778
M. HORIO,T. FUJII,AND S. ONOGI
Rheological Properties of Polyethylene Melts: Effects of Temperature and Blending’
by Masao Horio, Tsuguo Fujii, and Shigeharu Onogi Department of Polymer Chemistry, Kyoto University, Kyoto, Japan
(Received September 96,186s)
Dynamic viscosity q’, dynamic rigidity G‘, and apparent viscosity qa of polyethylene blends in the molten state have been measured by means of a concentric cylinder-type rheometer which-enables us to measure not only dynamic but also steady flow properties. The frequency ranges from about 5 X to 1 c.P.s., and the rate of shear from about 0.004 to 4 set.-'. q’ and G’ as functions of frequency as well as qa as a function of rate of shear for each blend of two components a t different temperatures (140-200’) can be superposed according to the usual time-temperature superposition principle, and shift factors UT from r]’ and G’ are practically the same. Master curves superposed with respect to temperature can also be superposed very well with respect to the blending ratio or to the weight-average molecular weight. For blends of two components whose molecular weights are not so different, the logarithm of the shift factor a~ bears a linear relationship to the blending ratio. On the other hand, for blends of two components differing very much in their molecular weights, the linearity holds only approximately. The theory proposed by Ninomiya for polymer blends can also be applied to G’ of our systems, and the equilibrium compliance J , and viscosity have been evaluated. The evaluated values coincide fairly well with the observed values, but J , plotted against blending ratio shows no peak. This result differs from those reported by the previous authors for blends of amorphous polymers having different molecular weights.
Introduction The flow properties of polymer melts are significant in connection with their internal structure and with their processing, and therefore have been studied by many authors. However, the viscoelastic properties of polymer melts in a wide range of frequency have been studied’ only by Cox, et al.,a for polystyrene and polyethylene and by Ballman and Simon4 for polystyrene, so far as the authors know. In the previous paper,5 a concentric cylinder-type rheometer has been described, which was designed to measure not only the dynamic but also steady flow properties of polymer melts and solutions over the wide ranges of frequency and rate of shear. Measurements with this rheometer of rheological properties such as the dynamic viscosity r]’, the dynamic rigidity G‘, and the apparent viscosity va of polyethylene blends in a molten state have been reported in this paper. Our main The Journal of Physical Chemistry
purpose is to investigate the effects of temperature and blending on the flow properties of the blends.
Experimental Materials. Three types of commercial polyethylene were used as original samples. Two of them were Dow polyethylene 544 and 910M having melt indices (1) Presented at the 145th National Meeting of the American Chemical Society, New York, N. Y., Sept., 1963, and supported by a grant from the scientific research funds (Kagaku Kenkyu-hi) of the Ministry of Education, Japan. (2) See, for example, T. C Fox, S. Gratch, and S. Loshaek, “Rheology Theory and Applications,” Vol. I, F. R. Eirich. Ed., Academic Press, New York, N. Y., 1956, Chapter 12. (3) W. P. Cox, L. E. Nielsen, and R. Keeney, J . Polymer Sci., 26,. 365 (1957); W. P. Cox and E. H. Merz. Special Technical Publication of ASTM, KO.247, 1958, p. 178. (4) R. L. Ballman and R. H. Simon, paper presented at the 145th National Meeting of the American Chemical Society, Xew York, N. Y., Sept., 1963. (5) M. Horio, S. Onogi, and S. Ogihara. J . Japan. SOC. Testing Mater.. 10, 350 (1961).
RHEOLOGICAL PROPERTIES OF POLYETHYLENE MELTS
2.2 and 20, respectively. The other was Epolene C of Eastman Chemical Products having a very low molecular weight. They will be designated hereafter as polymers A, B, and E. Polymers A and B were blended in four different ratios by passing them through a nonvent-type extruder equipped with du Pont-type screw, whose diameter D = 1.5 in. and the ratio of length L to D was equal to 20. Stainless steel screens of 60, 100, and 60 mesh were mounted in front of a breaker plate of the extruder in order to remove impurities and enhance the blending effect. The blended polymer was obtained in a form of bristle having a diameter of 0.125 in. Polymers A and E, on t h e {other hand, were blended betwelen two rollers having 4 in. diameter and 15 in. length for 20 min. a t 140°, because the difference in viscosities of these two polymers was too large to blend uniformly with the above extruder. The blends were obtained in a sheet form. Uniformity of the blending was considered to be satisfactory, becaur,e the intrinsic viscosity and the melt viscosity of the blended samples from different portions of the bristles and sheets gave practically the same values. Measurements. As mentioned above, the dynamic viscosity 7’) the dynamic rigidity G’, and the apparent viscosity 7%were mleasured by means of a concentric cylinder-type rheometer specially designed for our study. The detaik, of this rheometer have been described in the previous papere5 A. merit of this apparatus is that it can be used as a torsionally oscillating rheometer, a forced vibration torsion pendulum, or a Couette-type viscometer by a minor change in the driving system. Another merit is that the oscillation and rotation of the outer and/or inner cylinders during the measurements are changed into electrical potential by means of a differential transformer device, and after being amplified m e recorded on a X-Y recorder. The thermostat has been designed to keep temperature constant from room temperature to 300°, and inert gas such as nitrogen flows under a slight positive pressure through a spiral pipe in the thermostat over the surface of the sample in order to minimize chemical degradation a t higher temperatures. By using many torsion wires and bobs having different diameters, a very wide range of rheologicd properties can be measured. The frequency and number of revolutions of the cup range from 5 X to 1 C.P.S. and from 0.122 to 240 r. p.m. , respectively. When we use the rheometer as a torsionally oscillating rheometer, the complex viscosity Q* can be evaluated from the following equation, which is a reduced form of a general equation given by Nlarkovitz61~
779
sin 4
C w
where AI, B1, and C1 are apparatus constants, w is the angular frequency, m is the amplitude ratio, +is the phase angle, p is the density of the sample, and i = (- 1)”’ When the rheometer is used as a forced vibration torsion pendulum, 7‘ and G’ can be evaluated from the following eqdationss
R
(L
17‘ = 4711 - rI2-
$),G’
K =
l
($
-
2;)
where, r1 and r2 are the radii of the bob and cup, 1 is an immersion length of the bob, and
R
=
lcTf sin 4 ____ K 2nm J
=
k(
cos 4
4rI
- 1)
+ T,.
where k is a torsion constant of the wire, Tr is the period of vibration of the bob, 4 is the phase angle, m is the amplitude ratio, and I is the moment of inertia. In general the results obtained by the above two methods are practically the same as have been reported in the previous paper,5 and therefore the former method was chiefly employed in this study. Finally, when we use the rheometer as a Couettetype viscometer, the flow curves of non-Newtonian liquids can be determined accurately by the singlebob method proposed by Krieger and Maron.9 Then the apparent viscosity v8 can be evaluated as a ratio of shearing stress to rate of shear or velocity gradient D. The most important thing in the dynamic measurements is to choose a suitable torsion wire to give sufficient value to m and 4. Otherwise, one will obtain the final result including a systematic error which can not easily be detected when one relies upon only one method. The choice of the wire depends not only upon the nature of the sample but also upon the measuring frequency. This forced us to interchange wires very often even in a series of frequency-varying experiments of the same sample.
Results and Discussion Eflect of Temperature. The frequency dependence curves of r)‘ and G‘ as well as the rate of shear dependence curves of
for blends and their components a t
(6) H. Markovitz, J . A p p l . Phys., 23, 1070 (1952). (7) H. Markovitz, P. M. Yavomky, R. C. Harper, Jr., L. J. Zapas, and T. W. DeWitt, Reo. Sci. I n s t r . , 23, 430 (1952). (8) T. Nakagawa, “Jikken Kagaku Kozs,” Vol. 8, Maruzen, Tokyo, 1957, Chapter 6. (9) I. M. Krieger and S. H. Maron, J. A p p l . Phys., 25, 72 (1954).
Volume 68, Number 4
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780
M. HORIO, T. FUJII,AND S. ONOGI
blends, as illustrated in Fig. 5 for the blends from polymers A and B. Log UT plotted against the temperature is almost linear and the activation energy for relaxation processes therefore varies with the temperature. For example, its value for polymer A a t 160' is about 13.7 kcal./mole. Ej'ect of Blending. As is seen from Fig. 1 to 4, the rheological properties of the blends change systematically with their composition, indicating that there is great possibility of superposition in respect to the blending ratio or to the weight average molecular weight similar to the time-temperature superposition just men-
200
lo3. ,
1
Figure 1. Master curves of 7' for the system of polymers A and B. The reference temperature is 160". w denotes the angular frequency in set.-'.
1
I
2! w" ! I@/ 0
a
0.00 I
0.0I
0.1
I
0 Figure 3. Master curves of 7' for the system of polymers A and E. The reference temperature is 160". w denotes the angular frequency in set.-'.
0.001
0.I
0.01
I
IO I
0 Figure 2. Master curves of G' for the system of polymers A and B. The reference temperature is 160". w denotes the angular frequency in sec.-l.
various temperatures can be superposed very well to give master curves according to the usual method of time-temperature superposition without any correction for temperatures. Figures 1 and 2, for instance, give master curves of 8' and G' measured for polymers A, B, and their blends a t 140", 160", 180°, and 200". Similarly, Fig. 3 and 4 give master curves of 7 ' and G' for the blends from polymers A and E at the same temperatures, respectively. The ratio on the curves denotes the blending ratio in weight, A : B in Fig. 1 and 2 and A : E in Fig. 3 and 4. The values of the shift factor UT determined from the data of q', G', and are almost the same, and moreover independent of the composition or the blending ratio of the The Journal of Physkal Chemistry
0 Figure 4. Master curves of G' for the system of polymers A and E. The reference temperature is 160". w denotes the angular frequency in sec. -l.
IO
781
RHEOLOGICAL PROPERTIES OF POLYETHYLENE MELTS
0.5
& a
s
0 -0.5
140
180 TEMP. "C
140 180 TEMP. "C
140 180 TEMP."C
J
0
s- 0.5 O
'
~
Id
~
0.001
~
0.01
~
0.1
IO
I
~
w 160
200
160 200 TEMP. "C
TEMP. O C
160 200 TEMP.%
Figure 5. Log a~ us. temperature for the system of polymers A and B.
Figure 7. Composite curves of 9' and G' for the system of polymers A and E. The reference temperature is 160" and the reference composition is 8 : 2. w denotes the angular frequency in sec. -1.
0.5 z
f U
fn
s
Q
104y
W
z
&
0-
103 i3
I 0.00I
0.0I
0.1
1
IO
0 Figure 6. Composite curves of 9' and G' for the system of polymers A and B. The reference temperature is 160" and the reference composition is 6:4. w denotes the angular frequency in see. -l.
tioned above. In fact, this superposition was applied satisfactorily t o the master curves shown in Fig 1-4. By shifting the viscosity curves along straight line having slope -1 and the rigidity curves along the abscissa, we could obtain new composite curves, which are shown in Ii'ig. 6 for the blends from polymers A and B, and in Fig. 7 for the blends from polymers A and E:. These composite curves include all the data for the blends having different blending ratios and the component polymers a t different temperatures. The reference temperature and reference composition are, respectively, 160" and 6:4 for the system of polymers A and B, and 160" and 8 : 2 for the system of polymers A and E. In making this superposition, we can determine a new shift factor aM similar to aT in the case
4
I
A10 B O
8 2
6
4
4
6
2 8
0
IO
Figure 8. Log as%us. blending ratio for the system of polyrriers A and B.
0.5 I c3
a 0
0
-I
-0.5 A IO E O
9 I
8 2
7
3
Figure 9. Log U M us. blending ratio for the system of polymers A and E.
Volume 68, Number 4 A p ~ i l1964 ,
782
M. HORIO, T. FUJII,AND S. ONOGI
6
in Fig. 10 and 11 for the two systems. In the first system, in which the two components A and B do not differ greatly in their molecular weights, all the points for the blends are located on a straight line connecting the two points for the component polymers. This indicates that the zero shear viscosity r o b and shift factor a M b of the blends can be represented by the following equations, respectively
s g 5 -.I
1%
Uob
log ahlb
4
,
1
6
4
2
4
6
8 IO
1
A 1 0 8 B O 2
0
Figure 10. Log 90 us. blending ratio for the system of polymers A and B.
=
201
= w1
log Uo1
+ wz log
log aM1
702,
+ wz log
aM2
where w denotes the weight fraction of each component, and the subscripts 1 and 2 refer to the components of higher and lower molecular weight. On the other hand, in the case of the second system, in which the two components do have greatly differing molecular weights, the plots for the intermediate blends have a tendency to deviate somewhat from the straight line. To the dynamic viscosity and rigidity data given above, the theory presented by NinomiyalO for polymer blends composed of two components differing only in molecular weights from each other was applied, and the interaction parameters X1 and X t were determined from the rigidity data. These values for the system of polymers A and B are tabulated in Table I as an example. As is seen from this table, X1 increases and A 2 decreases Table I : Interaction Parameters XI and XZ for the System from Polymers A and B a t 160"
E
O
2
4
6
8 1 0
Figure 11. Log 9 0 vs. blending ratio for the system of polymers A and E.
of the time-temperature superposition. Log a x corresponds to the distance by which the viscosity or rigidity curve for any blend or component was shifted in the horizontal direction along the abscissa. Log a x thus determined was plotted against the blending ratio in Fig. 8 for the first system and Fig. 9 for the second. The plots are substantially linear, and the shift factor from the viscosity data gives almost the same values as those from the rigidity data. Since aM is equal to the ratio of the steady flow viscosity of any blend or component to that in the reference state, the zero shear or zero frequency viscosity plotted logarithmically against the blending ratio should also give a straight line. These plots are shown The Journal of Physical Chemistry
Blending ratio
A1
8:2 6:4
1.33 1.45
0.678
4:6
1.55 1.56
0.320 0.295
2:8
XZ
0.443
monotonously with the blending ratio. With these interaction parameters and weight fractions of two components, w1 and w2, the steady flow viscosity v0 and steady state compliance Jeof the blend are given, respectively, by the VOb
Jeb
=
=
WlXlrlOl
(w1X12V12Je1
+
wZA2l)OZ
W~X22~22Je~)/V~b2
In Table 11, the observed values of 70 and Je for the above system are compared with those calculated from these equations. The latter coincides fairly well with (10) K. Ninomiya, J . Colloid Sci., 14, 49 (1959). (11) K. Ninomiya, ibid., 17, 759 (19621.
RHEOLOGICAL PROPERTIES OF POLYETHYLENE MELTS
Table I1 : A Comparison of the Observed Values of J, with the Calculated Values for the Same System Blending ratio
lo:o 8:2 6:4 4:6 2: 8 0: 10
70, 106
Obsd.
poises (160") Calcd.
4.30 2.32 1.30 0.740 0.480 0.250
2.39 1.29 0.782 0.564
70 and
=
(7702/7701)wz
A2
=
(7701/7702)w1
into Ninomiya's formulation, then obtain VOb
=
(w1
J , , lo-* crn.z/dyne (140") Obsd. Calcd.
1.19 1.64 2.02 2.68 4.32 6.68
1.51 1.73 2.73 5.19
the former. However, J , decreases monotonous1.y with the blending ratio and does not, show any peak at the intermediate composition. This result differs from those reported previously on other polymers such as polyisobutylene12 and polyvinyl acetate. lo The difference might be due to the polyethylene samples used in this study, which were different in their nature, especially in molecular weight distribution, from the other polymers cited above. A further study with fractionated species will be required. Now, it is interesting to make clear the relation between our viscosity equation and Ninomiya's. When we put A1
783
+
w2)7lOlw'
= ??0lW1
x
x
7702
WP
7702w*
This is the same as our equation given above. As seen from this derivation, our case corresponds to a simple one of Ninomiya's general treatment in which the interaction parameters are functions of only weight fractions of the components, The ratio hl/Xz is very simple and equal to the ratio tlo2/qol. Consequently, we can obtain ?Ob
=
7701x1
= 702h
and the shift factor a M is given as 70b
7701x1
702x2
a M = - = - = __
7ObO
"Ob0
77ObO
or
where, vobo is the steady flow viscosity of the blend having the reference composition. These equations give connection between the shift factor aM and the interaction parameters XI and Xz given by Sinomiya, respectively .
and (12) H. Leaderman, R. G. Smith, and R. W. Jones, J . PoZumer Sci., 14, 47 (1954).
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April, 2964
