INTRINSIC VISCOSITY-MOLECULARWEIGHTRELATIONSHIP FOR POLYETHYLENE
1645
Intrinsic Viscosity-Molecular Weight Relationship for Fractions of Linear Polyethylene'
by R. Chiang Contribution N o . 881 from the Chematrand Research Center, Inc., Durham, North Carolina (Received November 84, 1964)
Light scattering measurements have been made in a-chloronaphthalene a t 135' on linear polyethylene fractions obtained from a Celite column. Linear Zimm plots have been obtained over the entire angular range from 30 to 150". The intrinsic viscosity-molecular weight relationship, [77ldeealin, 1350 = 6.2 X 10-4M,0.70,suggested by us earlier, is confirmed, using fractions covering a wide range of molecular weights from 20,000 to 1,000,000. The hydrodynamic constant 3 for linear polyethylene in the Flory-Fox viscosity equation was found to be 1.7 X loz1in a-chloronaphthalene a t 135'. Applying proper correction for the probable heterogeneity in the sample would bring the value of 3 to the range of 1.9 to 2.1 X loP1,in agreement with the 3 values observed for other flexible polymer molecules in good solvents. The dependence of the second virial coefficient, A P ,on molecular weight can be represented by the empirical equation Az = 6.3 X 10-3Mw-0.15 cc. g.-2 mole. (where (rz)ois the unperturbated mean-square end-to-end The dimensionless ratio, (r2)O/n12 distance, n is the number of bonds, and 1 is the carbon-carbon bond distance), as calculated from the second virial coefficient, intrinsic viscosity, and molecular weight by the Orofino equation was 6.77 a t 140'. Direct intrinsic viscosity measurement in a @solvent (diwhich leads to the phenyl ether a t 161.4') gave the ratio [771e/M"' a value of 2.95 X same result of (r2))o/nE2 as that given above. I t is concluded that the hydrodynamic behavior of polyethylene appears to be similar to that of other flexible polymer molecules. Results on intrinsic viscosity measurement a t the 0-point lend additional evidence to the validity of the viscosity-molecular weight relationship for fractions of linear polyethylene. These results also provide the most direct experimental information in support of theoretical calculations of configurational dimensions of high polymers in solution.
Introduction Since the first application of the light scattering. technique to the characterization of polyethylene in solution about a decade ago, a large number of papers have appeared in the literature in an effort to correlate the intrinsic viscosities and molecular weightsS2 However, these reported results are often difficult to compare because of the coniplications arising from the degree of branching and the very broad molecular weight distribution often found in various types of polyethylene-free-radical, Marlex, or Ziegler. The presence of very high molecular weight species (as insoluble gels or particles) renders the purification of the solution for light scattering measurement very
difficult. This is evidenced by the fact that linear Zimm plots are extremely hard to obtain on unfractionated samples, but readily obtainable on fractions, particularly fractions obtained from a Celite or sand column. Even under the most favorable conditions using fractionated samples of linear polyethylene, results still vary depending on the method of fractionation. Our own laboratory experiences indicate that fractions (1) Presented in part before the Division of Polymer Chemistry of the American Chemical Society, Chicago, Ill., Sept. 3, 1964. (2) A review on this subject is given by M . 0. DeLa Custa and F. W . Billmeyer, Jr., J . Polymer Sci., Al, 1721 (1963). (3) R. Chiang, ibid., 36, 91 (1959).
Volume 69, Number 6
May 1966
R. CHIANG
1646
recovered from a Celite or sand column are most suitable for light scattering measurements. These samples are purified by continuous filtration through the column; even minute quantities of gel particles or imperfectly soluble materials which interfere with the light scattering measurements are thus removed. This is demonstrated by the results obtained by Henry4 and by Chiang.3 Both authors used fractions of linear polyethylene from a Celite column and obtained essentially identical results for molecular weights, second virial coefficients, and dimensions of the polymer.5 However, Henry's results were rather scattered and Chiang's earlier work covered only a narrow range of molecular weights that precise values of K' and a in the viscosity-molecular weight equation, [ q ] = K'M", still could not be ascertained. With recent improvements in the instrumentation and techniques for light scattering a t elevated temperatures, it seems desirable to re-examine our early results using linear polyethylene fractions. In this present work, fractions covering a *wide range of molecular weights were used in order to establish an accurate intrinsic viscosity-molecular weight relationship. Intrinsic viscosities were measured both in a thermodynamically good solvent, ie., decalin a t 1 3 5 O , and in a €)-solvent. The results on intrinsic viscosities in a 8-solvent, as shown below, further substantiate the validity of the intrinsic viscosity-molecular weight relationship.
Experimental Fractionation. Marlex 50, a linear polyethylene, wasinitially fractionated into 11 fractions by the column technique first developed by Desreuxa and subsequently perfected by a group of research workers a t the Hercules Research Center, Wilniington, Del.' Alarlex 50 (20.3 g.) was dissolved in xylene a t 140' and precipitated upon cooling onto Celite (NO. 545 obtained from Johns-Manville), with constant stirring. After complete precipitation, xylene was removed by filtration. The Celite coated with the polymer was homogeneously dispersed in hot 2-butoxyethanol which had been degassed a t 130' prior to use. The slurry was packed into the column a t 127' with special measures to assure uniform packing and to avoid bubbling and channeling of liquid through the column.8 The polymer was eluted with mixtures of xylene and 2butoxyethanol with increasing solvent power. Each of the fractions was filtered, washed with acetone, and dried to constant weight under vacuum a t 60'. Even though the sharpness of the fraction is not critical for the present purpose of establishing a weightaverage niolecular weight-viscosity relationship, neverThe Journal of Physical Chemistry
theless precautions were taken to prevent degradation and to obtain good resolution. For this purpose 0.2%
Table I : Fractionation Data of Marlex 50" Frao-
Wt. of fraction, g
tion
I I1
1,2434 1..2661
-1
V
VI VI1
0.7565 1.5504 1.6802 1.0723 2.7879
-1 -2 -3 VI11
0,0384 0.0786 0.0852 0.0544 0,1373 0.0266 0.0778 0.0329
6.9205
-1 -2 -3 -4 -5 -6 -7
0.3472 0.0054 0.0132 0,0170 0.0362 0.0412 0.1123 0.0457 0.0654 0.0108
-8 -9
IX X XI
0.0630 0.0621 0.0056 0.0120 0.0166 0,0102 0,0069 0.0108
72 -3 -4 -5 -6
I11 IV
Wt. of fraction, W i , g.
1 6773 0,7418 0,2073
Total 19.9937 (98.47" recovery)
0.0850 0.0376 0.0105 __ 0.9993
l~li
0.11 0.163
Huggins' constant, kE
. . .b
. .b
0 . 128c 0.136" 0. 14OC 0 . 183c 0,197' 0.252" 0.241 0.291 0,392 0.477" 0.651"
0 .530b 0,618 0,835
. . .b 0.355 0.395
0.390 0.410
1.47c 0.748" 0 . 786c 0.852" 0.936' 1.055" 1 ,445 1.885" 2.13 2.06 3.80 9.85 8.59
0.405 0.413 0.370 0.395 0.407 0.412
Zwi[q]i = 1.50 for all the fractions recovered from t h e column; [o] for t h e original polymer = 1.59 measured in decalin at 135'. Intrinsic viscosities are too small fork= to be meamred accurately. Calculated from t h e specific viscosity measured at only one concentration.
(4) P. M. Henry, J . Polymer Sci., 36, 3 (1959). (5) R. Chiang, Polymer Letters, 2, 855 (1964). (6) V. Desreux, Rec. trav. chim., 68, 789 (1949); V. Desreux and M. C. Spiegels. Bull. soc. chim. Belges, 59, 476 (1950). (7) P. S. Francis, R. C. Cooke, and J. H. Elliott, J . Polymer Sci., 31, 453 (1958); P. M. Henry, ref. 4; 9. Shyluk, J . Polymer Sci.. 62, 317 (1962). ( 8 ) The column was packed by means of a plunger with a perforated disk, following a procedure described by A. J. P. Martin in "Practical Chromatography," It. C. Brimley and F. C. Barrett, Ed., Reinhold Publishing Corp., New York, N. Y., 1953, p. 66.
INTRINSIC VISCOSITY-MOLECULAR WEIGHTRELATIONSHIP FOR POLYETHYLENE
of phenyl-@-naphthylamine,used as a stabilizer, was introduced into xylene and 2-butoxyethanol at room temperature. The solution was heated to about 140°, while nitrogen was bubbling through, to decompose any peroxides originally present in the liquid. Fractions 11, VII, and VI11 were subsequently separated into subfractions by refractionation. A summary of the fraction data is given in Table I. The amount of the polymer recovered in each fractionation was in the range of 97-99%. As shown in Table I, the intrinsic viscosities of the fractions increased regularly with the order in which the fractions were recovered from the column (except fraction XI, the last fraction, which was only 1% of the total; this “backlash” would not show if the size of this fraction were made comparable to others). The intrinsic viscosity of the original sample was found to be very close to the sum of the products of the intrinsic viscosity, [ q ] , , and the respective weight fraction, w,,of each fraction, indicating that no serious degradation had taken place. Liquid-Liquid Phase Separation. The @point was determined in diphenyl ether by measuring the critical precipitation temperatures, T,, for three fractions with widely different iiiolecular weights and extrapolating the critical temperatures to infinite molecular eight.^ To prevent degradation of the polymer, diphenyl ether containing 0.4% of Tenox BHT was heated to ca. 160’ under nitrogen before it was allowed to come into contact with the polymer. Precipitation temperatures were determined as a function of concentration by visual observation of the appearance of turbidity of the polymer-diluent mixture upon cooling and checked by the disappearance of the turbidity upon warming. The precipitation and dissolution temperatures agreed within zk0.1’. The @point obtained as the critical temperature for M = a was 161.4’. Viscosity Measurements. Viscosities of polyethylene fractions were measured a t 135’ in decalin containing 0.2% phenyl-@-naphthylamine, with a modified Cannon-Ubbelohde dilution viscometer. A coarse sintered glass filter was fitted in the to remove any extraneous insoluble material before the solution was allowed to come into the capillary. Solutions were prepared by dissolving a measured quantity of sample in decalin in the viscometer. Concentrations of the solutions were so adjusted that the specific viscosities ranged from 0.1 to 0.6. The flow time of decalin was 179.6 sec.; thus no kinetic energy correction was required. The shear rate corrections for intrinsic viscosities lower than 3.8 dl./g. were negligible and therefore were omitted. For intrinsic viscosities higher than 4, the intrinsic viscosities were
1647
corrected by applying appropriate factors as described by Wesslau. * l The values of qsp/c were plotted against c and extrapolated to c = 0. Values for the Huggins’ constant k~ calculated from the equation, qsp/c = [ q ] k ~ [ ~ are ] ~ also c , given in Table I. The values of l c H fell within the range of 0.390 to 0.415. The intrinsic viscosities in diphenyl ether a t 161.4’ were determined similarly with special precautions against oxidation. The flow time of the solvent was 130.5 see. Tenox BHT (0.4%) was added as stabilizer in the manner described above. With this stabilizer, the flow time of the solution remained unchanged for a t least 8 hr. a t a temperature as high as 161.4’. The time required for measurements was less than 4 hr. Light Scattering. Light scattering measurements were made in a-chloronaphthalene at 135’ with a PhotoGonio-Diff usoni8tre. Unpolarized light from a mercury lamp of wave length 5461 8. was used. The temperature was controlled by a heater in the instrument and by circulating ethylene glycol from a thermostat external to the instrument. Silicone oil was used as the therniostating liquid for regulating the temperature of the cell. The temperature of the solution was some 15’ below that of the regulating bath, but once regulated, it did not vary throughout the measuremen t . The scattering envelopes of carefully purified benzene and a-chloronaphthalene given in Table I1 serve to indicate the adequacy of the optical At frequent intervals the intensity of the incident beam was checked for constancy against the reading at 90’ for the standard diffusor. a-Chloronaphthalene was purified by washing first with concentrated sulfuric acid, then with iYaHC03 solution, and finally with distilled water. After drying with anhydrous MgS04,it was distilled under nitrogen a t reduced pressure. The colorless middle fraction boiling a t approximately 90’ ( 2 mm.) was collected and stored under nitrogen in the dark. Solutions were prepared by dissolving a measured quantity of polyethylene in a-chloronaphthalene in a volumetric flask at 140’. After complete solution, the volume was brought to the mark with the solvent. Concentrations were calculated using the specific volunies of the solvent at the respective temperatures.
+
(9) P. J. Flory, “Principles of Polymer Chemistry,” Cornell University Press, Ithaca, N. Y.,1953, eq. XIII-7 and Figure 122, p. 548. (10) 1’. J. Flory, A. Ciferri, and K. Chiang, J . A m . Chem. Soc., 8 3 , 1023 (1961). (11) H. Wesslau, Makromol. Chem., 2 0 , 111 (1956). (12) M .Gubler, C. Reiss. and H. Benoit, J . cham. p h y s . . 59, 42 (1962).
Volume 69, Number 6
M a y 1965
1648
R . CHIANG
Table 11: Scattering Envelope of Benzene and a-Chloronaphthalene Measured a t 5461 b. deg.90
--g
_ _ _ _ _ _ _ I _
Io for benzene a t 25' Literature value12 a-Chloronaphthalene a t 135"
-
30
37.5
45
60
75
266 268 1135
208 213 887
170.5 172 744
127 127 579
106.5 106.5 500
Teflon Sheet
Filter Papers Heating Block Heating W i r e Teflon
Disc
's-
Jack for Adjusting Height
Figure 1. Filtration apparatus.
The concentrations used varied with the molecular weights of the samples used; in no case was the excess scattering less than 30% of that of the solvent. Solutions were filtered a t 140' directly into the light scattering cell by nieans of a millipore filter (RIillipore Filter Corp., Bedford, Mass.) as shown in Figure 1, the porosity being 0.45 p . Two layers of filter paper were used. 'The stainless steel holder was maintained a t 140' with a heating tape. A heating block was attached to the stem of the filter to prevent the polymer from precipitating before it reached the light scattering cell. The solution in the cell was protected from dust in the air by nieans of a Teflon cover during filtration. The filtering area was first rinsed with 30 to 50 cc. of the solvent. To niininiize the change in concentration, the filter was rinsed with about 10 cc. of the solution prior to filtration. The solution went through the filter snioothly by gravity and no applied pressure was needed. Solution concentrations determined by precipitation from aliquots and those calculated from the weight of the polymer originally used were practically identical within experimental error. The change in intrinsic viscosity before and The Journal of Physical Chemistry
__
~
100 100 476
7
105
120
135
142.5
150
106.5 106.5 500
127.5 127 579
170 171 744
206 209 882
260 1105
after filtration was also insignificant; in one instance, the intrinsic viscosity of a sample recovered from the light scattering cell was 1.15 as compared to 1.12 for the sample before heating. Solutions were blanketed with nitrogen during filtration, although occasional exposure to air was found to cause no adverse effect. Solutions, thus purified, were free of solid suspensions when exanlined under strong illuniination with a mirror placed a t low angles to the incident beam. The instrunient was calibrated with benzene and the instrument constant was checked against a standard polystyrene ( S l l l ) of known molecular weight.13 The molecular weight of the sample calculated from the accepted value of the Rayleigh ratio of benzene (16.3 X was 230,000. The average molecular weight of this polystyrene sample obtained independently by six different laboratories was 234,000.l4 We therefore used benzene as a standard for converting the phototube reading to the absolute scattering intensity by the equation
= QI
Rb(do/lb)
= sin e/(l
(n/nbI2
+ cos20 )
(1)
where Re is the Rayleigh ratio (corrected for scattering by the solvent) a t any angle 0, Rb is the Rayleigh ratio of pure benzene a t 90°, which is taken to be 16.3 X lo", le is the galvanometer deflection for the solution in excess of that of the solvent, IL,is the galvanometer deflection for pure benzene, (n/nb)' is the square of the ratio of the refractive index of the solution to that of benzene, introduced to correct for the scattering volume affected by the refractive index of the solution. Sin e is the correction factor for converting the scattering volume viewed a t angle e into that viewed a t 90°, and (1 cos2 e) is the correction factor introduced
+ ~~~
~
~
(13) The kind assistance of Dr. D. A . Brant in calibrating the instru-
ment is hereby acknowledged. (14) The author is indebted to Prof. H. Mark of Brooklyn Polytechnic Institute for supplying us with this sample and his report of results.
INTRINSIC VISCOSITY-MOLECULAR WEIGHTRELATIONSHIP FOR POLYETHYLENE
when unpolarized light was used. Substituting eq. 1 into the familiar light scattering equation
5 1 c
.o
"
&
[Kc/R,],= o e=o
where K
=
(2)
= l/Ww
Note that the refractive index of the solution, n, cancels out, since it appears as a squared term in both the denominator and the numerator. Substituting the numerical constants, X = 5461 X IO-', Rb = 16 3 X N = 6.023 X nb = 1.496, into eq. 3, we have 0.506(tlnldc), ( I b )
(C/ d
o)
=0
e=o
=
1/ W
w
(4)
For polyethylene in a-chloronaphthalene a t 135') the average specific refractive index ina t 5416 crement was -0.191 0.002 c ~ . / g . ' ~Using this dn/dc value and settinglb = 100, eq. 4 becomes
s.,
*
I .85(c/aIs),= 0 e=o
=
I/Ww
(5)
In accordance with eq. 5 , Zimni plots were obtained by plotting c / d e against sin2 (8/2) kc (k is taken arbitrarily to be 100 in this case). The extrapolated lines c = 0 and 8 = 0 intercept the ordinate a t the same point, the reciprocal of which value, divided by 1.85 is the weight-average molecular weight. The second virial coefficients, A 2 , and the z-average rootmean-square end-to-end distances are calculated in the usual manner from the equations
+
1 nw= 1.85(c/aIe)c
=0
e=o
dflz= 2__,3A' 4 = 1160
slope of the line c = 0 intercept
[
slope of the line c intercept
=
]
0
1 (in
8.)
(6b)
where A', the wave length of the ligkt in a-chloronaphthalene, equals 5461/1.590 or 3434 A., and
A,
=
1.85k(slope of the line 8
=
0)/2
10-
?
LL
c n .-
2~~(ndn/dc)~/N weAhave ~,
0
08-
.
00
0
.
Figure 2. Cumulative distribution curve for Marlex 50 obtained: by initial fractionation ( + ) ; by combining fractionation and refractionation data (0); and by Tung" with a fractional precipitation method.
a, an
The ratio of to calculated by summation from our fractionation data for Marlex 50 was 8.9, indicating that Marlex 50 is a sample of broad molecular weight distribution, a conclusion reached independently by Schindler16and by Tung. l7 Using a fractional precipitation method, Tung obtained a value of 6.5 for While the ratio of ATw/ATn calculated by the summation method niay vary a little, the difference, 8.9 us. 6.5, is most significant; the column fractionation method yields fractions sharper than those obtained by the fractional precipitation method. Coniparison of the distribution curves obtained by these two methods as shown in Figure 2 reveals the same conclusion that the column fractionation method used in this work gives better resolution than the fractional precipitation method. With the column fractionation technique, fractions of both very high and low molecular weights are isolated; the intrinsic viscosity of the highest molecular weight fraction was 9.85 as compared to 6.64, the value obtained by Tung when corrected for the difference in intrinsic viscosity in decalin at 135' and in tetralin a t 130'. Tung measured the number-average molecular weight of the fractions by the osmotic pressure method and obtained the equation
flw/nn.
(6c) lloo
Results and Discussion Fractionation Curve. A summary of the fractionation data of hlarlex 50 is shown in Table I and its cumulative distribution curve is shown in Figure 2. While refractionation results in sharper fractions, the cuniulative curves constructed from the fractionation and refractionation data are almost identical.
1649
x
=
5.10
10-4~~0.725
=
5.86 X 10-4iVn0.725
or [77]decailn. 1350
(7)
(15) R.Chiang and J. H. Rhodes, t o be published. (16) A. Schindler, Monatsh., 95,868 (1964). (17) L.H.Tung, J . Polymer Sci., 24, 333 (1957).
Volume 69, Number 6 May 1965
R. CHIANG
1650
In view of the inhomogeneity of the fractions discussed above, eq. 7 can be expected to deviate from the true intrinsic viscosity-molecular weight relationship to an extent depending on the polydispersity of the fraction. The disparity between eq. 7 by Tung and our eq. 8 given below has long been recognized, yet hitherto unexplained. A possible explanation can now be advanced through the knowledge of the molecular weight distributions of the fractions used for osmotic pressure measurements. Molecular Weights, A 2 , and (r2),. Linear Zimm plots obtained for fractions IX and X are given in Figures 3 and 4 for illustration. In view of the difficulties encountered in the light scattering measurement on unfractionated or branched polyethylene at elevated temperatures, it is remarkable that the plots here remained linear throughout the entire angular range of 30 to 150'; no sign of downward curvature a t lower angles was noticed. The weight-average molecular weights of all the samples measured, together with the second virial coefficients, A2, and the z-average root-mean-square are given in Table 111. end-to-end distances,
l0
6 4.
CC-'
5
M,
:
299,000
'
I 00
I
I
05
I .o
1
1.5
s q 1 +IOOC Figure 3. Zimrn plot for fraction I X in a-chloronaphthalene a t 135".
Gz,
Table 111: Light Scattering Results of Linear Polyethylene Fractions in a-Chloronaphthalene a t 135'
VII-2 VI13 VIII-4
F-1' VIII-6
VIII-8 F-2' IX
F-38 X
0.618 0.836 0.936 1.3 1.445 2.13 3.7 3.80 4.3 9.85b
21.9 31.2 35.6 63.0 75.8 73.0 126 260 299 338 11035
< 1.01 < 1.015 < 1.015
