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First normal stress difference in capillary extrusion flow of nanometer calcium carbonate-filled PLLA biocomposites.

INTRODUCTION

Polymer melts present complicated rheological behavior during extrusion flow due to their viscoelasticity, these include end pressure losses, normal stress effect, extrudate swell, and unsteady flow or melt fracture. The normal stress effect is produced due to the anisotropy of a polymer melt. From a viewpoint of macroscopic rheology, the extrudate swell is the elastic recovery of the shear and extension deformation generated in die flow of polymer melt when it leaves from the channel. Usually, the extrudate swell is attributed to a contribution of the normal stress effect (1). In general, the normal stress effect during extrusion of a polymer melt is characterized by the normal stress difference, including the first normal stress difference ([N.sub.1]) and the second normal stress difference ([N.sub.2]). It is extensively believed that the [N.sub.1] is major contribution of the normal stress difference (2-4). In general, the normal stress difference was related to the exit pressure losses ( [DELTA][P.sub.exit]), that is (5),

[N.sub.1] + [N.sub.2] = [DELTA][P.sub.exit] * (1)

Biodegradable polymers have been developed quickly in the past decade and have been started to be produced on a commercial scale. They have been widely used in various applications such as bags, sacks, and food packaging, because these polymers prepared from renewable resources can undergo biodegradation upon disposal. Poly(lactic acid) (PLA) is one of the biodegradable polymers, which are derived from renewable sources such as starch and sugar (6), (7). Because of its low molecular weight and brittleness as well as relatively high cost, PLA has been limited to biomedical and pharmaceutical applications. Poly-L-lactide (PLLA) is one kind of PLA. Besides good biodegradable properties, PLLA has certain shape memory performance. Ublekov et al. (8) investigated the effects of organophilic clay concentration on nonisothermal crystallization of poly(L-lactic acid) (PLLA)/montmorillonite (MMT) nanocomposites. The results showed that the crystallinity of PLLA/MMT composites increased drastically at high clay loadings (59 wt%), and the intercalation of the clay was observed at filler loadings higher than 3 wt%. Zhang et al. (9) examined the influence of nanoparticle concentration on the co-continuity intervals and rheological properties of polystyrene (PS)/PLLA blends and found that the incorporation of silica nanoparticles into PS/PLLA blends could be used to prepare macroporous PLLA structure with controllable pore size at lower PLLA content.

As stated earlier, although PLA has a combination of high tensile strength, high elastic modulus, and good biodegradable property, it will become a brittle, glassy polymer if produced through a conventional condensation polymerization of lactic acid, the result is relatively low molecular weight. In view of this, there have been extensive studies on modification by filling with inorganic particles (8-16) and blending with other resin (7), (17-20). However, the focus of these studies has been made on biocompatibility, biodegradability, and mechanical properties. Several papers (21-24) have reported the effects of volume fraction, surface treatment, and size of the calcium carbonate (CaC[O.sub.3]) particles on the physical properties and enzymatic hydrolysis as well as mechanical properties of PLLA--CaC[O.sub.3] composites and found that the mechanical and thermal properties as well enzymatic hydrolysis were improved with the filler. There have been some studies on rheological properties of the PLA blends and composites (7), (9), (21), but there were only a few studies for the flow behavior of inorganic particulate-filled PLA composites (15), (17), especially for the normal stress difference in flow. Nanometer calcium carbonate (nano-CaC[O.sub.3]) is a kind of inorganic particle used extensively in the polymer industry due to its reinforcing and toughening effects besides low cost, we consider here its effect on the rheological behavior of PLLA/nano-CaC[O.sub.3] composites.

The rheological properties of polymer melts are usually measured using a capillary rheometer due to the tube flow being similar to extruder dies used in the extrusion process. Recently, Liang (25-29) has investigated the viscoelastic properties of inorganic particulate-filled polyolefin composites by applying a capillary rheometer to reveal the flow mechanisms and determine useful guidelines to achieve optimum processing conditions for particle-filled polymer systems. It is quite meaningful for both polymer processing and polymer rheology that the first normal stress difference and factors affecting it during extrusion flow of polymer melts are investigated deeply. More recently. Liang et al. (29) studied the flow properties such as melt viscosity of PLLA composites filled with nano-CaC[O.sub.3] under shear rates varying from 10 to [10.sup.3] [s.sup.-1] and found that the melt shear flow obeyed roughly a power law under the similar experimental conditions. The objective of this article is to investigate the influence of the experimental conditions on the first normal stress difference of PLLA/nano-CaC[O.sub,3] composites by means of a capillary rheometer.

EXPERIMENTAL

Raw Materials

A biodegradable resin, PLLA, with the trademark of Al-1001, serving as the matrix material, was supplied by Shenzhen Bright China Industrial Co. Ltd (Shenzhen, China). Its density and melt flow rate were 1.25 g/[cm.sup.3] and 7.5 g/10 min, respectively. The filler was nano-CaC[O.sub.3] particles, manufactured by Anyuan Scientific and Technological Chemical Plant (Anyuan, China). Its mean diameter and the particle density were 40 nm and 2.55 g/[cm.sup.3], respectively.

Preparation

The surface of the nano-CaC[O.sub.3] particles was pretreated with stearic acid with trade mark of SA 1801 supplied by Oleo Chemical Industry (Indonesia), and the weight fraction of the stearic acid was 3% of the nano-CaC[O.sub.3]. The surface-treated particles were simply mixed with the PLLA resin in a high-speed compounding machine. The mixture was then put into a twin-screw extruder for molten blending at a screw speed of 25 rev/min and temperatures ranging from 140 to 170[degrees]C. The diameter and length--diameter ratio of the screw were 35 mm and 40, respectively. The composite extrudate was subsequently granulated. The weight fractions ([[empty set].sub.f]) of the filler particles in the composite were 1, 2, 3, and 4%. Finally, the composites were dried at 80[degrees]C for 5 h before the rheological testing.

Apparatus and Methodology

The extrusion flow tests were performed using a capillary rheometer (Gottfert Rheograph 25) supplied by Gottfert Co. (Germany). The test temperatures ranged from 170 to 200[degrees]C and apparent shear rate varied from 50 to [10.sup.3] [s.sup.-1]. The capillary diameter (D) was 1 mm and the ratios of die length (L) to D were 10, 20, and 30, respectively, while the entry angle was 180[degrees]. Two pressure transducers were installed at the top of the piston and the exit of the capillary die, respectively, to measure the relevant pressures. Thus, the first normal stress difference ([N.sub.1]) of the composite melts might be determined under the experimental conditions. The general expression of the first normal stress difference is as follows:

[N.sub.1] = [[sigma].sub.11] - [[sigma].sub.22] (2)

where [[sigma].sub.11] and [[sigma].sub.22] are the stress along the flow direction and the stress which is perpendicular to the flow direction. The values of [N.sub.1] under test conditions may be determined by means of the instrument.

RESULTS AND DISCUSSION

Correlation Between First Normal Stress Difference and Total Pressure Drop

Figure 1 shows the correlation between the first normal stress difference and the total pressure drop ([DELTA]P) of the composites with various filler content under experimental conditions including test temperature of 180[degrees]C and the capillary length to diameter ratio (L/D) of 30. It can be seen that the value of [N.sub.1] increases linearly with increasing [DELTA]P when the filler weight fraction is constant, the correlation between [N.sub.1] and [DELTA]P may be expressed as follows:

[FIGURE 1 OMITTED]

[N.sub.1] = [A.sub.0] + [A.sub.1][empty set]P (3)

where [A.sub.0] and [A.sub.1] are constants related to the elastic properties of the polymer melt with different pressures. Parameter [A.sub.1] is the slope of the curves, and [A.sub.0] is the ordinate intercept of the curves that reflects the sensitivity of the first normal stress difference to the total pressure losses.

The values of [A.sub.0] and [A.sub.1] may be determined using a linear regression analysis method. It is found that the values of [A.sub.0] and [A.sub.1] of all the filled systems under different shear rates are about -0.376 and 1.002, respectively. The correlation coefficient is 0.99996. This indicates that the influence of the filler content on the sensitivity of the first normal stress difference to the total pressure drop is insignificant.

When a polymer melt is extruded through a die, it will consume large amount of deformation energy in the entry flow, tube flow, and exit flow owing to its viscoelasticity and flow velocity rearrangement and will generate obvious pressure losses. The total pressure drop is the sum of that in each of these three parts. That is,

[DELTA]P = [DELTA][P.sub.en] + [DELTA][P.sub.d] + [DELTA][P.sub.ex] = [DELTA][P.sub.end] + [DELTA][P.sub.d] (4)

where [DELTA][P.sub.en], [DELTA][P.sub.d] , and [DELTA][P.sub.ex] are the pressure drop in the entrance, inner region, and exit of the die, respectively. [DELTA][P.sub.end] is the end pressure drop, it may be determined using the Bagley entry correction method. As stated earlier, the normal stress difference is closely related to the exit pressure losses, while the end pressure drop is the sum of the entry pressure losses and exit pressure losses.

Relationship Between First Normal Stress Difference and Shear Stress

Figure 2 displays the relationship between the first normal stress difference and shear stress at the channel wall ([[aut].sub.w]) of the pure PLLA resin (i.e., [[empty set].sub.f] = 0%) and the PLLA/nano-CaC[O.sub.3] composite melts with various filler content under test conditions including test temperature of 180[degrees]C and the capillary length to diameter ratio (LID) of 30. The value of [N.sub.1] increases linearly with increasing [[aut].sub.w] for both the pure PLLA melt and the filled PLLA composite melts when the filler weight fraction is constant, and the correlation between [N.sub.1] and [[aut].sub.w] may be expressed as follows:

[FIGURE 2 OMITTED]

[N.sub.1] = [B.sub.0] +[B.sub.1][[aut].sub.w] (5)

where [B.sub.0] and [B.sub.1] are constants related to the viscoelastic properties of the polymer melt with different shear stresses. Parameter [B.sub.1] is the slope of the curves, and [B.sub.0] is the ordinate intercept of the curves that shows the sensitivity of the first normal stress difference to shear stress.

It may be observed from Fig. 2 that for the composite with [[empty set].sub.f] of 1%, the slope of the [N.sub.1] versus [[aut].sub.w] curve is lower than that of the other curves. In other words, the sensitivity of the first normal stress difference to the total pressure drop and shear stress is weakened in the case of low filler weight fraction. This suggests that there is some effect in the extrusion flow of the PLLA/nano-CaC[O.sub.3] composite melt at lower filler concentration.

In general, the elongation and shear deformation generated in melt flow increases with increasing shear stress, and the molecular chain orientation will be enhanced when temperature is constant, and the anisotropy in stress will be increased in this case. The storage and dissipation of deformation energy and the normal stress effect increases correspondingly. Hence, the first normal stress difference increases with an increase of shear stress. If assuming no wall-slip during extrusion flow of polymer melt, then the shear stress at the channel wall is given by:

[[aut].sub.w] = ([DELTA]P - [DELTA][P.sub.en])D/4L (6)

where [DELTA][P.sub.en] is the entry pressure drop.

Figure 3 illustrates the correlation between the first normal stress difference and shear stress at wall of PLLA/nano-CaC[O.sub.3] composite melt under experimental conditions with various die length to diameter ratios and test temperature of 180[degrees]C. It can be seen that the value of [N.sub.1] increases linearly with increasing [[aut].sub.w] when the die length to diameter ratio is fixed. The slope of the [N.sub.1] against [[aut].sub.w] curves increases with increasing the die length to diameter ratio. This indicates that sensitivity of the first normal stress difference to the shear stress is enhanced with an increase of the die length to diameter ratio.

The values of [B.sub.0] and [B.sub.1] may also be determined using a linear regression analysis method. The parameter [B.sub.1] characterizes the dependence of the first normal stress difference on the shear stress. The values of [B.sub.0] and [B.sub.1] of the composite for different shear rates are summarized in Table 1. The value of Bi increases with an increase of the die length to diameter ratio, the correlation coefficient is more than 0.999. The main reason might be that the shear flow field action subjected by the melt will be enhanced with an increase of channel length under the same extrusion flow conditions, the orientation of the macromolecular chains will be increased correspondingly. As stated earlier, the anisotropy in stress will be increased in this case. The storage and dissipation of deformation energy and the normal stress effect increases correspondingly. Hence, the first normal stress difference increases with an increase of the die length to diameter ratio.
TABLE 1. Values of [B.sub.0] and [B.sub.1] at different LID
(180[degrees]C).

L/D           [B.sub.0]  [B.sub.1]         R

10              -0.0835    38.6324    0.9997
20              -0.1792    78.8249    0.9999
30              -0.2738   119.3191    0.9999


It can also be observed from Figs. 1 and 2 that the measured data fluctuation is very small, even though at higher shear stress level, it means that the melt flow in the capillary is roughly steady. In the previous work, Liang (28) studied the melt viscoelastic behavior in capillary extrusion of polypropylene/ethylene-propylenediene monomer/glass bead ternary composites and got the similar results.

Dependence of First Normal Stress Difference on Temperature

Figure 4 presents the dependence of the first normal stress difference on temperature of PLLA/nano-CaC[O.sub.3] composite melt with the filler weight fraction of 3% at various apparent shear rates when the die length to diameter ratio is 30. The values of [N.sub.1] decreases roughly linearly with a rise of temperature, and the values of [N.sub.1] increases with increasing the apparent shear rate when the test temperature is fixed. The relationship between the first normal stress difference and temperature may be expressed as follows:

[FIGURE 4 OMITTED]

[N.sub.1] = [C.sub.0] + [C.sub.1]T (7)

where [C.sub.0] and [C.sub.1] are the constants related to the viscoelastic properties of polymer melt with different temperatures, because the first normal stress difference is the characterization of viscoelastic properties during extrusion of polymer melt. The values of the parameters [C.sub.0] and [C.sub.1] may be determined using a linear regression analysis method from the measured first normal stress difference versus test temperature. Parameter [C.sub.0] is the ordinate intercept of the curves, and [C.sub.1] is the slope of the curves that presents the sensitivity of the first normal stress difference to test temperature.

The apparent shear rate is given by:

[[gamma].sub.a] = 32Q/[pi][D.sup.3] (8)

where Q is the melt volume flow rate.

It is generally believed that the melt free volume increases with a rise of temperature, and the activity mobility of the macromolecular chains is enhanced. Thus, the interaction between the macromolecular chains is weakened and the flow properties of the melt are improved. As a result, the orientation of the melt molecular chains will be weakened at given flow rate, and the anisotropy in stress will be decreased in this case. The storage and dissipation of deformation energy and the normal stress effect reduces correspondingly during the melt extrusion flow. Hence, the first normal stress difference decreases with a rise of temperature. The values of [C.sub.0] and [C.sub.1] of the composites under the experimental conditions are summarized in Table 2. The parameter [C.sub.1] characterizes the sensitivity of the first normal stress difference to temperature. The value of [C.sub.1] increases with increasing shear rate, and the correlation coefficient is more than 0.99.
TABLE 2. Values of [C.sub.0] and [C.sub.1] at
different shear rate ([[empty set].sub.f] = 3%).

Shear rate ([s.sub.-1])   [C.sub.0]  [C.sub.1]        R

300                         136.140    -0.6825  -0.9984
800                         169.351    -0.8459  -0.9989
1000                        185.856    -0.9256  -0.9977


Dependence of First Normal Stress Difference on Filler Content

Figure 5 presents the dependence of the first normal stress difference on the filler weight fraction for the PLLA/nano-CaC[O.sub.3] composite melt under different shear stresses and test temperature of 180[degrees]C. It can be seen that the first normal stress difference of the PLLA/nano-CaC[O.sub.3] composite melt increases slightly with an increase of the filler weight fraction except for the individual data point. When the filler weight fraction is 1%, the first normal stress difference of the PLLA/nano-CaC[O.sub.3] composite melt is lower than that of the unfilled PLLA melt for both shear stresses, and then the value of [N.sub.1] varies slightly with increasing the filler weight fraction. This indicates that the influence of the nano-CaC[O.sub.3] content on the first normal stress difference is insignificant under the experimental conditions when the filler weight fraction is varied from 0% to 4%, except for 1%.

[FIGURE 5 OMITTED]

The above results suggest that there is a certain "bearing effect" of the nano-CaC[O.sub.3] particle during the composite melt flow in the case of the low filler concentration under these experimental conditions; the flow resistance decreases and the stored elastic deformation energy also decreases in this case. Consequently, the normal stress effect is weakened, leading to reduction of the first normal stress difference (see Fig. 5).

Discussion

It is generally believed that polymer fluid (including melt and liquid) will present the anisotropy of stress owing to its viscoelasticity during the fluid flow including shear flow and pressure flow, leading to production of the normal stress effect. The normal stress effect varies with the flow conditions such as temperature and flow rate. As stated earlier, the normal stress difference is the important characterization for the normal stress effect, and the first normal stress difference is the main component of the normal stress difference. Extrusion flow is one of the pressure flows. It is found that the first normal stress difference increases with increasing shear rate during die extrusion flow of the PLLA/nano-CaC[O.sub.3] composite melt (see Fig. 4). It is necessary to note that it is convenient to determine the first normal stress difference during die extrusion flow of polymer melts, although there is some debate in the literature regarding the use of a capillary rheometer for measurement of the first normal stress difference.

CONCLUSIONS

The influence of the content of the nano-CaC[O.sub.3] on the first normal stress difference of filled PLLA biocomposites was essentially insignificant under experimental conditions. The first normal stress difference increased linearly with increasing shear stress and was also minimum when the filler weight fraction was 1%. It might be attributed to a "bearing effect" of the nanometer particles in the matrix melt during extrusion flow of the composites in the case of low filler concentration. The first normal stress difference decreased roughly linearly with a rise of temperature. Moreover, the first normal stress difference increased with an increase of the die length to diameter ratio under given shear stress level.

ACKNOWLEDGMENT

The authors would like to thank Mr. L. Zhou for his help in the experiments.

Correspondence to: Ji-Zhao Liang; e-mail: scutjzl@sohu.com

DOI 10.1002/pen.23435

Published online in Wiley Online Library (wileyonlinelibrary.com).

[c] 2012 Society of Plastics Engineers

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Ji-Zhao Liang

Research Division of Green Function Materials and Equipment, School of Mechanical and Automotive Engineering, South China University of Technology, Guangzhou 510640, People's Republic of China
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Date:Aug 1, 2013
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