I
H. J. KARAM Plastics Production Laboratory, The Dow Chemical Co., Midland, Mich.
Flow Properties of
Linear Polymers The Row viscosity of a polymer is an important parameter when fabrication and processing performance of a polymer are to be correlated. To characterize the polymer, data should be over a range of shear and temperature
IN
recent years much work has been directed on the rheological behavior of linear high polymer-a very important property of molding and extrusion grade polymers. Most polymeric materials are fabricated and processed by applying heat and pressure. By a thoro@ understanding of rheological behavior, onecan evaluate fabrication performance, better design of processing machinery, and lastly as a tool can determine molecular structure. The purpose of this article is to show the role of molecular weight, orientation, molecular weight distribution, branching, and crystallinity on the rheological behavior of high polymers; and to show the application of rheology to practical problems encountered in the field. Description of Rheometer
The data reported were obtained on a capillary rheometer. Details of the viscometer and method have been discussed (8). Flow viscosity data can be obtained on other types of rheometers such as Nason (72)) flat plate ( 4 ) ,cone and plate (70), rotational (2), coaxial (6), and melt indexer (75). The flow of a high polymer is characterized by the parameters (8, 73). Rheological Behavior linear Polymers
of
Most linear polymers are non-Newtonian pseudoplastic materials-i.e., the viscosity decreases with increasing shear stress. This is true of polystyrene, copolymers of styrene, low and high pres-
sure polyethylene, Ethocel, rubber modified styrene polymers, and polymers made from derivatives of styrene monomers. High polymers may have Newtonian flow properties-i.e., viscosity independent of shear-such as saran and polycarbonates. Many materiaIs such as latex exhibit a change of resistance at constant shear with time ( I ) . Polystyrene, polyethylene copolymers of styrene, rubber modified polystyrene and Ethocel do not exhibit time dependent viscosity behavior in the temperature range studied. Rheological Behavior of Molecular Parameters
Molecular Weight. The log of the zero shear viscosity of a high polymer us. the square root of the weight of average molecular weight is a linear function. This type of plot has been used by Flory for the flow of polyesters ( 5 ), and by Dienes for the flow of polyethylene (#). Eyring (9) and coworkers have justified the dependency of viscosity upon chain length. I t is important that the samples to show the validity of this type of plot have the same polymerization history. The flow of a high polymer as function of temperature can be represented by an Arrhenius plot for a narrow temperature range. The flow viscosity of a high polymer increases sharply as it approaches its transition temperature (3, 6). Experimentally, the activation energy (slope of the log viscosity-temperature curve) was found to be independent of molecular weight. The experimental
evidence further substantiated Eyring’s (9) flow picture a t low shear. Molecular Orientation. Eyring’s theory adequately described the low shear viscosity in terms of segment jumps. Under high shear stress, the theory is inadequate to explain the shear dependency of viscosity because of orientation of these segments in direction of shearing stress. A polymer which orients more readily when sheared will show a greater change of viscosity for a change of stress. The polymer is more non-Newtonian. It is important to know the shear dependency if fabrication performance is to be correlated with rheological measurements ( 74). Branching. Many polymers have a branched structure-for example, low and high pressure polyethylene and polystyrene-divinyl benzene polymers. Theoretically, a branched molecule is more symmetrical in structure and therefore is less likely to orient when sheared. Physically it possesses more Newtonian flow properties-Le., less change of viscosity with shear. Molecular Weight Distribution. A high polymer is characterized by the molecular weight distribution. When comparing two samples of equal weight of the average molecular weight, the sample with the wider molecular weight distribution will have lower melt viscosity. This can be explained on the basis that the larger lower molecular weight component of the sample with the wide distribution acts as a plasticizer. The plasticizing action results in lower flow viscosity. The effect was observed for polyethylene (7) and polystyrene. VOL. 51, NO. 7
JULY 1959
851
Rheological Measurements
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Rheological measurements are applied to everyday problems. Two problems, which are commonly encountered, are degradation studies and plasticizer evaluation. Degradation Studies. The degradation test measures the flow viscosity of a polymer as a function of time and temperature. The results are plotted in the logarithmic of melt viscosity us. time. The slope of the line is a measure of the stability, and can be determined by the following equation :
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POLYSTYRENE
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/m/ = absolute value of slope = stability = flow viscosity a t time, tZ = flow viscosity a t time, tl
qz q1
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The material investigated is poly(crmethylstyrene). In the figure, the slope of the plot of the stability us. reciprocal of the absolute temperature is defined as the activation energy of degradation. The value obtained for poly(cr-methylstyrene) is 59.5 cal. compared with 58.0 kcal. reported by Madorsky ( 7 7 ) using a more elaborate procedure. This type of degradation test has several advantages:
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1. Conditions at which polymer sample is subjected are comparable to fabricating and processing variables. 2. A small sample is required which is to be desired for experimental material. 3. Test conditions can be varied over a wide range. 4. Test is sensitive to slight changes in molecular weight or structure. 5. Sample can be removed from viscometer and subjected to other tests. 6. Test is performed under a nitrogen or oxygen atmosphere. By studying degradation under various atmospheres degradation mechanisms can be correlated. 7. Surface area to volume ratio is large for capillary. Heat generated during the shearing of the plastic is easily dissipated.
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The role of orientation in flow behavior of high polymer These two polymers have a different shear viscosity but equal non-Newtonian constani. The abilities of these segments to orient are equal and hence, have equal slope of the curve. Rubber modified polystyrene is stiffer than polystyrene owing t o its higher initial viscosity These two polymers have equal zero shear viscosity but orient differently under shear-stress action. Physically, one polymer is more nowNewtonian in flow behavior. When sheared polystyrene i s more fluid than styrene-a-methylstyrene copolymer or acrylonitrile styrene copolymer. The CHI or CN group of two polymers apparently affords more steric hindrance causing the molecules to orient less when sheared compared to polystyrene In this case, boih zero shear viscosity and shear dependency of viscosity are different but the high shear viscosity of the two samples are equal. Viscosity i s compared for plasticized and unplasticized polystyrene
Observed and Calculated Data
Two samples of a high heat distortion styrene copolymer were plasticized with a Newtonian and non-Newtonian compatible plasticizer, respectively. In both cases, the plasticizer decreased the heat distortion of the polymers. The plasticizer efficiency is, in this case, the ratio of the melt viscosity change over the change in heat distortion. To determine plasticizer efficiency, the solution viscosity for constant volatile must first be recalculated. Then the melt viscosity of each sample assuming no plasticizer present must be recalcdated. Soln. Vise., Cps. Calcd.
Sample
Obsd.
Poises Calcd.
~ ~ o l a t i l e ,Heat Distortion, ' F. Obsd. hleasd. A
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A
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Plasticizer A
Blank 1% Newtonian compatible 2% plasticizer
17.1 16.0 15.1
17.1 16.1 15.5
5600 3800 2600
5600 5200 4950
4.8y0 non-Newtonian 9.1% compatible 13.6% plasticizer
15.2 14.3 13.6
15.2 14.3 14.0
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4800 4500 4350
0 1400 2350 Plasticizer
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INDUSTRIAL AND ENGINEERING CHEMISTRY
1300 1900 2350
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0.64 1.02 2.71
218 211 194
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200 98
0.75 0.76 1.05
214 209 204
4 9 14
325 211 180
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N O W - N E W T O N I A N FLUIDS One problem is to determine the effectivenessof a plasticizer. An empirical method is to determine the plasticizer efficiency. This factor is defined by ihe following equation:
E = Aq,/AP
(2)
E = plasticizer efficiency q7
= change in high shear viscosity due
to the addition of plasticizer AP = change of a n important physical property due to the addition of a plasticizer I t can be seen from the relationship that the higher the ratio, the more effective is the plasticizer. The following example will illustrate the method (see the table). Analyzing the data by the above procedure, it is evident which is the most efficient plasticizer.
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PLASTIC TEMPERATURE INDICATED ON CURVE
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TIME, MINUTES
The slope of plot of stability vs. reciprocal of absolute temperature shows that activated energy of degradation of poly(cr-methylstyrene) compares well with data obtained by others using a more elaborate procedure
There are also some disadvantages of this test. 1. The viscometer is not completely closed. Therefore, some volatile is lost during the measurement. 2. The test fails to identify the molecular mechanism of degradation. Independent measurements must be made to determine these factors and can be accomplished by removing sample from viscometer. Knowledge of degradation properties should not be overlooked from a theoretical or a practical viewpoint. These properties play a n important role in determining fabrication characteristics and in the design of processing equipment. Theoretically results can be applied to determine molecular structure. Plasticizer Evaluation. A plasticizer is defined as any additive that decreases the flow viscosity of a polymer. There are two types of plasticizers for
nonpolar linear polymers. 1. A Newtonian plasticizer. This is a plasticizer with Newtonian flow properties-for example, mineral oil for polystyrene. 2 . A non-Newtonian plasticizer is one in which the viscosity is a function of shear stress-for example, a low molecular weight resin. T h e two major groups of plasticizers can be further divided into two subgroups-compatible and noncompatible. A compatible plasticizer does not exude. The effect of the plasticizer on the flow viscosity polymer is consistent with theory. The Newtonian plasticizer has lower viscosity and is not shear sensitive. These characteristics are imparted to polymer. Conversely n plasticizer is stiffer and shear sensitive. Hence, the flow of the plasticized sample is affected likewise to a limited degree.
The mechanism of flow at low shear can be adequately explained by the Eyring theory. At high shear, orientaiion of the molecular segments plays a dominant role in determining the flow viscosity. Crystallinity, branching, and type of molecule affect the orientation of the segments. Rheological measurements can be applied to study practical problems. Methods of studying degradation and evaluating plasticizers are given to show the practical application of rheology.
Literature Cited (1) Alfrey, T., Jr., “Mechanical Behavior of High Polymers,” p. 46, Interscience,
New York, 1948. (2) Buchdahl, R., J. Colloid Sci. 3, 87 (1948). (3)’ Cleereman, K. J., Karman, H. J., Williams, J. L., Modern Plastzcs 30, 119 (May 1953). (4) Dienes, G. J., Klemm, H. F., J . Apisl. Phys. 17, 458 (1946). (5) Flory, P. J., J.Am. Chem. SOC.62, 1057 (1940). (6) Fox, T. G., Jr., Flory, P. J., Bid., 70, 2384 11948). ( 7 ) Hawkins, S. W., Gordon Research Conf. Rept. (July 1955). (8) Karam, H. J., Cleereman, K. J., Williams, J. L., Modern Plastics 32, 129 (March 1955). (9) Kauzmann, W., Eyring, H., J . Am. 62, 3113 (1940). Chem. SOC. (10) McKennell, Proc. Intern. Congr. on Rheol., 2nd Congr., 1953,p. 350. (11) Madorsky, S . L., J. Polymer Sci. 11,491 (1953). (12) Nason, H. K., J. A@l. Phys. 16, 338-43 (1945). (13) Spencer, R. S., J . Polymer Sci. 5, 591 (1950). (14) Spencer, R . S., Gilmore, G. D., Modern Plastics 28, 97 (December 1950). (15) Tordella, J. P., Jolly, R. E., Ibid., 31, 146 (October 1953). I
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RECEIVED for review January 7, 1959 ACCEPTED April 21, 1959 VOL. 51, NO. 7
JULY 1959
853
