**4.1. Model**

To account for the structural effects due to elongational flow along the centerline region in the capillary die, the overall melt flow characteristics are divided into three regions depending on the magnitude of the maximum fluid velocity in the capillary that is usually along the centerline in converging flows. This critical fluid velocity corresponds to the maximum stretching rate of the TLCP (or TC3 white) domains at which irreversible TLCP (or TC3 white) domain elongation into slender filament occurs. The three regimes are:

Region I: The fluid velocity is below the critical velocity for irreversible TLCP (or TC3 white) domain elongation, and the flow of the blends is dominated by the melt flow behavior of the matrix polymer HMMPE melt, independent of TLCP (or TC3 white). A schematic illustration of the melt structure during flow in Region I is shown in Figure 20(a). PE chains formed random coiled conformation and TLCP (or TC3 white) has ellipse shapes with uniformed dispersion in PE matrix. The insert in Figure 20(a) shows the organoclay and TLCP chain conformation at this region. Organoclays of uniform size were well and irregularly dispersed in the nematic phase TLCP.

**Figure 20.** Schematic drawing of HMMPE chains, TLCP chains and organoclay morphological change in capillary die at 190 oC (a) before and (b) after critical shear rates.

Region II: The maximum fluid velocity within the capillary reaches the critical velocity at the entrance of the capillary and irreversible elongational deformation of the TLCP (or TC3 white) domains into long slender fibrous forms begin to occur. This causes a rapid chain elongation and disengagement in the PE melt adjacent to the TLCP (or TC3 white) domains. Consequently, a region of low viscosity melt is formed in the center core of the capillary die. This center region expands as the flow rate increases until all fluid within the capillary is filled with such melt. The simulated velocity profile developments of fluid flowing through a capillary die to describe the above phenomenon will be presented later in this study. A schematic illustration of the melt structure during flow in Region II is shown in Figure 20(b). The insert in Figure 20(b) shows the chain conformations of TLCP molecules with help of organoclay. Shear-induced molecular alignment occurs with TLCP molecules and organoclay oriented along the elongation direction.

Region III: After all low viscosity fluid is formed across the entire capillary die diameter, a homogeneous melt flow corresponding to the low viscosity melt may be assumed again.

## **4.2. Velocity profiles**

296 Viscoelasticity – From Theory to Biological Applications

irregularly dispersed in the nematic phase TLCP.

in capillary die at 190 oC (a) before and (b) after critical shear rates.

blends in this study.

**4.1. Model** 

**4. Predictions based on a phenomenological model** 

A binary flow pattern model, previously used for prediction of the effects of a small amount of TLCP in HMMPE (TR570) [40] was used to simulate the rheological responses of the

To account for the structural effects due to elongational flow along the centerline region in the capillary die, the overall melt flow characteristics are divided into three regions depending on the magnitude of the maximum fluid velocity in the capillary that is usually along the centerline in converging flows. This critical fluid velocity corresponds to the maximum stretching rate of the TLCP (or TC3 white) domains at which irreversible TLCP (or TC3 white) domain elongation into slender filament occurs. The three regimes are:

Region I: The fluid velocity is below the critical velocity for irreversible TLCP (or TC3 white) domain elongation, and the flow of the blends is dominated by the melt flow behavior of the matrix polymer HMMPE melt, independent of TLCP (or TC3 white). A schematic illustration of the melt structure during flow in Region I is shown in Figure 20(a). PE chains formed random coiled conformation and TLCP (or TC3 white) has ellipse shapes with uniformed dispersion in PE matrix. The insert in Figure 20(a) shows the organoclay and TLCP chain conformation at this region. Organoclays of uniform size were well and

**Figure 20.** Schematic drawing of HMMPE chains, TLCP chains and organoclay morphological change

Region II: The maximum fluid velocity within the capillary reaches the critical velocity at the entrance of the capillary and irreversible elongational deformation of the TLCP (or TC3 white) domains into long slender fibrous forms begin to occur. This causes a rapid chain elongation and disengagement in the PE melt adjacent to the TLCP (or TC3 white) domains. Consequently, a region of low viscosity melt is formed in the center core of the capillary die.

The velocity profile developments of fluid flowing through capillary dies are shown in Figure 21.

**Figure 21.** Velocity profile development in region II of flow at R = 0.462 mm for (a) HMMPE/TLCP 1.0 wt% and (b)HMMPE/TC3 white 1.0 wt% at 190 oC by simulation.

As shear rate increases, the center core region characterized by low viscosity melt flow characteristics expands from the center core towards the die wall. Close to the wall, the velocity profiles are independent of apparent shear rates. This implies that the shear rates at the wall are independent of flow rates of fluid during the melt structure transition period. Consequently, the wall shear stresses will remain constant throughout this transition period. In the velocity profiles for the different blends, the real die diameters were used instead of the nominal diameters. For nominal diameters 1.0 mm and 0.7 mm, the real calibrated diameters were 0.924 mm and 0.542 mm. Table 1 shows the predicted yielding stress and transition shear rates with the experimental data. The predicted data coincide well with the experimental results. The prediction results also give the end transition shear rates for PT1 at 190 oC with different die diameters, which cannot be obtained experimentally due to the flow oscillation.

## **4.3. Flow curves simulation**

The flow curves are divided into three regimes as described above. In Regions (I) and (III), simple power-law constitutive relations are assumed. In Region (I), because of the relatively lower yielding shear rates for these blends, dynamic frequency sweep data performed on ARES were used combined with data from CR for simulation. The flow curves in Region (II) were obtained using the velocity profiles together with the power-law parameters in Regions (I) and (III). Figure 22 shows the schematic drawing of apparent shear viscosity as a function of shear stress at wall at the different stages in capillary die. Precise flow curves with Matlab program simulation for the blends are plotted in Figure 15 together with experimental data. Excellent agreement between the model prediction and the experimentally measured flow curves are obtained.

Micro-Rheological Study on Fully Exfoliated Organoclay Modified Thermotropic Liquid Crystalline Polymer and Its Viscosity Reduction Effect on High Molecular Mass Polyethylene 299

displayed a continuous nematic phase with a few isotropic phases. The interactions between organoclays with TLCP molecules at the molecular level enhanced the rigidity of the TLCP molecules, displaying the nematic order structure even at higher temperature. The rheological experiments using CR with a nominal die of L/D = 30 and diameter 1.0 mm showed even higher viscosity reduction ability with a wider processing window for TC3 white than for the purified TLCP in the PE matrix. In addition, a much lower yielding stress with a narrower transition window was obtained in the TC3 white/PE blend than in the purified TLCP/PE blend. These findings have promising potential for industrial application to save energy and increase processing efficiency when used in processing such thermoplastics. Mechanism study confirmed that the binary flow model can be applied to describe the rheological behaviours of both blends and shear induced phase transitions and alignment of in-situ formation of fibrils are the primary reasons for viscosity reduction.

**Author details** 

**Acknowledgement** 

**6. References** 

*Flinders University, Adelaide, South Australia, Australia* 

Vol. 41, No. 5, pp. 1117-1145, ISSN 0148-6055

Vol. 39, No.8, pp.1353-1364, ISSN 0032-3888

632-636, ISSN 0032-3888

0032-3888

*The Hong Kong University of Science and Technology, Kowloon, Hong Kong, China* 

Research Council – Discovery Early Career Researcher Award (ARC-DECRA).

*Engineering and Science*, Vol 37, No. 12, pp. 1944-1958, ISSN 0032-3888

This project was funded by Research Grant Council (RGC) of Hong Kong and Australian

[1] Romo-Uribe, A.; Lemmon, T. J. & Windle, A. H. (1997). Structure and linear viscoelastic behaivor of main-chain thermotropic liquid crystalline polymers. *Journal of Rheology*,

[2] Chan, C. K.; Whitehouse, C. & Gao, P. (1999). The effect of TLCP melt structure on the bulk viscosity of high molecular mass polyethylene. *Polymer Engineering and Science*,

[3] Whitehouse, C.; Lu, X. H.; Gao, P. & Chai, C. K. (1997). The viscosity reducing effects of very low concentrations of a thermotropic copolyester in a matrix of HDPE. *Polymer* 

[4] Baird, D. G. & Wilkes, G. L. (1983). Sandwich injection-molding of thermotropic copolyesters and filled polyester. *Polymer Engineering and Science*, Vol. 23, No. 11, pp.

[5] Bafna, S. S.; de Souza, J. P.; Sun, T. & Baird, D. G. (1993). Mechanical-properties of in-situ composites based on partially miscible blendd of glass-filled polyetherimide and liquidcrystalline polymers. *Polymer Engineering and Science*, Vol. 33, No. 13, pp. 808-818, ISSN

Youhong Tang

Ping Gao

**Figure 22.** Schematic drawing of apparent shear viscosity evolution as a function of stress at wall at different stages in capillary die at 190 oC.

### **5. Conclusions**

An organoclay-modified TLCP nanocomposite (TC3 white) with the organoclays of uniform size 15-25 nm in length well dispersed in thermotropic liquid crystalline polymer (TLCP) with fully exfoliated structures was designed and prepared by a combination method. Polarized optical microscope images showed that the organoclay did not affect the liquid crystallinity and mesophase structures of the TLCP matrix. However, thermal stability and thermal properties were affected by the organoclay, enhancing the thermal stability of TLCP and shifting the transition temperatures to the high ends. The presence of organoclays caused the nanocomposite to present different rheological behaviours with TLCP at the nematic temperature, i.e. 185 oC. Dynamic experiments demonstrated that TC3 white displayed higher pseudo-solidlike behaviour than TLCP alone in the low frequency region. TC3 white had a similar but even lower viscosity and the first normal stress difference (N1) than TLCP, but the rate of N1 increase in TC3 white was greater than that in TLCP. When enhanced with organoclays, TLCP became more rigid, and with a slight deformation in the TC3 white melt, organoclay helped the TLCP molecules to align in the shear direction and to retain the orientation.

The rheological behaviours of purified TLCP and TC3 white in high molecular mass polyethylene (HMMPE) were characterized by capillary rheometer (CR) with nominal dies of L/D = 30 and diameters 0.7 mm and 1.0 mm at 190 oC, where purified TLCP and TC3 white showed similar nematic phase structures. At 230 oC, purified TLCP presented as a continuous isotropic phase with a minority of discrete nematic phase, whereas TC3 white displayed a continuous nematic phase with a few isotropic phases. The interactions between organoclays with TLCP molecules at the molecular level enhanced the rigidity of the TLCP molecules, displaying the nematic order structure even at higher temperature. The rheological experiments using CR with a nominal die of L/D = 30 and diameter 1.0 mm showed even higher viscosity reduction ability with a wider processing window for TC3 white than for the purified TLCP in the PE matrix. In addition, a much lower yielding stress with a narrower transition window was obtained in the TC3 white/PE blend than in the purified TLCP/PE blend. These findings have promising potential for industrial application to save energy and increase processing efficiency when used in processing such thermoplastics. Mechanism study confirmed that the binary flow model can be applied to describe the rheological behaviours of both blends and shear induced phase transitions and alignment of in-situ formation of fibrils are the primary reasons for viscosity reduction.
