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Real-time ultrasonic characterization of the chain orientation of high density polyethylene melts during processing.

INTRODUCTION

It is now well accepted that the microstructure of polymer could directly affect its macroscopic physical properties (1-5). At a certain shear stress and shear rate during processing, the polymer molecular chains disentangle and align along the direction of the external force. The oriented materials become anisotropic, due to the long chain structure of polymer and the tremendous difference in the strength between intramolecular covalent bond and intermolecular Van der Waals force. The oriented polymers have attracted considerable attention because their physical properties change significantly compared with those of unoriented polymers. The mechanical properties, such as the tensile modulus, the impact resistance, and the yield stress increase in the orientation direction because of the orientation (6), (7). The barrier properties, for instance, the water vapor transmission of the polyethylene films in an ultra-oriented state have been shown to be equivalent to that of poly(vinylidene chloride) (PVDC) (8). The thermal expansion coefficient in the flow direction (FD) of injection molded specimens is observed to be significantly lower than in the transverse direction (TD), owing to a lower degree of alignment of the exfoliated platelets in the TD compared with that in the FD (9). The effects of molecular orientation on crystalline morphology and crystallization kinetics have been widely investigated. When polymers crystallize from an oriented melt, shish-kebab texture is usually a predominant feature in the morphology (10), (11). The crystallization kinetics of shear-induced crystallization of isotactic polypropylene (iPP) is found to increase by two orders of magnitude when compared with that of quiescent crystallization (12).

The physical properties of the oriented materials directly depend on the degree of orientation, which is greatly affected by the polymer bulk properties, the manufacturing methods, and the processing conditions. Ben Daly et al. (13) have used poly(ethylene terephthalate) (PET), polystyrene (PS), high density polyethylene (HDPE), and liquid crystal polymer to evaluate the effects of polymer bulk properties on the orientation of injection-molded parts. It has been found that the molecular orientation at the skin layer of the injection molding increases with the relaxation time, the rigidity, and the crystallization rate of polymer. A specific manufacturing method leads to specific orientation distribution of the final products. In injection molding, for example, polymer chains at the surface of the parts are oriented along the flow direction parallel to the mold wall, but in the center the chains may be completely random (14). It is also pointed out that the oriented structure depends on the means used for orientation, such as magnetic fields and mechanical methods (15). Numerous studies have focused on the effects of processing conditions on orientation (6), (16). Temperature and shear rate are the most important factors in determining the level of orientation.

It is an important issue that how to characterize the orientation of the polymer chain during processing, considering its great effects on the mechanical and other properties of the final products. Many methods have been developed to detect the orientation of polymer, including wide-angle X-ray diffraction (WAXD) (15-17), X-ray scattering (18), (19), optical birefringence (20), infrared (IR) dichroism (16), (21-23), nuclear magnetic resonance (NMR) (24). X-ray measurement provides opportunities to analyze the orientation of the crystalline polymer. Optical birefringence has been shown to be a powerful technique to investigate the total orientation of crystalline and amorphous area, reflecting segmental orientation. According to the selected vibration band of IR spectroscopy, IR dichroism can be applied to study the orientation of the crystalline and amorphous polymer. NMR is a useful tool for investigating the orientation distribution on the atomic level. However, they are off-line methods by inspecting the quenched samples after they have been sheared for different time. Because of the difficulty of introducing characterization methods into the real machining process, these approaches could not be directly applied to monitor the orientation of polymer melt, which is obtained under shear flow during melt processing, such as injection, extrusion, blow molding, and melt spinning. Therefore, it is important to develop a real-time technique to detect the structure of polymer melt during processing.

Ultrasonic measurements are widely used in recent industries, owing to their robustness, safety, simplicity, fast response, nondestructiveness, noninvasiveness, cost-effectiveness, and high sensitivity to material properties and processing conditions. As far as the polymer melts are concerned, high temperature and viscosity limit the application of ultrasound. Therefore, most of the studies focus on the polymer solids and solutions (25-27). Jen et al. (28) invented a set of in-process ultrasonic testing equipment, using a clad metallic buffer rod to avoid damaging the ultrasound sensors by high temperature. One of the buffer rod ends is in contact with the polymer melt, and the other end equipped with an ultrasonic transducer which can be cooled by water or air, so the ultrasonic testing equipment is especially suitable for the polymer melt. Most of their works are focused on the characterization of the macroscopic properties of polymer, such as the residence time distribution (29), the filler dispersion (30), and the polymer degradation (31). However, researches on the change of microscopic molecular structure during polymer processing determined by the ultrasonic measurements are relatively limited. Recently, on the base of the principle that an alteration in molecular chain orientation could result in a change in the ultrasonic velocity in the polymer melt, ultrasonic measurements are utilized to investigate the relaxation of orientation and disorientation of low density polyethylene (LDPE) and PP melts (32). However, some basic characteristics of ultrasonic measurement of general plastics, such as the effects of the molecular weight of polymer on the ultrasonic velocity, are still not clear.

HDPE, as one of the most important general plastics, is extensively used in industry to manufacture films, pipes, bottles, and electric wires and cables, and easy to orient during the processing. There exist different grades of HDPE resins with different melt flow index (namely different molecular weight). It is controversial that how the molecular weight affects the degree of orientation, which still needs further study. In this work, HDPE resins with different molecular weights have been chosen to study the chain orientation and its subsequent disorientation using a real-time ultrasonic system at various temperatures and shear rates, due to the fact that HDPEs with the linear molecular structure could be oriented easily. The objective of this research is to understand the underlying mechanisms of the relationships between the ultrasound signals and the bulk properties and processing conditions of HDPE melts. The discrete relaxation spectrum, stress relaxation, and characteristic relaxation time of HDPE melts are also investigated by rheological measurements.

EXPERIMENTAL

Materials

Three kinds of commercial-grade HDPEs with different melt flow indices are used to evaluate the ultrasonic behavior of the polymer melts. The main characteristics of them, as provided by the manufacturers, are listed in Table 1. Prior to experiments, the materials are dried at 80[degrees]C for 12 h in an oven to eliminate the influences of moisture on the experimental results.
TABLE 1. Characteristics of high density polyethylenes used in this
experiment.

Sample  Grade     Density (g    MFI, g/10min        Supplier
                  /[cm.sup.3])  (190[degrees]C,
                                  2.16 kg)

HOPE    JHC7260      0.957          8.0          Ji Lin Petroleum
                                                 Chemical Corp.,
                                                 Jilin, China

        5000S        0.950          0.9          Yan Shan Petroleum
                                                 Chemical Corp.,
                                                 Beijing. China

        DGDB2480     0.945          0.1          Lan Zhou Petroleum
                                                 Chemical Corp.,
                                                 Lanzhou, China


Apparatus

An in-line ultrasonic measuring system composed of a capillary rheometer (RH7, Malvern) and an instrumented slit die is established to measure the ultrasonic velocity of polymer melts during processing. The schematic of the system is presented in Fig. 1. In the slit die, the flow channel has a width of 20 mm, a height of 2 mm, and a length of 250 mm. A connecter is employed to fit the slit die to the barrel exit of the capillary rheometer. The samples are first held in the barrel of capillary rheometer at a set temperature for 10 min, and then forced through the slit die with a piston attached to the moving crosshead, and finally stopped. A transmission mode is used in this study, with one transducer to emit ultrasonic waves and the other one on the opposite side to receive ultrasonic waves. The details of the ultrasonic sensors (US) in this research are described in the works of Jen et al. (29), (33). Two US, two pressure/temperature transducers (PT2 and PT3) with J-type thermocouples to measure the pressure and temperature of polymer melt simultaneously and a die temperature sensor ([T.sub.die]) are located in cross-sections I, II, and III. Except for [T.sub.die], all sensors are flush-mounted with the die wall, so as not to disturb the flow of the polymer melt. The cross-sections I, II, and III were equidistantly located from the exit of the slit die. A wrapped-on heating jacket with a piece-wise proportion integral differential (PID) controller is employed to keep the temperature of the polymer melt consistent with that of the capillary rheometer. The data acquisition on a computer is at every 0.1 sec, so we could track the evolution of the temperature, the pressure, and the ultrasonic velocity when the polymer melt was extruded through the slit die.

[FIGURE 1 OMITTED]

Ultrasonic Measurements

As mentioned earlier, two US are axially aligned in cross-section I, but on the opposite sides of the slit die, respectively, shown in Fig. 2. In this work, longitudinal waves produced with the left US are sent through the molten polymer and received by the right US. The ultrasonic waves are reflected back and forth several times between the US, and their energy dissipates exponentially in each reflection and propagation. Figure 3 displays the typical ultrasonic signals received by the US. A series of echo signals ([A.sub.1], [A.sub.2], ..., [A.sub.n]) are obtained. In this experiment, ultrasound waves with a center frequency of 5 MHz are used.

[FIGURE 2 OMITTED]

[FIGURE 3 OMITTED]

By measuring the time delay difference ([DELTA]t) between two consecutive echoes ([A.sub.1] and [A.sub.2]) and the height of the slit die (h = 2 mm), the ultrasonic velocity in the molten polymer can be calculated as:

C = 2h/[DELTA]t (1)

Rheological Measurements

The linear viscoelastic properties of the samples are measured using an oscillatory rheometer (AR1500EX, TA) under a nitrogen atmosphere with 25 mm diameter plate and 1 mm gap. Frequency sweeps are performed in the range varied from 0.01 to 100 Hz at three different temperatures, i.e., 185, 215, and 230[degrees]C, respectively. The temperature is in accordance with the ultrasonic measurements. Stress relaxation sweeps are utilized to determine the stress relaxation time. The applied most strain amplitude is determined to be 5% to keep within the linear viscoelastic region.

WAXD Measurements

WAXD measurements in reflection mode are conducted using a DX-1000 diffracometer, at a scan rate of 1[degrees][min.sup.-1]. The generator is set up at 40 kV and 40 mA and the Cu-K[alpha] radiation is selected. The 2[theta] scans are made ranging from 2[degrees] to 40[degrees] with steps of 0.06[degrees]. The samples investigated are extruded from the die and then rapidly quenched in liquid nitrogen. The detected interface is in the middle of the samples along the flow direction.

IR Dichroism

A 10-[micro]m film was cut from the surface of sample extruded from the die and then rapidly quenched in liquid nitrogen for 5 min. A Tunser-27 Fourier Transform Infrared (FTIR) Spectrometer equipped with a polarizer was used to determine IR dichroism of the films at a resolution of 2 [cm.sup.-1]. The absorption bands at 730 and 719 [cm.sup.-1] were employed to evaluate the orientations of the crystal a-axis and b-axis, respectively (34), (35). Dichroic ratio (D) was taken as the ratio of the absorbance measured with radiation polarized in the direction perpendicular to flow direction (Y) that measured with radiation polarized in the flow direction (X). The orientation functions of crystal axes [f.sub.a], [f.sub.b], and [f.sub.c] were calculated as following:

[f.sub.a] = ([D.sub.730] - 1)/([D.sub.730] + 2) (2)

[f.sub.b] = ([D.sub.719] - 1)/([D.sub.719] + 2) (3)

[f.sub.c] = -([f.sub.a] + [f.sub.b]) (4)

RESULTS AND DISCUSSION

Characteristic Ultrasonic Behavior of Polymer Melts

The propagation velocity of longitudinal waves (C) can be defined as a function of the bulk modulus (K), the shear modulus (G), and the density ([rho]) using the following equation:

C = [square root of (1/[rho] (K + 4G/3))] (5)

As the shear modulus was relatively small for the polymer melt in comparison with the bulk modulus, Eq. 5 is usually simplified to (36):

C = [square root of (K/[rho])] (6)

During the extrusion, the density of polymer melts is regarded as a constant value, and therefore, the velocity of ultrasound is only dependent on the bulk modulus, which varied with the change of melt pressure or molecular orientation.

In this part, HDPEs have been adopted to investigate the ultrasonic characterization of polymer melts during the extrusion. Figure 4 demonstrates the variation of the temperature, the pressure and the ultrasonic velocity with the processing time for JHC7260 as an example at a shear rate of 22.1 [s.sup.-1]. In terms of the shear rate, the process could be divided into three characteristic stages labeled on the figure. The first stage occurred between 0 and 9 s is in a static state without pressure. In the second region (from 9 to 52 s), polymer melts are pushed through the slit die with the piston of the capillary rheometer moving at a constant rate (v). In this article, the shear rate ([gamma]) could be calculated from [gamma] = 6v[pi][R.sup.2]/[h.sup.2]w, where R, h, and w, are the barrel radius of capillary rheometer, slit height, and slit width. Then we can derive the fact easily that the shear rate is constant in this stage. However, this is a complicated stage where the pressure and orientation coexist because of the shear stress. Generally speaking, increasing the melt pressure leads to the increase of the bulk modulus, whereas in the direction perpendicular to shear flow, the bulk modulus decreases due to the orientation along the shear flow. It can be found from Fig. 4 that at the beginning of the second stage, the melt pressure increases rapidly. Correspondingly, the ultrasonic velocity increase sharply according to Eq. 6, which means the melt pressure dominates at this state. After the ultrasonic velocity reaches a maximum, it decreases slowly as a result of the slow relaxation process of the orientation, till a limited value, indicating that the orientation reaches the equilibrium. During the third stage from 52 to 100 s with the piston stop, the melt pressure decreases quickly to zero and the chains are disoriented slowly, resulting in change in the ultrasonic velocity which is utterly opposite to the second stage. As a result of the abrupt drop of pressure, the ultrasonic velocity suddenly reduces at the beginning of this stage. Afterwards, the ultrasonic velocity starts to progressively increase as a result of the chain disorientation after the cessation of shear. The conformation of polymer chain gets more and more random, leading to an increase in the bulk modulus, correspondingly. At the end of this stage, the ultrasonic velocity reaches a plateau and almost returns to the original base line before shear. It suggests that the orientation of the polymer melt obtained under shear could almost relax. It should be pointed out that the ultrasound velocity at the end of the third stage does not return completely to the original base line value, which could be a consequence of melt temperature increase during the process.

[FIGURE 4 OMITTED]

Ultrasonic velocity is a function of the temperature, the pressure, and the bulk properties of the materials. In this article, the variations of ultrasonic velocity occurring during the second and third stages are, respectively, used to explore the molecular orientation and disorientation. However, as revealed in Fig. 4, the temperature and pressure of polymer melt are not constant in these two stages. Therefore, the change of velocity caused by the variation of temperature and pressure must be excluded. The relationship of temperature and pressure of JHC7260 in a static state on the ultrasonic velocity is plotted in Figs. 5 and 6. It is obvious that the ultrasonic velocity varies linearly with the temperature and pressure. To reflect the real ultrasonic velocity, which is only dependent on the molecular orientation status, a parameter C'([T.sub.0], [P.sub.0]) is introduced to represent the ultrasonic velocity with the temperature and pressure effects eliminated:

C' ([T.sub.0], [P.sub.0]) = C(T, P) - [k.sub.T](T - [T.sub.0]) - [k.sub.P](P - [P.sub.0]) (7)

[FIGURE 5 OMITTED]

[FIGURE 6 OMITTED]

where C'([T.sub.0] [P.sub.0]) indicates the ultrasonic velocity at the reference temperature and pressure of [T.sub.0] and [P.sub.0], C(T, P) is the ultrasonic velocity directly obtained from the experiments at the temperature T and pressure P, [k.sub.T], and [k.sub.P] are. respectively, the coefficients of ultrasonic velocity to temperature and pressure, which are acquired from the slope of the lines in Figs. 5 and 6. The data of ultrasonic velocity below are corrected according to Eq. 7, and thus, only depend on the orientation degree of macromolecules.

Model of Orientation and Disorientation Monitoring by Ultrasonic Measurements

In this work, the relative ultrasonic velocity ([C.sub.R]) is applied to representing the variation of ultrasonic velocity:

[C.sub.R](t) = C'(t) - C'([t.sub.0]) (8)

where C'([t.sub.0]) denotes the corrected ultrasonic velocity of melts in the unoriented state of the second or third stages, and C'(t) indicates the corrected ultrasonic velocity at the time t. An increase in the absolute value of [C.sub.R] suggests that the degree of orientation is enhanced. In this article, we use the absolute value of [C.sub.R] to represent the degree of orientation.

The polymer transits from one equilibrium state to another equilibrium state via the molecular motion, known as the relaxation process. The speed of this process is characterized by the relaxation time. Obviously, the evolutions of molecular orientation and disorientation depend on the relaxation process due to the undergone great friction when macromolecular chains move. As analyzed above, in the second stage (shearing stage), polymer chains get oriented along the flow direction, and the ultrasonic velocity in the direction of perpendicular to shear flow decreases with the shearing time. A model is used to characterize the relaxation of orientation:

[C.sub.R](t) = [C.sub.1](1 - [e.sup.-1/[tau]]) (9)

where [C.sub.1] denotes the maximum relative velocity which manifests the maximum degree of chain orientation, [tau] is the relaxation time of orientation, defined as the required time of [C.sub.R] reaching to the (e - 1)/e of [C.sub.1]

In the third stage (post-shearing stage), the chain disorientation takes place after the cessation of shear. The following model is adopted to describe the relaxation of disorientation:

[C.sub.R](t) = [C.sub.0][e.sup.-t/[tau]] (10)

In Eq. 10, [tau] is the relaxation time of disorientation, and [C.sub.0] expresses the maximum relative velocity. Figure 7 gives the model prediction of the experimental data with the method of least squares fitting for JHC7260 at a temperature of 185[degrees]C and a shear rate of 22.1 [s.sup.-1] during orientation and disorientation. It can be seen that the experimental data can well fit into the models. The values of [C.sub.1] and [C.sub.0] for JHC7260 should be equal theoretically, but the experimental error of 5% is exhibited in this study, being attributed to the limitation and accuracy of the measurements.

Effects of Shear Rate on Orientation and Disorientation

[FIGURE 7 OMITTED]

Molecular orientation is an ordering process, which is not spontaneous and relies on the existence of the external force. Therefore, the degree of orientation is associated with the shear rate, on account of the role of shear stress on the deformation of the molecular chain. The strong shear stress brings on the disentanglement of molecular chain and the decrease of viscosity, so the motion of molecular chain becomes easier.

Figure 8 depicts the maximal degree of orientation and relaxation time as a function of shear rate at 185[degrees]C. It is noted that the maximal degree of orientation ([C.sub.1] and [C.sub.0]) is significantly affected by the shear rate. The variation trends of [C.sub.1] and [C.sub.0] are similar for all samples. The absolute values of them increase with increasing shear rate, suggesting that the maximal degree of orientation increases. It can be seen that the maximal degree of orientation of DGDB2480 with a low melt index is much bigger than that of the others and shows high sensitivity to the shear rate in the investigated range. The maximal degree of orientation of JHC7260 with a high melt index is smallest and manifests a slight increase with the shear rate. The maximal degree of orientation of 5000S with a moderate melt index is not susceptible to the shear rate lower than 20 [s.sup.-1]. However, it starts to increase dramatically when the shear rate increases to 20 [s.sup.-1]. The experimental results provide scientific basis for how to control orientation during processing.

[FIGURE 8 OMITTED]

The dependence of the relaxation time of orientation and disorientation on shear rate for HDPEs with different melt indices at 185[degrees]C is explored in Fig. 8c and d. It is noticeable in Fig. 8c that the relaxation time of orientation is strongly dependent on the shear rate, namely, the relaxation time of orientation decreases with the shear rate. The relaxation time of orientation is determined by the molecular structure, the external force, and the temperature:

[tau] = [[tau].sub.0][e.sup.[DELTA]E - [gamma][sigma]/RT] (11)

where [DELTA]E represents the activation energy, [gamma] is a coefficient, [sigma] describes the shear stress, [[tau].sub.0] is a constant, R is the universal gas constant, and T indicates the absolute temperature. The relationship between relaxation time of orientation and shear rate can be explained by Eq. 11 that an increase in shear stress ([sigma]) shortens the relaxation time. On the other hand, a decrease in the melt index is found to increase the relaxation time of orientation, because the stronger molecular interaction results in the longer time to reach an equilibrium state. In addition, the relaxation times of orientation of the samples with different melt indices display different sensitivities to the shear rate, as shown in Fig. 8c. The relaxation time of orientation of DGDB2480 decreases markedly with the shear rate compared with the other samples.

As the orientation state of polymer melt is a thermodynamically nonequilibrium state, once the external force has been removed, disorientation takes place. Figure 8d indicates the relaxation time of disorientation under different shear rates at 185[degrees]C. It is interesting to note that no pronounced variety of relaxation time is revealed during disorientation, which indicates that the contribution of the shear rate is negligible. The relaxation time of orientation of DGDB2480 obviously depends on the shear rate, but its relaxation time of disorientation is irrelevant to the shear rate with a constant value of 40.5 s approximately. In addition, a decrease in the melt index obviously shifts the disorientation time to higher values.

As can be seen from Fig. 8c and d, the relaxation time of disorientation is relatively higher than that of orientation for the same sample at the same temperature and shear rate. Although the disorientation is a reverse process of orientation, the latter is not spontaneous. The existence of external force is thermodynamically in favor of the motion of molecular chains, therefore, leads to a quicker relaxation of orientation compared with disorientation.

Effects of Temperature on Orientation and Disorientation

The influences of temperature on the maximal degree of orientation [C.sub.1] and [C.sub.0] for JHC7260 is given in Fig. 9a and b, respectively. It is inferred from these figures that an increase in the temperature causes a downward shift of the curve, indicating an obvious enhancement of the maximal degree of orientation. This is ascribed to the fact that the potential energy of molecular motion is deduced by an increase of the temperature.

[FIGURE 9 OMITTED]

It can be clearly seen from Fig. 9c that JHC7260 reveals a strong dependence of the relaxation time of orientation on the temperature. An increase in temperature shortens the relaxation time of orientation. This trend can also be explained by Eq. 11. The high active energy ([DELTA]E) of molecular motion induced by the strong interaction of molecular chain results in the high sensitivity of the relaxation time of orientation to temperature.

As clearly demonstrated in Fig. 9d, a common characteristic in the relaxation time of disorientation is that no distinct variation is observed for JHC7260 at different temperatures. It suggests that when compared with the orientation process, the sensitivity of the relaxation time of disorientation to temperature is too low to be capable of being inspected. Combined with the effects of shear rate discussed earlier, it can be seen that the relaxation time of disorientation is irrelevant to the shear rate and the temperature. These phenomena are closely associated with the characteristics of spontaneous process. Therefore, it suggests that relaxation time of disorientation may be taken as a characteristic relaxation time of materials, which is only dependent of the bulk properties of materials.

Similar results have been found for the other HDPEs used in this study.

Rheological Behaviors

Traditionally, the relaxation of polymer melts has been studied under a small scale deformation using the dynamic rheological measurements (2). In this part, the results from real-time ultrasonic diagnosis, obtained under a large scale deformation, are compared with ones from rheological measurements, i.e., the discrete relaxation spectrum, the stress relaxation, and the characteristic relaxation time.

Macromolecules relax in a broad spectrum of relaxation time due to the dramatical difference in the dimension of motion units. According to the Maxwell model, the storage modulus (G') and loss modulus (G") can be expressed as the following equations:

G'([omega]) = [N.summation over (i=1)] [g.sub.i] [[([omega][[lambda].sub.i]).sup.2]/1 + [([omega][[lambda].sub.i]).sup.2]] (12)

G"([omega]) = [N.summation over (i=1)] [g.sub.i] [[omega][[lambda].sub.i]/1 + [([omega][[lambda].sub.i]).sup.2]] (13)

where [omega] is the shear oscillatory frequency, N denotes the number of Maxwell motion units, N pairs ([[lambda].sub.i], [g.sub.i]) make up of the discrete relaxation time spectrum. The discrete relaxation time spectrum cannot be obtained directly from the experiments. The relaxation time spectra for the HDPE samples, determined from a least-squares fit. of a generalized Maxwell model to linear viscoelastic data obtained in small-amplitude oscillatory shear flow, are displayed in Fig. 10. As can be seen from Fig. 10, the influences of temperature on the discrete relaxation spectra are neglectable, because all the resulting data fall on the same curve in the range of examined temperature. This result is in agreement with the observation that no distinct variation of the relaxation time of disorientation is discovered by ultrasonic measurements.

[FIGURE 10 OMITTED]

Measuring the stress relaxation of polymer melts is one of most common methods to obtain the characteristic relaxation time of molecules. It is generally known that the stress to maintain a constant strain decays with the increasing time. The stress relaxation is the macro-behavior of the response of all motion units with different relaxation time to outside stimulation in succession. According to the Maxwell model, the stress can be fitted as follows:

[sigma](t) = [[sigma].sub.0][e.sup.-t/[tau]] (14)

where [[sigma].sub.0] is the initial stress and [tau] is the stress relaxation time. The stress relaxation curves are plotted in Fig. 11. It can be seen that the stress of DGDB2480 to maintain the same stain is the highest in three samples.

[FIGURE 11 OMITTED]

The characteristic relaxation time of polymer melts can be obtained by measuring the crossover frequency of the storage (G') and loss (G") modulus. Its reciprocal may represent a single characteristic relaxation time of a given resin (2), (37). Figure 12 shows the variations of dynamic modulus of three kinds of HDPE at the reference temperature of 185[degrees]C as functions of [a.sub.T] [omega], with [a.sub.T] being the shift factor used to obtain a master curve, and [omega] being the angular frequency. Clearly, there is a cross point, denominated as [[omega].sub.c], in the studied frequency range, where G' and G" are equal.

[FIGURE 12 OMITTED]

Table 2 lists the characteristic relaxation time calculated from the aforementioned two methods and the average relaxation time during disorientation gained from ultrasonic measurements at the reference temperature of 185[degrees]C. A good agreement exists in the changing trend of each characteristic relaxation time, i.e., all kinds of relaxation time prolong with the decreasing melt index. It is noted that the average relaxation time of disorientation detected by ultrasonic measurements is much longer than the others. The ultrasonic measurements are carried out under a larger deformation of polymer melts, and the ultrasonic results reflect to the motion of whole macromolecular chain. Molecular chain is large scale of molecular structure, and the relaxation of molecular chain is more difficult when compared with that of the smaller structure units, such as segment, bond length, and bond angle. However, the rheological measurements are conducted in small deformation, suggesting the response of all smaller motion units with shorter relaxation time.
TABLE 2. Values of the characteristic relaxation time defined by
[[omega].sub.c], stress relaxation time, and average relaxation time of
disorientation detected by ultrasonic measurement.

Sample    I/[[omega].sub.c] (s)  Stress relaxation    Average
                                     time (s)        relaxation
                                                        time of
                                                    disorientation (s)

JHC7260   1.0 X [10.sup.-2]          0.30                 5.9
5000S     5.3 x [10.sup.-2]          0.98                10.8
DGDB2480      4.8                    6.87                40.5


WAXD and IR Dichroism

The XRD measurement is a useful off-line method to characterize the orientation of crystalline polymer (15).The XRD patterns over the 2[theta] range between 2[degrees] and 40[degrees] for JHC7260 are shown in Fig. 13. The peaks at 2[theta] = 21.5[degrees] and 23.9[degrees] correspond to the (110) and (200) crystal plane reflections of HDPE. It can be seen that the intensity ratio [I.sub.110]/[I.sub.200] for JHC7260 at the shear rate of 6.62, 19.87, and 33. 32 [s.sup.-1] are 3.45, 3.19, and 2.90, respectively. For unoriented HDPE, the ratio [I.sub.110]/[I.sub.200] is about 4.0 (35). The ratio [I.sub.110]/[I.sub.200] in patterns decreases from 3.45 to 2.90 suggests that the degree of orientation of HDPE increases with increasing shear rate (38), (39). The XRD results are consistent with that of ultrasonic measurements.

[FIGURE 13 OMITTED]

Polarizing IR ray spectra and IR dichroism data are shown in Fig. 14 and Table 3. In general, the higher the orientation function of c-axis is, the higher the orientation degree is. According to this rule, the orientation degree of JHC7260 at 33.12 [s.sup.-1], which suffers a strong shear force during the extrusion, is higher than that at lower shear rates. The results are in agreement with that of XRD and ultrasonic measurements.

[FIGURE 14 OMITTED]
TABLE 3. The orientation functions of crystal axes [f.sub.a],
[f.sub.b], and [f.sub.c] of JHC7260 with different shear
rates.

Shear rate ([s.sup.-1])  [D.sub.730]     [f.sub.a]     [D.sub.719]

6.62                       1.037          0.0122            0.820
19.87                      1.056          0.0183            0.800
33.12                      1.080          0.0260            0.752

Shear rate ([s.sup.-1])    [f.sub.b]        [f.sub.c]

6.62                        -0.0638           0.0516
19.87                       -0.0714           0.0531
33.12                       -0.0901           0.0641


CONCLUSIONS

Ultrasonic measurements were used to real-time studying the orientation and disorientation behaviors of high density polyethylene melts with the advantages of nondestructiveness, cost-effectiveness, and high sensitivity to material properties and process conditions. The experimental results indicated that: (1) the maximal degree of orientation was affected evidently by the shear rate, the temperature, and the melt index. It was found that an increase of the maximal degree of orientation was attributed to the enhancement of shear rate and temperature or the decrease of melt index; (2) the relaxation time of orientation was also sensitive to shear rate, the temperature, and the melt index. However, the relaxation time of disorientation was irrelevant to the external conditions, such as the shear rate and the temperature, owing to the various mechanisms based on; (3) compared with other dynamic rheological methods, the ultrasonic measurements were carried out under a large-scale deformation of polymer melts and reflect to the motion of macromolecular chain. Therefore, the relaxation time of disorientation obtained through this method was longer. Meanwhile, the relaxation time of disorientation may be taken as a characteristic relaxation time for materials, which was consistent with the characteristic relaxation time obtained from dynamic linear viscoelastic data. The results showed that the velocity of ultrasonic longitudinal waves, which was quite sensitive to the molecular orientation, could be used to detect the anisotropic behaviors in polymer melts.

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Congmei Lin, Shan Wang, Huimin Sun, Jiang Li, Shaoyun Guo

The State Key Laboratory of Polymer Materials Engineering, Polymer Research Institute of Sichuan University, Chengdu 610065, China

Congmei Lin, Shan Wang, Huimin Sun, Jiang Li, Shaoyun Guo

The State Key Laboratory of Polymer Materials Engineering, Polymer Research Institute of Sichuan University, Chengdu 610065, China

Correspondence to: Jiang Li; e-mail: li_jiang@scu.edu.cn or Shaoyu Guo; e-mail: nic7702@scu.edu.cn

Contract grant sponsor: National Natural Science Foundation of China; contract grant number: 50973075; contract grant sponsor: Scientific Research Foundation for the Returned Overseas Chinese Scholars; contract grant sponsor: State Education Ministry; contract grant number: 2008890-19-8.

Published online in Wiley InterScience (www.interscience.wiley.com).

[C]2009 Society of Plastics Engineers

DOI 10.1002/pen.21634
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