Polymer Mechanics

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Polymer Mechanics

• Chapter 6
• Howard

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Mechanical Properties of Slender Rods

• Response to mechanical and hydrodynamic forces?
• Force needed to buckle rods and how quickly will
  they buckle?
• Shape fluctuations in response to thermal
  fluctuations
• Cytoskeletal properties mechanical properties
  of cell, tissues and organs
• Entropic stiffness enthalpic stiffness

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Flexural Rigidity

• M EI(1/R), M FX
• EI flexural rigidity, E youngs modulus, I
  moment of inertia of the cross-section
• Separation of flexural rigidity moment of
  inertia depends on geometry (table 6.1)

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Applications of the Beam Equation

• Cantilever Beam spring with a spring constant,
  k F/(y(L)) 3EI/L3
• Examples Glass Fiber, Microtubules, Coiled-coil

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Buckling

• Fc ?2(EI/L2)

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Drag Forces on Slender Rods

• Depends on hydrodymamic properties of the rod
• Larger near surfaces than free in solution
• Table 6.2

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Thermal Bending of Filaments

• How rigid must a filament be to have structure
• Persistence length length over which thermal
  bending becomes appreciable
• Proportional to flexural rigidity Lp EI/kT
• Table 6.4

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Entropic Elasticity of a Freely Jointed Chain

• Filament composed of n segments
• Proteins with segmental flexibility
• F (3kT)/nb2ltxgt
• Spring constant (3kT)/nb2, resistance to
  extension (decreases disorder costs free energy)
• Example 6.10

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Worm-like Chain

• Length is much greater than persistence length
• 2Lp b absence of force the worm-like chain is
  similar to a freely jointed chain whose segments
  are of length 2x the persistence length