**3.2. Molecular interactions in nanocomposite**

IR spectroscopy is very sensitive to polymer microstructure and has been widely used in the investigation of hydrogen bonding, macromolecular orientation and crystallinity in polymer materials. FTIR with liquid cell was used with chloroform as background. Figure 3 shows the FTIR spectra for chloroform solutions with TLCP and TC3 white under ultrasonic irradiation at room temperature. It can be seen that the peak at the wavenumber of 1060 cm-1 in TLCP shifts to the wavenumber of 1045 cm-1 in TC3 white. The absorption peak at 1060 cm-1 is believed to represent *C O* in the TLCP molecules. The peak shift is the result of weak interaction between the positively changed N+ ion in the surfactant 2M2HT residing on the surface of the organoclay Closite 20A with *C O* group in the TLCP molecules.

Micro-Rheological Study on Fully Exfoliated Organoclay Modified Thermotropic Liquid Crystalline Polymer and Its Viscosity Reduction Effect on High Molecular Mass Polyethylene 283

with few other colors because of the lower light intensity. Upon startup of the shear flow, the domain textures became deformed, stretched and aligned along the shear direction. A gradual increase in the light intensity was observed. During shearing, TLCP (in Figure 5(c)) exhibited colorful textures (yellow, red and blue with some dark areas). TC3 white (Figure 5(d)) exhibited a mainly color (yellow with a few blue and red areas). With the polarized light, darkening may result from the structure becoming either completely isotropic or perfectly oriented along the principal axes. However, the darkening was not observed without the use of a polarizer; therefore isotropy can be ruled out as the primary cause for

**Figure 5.** POM images of TLCP (a, c, e) and TC3 white (b, d, f) at 185 oC (a) and (b) before steady shear (X4); (c) and (d) during steady shear at 0.5 1/s (X20); (e) and (f) after steady shear and relax to steady

The microstructures relaxation after the flow cessation is illustrated in Figure 5 (e) and 5(f). Once a steady flow was reached, a monodomain with a few defect structures was formed. After the same shear history, TLCP and TC3 white showed different colors. The areas of high Frank elasticity around the ±1/2 strength defects showed the highest and lowest retardation colors, whereas the bulk of the texture showed an intermediate retardation color. The static texture of the nanocomposite after steady shear is similar to that of the homopolymer. The existence of the fully exfoliated organoclays did not affect the mesophase structure of the TLCP molecules, which may due to the good dispersion of

this darkening phenomenon.

state (X20).

organoclays and their small sizes.

**Figure 3.** FTIR of TLCP and TC3 white chloroform at room temperature with liquid cell.

Figure 4 shows 13C NMR spectra obtained from TLCP and TC3 white at room temperature. It is well known that a chemical shift between 0-40 pm corresponds to *C C* coupling. After careful analysis of these regions, it was determined that the peaks at 25.2, 29.4 and 34.7 ppm shown in Figure 4(a), 4(b) and 4(c) belong to the spacer 2 8 ( ) *CH* in TLCP. No chemical shift occurred but the peaks width increased after addition of the organoclay. The relatively broad peaks are probably due to the shielding effects of the layered silicate gallery on the alkyl chains.

**Figure 4.** 13C NMR spectroscopes of TLCP and TC3 white in CDCl3 at room temperature.

## **3.3. Liquid crystalline mesophase**

Figure 5 displays the in-situ microstructure evolution of TLCP and TC3 white using polarization transmission optical microscopy. The incident polarization was oriented along the flow direction and the analyzer was oriented perpendicular to this polarization. The first images are the microstructures of the melted TLCP (Figure 5 (a)) and TC3 white (Figure 5(b)) in the quiescent state at 185 oC. The TLCP micrograph shows textures surrounding different colors (blue, yellow and pink) regions, which indicate domains of different orientations. Compared with TLCP, TC3 white shows the domains (mainly darker yellow) with few other colors because of the lower light intensity. Upon startup of the shear flow, the domain textures became deformed, stretched and aligned along the shear direction. A gradual increase in the light intensity was observed. During shearing, TLCP (in Figure 5(c)) exhibited colorful textures (yellow, red and blue with some dark areas). TC3 white (Figure 5(d)) exhibited a mainly color (yellow with a few blue and red areas). With the polarized light, darkening may result from the structure becoming either completely isotropic or perfectly oriented along the principal axes. However, the darkening was not observed without the use of a polarizer; therefore isotropy can be ruled out as the primary cause for this darkening phenomenon.

282 Viscoelasticity – From Theory to Biological Applications

on the alkyl chains.

**3.3. Liquid crystalline mesophase** 

**Figure 3.** FTIR of TLCP and TC3 white chloroform at room temperature with liquid cell.

**Figure 4.** 13C NMR spectroscopes of TLCP and TC3 white in CDCl3 at room temperature.

Figure 5 displays the in-situ microstructure evolution of TLCP and TC3 white using polarization transmission optical microscopy. The incident polarization was oriented along the flow direction and the analyzer was oriented perpendicular to this polarization. The first images are the microstructures of the melted TLCP (Figure 5 (a)) and TC3 white (Figure 5(b)) in the quiescent state at 185 oC. The TLCP micrograph shows textures surrounding different colors (blue, yellow and pink) regions, which indicate domains of different orientations. Compared with TLCP, TC3 white shows the domains (mainly darker yellow)

Figure 4 shows 13C NMR spectra obtained from TLCP and TC3 white at room temperature. It is well known that a chemical shift between 0-40 pm corresponds to *C C* coupling. After careful analysis of these regions, it was determined that the peaks at 25.2, 29.4 and 34.7 ppm shown in Figure 4(a), 4(b) and 4(c) belong to the spacer 2 8 ( ) *CH* in TLCP. No chemical shift occurred but the peaks width increased after addition of the organoclay. The relatively broad peaks are probably due to the shielding effects of the layered silicate gallery

**Figure 5.** POM images of TLCP (a, c, e) and TC3 white (b, d, f) at 185 oC (a) and (b) before steady shear (X4); (c) and (d) during steady shear at 0.5 1/s (X20); (e) and (f) after steady shear and relax to steady state (X20).

The microstructures relaxation after the flow cessation is illustrated in Figure 5 (e) and 5(f). Once a steady flow was reached, a monodomain with a few defect structures was formed. After the same shear history, TLCP and TC3 white showed different colors. The areas of high Frank elasticity around the ±1/2 strength defects showed the highest and lowest retardation colors, whereas the bulk of the texture showed an intermediate retardation color. The static texture of the nanocomposite after steady shear is similar to that of the homopolymer. The existence of the fully exfoliated organoclays did not affect the mesophase structure of the TLCP molecules, which may due to the good dispersion of organoclays and their small sizes.

#### **3.4. Thermal properties**

The thermal stability of polymeric material is usually studied by thermogravimetric analysis. Generally, the incorporation of clay into the polymer matrix is found to enhance thermal stability, as the clay acts as a superior insulator and mass transport barrier to oxygen during oxidation in the air condition.

Micro-Rheological Study on Fully Exfoliated Organoclay Modified Thermotropic Liquid Crystalline Polymer and Its Viscosity Reduction Effect on High Molecular Mass Polyethylene 285

polymer chains became more ordered. There is no doubt that the transition temperatures in

**Figure 7.** Second heating (a) and cooling (b) curves of TLCP and TC3 white at N2 atmosphere.

Dynamic frequency sweeps at strains well within the linear viscoelastic regime of each material were performed in a range of frequencies covering 5 decades (0.01 – 1000 rad/s). The results shown in Figure 8 exhibit the storage modulus *G*' , loss modulus *G*'' and

for TLCP and TC3 white. For TLCP, *G*' , *G*'' and \*

and scattered for accurate measurement at lower frequencies (in the region of 0.04 rad/s to 0.25 rad/s ). This was due to the low viscosity of the melt at 185 oC, which led to torque values beyond the limits of the transducer. In the low frequency region (0.04 rad/s to 0.25 rad/s), TC3 white had dependable data but the TLCP data was scattered. In this region,

TLCP and TC3 white, with TC3 white exhibiting more solidlike behavior than TLCP. The polydomain structure in the bulk state of TLCP is the reason for TLCP behavior [25]. The percolated network formed by the exfoliated organoclay with the TLCP molecules enhanced

frequency region in TC3 white. In the middle frequency region, both showed plateaus of nearly constant viscosity. The TC3 white curve paralleled the x-axis and TLCP had a small slope value of -0.15. At high frequencies, TC3 white showed a gradual change of slope to -

TLCP were 0.70 and 0.86 but for TC3 white, they were 1.83 and 0.92. There were dramatic differences between the two materials. The slopes for TC3 white approached the theoretical values for polymers with flexible chains, which are 2 and 1, respectively. With the help of exfoliated clay in high frequencies, TC3 white performed like flexible chains, whereas TLCP

were 0.12 and 0.31 for TC3 white, and 0.30 and 0.55 for TLCP. The

were 0.83 and 0.58. Pseudo-solidlike behaviors existed in

 and *G*for

became too small

in the lower

the heating and cooling curves increased in TC3 white.

**3.5. Rheological properties** 

still showed some entanglement behavior.

those polydomain structures, causing more solidlike behavior and higher \*

0.21, whereas TLCP maintained the same slope. In this region, the slopes of G

corresponding slope values for \*

**Linear viscoelasticity** 

complex viscosity \*

slopes for G and G

*3.5.1. Organoclay modified TLCP nanocomposite* 

The TGA curves of clay, TLCP, and TC3 white in the air flow condition are shown in Figure 6. No weight loss occurred below 200 oC in any of the samples. Because of the presence of some organic molecules in interlayer spaces, the clay began to lose weight at 230 oC; at 600 oC, the clay weight loss was 30 %, similar to the result reported by Chiu et al. [23] Comparing TLCP with TC3 white, the thermal stability of TC3 white increased. For example, for TLCP, the temperature at which the weight loss started was 335 oC whereas for TC3 white, it was 349 oC. For TLCP, the temperature at which the weight loss was halved was 530 oC and for the nanocomposite, it was 549 oC.

**Figure 6.** TGA of organoclay, TLCP and TC3 white in air.

TLCP used here was a semicrystalline nematic forming TLCP. From the DSC results, as shown in Figure 7(a), the endothermic peak appearing at ~ 125.5 oC represented the glass transition temperature of TLCP. Due to the broad sequential distribution of the HBA and SA-HQ segments in TLCP [24], two broad endothermic peaks at ~152 oC and ~164 oC represented the melting temperatures of the crystalline phase of TLCP with different segments. With the introduction of the well-dispersed nanoclay into the system, the glass transition temperature shifted to a higher temperature, peaking at ~ 142 oC, and the two melting temperatures peaked at ~ 159 oC and ~ 167 oC. The exothermic peaks are exhibited in Figure 7(b). The exothermic peak positions also changed and became sharper with the introduction of clay. For TLCP, there were two peaks, at ~166 oC and ~159 oC, corresponding to the different crystalline peaks with different molecular chain lengths as shown. With the introduction of the exfoliated layered silicates, the sharp exothermic peak was followed by a broad peak in the nanocomposite at corresponding temperatures of 163.5 oC and 169 oC respectively. With the effect of the layered structure, the arrangement of liquid-crystalline polymer chains became more ordered. There is no doubt that the transition temperatures in the heating and cooling curves increased in TC3 white.

**Figure 7.** Second heating (a) and cooling (b) curves of TLCP and TC3 white at N2 atmosphere.

#### **3.5. Rheological properties**

#### *3.5.1. Organoclay modified TLCP nanocomposite*

#### **Linear viscoelasticity**

284 Viscoelasticity – From Theory to Biological Applications

oxygen during oxidation in the air condition.

was 530 oC and for the nanocomposite, it was 549 oC.

**Figure 6.** TGA of organoclay, TLCP and TC3 white in air.

The thermal stability of polymeric material is usually studied by thermogravimetric analysis. Generally, the incorporation of clay into the polymer matrix is found to enhance thermal stability, as the clay acts as a superior insulator and mass transport barrier to

The TGA curves of clay, TLCP, and TC3 white in the air flow condition are shown in Figure 6. No weight loss occurred below 200 oC in any of the samples. Because of the presence of some organic molecules in interlayer spaces, the clay began to lose weight at 230 oC; at 600 oC, the clay weight loss was 30 %, similar to the result reported by Chiu et al. [23] Comparing TLCP with TC3 white, the thermal stability of TC3 white increased. For example, for TLCP, the temperature at which the weight loss started was 335 oC whereas for TC3 white, it was 349 oC. For TLCP, the temperature at which the weight loss was halved

TLCP used here was a semicrystalline nematic forming TLCP. From the DSC results, as shown in Figure 7(a), the endothermic peak appearing at ~ 125.5 oC represented the glass transition temperature of TLCP. Due to the broad sequential distribution of the HBA and SA-HQ segments in TLCP [24], two broad endothermic peaks at ~152 oC and ~164 oC represented the melting temperatures of the crystalline phase of TLCP with different segments. With the introduction of the well-dispersed nanoclay into the system, the glass transition temperature shifted to a higher temperature, peaking at ~ 142 oC, and the two melting temperatures peaked at ~ 159 oC and ~ 167 oC. The exothermic peaks are exhibited in Figure 7(b). The exothermic peak positions also changed and became sharper with the introduction of clay. For TLCP, there were two peaks, at ~166 oC and ~159 oC, corresponding to the different crystalline peaks with different molecular chain lengths as shown. With the introduction of the exfoliated layered silicates, the sharp exothermic peak was followed by a broad peak in the nanocomposite at corresponding temperatures of 163.5 oC and 169 oC respectively. With the effect of the layered structure, the arrangement of liquid-crystalline

**3.4. Thermal properties** 

Dynamic frequency sweeps at strains well within the linear viscoelastic regime of each material were performed in a range of frequencies covering 5 decades (0.01 – 1000 rad/s). The results shown in Figure 8 exhibit the storage modulus *G*' , loss modulus *G*'' and complex viscosity \* for TLCP and TC3 white. For TLCP, *G*' , *G*'' and \* became too small and scattered for accurate measurement at lower frequencies (in the region of 0.04 rad/s to 0.25 rad/s ). This was due to the low viscosity of the melt at 185 oC, which led to torque values beyond the limits of the transducer. In the low frequency region (0.04 rad/s to 0.25 rad/s), TC3 white had dependable data but the TLCP data was scattered. In this region, slopes for G and G were 0.12 and 0.31 for TC3 white, and 0.30 and 0.55 for TLCP. The corresponding slope values for \* were 0.83 and 0.58. Pseudo-solidlike behaviors existed in TLCP and TC3 white, with TC3 white exhibiting more solidlike behavior than TLCP. The polydomain structure in the bulk state of TLCP is the reason for TLCP behavior [25]. The percolated network formed by the exfoliated organoclay with the TLCP molecules enhanced those polydomain structures, causing more solidlike behavior and higher \* in the lower frequency region in TC3 white. In the middle frequency region, both showed plateaus of nearly constant viscosity. The TC3 white curve paralleled the x-axis and TLCP had a small slope value of -0.15. At high frequencies, TC3 white showed a gradual change of slope to - 0.21, whereas TLCP maintained the same slope. In this region, the slopes of G and *G* for TLCP were 0.70 and 0.86 but for TC3 white, they were 1.83 and 0.92. There were dramatic differences between the two materials. The slopes for TC3 white approached the theoretical values for polymers with flexible chains, which are 2 and 1, respectively. With the help of exfoliated clay in high frequencies, TC3 white performed like flexible chains, whereas TLCP still showed some entanglement behavior.

Micro-Rheological Study on Fully Exfoliated Organoclay Modified Thermotropic Liquid Crystalline Polymer and Its Viscosity Reduction Effect on High Molecular Mass Polyethylene 287

. However, the Cox-Merz rule failed for

measured viscosity of TC3 white is similar to that of the TLCP matrix at the same frequency or shear rate. The curves, especially the TC3 white curve, are reminiscent of the three-region viscosity curve reported by Onogi and Asada [25] for lyotropic polymer. The phenomenon can be explained by polydomain structures. With the addition of the organoclay, the threeregion viscosity phenomenon was enhanced. TC3 white performs more like lyotropic polymer, with a more rigid structure than the semi-rigid TLCP. The TC3 white curves fitted

The cone and plate fixture, with its constant rate of shear and direct measurement of the first normal stress difference N1 by total thrust, is probably the most popular rotational geometry for studying non-Newtonian effects. Figure 11 shows the total thrust (normal force) for TLCP and TC3 white at different shear rates at 185 oC using a 50 mm diameter cone and plate fixture. The normal force evolution at a particular constant shear rate was clearly exhibited with a few peaks (or shoulders) at small strain before reaching a steady state. These peaks

**Figure 11.** Normal force for TLCP and TC3 white at different shear rates with cone and plate fixture at

corresponded to the structure being broken and aligning during shear [27].

the Cox-Merz rule, i.e. \*

**Figure 10.** Cox-Merz rule on TLCP and TC3 white at 185 oC.

**The first normal stress difference measurement** 

185 oC.

() ( ) 

, where

TLCP, a finding which has also been reported by other researchers [26].

**Figure 8.** Storage modulus *G*' , loss modulus *G*'' and complex viscosity Eta\* in dynamic frequency sweep for TLCP and TC3 white at 185 oC.

It has been claimed that the Cole-Cole plot of storage modules vs. loss modulus can provide information about structures. The Cole-Cole plot for TLCP and TC3 white is shown in Figure 9. From a log-log plot of *G*'' vs. *G*' , we can determine that the slope in *G*' ~ '' ( ) *G* . For a single Maxwell element, 2 , however, complex systems with associations often deviate from the single element, and this can be seen by an exponent that deviates from 2. For TLCP, the slope was constant with a value of 0.776 in the whole region, which has a large deviation with flexible chain polymers ( 2 ). This is due to TLCP intrinsic anisotropic properties. For TC3 white, with the loss modulus increasing, the slope changed dynamically from almost zero (pseudo-percolation behavior or solid-like behavior), gradually approaching the theatrical flexible chain value, 2. This plot showed that there were different structural responses for TC3 white in different frequency regions.

**Figure 9.** The cole-cole plot of loss modulus '' *G* vs. storage modulus ' *G* for TLCP and TC3 white at 185 oC.

#### **Cox-Merz rule**

Figure 10 provides global view of TLCP and TC3 white viscosities as a function of frequency or steady shear rate. Unlike other organoclay based polymeric nanocomposites, the measured viscosity of TC3 white is similar to that of the TLCP matrix at the same frequency or shear rate. The curves, especially the TC3 white curve, are reminiscent of the three-region viscosity curve reported by Onogi and Asada [25] for lyotropic polymer. The phenomenon can be explained by polydomain structures. With the addition of the organoclay, the threeregion viscosity phenomenon was enhanced. TC3 white performs more like lyotropic polymer, with a more rigid structure than the semi-rigid TLCP. The TC3 white curves fitted the Cox-Merz rule, i.e. \* () ( ) , where . However, the Cox-Merz rule failed for TLCP, a finding which has also been reported by other researchers [26].

**Figure 10.** Cox-Merz rule on TLCP and TC3 white at 185 oC.

#### **The first normal stress difference measurement**

286 Viscoelasticity – From Theory to Biological Applications

sweep for TLCP and TC3 white at 185 oC.

For a single Maxwell element,

at 185 oC.

**Cox-Merz rule** 

**Figure 8.** Storage modulus *G*' , loss modulus *G*'' and complex viscosity Eta\*

large deviation with flexible chain polymers (

deviate from the single element, and this can be seen by an exponent

Figure 9. From a log-log plot of *G*'' vs. *G*' , we can determine that the slope

were different structural responses for TC3 white in different frequency regions.

**Figure 9.** The cole-cole plot of loss modulus '' *G* vs. storage modulus ' *G* for TLCP and TC3 white

Figure 10 provides global view of TLCP and TC3 white viscosities as a function of frequency or steady shear rate. Unlike other organoclay based polymeric nanocomposites, the

It has been claimed that the Cole-Cole plot of storage modules vs. loss modulus can provide information about structures. The Cole-Cole plot for TLCP and TC3 white is shown in

2. For TLCP, the slope was constant with a value of 0.776 in the whole region, which has a

anisotropic properties. For TC3 white, with the loss modulus increasing, the slope changed dynamically from almost zero (pseudo-percolation behavior or solid-like behavior), gradually approaching the theatrical flexible chain value, 2. This plot showed that there

in dynamic frequency

2 ). This is due to TLCP intrinsic

2 , however, complex systems with associations often

in *G*' ~ '' ( ) *G*

that deviates from

.

> The cone and plate fixture, with its constant rate of shear and direct measurement of the first normal stress difference N1 by total thrust, is probably the most popular rotational geometry for studying non-Newtonian effects. Figure 11 shows the total thrust (normal force) for TLCP and TC3 white at different shear rates at 185 oC using a 50 mm diameter cone and plate fixture. The normal force evolution at a particular constant shear rate was clearly exhibited with a few peaks (or shoulders) at small strain before reaching a steady state. These peaks corresponded to the structure being broken and aligning during shear [27].

**Figure 11.** Normal force for TLCP and TC3 white at different shear rates with cone and plate fixture at 185 oC.

For the total thrust data measured in the cone and plate fixture, some equations can be used to calculate the N1 for TLCP and TC3 white [28].

For the cone and plate fixture:

$$N\_1 = \frac{2F\_z}{\pi R^2} \tag{1}$$

Micro-Rheological Study on Fully Exfoliated Organoclay Modified Thermotropic Liquid Crystalline Polymer and Its Viscosity Reduction Effect on High Molecular Mass Polyethylene 289

For N1, molecular theory, especially the Doi theory (for rod-like nematics) [29] predicts that the director (or local average orientation) will rotate or tumble with the flow. At low shear rates, N1 will be positive. At intermediate rates (when the flow rate is a little slower than the reciprocal of the longest molecular relaxation time), nonlinear effects are important, producing competition between tumbling and steady alignment of the director along the flow. As a result, the director oscillates about a steady value [30]. In this "wagging" regime, which is peculiar to tumbling, polymeric nematics and the local molecular order are significantly weakened, and N1 is negative. At very high rates of shear, the director aligns in the flow direction, and N1 is again positive. The Doi molecular theory for rod-like nematics was remarkably applicable with experimental data for PBG solutions [31]. Although a similar coupling between flow and liquid-crystalline order is conceivable in thermotropics, experiments have not yielded a corresponding agreement with theory. In fact, the expected pattern of sign changes in N1 has not been observed [32]. The N1 curves in Figure 12 for these two systems are in the high-shear-rate region, with N10. Figure 12 displays the shear rate dependence of and N1 for TLCP and TC3 white at 185 oC. From comparison of the N1 values between TLCP and TC3 white, it can be observed that the values of N1 for TC3 white are a little lower than those for TLCP, but the rate of the N1 increase in TC3 white is higher. Combined with the viscosity variations with shear rate, these phenomena indicate that the presence of exfoliated clay increases elasticity in a flow-aligning state, and the exfoliated clay is oriented along the shear direction, even assisting the neighboring TLCP molecules to align in the flow direction, with the result that there is a decrease of viscosity and an

The dispersion of the exfoliated clay in the TLCP matrix without and with deformation is depicted schematically in Figure 13(a) and 13(b), respectively, where the dark ellipses represent clay platelets, the wavy lines and cylinders represent TLCP chains with flexible and rigid components, and the short dashed lines represent the interaction between TLCP and clay. It should be noted that in the conformation of TLCP, the phenyls in HBA and HQ are not coplanar, and hence the SA flexible segments connected to the HQ are not in a line with HBA. In the schematic diagram, the effect of the exfoliated clay on TLCP is clearly delineated. Without deformation (Figure 13(a)), the disordered dispersion of the exfoliated clays in the TLCP matrix is presented. On the other hand, with deformation (Figure 13(b)), shear-induced molecular alignment in both TLCP and TC3 white occurs along the shear

**Figure 13.** Schematic drawing of TLCP molecular chains influenced by the exfoliated organoclays

increase of N1 slope, as shown in Figure 12.

(a) without and (b) with deformation.

direction.

Where, Fz is the total thrust measured in the cone and plate fixture. R is the radius of the cone and plate fixture.

Due to the inertia and secondary flow effect, i.e. in cone and plate rheometers, inertia forces tend to pull the plates together rather than push them apart, a corrected term must be introduced to eliminate this effect:

$$(F\_z)\_{inert} = 0.075 \pi \rho \Omega^2 R^4 \tag{2}$$

Where, ρ is the density of the material, Ω is the angular rotation rate.

After this correction the N1 can be calculated:

$$N\_1 = \frac{2F\_z}{\pi R^2} - 0.15\rho\Omega^2 R^2\tag{3}$$

The steady state N1 at different shear rates at 185 oC can then be calculated. The graph is shown in Figure 12. Due to the low viscosity, the maximum shear rate that could be measured was 300 1/s for TLCP and 600 1/s for TC3 white. The sample spun out with a dramatic and continuous decrease in stress and viscosity when the shear rate was larger than the above value. In Figure 12, N1s are positive for TLCP and TC3 white with comparable values.

**Figure 12.** Shear rate dependence of shear viscosity Eta and first normal stress difference N1 for TLCP and TC3 white at 185 oC.

For N1, molecular theory, especially the Doi theory (for rod-like nematics) [29] predicts that the director (or local average orientation) will rotate or tumble with the flow. At low shear rates, N1 will be positive. At intermediate rates (when the flow rate is a little slower than the reciprocal of the longest molecular relaxation time), nonlinear effects are important, producing competition between tumbling and steady alignment of the director along the flow. As a result, the director oscillates about a steady value [30]. In this "wagging" regime, which is peculiar to tumbling, polymeric nematics and the local molecular order are significantly weakened, and N1 is negative. At very high rates of shear, the director aligns in the flow direction, and N1 is again positive. The Doi molecular theory for rod-like nematics was remarkably applicable with experimental data for PBG solutions [31]. Although a similar coupling between flow and liquid-crystalline order is conceivable in thermotropics, experiments have not yielded a corresponding agreement with theory. In fact, the expected pattern of sign changes in N1 has not been observed [32]. The N1 curves in Figure 12 for these two systems are in the high-shear-rate region, with N10. Figure 12 displays the shear rate dependence of and N1 for TLCP and TC3 white at 185 oC. From comparison of the N1 values between TLCP and TC3 white, it can be observed that the values of N1 for TC3 white are a little lower than those for TLCP, but the rate of the N1 increase in TC3 white is higher. Combined with the viscosity variations with shear rate, these phenomena indicate that the presence of exfoliated clay increases elasticity in a flow-aligning state, and the exfoliated clay is oriented along the shear direction, even assisting the neighboring TLCP molecules to align in the flow direction, with the result that there is a decrease of viscosity and an increase of N1 slope, as shown in Figure 12.

288 Viscoelasticity – From Theory to Biological Applications

For the cone and plate fixture:

introduced to eliminate this effect:

After this correction the N1 can be calculated:

cone and plate fixture.

comparable values.

and TC3 white at 185 oC.

to calculate the N1 for TLCP and TC3 white [28].

For the total thrust data measured in the cone and plate fixture, some equations can be used

1 2 2 *<sup>z</sup> F*

Where, Fz is the total thrust measured in the cone and plate fixture. R is the radius of the

Due to the inertia and secondary flow effect, i.e. in cone and plate rheometers, inertia forces tend to pull the plates together rather than push them apart, a corrected term must be

2 4 ( ) 0.075 *z inert F R*

0.15 *<sup>z</sup> <sup>F</sup> N R R*

The steady state N1 at different shear rates at 185 oC can then be calculated. The graph is shown in Figure 12. Due to the low viscosity, the maximum shear rate that could be measured was 300 1/s for TLCP and 600 1/s for TC3 white. The sample spun out with a dramatic and continuous decrease in stress and viscosity when the shear rate was larger than the above value. In Figure 12, N1s are positive for TLCP and TC3 white with

**Figure 12.** Shear rate dependence of shear viscosity Eta and first normal stress difference N1 for TLCP

Where, ρ is the density of the material, Ω is the angular rotation rate.

1 2 2

2 2

(3)

*<sup>R</sup>* (1)

(2)

*N*

The dispersion of the exfoliated clay in the TLCP matrix without and with deformation is depicted schematically in Figure 13(a) and 13(b), respectively, where the dark ellipses represent clay platelets, the wavy lines and cylinders represent TLCP chains with flexible and rigid components, and the short dashed lines represent the interaction between TLCP and clay. It should be noted that in the conformation of TLCP, the phenyls in HBA and HQ are not coplanar, and hence the SA flexible segments connected to the HQ are not in a line with HBA. In the schematic diagram, the effect of the exfoliated clay on TLCP is clearly delineated. Without deformation (Figure 13(a)), the disordered dispersion of the exfoliated clays in the TLCP matrix is presented. On the other hand, with deformation (Figure 13(b)), shear-induced molecular alignment in both TLCP and TC3 white occurs along the shear direction.

**Figure 13.** Schematic drawing of TLCP molecular chains influenced by the exfoliated organoclays (a) without and (b) with deformation.
