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Melt rheology of poly(lactic acid): Consequences of blending chain architectures.

John R. Dorgan (*)


Currently, most polymeric packaging materials are base on non-renewable fossil resources. Incineration of these materials makes a net contribution to atmospheric [CO.sub.2] and plastics currently account for more than 20% of the nation's landfills (1). Clearly, a need exists for the development of "green" polymeric materials that are based on renewable resources, do not involve the use of toxic or noxious components in their manufacture, and can be easily recycled. One such family of polymers made from monomers obtained from renewable sources can be produced and will soon be commercialized. This material is poly(lactic acid) (PLA), the polymer of lactic acid, which is made by the fermentation of corn.

In this paper, the rheological properties obtainable by blending branched and linear chain architectures of PLAs are examined. Earlier works report on the rheological properties of linear chains (2-4). Also, rheological properties for branched PLAs, in the form of star molecules, are available (2). Blending provides a means of controlling rheological response and thus of tailoring flow properties for specific applications.

Because of the chiral nature of lactic acid, the stereochemistry of PTA is complex. Figure 1 shows the L and D enantiomers of lactic acid along with its possible dimer rings and the polymer chain structure. The lactide rings were used as the monomer for the polymers used in this study. Control of the ratio of L to D monomer content is an important molecular feature of PLAs that has a large effect on material properties primarily through affecting the percent of crystallization.


All polymers used in this study were supplied by Cargill-Dow Polymers (Minnetonka, MN) and were synthesized via melt polymerization with stannous octoate as the catalyst. Polymers with an L:D ratio of 96:4 were used. A common method of imparting different melt flow properties into plastics is to alter the chain architecture through the introduction of branching.

Chain branching was produced by Cargill-Dow through peroxide initiated crosslinking of a linear material by reactive extrusion (5, 6). Long and short branches do exist in the branched material, but comparison with previous results reveals that the branches are long enough to entangle (the zero shear viscosity is elevated relative to a linear PTA of the same molecular weight as the branched material) (2-4). Six different blends of the same materials, varying only in the ratio of branched to linear content, were studied. Mixing in a twin-screw extruder produced blends having compositional increments of 20% by weight; the original linear and branched samples were also passed through the same extruder so that all materials studied experienced the same thermal and shear history. Tris(nonylphenyl) phosphite (TNPP) was obtained from Aldrich and used as received.

PLA degrades in the presence of moisture and elevated temperatures. Reformation of monomer, hydrolysis, and thermolysis are all possible depending on the conditions encountered (7). This makes it difficult to measure fundamental melt properties. For this reason two methods of testing PTA were evaluated to determine the effects of degradation on rheological properties. In the first method PTA was tested as quickly as possible (unstabilized) without additional stabilizer or conditioning. For the second method, tris(nonylphenyl) phosphite (TNPP) was used as a stabilizer during testing. In effect, TNPP acts as a chain extender reconnecting polymer chains that have broken due to moisture and elevated testing temperatures (8). Too low a TNPP concentration results in the breakdown of polymer chains, and too high a concentration results in an increase in the polymer's molecular weight. Chain extension proceeds without additional branching and should only reconnect cleaved chains. Based on the effectiveness of the sta bilizer and the proposed mechanism of Cheung et al (8), it should not be possible for the branched material to change its structure. Chain ends serve to initiate transesterification, so branch length (and chain length in the linear case) are dynamic. Proper stabilization implies that a steady-state distribution is reached, which is characterized by a time invariant average that produces constant dynamic moduli. By performing time sweeps (measuring modulus as a function of time at different temperatures), it was determined that 0.35 wt% TNPP yielded the optimum stabilization level for the temperatures studied (see below--this level led to constant moduli for more than an hour).

The glass transition and melting temperatures of the six blends without TNPP stabilizer were measured on a Perkin Elmer DSC 7 differential scanning calorimeter. The samples were conditioned prior to testing by 1) heating from 0[degrees]C to 200[degrees]C at 10[degrees]C/min, 2) holding at 200[degrees]C for 5 minutes, and 3) cooling from 200[degrees]C to 0[degrees]C at 5[degrees]C/min. The samples were then tested by ramping the temperature from 0 to 200[degrees]C at 10[degrees]C/ min. The glass transition temperature was determined at the inflection point in a heat flow versus temperature plot. The melting temperature was determined as the point where the endotherm reached a maximum.

Absolute molecular weight and its distribution were measured by gel permeation chromatography (GPO) coupled with light scattering detection. These experiments were performed at 3500 in chromatography grade tetrahydrofuran (THF) using 3XPLgel 10 [micro]m columns at a flow rate of 1 ml/min.

The TNPP stabilized samples were mixed to 0.35 wt% TNPP in a Haake Rheodrive 5000 mixing bowl at 180[degrees]C. Both before and after running in the Haake, all samples were dried overnight in a vacuum oven at 40[degrees]C and 2500 Pa vacuum. Rheometer samples were compression molded at 180[degrees]C into 50-mm-diameter discs approximately 3.2 mm thick and were again dried in the vacuum oven overnight at 40[degrees]C prior to testing.

Dynamic moduli and viscosity were measured in a Rheometrics RMS-605 rheometer using parallel plates. A special pressure canister containing molecular sieves was installed in the air inlet to the oven to exclude moisture and prevent hydrolytic degradation during testing. Measurements were made from high frequencies to low (500 down to 0.5 rad/s) and were started when the temperature had stabilized after loading the sample into the rheometer; typical stabilization times were less than 10 minutes.

Steady shear measurements were performed in both a Kayeness LCR5000 capillary rheometer and a Rheometrics RMS-605 rheometer. The capillary rheometer holds a finite amount of sample that is extruded during the experiment. Thus in order to test samples for a wide range of shear rates, two separate charges were utilized and combined into one data set. This allowed testing at shear rates from 1 1/s to 20,000 1/s. A capillary die having an L/D of 30 was employed, and the Rabinowitsch correction was applied to the data. A 0.1 radian cone and plate configuration with plate diameters of 50 mm was used with the Rheometrics rheometer.

Tensile testing was performed on an Instron tensile testing apparatus. ASTM standard D638 was followed: the rate of deformation was 2 inch/min and five specimens of each sample were tested.


Measured glass transition and melting temperatures are obtained from five duplicate runs for each virgin blend. The glass transition temperature is approximately 57.7 [+ or -] 0.2[degrees]C and the [DELTA][C.sub.p] is approximately 0.50 [+ or -] 0.3 J/g [degrees]C for all of the blends and no trend is evident. The melting temperature slightly decreases with decreasing branched content from a value of 152.6 [+ or -] 0.3[degrees]C to 151.0 [+ or -] 0.3[degrees]C. These results are interpreted to imply that the blending has not significantly altered the thermal properties away from the base materials. Percent cystalization is not reported because the as-received pellets are largely amorphous, and recrystallization during heating is more pronounced for the branched material than for the linear, making a direct comparison difficult (9).

Figure 2 shows the effect of various TNPP concentrations on the complex viscosity for the 40% linear blend at 160[degrees]C, 200[degrees]C, and 220[degrees]. Addition of 0.50 wt% TNPP results in the viscosity increasing with time, which is evidently due to an increasing molecular weight. Adding 0.25 wt% TNPP yields acceptable results at low temperatures; however, at 220[degrees]C, the viscosity decreases a significant amount; this is due to a loss of molecular weight. Addition of 0.35 wt% TNPP dramatically improves the stabilization of the viscosity over the entire range of temperatures. For this reason, 0.35 wt% TNPP is the stabilizer concentration used in this study and denoted as a "stabilized" sample. Measurements of the weight averaged molecular weight ([M.sub.w]) for the stabilized samples recovered from the Haake mixer and the post-test recovered samples show only small changes (1%-5%).

Figures 3 and 4 show master curves created by time temperature superposition performed on the unstabilized 100% branched and 100% linear samples. The master curves are referenced to 180[degrees]C and are constructed from isothermal curves obtained at three different temperatures (160[degrees]C, 180[degrees]C, and 200[degrees]C). A couple of noteworthy features are the drop-off of the zero shear viscosities and the broad curvature of the G' and G" curves in the low frequency terminal regime. The zero shear viscosity and other properties of interest are only truly observable when the measurements reach the low frequency terminal regime, which is confirmed by slopes of 2 for G' and 1 for G". Without proper stabilization, such properties are impossible to determine because of the dispersion in the data observed at low frequencies. In fact, these unstabilized samples are not truly superimposable, that is, degradation effects during the course of testing have caused the material to lose thermorheological simplicity . Only through stabilization is it possible to achieve a thermorheological simple material behavior. This finding has obvious importance in the prediction of rheological properties for processes having long residence times at elevated temperatures. These features are due to degradation effects, as can be seen through comparison with the results for stabilized samples.

Master curves for 100% branched and 100% linear samples stabilized with 0.35 wt% TNPP are shown in Figs. 5 and 6, respectively. In this case, the master curves are again referenced to 180[degrees]C and are constructed from isothermal curves obtained at three different temperatures (160[degrees]C, 180[degrees]C, and 220[degrees]C). From a comparison of Figs. 3 through 6, the general effects of adding an appropriate amount of stabilizer can be examined. First, the zero shear viscosities are decreased through the process of adding stabilizer. As mentioned above, molecular weight measurements show that the process of adding stabilizer in the Haake mixer decreases the initial molecular weight (the PLA put in the mixer is initially unstabilized and exposed to high temperatures and atmospheric moisture). This decrease in the initial molecular weight of the material being tested explains the reduced zero shear viscosity (which scales, at least roughly, with the expected 3.4 power). The other important observation fro m these figures is that stabilization leads to a constant plateau in the low frequency region whereas the unstabilized samples show a profound downturn with decreasing frequency. Low frequency points take a long time (20 to 30 minutes) to acquire; degradation of molecular weight is a significant effect during this testing leading to the downturn.

Shift factors and the activation energy for the viscosity ([E.sub.a]) calculated from constructing the 'ITS master curves are given in Table 1 for the TNPP stabilized samples. Trends with blend composition are not strong, but it is noted that the flow activation energy does roughly increase with increasing branched composition. Similar results are found for unstabilized samples.

Owing to the possibility of degradation affecting the rheology measurements, a comparison of the dynamic measurements with steady-state cone and plate measurements is useful. For a single shear rate, steady shearing in a cone and plate geometry provides a viscosity value in a short period of time (less than 1 minute). Accordingly, degradation effects are minimized. Measurements using the cone and plate configuration at a steady shear rate of 0.01 [s.sup.-1] are compared to the zero shear viscosity determined from the dynamic measurements in Fig. 7. Excellent agreement is found, indicating that despite the downturn in viscosity found in the unstabilized samples, it is still possible to extract a meaningful zero shear viscosity from dynamic experiments.

Capillary measurements are complementary to the dynamic measurements described above. A common feature of most capillary rheometers is the inability to run at very low shear rates. However, the great advantage of the technique is the ability to reach much higher shear rates than are possible with a cone and plate or parallel plate configurations, both of which are subject to edge fracture and sample destruction at high shear rates. The capillary results are performed at shear rates up to 20,000 (1/s); no evidence of an upper Newtonian plateau is present in any of the data.

Figures 8 and 9 show [[eta].sup.*] and [[eta]] versus [a.sub.T][omega] and [gamma] for the unstabilized 100% branched and 100% linear PLA, respectively. It should be remembered that the total testing time for the capillary is shorter than for the rotational testing. Also, capillary testing takes place in a closed environment, while the rotational samples are continuously exposed to the air of the convection oven (albeit, this medium is kept as dry as possible). Despite these effects, there is general agreement between the two types of viscosities over a surprisingly large range of deformation rates. The availability of this data over six orders of magnitude in the rate of deformation provides a complete description of the viscosity for most practical processing operations.

In order to parameterize the data into a descriptive model, the combined data sets for each of the blends are fit to the Carreau-Yasuda model. The form of the model used is given by (10)

= [C.sub.1][[1 + [([C.sub.2[gamma]]).sup.[C.sub.3]].([C.sub.4] - 1)/[C.sub.3])] (1)

where [eta] is the viscosity, [gamma] is the shear rate (which can be replaced with [a.sub.t][omega]), and [C.sub.1]-[C.sub.4] are the material dependent parameters. Table 2 presents the parameter values as a function of blend composition. [C.sub.1] represents the zero shear viscosity and decreases with increasing linear content. [C.sub.3] represents the shear thinning strength and generally increases with increasing linear content (that is, the branched material shear thins more strongly than the linear material). [C.sub.2] is a relaxation time roughly corresponding to the reciprocal of the frequency for the onset of shear thinning. The finding of stronger shear thinning in the highly branched material is consistent with results for PLA star architectures (2).

The Cox-Merz rule states that the complex ([[eta].sup.*]) and steady shear ([[eta]]) viscosities are equal when evaluated at the same numerical values of shear rate and frequency (11). A plot of [[eta]]([gamma]) versus [[eta].sup.*]([a.sub.T][omega])for the linear and branched samples at 180[degrees]C is shown in Fig. 10. Because the Cox-Merz rule requires the viscosities to be at the same numerical values of frequency and shear rate, the steady shear viscosities are interpolated from the measured data. In this way of viewing the data, it becomes apparent that the agreement between the two types of viscosities is better for the linear than for the branched architecture. This is not an unexpected result (10). Results for the blends show a trend interpolating between this behavior; at intermediate frequencies/shear rates, the amount of departure from the strict equality increases is found to increase with increasing branched content; however, at higher rates of deformation, the viscosities again c ollapse towards similar values.

The recoverable compliance characterizes the elastic response of a viscoelastic system. The compliance is given by (12):

[J.sup.o.sub.e] = 1/[[eta].sup.2.sub.o] [lim.sub.[omega][right arrow]o] G'([omega])/[[omega].sup.2] (2)

A graphical method used to verify a constant value of [G.sup.1]/[w.sup.2] is reached for low frequencies and this is combined with the zero shear viscosity to calculate the compliance. In the unstabilized samples, considerable noise is present in the low frequency data, making it impossible to determine the compliance accurately.

The zero shear complex viscosities for the six unstabilized blends at reference temperatures of 160[degrees]C, 180[degrees]C, and 200[degrees]C are shown in Fig. 11. The lines represent the log additivity rule calculated from (13): ln [([[eta]]).sub.blend] = [summation over (i)] [w.sub.i] ln [([[eta]]).sub.i] (3)

where [[eta]] is the apparent (blend) viscosity and [w.sub.i] is the weight fraction of the ith component of the blend. A positive deviation from the log additivity rule is often observed in blends of linear architectures that are miscible with one another but possess different chemical structures. The results for the TNPP stabilized blends are shown in Fig. 12. Here relatively good agreement is observed with the law of mixtures represented by Eq 3, but the data do appear to lie higher than the predicted values at lower temperatures.

The recoverable shear compliance versus blend composition for the stabilized blends is shown in Fig. 13. A meaningful value of the compliance could not be calculated for the unstabilized samples, because the degradation induced noise that prevents the attainment of a constant value for G'/[[omega].sup.2]. The relative temperature independence of the compliance for linear chains is observed in the region where the compliance becomes independent of molecular weight. However, it should be remembered that theoretical descriptions (in particular, the Doi-Edwards theory) predict that the compliance is inversely proportional to temperature and density. The compensating effects of decreasing density with increasing temperature produce a nearly temperature independent compliance. For branched materials, the situation is very different. For stars it is known that the compliance does not become independent of molecular weight but continues to increase with increasing branch length (12). For entangled branches, branch po int withdrawal is an important relaxation mechanism (14). This is an activated diffusion process accompanied by an activation energy for arm retraction. Finally, the PVT properties of branched materials are influenced by the number of end groups per unit mass, leading to different density dependence on temperature than in the linear case. Despite these effects, it is important to note that the compliance is also extremely sensitive to molecular weight distribution, and the lack of melt stability could easily play a role in the present finding. The relative changes in the compliance may fall within the statistical uncertainty of the data.

A law of mixtures for the compliance may be found; however, the dependence is not as simple as for the viscosity. Several mixing rules were studied including the log additivity rule given in Eq 3 (substituting ([J.sup.o.sub.e]) for [[eta]]), a linear additivity rule given by

[([J.sup.o.sub.e]).sub.blend] = [summation over (i)] [w.sub.i] [([J.sup.o.sub.e]).sub.i] + [W.sub.linear] [W.sub.branched] [([J.sub.0.sub.e]).sub.LB] (4)

and a mixing rule containing a cross coefficient term:

[([J.sup.o.sub.e]).sub.blend] = [summation over (i)] [w.sub.i] [([J.sup.o.sub.e]).sub.i] + [w.sub.linear] [w.sub.branched] [([J.sup.o.sub.e]).sub.LB] (5)

where [w.sub.linear] and [w.sub.branched] are the linear and branched weight fractions for the blend and [([J.sup.o.sub.e]).sub.LB] is the cross coefficient term. Recall from Eq 2 that the recoverable shear compliance depends upon both the zero shear viscosity and G'/[[omega].sup.2] Plots of G'/[[omega].sup.2] versus blend composition appear to follow the arithmetic mean of the log additivity rule and the linear additivity rule. After analyzing various combinations of the log and linear additivity rules for the compliance, it was determined that the best results are obtained from the mixing rule containing a cross coefficient term (Eq 5). The fit can be improved by allowing for a temperature dependence of [([J.sup.o.sub.e]).sub.LB]; however, because the present study contains only three different temperatures, the temperature dependence of [([J.sup.o.sub.e]).sub.LB]; cannot be precisely determined. Therefore, a value of 5.5 X [10.sup.-5] for [([J.sup.o.sub.e]).sub.LB]; was used at all temperatures.

All of the linear viscoelastic properties are obtainable from the stress. relaxation modulus. The stress relaxation modulus can be determined from the master curve [G.sup.1] and [G.sup.11] data using numerical techniques. An example of this type of transformation is shown in Fig. 14. Here the stress relaxation modulus is plotted for each of the blends, from 100% branched to 100% linear. A clear trend is evident. As expected, increasing the branching content leads to a slower relaxation. That is, at long times the value of the modulus is higher for the branched material than for the linear material. The blends exhibit an intermediate response with the modulus increasing monotonically with branched content.

Figure 15 shows the results of tensile testing on unstabilized blends. It is easily seen that within the standard deviation of the test results, there are no differences in the tensile properties of the linear-branched blends. This demonstrates that the rheological properties may be controlled independently of this mechanical property.


The present study examines the rheological properties for blends of linear and branched poly(lactic acid) in a comprehensive fashion. Measurement of the melt rheological properties of PLA is complicated by degradation effects. The addition of tris(nonylphenyl) phosphite (TNPP) as a stabilizer has a profound effect on the melt stability; addition of 0.35 wt% TNPP dramatically improves the stabilization of the viscosity over a range of processing temperatures. Unstabilized PLA samples were also measured to provide a comparison with TNPP stabilized samples. Time-temperature superposition plots for the unstabilized samples of PLA show some overlap at higher frequencies but significant dispersion at low frequencies. Testing is conducted from high frequencies to low, so samples experiencing a short thermal history (corresponding to high frequencies) produce a satisfactory overlapping of the curves for almost two frequency decades. However, longer thermal exposures produce significant departures from time-temperatur e superposition due to the ongoing degradation. The TNPP stabilized samples show excellent superposition throughout the entire frequency range.

For packaging and coating applications, degradability is desirable, and this means PLA resins will be marketed without stabilization for many applications. In such situations, rheological changes associated with molecular weight loss will take place during processing. The present comparison serves to demonstrate that for applications in which some molecular weight loss is not acceptable, stabilization is needed. The study outlines a methodology for using rheology to evaluate new stabilization packages. In addition, the work clearly establishes a baseline performance for stabilization effectiveness.

The mixing rule given by Eq 3 is often used to predict the viscosity for a system of polymer blends. Both the unstabilized samples and the TNPP stabilized samples appear to follow this rule over the limited range of the data. The mixing rule for compliance, given by Eq 5, requires a cross coefficient term to adequately describe the blend properties. The cross coefficient term appears to show a temperature dependence, but a constant value was used in this study because of the narrow range of temperatures studied.

Plots of the stress relaxation modulus for TNPP stabilized samples show that as the linear content of the sample is increased, the time required to reach a fixed relaxation level decreases. The polymer chain branches can be thought of as long chain side groups that require a longer time to return to their original conformation. However, at shorter times the relaxation of the blends is virtually indistinguishable. This means rapid, small scale molecular motions are not affected by the presence of gross chain topology.

The tensile properties of the linear/branched blends are not statistically different from each other. This is an important finding, because it allows the viscosity and/or the compliance to be tailored to the desired level without affecting mechanical properties.


Funding was provided by the EPA/NSF Technology for a Sustainable Environment Program (No. R 826733-01-0) and the DOE OIT Industries of the Future Program. Molecular weight measurements and PTA samples were donated by Cargill-Dow Polymers (Minnetonka, MN).

(*.) To whom correspondence should be sent: Email:


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(3.) J. J. Cooper-White and M. M. Mackay, J. Polym. Sci., Part B: Polym. Phys., 37, 1803 (1999).

(4.) L. I. Palade, H. J. Lehermeier, and J. R. Dorgan, Macromolecules, 34, 1384 (2001).

(5.) P. R. Gruber, M. H. Hartmann. J. J. Kolstad, D. R. Witzke. and A. L. Brosch, U.S. Patent 94/08 508 (1996).

(6.) D. Carison, P. DuBois. L. Nie, and R. Narayan, Polym. Eng. Sci., 38, 311 (1998).

(7.) D. R. Witzke, PhD thesis, Michigan State University (1997).

(8.) M. F. Cheung, K. R. Carduner, A. Golovoy, and H. Van Oene, J. Appl. Polym. Sci., 40, 977(1990).

(9.) J. R. Dorgan, H. J. Lehermeier, and M. Mang, J. Polymers and The Environment 8, 1 (2000).

(10.) J. M. Dealy and K. F Wissbrun, Melt Rheology and Its Role in Plastics Processing, Van Nostrand Reinhold, New York (1990).

(11.) D. G. Baird and D. I. Collias, Polymer Processing: Principles and Design, John Wiley & Sons: New York, (1998).

(12.) W. W. Graessley, in Physical Properties of Polymers, 2nd Ed., J. E. Mark, et al., eds., American Chemical Society, Baltimore (1993).

(13.) D. G. Abraham, K. E. George, and D. J. Francis, J. Appl. Polym. Sci., 62, 59 (1996).

(14.) T. C. B. McLeish and S. T. Milner, Adv. Polym. Sci., 143, 195 (1998).

[Figure 2 omitted]

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[Figure 15 omitted]
Table 1.

TTS Shift Factors and Viscosity Activation Energy for 0.35 wt% TNPP
Stabilized Samples. The Reference Temperature is 180[degrees]C.

 Blend [a.sub.T] [b.sub.T]
(% Linear) 160[degrees]C 180[degrees]C 220[degrees]C 160[degrees]C

 0 3.502 1 0.139 1.101
 20 3.177 1 0.130 1.025
 40 2.978 1 0.159 0.971
 60 3.172 1 0.159 1.144
 80 2.652 1 0.179 0.980
 100 2.610 1 0.219 0.968

 Blend [b.sub.T] [E.sub.a] x [10.sup.4]
(% Linear) 180[degrees]C 220[degrees]C (J/mol)

 0 1 0.786 7.79
 20 1 0.785 8.09
 40 1 0.871 7.81
 60 1 0.951 7.69
 80 1 0.930 7.33
 100 1 1.050 7.19
Table 2.

Carreau Model Parameters for Unstabilized PLA Blends.

 Blend Carreau Parameters
(% Linear) [C.sub.1] (Pa-s) [C.sub.2](s) [C.sub.3] [C.sub.4]

 0 10,303 0.01022 0.3572 -0.0340
 20 8,418 0.00664 0.3612 -0.0731
 40 6,409 0.01364 0.4523 0.0523
 60 5,647 0.00513 0.4356 -0.1002
 80 4,683 0.00450 0.4754 -0.1108
 100 3,824 0.01122 0.7283 0.0889
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Author:Lehermeier, Hans J.; Dorgan, John R.
Publication:Polymer Engineering and Science
Article Type:Statistical Data Included
Geographic Code:1USA
Date:Dec 1, 2001
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