Melt shear flow behavior of flame-retardant polypropylene composites filled with microencapsulated red phosphorus

Abstract

Melt shear flow behavior and melt shear viscosity are important characterization of processing properties for polymeric materials. The effects of microencapsulated red phosphorus (MRP) content and experimental conditions on the melt shear flow behavior of the polypropylene (PP) composites were investigated using a torque rheometer. It was found that the melt shear viscosity, the torque, and energy consumption at balance state of the composites increased nonlinearly with increasing MRP weight fraction while decreased slightly with increasing temperature, the maximum torque increased with increasing the roller speed, and the dependence of the melt shear viscosity and the energy consumption at balance state on temperature roughly obeyed the Arrhenius equation. These findings would provide useful data for processing these flame-retardant PP composites.

Keywords

Polymer–matrix composites shear flow melt shear viscosity rheology polypropylene

Introduction

Melt shear flow is one of the common flow patterns in polymer processing such as the flow in extruder, mixer, and two-roll mill. The melt shear flow behavior and its mechanisms affect directly the technology and machinery design of polymer processing. Therefore, deeply studying the melt shear flow properties and their affecting factors is helpful to reveal the rheological behavior mechanisms and to provide useful guidelines of the processing technology of polymer materials.^1
–3 Since 1995, Liang and his coworkers^4

–7 have investigated the effects of operation conditions on the melt flow behavior and its mechanisms of polymer, polymer blends, and polymer composites using capillary rheometer and observed some interesting findings. Melt shear flow properties and melt shear viscosity can be measured by means of a torque rheometry. Therefore, torque rheometry is usually used in polymer processing for characterizing the processing properties of polymeric materials.^8
–10 In 2009, Freire et al.¹¹ studied the processability of poly(vinylidene fluoride)/poly(methyl methacrylate) blends using a torque rheometry and found that the increase in the poly(methyl methacrylate) content improved the processability of the blends, in spite of an increase in the activation energy of flow.

Polypropylene (PP) is a general resin and is extensively used in industries due to its good insulation properties, small dielectric constant, good stress crack resistance, and chemical resistance.¹² However, the applications of PP have been somewhat limited because of its some weaknesses including poor flammability resistance and impact fracture toughness. In order to widen the applications of PP, flame retardants are usually added into this resin for enhancing its flame-retarding ability. Recently, the flame-retardant modification for PP has been received increasing attention.^13,14 Aluminum hydroxide (Al(OH)₃) and magnesium hydroxide (Mg(OH)₂), a kind of halogen-free flame retardants, have been widely used in various polymers such as PP because of its triple functions: filler, flame retardant, and smoke suppressant.^15

–19 In addition, modified graphene oxide,²⁰ phosphorus flame retardant,²¹ and intumescent flame retardant²² have been extensively applied in PP resin. Microencapsulated red phosphorus (MRP) is an effective flame retardant for polymer materials. Also, MRP is a kind of synergist for flame retardant and can be used with other flame retardants such as Al(OH)₃ and Mg(OH)₂ in producing flame-retardant–filled polymer composites.²³ Recently, Liang et al.¹⁴ tested mechanical and flame-retardant properties of PP/MRP/Mg(OH)₂/Al(OH)₃ composites and found that the synergistic effects of the MRP on the flame-retardant properties of the composites were significant.

The introduction of MRP into resins will affect the flow behavior and processing properties of the composite melts. Liang et al.²⁴ investigated the effects of extrusion conditions on the melt flow properties during die flow of PP/MRP composites; the results showed that the melt volume flow rate of the composites increased nonlinearly with increasing temperature and load. However, there have been relatively few studies on the shear flow properties for the PP/MRP composite melts, especially on the shear flow behavior in torque rheometer. The objectives of this study are to investigate the effects of the MRP content and operation conditions (e.g. temperature and torque) on the melt flow behavior of the PP/MRP composites during shear flow using a torque rheometer to characterize the processing properties and to provide useful data for processing.

Experimental

Raw materials

The PP with a trademark of CJS-700G was used as a matrix resin in the present work. This resin was supplied by the Guangzhou Petrochemical Works in Guangdong Province (Guangzhou, China), and its density in a solid form and melt flow rate were 910 kg/m³ and 10 g/10 min (190°C, 2.16 kg), respectively.

The MRP with an FRP-950-9 trademark, produced by the Guangzhou Yinsu Flame-Retardant Materials Co. Ltd (Guangzhou, China), was used as the filler. The mean diameter was about 10 μm; the density and melting temperature of the MRP were 1200 kg/m³ and 140°C, respectively.

Preparation

To improve the uniformity of the dispersion of the MRP in the PP matrix, the PP resin and the MRP were blended in a twin-screw corotation extruder supplied by the Nanjing Chengmeng Machinery Co., Ltd (model SHJ-26; Nanjing, China) within the temperature range from 165°C to 180°C and at a screw speed of 200 r/min. The diameter and length to diameter ratio of the screw were 24.5 mm and 40, respectively. The extrudates of the PP/MRP composites were granulated after water cooling. The weight fraction of MRP (φ_MRP) was 2, 4, 6, 8, and 10 wt%. The granulates of the prepared PP/MRP composites were dried for 5 h at 80°C before the rheological tests.

Apparatus and methodology

The shear flow tests were performed by means of a torque rheometer supplied by the Hapu Electrical Technology Ltd (model RM-200A; Harbin, China) at temperatures ranging from 180°C to 220°C, and roller speeds were 35 and 50 r/min, respectively. The roller radius (R_i) and the length (L) were 47.2 and 39 mm, respectively. The apparent shear viscosity of polymer composite melts in these tests is given by

η_{c} = 1.52 \frac{M_{b}}{R_{r}^{2} L V}

where M_b is the torque at balance state in Newton meter, R_r is the roller radius in meters, and V is the roller speed in revolutions per minute. There have been some quantitative descriptions of the shear viscosity of polymeric materials for torque rheometry,^25,26 while equation (1) is relatively simple and convenient to use.

Results and discussion

Curves of torque versus time

Curves of torque versus time present the variation of the energy consumption during shear flow of polymer melts under operation conditions including temperature and roller speed. The variation of the energy consumption in shear flow is related closely to the viscous and elastic properties of polymer melts; thus, the torque versus time curves can characterize the viscous and elastic properties of the melts. Figure 1 illustrates the curves of the torque versus time of the composite melts under test conditions with a temperature of 180°C and a roller speed of 50 r/min. It can be observed that the values of the torque increase quickly at the beginning stage and then decrease rapidly; when the time is more than 100 s, the values of the torque decrease slightly. In addition, the maximum torque increases and its position move to the left of the abscissa axis with increasing the MRP weight fraction. This is because the flow resistance increases with increasing the filler concentration, and the viscosity of the composite melts increases correspondingly, leading to the position of the maximum torque moving to the left of the abscissa axis with increasing the MRP weight fraction.

Figure 1.

Curves of torque versus time of the composite melts (180°C, 50 r/min).

Figure 2 shows the curves of the torque versus time of the composite melt with the MRP weight fraction of 6 wt% under different test temperatures and a roller speed of 50 r/min. Similarly, the values of the torque increase quickly at the beginning stage and then decrease rapidly. The maximum torque of the composite melt decreases with a rise in test temperature. Moreover, the positions of the maximum torque are roughly same when the test temperature is higher than 180°C. This means that the influence of the test temperature on the positions of the maximum torque is insignificant under higher temperature condition. The reason should be that the mobility of the PP composite macromolecular chains tends to stability under higher temperature condition, and thus the effect of temperature on the torque is insignificant in this case.

Figure 2.

Curves of torque versus time of the composite melt under different temperatures (6 wt%, 50 r/min).

Figure 3 presents the curves of the torque versus time of the composite melt with the MRP weight fraction of 10 wt% under different roller speeds and at the test temperature of 190°C. It can be found that the maximum torque of the composite melt at a roller speed of 50 r/min is obviously higher than that of at a roller speed of 35 r/min. This is because when the molten polymer flows through the gap between the two rollers and the clearance between the roller and the chamber, the molecular chains would deviate from equilibrium conformations and orient along the flow direction due to the applied shear and extension from the shear flow field. In general, the shear flow field is enhanced with increasing the roller speed. Consequently, the torque increases correspondingly in this case.

Figure 3.

Curves of torque versus time of the composite melt under different roller speeds (6 wt%, 190°C).

Influence of filler content and operation conditions on torque

Torque at balance state (M_b) is an important parameter for characterizing the viscoelasticity of polymer melts during shear flow in the torque rheometer, and the melt shear viscosity is proportional to the torque at balance state (see equation (1)). Figure 4 presents the relationship between the torque at balance state and the MRP weight fraction of the PP/MRP composites under test conditions with a temperature of 180°C and a roller speed of 50 r/min. It can be seen that the values of M_b increase with increasing the MRP weight fraction, especially when the MRP weight fraction is more than 4 wt%. This indicates that the influence of the filler content on the torque at balance state is relatively significant at higher filler concentration. The reason should be that the mobility of the molecular chains of the composite melts is weakened with increasing the filler concentration under given conditions; and the melt shear viscosity increases correspondingly, leading to increase of the torque in this case.

Figure 4.

Relationship between torque at balance state and MRP weight fraction (180°C, 50 r/min). MRP: microencapsulated red phosphorus.

Figure 5 presents the dependence of the torque at balance state on the test temperatures (T) of the PP/MRP composite with the MRP weight fraction of 6 wt% at a roller speed of 50 r/min. It can be observed that the values of M_b decrease roughly linearly with a rise in temperature, that is

Figure 5.

Dependence of torque at balance state on temperature (6 wt%, 50 r/min).

M_{b} = α + β T

where α and β are the parameters related to the torque of polymer melts during shear flow, and they characterize the viscosity and elasticity properties of polymer melts in shear flow. The values of α and β can be determined by means of the linear regression analysis method. Table 1 lists the values of α and β of the composite with the MRP weight fraction of 6 wt% under experimental conditions. It can be seen that the absolute value of the correlation coefficient (R_m) is more than 0.99.

Table 1.

The values of α and β (φ_MRP = 6 wt%, roller speed = 50 r/min).

α	β	R_m
16.770	−0.058	−0.9948

Effects of temperature and filler content on shear time at balance state

In general, polymer melt shear stress is determined based on the torque at the time when torque is in balance state, and the time is defined as the shear time at balance state (t_b). Thus, t_b is also an important parameter for characterizing the viscoelasticity of polymer melts during flow in the torque rheometer. Figure 6 illustrates the relationship between the shear time at balance state and the MRP weight fraction of the PP/MRP composites under test conditions at a temperature of 180°C and a roller speed of 50 r/min. It can be observed that the values of the shear time at balance state increase roughly linearly with increasing the MRP weight fraction $(φ_{MRP})$ and the correlation between them can be expressed as follows:

t_{b} = A_{0} + A_{1} φ_{MRP}

Figure 6.

Correlation between time at balance state and MRP weight fraction (180°C, 50 r/min). MRP: microencapsulated red phosphorus.

As stated above, the melt shear viscosity of polymers is determined based on the shear stress at the time when the torque is in balance state; thus, parameters A₀ and A₁ are related to the viscosity of polymer melts. Among them, parameter A₁ characterizes the sensitivity of shear time at balance state of the composites to the filler content. The values of A₀ and A₁ can also be determined by means of a linear regression analysis method. Table 2 lists the values of A₀ and A₁ of the composite under experimental conditions. It can be seen that the value of A₁ is more than 6.4, and the value of the absolute value of the correlation coefficient (R_t) is more than 0.99. It means that the sensitivity of the shear time at balance state of the PP composites to the MRP weight fraction is strong (see Figure 6).

Table 2.

The values of A₀ and A₁ (180°C, roller speed = 50 r/min).

A ₀	A ₁	R _t
150.685	6.455	0.9937

Figure 7 shows the dependence of the shear time at balance state on the test temperature (T) of the PP/MRP composite with the filler weight fraction of 6 wt% at a roller speed of 50 r/min. It can be found that the values of the shear time at balance state of the composite decrease roughly linearly with a rise in test temperature, and the relationship between them can be presented as follows:

t_{b} = B_{0} + B_{1} T

Figure 7.

Dependence of time at balance state on temperature (6 wt%, 50 r/min).

Similarly, parameters B₀ and B₁ are also related to the viscosity of polymer melts. Among them, parameter B₁ characterizes the sensitivity of shear time at balance state of composites to test temperature. The values of B₀ and B₁can also be determined by means of a linear regression analysis method. Table 3 lists the values of B₀ and B₁ of the composite under experimental conditions. It can be seen that the absolute value of B₁ and the correlation coefficient (R_t) are, respectively, more than 1.55 and 0.98. It means that the sensitivity of the shear time at balance state of the PP composites to temperature is strong (see Figure 7).

Table 3.

The values of B₀ and B₁ ( $φ_{MRP} =$ 6 wt%, roller speed = 50 r/min).

B ₀	B ₁	R _t
462.869	−1.555	0.9890

Effects of temperature and filler content on energy consumption at balance state

A large energy is consumed during shear flow of polymer melts due to the viscoelastic properties. Energy consumption at balance state (E_b) is an important parameter for characterizing the viscoelasticity during shear flow of polymer melts. Figure 8 presents the correlation between the energy consumption at balance state and the MRP weight fractions of the PP/MRP composites under experimental conditions with a temperature of 180°C and a roller speed of 50 r/min. It can be found that the values of the energy consumption at balance state increase nonlinearly with increasing the MRP weight fraction. It is known through further analyzing that the correlation between them obeys a quadratic equation, that is

E_{b} = C_{0} + C_{1} φ_{MRP} + C_{2} φ_{MRP}^{2}

Figure 8.

Relationship between energy consumption and MRP weight fraction (180°C, 50 r/min). MRP: microencapsulated red phosphorus.

where C₀, C₁, and C₂ are the parameters related to the viscosity of polymer melts. The values of C₀, C₁, and C₂ can also be determined using a regression analysis method. Table 4 lists the values of C₀, C₁, and C₂ of the composite under experimental conditions. It can be seen that the absolute value of the correlation coefficient ( $R_{t}^{2}$ ) is more than 0.97.

Table 4.

The values of C₀, C₁, and C₂ (180°C, roller speed = 50 r/min).

C ₀	C ₁	C ₂	$R_{t}^{2}$
9.426	0.005	0.052	0.9758

Figure 9 illustrates the dependence of the energy consumption at balance state on test temperatures of the PP/MRP composite with MRP weight fraction of 6 wt% at a roller speed of 50 r/min. It can be seen that the values of $ln E_{b}$ of the composite melt increase almost linearly with increasing the reciprocal of the absolute temperature (1/T). This means that the dependence of the energy consumption at balance state on test temperature of the PP/MRP composite obeys the Arrhenius equation, that is

E_{b} = K_{e} exp (\frac{E_{e}}{R T})

Figure 9.

Dependence of energy consumption on temperature (6 wt%, 50 r/min).

where R is the universal gas constant. The energy consumption at balance state increases with increasing the melt viscosity under given shear flow conditions. Therefore, parameters K_e and E_e are related to the viscosity of polymer melts. The values of K_e and $E_{e} / R$ can also be determined by means of a linear regression analysis method. Table 5 lists the values of K_e and $E_{e} / R$ of the composite under experimental conditions. It can be seen that the value of the correlation coefficient (R_e) is more than 0.99.

Table 5.

The values of K_e and $E_{e} / R$ ( $φ_{MRP} = 6$ wt%, roller speed = 50 r/min).

K _e	$E_{e} / R$	R _e
−10.551	5.891	0.9982

In general, shear rate increases with an increase of flow rate, the resident time of polymer melt in a channel is shortened during shear flow, and the energy consumption would be increased, leading to increase in the energy consumption at balance state.

Effects of temperature and filler content on apparent shear viscosity

Apparent shear viscosity is an important parameter for characterizing the viscosity of polymer melts during shear flow. Figure 10 demonstrates the correlation between the apparent shear viscosity and the MRP weight fractions of the PP/MRP composites under experimental conditions with a temperature of 180°C and a roller speed of 50 r/min. It can be observed that the values of the apparent shear viscosity of the composite melts increase nonlinearly with increasing the MRP weight fraction. So far, there have been a number of the quantitative descriptions of the apparent shear viscosity of polymer composites. Einstein²⁷ proposed a simple expression as follows:

η_{c} = η_{m} (1 + K_{E} ϕ_{f})

Figure 10.

Relationship between apparent shear viscosity and MRP weight fraction (180°C, 50 r/min). MRP: microencapsulated red phosphorus.

where K_E is the Einstein coefficient and ϕ_f is the filler volume fraction. For sphere fillers, $K_{E} = 2.5$ . Guth and Gold.²⁸ modified equation (7) through including a second-order power of ϕ_f . The modified Einstein equation becomes

η_{c} = η_{m} (1 + 2.5 ϕ_{f} + 14.1 ϕ_{f}^{2})

where η_m is the shear viscosity of the matrix resin. For a filled polymer composite system, the relationship between ϕ_f and φ_f can be expressed as follows²⁹:

ϕ_{f} = \frac{φ_{f}}{φ_{f} (1 - χ) + χ}

and

χ = \frac{ρ_{f}}{ρ_{m}}

where ρ_f and ρ_m are the density of the filler and matrix, respectively.

Submitting the parameters including the weight fraction and density of the MRP, the melt shear viscosity, and density of the PP into equations (8), (9) and (10), respectively, one can estimate the melt shear viscosity of the PP/MRP composites. Hear, $φ_{f} = φ_{MRP}$ , $ϕ_{f} = ϕ_{MRP}$ , $ρ_{f} = ϕ_{MRP}$ , and $η_{m} = η_{PP}$ . Plotting the estimated melt shear viscosity against the MRP volume fraction, one can obtain the relationship between the estimated melt shear viscosity and the MRP volume fraction; then the values of the estimated melt shear viscosity are compared with the measured data, and the results are shown in Figure 11. It can be seen that the values of the estimated melt shear viscosity are approximate to the measured data, especially in the case of low MRP concentration.

Figure 11.

Correlation between estimated apparent shear viscosity and measured data under various MRP volume fraction (180°C, 50 r/min). MRP: microencapsulated red phosphorus.

Figure 12 presents the dependence of the apparent shear viscosity on test temperatures of the PP/MRP composite with MRP weight fraction of 6 wt% at a roller speed of 50 r/min. It can be seen that the values of $ln η_{a}$ of the composite melt increase roughly linearly with increasing the reciprocal of the absolute temperature (1/T). This means that the dependence of the apparent shear viscosity on test temperatures of the PP/MRP composite obeys the Arrhenius equation, that is

η_{c} = K_{a} exp (\frac{E_{a}}{R T})

Figure 12.

Dependence of apparent shear viscosity on temperature (6 wt%, 50 r/min).

where K_a and E_a are the parameters related to the viscosity of polymer melts; R is the universal gas constant. The values of K_a and $E_{a} / R$ can also be determined by means of the linear regression analysis method. Table 6 lists the values of K_a and $E_{a} / R$ of the composite under experimental conditions. It can be found that the value of the linear correlation coefficient (R_a) is more than 0.97.

Table 6.

The values of K_a and $E_{a} / R$ (φ_MRP = 6 wt%, roller speed = 50 r/min).

K _a	$E_{a} / R$	R _a
−23.063	15.563	0.97998

In general, the activities or transition ability of the macromolecular chain of the resin increase with a rise in temperature; meanwhile, the flow resistance decreases, and the melt viscosity reduces correspondingly. In this case, the viscous dissipation of the deformation energy stored in shear flow decreases, resulting in the energy consumption of the composite melts reduces. On the other hand, the activities or transition ability of the macromolecular chains of the matrix melt will be blocked to some extent by the inclusions, and the elastic recovery of the deformation during the composites melt shear flow will be weakened, leading to the sensitivity of the composite melt shear viscosity to temperature decreases with increasing the filler content.

Conclusions

The effects of the MRP content and the experimental conditions including temperature and roller speed on the melt shear flow properties of the PP composites were significant. The torque, the energy consumption at balance state, and the melt shear viscosity of the composites increased nonlinearly with increasing the MRP weight fraction while decreased slightly with a rise in temperature; the maximum torque increased with increasing roller speed; and the dependence of the melt shear viscosity and energy consumption at balance state of the composites on temperature approximately obeyed the Arrhenius equation. This study would be beneficial for processing these flame-retardant PP composite systems.

Footnotes

Acknowledgements

The authors would like to thank Professor CY Tang and Dr CP Tsui for their help in this study.

Funding

The author(s) received no financial support for the research, authorship, and/or publication of this article.

ORCID iD

Ji-Zhao Liang

References

Sousa Pires Xavier

Agrawal

de Figueiredo Brito

, et al. Study of the rheological properties of PP/clay systems under steady and oscillatory shear flows. Mater Sci Forum 2014; 775-776: 75–79.

Liang

. Rheology in polymer materials processing. Guangzhou: South China University Press, 2007.

Le Moigne

van den Oever

Budtova

. Dynamic and capillary shear rheology of natural fiber-reinforced composites. Polym Eng Sci 2013; 53(12): 2582–2593.

Liang

Tang

Lee

. A study of the flow properties of glass fibre reinforced PBT in extrusion. J Mater Process Technol 1995; 48: 707–712.

Liang

Tang

. Studies of melt flow properties during extrusion of polycarbonate. J Mater Process Technol 1997; 63: 501–504.

Liang

RKY

. Rheological properties of glass bead-filled low density polyethylene composite melts in capillary extrusion. J Appl Polym Sci 1999; 73(8): 1451–1456.

Liang

Tang

Zhou

, et al. Melt flow behavior in capillary extrusion of nanosized calcium carbonate filled poly(L-lactic acid) bio-composites. Polym Eng Sci 2012; 52(9): 1839–1844.

Bhadu

Kumar

Choudhary

. Rheological, melting and crystallization behaviour of an open cage POSS/PTT nanocomposite prepared by melt blending. Int J Plast Technol 2010; 14(1): S7–S23.

Gao

. Rheological behavior and mechanical properties of PVC/V-POSS nanocomposites. Adv Mater Research 2011; 217-218: 555–558.

10.

Loux

Prashantha

Roger

, et al. Qualifying dispersion and distribution of carbon nanotubes in polyamide matrix during melt-mixing by flow simulation. Polym Polym Compos 2015; 23(5): 305–315.

11.

Freire

Bianchi

Monteiro

EEC

, et al. Processability of PVDF/PMMA blends studied by torque rheometry. Mater Sci Eng Part C 2009; 29(2):657–661.

12.

Liang

Yang

Tang

. Melt shear viscosity of PP/Al(OH)₃/Mg(OH)₂ flame retardant composites at high extrusion rates. J Appl Polym Sci 2011; 119(3): 1835–1841.

13.

Liang

Zhang

. A study on flame retardant properties of PP/Al(OH)₃/Mg(OH)₂ composites. Polym Int 2010; 59: 539–542.

14.

Liang

Feng

Tsui

, et al. Mechanical properties and flame-retardant of PP/MRP/Mg(OH)₂/Al(OH)₃ composites. Compos Part B 2015; 71: 74–81.

15.

Lin

Qiu

Mai

. Crystallization and melt behavior of magnesium hydroxide/polypropylene composites modified by functionalized polypropylene. J Appl Polym Sci 2004; 91: 3899–3908.

16.

Hong

Lee

. Tensile properties and stress whiting of polypropylene/polyolefin elastomer/magnesium hydroxide flame retardant composites for cable insulating application. J Appl Polym Sci 2005; 97: 2311–2318.

17.

Sain

Park

Suhara

. Flame retardant and mechanical properties of natural fibre-PP composites containing magnesium hydroxide. Polym Degrad Stab 2004; 83: 363–367.

18.

Jiao

Chen

. Flame retardant synergism of hydroxy silicone oil and Al (OH)₃ in EVA composites. Polym-Plast Technol Eng 2009; 48: 665–670.

19.

Fang

Song

, et al. Mechanical properties, fire performance and thermal stability of magnesium hydroxide sulfate hydrate whiskers flame retardant silicone rubber. J Mater Sci 2008; 43: 1057–1062.

20.

Yuan

Sheng

, et al. Enhanced flame retardancy of polypropylene by melamine-modified graphene oxide. J Mater Sci 2015; 50: 5389–5401.

21.

Sauca

Giamberini

Cerruti

, et al. Effect of phosphorous-containing modified poly(vinyl alcohol) on the mechanical and flame retardant properties of polypropylene. Express Polym Lett 2015; 9: 330–343.

22.

Lai

Tang

, et al. Flame-retardant mechanism of a novel polymeric intumescent flame retardant containing caged bicyclic phosphate for polypropylene. Polym Degrad Stab 2015; 113: 22–31.

23.

Jiang

Zhang

, et al. Preparation of microencapsulated red phosphorus and its flame-retardant application in PP composites. Spectros Spect Analys 2010; 30: 1329–1335.

24.

Liang

Feng

Tsui

, et al. Melt flow properties and morphology of polypropylene composites filled with microencapsulated red phosphorus. J Thermoplast Mater Compos 2015; 28(2): 275–286.

25.

Bousmina

Ait-Kadi

Faisant

. Determination of shear rate and viscosity from batch mixer data. J Rheol 1999; 43: 415–433.

26.

Santi

Hage

Correa

, et al. Torque viscometry of molten polymers and composites. Appl Rheol 2009; 19(1): 13148.

27.

Einstein

. Eine neue bestimmung der molekul dimensionen. Annals of Physics 1911; 34: 591–602.

28.

Guth

Gold

. On the hydrodynamical theory of viscosity of suspensions. Phys Rev 1938; 53: 322–326.

29.

Liang

RKY

. Measurement of dispersion of glass beads in PP matrix. J Reinf Plast Compos 2001; 20: 630–638.