Dynamic-Mechanical Analysis of Materials (Polymers)

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• Dynamic-Mechanical Analysis of Materials
  (Polymers)
• Big Assist Ioan I. Negulescu

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• Viscoelasticity
• According to rheology (the science of flow),
  viscous flow and elasticity are only two extreme
  forms of rheology. Other cases entropic-elastic
  (or rubber-elastic), viscoelastic crystalline
  plastic.

SINGLE MAXWELL ELEMENT (viscoelastic visco.)
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• All real polymeric materials have
  viscoelasticity, viscosity and elasticity in
  varying amounts. When visco. is measured
  dynamically, there is a phase shift (?) between
  the force applied (stress) and the deformation
  (strain) in response.
• The tensile stress ? and the deformation (strain)
  ? for a Maxwellian material

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• Generally, measurements for visco. materials are
  represented as a complex modulus E to capture
  both viscous and elastic behavior
• E E iE
• ? ?0 exp(i (?t ?)) ? ?0 exp(i?t)
• ?E?2 ?E?2 ?E?2
• Its solved in complex domain, but only the real
  parts are used.

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• In dynamic mechanical analysis (DMA, aka
  oscillatory shear or viscometry), a sinusoidal ?
  or ? applied.
• For visco. materials, ? lags behind ?. E.G.,
  solution for a single Maxwell element
• ?0 EM ? ? ?0 / 1 ?2?2
• E EM ?2 ?2 / 1 ?2?2 ?0 cos?/?0
• E EM ? ? / 1 ?2?2 ?0 sin?/?0
• ? ?M/EM Maxwellian relax. t

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• Schematic of stress ? as a function of t with
  dynamic (sinusoidal) loading (strain).

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• Parallel-plate geometry for shearing of viscous
  materials (DSR instrument).

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• The Es (Youngs moduli) can all be replaced
  with Gs (rigidity or shear moduli), when
  appropriate. Therefore
• G G iG"
• where the shearing stress is ? and the
  deformation (strain) is ?. Theory SAME.

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• Definition of elastic and viscous materials under
  shear.

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• In analyzing polymeric materials
• ?G? (?0)/(?0), total stiffness.
• In-phase component of IGI shear storage
  modulus G elastic portion of input energy
• ?G?cos?

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• The out-of-phase component, G" represents the
  viscous component of G, the loss of useful
  mechanical energy as heat
• ?G?sin? loss modulus
• The complex dynamic shear viscosity ? is G/?,
  while the dynamic viscosity is
• ? G"/? or ? G"/2?f

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• For purely elastic materials, the phase angle ?
  0, for purely viscous materials, 90?.
• The tan(?) is an important parameter for
  describing the viscoelastic properties it is
  the ratio of the loss to storage moduli
• tan ? G"/ G',

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• A transition T is detected by a spike in G or
  tan(?). The trans. T shifts as ? changes. This
  phenomenon is based on the time-temperature
  superposition principle, as in the WLF eq. (aT).
• The trans. T ? as ?? (characteristic t ?)
• E.G., for single Maxwell element
• tan? (? ?)-1 and W for a full period (2?/?)
  is
• W ? ?02 E work

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• Dynamic mechanical analysis of a viscous polymer
  solution (Lyocell). Dependence of tan ? on ? -
  due to complex formation.

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• DMA very sensitive to T.
• Secondary transitions, observed with
  difficulty by DSC or DTA, are clear in DMA.
• Any thermal transition in polymers will
  generate a peak for tan?, E, G
• But the peak maxima for G" (or E") and tan? do
  not occur at the same T, and the simple
  Maxwellian formulas seldom followed.

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• DMA of recyclable HDPE. Dependence of tan ? on ?.
  The ? transition is at 62?C, the ? transition at
  -117?C.

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• Dependence of G", G' and tan? on ? for HDPE at
  180?C. More elastic at high ?!

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• Data obtained at 2?C/min showing Tg -40?C (max.
  tan?) and a false transition at 15.5?C due to the
  nonlinear increase of T vs. t.

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DMA of low cryst. poly(lactic acid) Dependence
of tan? upon T and ? for 1st heating run

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DMA of Low Cryst. Poly(lactic acid). Dependence
of E on thermal history. Bottom line high
info. content, little work.