KEVOS® MAKEOS · Materials
Polymer Melting or Dissolution Temperature with a Diluent (Flory Melting-Point Depression)
How far does a solvent, plasticiser or other diluent lower the melting point of a semicrystalline polymer, and will its crystals melt (or survive) at my process or service temperature?
Flory’s equation for the melting (liquidus) temperature of a semicrystalline polymer swollen by a diluent: the diluent volume fraction from the mass share and densities, the depressed melting temperature from the pure polymer’s melting point, the heat of fusion and molar volume of its repeat unit, the diluent’s molar volume and the interaction parameter, the depression in kelvin, and the result against a process temperature at which the crystals must melt or dissolve, or a service temperature at which they must survive, with a table of melting temperature against diluent content.
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How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| What the crystals must do | choice | Choose whether the crystals must melt at the process temperature or survive at the service temperature. |
| Polymer | ||
| Melting temperature of the pure polymer | °C | Melting temperature of the pure polymer, preferably its equilibrium melting point from the literature or DSC. |
| Heat of fusion per mole of repeat unit | J/mol | Heat of fusion of fully crystalline polymer per mole of repeat unit, from the literature (heat per gram × repeat-unit molar mass). |
| Molar volume of the repeat unit | cm³/mol | Molar volume of the repeat unit: its molar mass ÷ the amorphous density. |
| Density of the amorphous polymer | g/cm³ | Density of the amorphous polymer, used to turn the mass share into a volume fraction. |
| Diluent | ||
| Molar volume of the diluent | cm³/mol | Molar volume of the diluent: its molar mass ÷ its density. |
| Density of the diluent | g/cm³ | Density of the diluent near the working temperature. |
| Diluent share of the mixture by mass | % | Share of diluent in the mixture by mass, from the recipe or the measured uptake. |
| Polymer–diluent interaction parameter χ | Interaction parameter of the polymer with this diluent, from the literature, a swelling test or a fit to measured melting points. | |
| Temperature | ||
| Process or service temperature | °C | Temperature of the process step or of service. |
| Required temperature margin | K | Distance you require between that temperature and the melting temperature. |
What each input means
Open an input to see what it is, its units, the worked example and the common mistakes, with a small diagram.
What this means: What the crystals must do
- What it is
- Whether a good result means the crystals melt or dissolve, as in solution processing, or that they survive, as for a swollen semicrystalline part in service.
- Units and format
- Choose one of 2 options from the list: Melt or dissolve at the process temperature; Survive at the service temperature.
- Example
- The form opens with “Melt or dissolve at the process temperature” selected as a worked example. Choose the option that matches your case.
- Effect on the result
- Reverses which side of the melting temperature passes.
- Get it right
- Choose survive for a part exposed to oil, fuel or solvent at temperature.
Polymer
What this means: Melting temperature of the pure polymer
- What it is
- The melting temperature of the pure, undiluted polymer, ideally its equilibrium melting point for crystals of infinite thickness; the diluent lowers the melting temperature from here.
- Units and format
- Enter a number in °C: degrees Celsius. The form accepts -100 °C to 500 °C. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 140 °C as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- The diluted melting temperature moves almost one for one with it.
- Get it right
- A DSC peak of an ordinary moulding is several kelvin below the equilibrium value; use the value matched to your data source.
What this means: Heat of fusion per mole of repeat unit
- What it is
- The heat absorbed when one mole of repeat units of perfectly crystalline polymer melts; the larger it is, the less a diluent lowers the melting point.
- Units and format
- Enter a number in J/mol: J/mol. The form accepts 100 J/mol to 200000 J/mol. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 8000 J/mol as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- The depression is roughly inversely proportional to the heat of fusion.
- Get it right
- Literature often gives it per gram for 100 % crystalline polymer: multiply by the repeat unit’s molar mass.
What this means: Molar volume of the repeat unit
- What it is
- The molar volume of one repeat unit of the polymer, its molar mass divided by the amorphous density; it pairs with the heat of fusion per mole of the same unit.
- Units and format
- Enter a number in cm³/mol: cm³/mol. The form accepts 5 cm³/mol to 2000 cm³/mol. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 33 cm³/mol as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- The depression is roughly proportional to the ratio of this volume to the diluent’s.
- Get it right
- Use the same repeat unit for the heat of fusion and this volume.
What this means: Density of the amorphous polymer
- What it is
- The density of the amorphous polymer, used to turn the polymer’s mass share into its volume share in the mixture.
- Units and format
- Enter a number in g/cm³: grams per cubic centimetre (1 g/cm³ = 1000 kg/m³). The form accepts 0.5 g/cm³ to 3 g/cm³. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 0.85 g/cm³ as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Use the amorphous density, not that of the semicrystalline solid.
Diluent
What this means: Molar volume of the diluent
- What it is
- The molar volume of the diluent, its molar mass divided by its density; small diluent molecules lower the melting point more than large ones.
- Units and format
- Enter a number in cm³/mol: cm³/mol. The form accepts 10 cm³/mol to 5000 cm³/mol. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 150 cm³/mol as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- The depression is roughly inversely proportional to the diluent’s molar volume.
- Get it right
- For a plasticiser or oil use its number-average molar mass.
What this means: Density of the diluent
- What it is
- The density of the diluent, used to turn its mass share into its volume fraction in the mixture.
- Units and format
- Enter a number in g/cm³: grams per cubic centimetre (1 g/cm³ = 1000 kg/m³). The form accepts 0.5 g/cm³ to 3 g/cm³. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 0.9 g/cm³ as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Use the density near the process temperature for a hot process.
What this means: Diluent share of the mixture by mass
- What it is
- The share of the mixture’s mass that is diluent, converted to a volume fraction for Flory’s equation.
- Units and format
- Enter a number in %: percent: the number is read as a percentage, so type 8 for 8 %. The form accepts 0% to 99.9%. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 50% as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- More diluent lowers the melting temperature, roughly in proportion at small contents.
- Get it right
- For a part swollen in service use the measured uptake, not the liquid around it.
What this means: Polymer–diluent interaction parameter χ
- What it is
- The Flory–Huggins interaction parameter between the polymer and the diluent; it reduces the depression, and at 0.5 or more long chains and diluent can separate into two liquids.
- Units and format
- Enter a plain number with no unit. The form accepts -2 to 2. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 0.3 as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- A higher χ makes the depression smaller.
- Get it right
- Values fitted to melting points of the same system are the most reliable for this use.
Temperature
What this means: Process or service temperature
- What it is
- The temperature of the process step at which the crystals must melt or dissolve, or of the service at which they must survive, compared with the diluted melting temperature.
- Units and format
- Enter a number in °C: degrees Celsius. The form accepts -100 °C to 500 °C. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 135 °C as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Use the coolest point of the process for melting, and the hottest point of service for survival.
What this means: Required temperature margin
- What it is
- The smallest acceptable distance between that temperature and the diluted melting temperature, allowing for the uncertainty of the inputs and for crystals that are not at equilibrium.
- Units and format
- Enter a number in K: kelvin (a difference of 1 K equals 1 °C). The form accepts 0 K to 100 K. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 5 K as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Only moves the line between a clear result and a small margin.
- Get it right
- Allow more margin when χ or the equilibrium melting point is uncertain.
Method and formulas
- Diluent volume fraction φ₁ = (w₁ ÷ ρ₁) ÷ [w₁ ÷ ρ₁ + (1 − w₁) ÷ ρp].
- Equal chemical potentials of the polymer in the crystal and in the solution (Klenin §6.1, Flory 1949) give 1 ÷ Tm − 1 ÷ Tm₀ = (R ÷ ΔHu)(Vu ÷ V₁)(φ₁ − χφ₁²), temperatures in kelvin.
- Example: 50 % by mass of a diluent (0.90 g/cm³, 150 cm³/mol) in a polymer melting at 140 °C (8,000 J/mol and 33 cm³/mol per repeat unit, 0.85 g/cm³) with χ = 0.3: φ₁ = 48.6 %, Tm = 124.4 °C, a depression of 15.6 K; at 135 °C the margin is 10.6 K, so the crystals melt.
Limitations
- Equilibrium theory for long chains with the diluent excluded from the crystals; real crystals are thinner than equilibrium and melt lower.
- χ is taken as independent of concentration and temperature.
- When χ is 0.5 or more the melt and diluent can also separate into two liquids, which this equation does not describe (Klenin §6.3).
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Set the dissolution temperature for solution or gel processing of a semicrystalline polymer
- Estimate how far a plasticiser, oil or absorbed liquid lowers a polymer’s melting point
- Check that a swollen semicrystalline part keeps its crystals at its service temperature
- Plan a phase analysis of a polymer–liquid system
Who it is for
- Polymer process engineers
- Materials engineers
- Laboratory staff
What you get
- Diluent volume fraction
- Melting temperature with the diluent and the depression
- Margin against the process or service temperature
- Table of melting temperature against diluent content
Interpreting the result
- A good solvent (small χ, small molar volume) lowers the melting point most; a large or poorly compatible diluent hardly lowers it.
- The table is the liquidus of the state diagram: above it the crystals melt or dissolve, below it they can form.
Before relying on the result
- Measure the melting or dissolution temperature of the actual mixture by DSC at a slow heating rate.
References
- Flory P. J., J. Chem. Phys. 17, 223 (1949): thermodynamics of crystallisation in high polymers, melting-point depression by diluents.
- Klenin V. J., Thermodynamics of Systems Containing Flexible-Chain Polymers (Elsevier, 1999; ISBN 0-444-82373-5), §6.1 (conditions of phase equilibrium between polymer crystals and solution, Eqs. 6.1-1 to 6.1-5) and §6.3 (mixed types of phase separation). Method reference; no tables or figures are reproduced.
- Mandelkern L., Crystallization of Polymers, 2nd edition, Volume 1 (Cambridge University Press, 2002): melting of polymer–diluent mixtures.
Learn the Concepts Behind This Tool
These KEVOS® Library readings explain the method this tool uses, with worked examples.
Method explained here · KEVOS® original book
Crystals, diluents and melting-point depression
In Polymer Chains by the Numbers
What it covers: Use Flory's equation to find how far a solvent or plasticiser lowers the melting point of a semicrystalline polymer, judge solvent containers and hot dissolution, and see why crystals resist solvents.
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