Chinese Chemical Letters  2016, Vol.27 Issue (04): 588-592   PDF    
Detection of long-chain branches in polyethylene via rheological measurements
Yun-Fan Mei, Bao-Hua Guo, Jun Xu     
Department of Chemical Engineering, Tsinghua University, Beijing 100084, China
Abstract: The detection of long-chain branches (LCB) in polyethylene is of considerable importance as the processing properties of polyethylene are strongly affected by even a small amount of LCB. While the conventional characterization techniques such as GPC-MALS and 13C NMR fail or take very long time to detect low content of LCB, we turn to the rheological method, which is more sensitive to LCB. In our study, we performed oscillatory shear test, creep test and stress relaxation test on two series of metallocene linear low density polyethylene (LLDPE), revealing that the resins with LCB show higher zero-shear-rate viscosity, retarded relaxation and higher flow activation energy than those without or with less LCB. The resins with LCB showed shear thinning at very low shear rate and their zero-shear-rate viscosities were obtained via creep test. The content of LCB was quantitatively estimated from the flow activation energy. In addition, the modulus-time curves during stress relaxation of melt of the different resins obeyed the power law. The exponent of the resins with more LCB was -0.7, different from that of the resins with less LCB, around -1.7.
Key words: Metallocene polyethylene     Long-chain branch     Rheology     Stress relaxation    
1. Introduction

Polyethylene is nowadays the most widely used polymer, which finds applications ranging from the plastic bags to engineering plastics such as ultra-high molecular weight polyethylene. Metallocene polyethylene is the most recent progress among the list of various polyethylene owing to the innovation of metallocene catalysts [1, 2, 3, 4, 5, 6, 7, 8, 9]. Compared to previous species of polyethylene such as low density polyethylene (LDPE) and Ziegler-Natta catalyzed linear low density polyethylene (LLDPE), metallocene polyethylene is more regular in molecular structure and narrower in molar mass distribution, which improves its crystalline properties [10]. The crystals in metallocene polyethylene tend to be small and have similar sizes, enhancing the mechanical properties of its blown film, such as tear resistance [10]. However, the metallocene polyethylene is linear and has narrow molar mass distribution (the polydispersity is close to 2 and consequently there is no high molar mass component), resulting in a narrow processing window which is a notable disadvantage for industrial application [11]. Fortunately the molecular structure of metallocene polyethylene can be relatively easily modified [11, 12, 13, 14]. For example, the short-chain branches (SCB) can be incorporated into polyethylene via copolymerization with 1-olefin and the long-chain branching (LCB) is believed to take place via a copolymerization route, in which a vinyl terminated polyethylene chain is incorporated into a growing polymer chain [11]. In order to improve the processing properties, manufacturers tried to mix metallocene polyethylene with Ziegler-Natta catalyzed LLDPE and LDPE, but in some cases they may show immiscibility [15, 16]. In addition, the molecular structure of the metallocene polyethylene is modified by adding long-chain branches or synthesizing bimodal or even trimodal distribution metallocene polyethylene [11, 17]. The presence of long-chain branches or high molar mass component in the polyethylene will enhance the melt strength and improve the processing properties.

Long chain branches, even a very low content, strongly affect the processing properties [11, 18], so it is important to detect low content of LCB. There are some conventional methods used to detect LCB, such as the size-exclusion chromatography coupled with multi-angle light scattering (SEC-MALS) and the carbon-13 nuclear magnetic resonance (13C NMR). SEC-MALS method is able to measure the content of LCB theoretically, but it is necessary to calibrate the chromatographic column and get the working curve by measuring several standard samples with already known LCB content before one could determine the exact LCB content of the sample from the SEC results [19, 20, 21]. There are two aspects of difficulty for the SEC-MALS method to detect LCB, one is the availability of suitable standard samples (having similar branch topology but different LCB contents), the other is that the SEC- MALS method is quite time-consuming as one has to calibrate the chromatographic column every time when the chromatographic column is changed [19]. Another noteworthy point is that the background noise will increase rapidly (much higher than 0.01 LCB/1000 carbons) when the weight averaged molecular weight of the sample is below 200, 000 g/mol, which is unfortunately right the case of our samples [19]. As for the 13C NMR method, on one hand it takes tens of hours to obtain high signal-to-noise-ratio results because of the low abundance of 13C and the sparse distribution of LCB along the backbones; on the other hand the 13C NMR can only recognize branches longer than 6 carbon atoms and those shorter than 6 carbon atoms, which means all branches longer than 6 carbon atoms are categorized as long-chain branches [8, 22, 23, 24]. As we know, the length of LCB affecting the processing properties is above 270 carbon atoms (3800 g/mol), well exceeding 6 carbon atoms [25]. So the NMR method is not a suitable solution to our task.

As the conventional methods have difficulty in detecting LCB in our case, we then turn to the rheological method. According to the previous research, long-chain branching, compared to linear samples of similar molar mass and molar mass distribution, will elevate the shear viscosity, enhance the sensitivity to shear rate, postpone the relaxation of dynamic moduli G' and G" in terminal zone, bring about the strain hardening in elongation test, increase the flow activation energy and make the η'-η" curve deviate from the original semi-circle in Cole-Cole plot [26, 27, 28, 29, 30, 31, 32, 33]. All these traits imply the possible existence of LCB but usually we cannot confirm it with only one or two of these evidences because some other factors may also result in these traits such as high molar mass component [11].

2. Experimental 2.1. Materials

Four species of commercial LLDPE are included in our study. They are all linear low density metallocene polyethylene containing 1-hexene co-monomers according to the supplier. They have very similar densities, but their processing behaviors vary obviously, i.e. the A-series resins are easier to blow film than the B-series. To investigate this problem, we firstly carried out some basic characterization of these resins. The molar mass and its distribution were measured via high temperature gel permeation chromatography (GPC). The melting temperature was measured in a differential scanning calorimeter (DSC-60, Shimadzu) at a heating rate of 10 ℃/min and the temperature corresponding to the peak of the endotherm was taken as the melting point. The melt flow rate (MFR) and the density were measured by the sample provider. All material information mentioned above are presented in Table 1.

Table 1
Material information of the studied resins.
2.2. Preparation of sample for rheological measurement

Firstly the polyethylene pellets were hot compressed into discs with diameter of 25 mm and thickness of 1.25 mm in a vacuum compressor at 160 ℃. Then the discs were quenched in ambient air. The mold was coated with Teflon so that the polymer melt would not stick to it and the surface of the samples were smooth. The samples were placed at room temperature for at least 48 h before the rheological measurement.

2.3. General method of rheology

A rheometer (Physica MCR 301, Anton Paar) was employed to measure the rheological behaviors of the resins. All tests were conducted under the plate-plate configuration. Textured plates were chosen in order to avoid possible slippage between the sample and the plates when we were performing the tests under some relatively low temperatures and the sample became less adherent to the plates [34]. Samples were kept at the measuring temperature for at least 10 min to assure thermal equilibrium before the test. Then we started an oscillatory test, recording the complex viscosity under a constant frequency (for example 10 Hz) until the value of complex viscosity no longer changed, meaning that the sample had fully stuck to the plates of the rheometer and reached an equilibrium. All tests were carried out under the protection of nitrogen atmosphere.

Each sample was then measured successively under oscillatory mode, creep mode and stress relaxation mode. When one mode finished, the sample would be left unstressed for about 10 min before the next measurement.

Under oscillatory mode the value of complex viscosity was recorded with the frequency ranging from 100 Hz to 0.01 Hz. The shear strain was fixed at 0.1% within the linear visco-elastic region for all the four samples.

Under the stress relaxation mode, a step shear strain was applied onto the sample and the strain kept constant afterwards. The relaxation modulus was recorded as the function of time until the stress relaxed to infinitesimal and the signal began to drift considerably. The applied strain 1% was chosen as it was neither too small to give significant signals, nor too large to keep the aroused stress within the measuring range. The first three data (corresponding to the time range from 0 to 0.05 s) were omitted because the shear strain did not reach the prefixed value of 1% until t = 0.05 s.

In the creep mode, a constant shear stress was applied onto the sample and the shear strain was measured as the function of time. The sample would start viscous flow after elastic deformation and the viscosity could be obtained from the viscous flow behavior, as shown in the following discussion.

3. Results and discussion 3.1. Measurement of zero-shear-rate viscosity

Zero-shear-rate viscosity, by definition, can be obtained by measuring the viscosity at a low range of shear rates where the viscosity will remain constant though the shear rate changes. In practice, zero-shear-rate viscosity is usually obtained by extending the oscillatory rheological measurement to low frequency range until the complex viscosity reaches a plateau. The plateau complex viscosity equals the zero-shear-rate viscosity according to the Cox- Merz rule. The results of oscillatory test of various resins at 160 ℃ are shown in Fig. 1.

Fig. 1.Complex viscosity versus angular frequency of various resins measured at 160 ℃.

It is obvious that the complex viscosity of the B-series samples reaches a plateau at the frequency lower than about 0.1 Hz. But the complex viscosity of A-series is still increasing even near the low frequency limit of the rheometer, which means we cannot get the zero-shear-rate viscosity from the oscillatory test in Fig. 1. In order to get the zero-shear-rate viscosity of A-series resins we conducted the creep test, in which the creep compliance increased linearly with time after elastic deformation, as shown in Fig. 2.

Fig. 2.Creep tests on various resins at 160 ℃ and under 10 Pa stress.

By differentiating the creep compliance with time, we can get the reciprocal of the viscosity, as in follows:

where J is the creep compliance, t is time, $\dot \gamma $ is the shear rate, σ is the shear stress, η is the viscosity. For the same sample, if we decrease the shear stress applied on it, the slope of creep compliance will be less steep, indicating the increase of the viscosity. If we decrease the shear stress to such a low range that the viscosity will no longer change, we will get the zero-shear-rate viscosity. This method proves valid for B-series as the zero-shear-rate viscosity obtained from the oscillatory test and the creep test coincided with each other. For A-series, we could only get the zero-shear-rate viscosity from the creep mode measurements. The zero-shear-rate viscosity obtained from creep test are shown in Table 2.

Table 2
Flow activation energy and estimated LCB content of resins.

Table 2 shows that A-series have much higher zero-shear-rate viscosity than B-series. The molar mass Mw dependence of zeroshear- rate viscosity of linear polymer is usually described as follows [35]:

where a is reported to lie between 3.4 and 3.6. K1 and K2 are parameters that depends on the polymer structure and the temperature. Mc is the critical molar mass about two times the entanglement molar mass Me. Me is approximately 3800 g/mol for polyethylene according to the literature [25]. If the resin has LCB, the zero-shear-rate viscosity will become higher than the value predicted by Eqs. (2)-(4) above. In our case, the molar masses of all the four resins exceed the critical molar mass. Since the four resins have similar molar masses, the much higher viscosities of the A-series resins imply that they may have long-chain branches [36].

3.2. Flow activation energy and the LCB content

The flow activation energy can be obtained by fitting the zeroshear- rate viscosities at different temperatures into the following equation:

where η0(T) is the zero-shear-rate viscosity at the temperature T. Tr is the reference temperature (160 ℃ in this case). Ea is the flow activation energy. R is the ideal gas constant.

Both the fitting curves and the original data are plotted in Fig. 3. The flow activation energies of the various resins are summarized in Table 2.

Fig. 3.Plot showing calculation of flow activation energy from zero-shear viscosity.

The flow activation energy is related to the friction that the moving polymer segments encounter and irrelevant to the molar mass. According to the literature, the flow activation energy of linear polyethylene is around 26.1 kJ/mol [37]. The flow activation energies of all the four resins are higher than 26.1 kJ/mol. The flow activation energies of B-series of resins are slightly higher than that of linear polyethylene, but those of the A-series are much higher, which means the A-series of resins have higher LCB content than the B-series.

The content of LCB can be estimated from the following empirical equation [38]:

where the unit of LCB and Ea is mol/g and kJ/mol, respectively. The flow activation energy and LCB content of the resins are summarized in Table 2. The estimated LCB content of A-series is about 2 times higher than that of B-series.

3.3. Shear thinning behavior of the resins

As seen in Fig. 1, the complex viscosity of all the four resins decreases with increasing frequency. The complex viscosity of Aseries starts to drop at lower range of frequency, demonstrating that A-series resins are more sensitive to shear rate and show stronger shear thinning phenomenon. To quantitatively show the sensitivity to shear rate, the complex viscosity-frequency curves were fitted into the Cross model as shown in the following equation [39]:

where ηa is the complex viscosity obtained fromthe oscillatory shear test. h0 is the zero-shear-rate viscosity, which in this case is assigned with the values obtained fromthe creep tests.vis the frequency. n is the non-Newtonian exponent indicating the significance of the shear thinning phenomenon (smaller n means more significant shear thinning phenomenon). l is a relaxation time defined by the Cross model, whose reciprocal is a critical frequency indicating the start of shear thinning, i.e. the point at which the rheological behavior of the sample is converting from Newtonian to non-Newtonian and the equilibrium state of the molecules is broken and disturbed with the increase of frequency. The fitting results are displayed in Table 3. A-seriesof resins havemuchsmallernon-Newtonianexponents than B-series, demonstrating that A-series aremore sensitive to shear rate and their relaxation time are much larger than B-series, which is in agreement with our above proposition. The shear thinning phenomenon is usually related to high molar mass component or more long-chain branches [40]. As the four resins have similarmolar mass and molar mass distribution, the stronger shear thinning phenomenon of A-series should be attributed to higher LCB content.

Table 3
Fitting results of oscillatory shear data into the Cross model.
3.4. Stress relaxation of resins with different contents of LCB

In the stress relaxation test, a step shear strain was applied on the sample and then the shear stress was recorded with time. As seen in Fig. 4, the relaxation modulus versus time curves are presented in double logarithmic coordinate and the relaxation modulus of A-series decreases at a much lower rate than that of Bseries. The stress relaxation originates from movement and flow of polymer chains under the applied strain. The long-chain branched macromolecules will encounter more obstacles than the linear macromolecules of similar molar mass, so the A-series of resins with more LCB relax more slowly than the B-series. From the various rheological measurements above, we are here quite sure that the A-series of specimens have more long-chain branches than the B-series. Now let us have a closer look at the stress relaxation results. As seen in Fig. 4, the moduli of all four specimens decline almost linearly with time in the double logarithmic coordinate, indicating a power law between relaxation modulus and time as shown below:

The exponent n is approximately 0.7 for the A-series and 1.7 for the B-series. The retarded relaxation rate of A-series reflects that the LCB considerably slows down the macromolecular motion.

4. Conclusion

In summary, we have detected LCB in metallocene linear low density polyethylene via various rheological methods mentioned above. The zero-shear-rate viscosity was obtained from the oscillatory test and the creep test. The flow activation energy was calculated by fitting the zero-shear-rate viscosities at different temperatures. The LCB content was estimated from the flow activation energy according to an empirical equation and the Aseries resins have about 2 times more LCB than the B-series. The shear viscosity of the A-series of resins with higher content of LCB was more sensitive to shear rate than that of the B-series of resins with less LCB. The stress relaxation tests showed that the A-series of resins with more LCB relaxed much more slowly than the B-series.


This work was financially supported by the National Natural Science Foundation of China (No. 21374054) and the Sino-German Center for Research Promotion. We are deeply grateful to Prof. Gu¨ nter Reiter and Dr. Renate Reiter for the inspiring discussions.

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