Printer Friendly

Shear-induced crystallization of isotactic polypropylene studied by simultaneous light intensity and rheological measurements.

INTRODUCTION

Crystallization that occurs during or after shearing a polymer melt is important in plastics processing, because production rates and product properties are strongly affected by kinetic and morphological changes induced by flow, and this phenomenon has been extensively reviewed (1-6). In contrast to quiescent crystallization, shear-induced crystallization is generally characterized by a significant reduction of crystallization time, a marked increase in number of nuclei, and a transition from relatively isotropic structures such as spherulites to a highly oriented morphology exemplified by shish-kebabs (5).

The focus of the present work is the effects of high shear rate and nucleating agent. These variables are of industrial relevance, because fast processing is desired in melt forming operations, and nucleating agents are commonly added to isotactic polypropylene (iPP) at low concentrations to shorten cycle time, reduce spherulite size, enhance optical clarity, and promote the formation of certain crystal forms (7), (8). There have been many studies of the effects of these two variables on the morphology and mechanical properties of products made by extrusion and injection molding (9-13), but the data analysis is often complicated by the complex thermal and flow histories involved in most of these studies. In our experiments, thermal and flow conditions are well-controlled and uniform throughout the sample.

Acting alone, both shear flow and nucleating agents can increase the number density of nuclei (14-17) and shorten the induction time (15), (17-19), which is defined as the time before crystallization is first detectable (20). However, the mechanisms by which these effects are achieved are quite different. Flow induces nuclei from chains that have been distorted from their initial conformations, whereas nuclei activated by a nucleating agent under quiescent conditions come from chains undisturbed from their random-coil, equilibrium conformations. It is through reduction in the free-energy barrier to nucleation that quiescent crystallization of nucleated polymers is facilitated (7), but after the application of a strong shear, it is not clear whether the nucleation pathway is still influenced by the nucleating agent. Also of interest if how the morphologies promoted by flow in nucleated polymers differ from those in non-nucleated ones.

A nucleating agent can be either chemical or physical (21); the latter is more commonly used and is generally classified according to its melting temperature as either melt-insensitive or melt-sensitive (7), (8). Having a melting point that is much higher than the polymer processing temperature, melt-insensitive agents are insoluble and simply provide nucleation sites, whereas melt-sensitive agents consisting mainly of organogelator molecules dissolve in the melt, readily phase separate upon cooling, and self-assemble into a physical gel network of nanofibers (7), (8). For the latter, particularly sorbitol derivatives with clarifying effect (22), the interactions with flow are more complicated, because shearing at certain temperatures and concentrations facilitates alignment of the nanofibrillar network in the flow direction which then acts as a template for the development of shish-kebabs, i.e., the organogelator fibrils form shish on which polymer lamellae grow as kebabs (23), (24). As nucleating agent, we used an organophosphate salt, CAS 85209-1-2, a melt-insensitive agent which we call NA-11. While we need not consider phase separation and fibrillar gelation, there remain questions about the interplay between high shear rate and nucleation efficiency, which depends on molecular characteristics, concentration, shape, size, and dispersion of the nucleating agent (25-27).

It is more difficult to see the effect of flow on crystallization in a nucleated polymer than in a non-nucleated one at low shear rates, because the former already possesses a fair number of preferential nucleation sites. Particularly, if the nucleating agent is highly efficient, as in the present case, the small effect of weak shear can be masked. High shear rates are thus of practical interest. While a number of studies have used pressure-driven channel flows (28-30) and sliding plate devices (16), (31-33) to generate high shear rates, few of these have involved nucleated polymers (26), (28), (34). Pressure flow has two disadvantages. First, since neither shear stress nor shear rate is uniform, crystalline structures vary in size and anisotropy with distance from the wall. The resulting skin-core morphology complicates the interpretation of data, although it was recently proposed to overcome this problem by use of real-time depth sectioning (35). Second, because pressure not only shifts the equilibrium melting temperature but also favors formation of the orlhorhombic [gamma]-iPP (36), (37), the effects of pressure and shear stress on crystallization cannot be decoupled. We avoid these issues by using a sliding plate rheometer that generates homogeneous flow with uniform shear stress, strain, and rate. Unlike similar devices reported in the literature (16), (26), (32), (33), our apparatus allows simultaneous acquisition of Theological and light intensity data during crystallization.

The important role of a high weight-average molecular weight ([M.sub.w]) or the presence of a small concentration of very long chains in enhancing changes in shear-induced crystallization is well documented for non-nucleated polymers (38-45), but little is known about nucleated ones. Earlier investigations often used only one polymer and tended to focus on factors such as the presence or absence of a nucleating agent (18), (34) and variations in its concentration, shape, size, or type (23-27), (46). The present work studies two nucleated iPPs having the same concentration of highly efficient NA-11 as well as similar molecular weight distributions and tacticities, but distinctly different [M.sub.w] values. Included for comparison are two non-nucleated samples.

Light intensity and rheology are normally regarded as secondary tools to study crystallization, because the data analysis is not straightforward. However, they are simple to use and advantageous in several other respects. For example, measurement of turbidity or attenuation in the intensity of a beam of unpolarized light through a sample at the onset of crystallization due to scattering at all angles does not suffer some of the limitations of small-angle light scattering (SALS) and is also more useful for probing early kinetics than well-established techniques such as dilalometry, differential scanning calorimetry (DSC), X-ray scattering, and optical microscopy (47-49). This is particularly important in light of the renewed interest in the initial stages of crystallization (50), (51).

Rheometry has been used for many years for tracking How-induced crystallization during continuous shearing (18), (31), (52-54) and for measuring viscoelastic behavior under quasi-quiescent crystallization (17), (55-64). For the latter, small-amplitude oscillatory shear (SAOS) with a deformation that is small enough not to trigger How-induced crystallization is used. Some studies have concluded that rheometry is more sensitive than DSC and more reliable than optical microscopy (17), (63). Over the course of crystallization, chain mobility decreases and viscoelastic properties can change by one to live orders of magnitude depending on frequency. This remarkably large dynamic range is comparable to that using turbidity and is much better than the two orders of magnitude achievable using conventional techniques (50). Rheology is also of direct relevance for modeling plastics forming processes, because the time evolution of viscosity during crystallization is needed (65). In this regard, crystallinity data obtained from such methods as DSC and X-ray scattering are not useful unless they can be related to rheological properties, and a variety of empirical relationships and suspension models have been proposed for this (61), (62), (65-67). For instance, in relating crystallinity to storage modulus, either a linear or a logarithmic expression is often assumed (17), (57), (63), (64), but there is no evidence to support their utility for all polymers.

EXPERIMENTAL

Materials

Table 1 summarizes the characteristics of the iPPs used in this study. Both iPP1 and iPP2 are nucleated samples produced by The Dow Chemical Company using a Ziegler-Natta catalyst, whereas iPP3 and iPP4 are non-nucleated resins obtained from Sigma-Aldrich Corporation. The two nucleated samples have similar molecular weight distributions and are not believed to have high-molecular weight tails. The molecular weight distributions can be found in the Appendix (A).

TABLE 1. Characteristics of isotactic polypropylene samples.

Sample                 IPP1       iPP2         iPP3           iPP4
                     Nucleated  Nucleated  Non-nucleated  Non-nucleated

% Pentad (a)             96.87      97.74            N/A            N/A

% Triad (mm) (a)         98.45      98.59            N/A            N/A
[M.sub.w]/(kg/mol)         384        160            340            580
(b)

[M.sub.w]/[M.sub.n]        5.4        5.2            3.5            3.5
(b)

MFI/(g/10 (mm) (c)         3.9       57.2            4.0            0.5
11

(a) Determined by carbon-13 nuclear magnetic resonance spectroscopy.
(b) For iPPl and iPP2, determined by high-temperature gel permeation
chromatography at I60[degrees]C using samples at concentration of 0.1g
of polymer in 50 mL of 1,2,4-lrichlorobenzene. Typical values reported
by resin supplier were used for iPP3 and iPP4.
(c) Melt flow index data provided by supplier, determined in accordance
with ASTM DI238 at 230[degrees]C and 2.16 kg load.


Both iPPl and iPP2 contain the following additives: 0.08 wt% of sodium 2, 2'-methylenebis(4, 6-di-rmbutyl-phenyl)phosphate (labeled as NA-I 1), 0.2 wt% of antioxidant IRGANOX B 225, and 0.04 wt% of hydrotalcile DHT-4A. Compounding of these additives was performed by the resin supplier, and the dispersion was found to be macroscopically uniform. The organophosphate NA-11 particles are mostly elongated in shape (68) and have a typical size distribution as follows: [d.sub.90] < 42 /mi, [d.sub.50] < 16 [micro]m, and dm < 5 [micro]m (69). In quiescent conditions, NA-11 favors the epitaxial crystallization of monoclinic [alpha]-iPP (70).

Sliding Plate Rheometer

We made use of a sliding plate rheometer (SPR) equipped with a shear stress transducer to generate and record the stress response to high shear rates and SAOS, and constructed a bifurcated optical fiber probe for light intensity measurements. Unlike rotational rheometers and the widely used Linkam shearing system, the SPR generates a spatially homogeneous rectilinear flow in which the shear rate, strain, and stress are all uniform. A detailed description of the apparatus can be found elsewhere (71).

Figure 1 is a schematic of the experimental setup. Capable of generating shear rates up to 500 [s.sup.-1]:, this device has been used for investigating nonlinear viscoelasticity and wall slip of polymer melts (72-74). A sample is placed between stationary and moving stainless steel plates with a gap of 1 mm. The moving plate is fitted with Teflon rails to suppress secondary flow due to normal stress gradients.

Because of the frequency-response limitation of the linear actuator, the velocity of the plate deviates from the command speed. This issue is discussed in the Appendix (B). For simplicity, we use the command value of strain rate in discussing high-shear-rate data. Another phenomenon that causes the shear rate and strain experienced by the sample to deviate from nominal values is wall slip, which is discussed in the Appendix (C). We do not report data from experiments in which slip occurred.

The SPR is mounted inside a closed, forced-convection oven. The stress transducer and the entire rheometer are at the same, uniform temperature. Because of the large thermal mass of the rheometer, the maximum cooling rate after installation of an ethylene glycol cooling system was 5 [degrees]C/min.

Optical System

We fabricated a bifurcated optical fiber probe similar to those previously used in injection molding studies (75), (76) and in the pharmaceutical and specialty chemical industries (77). As shown in Fig. 2, the probe consists of 19, fused silica fibers 200[micro]m in diameter. The libers transmit light in the wavelength range of 200-800 nm and are multimode, step-indexed, and buffered with polyimide for high-temperature operation. The 12 illumination fibers at the periphery transmit light from the light source to the sample, while the seven read fibers at the center transmit reflected light from the sample to the detector. A sapphire window is mounted flush with the stationary plate surface. The light path length is twice the sample thickness, because the light traverses the sample twice (75).

The key components connected to the optical probe are shown in Fig. 1. The light source is a 5-milliwatl helium-neon laser with a wavelength of 632.8 nm, and silicon photodiodes are used as detectors. A non-polarizing beam splitter divides the laser beam into two beams, one of which serves as a reference, with the other passing a neutral density filter and two dielectric mirrors before being coupled to the optical probe via a fiber coupler.

Experimental Protocol

We used the short-term shearing protocol of Jane-schilz-Kriegl and coworkers (28) in which the sample is sheared for a period of time several orders of magnitude shorter than the quiescent crystallization time. This technique makes it possible to separate the effect of shearing on nucleation from that on growth under isothermal, low-supercooling conditions. And by using our rheometer, we were able to vary the shear rate and strain independently.

Figure 3 shows the shearing and temperature profiles. Alter loading the sample in the rheometer, it is reheated to 214[degrees]C and kept at a temperature above 210 C for at least 5 min to erase thermal history (Fig. 3b). It is then cooled at a rale of 5[degrees]C/min and equilibrated to the crystallization temperature of 155.5 [+ or -] 0.5 C. When an isothermal condition is established (inset of Fig. 3b), we either start SAOS, to study quasi-quiescent crystallization, or apply a constant shear rate [[??.[gamma].sub.s] for a short time [t.sub.s] to generate a shear strain [[gamma].sub.s], to study shear-induced crystallization. In the latter case, we then allow the sample to rest for 30 s, and impose SAOS during the remainder of the experiment to track crystallization (Fig. 3a). The highest shear rate studied was 500 [s.sup.-1] and the largest strain used was 50, although slip occurred when the strain exceeded 20 at shear rales of 200 and 500 [s.sup.-1]. While the oscillatory shear stress [sigma](t) is being measured, the reflected light intensity I(t) from the optical probe is simultaneously recorded to monitor crystallization. The experiment ends when wall slip during the oscillatory shear is indicated by a sharp drop in the stress amplitude. The sample is then cooled to room temperature and removed for morphological analysis.

We studied crystallization at a relatively high temperature of 155.5[degrees]C for several reasons. First, given the low cooling rate attainable with our apparatus, experiments at large supercooling are impractical, as crystallization might occur during cooling. Second, it is desirable to have an adequately long crystallization time for an unambiguous correlation between the light intensity and rheological measurements. Third, it is at low supercooling conditions that studies of gel point (55), (57), (58) and spinodal decomposition (78) are usually conducted. Compared to typical crystallization studies of iPP1, our experimental temperature is several degrees higher, because we need to take into account the effect of nucleating agent.

For SAOS, we chose a constant frequency oj of 1 Hz and a strain amplitude 70[degrees]C 0-2. Although more useful for probing structural changes associated with slow relaxation, measurement at very low m is impractical, especially when the rheological properties change much faster than the time required to complete one oscillation cycle. Conversely, the dynamic range for measurement at high a) is inferior to that at low w. With a reasonable time resolution, w = 1 Hz enables a change of at least one order of magnitude in the stress amplitude during crystallization. The use of a small strain amplitude avoids nonlinear viscoelasticity, shear-induced crystallization, and disturbance of the evolving structures. A lower strain amplitude, however, is not feasible due to limitations of the apparatus. We found [[gamma].sub.0] = 0.2 yielded a linear stress signal with an acceptable signal-to-noise ratio. We also verified that the selected w and [[gamma].sub.0] had negligible effect on early crystallization by comparing light intensity data with and without simultaneous SAOS (71).

Morphological Analysis

Ex situ morphological examination of the solidified samples was performed under a polarizing optical microscope using 5 [m]m thick specimens prepared by means of an ultra-microtome with a glass knife.

RESULTS AND DISCUSSION

DSC Melting and Crystallization Behavior

A Pyris 1 DSC was used to characterize the melting and crystallization behavior of the samples using a mass of 4-6 mg at a scanning rate [+ or -] 10 [degrees]C/min between 50 and 210,;C in a dry nitrogen atmosphere. Figure 4 compares the results of the nucleated (iPP1 and iPP2) and non-nucleated samples (iPP3 and iPP4). The melting [T.sub.m] and crystallization [T.sub.c] temperatures indicated on the figure correspond to the maxima (on second heating) and minima on the DSC thermograms, respectively. In general agreement with the literature on NA-I1 (79), the nucleated samples show higher [T.sub.m] greater degrees of crystallinity (Fig. 4a), and [T.sub.c] more than 22[degrees]C higher than the non-nucleated samples (Fig. 4b). As has been reported earlier (79), with a nucleation efficiency as high as 71%, NA-11 is superior to a number of other commercial nucleating agents. The isothermal crystallization data and an Avrami analysis are provided in the Appendix (D).

Quasi-Quiescent Crystallization

Figure 5 shows the time evolution of the normalized light intensity I(t)/I(0), the magnitude of the complex viscosity |[eta] *|, and the loss angle [sigma], measured simultaneously under isothermal, quasi-quiescent crystallization for iPP1. To facilitate discussion of the sequence of events occurring during an experiment, we divide the crystallization process into three stages. This is a strictly empirical classification intended only to help describe the results. In the "initial stage," which extends to [t.sub.e], around 3800 s, changes in I(t)/I(0), |[eta] *|, and [sigma] are below the sensitivity of our measurements. The "early stage" begins at [t.sub.e], when I(t)/I(0) drops by 3%, which exceeds the 2% maximum intensity fluctuation of the laser used. At [t.sub.e], |[eta] *l has increased by about 1%, as shown in the inset of Fig. 5b. In the "late stage" I(t)/I(0) approaches a plateau, while |[eta] *| increases dramatically. The occurrence of prominent slip terminates the experiment before complete solidification.

The initial time [t.sub.e] is required for the formation of crystalline structures with sizes large enough to cause measurable light attenuation. The identification of an induction time is generally thought to depend on the type of detector used (20), although the work of Janeschitz-Kriegl (6) suggests that there is no induction time and that there is linear growth of the radii of spherulites starting at time t = 0. Here, we defined the initial stage based on the sensitivity of our instrument. According to StrobI and coworkers (47-49), initial structures, primarily spherulites, are expected to exhibit scattering in the Rayleigh-Debye-Gans range; thus the sizes of the nascent structures detected at [t.sub.e] are equal to or smaller than the incident laser wavelength of 632.8 nm.

It would be interesting to know the crystallinity at t& but we were not able to obtain this quantity from DSC, as the signal was too small at low supercooling, and we can only make an estimate based on information in the literature. Comparison of turbidity and dilatometry data (47), (49) has shown that the relative volume crystallinity detectable by turbidity is well below 0.3%. This means that light intensity and oscillatory shear are practical tools for probing very low levels of crystallinity.

In the early stage, 3800 s < t < 10,800 s in Fig. 5, there is a steep reduction in I(t)/I(Q), a gradual increase in [sigma], and a marginal decrease in 4 The structural development during this early period has markedly different effects on optical and viscoelastic properties; for example, at 8100 s, while l(t)fl(Q) has already fallen by 50%, l[eta] *l has only increased by about 10% (inset of Fig. 5b), and has dropped by only 0.8[degrees] (i.e., a 3% drop in loss tangent). These differences imply that light intensity is more useful than oscillatory shear at m -- 1 Hz for tracking early kinetics. We infer from the relatively small change in |[eta] *| that there is little interaction between the growing spherulites. The very slight drop in $ also signifies that the size and amount of the spherulites at this stage do not yet contribute to a significant change in elasticity.

In the late stage of crystallization, t > about 10,800 s in Fig. 5, 1(t)I(0) changes little, while |[eta] *| and S change substantially. These large changes in rheological behavior indicate that oscillatory shear is more useful than light intensity for monitoring late kinetics. It thus appears that the two measurements complement each other, providing useful information about the early and late stages.

Figure 5a shows that I(t)/I(0) approaches a plateau but then increases rapidly to a new level at about 14,600 s, just minutes before the onset of prominent slip. Stein and coworkers (80), (81) saw something similar to this using SALS. They observed a minimum in light transmission followed immediately by an increase nearly to its previous value and attributed the minimum to a maximum in scattering contributed by the average polarizability, i.e., density fluctuations. They estimated that this occurs when spherulites occupy about one-half the sample volume, but this does not mean that the crystal Unity is 50%, as the spherulites contain amorphous material. After the minimum, the contribution of average polarizability decreases, and I(t)/I(0) rises to a new level. They also found that the spherulite radius approaches a constant value, indicative of impingement between the spherulites, not long after the minimum (81), Even after the plateau in I(t)/I(0), crystallization continues by conversion of amorphous chains within the spherulites, and this internal perfection is sometimes called secondary crystallization (56). The system studied by Stein et al. was slightly different from the one studied here, and it is not clear that their observation is relevant to our case, but we have no other explanation for our finding.

The rapid rise in |[eta] *| by more than one order of magnitude during the late stage in Fig. 5b implies a significant increase in the size and quantity of spherulites. In principle, each spherulite is made up of segments of several chains, i.e., each chain participates in several spherulites. As spherulites grow in size and quantity, more chain segments are ordered and restricted to move along with a spherulite, resulting in the substantial increase in resistance to flow manifested by the upturn in |[eta] *|. The large increase in |[eta]| corresponds closely to the minimum in I(t)/I(0). As mentioned (81), about half of the sample volume is occupied by spherulites when I(t)/I(0) reaches its minimum. This means that the sharp rise in |[eta] *| is associated with the filling of a sample by spherulites close to a volume of 50%. As gel point studies have shown that gel time occurs when the SALS density fluctuations are near their maximum (56), (58), i.e., I(t)/I(0) is at its minimum, a critical gel network is believed to form around this time. It should also be mentioned that a long and predominantly flat period in I(t)/I(0) is found in Fig. 5a, whereas a brief and abrupt inflection point was reported in the literature (81). At present, we do not know the reason for this difference.

Shear-Induced Crystallization

To evaluate the effect of high shear rate on crystallization kinetics, data obtained after applying a command shear rate of 500 [s.sup.-1] and strain of 20 are compared with those obtained under quasi-quiescent crystallization in Fig. 6. Comparisons for non-nucleated samples are shown in Fig. 6a and b, and those for nucleated samples are shown in Fig. 6c and d. As explained earlier, light intensity and rheological data reveal the early and late stages of crystallization. Figure 6a and c provide information about early kinetics, as revealed by attenuation of I(t)/1(0), and Fig. 6b and d reveal late kinetics, as indicated by the large upturn in normalized magnitude of the complex viscosity |[eta] *| (t)/|[eta] *|q0.

Non-nucleated Samples

The data shown in Fig. 6a and b indicate that neither iPP3 nor iPP4 crystallizes under quasi-quiescent conditions during a period of 12 h. Crystallization is inhibited by the high free-energy nucleation barrier at 155.5[degrees]C, which is only 4.6 and 6.9CC below the nominal melting temperatures of iPP3 and iPP4, respectively, or a supercooling of 56.5[degrees]C based on an equilibrium melting temperature of 212[degrees]C (82). However, shearing for less than 0.04 s, corresponding to a strain of 20, at a command.shear rate of 500 [s.sup.-1]T readily induces crystallization. Sample iPP3 exhibits a relatively small [t.sub.e] value of about 980 s (Fig. 6a), while iPP4 crystallizes virtually instantaneously with [t.sub.e] < 0.1 s, with I(t)/I(0) falling to 60% in 150 s (Fig. 6a) and |[eta] *|(t)|q0 rising by 200% in 450 s (Fig. 6b). Relative to quasi-quiescent conditions, there is acceleration by at least two orders of magnitude for iPP3 (i.e., 980 s relative to > 12 h) and by as much as five orders of magnitude for iPP4.

The enormous enhancement of crystallization kinetics achieved by a deformation lasting less than 0.04 s reveals the effectiveness of high shear rate in initiating a crystallization that would otherwise be negligible at low supercooling. It also reveals the need to include this effect in processing models, for example, for injection molding, in which the melt experiences shear rates that can exceed [10.sup.4] [s.sup.-1]

Nucleated Samples

In comparison to non-nucleated samples iPP3 and iPP4, crystallization of nucleated iPP1 is modestly enhanced by shearing, while nucleated iPP2 exhibits hardly any enhancement of kinetics (Fig. 6c and d). Thus, highly efficient NA-11 can nearly eliminate the effectiveness of shear. While shearing iPP2 results in a slightly reduced [t.sub.e] compared with the quiescent case (~500 s), it does not lead to a steeper drop in I(T)/I(0); instead, both samples show similar kinetics at later times.

As shown in the polarized optical micrographs of solidified samples, the sheared sample iPP1 (Fig. 7c) has spherulites at least one order of magnitude smaller than those in the quasi-quiescent sample (about 50 [micro]m, Fig. 7a), which means that shearing reduces the spherulile size and increases the number density of nuclei. Due to the densely packed textures shown, it is not possible to determine the number of nuclei per unit volume using the technique proposed by Janeschitz-Kriegl et al. (16). Compared to iPP1, the morphological difference between the sheared and quasi-quiescent samples of iPP2 is much less obvious, except that there is a slightly higher proportion of smaller spherulites in the sheared sample (Fig. 7d) than in the quasi-quiescent sample (Fig. 7b).

The differences in [t.sub.e] and spherulitic morphology between iPP1 and iPP2 are attributed to the lower molecular weight of iPP2 ([M.sub.w] = 160 kg/mol, compared to 384 kg/mol for iPP1). A much larger shear rate, above the range of our apparatus, would be needed to effectively deform the shorter chains in iPP2 to yield crystallization behavior comparable to that of iPP1. Since shear has less effect on polymers of low molecular weight, the use of a nucleating agent is a more effective way to promote the desired fine spherulitic morphology and enhance crystallization kinetics in such materials.

Effect of Molecular Weight

Shear-induced crystallization kinetics of non-nucleated polymers is affected positively by increasing molecular weight. Although polydisperse samples are not ideal for evaluating the effect of molecular weight, [M.sub.w] has been widely used in the past to deal with non-nucleated polymers (39), (41), (45), (83), (84) and proved useful in the present case. This may be due to the small differences in polydis-persity and tacticity and the absence of very long chains in the samples studied. Figure 8 shows the influence of molecular weight on crystallization kinetics after shearing at a command rate of 500 p[.sup.-1] and a strain of 20. As shown in the inset of Fig. 8a, for both the nucleated and non-nucleated samples, [M.sub.w] is seen to have an important effect on the early crystallization kinetics, and this effect is most dramatic in the case of large values of [M.sub.w].

As the early stage is closely associated with nucleation, it is postulated that at high shear rates, molecular weight is the dominant factor controlling nucleation kinetics, and the influence of the highly efficient NA-11 is negligible. D'Haese et al. (26) reported similar observations, where the presence of zinc oxide particles of various sizes (35 nm to 1 /[micro]m) and nucleation efficiencies (4.3-21.7%) did not affect crystallization kinetics at high shear rates (400 [s.sup.-1]).

As noted, a shorter [t.sub.e] implies a larger number of nuclei, and since [t.sub.e] is significantly reduced at larger [M.sub.w], the nuclealion density should also be governed by [M.sub.w]. This is supported by the optical micrographs of sheared samples of iPP2, iPP3, and iPP1l (Fig. 7c-e), which show an increase in the number of spherulites (i.e., number of nuclei) and a decrease in spherulite size with increasing [M.sub.w]. The exception is iPP4, which has the largest [M.sub.w]: rather than showing very line spherulites, the micrograph of this polymer (Fig. 7f) indicates structures that are different and much larger than those of the other three samples (Fig. 7c-e).

As mentioned, crystallization of iPP4 was already initiated during shearing. Shearing a crystallizing polymer can readily induce threadlike structures, and it has been shown previously (85) by means of in. situ optical microscopy that the growth of very large spherulites subsequent to the emergence of threadlike structures can obscure a direct correlation between the final morphology observed in a micrograph and the actual nucleation density. This means that the nucleation density of iPP4 cannot be inferred from the solidified sample using the ex situ micrograph.

Inspection of Table 2 with reference to Table 1 reveals that [t.sub.e] for quasi-quiescent crystallization is not affected in a consistent manner by [M.sub.w]. The large difference in the dependence of [t.sub.e] on [M.sub.w] between shear-induced and quasi-quiescent crystallizations implies that the primary factor regulating the nucleation pathway is [M.sub.w] in shear induced crystallization but nucleating agent in quiescent crystallization. Using four non-nucleated polymers having [M.sub.w] in the range of 116-398 kg/mol, Acierno et al. (83) also found that crystallization kinetics is relatively independent of [M.sub.w] in quiescent experiment but increases considerably with [M.sub.w] in shear-induced crystallization.

TABLE 2. Characteristic times for quiescent crystallization (QC) and
shear-induced crystallization (SIC) at a command shear rate of 500
[s.sup.-1] and a shearing time of 0.04 s.

Sample                iPP1        iPP2             iPP3
Condition         QC   SIC    QC   SIC     QC       SIC     QC

[t.sub.e/s]     3800  350   3520  3000  >43,200     980   >43,200
[t.sub.0.51/s]  7990  2090  6400  6450  >43,200     8570  >43,200

Sample          iPP4
Condition        SIC

[t.sub.e/s]     <0.1
[t.sub.0.51/s]   650


Moving beyond the early stage, while accelerated nucleation with a shorter [t.sub.e] invariably enhances overall crystallization kinetics, this can be attenuated by sluggish growth. This is illustrated by the data at later times, e.g., t > 9000 s, in Fig. 8a and b; despite having the shortest [t.sub.e], iPP4 shows slower kinetics in the late stage, i.e., a much longer time for the decay of I(t)/I(0) to a minimum and a more gradual upturn in |[eta] |(t)/[eta] * |q0, compared to the two nucleated samples iPP1 and iPP2, which both lag in [t.sub.e] but outpace iPP4 at later times owing to rapid growth. In other words, what slows down the overall crystallization in the sheared sample iPP4 is growth, not nucleation, and this is opposite to quiescent crystallization where the rate-limiting step is nucleation. Exhibiting similar behavior is the other non-nucleated sample, iPP3, as evidenced by its very sluggish overall kinetics (Fig. 8b), despite a much shorter /e than iPP2 (Fig. 8a). Molecular weight is thus no longer the determining factor during the late stage of shear-induced crystallization, namely the growth process. Instead, the sequence of the growth kinetics appears to correlate with quiescent crystallization results where the overall crystallization rates are much higher for the nucleated than for the non-nucleated samples. This is demonstrated by the DSC data provided in the Appendix (D).

Collectively, these results can be summarized as follows: (i) the influence of a brief, strong shear flow on overall crystallization kinetics is primarily in inducing nucleation, and this effect is manifested most strongly in high-molecular weight polymers and is independent of the presence of a nucleating agent; and (ii) the subsequent growth of crystalline structures is only modestly affected by flow and thus less dependent on molecular weight. As a result, it follows closely the intrinsic kinetics observed under quiescent conditions. Applied shear must be sufficiently strong for the above points to be valid; otherwise, the nucleation and growth kinetics are both controlled by the nucleating agent.

Effects of Shear Rate and Strain

The effects of shear rate and strain were studied by varying [[??.[gamma].sub.s] at constant [[gamma].sub.s] = 20 and by varying ts at constant [??.[gamma].sub.s] = 200 [s.sup.-1] The I(t)/I(0) and |[eta] |(t)/|[eta] *|q0 data plot ted in Fig. 9a and b show the effect of shear rate on the early and late crystallization kinetics of iPP1, while those given in Fig. 9c and d show the effect of strain. Also included for comparison are quasi-quiescent crystallization data. As expected, when morphological transition is not involved, increasing either [??.[gamma].sub.s] or [gamma].sub.s] accelerates crystallization, i.e., shorter times for the onset of changes in I(t)/I(0) and |[eta] /|[eta] * |q0.

To allow a more quantitative analysis of the data, we use another characteristic time; [t.sub.0.51] is the time at which I(t)/I(0) drops to 50%. This time reveals growth kinetics and is widely used (29), (32). Figure 10 shows the dependence of [t.sub.e] and [t.sub.0.51] on [[gamma].sub.0.51] at [??.[gamma].sub.0.51] = 200 and 500 [s.sup.-1] We found that the slope for re reduces markedly to an apparent plateau around [[gamma].sub.0.51] = 10 at 500 [s.sup.-1] (Fig. 10b), and this observation has been reported previously (32), (63) to be due to saturation in point nuclei, which is followed by a morphological transition at much higher strains. For the shearing conditions studied, we do not see the plateau associated with saturation in the threadlike precursors reported in the literature (29).

Dependence of Crystallization Kinetics on Shearing Time

Figure 11 shows [t.sub.e] and [t.sub.0.51] versus [[gamma].sub.s] for various values of [[??[gamma]t.sub.e] for iPP1. The slope in this double logarithmic plot, i.e., the power-law exponent, plays a key role in models developed to date (3), (28), (86), (87). As shown, the slope is affected by the choice of characteristic time, and this effect is presently not accounted for in most models 13, 28, 86, 87]. Unlike the findings in some studies (3), (28), the exponent is not an integer but varies with [??[gamma].sub.s] and ranges from -0.1 to -1.1 for the shearing conditions tested.

Parameters Characterizing Shear-Induced Crystallization

Several parameters have been used to characterize the acceleration of crystallization. In examining some of our early data, Prof. Janeschitz-Kriegl noted that a reasonably good correlation could be obtained by use of the product of shear rate and strain, [??[gamma].sub.s] [gamma].sub.s]or [??[gamma].sub.s.sup.2] [t.sub.s]. His group had earlier used the parameter of [??[gamma].sub.w.sup.2] [t.sub.s], where [??[gamma].sub.w] is the extrapolated wall shear rate in channel flow (28). Figure 12 is a semi-logarithmic plot of [t.sub.e] and [t.sub.0.51] versus [??[gamma].sub.s] [gamma].sub.s] for data obtained in the ranges of 1 [s.sup.-1] [less than greater or equal to] [??[gamma].sub.s] [less than greater or equal to] 500 [s.sup.-1] and 5 [less than greater or equal to] [??[gamma].sub.s] [less than greater or equal to] 50 [s.sup.-1] for iPP1. The good correlation of the data shows that [??[gamma].sub.s] [gamma].sub.s] is a useful parameter for describing our observations of the effect of shear on crystallization kinetics.

The success of [??[gamma].sub.s] [gamma].sub.s] as a correlating parameter implies that [??[gamma].sub.s] and [gamma].sub.s] are equally effective in enhancing the number of nuclei, before reaching saturation. It has been reported previously 188] that the effect of [gamma].sub.s] is much stronger than that of [??[gamma].sub.s] at comparable values of [[??[gamma].sup.-1] [gamma].sub.s]; but that study only considered two pairs of data for a rather narrow range of shear rates, i.e., 30 [s.sup.-1] [less than or equal to] [[??[gamma]].sup.-1] [less than or equal to] 60 s '. The present observation is based on data for a much broader range of shearing conditions.

Specific work has also been used (6), (63), (89), (90), and this parameter is defined as the total mechanical work per unit volume done on the sample during shearing, as given by Eq.1.

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (1)

The use of this parameter was based on the idea that [sigmma] is a measure of chain orientation, whereas [[.?.[gamma]].sub.s] represents the probability of an encounter between oriented chains (6). Janeschitz-Kriegl (6) noted that there is a transition from chain dynamics (reflected by specific work) (o pure kinematics (reflected by a simple dependence on the square of the deformation rate). Figure 13 shows [t.sub.e] and [t.sub.0.51] versus w for iPP1. Note that the integral in Eq. I was evaluated based on the actual transient stress measured during shearing. Clearly, this correlation is not as successful in the case of our data as that based on [[.?.[gamma]].sub.s] [gamma].sub.s] shown in Fig. 12, thus suggesting specific work is not as effective as [[.?.[gamma]].sub.s] [gamma].sub.s] for characterizing the effect of shear on crystallization kinetics.

CONCLUSIONS

Unlike that in quiescent crystallization, the nucleation pathway of nucleated iPPs containing a highly efficient, melt-insensitive, organophosphate nucleating agent following a brief, strong shear was found to be governed by molecular weight and not by the presence of a nucleating agent. The influence of shear is primarily in inducing nucleation, and this effect is manifested most strongly in high-molecular weight polymers. The subsequent growth of crystalline structures is only modestly affected by flow and thus less dependent on molecular weight; as a result, it follows closely the intrinsic kinetics observed under quiescent conditions. Relative to quiescent crystallization, shear has a stronger effect on non-nucleated polymers than on nucleated polymers. For low-molecular weight polymers, a nucleating agent is more effective than flow in enhancing crystallization kinetics and reducing spherulite size. The product of shear rate and strain was found useful for describing our data.

ACKNOWLEDGMENTS

Hoang Pham of the Dow Chemical Company provided the samples and their molecular characterizations. Prof. Hermann Janeschitz-Kriegl provided helpful comments. Anne Leugers of Dow Chemical loaned us an optical fiber probe for a preliminary study. Anthony Bur of NIST provided valuable advice on construction of the optical probe. Prof. Julia Kornfield of Caltech recommended the all-important addition of optical measurements to the project originally proposed.

APPENDIX

A. Molecular Weight Distributions

Molecular weight distributions of the two nucleated samples are shown in Fig. Al. Sample iPP1 has the higher weight-and number-average molecular weights but the ratios of the two are nearly the same for both.

B. Command versus Actual Shear Rates and Strain

Because of the frequency-response limitation of the rheometer actuator, the plate speed deviates from the command vaiue. This is illustrated in Fig. A2. First, there is a delay in the start of motion, but this is never more than 0.01 s (insets of Fig. A2a and b), and is easily accounted for by use of an offset time in the analysis of data. Another effect is a variation of the plate speed during a test, which is most significant at the highest strain rate and smallest strain (Fig. A2d). As shown in the inset of Fig. A2c for a command shear rate of 500 s" 1 and a command strain of 20, the command plate speed is achieved only for the central 60% of the strain time; the average rate during this portion of the test was 494 [s.sup.-1]. During the initial and final stages of the test, the plate speed is somewhat less than the command rate. For simplicily, we use the command value of the strain rate in discussing high-shear-rate data.

C. Wall Slip

Wall slip was found at high shear rates and large strains. When slip occurs, the actual strain experienced by the sample can be much less than the nominal value cal-culaied from the plate speed, the gap between the plates, and the command shearing time. Its occurrence is revealed by the transient stress at the start-up of steady shear. Figure A3 shows shear stress versus time for iPPl under several conditions. Data for three runs at each condition are shown. Slip is revealed by irreproducible and erratic stress signals. Figure A3a shows that there is no slip for a shear rate of 50 [s.sup.-1] at either of the two strains used. Figure A3b and c show that for the two larger shear rates, there is no slip at a total strain of about 25, but slip is clearly present at strains of 30 and 50.

D. Isothermal Crystallization Kinetics and Avrami Analysis

The DSC data under isothermal, quiescent crystallization conditions are shown in Fig. A4a and b, and the results of an Avrami analysis are shown in Fig. A4c and d. As indicated by the larger values of Avrami exponent n, the nucleated samples (Fig. A4c) show faster overall crystallization kinetics than the non-nucleated samples (Fig. A4d). Because the signals were too small at the temperature used in shear-induced crystallization studies, DSC experiments were performed at temperatures lower than I55.5[degrees]C.

REFERENCES

(1.) G. Eder, H. Janeschitz-Kriegl, and S. Liedauer, Prog. Polym. Sci., 15, 629 (1990).

(2.) A. Keller and H.W.H. Kolnaar, "Flow-Induced Orientation and Structure Formation," inMaterials Science and Technology: A Comprehensive Treatment, R.W. Cahn, P. Haasen, and E.J. Kramer, Eds., Wiley-VCH, Weinheim, 189 (1997).

(3.) G. Eder and H. Janeschitz-Kriegl, "Crystallization," mMaterials Science and Technology: A Comprehensive Treatment, R.W. Cahn, P. Haasen, and E.J. Kramer, Eds., Wiley-VCH, Weinheim, 269 (1997).

(4.) J.A. Kornfield, G. Kumaraswamy, and A.M. Issaian, Ind. Eng. Chem. Res., 41, 6383 (2002).

(5.) G. Kumaraswamy, J. Macromol. Sci., Polym. Rev., 45, 375 (2005).

(6.) H. Janeschitz-Kriegl, Crystallization Modalities in Polymer Melt Processing: Fundamental Aspects of Structure Formation, Springer Wien, New York (2010).

(7.) J. Kurja and N. Mehl, "Nucleating agents for semi-crystalline polymers," inP/ast/cs Additives Handbook, H. ZweifeJ, R.D. Maier, and M. Schiller, Eds., Hanser Publishers, Munich, 967 (2009).

(8.) R.F. Becker, E. Burgin, and L.P.J. Burton, "Additives," mPolypropylene Handbook, N. Pasquini, Ed. Hanser Publishers, Munich, 280 (2005).

(9.) H. Dragaun, H. Hubeny, and H. Muschik, J. Polym. Sci., Polym. Phys. Ed., 15, 1779 (1977).

(10.) M. Fujiyama and T. Wakino, J. Appl. Polym. Sci., 42, 2739 (1991).

(11.) M. Gahleitner, J. Wolfschwengcr, C. Bachner, K. Bernreit-ner, and W. NeiBl,.J. Appl. Polym. Sci., 61, 649 (1996).

(12.) P.W. Zhu, J. Tung, A. Phillips, and G. Edward, Macromole-cuies, 39, 1821 (2006).

(13.) J.W. Housmans, M. Gahleitner, G.W.M. Peters, and H.E.H. Meijer, Polymer, 50, 2304 (2009).

(14.) M.D. Wolkowicz,.J. Polym. Sci., Polym. Symp., 63, 365 (1978).

(15.) C. Tribout, B. Monasse, and J.M. Haudin, Colloid Polym. Sci., 274, 197 (1996).

(16.) H. Janeschitz-Kriegl, E. Ratajski, and M. Stadlbaucr, Rheol. Acta, 42, 355 (2003).

(17.) Y. Khanna, Macromolecules, 26, 3639 (1993).

(18.) R.R. Lagasse and B. Maxwell, Polym. Eng. Sci., 16, 189 (1976).

(19.) C.H. Sherwood, F.P. Price, and R.S. Stein, J. Polym. Sci., Polym. Symp., 63, 77 (1978).

(20.) L. Mandelkern, Crystallization of Polymers. Vol. 2: Kinetics and Mechanisms, Cambridge University Press, Cambridge (2004).

(21.) J.P. Mercier, Polym. Eng. Sci., 30, 270 (1990).

(22.) M. Kristiansen, M. Werner, T. Tervoort, P. Smith, M. Blomenhofer, and H.W. Schmidt, Macromolecules, 36, 5150 (2003).

(23.) A. Nogalcs, G.R. Mitchell, and A.S. Vaughan, Macromolecules, 36, 4898 (2003).

(24.) L. Balzano, S. Rastogi, and G.W.M. Peters, Macromolecules, 41, 399 (2008).

(25.) D. Byelov, P. Panine, K. Remerie, E. Biemond, G.C. Alfonso, and W.H. de Jeu, Polymer, 49, 3076 (2008).

(26.) M. D'Haese, P. Van Puyvelde, and F. Langouche, Macro-molecules, 43 2933 (2010).

(27.) A.W. Phillips, A. Bhatia, P.-W. Zhu, and G. Edward, Macromolecules, 44, 3517 (2011).

(28.) S. Liedauer, G. Eder, H. Janeschitz-Kriegl, P. Jerschow, W. Geymayer, and E. Ingolic, Int. Polym. Process., 8, 236 (1993).

(29.) G. Kumaraswamy, A.M. Issaian, and J.A. Kornlield, Macro-molecules, 32, 7537 (1999).

(30.) C. Hadinata, C. Gabriel, M. Ruellmann, N. Kao, and H.M. Laun, Rheol. Acta, 45, 539 (2006).

(31.) T.W. Haas and B. Maxwell, Polym. Eng. Sci., 9, 225 (1969).

(32.) J. Baert, P. Van Puyvelde, and F. Langouche, Macromolecules, 39, 9215 (2006).

(33.) F. Langouche, Macromolecules, 39, 2568 (2006).

(34.) S. Naudy, L. David, C. Rochas, and R. Fulchiron, Polymer, 48, 3273 (2007).

(35.) L. Fernandez-Ballester, D.W. Thurman, and J.A. Kornfield, J. Rheol., 53, 1229(2009).

(36.) K. Mezghani and P.J. Phillips, Polymer, 39, 3735 (1998).

(37.) C. Angelloz, R. Fulchiron, A. Douillard, B. Chabert, R. Fillit, A. Vautrin, and L. David, Macromolecules, 33, 4138 (2000).

(38.) P. Jerschow and H. Janeschitz-Kriegl, Int. Polym. Process., 12,72(1997).

(39.) F. Jay, J.M. Haudin, and B. Monasse, J. Mater. Sci., 34, 2089(1999).

(40.) M. Seki, D.W. Thurman, J.P. Obcrhauser, and J.A. Kornfield, Macromolecules, 35, 2583 (2002).

(41.) C. Hadinata, C. Gabriel, M. Ruellman, and H.M. Laun, J. Rheol., 49, 327 (2005).

(42.) R.H. Somani, L. Yang, and B.S. Hsiao, Polymer, 47, 5657 (2006).

(43.) S. Kimata, T. Sakurai, Y. Nozue, T. Kasahara, N. Yamaguchi, T. Karino, M. Shibayama, and J.A. Kornfield, Science, 316, 1014 (2007).

(44.) A. Elmoumni, R.A. Gonzalez-Ruiz, E.B. Coughlin, and H.H. Winter, Macromoi. Chem. Phys., 206, 125 (2005).

(45.) J. Baert and P. Van Puyvelde, Polymer, 47, 5871 (2006).

(46.) H. Huo, S. Jiang, L. An, and J. Feng, Macromolecules, 31, 2478 (2004).

(47.) J. Fritsch, W. Stille, and G. Strobl, Colloid Polym. Sci., 284, 620 (2006).

(48.) B. Heck, T. Kawai, and G. Strobl, Polymer, 47, 5538 (2006).

(49.) R. Deltu, W. Stille, and G. Strobl, Macromolecules, 43, 1035 (2010).

(50.) G. Strobl, Prog. Polym. Sci., 31, 398 (2006).

(51.) G. Strobl, Rev. Mod. Phys., 81, 1287 (2009).

(52.) T. Kawai, T. Matsumoto, M. Kato, and H. Maeda, Kolloid-Z. u. Z. Potymere, 222, 1 (1968).

(53.) K. Kobayashi and T. Nagasawa, J. Macromoi. Sci., Phys., 4, 331 (1970).

(54.) A. Wereta Jr, and C.G. Gogos, Polym. Eng. Sci., 11, 19 (1971).

(55.) N.V. Pogodina and H.H. Winter, Macromolecules, 31, 8164 (1998).

(56.) N.V. Pogodina, S.K. Siddiquee, J.W. Van Egmond, and H.H. Winter, Macromolecules, 32, 1167 (1999).

(57.) N.V. Pogodina, H.H. Winter, and S. Srinivas,. J. Polym. Sci., Part B: Polym. Phys., 37, 3512 (1999).

(58.) N.V. Pogodina, V.P. Lavrenko, S. Srinivas, and H.H. Winter, Polymer, 42, 9031 (2001).

(59.) S. Coppola, S. Acierno, N. Grizzuti, and D. Vlassopoulos,

Macromolecules, 39, 1507 (2006).

(60.) C. Hadinata, C. Gabriel, M. Ruellmann, N. Kao. and H.M. Laun, Rheol. Acta, 45, 631 (2006).

(61.) K. Bouiahar, C. Carrot, and J. Guillet, Macromolecules, 31, 1921 (1998).

(62.) N.J.L. Van Ruth, J.F. Vega, S. Rastogi, and J. Martinez-Sal-azar, J. Mater. Sci., 41, 3899 (2006).

(63.) J.-W. Housmans, R.J.A. Steenbakkers, P.C. Roozemond, G.W.M. Peters, and H.E.H. Meijer, Macromolecules, 42, 5728 (2009).

(64.) F. Bustos, P. Cassagnau, and R. Fulchiron, J. Polym. Sci., Part B: Polym. Phys., 44, 1597 (2006).

(65.) R. Pantani, I. Coccorullo, V. Speranza, and G. Titomanlio, Prog. Polym. Sci., 30, 1185 (2005).

(66.) G. Lamberti, G.W.M. Peters, and G. Titomanlio, Int. Polym. Process., 22, 303 (2007).

(67.) R.J.A. Steenbakkers and G.W.M. Peters, Rheol. Acta, 47, 643 (2008).

(68.) S. Nagasawa, A. Fujimori, T. Masuko. and M. Iguchi, Polymer, 46, 5241 (2005).

(69.) N. Behrendt, N. Mohmeyer, J. Hillenbrand, M. Klaibcr, X. Zhang, G.M. Sessler, H.W. Schmidt, and V. Altstadt, .J. Appl. Polym. Sci., 99, 650 (2006).

(70.) S. Yoshimoto, T. Ueda, K. Yamanaka, A. Kawaguchi, E. Tobita, and T. Haruna, Polymer, 42, 9627 (2001).

(71.) J.S. Tiang, Shear-Induced Crystallization of Nucleated Polymers, McGill University, Montreal, Canada (2010).

(72.) S.G. Hatzikiriakos and J.M. Dealy,.J. Rheol., 35, 497 (1991).

(73.) J. Xu, S. Costeux, J.M. Dealy, and M.N. De Decker, Rheol. Ada, 46, 815 (2007).

(74.) H.E. Park, S.T. Lim, F. Smillo, J.M. Dealy. and C.G. Robertson, J. Rheol., 52, 1201 (2008).

(75.) C.L. Thomas and A.J. Bur, Polym. Eag, Sci., 39, 1291 (1999).

(76.) A.L. Marinelli, M. Farah, and R.E.S. Bretas, J. Appi. Polym. Sci., 99, 563 (2006).

(77.) R.S. Harner, R.J. Ressler, R.L. Briggs, J.E. Hitt. P.A. Larsen. and T.C. Frank, Org, Process Res. Dm., 13, 114 (2009).

(78.) E.L. Heeley, A.V. Maidens, P.D. Olmstead, IV. Bras, I.P. Dolbnya, J.P.A. Fairelough, N.J. Terrill, and A.J. Ryan, Macromoiecules, 36, 3656 (2003).

(79.) C. Marco, M.A. Gomez, G. Ellis, and J.M. Arribas, J. Appi. Polym. Set., 84, 1669(2002).

(80.) D.Y. Yoon and R.S. Stein. J. Polym. Sci., Polym. Phys. Ed., 12,735 (1974).

(81.) Y. Akpalu, L. Kiclhorn, B.S. Hsiao, R.S. Stein, T.P. Russell, J. Van Egmond, and M. Muthukumar. Macromoiecules, 32. 765 (1999).

(82.) J. Xu, S. Srinivas, H. Marand, and P. Agarwal, Macromole-cuks, 31, 8230 (1998).

(83.) S. Acierno, B. Palomba, H.H. Winter, and N. Griz/.uti, Rheol. Acta, 42. 243 (2003).

(84.) A. Nogales, B.S. Hsiao, R.H. Somani, S. Srinivas, A.H. Tsou, F.J. Balta-Calleja, and T.A. Ezquerra, Polymer, 42, 5247 (2001).

(85.) R.H. Somani, L. Yang, I. Sics, B.S. Hsiao, N.V. Pogodina, H.H. Winter, P. Agarwal, H. Fruitwala, and A. Tsou, Mac-romol. Symp., 185, 105 (2002).

(86.) R. Zheng and P.K. Kennedy, J. Rheol., 48, 823 (2004).

(87.) H. Zuidema, G.W.M. Peters, and H.E.IL Mcijer. Macromoi. Theory Simtil., 10. 447 (2001).

(88.) R.H. Somani, L. Yang, B.S. Hsiao, T. Sun, N.V. Pogodina. and A. Lustiger, Macromolectttes, 38, 1244 (2005).

(89.) H. Janeschitz-Kricgl and E. Ratajski, Polymer, 46, 3856 (2005).

(90.) O.O. Mykhaylyk, P. Chambon, R.S. Graham, J.P.A. Fair-dough, P.D. Olmsted, and A.J. Ryan, Macromoiecules, 41, 1901 (2008).

Correspondence to: John M. Dealy; e-mail: john.dea!y@mcgill.ca Jen Shueng Tiang is currently at AkzoNobel China Applied Research Group, No. 137 Jiangtian East Road, Songjiang Industrial Estate, Shanghai, 201600, P.R. China

Published online in Wiley Online Library (wileyonlinclibrary.com). [c] 2011 Society of Plastics Engineers

Jen Shueng Tiang, John M. Dealy Department of Chemical Engineering, McGill University, Montreal, Quebec H3A 2B2, Canada

DOI 10.1002/pcn.22150
COPYRIGHT 2012 Society of Plastics Engineers, Inc.
No portion of this article can be reproduced without the express written permission from the copyright holder.
Copyright 2012 Gale, Cengage Learning. All rights reserved.

Article Details
Printer friendly Cite/link Email Feedback
Author:Tiang, Jen Shueng; Dealy, John M.
Publication:Polymer Engineering and Science
Article Type:Report
Geographic Code:1CANA
Date:Apr 1, 2012
Words:8698
Previous Article:The application of digital image techniques to determine the large stress-strain behaviors of soft materials.
Next Article:Rheological properties and irreversible dispersion changes in Carbon nanotube/epoxy systems.
Topics:

Terms of use | Privacy policy | Copyright © 2021 Farlex, Inc. | Feedback | For webmasters |