Polymer properties

Viscosity

First model : Compute the viscosity as a function of the temperature and the shear stress

Reference : Mathematical Models of Polymer Melt Viscosity in Shearing Flow by Dodin (1986)

 

: Melt viscosity (Pa.s)

: Shear stress

: activation energy of viscous-elastic flow under condition of = constant

R : gas constant in J/(mol.K)

T : temperature of experiment in K

B, b, s : Constants of the material (in this case : s=1/2)

Second model : Compute de viscosity as a function of the temperature and the strain rate

Reference : Polymer processing: modeling and simulation by Osswald and Hernández-Ortiz (2006)

The Bird-Carreau-Yasuda Model

 

: Melt viscosity (Pa.s)

: constants for Carreau-Arrhenius model (semi-crystalline polymer)

in Pa.s, in s and no unit

: Arrhenius shift (no unit)

: strain rate (/s)

The Arrhenius shift for semi-crystalline polymers

 

T : Temperature (K)

: Reference temperature (K)

: Activation energy (J/mol)

R : Gas constant (J/(mol.K))

How this code works ?

Classes

• Deck : get the value in deck.yaml (in the folder common_classes)
• Polymer : stock the values of deck concerning the polymer in variables that will be reuse (in the folder common_classes)
• GraphFeatures : stock the values of deck concerning graphic features in variables that will be reuse (in the folder viscosity)
• Model : contain all equations to predict the viscosity (in the folder viscosity)
• Graph : calculate the data with the model, draw the graphic and save it in the folder Graphics (in the folder viscosity)

What the user have to do ?

• Adapt the values in the file deck.yaml :

For the First model :

Polymers:
  Name: 'PP Shell'
  Constant B: 1.5
  Constant b: 0.0043
  Activation Energy: 45522

Discretisation: 20

The Discretisation number is the number of points on the graphics.

• Install all required python packages listed in requirements.txt:

pip install -r requirements.txt

• The only file which need to be run is the example_viscosity.py. This script brings together all classes.

python example_viscosity.py

Surface tension

Calculate a polymer surface tension with the Parachor

• Calculate the molecular weight of the polymer :

M : Molecular weight of the polymer (g/mol)

: Number of Carbon, Hydrogen and Oxygen in a monomer unit

: Atomic weight of Carbon, Hydrogen and Oxygen (g/mol)

• Calculate the Molar Volume :

: Molar Volume ()

: Density of the polymer ()

• Calculate the Molecular Parachor

P : Molecular Parachor ()

: Contribution to Parachor of Carbon, Hydrogen and Oxygen ()

• Calculate the Surface Tension

: Surface Tension ()

How this code works ?

Classes

• Deck : get the value in deck.yaml (in the folder common_classes)
• Polymer : stock the values of deck concerning the polymer in variables that will be reuse (in the folder common_classes)
• Model : contain all functions required to predict the surface tension (in the folder surface_tension)
• Result : calculate the value of the surface tension with the functions in Model and print it (in the folder surface_tension)

What the user have to do ?

In the deck.yaml, the user can change the polymer and adapt the required values.

Surface Tension:
  Name: 'Polypropylene'
  Number of Carbon: 3
  Number of Hydrogen: 6
  Number of Oxygen: 0
  Density in g/cm^3: 0.9

• Install all required python packages listed in requirements.txt:

pip install -r requirements.txt

• The only file which need to be run is the example_surface_tension.py. This script brings together all classes.

python example_surface_tension.py