so1vent)
3111
@-SOLVENT
where Me is the symbol we give for that particular viscosity-average molecular weight appropriate under e-conditions and SO is the root-mean-square molecular radius. Since Me is the square of the weight average of MI/' and since the relation between M e and M , for our polymers (except polymer 11) is the same as that given by Chiang,'B we have Mw/Me = (Mw/Mn)"4 or Me = MW/(11.3)'I4for polymers 1-9. The values for Me so calculated are listed in Table I. The distribution of polymer 11 is narrow enough to estimate Mw/Me with little error regardless of its distribution form. We aasumed the logarithmic normal form and calculated M e = Mw/(l.6)'" to include in Table I. The second column of Table I was correlated with the fourth by the method of least squares allowing the exponent of Me to be an adjustable parameter. In the fitting each pair of variables was given a statistical weight in accord with the reliability of the determi-
+ C/t(solution) + C/t(solvent)
The constant C wm determined for each bulb in each viscometer.
1.0 .9
In q r C
III. Results and Discussion Treatment of Observations. The quantity, (In qr)/c, was fitted by the method of least squares to the equation2
1
.6
.l
.5
with the polymer concentration, c, in grams per deciliter. Values of k" so determined appeared to scatter in a random fashion, and, since there is no reason apparent for k" to differ among the polymers in thin series, we computed a mean k" weighting each value according to the goodness of fit of the data giving that value. The weighted mean for k" is 0.20 with an estimated standard deviation of 0.05. This numerical value was put back in eq. 1 and [ T ] ww redetermined by the method of least squares for each polymer. These final values of [ q ] are listed in Table I together with appropriate molecular weight data. It is estimated from prior measurements carried out in the same way that the standard error in determination of our intrinsic viscosities is 0.016. Figure 2 displays the fit of (In qr) vs. c with k" constant. There appears to be no significant departure from linearity. Molecular Weight Dependence. The Flory-Fox relation for €)-conditions and polydiaperse polymer can be written [q]e =
KM;";
K = @(6~o~/M)'/*
(2)
0.2
0.1
c g{too ml
0.3
0.4
Figure 2. Determinations of intrinsic viscosity.
20
I
:I 0.3
,
, , 50
I
,
~,
100
,
200
,
300
Me x
Figure 3. Molecular weight dependence of intrinsic viscosity of linear polyethylene in dodecanol-1 at 138'. (16) R. Chiang, J. PoZgmer Sci., 36,91 (1959).
Volumc 68, Number 0 S&er
10.96
3112
nations of [71e and Me.9 The value for the exponent found by this procedure was 0.46 with a standard error of estimate of 0.03. We conclude the exponent does not differ significantly from 1/2. With the exponent set at 1/2 a second least-squares fitting gave the value K = 3.16 X with a standard error of estimate of 0.07 X The data and the second fitted line are shown in Figure 3. Molecular Radius. In order to calculate a molecular dimension from the experimentally determined value of K by means of (2), it is necessary to have B value for the constant, 9. Numerical values of 9 calculated from theory are 2.86 X loz1 and 2.84 X loz1 as quoted by Volkenstein2 for the KirkwoodRiseman theory and Zi” theory, respectively. An experimentally determined value of 9 = 2.5 X 1021 is quoted by McIntyre, et a1.I’ Each of these values is judged to be that appropriate for @-conditions,and each is the value for [71e expressed in deciliters per gram, so in centimeters, and M in grams per mole. Solving (2) for 6s02/M (=(K/@)*”)we find 1.07 X cm.2 mole/g. when the theoretical value of @ is used from the experimental value. The and 1.17 X estimated standard deviation (occasioned by the uncertainty in K ) for each of these values is 0.02 X 10-l6.
Tha Journal of Physical Chemistry
CARLJ. STACY AND RAYMOND L. ARNETT
Hoeve4 has made a direct calculation of 6s02/M for polymethylene taking into account the possibility of additional steric hindrance from certain conformations of adjacent gauche states. His result is given in terms of an undetermined parameter having the meaning of the frequency of occurrence of these adjacent states. The parameter can be ked by forcing agreement between calculation and experiment for the temperature coefficient d In so2/d In T. When this is done using the weighted mean of the observations of Ciferri, Hoeve, and Flory18 (d In so2/d In T = -0.433), the calculated value for 6s02/M becomes 1.133 X 10-l6 cm.2 mole/g. at 160°.19 On using this same temperature coefficient, the calculated value becomes 1.159 X at 138”. Thus, this work coupled with the works of Hoeve and Ciferri, et al., supports the value 2.5 X 1021for 9.
(17) D. McIntyre, A. Wims, L. C. Williams, and L. Mandelkern, J . Phys. Chem., 66, 1932 (1962). (18) A. Ciferri, C. A. J. Hoeve, and P. J. Flory, J . Am. Chem. SOC., 83, 1016 (1961). (19) Hoeve‘ chose the value d In s$/d In T = -0.44 and so obtained 6s$/M = 1.128 X 10-1Bat 160’.
