Open Source Melt Flow Indexer Literature Review

Melt Flow Indexer is also known as an Extrusion Plastometer

ISO Standard 1133-1 Determination of Melt Flow Rate and Melt Volume Flow Rate of Thermoplastics[edit | edit source]

I am unsure of how to properly cite this. Voted on by multiple parties so no clear author. From 2011.

General[edit | edit source]

-1133-1 good for materials that won't degrade during the test because of temperature, 1133-2 for materials sensitive to time-temperature history
-Test conditions often specified by material's standard, common ones are listed in Annex A
-MFI mainly for quality control, may not represent behaviour during processing since lower shear rates
Melt Mass-Flow Rate is MFR, Melt Mass-Flow Index is MFI (same thing), Melt Volume-Flow Rate is MVR
Procedure A: Timed segments of extrudate weighed and used to calculate MFR
Procedure B: Distance piston travels in a specified time, or time for piston to travel a specified distance used to calculate MVR
If Melt Density known can convert between MFR and MVR
All dimensions have tolerances that are not included

Apparatus[edit | edit source]

Extrusion Plastometer[edit | edit source]

Thermoplastic in a vertical cylinder at specific temperature, loaded with known weight, extruded through known die.

Cylinder
- 115-180 mm Length
- 9.550 mm ID
- Fixed vertically, level should be used to check and ensure vertical position
- Resistant to wear/corrosion at operating temp.
- Vickers hardness > 500
- Smooth finish - not affected by material
- Thermally insulated - exposed area < 4cm^2 - recommend using insulation that plastic does not stick to
- Piston Guide, prevent misalignment
Piston
- As long as Cyl. or longer
- Piston Head: 6.35mm Length, 9.474mm Diameter, 0.4mm lower edge radius, upper edge - sharpness removed
- Diameter <9mm everywhere other than head
- same corrosion/wear requirements as Cyl. should be softer, easier to replace than Cyl.
- Two reference marks, 30mm apart, upper mark aligned with top of Cyl. when bottom of piston head is 20mm from top of die
- Weights thermally insulated from piston
- Solid or Hollow
Temperature Control System
- 10mm above die within 1C of test temp. 70mm above die within 2C (goes to 2.5C and to 3C as test Temp. increases) of 10mm
- Test temp. to be set in steps of 0.1C
- May measure temperature on outside/intermediate portion of Cyl. wall, must calibrate
Die
- Tungsten Carbide or Hardened steel, can use other if materials potentially corrosive
- 8mm Length
- 2.095 mm Bore Diameter
- Go/no-go gauge - double sided gauge, one side should barely fit, one side should barely not
- Vickers Hardness > 500
- Smooth finish Ra = 0.25 μm
- Flat faces, normal to bore axis - free from visible machining
- OD so can move freely up and down Cyl, no flow around die
- Not project beyond Cyl. - Can be held in place by Die retaining plate, which extends past the edge of the cylinder, under the die but not over bore
- Bore co-axial with Die
Level
- Two-directional bubble level
- Or can use dummy piston with spirit level
- Adjustable supports recommended to correct levelness - (Can we not just make it level to begin with and have supports non-adjustable? Maybe harder to produce)
Load
- Removable weights + weight of Piston = required load
- Can use mechanical loading device with load cell
- Can use pneumatic loading device with pressure sensor
- Need within 0.5% of required load

Accessories[edit | edit source]

Packing Rod - non-abrasive packs materials into Cyl
Cleaning equipment
Go/no-go gauge - tests entire length of bore
Temperature Calibration device - rod fitted with temperature sensors, measures 10, 30, 50, 70 mm above die, calibrates temperature controller
Die-Plug - Prevent drool prior to test, easy to remove
Piston/Weight Support - hold piston so lower mark is 25mm above cylinder
Preforming device - preforms samples into single charge for powder/flakes to ensure material void-free

Equipment for Procedure A[edit | edit source]

Cutting tool - sharp-edge spatula or rotating cutter blade with motor drive recommended - can be manual but motor better
Timer - max permissible error within 1% of cut interval - cut intervals get closer together with higher MFRs
Balance - 1mg error max

Test Sample[edit | edit source]

Sample Form
- May be in any form that can be added to Cyl.
  - Granules/pellets
  - Strips of film
  - Powder
  - Sections of moulded/extruded parts
  - etc.
- Maybe necessary to preform into single charge/pellets to prevent voids
- Form can be significant factor in reproducibility - controlled to reduce variance and improve comparability of inter-laboratory results
Conditioning - Test sample conditioned and stabilized in accordance with material standard

Procedure A[edit | edit source]

Selection of temperature and load
1. Refer to material specification standard if unable to,
2. Use table A.1 to select conditions based on melting point/processing conditions
Clean Apparatus
1. Refer to Section 7.2
Ensure Cylinder and Piston are at selected temperature for >15 minutes prior to starting testing
Selection of sample mass and charging the Cylinder
1. 3g to 8g sample based on anticipated MFR/MVR - refer to Table 4
2. Charge Cylinder with sample (add the plastic)
  1. Pack sample with packing rod using hand pressure
  2. Remove as much air from material as possible - variation in packing pressure can cause error
  3. Complete charging in 1 minute or less - PREHEAT TIMER STARTS INSTANTLY
3. Preheat sample for 5 minutes
  1. Put the piston in the Cylinder, may be loaded, unloaded, or supported - depends on MFI (how much comes out of die during preheat, higher MFI, less weight)
  2. For materials with especially high MFI die plug can be used to prevent material loss
  3. Verify that temperature has remained at test temperature
Measurements
1. After preheat period, apply required load to piston
  1. If die plug used, wait a few seconds for the material to stabilize after loading, remove Piston support, then die plug. Heat resistant gloves strongly recommended
2. Allow piston to descend by gravity until bubble-free extrudate comes out
3. Cut off and discard extrudate and continue to let piston descend
4. When lower reference point reaches the top of the Cylinder, cut extrudate and start the timer simultaneously. Discard extrudate. Measurements start now.
5. Collect successive cut-offs
6. Choose time interval such that sections are >10 mm in length, preferably 10mm < Length < 20mm.
  1. Sometimes cannot reach 10 mm in the maximum time interval (240s)
  2. If mass of these cut-offs >.04g they are usable
  3. If not, stop test and use procedure B
7. Test ends when upper reference mark reaches top of Cylinder
8. Allow cut-offs to cool
9. Discard cut-offs with visible air bubbles, preferably 3 or more left
10. Weigh cut-offs individually in the order they were extruded
  1. If continuous change in mass is observed, discard results and repeat with fresh sample
11. Calculate the Average weight.
  1. If (highest weight) - (lowest weight) > 15% Avg. weight, discard results and repeat with fresh sample
12. Calculate MFR from average weight
13. Time between end of charging and end of last measurement < 25 minutes to prevent degradation

From melt flow index to rheogram[edit | edit source]

Shenoy, A. V., Chattopadhyay, S., & Nadkarni, V. M. (1983). From melt flow index to rheogram. Rheologica Acta, 22(1), 12.

"A knowledge of the complete flow curve or rheogram of a polymeric melt depicting the variation of the melt viscosity over industrially relevant range of shear rate and temperature is essential in the design of polymer processing equipment, process optimization and trouble-shooting. These data are generated on sophisticated rheometers that are beyond the financial and technical means of most plastics processors. The only flow parameter available to the processor is the melt flow index of the material."

Notes[edit | edit source]

Knowledge of flow curve/rheogram (depicts the variation of melt viscosity over industrially relevant range of shear rate and temp.) of polymeric melts essential in polymer processing.
At time, data gotten from sophisticated rheometers beyond financial and technical means of most plastics processors. required trained operators.
Can estimate rheograms at temps relevant to processing conditions using master curve, knowing MFI and glass transition temperature
Says "MFI is a good indicator of the most suitable end use for which the particular grade can be used" and cites "Van Krevelan, D. W., Properties of Polymers, p. 488, Elsevier Scientific Publishing Company (Amsterdam 1976)."
MFI not a fundamental polymer property - an empirically defined parameter critically influenced by conditions of measurement. A single point viscosity measurement at relatively low shear rate and temperature
Temps and shear rate often much different in actual processing -results do not directly correlate with processing behaviour.
Smith (above) also shows the insensitivity of MFI to the effects of molecular-weight distribution. Molecular-weight distribution normally affects flow behaviour at very low (10^-1 s^-1) and very high (10^4 s^-1) shear rates.
Despite limitations, MFI is still a simple, easily obtainable viscosity paramater.
Menges, G., J. Wortberg, W. Michaeli, Kunststoffe 68, 47 (1973). suggested mathematical equation as universal viscosity function based on zero-shear viscosity, and shown the function can be used to estimate rheogram with knowledge of glass-transition temperature. Zero-shear viscosity hard to obtain experimentally - this paper uses MFI as normalizing parameter.
MFI proportional to apparent shear rate and inversely proportional to apparent viscosity. Possible to coalesce apparent viscosity vs apparent shear rate rheograms of polymer grades of different MFI by plotting (MFI*apparent viscosity) vs (MFI*apparent shear rate) on log-log scale at given temp and pressure.
ln(MFI2/MFI1) = (8.86*(T2-Ts)/(101.6+(T2-Ts))) - (8.86*(T1-Ts)/(101.6+(T1-Ts))). Where Ts is the glass transition temperature + 50K. Therefore effective MFI at given processing temp. can be estimated using MFIs reported as (think this might be typo and supposed to be "at") the ASTM test temp.
Necessary eliminate MFI test load on master curve. MFI measurement done under constant shear stress, directly proportional to load. τ α L or apparent viscosity α L/(shear rate) -- Where L is the total load
MFI directly related to shear rate through geometry of melt flow apparatus, MFI α shear rate
Few more steps gets us to (MFI2/MFI1) = (L2/L1)^(1/n) where (n-1) is the slope of the viscosity vs shear rate curve
Entire viscosity vs shear rate curves can be generated at any temperature simply from MFI. Steps to do so are as follows:

Obtain MFI value at standard specified conditions
If loading condition diff. from the one used in generating master curve, obtain value of MFI at the loading condition of the master curve using eq'n 21 and calcing n from value of the slope of master curve in newtonian region
If specified temp condition of MFI also diff from temp of interest, calculate new MFI value using eq'n 15 and correct determined value of Ts
Knowing effective MFI at temp of interest, rheogram can be generated by substituting value in master curve

For resins (unclear to me if talking about only resins or in gen.) eq'n 15 very sensitive to value of Ts used, recommended the actual glass transition temperature be determined whenever possible.

Melt Flow Index, More Than Just a Quality Control Rheological Parameter[edit | edit source]

Part I[edit | edit source]

Shenoy, A., & Saini, D. (1986). Melt Flow Index: More Than Just a Quality Control Rheological Parameter. Part I. Advances in Polymer Technology, 6, 1–58. https://doi.org/10.1002/adv.1986.060060101

Abstract[edit | edit source]

"Despite the fact that MFI is an empirically defined parameter with certain limitations as described above, it is still one of the most popular parameters in the plastics industry for distinguishing various grades of polymers. Polymer manufacturers have used it routinely to specify the most suitable end use of a particular grade of the polymer. Over the years, it has been found that MFI correlates well with a number of other useful parameters. With these enhanced abilities to predict a variety of properties, MFI has certainly been upgraded in its value. The possible existing correlations between MFI and various other important parameters encountered in polymer manufacture, polymer processing, and end-product properties evaluation are discussed in detail."

Notes[edit | edit source]

MFI test carried out by dif. operators in dif. locations can vary +/-9% - +/-15%
Table showing possible sources of error and percentage error they can cause
Google capillary viscometer, sounds like might be same as cap. rheo. but should check
Might be good to modify MFIer so dry nitrogen purging is possible for moisture sensitivity
Tables showing MFI values at specific test conditions, and recommended end-use application for that MFI
During polymer manufacture, reaction temp., catalyst activation temp., molecular weight build-up, etc. can be correlated with MFI
Zero shear viscosity, viscosity vs shear rate relationship, elasticity vs. shear rate relationship, die swell, elongational viscosity, activation energy for viscous flow,etc. can be determined through only MFI. Talked about in from MFI to rheogram above
Stability during processing, reprocessibility, die design, mold filling behaviour adjudged through only MFI
Physical, mechanical, thermal, certain optical properties *could be* related very well to MFI of raw material

-Just a note from myself on that stuff, that article and this one are from the 80s, and talk about everything you can do with only the MFI, but more recent texts make no mention of this stuff. They talk about how it's "only a single point on the viscosity vs shear rate curve" and make no mention of the master curves that article above talks about, how it is only a relative parameter. Maybe I just haven't read articles that do, maybe it's been proven to not work and/or has fallen out of use, I don't know. I will look at articles that cite this one and the one above and look for recency

Rest of article is quite detailed analysis of how MFI is related to these

Mathematical expressions, and graphs showing relationship of MFI and these properties (relationships obv. arent exact, and often different expressions for different types of polymers i.e. branched vs unbranched)

Weight-avg. MW
- Linear/Low density increase MFI with lower MW vice versa.
- Branched/High density Decrease MFI with lower MW vice versa
Number-avg. MW
MW distribution
Solution viscosity
Zero-shear Viscosity

MFI and use in polymer product fabrication discussed in detail:

MFI and relation to Rheological Considerations:

MFI to rheogram (upgraded in the Low shear region)
- Correction factor used when coalescing low shear viscosity for polymers with wildly different MW distributions
- graphs coalesce much better onto single curve
Normal Stress Difference
Die Swell
Melt Strength
Breakage Stretch Ratio and Elongation Viscosity
Flow activation energy

Shown that number of parameters in polymer processing can be estimated within reasonable accuracy using only MFI. Specifically talks about MFI and these aspects/techniques:

Techniques:

Injection Molding
Compression Molding
Calendering
Extruding
- Many different channel shapes talked about

Aspects:

Viscous heat dissipation
Blending and Filling
Curing and crosslinking
Degradation and stability
- thermal oxidative
- shear degradation causing molecular scission
- hydrolysis
- aging

Part 2[edit | edit source]

Shenoy, A., & Saini, D. (1986). Melt flow index: More than just a quality control rheological parameter. Part II. Advances in Polymer Technology - ADV POLYM TECHNOL, 6, 125–145. https://doi.org/10.1002/adv.1986.060060201

Product Property Evaluation[edit | edit source]

Part 2 is much shorter than Part 1, and focuses on MFI's relation to these properties/performances of a product post-processing.\

Tensile Strength (TS)
- TS at yield and ultimate TS at break, reasonably-strong dependence on MFI
- Yield strength not incredibly dependent on MFI, sometimes dependent on other things that MFI also depends on
- TS @ break very dependent on MW so sensitive to changes in MFI
  - Low density/linear, as tensile strength in both cross and machine directions increases MFI decreases
  - High density/branched as TS in cross direction increase, machine direction decrease MFI decrease
Ultimate Elongation
- Slight dependence on MFI, more dependent on density
Tenacity (of film tapes)
- For tenacity to be high MFI has to be as low as possible
Elastic Modulus and Flexural Stress
- Both are criteria for rigidity of material
- Elastic Modulus higher for lower MFI (general), flexural stress at max deflection follows same trend but values are ~10x less
- Flexural Modulus increases rapidly with density, largely unaffected by MFI
Impact Strength
- can be seen as determination of flexural stress at rapid rate with load increase
- Depends on both density and MFI, highest for lowest MFI
Brittle Temperature
- With increasing MW, Brittle Temp. decreases. so follow to relation with the high/low density MFIs
Tear Strength (films)
- Elmendorf tear inversely related to density & MFI
Environmental Stress Cracking (ESC)
- Polymer under high stress crack when in contact with active environments such as
  - detergents
  - fats
  - silicone fluids
- vulnerability to ESC decreases rapidly with MFI decreasing
Thermal Effects
- Similar relation as ESC
- In certain cases there exists a particular MFI where shrinkage is minimal (good)
Gloss and Clarity
- Assessed visually and measuring light reflected by surface of moldings
- The higher the MFI, the lower temp. high gloss moldings can be produced
- For extruded films, maybe this is general but wording is a bit unclear
  - Low MW favours high clarity and gloss
  - narrow molecular distribution favours high clarity
  - broad distribution favours high gloss
  - By proper balance of MW distribution, and MFI, can get desired levels

Measurement Techniques (Melt Rheology and its Applications in the Plastics Industry)[edit | edit source]

Dealy, J. M., & Wang, J. (2013). Measurement Techniques. In Melt Rheology and its Applications in the Plastics Industry (pp. 139–179). Springer, Dordrecht. https://doi.org/10.1007/978-94-007-6395-1_6

Abstract[edit | edit source]

"The measurement of the rheological behavior of viscoelastic melts is much more challenging than determining the viscosity of a Newtonian fluid, but reliable data on melts are essential for resin characterization, quality control, evaluating processability and for use in process simulation. This chapter describes the instruments and techniques used to learn about the rheological behavior of molten polymers. Rotational rheometers are used to obtain linear behavior but are of limited utility in exploring nonlinear behavior. Capillary rheometers are used to determine viscosity at moderate to high shear rates and to study the occurrence of flow instabilities and melt fracture. The extrusion plastometer, commonly called a melt indexer and widely used in the plastics industry, is a useful tool although not a true rheometer. The use of rheometers as process instruments and in high-throughput resin development is described. Finally, extensional rheometers for melts are described, and applications are discussed."

Introduction[edit | edit source]

Uses for data from rheological measurements:

Polymer Characterization
Quality Control - statistical process control
Measure of processability
Data for process simulation

Important to distinguish rheological characterizations
Measurement of well-defined property - viscosity - storage and loss moduli
Empirical test, no well-defined property, used to compare materials from single figure of basic test - MFI!!
- Primarily for quality control and statistical process control
Rotational, Capillary, and Extensional Rheometers
Issues of concern in rheological measurements:
Residual stresses
Flow instabilities
Thermo-oxidative degradation
Wall slip
Rotational Rheometer Specific
- Fixture alignment
- Sample rim trimming
No fully-reliable way to measure viscoelasticity

Rotational and Other Drag-Flow Rheometers[edit | edit source]

One surfaced moved relative to another, generate shear in fluid between them
Simplest example is flow between 2 flat plates - sliding plate rheometer
Study wall-slip and non-linear viscoelasticity
Not good for linear viscoelasticity
Avoiding residual stress from sample molding important in Drag-Flow Rheos (excess compression, for example)
Ensure samples are free of moisture, monomer, dissolved gases - usually requires vacuum drying
Determination of viscoelastic behaviour in shear, rotational rheos commonly used
Melt between two circular plates, one spins w.r.t. other
cone-and-plate and parallel disk geometries
cone-plate have advantage - shear rate nearly uniform throughout sample
Sample prep and loading simpler with parallel plate
Parallel-plate preferred for linear viscoelasticity
Rot. Rheos. cant access high shear rates, limited ability in nonlinear behaviour
Variations in results from gap spacing, sample trimming, and temperature. Lab to lab more variable than within lab
"When establishing the limiting strain amplitude for linear behaviour, it is important to realize that this depends on frequency"
Not exactly sure what this means, comes directly after note above, no mention of limiting strain amplitude or frequency earlier in article
Added after: There is more talk of stress/strain amplitudes and "oscillatory motion/shear" but no explanation of what this means. My guess is maybe the moving fixture translates/rotates back and forth at some frequency, and waves of shear are created
- This is correct, in some configurations both surfaces oscillate in opposite directions
To paraphrase above, A material will move from linear viscoelasticity (straightforward to measure) to non-linear viscoelasticity (not straightforward) at some strain amplitude, the value of that amplitude changes based on how fast the plate is oscillating.
Two types of motor-drive - Controlled-strain/Controlled-rate (CR) or Controlled-stress (CS)
CR - motor rotates one fixutre, torque & norm. force transducers coupled to stationary fixture, Suitable for:
- Oscillatory shear at moderate/high frequencies
- Steady shear, including start-up of steady shear
- Measurement of viscosity and first normal stress difference
CS - motor rotates fixture with a prescribed toque, torque determination and motion generation combined, Advantageous for:
- Creep & recoil - important to minimize friction
- When low strain rates needed to probe terminal region
Assumptions made for equations for cone-plate and parallel plate Rheos.:

Inertia neglected - high viscosity of melts
Surface tension at exposed edges not impact torque
Free surface at edge is spherical in shape
Flow is uniform out to edge
Cone-plate geometry - cone angle is sufficiently small that certain trig identities can be used

1 & 2 generally valid for melts
4 not always valid, particularly in cone-plate
Care required to ensure 3 valid
Use sample slightly larger than needed, bring together until gap is bit larger than needed, trim extruded polymer to smooth surface, set final gap spacing
Edge shape can change with repeated test on same sample, cause large reduction in stress
Concave must be avoided, initiates unstable flow
Always small uncertainty due to this issue - best accuracy of commercial rheos. is about +/-3%

Cone-Plate Rheometers (CP)[edit | edit source]

Fixture parameters are radius and cone angle
Either torque or angular displacement programmed to vary with time in known way
For steady shear, torque and ang. vel. constant
If cone angle less than 0.1 rad, error from assumption 5 <1%, if angle <0.2 rad, error from 5 <2%
Expressions given for shear strain, strain rate, shear stress, and normal stress differences
CS is preffered mode for non-linear studies
step-strain experiments important source of error is deviation of strain history from perfect step
Uncertainty from precision which cone was fabricated, cones are truncated, virtual height of missing tip calculated for gap-setting
Forces generated by fluid can twist/compress rheo. - means of getting around this
Wall slip issue if shear stress sufficiently large of period of time. Serious limitation in study of nonlinear viscoelasticity (strain and strain rate are large)
In step strain or steady shear, if true strain or strain rate known, can correct for slip
In transient flows with slip, useful information is unattainable
Several types of flow-irregularities can occur, limit these to low shear rates
Disk-shaped samples squeezed between cone and plate, introduces normal thrust, can take long time to relax
Molten sample may not be centred after squeezing

Parallel-Disk Rheometers (PD)[edit | edit source]

Primarily determine linear viscoelastic behaviour
Methods to determine viscosity & the non-linear relaxation modulus proposed, not recommended over cone-plate because approximate uniformity of strain and stresses throughout sample
Equations given for storage and loss moduli given, using torque amplitude, phase angle, disk radius, gap, and angular amplitude
Flow irregularities from CP still occur, less troublesome because small strain
Creep tests within regime of linear viscoelasticity.
Creep compliance independent of radius, torque is fixed, angular displacement is measured as function of time. straightforward calculation

Accessing the Terminal Zone using Creep and Creep Recovery[edit | edit source]

Not exactly sure what Terminal Zone is, google is not being too helpful. I think the terminal zone is when the polymer begins to flow like a liquid and moves past its rubbery state. There are terminal, rubbery plateau, transition, and glassy regions (in that order, or reversed). Maybe this is how "melted" they are, where glassy is full solid, and terminal is "full" liquid
Plateau and terminal zones of interest, viscoelastic behaviour most related to molecular structure
May not be possible reaching these zones with small-amplitude oscillatory shear, takes too long or torque too low
Creep measurements using torque-controlled Rheo. can probe (these authors love the word probe) terminal zone.
Polydisperse polymers, with even a small amount of high MW polymer - creep measurements problematic, measure extremely low strain, maintain stress very-low constant
Thermo-oxidative degradation
Not possible to maintain torque at 0 with air bearings, can use magnetic bearing
Technique for creep compliance up to steady-state without leaving regime of linear behviour, measure creep compliance from t=0 to t1, than math to get from t1 to t2, then t2 to t3, and so on until terminal zone is reached - creep compliance (t) is a line, reciprocal of this slope is 0 shear viscosity

Pressure-Driven Rheometers[edit | edit source]

Capillary and Slit Rheometers[edit | edit source]

Determine melt viscosity at high shear rates, "rheological work-horses for many years"
Use recently decreasing rotational rheos. used more, complex viscosity used instead of viscosity
Observe extrudate swell, sharkskin melt fracture, die build-up
Flow generated either from piston or gas pressure in reservoir
Downstream from an entrance, flow in capillary fully-developed - velocity & shear stress profiles independent of dist. from entrance, if assumed isothermal and neglect effect of pressure and viscosity
Raw data is reservoir pressure and corresponding volumetric flow rate. To find viscosity, need wall shear stress (wss) and wall shear rate (wsr), expression given
Data sometimes reported in flow curve of apparent wss (ignores entrance correction) vs. apparent wsr (shear rate for newtonian fluid) expressions for apparent wall shears given
eq'n for true wss and wsr given. Approximate, from experimental data
shifting log-log plot of true wss vs apparent wsr 0.83 units to the left is reasonable approximation of true curve
Slit rheometers difficult to build & use, preferred for research studies, flat flow channel allows pressure sensors and optical measurements
Standard methods assume temp. and density uniform, axial pressure variation has no effect on viscosity (not true) - variation in melt density has less than 5% effect, others more significant
Wall slip can be issue, can be easy to spot at high enough pressures, not apparent in lower pressures
Determine effect of pressure on viscosity
Piston-driven with throttling valve so fixed flow rate
Controlling pressure at entrance and exit, operating at fixed pressure drop.
Pressure driven useful for melt viscosity at higher shear rates than rotational. at high shear rates, pressure and temperature variation need accounted for. occurrence of slip may limit the shear rate where reliable data obtainable

Extrudate Distortion: Gross Melt Fracture and Sharkskin[edit | edit source]

Gross Melt Fracture - when tensile stress at entrance causes melt to rupture
Surface Melt Fracture - Sharkskin - tensile failure of melt at exit of die, from sudden acceleration when freed from restraint of wall - occurs before visible to naked eye

The Spurt Effect, Oscillating Flow, and Wall Slip[edit | edit source]

Odd phenomena that occur in pressure-driven rheos. and explanations of why/where they occur

The Extrusion Plastometer (Melt Indexer) (This is us!!)[edit | edit source]

Developed around 1950, calls it primitive
MFI cannot be used to find well-defined physical property
Not a rheometer, empirically-based melt characterization
ASTM Standard warns about fundamental significance of results
Temperature history of the sample has effect on outcome
Measuring MFR at two or more loads provides information about degree of shear thinning.
Ratio of Higher-Load MFR/Lower-Load MFR is used to characterize

On-Line Rheometers[edit | edit source]

Mounted directly on process stream, near real-time indication of state of melt
Less control of test conditions, in exchange for on-line monitoring
Common one is bypass rheometer
Temp largely affects output

On-Line Detection of Melt Index[edit | edit source]

MFR useful tracking variations in average MW. Sometimes good to have continuous indication of MFR
Gear pumps used to simulate standard test conditions, MVR found and converted
Never possible to reproduce temperature history of sample on-line vs in lab

High-Throughput Rheometry[edit | edit source]

Rheological Devices for rapid evaluation of multiple samples.
Speed remains a challenge
Group at NIST developed multi-sample micro-slit rheometer, can measure viscosity of 4 samples at once.
2 commercially available apparatuses, both based on oscillatory shear

VTM Rheometer from Dynisco
- Pre-molded samples clamped between sheets of film in closed-cavity shearing chamber
- Some uncertainty of exact sample size
- Since cavity is closed around rim, and shape is neither cone-plate or parallel disk
  - Data not reliable for storage and loss moduli
The High-Throughput Rheometer from Anton Paar
- Standard parallel-disk rotational rheo. in conjunction with multi-axis robot to carry out technician's job
- High-quality, large and expensive

Extensional Rheometers[edit | edit source]

More difficult to measure response to stretching than to shearing
Reveal aspects of non-linear viscoelasticity can't be predicted from shear data
Uniaxial Extensional Flow (called simple or tensile)
Biaxial Extentional Flow
Planar Extensional Flow

Only Uniaxial in general use and described here. Paper about non-linear viscoelasticity, including descriptions of all three: https://link.springer.com/chapter/10.1007/978-94-007-6395-1_4

Limited to strain rates well below 10 s^-1 - to reach higher rates, drawdown of extrudate and converging flow at capillary entrance used to determine apparent extensional viscosities, can not infer well-defined material properties.

Rheometers for Uniaxial (Simple) Extension[edit | edit source]

Deformation where Hencky strain rate constant
Tensile stress growth coefficient determined
Two example rheometers that are "inconvenient" talked about
Can have extensional rheos that attach to rotational rheos, simpler/easier to use
2 rotating drums, with parallel axes, sample attached to each drum. Drums rotate in opposite direction, winding sample around both drums, uniaxially stretching section of sample connecting the 2.
If Height and width ratio not right can have planar extension, can correct for this
a few sources of error, most can be corrected for straightforwardly
Necking of sample causes issues, no real way to get around it. Can determine when/where necking begins to affect data
Therefore limited to low Hencky strain rates

Converging Flow and Melt Strength[edit | edit source]

Drawdown test, material is extruded, attached to rotating cylinder, and drawn out of capillary (after being drawn out, extrudate has turned 90 degrees to full horizontal), being cooled by ambient air, vertical force on cylinder is monitored and stress when extrudate breaks is called melt strength
Not rheological property, but heavily dependant on extensional flow properties

Torque Rheometers[edit | edit source]

Powerful motor, different polymers loaded into cavities under pressure and mixed using a mixing head attached to motor (head geom. changes with wanted shear/mixing patterns) Torque on drive shaft is measured
Attempts to find relationships between torque and viscosity, complexity of flow makes unreliable
For certain applications, reasonably repeatable and used for process control
Good for simulating industrial mixing in laboratory
PVC compounds, crosslinking polymers, elastomers: GOOD

Using Rheology for Statistical Process Control[edit | edit source]

Quality control is checking samples of product along production line to ensure on-spec. By time off-spec is noticed, substantial amount has been produced
Statistical process control gets around this (?)
Melt index or apparent viscosity commonly used
Confusing wording about how this is done. Set upper/lower control limits (well within specification limits) by successive testing, create control chart showing acceptable range and normal variations in MFR or App. Visc.. Monitor control chart for signs process out of control, before off-spec produced.
that last part confuses me, I don't know how the control chart updates during processing, maybe with on-line rheometers but those are not mentioned.
There is a book all about this process, if I need to read more. Can't legally access it without paying...:)

Sample Stability: Thermo-Oxidative Degradation and Hydrolysis[edit | edit source]

Time spent at high temperature with oxygen present causes degradation, affects results
Control oxygen by filling rheometer oven with nitrogen, or use stabilizer
Verify time available to do test by doing time sweep in rotational rheometer at fixed frequency
Too much or too little moisture causes hydrolysis/polymerization, affects results
Vacuum dry samples, control humidity

Melt Flow Rate Testing Parts 1-10[edit | edit source]

Note, these have a slight focus on the use of MFR in molding processes, may make some of it unapplicable to FAST's intended use for the MFI

Part 1[edit | edit source]

Sepe, M. (2013, June 24). Melt Flow Rate Testing–Part 1. Plastics Technology. https://www.ptonline.com/articles/melt-flow-rate-testingpart-1

Abstract/Introduction - "Though often criticized, MFR is a very good gauge of the relative average molecular weight of the polymer. Since molecular weight (MW) is the driving force behind performance in polymers, it turns out to be a very useful number."

MFR "gets no respect" - People downplay value/usefulness. MFR is single point on curve characterizing viscosity and shear rate - plastic's viscosity varies with shear rate
Shear stress is constant, but shear rate is an output of test, not controlled
How to convert from grams/10 min to grams/mole? will be answered.
Not good tool for gauging processability - not supposed to be - Isn't a "poor man's capillary rheometer"
Relationship between MFR and molecular weight (MW) is relative - ingredients such as glass fibres, impact modifiers, etc. can change MFR and not MW.
Despite this, is often key characteristic distinguishing one grade from another within polymer family
In diverse materials like polycarbonate, acetal, polystyrene, MFR may be only value to differ significantly from grade to grade
Higher MW polymers have lower MFR, lower MW higher MFR
Injection molding often prefers low MW to help with demanding flow paths. Extruders/blow molders prefer high MW because of higher melt-strength. Higher MW also correlates to better product performance - impact resistance, environmental stress-crack resistance, etc.
MFR very good indication of impact resistance - gives example of two materials that have the same notched Izod impact values, one has 5g/10 MFI and one 10g/10 MFI. The higher MFI processed in a way that should've reduced internal stress and thus increased impact resistance. But lower MFI actually performs much better.

Part 2[edit | edit source]

Sepe, M. (2013, 2013). Melt Flow Rate Testing – Part 2. Plastics Technology. https://www.ptonline.com/articles/melt-flow-rate-testing-part-2

Abstract/Introduction - "To fully appreciate the strengths and weaknesses of the melt-flow-rate (MFR) test it is important to know something about the way the test is performed."

Part 2 mainly about how test is performed, strengths and weaknesses
Methodology covered is ASTM D 1238, corresponding international standard ISO 1133 (covered above) - small differences, essentially perform the same function
Very specific conditions, very specific geometry
Cleaning of die can reduce height/diameter of bore, can detract from accuracy of measurements
Prescribes temperatures are polymer specific - temperature calibration very important
Different from capillary rheometer, which measures viscosity - controls/varies flow-rate while measuring force required. MFR controls force and measures flow-rate - MFR controlled shear-stress, Cap Rheo controlled shear rate
Cap Rheo is true measurement of viscosity
MFR is measure of relative MW, doesn't give full picture - so what? - MW drives performance in polymeric materials, so of interest.
Actual MFR value has implications for processing, 20g/10min will flow further than 4g/10min under same conditions and path. But actual viscosity is closer than these values would suggest.
Difference in flow-rate means a difference in shear rate, higher shear rate means lower viscosity. 20g/10min is tested under higher shear-rate, which is why MFR is much higher than 4g/10min
Multiplying MFR by approximately 2.2 gives shear rate at which test was performed (at least for ASTM)

Part 3[edit | edit source]

Sepe, M. (2013, September 23). Melt Flow Rate Testing—Part 3 | Plastics Technology. https://www.ptonline.com/articles/melt-flow-rate-testingpart-3

Well established relationship between viscosity at zero shear rate and weight-average molecular weight
Viscosity at zero shear rate is impossible to measure because viscosity is resistance to flow, and once material is flowing, shear rate is non-zero by definition
Zero-shear viscosity is extrapolated from a log plot of viscosity vs shear rate
Relationship shows that relatively small changes in MW result in large changes in melt viscosity at low shear rate
MFR test is performed at low shear-rates, just after entering the non-newtonian shear-thinning region of polymer, which means as shear rate increases viscosity decreases
Results approximate zero-shear viscosity. - since shear-rate is not controlled, but relatively low, Differences in melt viscosity at actual processing conditions is exaggerated in results.

Part 4[edit | edit source]

Sepe, M. (2013, October 24). Melt Flow Rate Testing—Part 4. Plastics Technology. https://www.ptonline.com/articles/melt-flow-rate-testingpart-4

MFR instrument is pressure-limited, constant load.
If the machine processing the polymer "notices" the MFI, it is because it is also pressure limited.
If the pressure is limited, when material viscosity increases the time required to deliver the material becomes longer
If the process is velocity controlled (able to deliver more pressure than needed - delivers desired volume in fixed time) the effect of changing viscosity on stability is minimized
If process is velocity controlled, typical fluctuations in MFR for given grade of material should have no significant effect on process.

Part 5[edit | edit source]

Sepe, M. (2013, November 26). Melt Flow Rate Testing—Part 5. Plastics Technology. https://www.ptonline.com/articles/melt-flow-rate-testingpart-5

How should MFR be used?

Two points in manufacturing supply chain where determination of average MW is important.

When material first recieved by "molder"
After molding

Suppliers often list MFR for material, with maximum and minimum specification value for lot. There are good reasons to verify number in-house.
Three reasons given, all about improving consistency of quality of end-products
MFR typically increases during processing - indicates MW decreases under influence of heat and shear - polymer degradation
Little consensus on allowable change, typically within range of 20% and 50%
Again, MFR is used relatively, increase in MFR during processing expected, not necessarily bad. A greater increase in MFR during processing is worse than a lesser increase

Part 6[edit | edit source]

Sepe, M. (2013, December 29). Melt Flow Rate Testing—Part 6. Plastics Technology. https://www.ptonline.com/articles/melt-flow-rate-testingpart-6-

Focusses on why MFR increases during processing, not particularly relevant
Universal concern for polymers is combined effect of heat and time while in melt state. Since typically organic, causes degradation
Another major contribution is moisture - can break chemical bonds in some if theres too much, happens more rapidly at higher temperatures
Materials can also be over dried, drying requires heat, oxidization - really only a concern with nylons
Risk of not drying enough far outweighs risk of drying too much

Part 7[edit | edit source]

Sepe, M. (2014, January 23). Melt Flow Rate Testing—Part 7. Plastics Technology. https://www.ptonline.com/articles/melt-flow-rate-testingpart-7

Why the melt flow test is not universal
Remember. test, fundamentally, is documenting differences in MW
Several factors make interpretation difficult
First is with polymers that don't initially degrade with chain scission, PVC good example
PVC degrades by losing hydrogen chloride much before chain scission, undergoes considerable modification with no evidence of reduction in MW
Second is competing reactions can increase and decrease MW at same time
Different kinds of degradation happen at different speeds. additives can cause same effect. MFR can increase/decrease though MW stays constant
More additives, more difficulty interpreting results
Fillers especially, they do not melt at processing temps, and have large effect on melt viscosity, esp. at low shear rates
At 10% loading of glass fibre, MFR can increase by 75% before concerns about degradation. 30% can cause MFR increase by 200%
Ideally, not perform MFR test on filled mats. Instead emply solution-based measurements. - dissolve polymer, removing filler.
Many suppliers of filled materials still use MFR
Acetal has particular problem with degradation making a lot of techniques, MFR included, ineffective

Part 8[edit | edit source]

Sepe, M. (2014, February 25). Melt Flow Rate Testing–Part 8. Plastics Technology. https://www.ptonline.com/articles/melt-flow-rate-testingpart-8

Steps to take when MFR is not provided by supplier, and why it isn't
Some polymers where availability of MFR is inconsistent, some families where MFR is rarely provided
Some use intrinsic viscosity instead. - Involves creating dilute solution in proper solvent and comparing flow rate of this solution to flow rate of solvent alone - standardized flow path and geometry - greater the difference, higher the intrinsic viscosity, higher the average MW
Intrinsic Viscosity test requires delicate apparaturs, and use of noxious chemicals. However can be done "practically" at room temperature. removes need for drying the material.
Repeated, use of fillers in polymers means MFR sometimes isn't used
Nylons almost never use MFR. If any measure of MW is provided/needed, comes from value of relative viscosity. Similar to intrinsic viscosity test, but units of the results are different.
Nylons' melt viscosity heavily varies with moisture content, so making lot to lot comparisons does not help determine differences in avg. molecular weight rather lot to lot differences in moisture content.
Can be accounted for by measuring moisture content at same time as MFR and normalizing to particular moisture content

Part 9[edit | edit source]

Sepe, M. (2014, March 21). Melt Flow Rate Testing—Part 9. Plastics Technology. https://www.ptonline.com/articles/melt-flow-rate-testingpart-9

Understanding Melt-Volume Rate (MVR) and relation to MFR
MFR divided by MVR is the Melt Density of material. - Different from solid state density
Equations in rheology that contain term for flow rate use volumetric flow rate, not mass flow
Polymers with pigments added can show different Melt Flow Rates, while having the same MVR, because of density changes
Can measure MFR and MVR at same time, to find melt density - If you have two marks on piston a set distance apart, and measure time and mass extruded for the piston to descend from one mark to the next, you have MFR and MVR. Time actually unnecessary, can just measure volume and mass extruded to get melt density.

Part 10[edit | edit source]

Sepe, M. (2014, April 23). MATERIALS: Melt Flow Rate Testing—Part 10. Plastics Technology. https://www.ptonline.com/articles/melt-flow-rate-testingpart-10

Limitations of the method
Discussed before, only gives one value for set temperature and uncontrolled Shear rate. - Characterizing behaviour across range of shear rates is important
MFR and capillary rheometer are open systems, utilize flow path where all material is molten. In real world, material begins to freeze and change flow path during processing. - These tests are not reflective of actual processing conditions
Shear-induced flow imbalances cause temperature gradient to develop with layers of flowing material, not accounted for
Inability to account for or measure melt elasticity. In blow molding and extrusion, melt elasticity means die swell
Test for melt elasticity was designed, but never standardized or used. Would've likely represented same type of lower-cost alternative to parallel-plate/cone- and-plate rheometry as MFR represents for capillary rheometry

Ystruder: Open source multifunction extruder with sensing and monitoring capabilities[edit | edit source]

Klar, V., Pearce, J. M., Kärki, P., & Kuosmanen, P. (2019). Ystruder: Open source multifunction extruder with sensing and monitoring capabilities. HardwareX, 6, e00080. https://doi.org/10.1016/j.ohx.2019.e00080

Abstract[edit | edit source]

"Syringe pumps are widely used in a multitude of tasks where precise volumes of an extrudate need to be delivered at a specific flow rate. In the past decade various open source syringe pump designs have accelerated scientific research and exploration by reducing costs and introducing new ideas. To further expand the capabilities of open source syringe pumps we introduce a novel syringe pump design, the Ystruder. It features a load cell to monitor the piston force. This capability enables clog detection as well as development of advanced dosing algorithms. The Ystruder can be monitored wirelessly through a browser-based interface that is integrated into the embedded system. The design is modular and simple which facilitates different syringe and motor configurations, to meet a wide range of use cases. Finally, the Ystruder is not limited to functioning solely as a pump as it can be integrated into a wide range of devices such as three-dimensional motion systems. Here the dosing accuracy and repeatability of the Ystruder are quantified, and we demonstrate its functionality both as a syringe pump and a paste extruder for 3D printing."

Notes[edit | edit source]

This is the device that will be used to apply load pressure to the material in my design
Reducing costs of high-performance tool important in many areas
Manufactured for ~$150 USD - commercial pumps cost ten times that
Can be used as syringe pump or as extruder for 3D printing
- May need to modify design for correct cylinder/piston geometry/material requirements, and for heating/temperature-sensing/insulation
Advanced functionality can be easily added
in situ UV curing
heating (nice)
mixing
Possible to change syringe volume and motor size - can meet wide range of requirements
Piston load monitoring capability
Many monitoring capabilities
Mechanical, electronic, software components
Mechanical parts 3D printable/readily available
PCBs can be made cheaply
Software also OS
Browser interface to read time series measurement data
Begins to skip steps/stall at ~200N - deviation between target position and measured position at forces exceeding 50N
This may be an issue. MFI commonly performed between ~3N and ~50N. Can go up to ~211N for some materials/test conditions
Will not be setting a target position. MFI test is pressure restricted, apply known load and measure position. Maybe second part of above is unimportant
Will need to measure position because test starts after piston has descended to certain point

Simple Steady Shear Flow and the Viscometric Functions[edit | edit source]

Dealy, J. M., & Wissbrun, K. F. (1990). Steady Simple Shear Flow and the Viscometric Functions. In J. M. Dealy & K. F. Wissbrun (Eds.), Melt Rheology and Its Role in Plastics Processing: Theory and Applications (pp. 153–178). Springer US. https://doi.org/10.1007/978-1-4615-9738-4_4

Simple Steady Shear Flow, rectilinear motion of a flat plate relative to another, with fluid between them, separated by const. height h
flat plate moves distance ᐃX
flow completely defined by shear strain = ᐃX/h
derive w.r.t. time get shear rate = |ᐃV|/h
Non zero components in stress tensor: σ11, σ12, σ21, σ22, σ33
σ = |σ21| = |σ12|
If components change by same amount, no deformation, if there is difference in change, deformation & rheologically significant.
Customary to define first and second normal stress differences as

N1 = σ11 - σ22

N2 = σ22 - σ33

For simple shear flow σ, N1, N2 only rheologically significant features of stress tensor

Flow in Capillaries, Slits and Dies[edit | edit source]

Dealy, J. M., & Wissbrun, K. F. (1999). Flow in Capillaries, Slits and Dies. In Melt Rheology and Its Role in Plastics Processing: Theory and Applications (pp. 298–344). Springer Netherlands. https://doi.org/10.1007/978-94-009-2163-4_8

Flow used as basis for most popular melt rheometer, and very common in processing
For cylindrical coord. syst. only one independent, nonzero shear component in extra stress tensor. call σ
because symmetry, τrz = τzr = σ
Flow in tube radius R, pressure gradient dP/dz:

σ(r) = (r/2)(dP/dz), at wall r = R

σ(R) = (R/2)(dP/dz), σ(r) = (r/R)σ(R) --this is independent of rheo. properties, valid for both newtonian and non-newt

dP/dz negative, pressure drops in flow direction, σ(R) also neg, for ease define wall shear stress σw = -σ(R) = (R/2)(-dP/dz)
for fully developed flow, shear rate = shear rate rz = dv/dr
For a newtonian fluid: σ=η*shear rate -- η is a constant

SFI: A simple rheological parameter for estimating viscosity[edit | edit source]

Shenoy, A. V. (1993). SFI: A simple rheological parameter for estimating viscosity. Experimental Thermal and Fluid Science, 6(3), 324–332. https://doi.org/10.1016/0894-1777(93)90072-Q

Abstract[edit | edit source]

"A simple rheological parameter, namely, a solution flow index (SFI) for estimating the viscosity of Newtonian and non-Newtonian inelastic solutions, is introduced. SFI is defined as the weight of the solution that flows out of a capillary tube under gravity in 10 min. Test solutions are characterized on a standard Brookfield-type cone-and-plate viscometer, and the viscosity versus shear rate curves generated are coalesced into master curves that are concentration- and temperature-independent using SFI as a normalizing parameter. The master curves developed in this manner are useful in generating rheograms of uncharacterized samples merely from their SFI values. A modified Arrhenius-type equation is proposed for predicting the SFI of solutions at different temperatures. Further, a model based on the altered free volume state concept is proposed to predict the SFI values of solutions at various solute concentrations. The predictions of the model are compared with experimental data and found to give good agreement."

Notes[edit | edit source]

SFI = solution flow index.
Like MFI test but material is in solution rather than alone