Elastomers and Their Mechanical Behavior

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Questions and Answers

What is the primary characteristic of elastomers?

  • They can withstand very high temperatures without deforming.
  • They possess a high melting point.
  • They are highly crystalline in structure.
  • They can stretch 5-10 times their original length and quickly retract. (correct)

Which condition is NOT a requirement for a polymer to be classified as an elastomer?

  • It must be produced from synthetic materials. (correct)
  • It must have a very low degree of crystallinity.
  • It must be above its glass transition temperature.
  • It should be lightly crosslinked.

What is the effect of vulcanization on rubber?

  • It enhances the rubber's ability to stretch
  • It increases the crystallinity of rubber.
  • It lowers the melting point of rubber.
  • It promotes crosslinking using sulfur. (correct)

What characterizes the ideal structure of an elastomeric network?

<p>An amorphous network with junction points from which chains emanate. (A)</p> Signup and view all the answers

What fundamental assumption is made in the statistical theory of elastomer deformation?

<p>The displacement vector components relate directly to the specimen’s overall dimensions. (B)</p> Signup and view all the answers

How does the configuration of cis-1,4-polyisoprene affect crystallinity in natural rubber?

<p>Cis configuration reduces crystallinity. (D)</p> Signup and view all the answers

What happens to the structure of elastomers during short-term loading?

<p>Entanglements can act as effective crosslinks. (A)</p> Signup and view all the answers

Which of the following statements about the melting point of natural rubber is true?

<p>It is approximately 35 °C. (B)</p> Signup and view all the answers

What does the symbol $M_c$ represent in the expression for polymer density?

<p>Number-average molar mass of the chain lengths between crosslinks (D)</p> Signup and view all the answers

How does the shear modulus $G$ relate to the average molar mass $M_c$?

<p>G increases as Mc is reduced (D)</p> Signup and view all the answers

What effect do loops have on the mechanical behavior of elastomers?

<p>Do not affect the modulus (C)</p> Signup and view all the answers

Which statement is true about the effect of temperature on the modulus of elastomers?

<p>Modulus behaves oppositely to other materials upon heating (A), Modulus increases with temperature (C)</p> Signup and view all the answers

What aspect of elastomer deformation is primarily affected when the modulus increases with reduced $M_c$?

<p>Entropy changes (D)</p> Signup and view all the answers

Which of the following statements is incorrect regarding network defects in elastomers?

<p>Chain ends enhance elasticity of the network (D)</p> Signup and view all the answers

In the context of the given content, what does the term 'network density' refer to?

<p>Density of polymer chains between crosslinks (B)</p> Signup and view all the answers

What role do entanglements play in the behavior of elastomers?

<p>They act as physical crosslinks (B)</p> Signup and view all the answers

What is the equation for the change in entropy per unit volume during deformation?

<p>$ \Delta S = -\frac{1}{2}N k (\lambda_1^2 + \lambda_2^2 + \lambda_3^2 - 3) $ (A)</p> Signup and view all the answers

Which expression correctly represents the entropy of an individual chain before deformation?

<p>$ S = c - k \beta^2 (x^2 + y^2 + z^2) $ (D)</p> Signup and view all the answers

What determines the value of N in the context of polymer networks?

<p>The number of crosslink junctions and entanglements. (A)</p> Signup and view all the answers

Which of the following statements is incorrect regarding the change in Helmholtz free energy during deformation?

<p>The change in Helmholtz free energy increases with higher temperatures. (C)</p> Signup and view all the answers

What happens to the entropy of a chain after deformation according to the provided equations?

<p>It decreases when $ \lambda_i &lt; 1 $ for any i. (A)</p> Signup and view all the answers

Which of these correctly describes the probability function W(x,y,z)?

<p>It gives the probability of finding a single chain's end at any distance r. (B)</p> Signup and view all the answers

For isothermal deformation, how is the reversible work of deformation defined?

<p>$ w = -\frac{1}{2}NkT(\lambda_1^2 + \lambda_2^2 + \lambda_3^2 - 3) $ (D)</p> Signup and view all the answers

Which condition is a limitation of the Gaussian distribution in the context of polymer chains?

<p>It fails when chains become extended beyond typical lengths. (D)</p> Signup and view all the answers

Flashcards

Elastomers

Materials that can stretch to 5-10 times their original length and recover almost completely when the stress is removed. They are characterized by their ability to undergo large elastic deformations.

Glass Transition Temperature (Tg)

The temperature at which a polymer transitions from a rigid, glassy state to a flexible, rubbery state.

Crosslinking

The process of chemically linking polymer chains together to form a network structure, giving elastomers their elasticity.

Vulcanization

A type of crosslinking reaction used to enhance the properties of natural rubber. It involves heating rubber with sulfur, resulting in increased strength and durability.

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Elastomer Deformation

The unique ability of elastomers to deform under stress and then return to their original shape. It arises from the entropic changes within the polymer network.

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Statistical Theory of Elastomer Deformation

A statistical model that describes the behavior of polymer chains within an elastomer network. It's used to understand the relationship between stress, strain, and the network structure.

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Freely Jointed Chain Model

A theoretical model that assumes polymer chains in an elastomer are freely jointed, meaning they can bend at any point without restriction.

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Stress-Strain Relationship

The relationship between the applied stress and the resulting strain in an elastomer. It's an important characteristic that determines how an elastomer will behave under different loads.

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Constant volume condition

The product of the extension ratios in three dimensions for a constant volume deformation.

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Entropy of an individual chain

The entropy of an individual chain in a polymer network, where 'c' is a constant, 'k' is Boltzmann's constant, 'β' is the reciprocal of the absolute temperature, and 'r' is the end-to-end distance of the chain.

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Change in entropy of a single chain

The change in entropy of a single chain due to deformation, where 'k' is Boltzmann's constant, 'β' is the reciprocal of the absolute temperature, and 𝜆1, 𝜆2, 𝜆3 are the extension ratios in the three dimensions.

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Probability of finding a chain end

The probability of finding one end of a freely jointed chain at a specific point (x,y,z) in space, where 'r' is the distance between the two ends.

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Total entropy change of the network

The total entropy change per unit volume of a polymer network during deformation, where 'N' is the number of chains per unit volume, 'k' is Boltzmann's constant, and 𝜆1, 𝜆2, 𝜆3 are the extension ratios.

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Change in Helmholtz free energy

The change in Helmholtz free energy per unit volume during isothermal deformation, where 'N' is the number of chains per unit volume, 'k' is Boltzmann's constant, 'T' is the temperature, and 𝜆1, 𝜆2, 𝜆3 are the extension ratios.

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Reversible work of deformation

The isothermal reversible work of deformation per unit volume of a polymer network, where 'N' is the number of chains per unit volume, 'k' is Boltzmann's constant, 'T' is the temperature, and 𝜆1, 𝜆2, 𝜆3 are the extension ratios.

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Gaussian distribution limitations

The limitation of the Gaussian distribution for describing the behavior of polymer chains is that it is not applicable when the chains become highly extended.

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Polymer Density (ρ)

The density of the polymer, calculated based on the number-average molar mass (Mc) of chain segments between crosslinks and Avogadro's constant (NA).

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Number of Polymer Chains (N)

The number of polymer chains in a given volume, calculated using the density (ρ), Avogadro's constant (NA), and the number-average molar mass (Mc) of chain segments between crosslinks.

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Work of Deformation (w)

The work of deformation per unit volume. It describes the energy required to stretch an elastomer. It's proportional to the extension ratios and the temperature.

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Shear Modulus (G)

A measure of the stiffness of an elastomer, calculated based on the work of deformation (w), the number-average molar mass (Mc) of the chain segments between crosslinks, the gas constant (R), and the temperature (T). It represents the elastic resistance to deformation.

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Temperature Dependence of Modulus

The increase in shear modulus (G) with increasing temperature is a unique property of elastomers. It's explained by the entropic nature of their elasticity.

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Network Defects

Physical entanglements, loops, and chain ends are defects in the network structure of elastomers. Entanglements act like physical crosslinks, while loops and chain ends don't significantly affect the elasticity.

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Entanglement Effect on Modulus

Physical entanglements in the polymer network act like temporary crosslinks, enhancing the rigidity and stiffness of the material.

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Effect of Loops and Chain Ends

Loops and chain ends in the polymer network do not contribute to the network's elasticity. They don't affect the shear modulus of the material.

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Study Notes

Elastomers

  • Elastomers, also known as crosslinked rubbers, can be stretched 5-10 times their original length and return to their original shape when the stress is removed.
  • Three key requirements for elastomers:
    • The polymer must be above its glass transition temperature (Tg).
    • The polymer must have a very low degree of crystallinity (x→0).
    • The polymer should be lightly crosslinked.
  • Examples include ethylene/propylene rubbers (copolymerization reduces crystallinity).
  • Natural rubber is formed by the polymerization of cis-1, 4-polyisoprene. The cis configuration reduces crystallinity, leading to a low melting point (~35 °C).
  • Vulcanization is a process that crosslinks rubbers with sulfur, typically at temperatures between 120-180°C. A curing agent or accelerator may be used, with the amount designated by m (1 or 2).

Mechanical Behavior of Elastomers

  • Elastomers exhibit unique deformation due to their behavior as an "entropy spring".
  • Elastomer deformation has been studied since the 19th century.
  • Analysis can be done thermodynamically.
  • Key assumptions:
    • Freely jointed chains.
    • Change in displacement vector is proportional to change in specimen dimensions (x' = λ₁x, y' = λ₂y, z' = λ₃z).
    • Constant volume (λ₁λ₂λ₃ = 1).
  • Entropy of an individual chain (S = c − kß²r²).
  • The change in entropy (ΔS) during deformation is related to the extension ratios.
    • ΔS = -1/2Nk (λ₂² + λ₂² + λ₃² - 3)

Limitations and Use of Theory

  • The theory assumes freely jointed chains.

  • The theory can be limited when chains become extended.

  • The number of junctions (N) affects the polymer network. Crosslinks can be chemical or physical in nature

  • Chain ends and loops do not strongly contribute to network strength.

  • Density (ρ) of the polymer can be expressed as NMc / NA

    • Mc = average molar mass of chain length between crosslinks.
    • NA = Avogadro's constant

  • Parameter G relates work of deformation to extension ratios, also referred to as shear modulus for elastomers

  • G increases as chain length between crosslinks (Mc) decreases—meaning the material is becoming stiffer as crosslink density increases (tighter network).

  • In contrast to most other materials, the modulus of an elastomer (G) will typically increase with temperature.

  • Various network defects like entanglements, chain ends, and loops will have some mechanical impact.

    • Entanglements act like crosslinks and increase modulus.
    • Loops and chain ends have no noticeable effect on network elasticity.

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