Polymers- Viscoelastic Behaviour and Theory

Question 1

What is true for polymeric creep?

Answer 1

Linearly viscoelastic
Recoverable
Significant at all temperatures

Question 2

How to find Tg from the E vs t graph with lines for different temperatures

Answer 2

Tg is the line with the steepest gradient at some point

Question 3

Torsion pendulum for dynamic mechanical analysis

Answer 3

Specimen in cylinder shape with both ends fixed to something. Top end hangs down between two pulleys with equal masses hanging off them. Bottom face connected to something that can twist it controlled by linear differential transformer connected to a recorder

Question 4

Logarithmic decrement for torsion pendulum

Answer 4

Λ=ln(An/(An+1)=πtan(δ)

Question 5

Storage modulus for torsion pendulum

Answer 5

G’=KMω^2

But changes with T so hard to keep ω constant in the experiment

Question 6

What happens to logarithmic decrement at glass-rubber transition?

Answer 6

It was low (<1) then massive peak up to a lot more than 4

Question 7

What happens to storage modulus at glass-rubber transition?

Answer 7

Was high then sudden big drop to lower value then settles a bit after and curves back down

Question 8

What determines Tg in PMMA?

Answer 8

The temperature at which the C-C bond connecting a backbone C to C with the ester group can rotate

Question 9

Forced oscillation technique

Answer 9

Oscillatory force applied and the phase angle δ can be directly determined. Reliable for high δ. Very easy to change frequency. Find effect of timescale of glass-rubber relaxation. Longer time means lower T for relaxation

Question 10

Spring and dashpot models

Answer 10

Spring in the circuit has stress σ acting along its axis. Has a spring constant of G (relaxation modulus) which is reciprocal of J. Represents perfect elasticity. γ=σ/G=σJ.
Dashpot has some constant η which is viscosity? Represents perfect viscous behaviour. σ=dγ/dt.
Normally takes longer to respond than spring

Question 11

Maxwell model for creep

Answer 11

Dashpot in series with spring. The stress applied is constant.
γ+σ0/ηt + σ0/G
Spring moves first then dashpot slowly moves to reduce the extension of the spring.
Strain vs time graph is diagonal line from positive y intercept

Question 12

Maxwell model for stress relaxation

Answer 12

σ=σ0exp(-Gt/η)=σ0exp(-t/τ).

Stress vs time graph exponential decrease from positive y intercept of Gγ0

Question 13

Voigt-Kelvin model for creep and stress relaxation

Answer 13

Spring in parallel to dashpot.
γ=σ0J(1-exp(-t/ηJ))=σ0J(1-t/τR)
It’s τ sub R.
Strain vs time group is concave from origin reaching height of σ0J.
Stress vs time horizontal line from y intercept of Gγ0

Question 14

Zener models for standard linear solid

Answer 14

One has spring (Jd) and dashpot (η) in parallel and another spring in series (JU)which stress is applied to (stress splits along parallel routes so they add to total applied). Overall strain across whole arrangement.
Other has spring (Gd) and dashpot (η) in series and in parallel to spring (GR), stress applied to bottom of whole parallel thing

Question 15

Stress strain relationship of zener model

Answer 15

(1/JR)(γ+τsubσdγ/dt)=σ+τsubγdσ/dt
Where JsubR is relaxed compliance JU+Jd
τsubσ is retardation time Jdη
τsubγ is relaxation time (JU/JR)τsubσ

Question 16

Creep compliance of Zener model

Answer 16

J(t)=JU+(JR-JU)(1-exp(-t/τsubσ))

Question 17

Relaxation modulus of Zener model

Answer 17

G(t)=GU-(GU-GR)(1-exp(-t/τsubγ)

Question 18

Dynamic properties of Zener model

Answer 18

See p16 week 7 for formulae for storage compliance J’, loss compliance J”, storage modulus G’, loss modulus G”.
Maxima of J” and G” occur at 1/τsubσ and 1/τγ respectively

Question 19

When does maximum in tanδ occur?

Answer 19

At frequency ω=1/(τsubστsubγ)^1/2