10.1 Fundamentals of polymer rheology

Polymer rheology is all about how materials flow and deform under pressure. It's crucial for understanding how polymers behave during manufacturing and in finished products. Knowing this stuff helps engineers create better plastics and rubbers.

Stress, strain, and viscosity are key concepts in rheology. These properties determine how materials respond to forces, which is super important for designing everything from car tires to plastic bottles. Understanding these basics helps predict how polymers will act in different situations.

Introduction to Polymer Rheology

Rheology in polymer science

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• Rheology studies flow and deformation of materials under applied forces
  • Examines relationship between force, deformation, and time
• Rheological properties crucial in polymer processing and applications
  • Determines polymer behavior during manufacturing (extrusion, injection molding, fiber spinning)
  • Affects final product properties (mechanical strength, surface finish, dimensional stability)
• Understanding rheology optimizes processing conditions and designs materials with desired properties

Concepts of stress and viscosity

• Shear stress ($\tau$) is force applied per unit area parallel to surface
  • Measured in pascals (Pa) or dynes per square centimeter (dyn/cm²)
• Shear strain ($\gamma$) is relative deformation of material under shear stress
  • Defined as change in angle between two originally perpendicular lines
  • Dimensionless quantity
• Viscosity ($\eta$) measures material's resistance to flow under applied shear stress
  • Ratio of shear stress to shear rate ($\dot{\gamma}$): $\eta = \frac{\tau}{\dot{\gamma}}$
  • Measured in pascal-seconds (Pa·s) or poise (P)
• Shear rate is change in shear strain per unit time: $\dot{\gamma} = \frac{d\gamma}{dt}$
  • Measured in reciprocal seconds (s⁻¹)

Newtonian vs non-Newtonian flow

• Newtonian fluids have linear relationship between shear stress and shear rate
  • Viscosity constant regardless of shear rate (water, simple oils, low molecular weight polymers)
• Non-Newtonian fluids have non-linear relationship between shear stress and shear rate
  • Viscosity changes with shear rate
  • Most polymers exhibit non-Newtonian behavior
• Types of non-Newtonian behavior in polymers:
  1. Shear-thinning (pseudoplastic): viscosity decreases with increasing shear rate
     • Caused by alignment of polymer chains in flow direction
  2. Shear-thickening (dilatant): viscosity increases with increasing shear rate
     • Rare in polymers, can occur in highly concentrated suspensions
  3. Yield stress (Bingham plastic): material requires minimum stress to initiate flow
     • Observed in filled polymers, gels, concentrated suspensions

Factors affecting polymer rheology

• Temperature affects polymer rheology by influencing chain mobility and intermolecular interactions
  • Increasing temperature reduces viscosity, polymer chains have more thermal energy to overcome intermolecular forces
  • Glass transition temperature (Tg) marks significant change in rheological behavior
    • Below Tg, polymers are glassy and brittle, with high viscosity and elastic behavior
    • Above Tg, polymers are rubbery or melt-like, with lower viscosity and viscous behavior
• Molecular weight affects polymer rheology by determining chain length and entanglements
  • Higher molecular weight polymers have longer chains and more entanglements, resulting in higher viscosity
  • Relationship between viscosity and molecular weight follows power law: $\eta \propto M^a$
    • $M$ is molecular weight, $a$ is constant depending on polymer and temperature
  • Critical molecular weight (Mc) marks onset of significant entanglements
    • Below Mc, viscosity increases linearly with molecular weight
    • Above Mc, viscosity increases more rapidly, typically with $a \approx 3.4$