Polymers

Polymer Domain

The polymer domain provides evaluation models for polymer blends, filled composites, and coatings. It covers thermoplastics, thermosets, and elastomer formulations with processing condition optimization.

Physics Model

• Tensile strength is modeled using a modified rule of mixtures with interaction parameters from Flory-Huggins theory for blends and Halpin-Tsai equations for filled composites.
• Elongation at break combines empirical correlations with blend morphology predictions from viscosity ratio and interfacial tension estimates.
• Glass transition temperature (Tg) is calculated using the Fox equation for miscible blends and empirical models for semi-crystalline systems with processing-dependent crystallinity.
• Impact strength uses a crack propagation model accounting for rubber toughening, filler debonding, and matrix ductility.

Default Parameters

| Parameter | Type | Bounds | Unit | Description | |—————-|———|————|———|——————-| | polymer_a_fraction | continuous | [0.1, 0.9] | wt% | Primary polymer content | | filler_loading | continuous | [0.0, 0.40] | wt% | Mineral or fiber filler | | filler_type | categorical | [glass_fiber, carbon_fiber, talc, calcium_carbonate, nanoclay] | — | Filler material | | processing_temp | continuous | [150, 350] | C | Extrusion/molding temperature | | cooling_rate | categorical | [slow, medium, fast, quench] | — | Cooling protocol | | draw_ratio | continuous | [1.0, 8.0] | — | Uniaxial stretch ratio |

Default Objectives

| Objective | Direction | Unit | |—————-|—————-|———| | tensile_strength | maximize | MPa | | elongation_at_break | maximize | % | | impact_strength | maximize | kJ/m2 |

Key Trade-Offs

• Strength vs. ductility: The classic materials trade-off. Higher crystallinity and filler loading increase strength but reduce elongation and impact resistance.
• Stiffness vs. toughness: Glass fiber reinforcement increases modulus but reduces fracture toughness.
• Processing temperature vs. properties: Higher melt temperatures improve flow and mixing but may cause thermal degradation.

Example: Toughened Engineering Plastic

name: toughened-nylon
domain: polymer

parameters:
  - name: polymer_a_fraction
    type: continuous
    bounds: [0.5, 0.9]
    description: Nylon 6,6 fraction
  - name: filler_loading
    type: continuous
    bounds: [0.0, 0.30]
  - name: filler_type
    type: categorical
    choices: [glass_fiber, carbon_fiber, nanoclay]
  - name: processing_temp
    type: continuous
    bounds: [260, 310]
    unit: C
  - name: cooling_rate
    type: categorical
    choices: [slow, medium, fast]

objectives:
  - name: tensile_strength
    direction: maximize
    unit: MPa
  - name: impact_strength
    direction: maximize
    unit: kJ/m2

optimizer:
  method: cma-es
  budget: 250
  batch_size: 12

Typical Results

Toughened polymer campaigns show:

• High-strength solutions: 30% glass fiber, slow cooling -> 180 MPa strength, 8 kJ/m2 impact
• High-impact solutions: 5% nanoclay, fast cooling -> 75 MPa strength, 45 kJ/m2 impact
• Balanced solutions: 15% glass fiber, medium cooling -> 120 MPa strength, 22 kJ/m2 impact

Blend Morphology Prediction

The polymer domain includes a blend morphology predictor that estimates phase structure (dispersed, co-continuous, or lamellar) from composition and processing conditions. This information is included in the results:

materia results --show-metadata

Morphology predictions help interpret why certain compositions exhibit unexpected property jumps.