Melt Flow Rate, Molecular Weight and Rheological properties Syed, Tariq *, Singh, Rajendra., Abbasi, Sarfraz SABIC Polymer Application Development Center, Riyadh, KSA Introduction:

Polymeric material data sheets are usually packed with lots of information, but not all for obvious reasons. There are two properties listed in almost every data sheet namely Specific Gravity and Melt Flow Rate (MFR). These simple tests help to characterize polymers as quickly and inexpensively as possible. Relationship of MFR to average molecular weight of polymer yields a quick window to the rheological properties and toughness behavior of the polymer. Flow and molecular weights governs the key functions of part fabrication and part life cycle. Sophisticated analytical techniques are available to determine molecular weight and rheological properties, but are expensive, time consuming and need higher level of skill. Here we will outline a method to use MFR to equate and calculate other properties of interest and to obtain MFR at a desired (standard/Reference) condition if required from MFR data given at a non-standard condition on a data sheet. Theoretical Background:

MFR is inversely related to viscosity, i.e. higher the MFR lower the viscosity and vice versa. In simple terms, viscosity is resistance to flow. Mathematically viscosity (η) is the ratio of shear stress (σ) and the shear rate ( ), that can be represented in an equation as follows 1][2][3][13] ………………………………………………………………………………………………………1

If viscosity remains constant while changing strain rate the fluid is known as Newtonian and ones that deviates aforementioned principle is known as non-Newtonian fluids. Polymers in melt state exhibit both flow characteristics. Complicated constitutive equations were written to capture and explain polymer flow characteristics. Most wellknown constitutive equation is the K-BKZ equation9], which involves multiple experimental data and curve fitting parameters. But even this equation has its own short comings, namely strain hardening in some flow geometry. 6]10] Some other simple well known models are Power Law, WLF, Cross, Carreau-Yasuda and etc. Apparent stress (τ) and strain rate in a simple MFR die geometry is expressed as follows 1][2][4][13]

*

Corresponding author

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……….…………………………………………………………………………………2 ………………………………………………………………………………………………3

where Rd and l are the radius and length of the die, respectively. L is the load applied for the test and Q is the flow rate of the material. Dimensions of the melt indexers are fixed therefore, the above equations will reduce to …………………………………………………………………………………………4 ……………………………………….…………………………………………………….5

where “ρ” is the melt density of the polymer. Mass flow rate (Q) can be calculated as follows; [4][13] ……………………………………………………………………………………………………6

The non-Newtonian or the shear thinning behavior of polymers can be expressed by the well-known Power Law model as follows 2][11] ………………………………………………………………….…………………………….7 ……………………………………………………………………8

A log-log plot of viscosity versus shear rate will yield the slope (n-1) and intercept (m) of the line plotted. The index m is also termed as consistency index (the viscosity at a reference shear rate). An approximate calculation by MFR data for n and m using two different loads L (where L2 > L1), can be done as follows [7][13]

2]13][11]

From above equation;

…………..……………………………………………………………………9 ………………………………………………………………………………10

And m (consistency) is given by the following;

2][13][11]

…………………………………………………………………………………..…11

Polymers exhibit a Newtonian plateau at low shear rates (MFR region), a transition region (Curvature region), and then a power law region (Power Law/non-Newtonian region).

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Viscosity of polymer melt and thus MFR are functions of temperature. Often MFR data is reported by different resin manufacturers at different temperature. Bird-Carreau-Yasuda model was modified by Menges, Wortberg and Michaecli, which show viscosity as a function temperature and pressure, using a WLF relation, as follows 7][11][14] ……………………………….12

where p is in bar. A further modification to the above equation was suggested, as follows: ………….……………13 Where T0 = [Tg (glass transition temperature) + 50°K for amorphous polymers (per Van Krevelen recommendation)] or [Melt temperature for crystalline polymers].

T0 is a reference temperature, T1 temperature at which MFR is known and T2 is the temperature at which MFR is to be known. All temperatures are in °K.

Results and Discussions: MFR yields mass in grams collected over ten minutes, extruded out of a specific barrel and die geometry under the action of applied load in Kilograms. The details of the test and equipment can be found under ASTM-D1238 and ISO-1133. This simple rheological test is used for routine quality check. It gives a number for viscosity and is an indirect measure of average molecular weight, which in turn helps address flow anomalies and parts failures. This is a very quick, effective, inexpensive test and requires minimal training to perform the test. Often this is the only rheological data available for the technical or trade decision. Different manufacturers of similar product report MFR data on their data sheet at different test conditions rather than one standard condition. That renders the comparison of MFR difficult. For example, standard condition for measuring MFR of polycarbonate (PC) is 300°C and 1.2Kg of load. Thus there is a need to translate MFR data to a standard test condition. The reason being MFR depends on many variables such as entanglement of polymer chains, impurities, molecular forces, additives and etc. in addition to shear rate and temperature. Empirical data of molecular weight (by GPC) and MFR (2 – 80) for a general purpose polycarbonate is given in Table-1. These MFR data was used to calculate other rheological properties in the table using equation 1, 4, 5 and 6 respectively and subsequently plotted in Graph-1. Molecular weight, viscosity, shear rate and MFR can be correlated easily by fitted equations from Graph-1.

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Table-1: PC MFR (300°C&1.2Kg) & Molecular Weight with Calculated Rheological Values

Sample

MFR [gm/10min]

Q [cc/min]

Shear rate [1/sec)

1

2.0

0.19

3.48

2

2.8

0.26

4.86

3

4.0

0.38

6.94

4

5.3

0.50

9.19

5

6.0

0.57

10.40

6

6.0

0.57

10.40

7

6.7

0.63

11.62

8

7.1

0.67

12.31

9

7.5

0.71

13.00

10

8.0

0.75

13.87

11

8.2

0.77

14.22

12

9.7

0.92

16.82

13

10.8

1.02

18.73

14

11.1

1.05

19.25

15

11.8

1.11

20.46

16

12.0

1.13

20.81

17

12.8

1.21

22.19

18

12.8

1.21

22.19

19

14.0

1.32

24.28

20

14.8

1.40

25.66

21

16.2

1.53

28.09

22

17.3

1.63

30.00

23

18.0

1.70

31.21

24

18.2

1.72

31.56

25

19.0

1.79

32.95

Apparent Shear Stress [Pa] 10,750 10,750 10,750 10,750 10,750 10,750 10,750 10,750 10,750 10,750 10,750 10,750 10,750 10,750 10,750 10,750 10,750 10,750 10,750 10,750 10,750 10,750 10,750 10,750

Apparent Viscosity [Pa-s]

Molecular Weight (MWt)

3,100

36,000

2,214

36,496

1,550

33,000

1,170

32,000

1,033

30,000

1,033

31,000

925

30,000

873

28,856

827

28,361

775

27,000

756

27,098

639

27,100

574

25,405

559

26,100

525

27,102

517

24,000

484

25,100

484

25,100

443

24,500

419

24,100

383

23,500

358

23,100

344

22,000

341

24,226

326

22,500 Page 4 of 8

10,750 26

20.0

1.89

34.68

27

26.0

2.45

45.08

28

35.0

3.30

60.69

29

60.0

5.66

104.04

30

65.0

6.13

112.71

31

71.7

6.76

124.33

32

80.0

7.55

138.72

10,750 10,750 10,750 10,750 10,750 10,750 10,750

310

25,000

238

22,708

177

20,000

103

15,000

95

15,000

86

16,000

77

13,000

Graph-1: Molecular weight & Rheological Properties vs. MFR

MFR vs Strain Rate, Stress, Viscosity and Mol.Weight 1.E+05

1.E+04

Molecular Weight (X)

Apparent Strain , Stress and Viscosity

1.E+05

1.E+03 Apparent Shear Rate [1/s]

1.E+02

Apparent Viscosity [Pa-sec]

1.E+01

Apparent Stress [Pa] Molecular Weight

1.E+04

1.E+00

1

10

100

MFR (300°C/1.2Kg) [gm/10min]

Thus values can be estimated or calculated for any specific MFR data with ease. For illustration, shear rate, viscosity and molecular weight were calculated respectively for a 15 melt polycarbonate based on curve fittings from Graph-1 and is given in Table-2; Table-2: Shear Rate, Viscosity and Molecular Weight from fitted parameters for MFR 15 Properties MFR (melt flow rate) (shear rate)

η (viscosity) PC MW (molecular weight)

MFR (300°C/1.2Kg)

Units

15.000

gm/10min

26.258

1/sec

408

Pa-s

24061

gm/mol

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Problem arises when MFR data is given at a different MFR test condition then the standard test condition used to construct Graph-1. To address this problem we will use some experimental MFR data for five different polycarbonate samples at three different test conditions as listed in Table-3. Table-3: Five Samples, Three different Conditions, Empirical MFR Test Data Test Temp °C

Test load Kg

MFR [gm/10min]

250

2.16

2

300

1.2

7

300

10

70

250

2.16

2

300

1.2

7

300

10

70

250

2.16

3

300

1.2

13

300

10

118

250

2.16

7

300

1.2

22

300

10

218

250

2.16

18

300

1.2

57

300

10

558

Two non-standard MFR test conditions (250°C/2.16Kg and 300°C/10kg) data are also given in Table-3. These non-standard condition MFR data will be used to calculate MFR at a standard condition of 300°C/1.2Kg for PC. Two scenarios from Table- are as follows; Scenario I Scenario II

: For low to high temp (250°C to 300°C) and high to low load (2.16Kg – 1.2Kg) : Same temperature (300C) and high to low load (10kg to 1.2Kg)

MFR (300°C/1.2Kg) is calculated from known value of MFR (250°C/2.16Kg & 300°C/10Kg) using equation 9 and 13 for polycarbonate having a Tg of 148°C. Value of n was calculated using equation 10, resulting in five values of n, which were plotted verses MFR (300°C/1.2Kg). Fitted equation was derived from this graph and is listed in Table-4, row-3. In literature, n for PC is given by a single value of 0.98.[11][12][14] Using all aforementioned equations and values of n, MFR (300°C/1.2Kg ) was calculated and tabulated in Table-4.

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Table-4: MFR Prediction at Standard Condition (300°C/1.2Kg)

Test Temp [°C]

Test load [Kg]

MFR [cc/10min] ASTM D1238

MFR prediction (300C/1.2Kg) n= 0.0127MFR + 0.5647

250

2.16

2

7

2

300

1.2

7

Sample 3

300

10

66

Sample 4 Sample

250

2.16

2

5

300

1.2

7

Sample 6

300

10

66

Sample 7

250

2.16

3

Material

MFR prediction (300C/1.2Kg) n= 0.0004MFR + 1.1634

MFR predictio n (300C/1.2 Kg) n=0.98 4

Sample 1 Sample

Sampl e8

30 0

1.2

12

Sample 9 Sample 10

300 250

10 2.16

111 6

Sampl e 11

30 0

1.2

21

Sample 12 Sample 13

300 250

10 2.16

205 17

Sampl e 14

30 0

1.2

54

Sample 15

300

10

526

7

8 4

7

8 8

7

13

11

15 15

20

26 43

46

67

23

51

From Table-4 it appears that curve fitted equations for n predicts better MFR values over the range in comparison to just a single value of 0.98. Once MFR is obtained at a desired/standard condition then other properties can be calculated as shown in Graph-1. Further, if n is known then consistency m can be calculated using equation 11. Rabinowitsch correction can be applied if desired then power law viscosity at higher shears can be calculated using equation 7 and 13. Thus similar techniques can be used for any thermoplastic system and useful data will be at finger tips of design engineers and simulation work.

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Conclusions:

Due to inevitable importance of MFR data, it is necessary to extract all possible information out of it. MFR serves as a quick characterization tool for decision making, investigation and further design of experiments. Here a method is compiled to extract information from a given or known MFR data. It is further shown here, how one can obtain “n” using a fitted curve equation rather than a single value. This technique predicts better MFR values. Once MFR is known at a standard condition, other parameters can be calculated and estimated, as shown in Table-1 and Graph-1.

References 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14.

Vlachopoulos, J., Polychronopoulos, N., “Applied Polymer Rheology: Fluids with Industrial Applications”, 1st Edition, Edited by Marianna Kontopoulou. Vlachopoulos, J., Strutt, D., “The Role of Rheology in Polymer Extrusion”, online on http://www.polydynamics. com/Rheology.pdf. Rosato, D., Rosato’s Plastics Encyclopedia and Dictionary”, HANSER publication, Ohio (1993). Goff, J. Whelan, T., The Dynisco Extrusion Processors Handbook, 2nd Edition. Edited by DeLaney, D. LeGrand, D. G., Bendler. J. T., “Handbook of Polycarbonate Science and Technology”, Marcel Dekker Inc. NY. US. Venerus, D. C., Tariq, S. A., Bernstein, B., “On the use of stress growth data to determine strain-dependent material functions for factorable K-BKZ equations”, Journal of Non-Newtonian Fluid Mechanics, 49 (1993) 299-315. Shenoy, A. V., Saini, D. R., Nadkarni, V. M., “Rheograms for engineering thermoplastics from melt flow index”, Rheological Acta, Vol. 22, No.2 (1983). Dealy, J. M., Wissbrun, K. F., “Melt Rheology and its role in Plastics Processing”, Van Nostrand Reinhold N. Y. 1990. Berstein, B., Kearsley, E., Zapas L., Trans. Soc. Rheol., 7(1963) 391. Tariq, S. A., “Strain Coupling Effects in PE-LD and its Rheology”, MS Thesis, Illinois Institute of Technology, 1993. Osswald, T. A., Pablo, J., Ortiz, L,. “Polymer processing, modeling and simulation”, J. of Chemical Physics, issue 4. Oswald, T., Baur, E., Oberbach, K., Schmachtenberg, E., “International Plastic Handbook”, Table 3.11, HANSER, Ohio. Vlachopoulos, J., Wagner, J. R., (editors), “The SPE Guide on Extrusion Technology and Troubleshooting”. SPE, 2001. Osswald, T., Menges, G., “Material science for polymer engineers”. HANSER, Ohio.

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