Parte I viscoelasticity questions

Polymer Crosslinking and Intrinsic Properties

The crosslinking of a polymer creates an asymptote for infinite time, so we don’t have the transformation from rubbery to liquid state. Chemical bond between different polymer chains hinder their relative movement and so the flow.

a) The shear creep compliance curve is the reciprocal of the shear relaxation modulus. Temperature and time have the same proportionality, while frequency is inversed.

Questions

What is an intrinsic property?

Intrinsic property is not a value, but an equation, where there is no dependence from the geometry of the tested component. For example elastic modulus, compliance, storage and dissipative modulus and viscosity are intrinsic properties. Izod impact strength, flexibility and heat deflection temperature are strongly affected by geometry and cross section of the tested component.

What does “operationally defined” means?

It means that the property is not scientifically defined, but it is defined by the test used to measure it.

measure it. Forexample, the heat deflection temperature does not have a physical meaning, but it is defined as thetemperature at which a deformation of 2% of the heated sample is obtained under a load.

Describe the molecular model for non-newtonian fluids (pseudoplastic)
Molecules are described as random coils that can be deformed and elongated under stresses in certaindirections, modifying lowering the resistance to motion.

What are the parameters that influence the viscosity?
Viscosity is affected by molecular mass (entaglements), branching, quantity and dimension of fillers,solvents and plasticizers, temperature (free volume theory).

What are the theoretical basis for Arrhenius equation?
The main assumption is that molecular movements follow random directions and are thermally activated.They can occur only when a threshold potential energy, related to elastic distorsion is overcome. Theviscosity dependence on temperature is the same for the shear stresses.

What are the theoretical basis

1. The WLF model takes into account the free volume of the material, that is dependent on temperature.
2. The influence of free volume on viscosity is described by Doolittle's equation.
3. The assumptions for Eyring model are:
• The Arrhenius model is implemented.
• The shear stress effect on the activated complex results in a difference in the energy levels between a forward and backward jump.
• This leads to a preferential direction of the jumps in the same direction of the applied stress.
• The material properties required are the activation energy and the activation volume.
4. Eyring model is used to predict the change of shear yielding stress with temperature and strain.
5. The dependence of viscosity on temperature and pressure is:
• Pressure is directly proportional to viscosity. Lower pressure gives higher free volume, which means lower viscosity.
• Temperature is inversely proportional to viscosity. Higher temperature gives higher viscosity.

free volume that leads to lower viscosity.

What are the assumptions of laminar flow in a duct (Poiseuille flow)?

Fluid is incompressible, continuum, perfectly adhesion on the walls, the flow is laminar, steady, time-independent, isothermal, the duct is long (no end effect, steady), horizontal (no gravity effect), straight.

The viscosity is not affected by pressure.

What is the viscoelastic time dependence?

It is the fact that the output is delayed in time, but it maintains a memory effect.

What is the characteristic time?

It is the time at which the glassy transition appears. For a creep experiment, it corresponds to the flex present in the C(t) vs log(t) plot (retardation time), while for stress relaxation experiments it is the flex in the E(t) vs log(t) plot (relaxation time).

What is the Deborah number?

It is the ratio between the characteristic time of the material and the observation time.

When is a material linear?

A material is linear when the isochronous plot of stress vs strain is linear.

straight line. (n.b. look at the isochronous plots, not to constant rate).

What does linearity imply?

Linearity implies that the effects of the causes are independent, effect can be summed (additivity), effects are proportional to input (proportionality).

What are the main assumption of Boltzmann superposition principle?

Linearity is assumed.

What represent the tanδ peak?

It represents the frequency at which the glass transition happens. It represents the frequency at which the ratio between the dissipation energy and elastic energy is maximum. At this frequency, the dissipation energy reaches its maximum, the maximum dissipation is also in the liquid state, so at very high temperature above the rubber phase of the polymer.

What are the differences between storage and dissipative modulus in a glassy state and a rubbery state?

The storage modulus is higher in the glass phase and it decreases during viscoelastic transition reaching lower values in the rubber phase.

What are the assumptions of analogue

Elastic behavior is described by Hooke's law, while viscous behavior is described by Newton's law. They are both linear. Viscoelasticity is the combination of both. Models are simple mono-dimensional and elements can be connected in series or parallel.